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RAP-WAM: Learning World-Action Models through Predictive Rehearsal and Action Perturbations
Yuanpeng He, Ceyao Zhang, Fangjing Li, Kefei Zhu, Lijian Li, Yueheng Li, Tianjia He, Wenpin Jiao, Zhi Jin, Yaodong Yang, Yuanpei Chen
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Abstract:Recent world action models draw on video generation priors to jointly predict future observations and robot actions. Adapting these priors to control requires determining how future predictions should guide policy learning. RAP-WAM combines predictive Rehearsal and Action Perturbations (RAP) with future-supervised queries and Coupled Action Projection for policy learning. Predictive rehearsal trains on model-generated inputs while retaining recorded targets, and accumulates recurring errors into a spatial prior. We perturb actions and measure changes in video predictions. Action-response-based spatiotemporal credit assignment combines these responses, prediction error, and the rehearsal prior to allocate visual supervision; spatially aggregating the responses determines supervision intensity across future action steps. No separate scoring network or deployment-time probe is required. The base learns from a video-pretrained backbone without intermediate pretraining on external embodied data. We evaluate the fixed base and its agent-refined, task-conditioned system. On 42 RoboDojo tasks, their average success rates are 12.85% and 15.62%, with Scores of 17.86 and 20.59. Across 15 real-robot tasks, the complete system achieves 89.00% task-macro-average success, exceeding the strongest of five baselines by 37.67 percentage points. Across 315 fixed-output simulation windows, 45.21% of response-top20 positions fall outside error-top20, revealing information beyond prediction error.
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- Source: https://arxiv.org/abs/2610.16443v1
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RAP-WAM: Predictive Rehearsal and Action Perturbations RAP-WAM: LEARNING WORLD-ACTION MODELS THROUGH PREDICTIVE REHEARSAL AND ACTION PERTURBATIONS Yuanpeng He 1,4 , Ceyao Zhang 1,4 , Fangjing Li 2 , Kefei Zhu 4 , Lijian Li 3 , Yueheng Li 4 Tianjia He 4 , Wenpin Jiao 1 , Zhi Jin 1 , Yaodong Yang 1,4 , Yuanpei Chen 4 1 Peking University 2 Beijing Jiaotong University 3 University of Macau 4 PKU-PsiBot Joint Lab ABSTRACT Recent world action models draw on video generation priors to jointly predict future observations and robot actions. Adapting these priors to control requires determining how future predictions should guide policy learning. RAP-WAM com- bines predictive Rehearsal and Action Perturbations (RAP) with future-supervised queries and Coupled Action Projection for policy learning. Predictive rehearsal trains on model-generated inputs while retaining recorded targets, and accumulates recurring errors into a spatial prior. We perturb actions and measure changes in video predictions. Action-response-based spatiotemporal credit assignment com- bines these responses, prediction error, and the rehearsal prior to allocate visual supervision; spatially aggregating the responses determines supervision intensity across future action steps. No separate scoring network or deployment-time probe is required. The base learns from a video-pretrained backbone without interme- diate pretraining on external embodied data. We evaluate the fixed base and its agent-refined, task-conditioned system. On 42 RoboDojo tasks, their average success rates are 12.85% and 15.62%, with Scores of 17.86 and 20.59. Across 15 real-robot tasks, the complete system achieves 89.00% task-macro-average success, exceeding the strongest of five baselines by 37.67 percentage points. Across 315 fixed-output simulation windows, 45.21% of response-top20 positions fall outside error-top20, revealing information beyond prediction error. 1INTRODUCTION Generative robot policies combine visual representations with continuous action generation, as exemplified by Diffusion Policy and π 0 (Chi et al., 2025; Black et al., 2024). The π series has since advanced toward open-world generalization inπ 0.5 (Physical Intelligence et al., 2025) and multimodal steerability and compositional task generalization inπ 0.7 (Intelligence et al., 2026). World action models additionally predict future observations: UWM couples video and action diffusion (Zhu et al., 2025); DreamZero builds on pretrained video diffusion (Ye et al., 2026b); X-WAM incorporates multi-view RGB-D prediction and asynchronous denoising (Guo et al., 2026). OpenWAM studies backbone inheritance, world action interaction, and embodied-pretraining scale (Wang et al., 2026). We focus on adapting video priors directly to target-task demonstrations: which visual locations and future action steps should receive additional training emphasis? Earlier work offers complementary perspectives. Prioritized replay changes how frequently experience transitions are reused (Schaul et al., 2016), while value-aware model learning incorporates decision structure into prediction losses (Farahmand et al., 2017). These motivate distinguishing prediction accuracy from policy relevance; allocating supervision across visual locations and future action steps in joint video–action models remains an open problem. We introduce RAP-WAM, coupling predictive rehearsal with action perturbations to guide repre- sentations and supervision. Its central signal is the video prediction’s response to perturbations of the model’s action input. Prediction error measures target mismatch, whereas this response reveals which visual locations and future times depend more strongly on the action representation. Com- bining them distinguishes prediction difficulty from action dependence, providing a shared basis for prioritizing visual and action prediction. 1 arXiv:2610.16443v1 [cs.AI] 12 Oct 2026 RAP-WAM: Predictive Rehearsal and Action Perturbations The framework couples three designs. Recorded future observations supervise predictive queries, giving action generation access to future-oriented features. Predictive rehearsal conditions subsequent demonstration segments on model-predicted observations while retaining recorded targets (Huang et al., 2025; Bengio et al., 2015), and accumulates recurring errors into a spatial prior. The credit mechanism integrates this prior with current error and action response: spatial maps guide visual supervision, while spatially pooled response weights future action steps. Together, these designs turn existing demonstrations into representation targets, rehearsed inputs, and adaptive supervision without extra region annotations or a separate scoring network. Our contributions are as follows: •We develop RAP-WAM to adapt video priors through future-supervised action representations and predictive rehearsal: recorded futures shape action-generating features, while rehearsal exposes the policy to observations affected by its own prediction errors. • We design an action-response-driven spatiotemporal credit mechanism: action response, current prediction error, and a historical error prior guide visual supervision, while spatially pooling the same response allocates supervision across future action steps. •We integrate execution-guided post-training with task-specific policy retention, using evaluation feedback to refine demonstration sampling and preserve complementary specializations. 2RELATED WORK Generative control and world action models. Beyond the action and world action formulations introduced above, UniPi derives actions from video plans through inverse dynamics (Du et al., 2023). Motus and MotuBrain use multimodal expert architectures (Bi et al., 2026; MotuBrain Team et al., 2026). GigaWorld-Policy emphasizes action-centered joint learning (Ye et al., 2026a); AHA-WAM uses asynchronous video planning (Cai et al., 2026), while Fast-WAM retains video co-training without test-time future imagination (Yuan et al., 2026). Our focus is how existing target demonstrations supervise a joint policy. Further context on action interfaces and adaptive supervision appears in Appendix I. Post-training for embodied policies. RECAP improvesπ 0.6 intoπ ∗ 0.6 through reinforcement learning from demonstrations, autonomous experience, and expert corrections (Intelligence et al., 2025). SIME selects interaction segments (Jin et al., 2025); RISE optimizes policies through imagined outcomes (Yang et al., 2026a). ENPIRE supports agent-directed experiments (Xiao et al., 2026), while ASPIRE retains validated program repairs (Lu et al., 2026). Our agent instead guides world action policy training on existing demonstrations; response-based credit allocates supervision, and evaluation retains complementary task specialists. The reported gains concern this combined procedure. 3RAP-WAM: PREDICTIVE REHEARSAL AND ACTION PERTURBATIONS Figure 1 summarizes RAP-WAM: a future-supervised action interface, predictive rehearsal, and response-weighted supervision on target-task demonstrations. We separately evaluate post-training and task-specific selection, with full protocols in the appendix. 3.1A FUTURE-SUPERVISED ACTION INTERFACE A shared video–action predictor does not automatically give its action features an explicit repre- sentation of the future. We introduce a future-supervised interface within that predictor; standard conditioning and flow matching (Lipman et al., 2023) are described in Appendix C.1. Recent in- terfaces supervise observed geometry (Li et al., 2026) or latent foresight (Ma et al., 2026); ours aligns queries to recorded future video latents. We appendKlearned query tokensQto video V, noisy-actionA, and observed-stateStokens, forming[V,A,S,Q]. Video tokens contain the observed prefix and noisy future latents. Letzbe recorded-future latents andh k the final transformer representation of queryk. The alignment target is r k = sg[P t Pool G (z) k ], L align = 1 K K X k=1 [1− cos(P q h k ,r k )].(1) 2 RAP-WAM: Predictive Rehearsal and Action Perturbations a Future-supervised worldaction model Predicted future RGB (optional) Frozen VAE decoder Integrate denoising Video projection 푣 ! " 퐻 ! Compact MLP 퐻 " Time-modulated + Video 푉Actions 퐴State 푆 Queries 푄 Frozen VAE encoderEncoderEncoder 16 learned slots Observed + future frames Demo actionsJoint state4×4targets Future latents Clean / clampedNoised Observed visual latentsstay clamped CAPblock b Predictive learning feedback Predictive rehearsal Observe 푓 " Predict (no grad) Last frame Recorded future Prefix VAE re-encode "푎 #$%& ̃푠 Scheduled state 푓 " Rehearse Flow error EMA Prior 푃 14×14 Spatial creditTemp o ral c re d it ++ +1 푊 Video error × ℒ " * Weighted mean 푆 Time Spatial pool Norm+1/repeat 푤 16 action steps × Action error ℒ + , Base ℒ # · Rehearsal ℒ $ Update 휃 c Agent-guided capability accumulation Execute History Agent 푓 " Post-train 휋 " 휋 " Evaluate 휋 # 휋 $ 휋 % Retain Task ID One policy 휋 & Select by task Next round Action-response probe Original demo 퐴 ' 퐴 ' ( 훿 푓 " 푓 " Shared model 훥 Response 푆 훥 Error 퐸 푣 푣 - Stop grad Stop grad 푣 " ∗ Directional self-attention × 푉 푉 퐴 퐴 푆 푆 푄 푄 퐴 cannot read 푉 푉can read 퐴 Text cross-attention Feed-forward Instruction embedding Future supervision Query alignment (train only) Stop grad (P)(S)0.5(E) Denoise + unnormalize Action chunk v a θ ̂ A RAP-WAM Shared transformer a Future-supervised worldaction model Predicted future RGB (optional) Frozen VAE decoder Integrate denoising Video projection 푣 ! " 퐻 ! Compact MLP 퐻 " Time-modulated + Video 푉Actions 퐴State 푆 Queries 푄 Frozen VAE encoderEncoderEncoder 16 learned slots Observed + future frames Demo actionsJoint state4×4targets Future latents Clean / clampedNoised Observed visual latentsstay clamped CAPblock b Predictive learning feedback Predictive rehearsal Observe 푓 " Predict (no grad) Last frame Recorded future Prefix VAE re-encode "푎 #$%& ̃푠 Scheduled state 푓 " Rehearse Flow error EMA Prior 푃 14×14 Spatial creditTemp o ral c re d it ++ +1 푊 Video error × ℒ " * Weighted mean 푆 Time Spatial pool Norm+1/repeat 푤 16 action steps × Action error ℒ + , Base ℒ # · Rehearsal ℒ $ Update 휃 c Agent-guided capability accumulation Execute History Agent 푓 " Post-train 휋 " 휋 " Evaluate 휋 # 휋 $ 휋 % Retain Task ID One policy 휋 & Select by task Next round Action-response probe Original demo 퐴 ' 퐴 ' ( 훿 푓 " 푓 " Shared model 훥 Response 푆 훥 Error 퐸 푣 푣 - Stop grad Stop grad 푣 " ∗ Shared Wan-initialized transformer ×푁blocks Directional self-attention × 푉 푉 퐴 퐴 푆 푆 푄 푄 퐴 cannot read 푉 푉can read 퐴 Text cross-attention Feed-forward Instruction embedding Future supervision Query alignment (train only) Stop grad (P)(S)0.5(E) Denoise + unnormalize Action chunk v a θ ̂ A RAP-WAM Trainin Stopgradi Stop gradient Figure 1: Predictive learning and agent-guided policy refinement. a, future latents supervise query alignment during training. CAP predicts action flow-matching velocityv a θ ; denoising and unnormalization yield action chunk ˆ A . b, rehearsal updates spatial priorP. The matched probe produces video-denoising velocity predictionsvandv + under original and perturbed action inputs, sharing model, condition, video noise, and diffusion level.∆denotes channel-mean squared dis- crepancy:Scomparesv + withv, andEcomparesvwith flow-matching targetv ∗ z . Spatial weights combine separately normalized sources,W = 1 +N (P ) +N (S) + 0.5N (E). Temporal weights use1 +N t (mean hw S), repeated over action steps. Weight construction is detached. c, the agent proposes post-training interventions. Evaluation retains improvements by task; other tasks keep their policies. Accepted and rejected outcomes inform subsequent rounds. Each task selects one complete policy. Scenes and fields are schematic. HereP t ,P q project targets and queries to a common 128-dimensional space;sgstops gradients. We poolzonto a time–height–width gridG = (1, 4, 4), yieldingK = 16targets. Alignment updates P q and query representations, whileP t remains fixed. Learned query embeddings initializeQat each forward with action-side noise conditioning; recorded futures are needed only for training supervision. The base objective is L 0 =L z +L a + λ q L align ,(2) whereL z ,L a are mean-squared errors against video and action flow-matching targets; we set the alignment coefficientλ q = 0.1. To encourage actions to use the future-supervised query features, we make attention connectivity directional. Within each block, we remove direct reads from action-token query rows to video-token key columns. For their index setsA,V, M ij = −∞, i∈A, j ∈V, 0,otherwise. (3) The mask is added to attention logits. Action rows can read action, state, and predictive-query keys, but not video keys. Video rows can still read action keys, preserving the action-to-video path required by the response probe. State-mediated visual information remains accessible, so queries are not the sole visual pathway. GigaWorld-Policy also restricts future-video-to-action reads (Ye et al., 2026a). Coupled Action Projection (CAP) maps final action-token featuresh a to the action flow-matching velocityv a θ . A compact MLPH c and a time-modulated headH r predict the same velocity target through their sum: v a θ = H c (h a ) + H r (h a ,e σ ), H c (h) = W 2 GELU(W 1 LN(h) + b 1 ) + b 2 . (4) HereH r is the sequence head conditioned on the noise-level embeddinge σ ;H c uses a hidden width one quarter of the trunk width. Zero-initializingW 2 ,b 2 adds this path without initially changing the sequence-head output. Both branches learn through their sum against the same action-flow target, not separate coarse/fine labels. The MLP has no separate noise-level input, althoughh a already depends on that noise level. The added capacity therefore changes the action projection without introducing a second policy or task router. 3 RAP-WAM: Predictive Rehearsal and Action Perturbations 3.2REHEARSAL UNDER PREDICTED INPUTS Training uses recorded images and joint states; deployment instead supplies observations affected by the robot’s preceding actions (Ross et al., 2011). Scheduled sampling (Bengio et al., 2015) and Self Forcing (Huang et al., 2025) motivate exposing sequence models to their own predictions. For two adjacent demonstration chunks, we generate the first chunk’s future video and actions without gradients and replace the second chunk’s initial observation with the last predicted frame. Scheduled state substitution optionally replaces its initial state with the last predicted absolute-joint action, first unnormalized as an action and then normalized as a state. The predicted image and recorded second-chunk future frames are jointly VAE-encoded; recorded actions remain the targets. Their video/action flow losses formL 1 , without an extra query-alignment loss. This rehearsal trains on predicted inputs while retaining recorded supervision; its schedules are in Appendix C.1. An initially zero spatial priorPaccumulates the resulting prediction errors across updates. We average detached second-chunk video errors over channels, batch and future time, pool them onto ag P × g P grid to obtaine roll , and update P ← ρP + (1− ρ)e roll .(5) We use grid widthg P = 14and decayρ = 0.9. The first valid error map initializesPdirectly; later updates use the moving average above. Before weighting the video loss, we resizePto the future- latent spatial grid and repeat it across future latent times. The predicted joint action approximates the next state, without simulator interaction or new corrective labels. Unlike DAgger, this does not relabel visited states with an expert (Ross et al., 2011); it also differs from imagined-return optimization in RISE (Yang et al., 2026a). The prior records where rehearsal predictions have repeatedly been inaccurate. The next step measures which predictions also depend on the action input. 3.3RESPONSE-DERIVED SPATIOTEMPORAL CREDIT Prioritized replay and focal loss allocate learning emphasis using error signals (Schaul et al., 2016; Lin et al., 2017). Our credit mechanism adds action-conditioned response and shares it across visual and action supervision. response-based credit compares two forwards of the same recorded demonstration. We draw fresh, independent noise for its future latents and actions at a shared noise level, retaining the recorded conditioning inputs, and compute a reference prediction with gradients. A second forward uses the same model, condition, video noise, and noise level but addsδ ∼N (0,τ 2 I)to the normalized noisy actions; this forward has no gradients. At future spatiotemporal positioni, letv i ,v + i denote the reference and perturbed video velocities withCchannels. The target isv ∗ z,i = ε z,i − z i , wherez i is the clean recorded-future latent andε z,i ∼N (0,I)is its sampled noise, consistent with z σ = (1− σ)z + σε z . Hereiindexes a future spatiotemporal location and∗denotes the supervision target. Holding these predictions constant for coefficient construction gives S i = 1 C ∥v + i − sg(v i )∥ 2 , E i = 1 C ∥ sg(v i )− v ∗ z,i ∥ 2 .(6) We set the perturbation scaleτ = 0.1.Emeasures squared prediction error;Smeasures squared change after the action perturbation. These are changes in model outputs, not measured physical effects of executed actions (Appendices C.2–C.3). For each future visual position, we normalize the priorP, responseS, and errorEseparately, then combine them into a video-loss weight. HereNis per-sample min–max normalization over future time and spatial positions, with denominator floorε n : W i = 1 + α P N (P) i + α S N (S) i + α E N (E ) i .(7) The coefficients are nonnegative; we setα P = α S = 1,α E = 0.5, andε n = 10 −6 . The unit floor gives every location a nonzero loss coefficient, capped at 3.5 with these settings. To weight ac- tion steps, we first average the raw response over spatial positions, then normalize these means across future time: c t = 1 + α S N t (mean hw S) t , w j = c ⌊j/R⌋ , R =⌈H a /T⌉.(8) HereH a is the action-chunk length,Tthe number of future latent steps, andN t min–max normaliza- tion over thoseTsteps within each sample. Using zero-based indices, each coefficient is repeatedR times and truncated toH a actions; the reportedT = 4,H a = 16setting assigns one coefficient to four consecutive actions. This branch uses the raw response before spatial min–max normalization. 4 RAP-WAM: Predictive Rehearsal and Action Perturbations The prior is constant along time, so its normalized temporal contribution is zero;Edoes not enter this branch. Hence1 ≤ w j ≤ 1 + α S . Visual and action prediction share one response source, with separate spatial and temporal weighting. Action coefficients depend on normalized differences between future-step spatial means, not on the locations of individual response peaks. We apply these weights to video and action prediction errors. Letienumerate all future video locations across the batch andjall action steps across the batch. At current parameters ̄ θ , normalize the detached loss coefficients asq v i =W i / P ℓ W ℓ andq a j = w j / P ℓ w ℓ . For channel-mean video errorse z i and action-dimension-mean errorse a j , the auxiliary objective is e L P (θ; ̄ θ) = r P (k) λ z X i q v i ( ̄ θ)e z i (θ) + λ a X j q a j ( ̄ θ)e a j (θ) ,(9) wherekcounts training updates,W P is the credit warmup length, andr P (k) = min(1,k/W P ); we setλ z = 0.5andλ a = 0.3. The full update usesL = L 0 + b c λ c r c (k)L 1 + b P e L P , with b c ∼ Bernoulli(p c (k))andb P ∼ Bernoulli(p P ). Herer c (k),p c (k)are the rehearsal warmup and invocation schedules (Appendix C.1);λ c = 1andp P = 0.5. The video errore z i equalsE i numerically but retains gradients. Both video and action errors reuse the reference forward. Weight construction is detached, so backpropagation updates the predictor through these errors only; no additional forward is needed for this auxiliary loss. Unlike importance sampling with corrective weights (Katharopoulos & Fleuret, 2018), this deliberately changes the auxiliary loss emphasis. Positive, bounded coefficients retain every target while regulating relative emphasis, not gradient norms or capability preservation (Appendix C.4). No separate region-scoring network or reward head is needed. The base objective supervises predictions and query features, rehearsal substitutes predicted images and states, and credit scales individual loss terms. At deployment, the queries, directional mask, and CAP remain active during joint video-latent/action denoising. We return unnormalized actions without decoding future RGB; neither rehearsal nor credit estimation is invoked. Architecture and sampling details are given in Appendix C.1. 3.4POST-TRAINING AND TASK-SPECIFIC POLICY SELECTION We evaluate the fixed RAP-WAM base and a refined system separately. The latter extends the learner with an experiment stateX r = (B r ,g r ,H r ): available policies, task assignments, and intervention history. The initial repertoire contains the base. Following execution-feedback approaches (Xiao et al., 2026; Lu et al., 2026), task evaluation informs subsequent training; accepted specialists remain available rather than replacing the base on every task. From evidence to a training intervention. At roundr, the agent receives task outcomes, exe- cution evidence, and available diagnostics, denotedF r . Together with historyH r , these specify an interventionu r : the parent checkpoint, target behaviors, demonstration allocation, and trainable parameter set. HereAis the agent,π r the selected parent policy,D r the resampled demonstration windows, andU RAP the training operator producing candidateπ + r : u r =A(F r ,H r ), π + r =U RAP (π r ,D r ;u r ).(10) Agent-guided refinement yields multiple task specializations with only a few thousand fine-tuning steps. Parent policies and rejected outcomes remain available. Replay under recorded targets. We implement the replay intervention with 50% natural replay, 20% task-balanced replay, 15% failure-boundary windows, and 15% late-progress windows. Natural replay preserves coverage; task-balanced replay equalizes task sampling. Boundary replay favors demonstration phases near progress inferred from failed executions’ partial-completion scores; late replay favors the final portion of demonstrations. The score-to-progress mapping is a sampling heuristic, not a measured failure time. Training retains recorded images and action targets, uses the RAP-WAM objectives with separate backbone and interface learning rates, and evaluates intermediate checkpoints. Appendix H specifies eligibility, fallback rules, optimizer settings, and budgets. Retention without averaging policies.Letm t (π) = (SR t (π), Score t (π))denote success rate and mean partial-completion score from the same execution record. A task entersC r if the candidate 5 RAP-WAM: Predictive Rehearsal and Action Perturbations Table 1: RoboDojo comparison: Score / SR (%). Pretr.: external embodied pretraining reported for the method. Video/VLM initialization and target-task demonstrations are excluded.∗: AHA- WAM uses robot-data pretraining for real-world experiments, but not in its default simulation setup (Appendix B). Score and SR are ranked separately per column; highest and second-highest values are bold andunderlined, including ties.‡: VLA supervised by a frozen video generation model during training.§: matched 42-task coverage for our RAP-WAM base and post-training system; each task is averaged over its valid evaluation episodes. ModelPretr.Gen-Std Gen-RandPrecision Long-Hor.MemoryOpenAverage VLA and other action policies G0.5 (Liu et al., 2026)Yes 27.72/21.44 9.20/4.2228.25/20.4244.12/32.258.61/7.33 1.73/1.58 20.23/14.88 Xiaomi-Robotics-1 (Xiaomi Robotics Team et al., 2026) Yes 35.65/28.00 11.44/6.00 26.69/18.83 38.39/23.677.81/6.56 3.94/3.58 20.07/13.93 Hy-Embodied-0.5-VLA (Zhang et al., 2026) Yes 21.98/17.00 1.57/0.00 13.81/8.00 25.74/14.92 13.37 /12.110.65/0.58 13.07/8.80 KinRT (Yang et al., 2026c)Yes 20.94/14.78 7.09/2.44 15.65/9.92 26.40/18.084.82/3.56 4.23 /3.8313.02/8.80 SimpleMemVLA (Yin et al., 2026) No10.38/7.11 2.33/0.787.42/2.92 14.58/5.50 33.71/33.22 0.85/0.75 12.58/9.27 Pi-05 (Physical Intelligence et al., 2025) Yes 20.93/15.00 5.82/1.00 12.40/5.50 23.54/14.675.78/4.56 1.98/1.67 11.41/6.91 InternVLA-A1.5 ‡ (Ma et al., 2026) Yes 16.81/12.00 3.90/2.00 15.23/10.17 23.80/13.754.93/3.56 1.43/1.42 11.15/7.14 VLAct (Yang et al., 2026b)Yes 16.33/12.00 2.74/1.00 20.62/15.25 20.12/13.670.66/0.56 2.37/2.25 10.66/7.60 MolmoAct2 (Fang et al., 2026)Yes12.53/7.33 4.53/2.00 10.92/4.50 15.20/7.005.53/4.56 4.75/4.428.99/5.03 World-model-based policies OpenWAM-α (Wang et al., 2026) Yes 33.16/25.568.26/4.11 18.45/9.25 34.93/25.33 10.41/9.11 1.41/1.08 17.18/11.92 X-WAM (Guo et al., 2026)Yes11.24/5.00 3.54/1.006.72/1.83 17.47/9.086.32/4.67 0.57/0.257.69/3.83 GigaWorld-Policy-0 (Ye et al., 2026a) Yes10.28/6.00 0.41/0.006.15/1.83 15.51/8.923.46/2.22 0.54/0.506.20/3.27 AHA-WAM (Cai et al., 2026) Yes ∗ 10.32/6.00 1.26/0.005.86/2.428.61/2.672.97/2.78 0.88/0.834.82/2.39 Fast-WAM (Yuan et al., 2026)No4.33/2.00 0.34/0.001.96/0.009.14/5.173.55/3.44 0.42/0.423.48/2.03 World-model-based: ours RAP-WAM (base) § No 21.55/15.00 0.82/0.00 23.97/16.51 45.12/32.507.97/7.00 1.06/0.75 17.86/12.85 RAP-WAM + refinement § (Ours) No 27.82/21.00 0.93/0.00 28.66/21.03 48.43/36.50 10.32/9.33 1.16/0.75 20.59/15.62 improves SR over its currently assigned policy, or ties SR and improves Score; a tie in both retains the incumbent. The assignment updates as g r+1 (t) = id(π + r ), t∈C r , g r (t), t /∈C r . (11) Hereid(π)is a checkpoint identifier andg r (t)denotes the selected policy identity; the corresponding checkpoint remains inB r . An emptyC r leaves the active assignment unchanged. At inference, the task identity selects one whole checkpoint, with its architecture, normalizer, and inference settings. Parameters and within-episode action fragments are not averaged. This assignment operates across policies, whereas credit coefficients weight losses inside a policy’s training. The final assignment uses the base on 14 tasks and 16 other checkpoints on 28 tasks. History retains proposals, outcomes, and acceptance decisions for subsequent interventions. This is the recursive aspect of the experimental procedure; it does not establish autonomous improvement or a causal benefit from history reuse. Selection uses observed evaluation results, so independent policy-selection tests remain necessary. The complete state update and execution rule are retained in Appendix H.1. 4EXPERIMENTS We evaluate the fixed RAP-WAM base and the post-trained task-conditioned system on RoboDojo, analyze their supervision signals, and report physical execution results. 6 RAP-WAM: Predictive Rehearsal and Action Perturbations 0.00.51.0 0.0 0.5 1.0 Response rank 0246 P 5.47% S 2.22% ½E 1.14% 1–45–89–1213–16 Ref. W1 W2 W3 1.001.001.001.00 1.001.522.001.43 1.001.681.722.00 1.081.002.001.94 In error top20% Outside error top20% 0 50 100 54.8% 45.2% 0.0 0.5 1.0 Median 0.50 a Redistribution b Source sensitivity c Temporal credit d Response vs. error e Rank agreement Error rank -0.260.26 TV distance (%)Action steps 12 Share of high-response cells (%) Rank correlation Figure 2: Complementary response signals and spatiotemporal supervision. a, signed spatial credit redistribution. b, sensitivity to removing prior, response, or half-error. c, temporal action credit in three phone-packing windows (W1–W3), with a unit reference. d, response-top20 membership within or outside the error-top20 set. e, rank correlation across 35 condition medians. Panels a, b, d, and e use the same 315 RoboDojo windows. Squares and segments indicate medians and IQRs; these fixed-output diagnostics involve no retraining. 4.1BASE AND POST-TRAINED SYSTEM PERFORMANCE We report SR and partial-completion Score, averaged within each capability and then equally across the five capabilities (Chen et al., 2026b). Public results are taken from the RoboDojo leaderboard (Chen et al., 2026a); coverage and system accounting are specified in Appendices A and H. Across the 42 tasks, the full method achieves 15.62% average SR and 20.59 Score, compared with 12.85% and 17.86 for the RAP-WAM base. The gains are 2.77 percentage points in SR and 2.73 Score. Precision increases from 16.51% to 21.03%, Memory from 7.00% to 9.33%, and Generalization from 7.50% to 10.50%. These gains arise in the task-conditioned system, where retained specializations contribute across different capability groups. Long-Horizon success rises from 32.50% to 36.50%, with Score increasing from 45.12 to 48.43 (Table 1). At the task level, tower building increases from 60% to 72%, pen-holder filling from 6% to 18%, and tic-tac-toe from 80% to 86%. The task-policy breakdown is given in Appendix D. Open success remains 0.75%, and random-Generalization success remains zero, indicating that the observed gains do not resolve broad scene-shift robustness. The candidate comparison in Appendix Figure 12 helps explain this pattern: the base has the highest aggregate performance among individual checkpoints, yet candidates improve different task subsets. Task-specific retention preserves these local gains despite regressions elsewhere. Appendix Figure 11 shows how the retained specialists divide the task set; their value is not captured by ranking whole-policy averages alone. 4.2ACTION RESPONSE CHANGES THE LOCATIONS EMPHASIZED DURING TRAINING Figure 2a–b uses 315 RoboDojo windows across 35 conditions. Holding model predictions fixed, we separately remove the historical error prior, action response, or current-error contribution and renormalize the remaining weights to compare their effects on supervision allocation (Appendix E). Response redistributes spatial emphasis; the median shares of normalized coefficients redistributed are 5.47%, 2.22%, and 1.14% forP,S, 0.5E, respectively. The rehearsal prior produces the largest re- distribution. These distances combine magnitude and spatial shape, not additive contributions to task success. Figure 2c shows temporal supervision in three phone-packing demonstration windows. Spatially pooled action responses distinguish future action steps without an extra scoring network. Removing the response leaves all coefficients at one:Pis time-constant and this branch excludesE. Appendix E details reconstruction and four-action grouping. Figure 2d–e shows complementary rankings: on average, 45.21% of response-top20 positions lie outside the error-top20 set. The condition-level rank distribution further characterizes this difference over the full field. These measurements explain the local diagnostic signal; the supplementary comparison of normalized auxiliary-credit shares is retained in Appendix E. 7 RAP-WAM: Predictive Rehearsal and Action Perturbations 050100 0.01 0.1 0.291 0.046 0.047 0.014 0.007 0.012 a How the prior evolves 3.3%60%100% Mean stored prior (log scale) Training progress (%) bWhere response changes Group 1Group 2Group 3Group 4 High-response locations InitialKeptNewExited 0 50 100 080160 0.0 2.5 5.0 c How signals allocate credit P S 0.5E Share (%) Removal TV (%) Window start (frames) Figure 3: Credit across three timescales. a, prior spatial patterns at 3.3%, 60%, and 100% of the same can-placement run (top, independently normalized), and the raw spatial mean at six checkpoints (bottom, logarithmic axis). b, response-top40 locations across four future groups for the newly trained three-can tray-placement policy. c, stacked component shares (top) and fixed-output removal sensitivity (bottom) forP,S, and0.5Eacross all eleven exported windows of the same demonstration. Shares exclude the unit floor ofW; sensitivity is total variation (TV) between normalized full and component-removed weights, retaining the unit floor. Panel c uses all spatial cells and future groups. All panels use the same training run; b–c use its final checkpoint. Definitions and display protocols appear in Appendix F. Local sensitivity and relative credit. Under small isotropic action perturbations,E δ [S i ] ≈ (τ 2 /C)∥J i ∥ 2 F , whereJ i is the video-output Jacobian with respect to action inputs andCis the channel count (Appendix C.2). Response describes coupling at the current condition and diffusion level; a single direction gives a noisy estimate. Per-sample normalization expresses relative priority, not absolute sensitivity across tasks. Current error and rehearsal history complement this local coupling, while the unit floor preserves supervision at low-response locations. 4.3CREDIT EVOLUTION WITHIN A TASK Figure 3 follows one three-can tray-placement run. Panel a tracks spatial priors across training; b shows response locations across future groups at the final checkpoint; c summarizes component shares and removal sensitivity across eleven demonstration windows. The prior has the largest share and removal sensitivity, while response and error vary across windows. This distinguishes accumulated spatial difficulty from context-dependent reweighting: a final aggregate alone would hide variation over training and predicted time. The analysis characterizes fixed outputs, rather than retraining effects or object localization. 4.4REAL-ROBOT EVALUATION AND QUALITATIVE SEQUENCES Figure 4 compares fifteen tasks, five baselines, and Ours, alongside four recorded task sequences. Event-aligned frames illustrate intermediate object states; twelve further sequences appear in Ap- pendix G. The prediction-horizon analysis (Appendix Figure 13) separately evaluates all 50 illustrated training windows against a copy-condition baseline. Ours achieves 89.00% task-macro-average SR, compared with 51.33% for the strongest baseline, G0.5, a margin of 37.67 percentage points. Supplementary phone-box assembly achieves 85% versus 5% forπ 0.5 ; it is reported separately and excluded from the fifteen-task average (Appendix G). Task variation and aggregation. Ours has the highest reported SR on each of the 15 physical tasks, but performance is not uniform. SR ranges from 70% for fan insertion to 100% for three-can placement, food placement, and coaster placement. Height-based bottle ordering reaches 90%, compared with 30% for the best baseline on that task. Each task contributes equally to the reported macro-average; it is not a pooled episode success rate. Trial counts and uncertainty estimates are not supplied with these percentages, so the comparisons describe the recorded outcomes rather than establish statistical significance. The separately reported phone-box assembly result does not change the common 15-task comparison set. 8 RAP-WAM: Predictive Rehearsal and Action Perturbations 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 0 50 100 5 2525 30 45 95 10 25 30 4545 95 15 35 50 60 65 95 10 20 25 30 20 90 0 45 40 55 70 85 0 50 100 0 30 20 25 40 85 5 55 6565 70 100 0 30 35 30 40 90 20 60 80 70 65 100 45 75 95 90 85 100 0 50 100 5 35 55 45 25 70 0 30 45 55 45 80 30 50 75 80 70 90 0 10 20 25 35 85 0 35 4040 50 75 Cover largest and smallest circles Unwrap cake and place in bowl Place fruit on tray Order three bottle types by height Nest three bowls Rearrange numbered blocks Place three cans on tray Cover largest and smallest numbers Place foods in respective dishes Place can on coaster Insert fan into upright container Organize disposable towels; place thick towel on top Organize a pair of shoes Form a mahjong kong Pack hamburger and close box Success rate (%) 15 tasks; 6 methods; labels show success rate (%) π 0.5 X-WAM OpenWAM-α Xiaomi-Robotics-1G0.5Ours 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 0 50 100 5 2525 30 45 95 10 25 30 4545 95 15 35 50 60 65 95 10 20 25 30 20 90 0 45 40 55 70 95 0 50 100 0 30 20 25 40 85 5 55 6565 70 100 0 30 35 30 40 90 20 60 80 70 65 100 45 75 95 90 85 100 0 50 100 5 35 55 45 25 70 0 30 45 55 45 80 30 50 75 80 70 90 0 10 20 25 35 85 0 35 4040 50 90 Cover largest and smallest circles Unwrap cake and place in bowl Place fruit on tray Order three bottle types by height Nest three bowls Rearrange numbered blocks Place three cans on tray Cover largest and smallest numbers Place foods in respective dishes Place can on coaster Insert fan into upright container Organize disposable towels; place thick towel on top Organize a pair of shoes Form a mahjong kong Pack hamburger and close box Success rate (%) 15 tasks; 6 methods; labels show success rate (%) π 0.5 X-WAM OpenWAM-α Xiaomi-Robotics-1G0.5Ours 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 0 50 100 5 45 25 30 25 95 10 45 30 45 25 95 15 65 50 60 35 95 10 20 25 30 20 90 0 70 40 55 45 95 0 50 100 0 40 20 25 30 85 5 70 6565 55 100 0 40 35 3030 90 20 65 80 70 60 100 45 85 95 90 75 100 0 50 100 5 25 55 45 35 70 0 4545 55 30 80 30 70 75 80 50 90 0 35 20 25 10 85 0 50 4040 35 90 Cover largest and smallest circles Unwrap cake and place in bowl Place fruit on tray Order three bottle types by height Nest three bowls Rearrange numbered blocks Place three cans on tray Cover largest and smallest numbers Place foods in respective dishes Place can on coaster Insert fan into upright container Organize disposable towels; place thick towel on top Organize a pair of shoes Form a mahjong kong Pack hamburger and close box Success rate (%) 15 tasks; 6 methods; labels show success rate (%) π 0.5 G0.5 OpenWAM-α Xiaomi-Robotics-1X-WAMOurs 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 0 50 100 PENDINGPENDINGPENDINGPENDINGPENDING 0 50 100 PENDINGPENDINGPENDINGPENDINGPENDING 0 50 100 PENDINGPENDINGPENDINGPENDINGPENDING Task 1Task 2Task 3Task 4Task 5 Task 6Task 7Task 8Task 9Task 10 Task 11Task 12Task 13Task 14Task 15 Success rate (%) 15 tasks; 6 methods; placeholders only, not measurements π 0.5 G0.5 OpenWAM-α Xiaomi-Robotics-1X-WAMOurs 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 0 50 100 PENDINGPENDINGPENDINGPENDINGPENDING 0 50 100 PENDINGPENDINGPENDINGPENDINGPENDING 0 50 100 PENDINGPENDINGPENDINGPENDINGPENDING Task 1Task 2Task 3Task 4Task 5 Task 6Task 7Task 8Task 9Task 10 Task 11Task 12Task 13Task 14Task 15 Success rate (%) 15 tasks; 6 methods; placeholders only, not measurements π 0.5 G0.5 OpenWAM-α Xiaomi-Robotics-1X-WAMOurs 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 0 50 100 PENDINGPENDINGPENDINGPENDINGPENDING 0 50 100 PENDINGPENDINGPENDINGPENDINGPENDING 0 50 100 PENDINGPENDINGPENDINGPENDINGPENDING Task 1Task 2Task 3Task 4Task 5 Task 6Task 7Task 8Task 9Task 10 Task 11Task 12Task 13Task 14Task 15 Success rate (%) 15 tasks; 7 methods; placeholders only, not measurements π 0.5 G0.5 OpenWAM-α Xiaomi-Robotics-1X-WAMSARC-WAMSARC-WAM + Agentic RSI 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 0 50 100 PENDINGPENDINGPENDINGPENDINGPENDING 0 50 100 PENDINGPENDINGPENDINGPENDINGPENDING 0 50 100 PENDINGPENDINGPENDINGPENDINGPENDING Task 1Task 2Task 3Task 4Task 5 Task 6Task 7Task 8Task 9Task 10 Task 11Task 12Task 13Task 14Task 15 Success rate (%) 15 tasks; 7 methods; placeholders only, not measurements π 0.5 G0.5 OpenWAM-α Xiaomi-Robotics-1X-WAMSARC-WAMSARC-WAM + Agentic RSI 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 0 50 100 PENDINGPENDINGPENDINGPENDINGPENDING 0 50 100 PENDINGPENDINGPENDINGPENDINGPENDING 0 50 100 PENDINGPENDINGPENDINGPENDINGPENDING Task 1Task 2Task 3Task 4Task 5 Task 6Task 7Task 8Task 9Task 10 Task 11Task 12Task 13Task 14Task 15 Success rate (%) 15 tasks; 7 methods; placeholders only, not measurements π 0.5 G0.5 OpenWAM-α Xiaomi-Robotics-1 X-WAMSARC-WAMSARC-WAM + Agentic RSI 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison 0 50 100 PENDINGPENDINGPENDINGPENDINGPENDING 0 50 100 PENDINGPENDINGPENDINGPENDINGPENDING 0 50 100 PENDINGPENDINGPENDINGPENDINGPENDING Task 1Task 2Task 3Task 4Task 5 Task 6Task 7Task 8Task 9Task 10 Task 11Task 12Task 13Task 14Task 15 Success rate (%) 15 tasks; 5 baselines + SARC-WAM + Agentic RSI; placeholders only π 0.5 G0.5 OpenWAM-α Xiaomi-Robotics-1 X-WAMSARC-WAMSARC-WAM + Agentic RSI 0 50 100 PENDINGPENDINGPENDINGPENDINGPENDING 0 50 100 PENDINGPENDINGPENDINGPENDINGPENDING B1B2B3B4B5Ours Ours +Agentic RSI 0 50 100 PENDING B1B2B3B4B5Ours Ours +Agentic RSI PENDING B1B2B3B4B5Ours Ours +Agentic RSI PENDING B1B2B3B4B5Ours Ours +Agentic RSI PENDING B1B2B3B4B5Ours Ours +Agentic RSI PENDING Task 1Task 2Task 3Task 4Task 5 Task 6Task 7Task 8Task 9Task 10 Task 11Task 12Task 13Task 14Task 15 Success rate (%) 15 tasks · 5 baselines + Ours + Ours+Agentic RSI · slots only; no measured values Baseline 1Baseline 2Baseline 3Baseline 4Baseline 5OursOurs+Agentic RSI 1.2s11.3s26.6s36.7s1.3s12.6s29.7s41.0s 0.6s8.3s16.0s18.6s0.8s11.6s18.8s26.0s (b) 04 Order bottles by height InitialMoveReorderFinal (c) 06 Rearrange numbered blocks InitialMoveReorderFinal (d) 08 Cover largest and smallest numbers InitialCoverCoverFinal (e) 11 Insert fan into an open-top vessel InitialGraspInsertFinal (a) Real-robot success-rate comparison Figure 4: Real-robot evaluation and four recorded task sequences. (a) Success rates across fifteen tasks and six methods; bar labels show percentages. (b–e) Tasks 04, 06, 08, and 11 show height-based bottle ordering, numbered-block rearrangement, covering numerical extrema, and fan insertion. Each task occupies four consecutive frames in a two-row, eight-column grid. Timestamps refer to the source video. Frames are taken directly from the original videos with torsos and incidental text masked; task numerals are retained. The phone-box assembly task is provided in Appendix G. 4.5DISCUSSION Two complementary patterns emerge: response and error prioritize different prediction locations, whereas candidate policies specialize on different tasks. The former concerns within-policy su- pervision; the latter concerns task-level selection. Separating their contributions requires budget- matched training ablations and policy selection independent of final testing. Weak Open and random- Generalization performance motivates new-layout evaluation. Specialist retention additionally re- quires checkpoint storage and reliable task identities. 5CONCLUSION We presented RAP-WAM, a world action framework coupling future-supervised action representations with predictive rehearsal. Its action-response signal organizes both spatial visual and temporal action supervision, complemented by current and persistent prediction errors. The framework gives future prediction two connected roles: shaping representations for action generation and supplying feedback that guides subsequent learning. Simulation and physical evaluations demonstrate the capabilities of the resulting policies, while task-specific post-training preserves complementary specializations within the complete system. Together, these findings motivate a unified treatment of predictive representation, supervision allocation, and task-level capability retention for world action models. 9 RAP-WAM: Predictive Rehearsal and Action Perturbations AI USE STATEMENT Generative AI assisted with research discussions, post-training intervention design, implementation and experiment scripts, literature retrieval, manuscript drafting and translation, and figure preparation. The improvement agents used in the experimental workflow and their role in proposing training interventions are described in Section 3.4 and Appendix H; their outputs are part of the method under study. During manuscript preparation, assistance included checking citation records against primary sources, comparing reported values with saved experiment records, and compiling and inspecting the manuscript. All results reported in this paper have been manually reviewed by the authors. World- model predictions in Appendix J are identified as model outputs and paired with recorded targets. Reported quantitative results come from saved experiments or cited benchmark sources; pending measurements are not replaced with generated values. AI systems are not authors, and responsibility for the scientific claims, source attribution, code, and final submitted content remains with the authors. ETHICS STATEMENT This research does not involve human-subject experiments or user studies. We evaluate robot manipu- lation policies using robot demonstrations and simulation and real-robot execution records. Physical execution can cause unintended contact or motion; responsible deployment requires embodiment- specific checks of joint conventions and limits, an emergency stop, and supervised commission- ing. Improved benchmark performance does not establish safety outside the evaluated conditions. Recorded demonstration frames and training-sample predictions are presented as qualitative evidence, not as additional autonomous-success trials. Display copies mask incidental identifying text, visible robot torsos in external-view sequences, and background faces in prediction comparisons; task- relevant numerals and mahjong symbols are retained. Original scene content is otherwise preserved, and the processing is disclosed in Appendices G and J. Masking alone does not establish consent or authorize redistribution: public release of demonstrations or identifiable recordings remains sub- ject to the applicable dataset terms, participant permissions, and institutional requirements. No approval or consent status is inferred from the availability of these recordings. The limitations of task-conditioned selection, single-seed evaluation, and incomplete physical measurements are stated to avoid overstating generalization or autonomous capability. REPRODUCIBILITY STATEMENT We provide the source code in the supplementary materials. Section 3 defines the model interfaces, predictive rehearsal, response-based credit objective, and task-specific policy selection. Appendix A documents training and evaluation conventions, while Appendix C, including Algorithm 1, provides implementation details, assumptions, and derivations. Appendix H specifies post-training sampling, optimizer settings, checkpoint retention, inference, and aggregation; Appendix D reports task-level outcomes. Appendices E and F describe the diagnostic sampling and reconstruction procedures. The scope and processing of physical recordings and the selection of paired training predictions are described in Appendices G and J. The project records preserve source paths, hashes, selection manifests, and figure-generation scripts. These records support auditing the presented artifacts. Remaining reproducibility limits include the absence of independent policy-selection testing, multi- seed estimates, and completed physical-trial statistics. REFERENCES Samy Bengio, Oriol Vinyals, Navdeep Jaitly, and Noam Shazeer. Scheduled sampling for sequence prediction with recurrent neural networks. Advances in neural information processing systems, 28, 2015. Hongzhe Bi, Hengkai Tan, Shenghao Xie, Zeyuan Wang, Shuhe Huang, Haitian Liu, Ruowen Zhao, Yao Feng, Chendong Xiang, Yinze Rong, et al. Motus: A unified latent action world model. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, p. 35101–35113, 2026. Chris M Bishop. Training with noise is equivalent to tikhonov regularization. Neural computation, 7 (1):108–116, 1995. 10 RAP-WAM: Predictive Rehearsal and Action Perturbations Kevin Black, Noah Brown, Danny Driess, Adnan Esmail, Michael Equi, Chelsea Finn, Niccolo Fusai, Lachy Groom, Karol Hausman, Brian Ichter, et al.π 0 : A vision-language-action flow model for general robot control. arXiv preprint arXiv:2410.24164, 2024. Jisong Cai, Long Ling, Shiwei Chu, Zhongshan Liu, Jiayue Kang, Zhixuan Liang, Wenjie Xu, Yinan Mao, Weinan Zhang, Xiaokang Yang, et al. Aha-wam: Asynchronous horizon-adaptive world-action modeling with observation-guided context routing. arXiv preprint arXiv:2606.09811, 2026. Tianxing Chen, Zanxin Chen, Baijun Chen, Zijian Cai, Yibin Liu, Zixuan Li, Qiwei Liang, Xianliang Lin, Yiheng Ge, Zhenyu Gu, et al. Robotwin 2.0: A scalable data generator and benchmark with strong domain randomization for robust bimanual robotic manipulation. arXiv preprint arXiv:2506.18088, 2025. Tianxing Chen, Yue Chen, Zixuan Li, Junyuan Tang, Kailun Su, Haoran Lu, Weijie Wan, Baijun Chen, Songling Liu, Haowen Yan, Honghao Su, Zhiyang Dou, Kaixuan Wang, Dandan Zhang, Yunze Liu, Yan Qin, Qiwei Liang, Qiwei Wu, Zijian Lin, Wenwei Lin, Yuran Wang, Minghua He, Tianshu Wu, Ruihai Wu, Jingquan Zhou, Kai-Chong Lei, Haibao Yu, Yuanfeng Ji, Weiyang Jin, Guanyu Lin, Xiaofan Li, Qi Xiong, Renjing Xu, Zhongyu Li, Wenhao Chai, Enze Xie, Ziwei Wang, Yao Mu, Hao Dong, Wojciech Matusik, Mingyu Ding, Wenbo Ding, Ping Luo, and Masayoshi Tomizuka. Robodojo: A unified sim-and-real benchmark for comprehensive evaluation of generalist robot manipulation policies, 2026a. URL https://arxiv.org/abs/2607.04434. Tianxing Chen, Yue Chen, Zixuan Li, Junyuan Tang, Kailun Su, Haoran Lu, Weijie Wan, Baijun Chen, Songling Liu, Haowen Yan, et al. Robodojo: A unified sim-and-real benchmark for comprehensive evaluation of generalist robot manipulation policies. arXiv preprint arXiv:2607.04434, 2026b. Cheng Chi, Zhenjia Xu, Siyuan Feng, Eric Cousineau, Yilun Du, Benjamin Burchfiel, Russ Tedrake, and Shuran Song. Diffusion policy: Visuomotor policy learning via action diffusion. The International Journal of Robotics Research, 44(10-11):1684–1704, 2025. Yilun Du, Sherry Yang, Bo Dai, Hanjun Dai, Ofir Nachum, Josh Tenenbaum, Dale Schuurmans, and Pieter Abbeel. Learning universal policies via text-guided video generation. Advances in neural information processing systems, 36:9156–9172, 2023. Haoquan Fang, Jiafei Duan, Donovan Clay, Sam Wang, Shuo Liu, Weikai Huang, Xiang Fan, Wei- Chuan Tsai, Shirui Chen, Yi Ru Wang, et al. Molmoact2: Action reasoning models for real-world deployment. arXiv preprint arXiv:2605.02881, 2026. Amir-massoud Farahmand, Andre Barreto, and Daniel Nikovski. Value-aware loss function for model-based reinforcement learning. In Artificial Intelligence and Statistics, p. 1486–1494. PMLR, 2017. Jun Guo, Qiwei Li, Peiyan Li, Zilong Chen, Nan Sun, Yifei Su, Heyun Wang, Yuan Zhang, Xinghang Li, and Huaping Liu. Unified 4d world action modeling from video priors with asynchronous denoising. arXiv preprint arXiv:2604.26694, 2026. Xun Huang, Zhengqi Li, Guande He, Mingyuan Zhou, and Eli Shechtman. Self forcing: Bridging the train-test gap in autoregressive video diffusion. Advances in Neural Information Processing Systems, 38:167283–167308, 2025. Physical Intelligence, Ali Amin, Raichelle Aniceto, Ashwin Balakrishna, Kevin Black, Ken Conley, Grace Connors, James Darpinian, Karan Dhabalia, Jared DiCarlo, Danny Driess, Michael Equi, Adnan Esmail, Yunhao Fang, Chelsea Finn, Catherine Glossop, Thomas Godden, Ivan Goryachev, Lachy Groom, Hunter Hancock, Karol Hausman, Gashon Hussein, Brian Ichter, Szymon Jakubczak, Rowan Jen, Tim Jones, Ben Katz, Liyiming Ke, Chandra Kuchi, Marinda Lamb, Devin LeBlanc, Sergey Levine, Adrian Li-Bell, Yao Lu, Vishnu Mano, Mohith Mothukuri, Suraj Nair, Karl Pertsch, Allen Z. Ren, Charvi Sharma, Lucy Xiaoyang Shi, Laura Smith, Jost Tobias Springenberg, Kyle Stachowicz, Will Stoeckle, Alex Swerdlow, James Tanner, Marcel Torne, Quan Vuong, Anna Walling, Haohuan Wang, Blake Williams, Sukwon Yoo, Lili Yu, Ury Zhilinsky, and Zhiyuan Zhou.π ∗ 0.6 : a vla that learns from experience, 2025. URLhttps://arxiv.org/abs/2511. 14759. 11 RAP-WAM: Predictive Rehearsal and Action Perturbations Physical Intelligence, Bo Ai, Ali Amin, Raichelle Aniceto, Ashwin Balakrishna, Greg Balke, Kevin Black, George Bokinsky, Shihao Cao, Thomas Charbonnier, Vedant Choudhary, Foster Collins, Ken Conley, Grace Connors, James Darpinian, Karan Dhabalia, Maitrayee Dhaka, Jared DiCarlo, Danny Driess, Michael Equi, Adnan Esmail, Yunhao Fang, Chelsea Finn, Catherine Glossop, Thomas Godden, Ivan Goryachev, Lachlan Groom, Haroun Habeeb, Hunter Hancock, Karol Hausman, Gashon Hussein, Victor Hwang, Brian Ichter, Connor Jacobsen, Szymon Jakubczak, Rowan Jen, Tim Jones, Gregg Kammerer, Ben Katz, Liyiming Ke, Mairbek Khadikov, Chandra Kuchi, Marinda Lamb, Devin LeBlanc, Brendon LeCount, Sergey Levine, Xinyu Li, Adrian Li-Bell, Vladislav Lialin, Zhonglin Liang, Wallace Lim, Yao Lu, Enyu Luo, Vishnu Mano, Nandan Marwaha, Aikys Mongush, Liam Murphy, Suraj Nair, Tyler Patterson, Karl Pertsch, Allen Z. Ren, Gavin Schelske, Charvi Sharma, Baifeng Shi, Lucy Xiaoyang Shi, Laura Smith, Jost Tobias Springenberg, Kyle Stachowicz, Will Stoeckle, Jiaming Tang, Jimmy Tanner, Shalom Tekeste, Marcel Torne, Kyle Vedder, Quan Vuong, Anna Walling, Haohuan Wang, Jason Wang, XuDong Wang, Chris Whalen, Samuel Whitmore, Blake Williams, Charles Xu, Sukwon Yoo, Lili Yu, Wuming Zhang, Zhuoyang Zhang, and Ury Zhilinsky.π 0.7 : a steerable generalist robotic foundation model with emergent capabilities, 2026. URL https://arxiv.org/abs/2604.15483. Joel Jang, Seonghyeon Ye, Zongyu Lin, Jiannan Xiang, Johan Bjorck, Yu Fang, Fengyuan Hu, Spencer Huang, Kaushil Kundalia, Yen-Chen Lin, et al. Dreamgen: Unlocking generalization in robot learning through video world models. arXiv preprint arXiv:2505.12705, 2025. Yang Jin, Jun Lv, Wenye Yu, Hongjie Fang, Yong-Lu Li, and Cewu Lu. Sime: Enhancing policy self-improvement with modal-level exploration. In 2025 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), p. 9792–9799. IEEE, 2025. Angelos Katharopoulos and François Fleuret. Not all samples are created equal: Deep learning with importance sampling. In International conference on machine learning, p. 2525–2534. PMLR, 2018. Moo Jin Kim, Karl Pertsch, Siddharth Karamcheti, Ted Xiao, Ashwin Balakrishna, Suraj Nair, Rafael Rafailov, Ethan Foster, Grace Lam, Pannag Sanketi, et al. Openvla: An open-source vision-language-action model. arXiv preprint arXiv:2406.09246, 2024. Fuhao Li, Wenxuan Song, Han Zhao, Jingbo Wang, Pengxiang Ding, Donglin Wang, Long Zeng, and Haoang Li. Spatial forcing: Implicit spatial representation alignment for vision-language-action model. In International Conference on Learning Representations, 2026. Tsung-Yi Lin, Priya Goyal, Ross Girshick, Kaiming He, and Piotr Dollár. Focal loss for dense object detection. In Proceedings of the IEEE international conference on computer vision, p. 2980–2988, 2017. Yaron Lipman, Ricky TQ Chen, Heli Ben-Hamu, Maximilian Nickel, and Matt Le. Flow matching for generative modeling. In International Conference on Learning Representations, 2023. URL https://arxiv.org/abs/2210.02747. Yicheng Liu, Zibin Dong, Baijun Ye, Tianyuan Yuan, Tao Jiang, Anqi Yang, Shicheng Cao, Haonan Liu, Yue Sun, Zihan Guo, et al. G0.5: One autoregressive stream for robot reasoning and action. arXiv preprint arXiv:2608.11739, 2026. Runyu Lu, Yubo Wu, Ethan Kou, Letian Fu, Wenli Xiao, Ajay Mandlekar, Yinzhen Xu, Guanya Shi, Ken Goldberg, Ang Chen, et al. ASPIRE: Agentic /skills discovery for robotics. arXiv preprint arXiv:2607.00272, 2026. Haoxiang Ma, Junhao Cai, Xiaoxu Xu, Hao Li, Yuyin Yang, Yang Tian, Jiafei Cao, Hongrui Zhu, Zherui Qiu, Yuqiang Yang, et al. InternVLA-A1.5: Unifying understanding, latent foresight, and action for compositional generalization. arXiv preprint arXiv:2607.04988, 2026. MotuBrain Team, Chendong Xiang, Fan Bao, Haitian Liu, Hengkai Tan, Hongzhe Bi, James Li, Jiabao Liu, Jingrui Pang, Kiro Jing, et al. Motubrain: An advanced world action model for robot control. arXiv preprint arXiv:2604.27792, 2026. 12 RAP-WAM: Predictive Rehearsal and Action Perturbations Physical Intelligence, Kevin Black, Noah Brown, James Darpinian, Karan Dhabalia, Danny Driess, Adnan Esmail, Michael Equi, Chelsea Finn, Niccolo Fusai, et al.π 0.5 : a vision-language-action model with open-world generalization. arXiv preprint arXiv:2504.16054, 2025. Stéphane Ross, Geoffrey Gordon, and Drew Bagnell. A reduction of imitation learning and structured prediction to no-regret online learning. In Proceedings of the fourteenth international conference on artificial intelligence and statistics, p. 627–635. JMLR Workshop and Conference Proceedings, 2011. Tom Schaul, John Quan, Ioannis Antonoglou, and David Silver. Prioritized experience replay. In International Conference on Learning Representations, 2016. URLhttps://arxiv.org/ abs/1511.05952. Team Wan, Ang Wang, Baole Ai, Bin Wen, Chaojie Mao, et al. Wan: Open and advanced large-scale video generative models. arXiv preprint arXiv:2503.20314, 2025. Yuran Wang, Siqiao Huang, Mingleyang Li, Chenhao Zhang, Jiaqi Liang, Weiyang Jin, Yue Chen, Xuemin Chi, Donghao Zhou, Qize Yu, et al. Openwam: An open, modular exploration towards systematic world-action model pretraining. arXiv preprint arXiv:2609.07398, 2026. Zhou Wang, Alan C Bovik, Hamid R Sheikh, and Eero P Simoncelli. Image quality assessment: from error visibility to structural similarity. IEEE transactions on image processing, 13(4):600–612, 2004. Wenli Xiao, Jia Xie, Tonghe Zhang, Haotian Lin, Letian Fu, Haoru Xue, Jalen Lu, Yi Yang, Cunxi Dai, Zi Wang, et al. Enpire: Agentic robot policy self-improvement in the real world. arXiv preprint arXiv:2606.19980, 2026. Xiaomi Robotics Team, Jun Guo, Piaopiao Jin, Jason Li, Peiyan Li, Yingyan Li, Futeng Liu, Wanli Peng, Optimus Qin, Yifei Su, et al. Xiaomi-robotics-1: Scaling vision-language-action models with over 100k hours of real-world trajectories. arXiv preprint arXiv:2607.15330, 2026. Jiazhi Yang, Kunyang Lin, Jinwei Li, Wencong Zhang, Tianwei Lin, Longyan Wu, Zhizhong Su, Hao Zhao, Ya-Qin Zhang, Li Chen, et al. Rise: Self-improving robot policy with compositional world model. arXiv preprint arXiv:2602.11075, 2026a. Senqiao Yang, Chengyao Wang, Yuxin Chen, Zixuan Wang, Longxiang Tang, Haokun Gui, Jinhui Ye, Changsheng Lu, Xiaoyang Wu, Mingkang Zhu, et al. Beyond data scaling: Representation- centric continued pre-training for vision-language-action models. arXiv preprint arXiv:2608.27550, 2026b. Tianhang Yang, Yanze Zheng, Junjie Wang, Wei-Bin Kou, Ruotong Li, and Yujiu Yang. Route by kinematics, act by observation: Kinematics-supervised expert routing in moe-augmented vla. arXiv preprint arXiv:2607.26807, 2026c. Angen Ye, Boyuan Wang, Chaojun Ni, Guan Huang, Guosheng Zhao, Hao Li, Hengtao Li, Jie Li, Jindi Lv, Jingyu Liu, et al. Gigaworld-policy: An efficient action-centered world–action model. arXiv preprint arXiv:2603.17240, 2026a. Seonghyeon Ye, Yunhao Ge, Kaiyuan Zheng, Shenyuan Gao, Sihyun Yu, George Kurian, Suneel Indupuru, You Liang Tan, Chuning Zhu, Jiannan Xiang, et al. World action models are zero-shot policies. arXiv preprint arXiv:2602.15922, 2026b. Cheng Yin, Wang Xu, Junpeng Yang, Sikyuen Tam, Hanyu Liu, Yuan Yao, Xiangrui Zeng, Junbo Cui, Yequan Wang, Zhouping Yin, and Yankai Lin. Simplememvla: A simple but effective native-video memory for vision-language-action models, 2026. URLhttps://arxiv.org/abs/2609. 05533. Tianyuan Yuan, Zibin Dong, Yicheng Liu, and Hang Zhao. Fast-wam: Do world action models need test-time future imagination? arXiv preprint arXiv:2603.16666, 2026. He Zhang, Lingzhu Xiang, Haitao Lin, Zeyu Huang, Minghui Wang, Dingyan Zhong, Yubo Dong, Yihao Wu, Yongming Rao, Dongsheng Zhang, et al. Hy-embodied-0.5-vla: From vision-language- action models to a real-world robot learning stack. arXiv preprint arXiv:2606.14409, 2026. 13 RAP-WAM: Predictive Rehearsal and Action Perturbations Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In 2018 IEEE/CVF conference on computer vision and pattern recognition, p. 586–595. IEEE, 2018. Jinliang Zheng, Jianxiong Li, Zhihao Wang, Dongxiu Liu, Xirui Kang, Yuchun Feng, Yinan Zheng, Jiayin Zou, Yilun Chen, Jia Zeng, et al. X-vla: Soft-prompted transformer as scalable cross- embodiment vision-language-action model. In International Conference on Learning Representa- tions, 2026. Chuning Zhu, Raymond Yu, Siyuan Feng, Benjamin Burchfiel, Paarth Shah, and Abhishek Gupta. Unified world models: Coupling video and action diffusion for pretraining on large robotic datasets. arXiv preprint arXiv:2504.02792, 2025. 14 RAP-WAM: Predictive Rehearsal and Action Perturbations APPENDIX: SUPPLEMENTARY MATERIAL ATRAINING AND EVALUATION PROTOCOL Training was performed on NVIDIA A800 GPUs. RAP-WAM initializes its shared transformer from Wan2.2-TI2V-5B video weights (Team Wan et al., 2025) and jointly learns future video and robot actions from target RoboDojo demonstrations. Action/state encoders, queries, and CAP are initialized for target-task training, without initialization from a separately trained robot policy. The base architecture contains no additional memory, mixture- of-experts, or post-training extension. Thus “without embodied pretraining” excludes an intermediate pretraining stage on external embodied data, whether for action-policy learning or joint world action modeling. It retains Wan video pretraining, pretrained text embeddings, and joint world action training on target robot demonstrations. The collection has 3,500 episodes, with 3,499 used for training and one for validation. The fixed RAP-WAM base is the reference for local mechanism analyses. Table 1 reports the complete post-training system, whose retained task policies build on this substrate. The settings in Table 2 describe the base learner, not the cumulative computation of the entire improvement process. Table 2: Training settings. Physical training uses the same core with task-specific interfaces; physical success rates appear in Figure 4. SettingRoboDojoPhysical-robot data Video initializationWan2.2-TI2V-5BWan2.2-TI2V-5B InputHead/two-wrist384 × 320 mosaic Head 224× 224 Action/state dimension14/14Phone 28/28; numbers 32/32 LanguagePrecomputed instruction em- beddings None Observation/future/action length1/16/161/16/16 Queries/alignment width16/12816/128 Per-device/global batch1/961/120 Optimizer/peak LRAdamW/2× 10 −4 AdamW/2× 10 −4 Precision/parameter EMABF16/noneBF16/none Auxiliary warmup (updates)18,0006,000 Rehearsal probability/denoising0.25/four iterations0.25/four iterations Conditional state substitution0.50.5 response-based credit probability0.50.5 response-based credit video/action coefficients0.5/0.30.5/0.3 P,S,E coefficients1/1/0.51/1/0.5 VAE Cached recorded futures; pre- dicted inputs encoded live Live RoboDojo policy evaluation uses 30 denoising steps and executes eight actions before replanning. Action smoothing uses a Savitzky–Golay filter with window 9 and polynomial order 2 on all 14 action coordinates. Four-action boundary blending uses new-chunk coefficients(i + 1)/5fori = 0, 1, 2, 3. This filter is distinct from classifier-free guidance. Physical deployment additionally depends on robot-specific joint mappings, units, and control rates. Generalization has 12 tasks, Precision 8, Long-Horizon 8, Memory 6, and Open 8. Binary success rate (SR) and partial-completion Score are averaged within capabilities and then equally across the five capability means (Chen et al., 2026b): AvgSR = 1 5 5 X d=1 1 |T d | X j∈T d SR j .(12) HereT d contains the evaluated tasks in capabilityd; Score uses the same aggregation. Row-specific coverage is given in the table notes and Appendix D. Standard and random variants are combined into their parent Generalization task before aggregation. Both the base and agentic system cover all 42 task units: 12 Generalization, eight Precision, eight Long-Horizon, six Memory, and eight Open. 15 RAP-WAM: Predictive Rehearsal and Action Perturbations For taskt, SR is the number of successful valid episodes divided by its valid-episode countn t , and Score is the mean partial-completion score over the same episodes. Task means are averaged within capability and then equally across capabilities; tasks are not reweighted byn t . Layout identities and per-task denominators are retained in the result records. The target alignment projection is stopped along with its target features. The direct attention mask permits state-mediated information and shared-parameter updates. At per-device batch one, the optional local min–max difficulty correction vanishes. SpatialPbroadcasts uniformly in time, so its normalized temporal contribution also vanishes. The prior is zero until its first valid re- hearsal update. Rehearsal and response-based credit are invoked according to their respective sampling probabilities. Only successfully computed auxiliary losses with nonzero weights enter the training objective. For each branch, the effective participation rate is the fraction of training updates satisfying these conditions. BPUBLIC REFERENCES AND PRETRAINING ATTRIBUTION G0.5 pretrains on robot demonstrations and web-scale vision–language data, with 14 real/simulated embodiments mapped to a shared action space (Liu et al., 2026). G0.5 therefore uses external embodied pretraining. Xiaomi-Robotics-1 and Hy use action-policy pretraining on handheld UMI demonstrations (Xiaomi Robotics Team et al., 2026; Zhang et al., 2026); these are action-labeled embodied trajectories, not necessarily robot-collected data. OpenWAM-αjointly pretrains future- video and action prediction on egocentric and robot data (Wang et al., 2026). Its final mixture contains 6,369 hours of egocentric human and robot trajectories; human video is not itself labeled robot-action supervision. Our no-external-embodied-pretraining flag still includes Wan video initial- ization, pretrained text embeddings, and joint world action training on target robot demonstrations. Table 1 therefore defines “Pretrained” as an intermediate stage on external embodied data, includ- ing robot/UMI action-policy and joint world action pretraining, rather than asserting that every pretraining trajectory was robot-collected. External embodied pretraining.The pretraining column summarizes the method’s reported use of external embodied data. InternVLA-A1.5 uses robot-episode pretraining (Ma et al., 2026); VLAct and X-VLA use cross-embodiment robot pretraining, and MolmoAct2 uses action-data pretraining (Yang et al., 2026b; Zheng et al., 2026; Fang et al., 2026). Spatial Forcing inherits the Pi-05 base, so both carry a positive embodied-pretraining flag (Physical Intelligence et al., 2025). X-WAM reports more than 5,800 hours of robot-data pretraining (Guo et al., 2026). GigaWorld-Policy introduces embodied-video pretraining using robot and egocentric human data before target-task action training (Ye et al., 2026a). AHA-WAM reports no robot-data pretraining in its default simulation setting, but its real-world comparison pretrains both AHA-WAM and Fast-WAM on 24,600 RoboCOIN trajectories (approximately 165 hours) (Cai et al., 2026). The AHA-WAM Yes flag refers to this reported real-world variant; it does not establish the initialization of the RoboDojo checkpoint. X-WAM and GigaWorld-Policy-0 are marked Yes based on their reported pretraining. Fast-WAM’s reported simulation configuration uses Wan initialization without external embodied pretraining (Yuan et al., 2026). SimpleMemVLA training and comparison source. SimpleMemVLA uses timestamped visual history with a Qwen3.5-4B backbone and a flow-matching action head (Yin et al., 2026). Its released training recipe initializes the backbone from Qwen3.5-4B, constructs a new action head, and trains on each benchmark’s demonstrations without a separate embodied-pretraining stage. We therefore mark No under the definition above. The RoboDojo values use the official 23 September 2026 leaderboard snapshot, including separate standard and randomized Generalization results. World-model classification. Table 1 separates VLA and other action policies from world-model- based policies. The latter group includes OpenWAM-α, X-WAM, GigaWorld-Policy-0, AHA-WAM, Fast-WAM and our policy, which learn an explicit predictive world-model component alongside action generation. InternVLA-A1.5 is grouped with VLAs: its foresight tokens receive latent supervision from a frozen pretrained video model, but the policy does not learn pixel-level generation and discards the video branch at inference (Ma et al., 2026). Its‡marker records this supervision source without classifying the policy as a world action model. 16 RAP-WAM: Predictive Rehearsal and Action Perturbations Table 3: Post-training system results across 42 tasks. SR is in percent; Score measures partial completion. Each task is averaged over its valid evaluation episodes. TaskCapabilitySRScore Align blocksOpen0.000.00 Arrange largest numberGeneralization4.005.80 Build towerPrecision72.0079.60 Classify objectsLong-Horizon2.006.50 Classify objects by languageOpen0.001.60 Cover blocksMemory22.0026.10 Deposit coinPrecision10.2014.69 Fasten screwsPrecision8.0027.60 Fill egg holderLong-Horizon0.0012.95 Fill pen holderLong-Horizon18.0043.40 Fold clothesGeneralization12.0016.00 General pickupOpen6.006.00 Hang mugsGeneralization2.007.30 Imitate sorting sequenceMemory2.003.80 Insert keyPrecision0.0015.00 Insert tubesPrecision58.0072.40 Make kongLong-Horizon82.0082.00 Make toastGeneralization10.0018.00 Match and pick from conveyorMemory32.0032.00 Organize tableLong-Horizon10.0048.50 Pack objects into boxGeneralization6.0017.20 Pick from conveyor by imageOpen0.000.00 Play xylophonePrecision2.002.00 Play stacking toyLong-Horizon0.002.00 Play tic tac toeLong-Horizon86.0096.00 Plug in chargerPrecision4.004.00 Pour balls into vasePrecision14.0014.00 Pour by languageOpen0.000.00 Pour liquid into cupGeneralization4.004.00 Press by numberMemory0.000.00 Push tGeneralization0.000.00 Put bottles into dustbinLong-Horizon94.0096.10 Solve equationOpen0.000.00 Sort nesting dolls by sizeGeneralization8.008.00 Stack blocksGeneralization24.0028.20 Stack blocks by languageOpen0.001.20 Stack bowlsGeneralization42.0043.20 Store laptop and headphonesGeneralization14.0024.80 Store tools in toolboxOpen0.000.50 Swap tMemory0.000.00 Swap blocksMemory0.000.00 Sweep blocksGeneralization0.000.00 Xiaomi, Hy, Pi-05, VLAct, X-VLA and MolmoAct2 document action-generation objectives without an explicit predictive world-model component (Xiaomi Robotics Team et al., 2026; Zhang et al., 2026; Physical Intelligence et al., 2025; Yang et al., 2026b; Zheng et al., 2026; Fang et al., 2026). Spatial Forcing aligns observed geometry, not future scene evolution (Li et al., 2026); its benchmark identity is the Pi-05-based variant. Action flow matching, current depth prediction, and textual subtask planning alone do not qualify as world modeling here. KinRT uses kinematics-supervised expert routing for action generation and is grouped with non-world-model policies (Yang et al., 2026c). SimpleMemVLA is grouped with VLAs: its video context represents observed history, rather than an explicitly predicted future world state. These method-level labels neither make all architectures identical nor explain performance causally. 17 RAP-WAM: Predictive Rehearsal and Action Perturbations Table 4: RAP-WAM base results across 42 tasks, using the single step-742500 checkpoint before post-training. Task order and metric definitions match Table 3. SR (%) and Score are computed over valid evaluation episodes. TaskCapabilitySRScore Align blocksOpen0.000.00 Arrange largest numberGeneralization2.003.80 Build towerPrecision60.0069.80 Classify objectsLong-Horizon0.004.40 Classify objects by languageOpen0.001.60 Cover blocksMemory16.0020.60 Deposit coinPrecision4.087.76 Fasten screwsPrecision2.0018.60 Fill egg holderLong-Horizon0.0012.95 Fill pen holderLong-Horizon6.0032.00 Fold clothesGeneralization6.009.20 General pickupOpen6.006.00 Hang mugsGeneralization0.003.80 Imitate sorting sequenceMemory0.001.20 Insert keyPrecision0.0014.40 Insert tubesPrecision54.0069.20 Make kongLong-Horizon74.0074.00 Make toastGeneralization4.0014.00 Match and pick from conveyorMemory26.0026.00 Organize tableLong-Horizon10.0048.50 Pack objects into boxGeneralization2.0014.70 Pick from conveyor by imageOpen0.000.00 Play xylophonePrecision0.000.00 Play stacking toyLong-Horizon0.000.60 Play tic tac toeLong-Horizon80.0094.50 Plug in chargerPrecision0.000.00 Pour balls into vasePrecision12.0012.00 Pour by languageOpen0.000.00 Pour liquid into cupGeneralization0.000.00 Press by numberMemory0.000.00 Push tGeneralization0.000.00 Put bottles into dustbinLong-Horizon90.0094.00 Solve equationOpen0.000.00 Sort nesting dolls by sizeGeneralization2.002.00 Stack blocksGeneralization24.0027.00 Stack blocks by languageOpen0.000.40 Stack bowlsGeneralization40.0042.10 Store laptop and headphonesGeneralization10.0017.60 Store tools in toolboxOpen0.000.50 Swap tMemory0.000.00 Swap blocksMemory0.000.00 Sweep blocksGeneralization0.000.00 CMATHEMATICAL PROPERTIES AND OBJECTIVE DETAILS C.1PREDICTIVE REPRESENTATION AND TRAINING UPDATE Joint flow-matching substrate.We use the linear interpolation and velocity-regression formulation of flow matching (Lipman et al., 2023). A frozen VAE encodes observed and subsequent demonstration video, with fixed camera mosaics for multi-view observations. Actions and states use separate training-set normalizers. Video and actions share a noise levelσbut receive independent noises: z σ = (1− σ)z + σε z , a σ = (1− σ)a + σε a ,(v ∗ z ,v ∗ a ) = (ε z − z,ε a − a).(13) 18 RAP-WAM: Predictive Rehearsal and Action Perturbations Observed visual latents are clamped and excluded from the future-only video loss. The video- initialized trunk is trained together with newly initialized action/state encoders, queries, and CAP on target demonstrations. Tokenization, conditioning, and action projection.Action and state encoders use Linear–SiLU– Linear projections, learned position embeddings, and LayerNorm. All four token groups share each block’s self-attention projections, text cross-attention, and feed-forward layers; there are no modality-specific transformer experts. Rotary position encoding applies only to video-token queries and keys. Predictive queries use action-side diffusion-time modulation. State tokens receive no additional diffusion-time modulation, but still undergo the block’s learned modulation and all updates. The mask in Equation 3 is applied identically at training and sampling: fori∈A,j ∈V, the logit is suppressed; state-mediated paths remain. The two projections in Equation 1 have output width 128. The entire target branch, includingP t , is evaluated without gradients. Future latents are pooled over time and onto a spatial4× 4grid; the resulting targets supervise 16 distinct query slots. They are neither an online memory bank nor an independently trained teacher. In Equation 4, the MLP output projection and bias are zero-initialized; the time-modulated branch starts from the newly initialized sequence head. Its exact form is H r (h,e) = W r [LN(h)⊙ (1 + e + m s ) + (e + m b )] + b r ,(14) with learned offsetsm s ,m b . The two branches have separate normalization operators. The construc- tion introduces no low-pass filter, task routing, or independently supervised coarse/fine decomposition. Generated-image and state conditions. Rehearsal is invoked withp c (k) = ̄p c r c (k), where r c (k) = min(1,k/W c ). Conditional state substitution has probability ̄p s min(1,k/W s ). In the reported configuration, ̄p c = 0.25and ̄p s = 0.5. The first chunk usesS c gradient-free denoising steps, withS c = 4, before RGB decoding. Its last image replaces the next observed image; this prefix and the recorded next future frames are jointly re-encoded by the frozen VAE. Thus the recorded RGB targets are retained, but their temporal VAE latents need not equal those encoded with the recorded initial image. For action and state normalizersN a ,N s , the substituted normalized state is es 1 = N s (1− b s )s raw,∗ 1 + b s sg N −1 a (ba 0,H a −1 ) .(15) Hereba 0 is the sampled normalized action chunk andb s selects state substitution. This mapping assumes compatible absolute-joint action and state schemas. It does not model actuator dynamics or contact feedback. The base loss includes query alignment; rehearsal and credit auxiliaries supervise video/action flow outputs without additional alignment losses. The persistent prior is initially zero, so credit remains defined before a rehearsal update. The first valid rehearsal-error map initializes the prior directly; subsequent maps use the moving average. The reference predictions use the original demonstration batch with fresh noising, not the rehearsed input. Each credit invocation uses one gradient-carrying reference prediction and one gradient-free perturbed forward, in addition to the base and any rehearsal computations. The algorithm assumes valid training inputs, with a zero prior before its first valid rehearsal update. It specifies the update rule, not the empirical frequency with which each auxiliary branch contributes during training (Appendix A). It neither sends actions to an environment nor requests new corrective demonstration labels at predicted states. Joint sampling and deployment.Inference begins with independent future-video and action noise. At adjacent noise levels, Euler integration updates both modalities: (z n+1 ,a n+1 ) = (z n ,a n ) + (σ n+1 − σ n )(v z θ ,v a θ ).(16) The observed visual prefix is clamped at every iteration. Queries, directional attention, and CAP remain in each forward; the action output isN −1 a (a N ). Returning actions does not decode future RGB, but it does retain future-latent computation. Alignment targets, rehearsal, prior updates, and perturbation-based credit construction are absent at deployment. C.2LOCAL INTERPRETATION OF THE PERTURBATION RESPONSE Fixθ, observation, state, language, video noise, and diffusion level. Letf i : R d → R C map the flattened normalized noisy action chunk to the predicted video velocity at locationi. Forg ∼N (0,I d ) 19 RAP-WAM: Predictive Rehearsal and Action Perturbations Algorithm 1 One training update of RAP-WAM Require: Adjacent demonstration chunks, model θ, spatial priorP (initially zero), step k 1: Sample base noising; compute joint lossL←L 0 2: if b c ∼ Bernoulli(p c (k)) is one then 3:Generate the first chunk without gradients using S c denoising steps 4:Form the second-chunk image from the last predicted frame 5:Optionally substitute the last raw predicted joint action; normalize as state 6:Compute video/action flow lossL 1 against the recorded future/actions 7:UpdateP from detached second-chunk spatial errors 8: L←L + λ c r c (k)L 1 9: end if 10: if b P ∼ Bernoulli(p P ) is one then 11:Fresh auxiliary noising; compute gradient-carrying (v z ,v a ) 12:Evaluate the action perturbation without gradients; detachP,S,E 13:ComputeW,c,w and normalize their masses to q v ,q a 14: L←L + e L P (θ; ̄ θ) 15: end if 16: BackpropagateL and update the trainable parameters andδ = τg,S i = C −1 ∥f i (a +τg)−f i (a)∥ 2 . At the noisy action inputa σ , the local interpretation is E δ [S i ] = τ 2 C ∥J a f i (a σ )∥ 2 F + O(τ 4 ).(17) This perturbation argument (Bishop, 1995) motivates a forward-only sensitivity probe without explicit Jacobians or second-order derivatives, under the regularity conditions stated below. Proposition 1 (response interpretation). Supposef i is three times continuously differentiable onR d and its third derivative has globally bounded operator norm. At fixeda, ES i = τ 2 C ∥J a f i (a)∥ 2 F + O(τ 4 ) as τ → 0.(18) For an affinef i , the expression without the remainder is exact for everyτ. This is a standard local sensitivity calculation, not a new control guarantee or an assertion that a finite-precision model satisfies the assumptions. Proof. Write the Taylor expansion as f i (a +τg)−f i (a) = A +B +R, A = τJg, B = 1 2 τ 2 H[g,g], ∥R∥≤ M 3 τ 3 ∥g∥ 3 /6. (19) HereM 3 bounds the third derivative,M 1 = ∥J∥ op , andM 2 = ∥H∥ op ata. Gaussian second moments giveE∥A∥ 2 = τ 2 ∥J∥ 2 F , and symmetry makes the cubic linear–quadratic cross term vanish. Withm p = E∥g∥ p , the remaining terms satisfy ES i − τ 2 C ∥J∥ 2 F ≤ 1 C τ 4 M 2 2 4 + M 1 M 3 3 m 4 +τ 5 M 2 M 3 6 m 5 + τ 6 M 2 3 36 m 6 .(20) All Gaussian moments are finite, proving the asymptotic bound. Affine maps haveH = R = 0. The constants can depend on dimension and the fixed predictor.□ Single-direction and scale limitations. For an affine map, Var(S i ) = 2τ 4 C 2 tr[(J ⊤ J ) 2 ].(21) Thus shrinkingτdoes not eliminate the relative uncertainty of a single direction. The implementation uses one perturbation, and generallyEN (S)̸=N (ES); its normalized map is not an exact Jacobian- norm ranking. Nor does per-coordinateτ = 0.1imply a small whole-chunk perturbation: the RMS norm isτ √ d, approximately 1.50 ford = 16×14and 2.12 ford = 16×28in normalized coordinates. The analysis motivates perturbation-scale and repeatability checks, not an environment-causality interpretation or a prediction of task success. 20 RAP-WAM: Predictive Rehearsal and Action Perturbations C.3RESPONSE AND PREDICTION ERROR NEED NOT AGREE Figure 5 illustrates how prediction error, action response, and historical error yield different super- vision weights. Forf 1 (a) = bandf 2 (a) = κa, suitable targets give −0.30.00.3 Action input a 0 1 P r e d i c t i o n f ( a ) A:E=1,S=0 B:E=0,S=0.04 f A (a)=1f B (a)=2a PE S Raw values; color scaled per column A B C D 010 000.04 010.04 100 ABCD Location 0 1 2 3 W i 1.5 2 2.5 2 1 N(P) N( ̄ S) 0.5N(E) ABCD Location 0 10 20 30 Weight mass (%) 18.75 25 31.25 25 Dashed: uniform 25% Error only (a) Error is not sensitivity(b) Distinct supervision sources (c) Construction of local weights(d) Redistribution of loss mass Full Figure 5: Why error, response, and rehearsal prior provide different supervision. An exact constructed example, not measured robot results. At four locations, letf A (a) = 1,f B (a) = 2a, f C (a) = 1 + 2a, andf D (a) = 0, witha = 0, target zero, and priorP = (0, 0, 0, 1). For δ ∼ N (0, 0.1 2 ), use the expected response ̄ S = E δ S . (a) A has error without action sensitivity; B has sensitivity without error. (b) The four locations separate residual, response, combined, and historical signals. (c) Applying the spatial rule toP, ̄ S,Egives positive weights(1.5, 2, 2.5, 2). (d) After normalization, error-only allocation gives(30, 20, 30, 20)%, whereas the full rule (Full) gives (18.75, 25, 31.25, 25)%. Thus current error alone cannot reproduce the allocation. This illustration uses expected response; training uses a single sampled perturbation, as discussed in Appendix C.2. E 1 = (b− y 1 ) 2 > 0, E 2 = 0,ES 1 = 0, ES 2 = τ 2 κ 2 .(22) A constant action-independent output can have nonzero error but zero response; an accurately predicted linear output can have zero error but nonzero expected response. This demonstrates non- equivalence of signals, not an empirical improvement in robot success. The finite-perturbation and normalization qualifications above still apply. C.4FROZEN-WEIGHT SURROGATE AND REDISTRIBUTION IDENTITY For the main visual objective, bars denote uniform empirical averages andCov u the corresponding covariance over active locations: X i q v i e z i = ̄e z + Cov u (W,e z ) ̄ W ,(23) This separates prediction error from emphasis on particular locations. The general form and its gradient analogue follow below. Letienumerate all active batch/spatiotemporal locations, with 21 RAP-WAM: Predictive Rehearsal and Action Perturbations channel-mean errorse i (θ)and positive weightsW i . At current ̄ θ , freezeq i = W i / P j W j . The local surrogate and its gradient are e F (θ; ̄ θ) = X i q i ( ̄ θ)e i (θ), g q = X i q i ( ̄ θ)∇e i ( ̄ θ).(24) This is the precise backward-pass meaning of stop-gradient. At differentiable points, the fully adaptive valueF (θ) = P i q i (θ)e i (θ)has the additional derivative P i e i ∇q i , which the implementation inten- tionally omits. Ties in min–max normalization do not prevent defining the frozen-weight surrogate. Proposition 2 (redistribution identities). Let bars andCov u use uniform empirical averaging overnlocations, with covariance denominatorn, and letg i = ∇e i ( ̄ θ). Then X i q i e i = ̄e + Cov u (W,e) ̄ W , g q − ̄g = Cov u (W,g) ̄ W .(25) The second covariance is defined componentwise. These are explanatory identities, not original theorems of optimization or closed-loop improvement. Proof. For either scalarx i = e i or vectorx i = g i , expanding the empirical covariance gives n −1 P i W i x i = ̄ W ̄x + Cov u (W,x). Divide by ̄ W > 0 and use the definition of q.□ Consequently, normalized weighting can change gradient direction and/or magnitude when priorities correlate with location-wise gradients. It need not decrease the fully adaptive valueF, and it is not a corrected importance sampler for the uniform risk. Within a single sample,E i = e i , so its spatial/temporal empirical covariance satisfiesCov u,s (N (E ),e) = Var u,s (e)/ max(max i e i − min i e i ,ε n )≥ 0: part of response-based credit explicitly increases coefficients at high-error locations. Whether adding responseSor persistent priorPimproves control is an empirical question. Bounded emphasis without exclusion. Letκ v = 1 + α P + α S + α E andκ a = 1 + α S . ForN v video positions andN a action positions in their respective normalizations, nonnegative source coefficients imply 1 κ v N v ≤ q v i ≤ κ v N v , 1 κ a N a ≤ q a j ≤ κ a N a .(26) Our settings giveκ v = 3.5andκ a = 2. Thus selectivity retains every location. Detachment removes direct gradients through credit while allowing it to adapt across updates. These bounds regulate emphasis, not gradient norms, unbiased estimation, or preservation of previously acquired capabilities. C.5LIMITS OF THE INTERPRETATION The identities characterize the weighting rule, not its causal effect on success. No matched-budget, independently evaluated component ablation is reported here. A claim of signal-specific control benefit would require matching auxiliary computation, initialization, data, and checkpoint selection, and separating weighting information from gradient-scale changes. Normalizing weight sums does not match the full AdamW update. Numerical checks on affine and smooth toy maps verify the identities, not robot performance. DTASK-LEVEL BASE AND POST-TRAINING RESULTS Tables 3 and 4 report the post-training system and the fixed base on the same 42 tasks. The base achieves 12.85% SR and 17.86 Score under the capability-balanced aggregation. Base and system use identical task coverage and aggregation rules; per-task SR and Score come from one policy’s valid evaluation records. Generalization variants are combined within their parent task. Figure 6 compares the per-task changes in SR and Score relative to the base. 22 RAP-WAM: Predictive Rehearsal and Action Perturbations 04812 SR gain (percentage points) Fold clothes Make toast Sort nesting dolls by size Pack objects into box Pour liquid into cup Store laptop and headphones Arrange largest number Hang mugs Stack bowls Push t Stack blocks Sweep blocks Build tower Deposit coin Fasten screws Insert tubes Plug in charger Play xylophone Pour balls into vase Insert key Fill pen holder Make kong Play tic tac toe Put bottles into dustbin Classify objects Fill egg holder Organize table Play stacking toy Cover blocks Match and pick from conveyor Imitate sorting sequence Press by number Swap t Swap blocks Align blocks Classify objects by language General pickup Pick from conveyor by image Pour by language Solve equation Stack blocks by language Store tools in toolbox 04812 Score gain (a) Success rate(b) Partial completion Red: SR improves Blue: Score-only gain Gray: unchanged Figure 6: Task-level changes under the selected assignment. Aligned rows show all 42 tasks, grouped by capability: (a) SR changes and (b) partial-completion Score changes relative to the base. Red indicates 24 tasks with higher SR, blue four tasks with higher Score only, and gray 14 unchanged tasks. These are observed results under the selected task-policy assignment, not an independent test of regression-free improvement. ESUPERVISION ALLOCATION AND RESPONSE ANALYSIS The analyses use fixed-policy predictions to quantify supervision allocation. Simulation statistics use the RAP-WAM base and 35 conditions of nine demonstration windows each, separate from benchmark evaluation episodes. Physical-demonstration sources are specified in Appendix F. Field notation.P,S,E,Wdenote the cross-chunk prior, action response, prediction error, and composite visual-loss coefficient, respectively. The three simulation component fields used in the analyses below are normalized. 23 RAP-WAM: Predictive Rehearsal and Action Perturbations Arithmetic source-removal analysis. Figure 2a–b uses the same simulation component maps, with model outputs held fixed. Each of 315 windows hasN = 4× 24× 20 = 1,920native positions, giving 604,800 positions in total, not that many independent observations. Cast the normalized P,S,Earrays to float64 and reconstructW = 1 +P +S + 0.5Einstead of using the rounded stored composite. For eachX ∈ P,S, 0.5E, remove that source within the original window and recompute the sum-normalization: q −X i = W i − X i P j (W j − X j ) ,TV X = 1 2 X i q i − q −X i .(27) The unit floor and all other normalized components remain fixed. All 315 windows share the same savedPmap; its removal is not removal of a separate learned task-specific prior. For panel a, average tied ranks separately within each window and divide each rank by 1,920. The horizontal coordinate is theErank and the vertical coordinate is theSrank. Hexagonal binning with grid size 18 reports the arithmetic mean of∆ i = 1,920(q i − q −S i )over positions in each displayed hexagon. Color measures signed change relative to the uniform per-position coefficient1/N, not a ratio toq −S i or a density count. The diverging scale is symmetric about zero and covers all displayed means; no smoothing is applied. The native changes sum to zero in every window; recovering this property from bin means requires weighting by bin counts, not an unweighted mean of the displayed hexagons. Pooling preserves equal window representation overall, but the conditional mean in a hexagon weights conditions by their number of positions falling there. For panel b,TV X equals the sum of positive coefficient changes, the sum of negative changes in magnitude, and the largest absolute change in total coefficients assigned to any subset of native positions. Writingα X = P i X i / P i W i andp X i = X i / P j X j for P i X i > 0 gives q− q −X = α X (p X − q −X ),TV X = α X TV(p X ,q −X ).(28) Thus removal sensitivity combines the source’s summed coefficients with its normalized spatial shape. It is neither a causal importance estimate nor an additive decomposition across sources. If P i X i = 0 , removal instead leaves the normalized coefficients unchanged andTV X = 0. Compute TV on each window, take its median across nine windows per condition, and show all 35 condition medians. The cross-condition median [Q1,Q3] in percent is 5.4707 [5.2891,5.7790] forP, 2.2159 [1.9935,2.5100] forS, and 1.1405 [1.0422,1.2434] for0.5E. Each density is normalized to its own peak. Density smoothing is display-only; the marks are descriptive IQRs, not confidence intervals. These arithmetic removals hold model outputs fixed, do not retrain a policy, and measure neither gradient magnitude nor success rate. Panel c instead uses raw float32Sfrom one phone-packing validation demonstration, at window starts 63, 126, and 188. These windows use the physical-image diagnostic model and data described in Appendix F. Spatial means of rawSare normalized over the four native future bins using the implemented10 −6 denominator floor. Their temporal ranges are respectively3.6025× 10 −6 , 5.6887× 10 −6 , and1.8406× 10 −6 , so the floor is inactive in all three retained windows. The display shows four bin weights, each repeated over four consecutive action steps, alongside the exact unit reference whenSis removed. It does not use a normalized-map temporal proxy or 16 independently probed actions. BecausePis time-constant and this branch excludesE, removingSleaves unit temporal coefficients. The same action perturbation thus provides spatial and temporal selectivity without a second coefficient predictor. The displayedwprecedes the objective’s normalization q a j = w j / P k w k ; even its unit reference is not a retrained ablation. The companion reproducibility materials retain the source correspondence and display specification. Diagnostic conditions.Table 5 identifies the 35 conditions used for the response and error analyses in Figure 2. Each condition contains nine demonstration windows. Priority-set flow and condition rainclouds. In each simulation window, top-20% membership is defined on all 1,920 native positions, giving 384 effective members in either map. Boundary ties receive fractional membership. For membershipsa i ,b i ∈ [0, 1]inE,S, the four joint masses are the position means of(1− a i )(1− b i ),(1− a i )b i ,a i (1− b i )anda i b i , followed by an equal mean over all 315 windows. These fractions are 0.709583, 0.090417, 0.090417 and 0.109583, respectively. Figure 2d conditions on response-top20 membership: dividing the shared and response- only masses by 0.2 gives the displayed 54.7916% and 45.2084% bars. Each percentage uses the 24 RAP-WAM: Predictive Rehearsal and Action Perturbations Table 5: Task identities for the 35 diagnostic conditions. IndexTask 00Arrange largest number 01Build tower 02Classify objects 03Cover blocks 04Deposit coin 05Spell RoboDojo 06Fasten screws 07Fill egg holder 08Fill pen holder 09Fold clothes 10Hang mugs 11Imitate sorting sequence 12Insert key 13Insert tubes 14Make kong 15Make toast 16Match + pick from conveyor 17Organize table 18Pack objects into box 19Play xylophone 20Play stacking toy 21Play tic-tac-toe 22Plug in charger 23Pour balls into vase 24Pour liquid into cup 25Press by number 26Push T 27Put bottles in dustbin 28Sort nesting dolls by size 29Stack blocks 30Stack bowls 31Store laptop + headphones 32Swap T pieces 33Swap blocks 34Sweep blocks response top set as its denominator. Shared mass remains 10.9583% of all positions. The overlap compares signals within the same window. Raincloud points use the within-condition median of each window’s Spearman rank correlation. The cloud density is normalized to its own peak. The cloud and median/IQR marks describe 35 curated condition medians, not 315 independent evaluations. The separately summarized overlap median 0.559896 differs from the alluvial mean 0.547916. Distribution smoothing in the cloud is a display device, not an uncertainty model; no confidence interval, significance test, or success gain is inferred. Figure 2c labels the three original phone-packing windows (starts 63, 126, 188) as W1, W2, W3. The five-panel arrangement retains the original underlying statistics. Normalized auxiliary weight share. Appendix E evaluates P i b i W i / P i W i on the same win- dows under uniformW i = 1, post-hoc error-onlyW i = 1 + 0.5E i , and full response-based credit W i = 1 +P i +S i + 0.5E i rules. The saved component maps are normalized; full weights are reconstructed from them rather than taken from float16-rounded storedW. Each point is a median over nine windows in one condition, with median/IQR marks across 35 conditions. The respective medians are 20.00%, 20.9448% and 24.4003%; the error-only and response-based credit IQRs are 20.7050–21.2332% and 23.0325–25.3654%. Every condition-median share increases; the median paired difference is 3.7816 percentage points (range 0.8839–5.7004), not the difference of group medians. Adding bothPandSprevents attribution to either signal alone; enrichment partly follows from includingSin both the weights and the selected set. This measures normalized auxiliary coefficients, not gradient magnitude, task gain, or a retrained error-only control. Figure 7 shows that the full credit rule assigns a larger weight share to response-top20 positions than error-only reweighting in every displayed condition. The medians across conditions are 24.40% and 25 RAP-WAM: Predictive Rehearsal and Action Perturbations PS0.5E 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 Condition ID 5.32.21.3 5.72.41.3 5.22.60.9 6.12.71.4 5.32.31.1 5.32.51.5 5.32.71.3 5.12.21.2 5.52.31.1 6.42.41.3 5.32.11.1 6.02.81.1 5.12.51.2 6.22.01.3 5.52.10.8 6.02.21.2 5.81.71.1 6.21.71.3 5.51.91.1 4.92.71.0 5.71.90.9 5.62.01.0 5.52.80.9 5.81.70.9 5.32.21.1 5.42.91.2 5.41.91.1 5.31.91.3 5.72.00.8 6.12.21.0 5.12.51.2 5.51.81.1 5.52.50.7 6.02.81.2 5.72.01.1 036 202428 Weight on response-top20 cells (%) 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 Error-only (a) Removing a supervision source Redistributed weight mass (%) (b) Allocation to action-sensitive positions Full Figure 7: Condition-resolved supervision allocation. Both panels retain all 35 conditions, each with nine windows; IDs follow Table 5. (a) Median total-variation distance after removing each source from the normalized spatial weights, in percent. (b) Median normalized weight mass assigned to response-top20 positions under error-only reweighting (blue) and the full credit rule (red, labeled Full); each connector pairs the same condition. The dashed line is uniform allocation, 20%. The fields and predictions are fixed throughout. 20.94%, respectively. This supports the mechanism’s ability to alter supervision beyond error-only weighting; it does not measure a retrained success-rate gain. The source-removal distances also vary across conditions, showing that the same coefficient rule induces different allocations for different inputs. The 315 windows are descriptive samples, not independent policy evaluations; no confidence intervals or significance claims are inferred from these plots. FSPATIOTEMPORAL DIAGNOSTIC PROTOCOL The simulation analysis uses 35 conditions with nine distinct demonstrations each. Conditions are defined using initial image, state, and logarithmic trajectory length; each demonstration contributes one middle valid window and one seeded draw of diffusion noise and action perturbation. Each map contains four future bins on a24× 20grid. Within-window ranks use all 1,920 positions; 26 RAP-WAM: Predictive Rehearsal and Action Perturbations condition summaries aggregate nine windows. Pixels and windows from the same condition are not independent policy evaluations. The temporal-credit example in Figure 2c uses a phone-packing demonstration with window starts 63, 126, and 188. Its raw response maps have four14× 14bins; spatial averaging and the normalization in Equation 8 produce the displayed action weights. Figure 3 instead uses the three-can tray-placement run, with checkpoint and window details below. Both analyses use recorded demonstrations, not autonomous physical success trials. Three-timescale display and component accounting.Panel a of Figure 3 reads the native14× 14 EMA prior directly from the same can-placement run at steps 690, 4140, 8280, 12420, 16560, and 20700. Percentages are relative to the final step. The upper row selects steps 690, 12420 and 20700, independently normalized to show spatial shape. The lower row reports the arithmetic mean of the raw stored EMA at all six checkpoints on a logarithmic axis. The curve measures the training prior rather than held-out prediction error. The final prior is the one used in panels b–c. Panels b–c use the verified step-20,700 can-placement checkpoint and recorded training demonstration 8574282; these are not physical executions. Panel b retains start 112 (RGB offsets 114, 118, 122, 126), selected after screening 32 archived windows. Its square crop isx∈ [48, 176),y ∈ [96, 224); top40 membership and transitions are computed over the full14× 14grid before cropping. Thus the crop can show fewer than 40 selected cells. The archived full-field tensors retain background responses. Panel c instead includes all eleven exported windows, starts 0,16,...,160, without localization-based selection. For each window letC j ∈ P,S, 0.5EandW = 1 + P j C j . The upper row reports 100 P C j / P (W − 1), with sums over all four future groups and all 196 spatial positions. The unit floor is excluded only from this composition ratio. The lower row normalizesWandW − C j separately over the same positions and reports100 TV, whereTV(p,q) = 1 2 P |p− q|. The unit floor is retained in both distributions; no remaining component is recomputed or renormalized before this final distribution normalization. This measures sensitivity of the allocation rule at fixed outputs, not the effect of training without a component. Shared row scales are 0–100% and 0–5%; lower-row points denote available windows and lines connect adjacent observations. Upper-row stacked shares are linearly connected between adjacent windows. Component share measures weight magnitude, whereas removal TV measures its effect on the normal- ized allocation. These complementary statistics describe one demonstration at fixed model parameters. GSCOPE OF PHYSICAL-ROBOT EVIDENCE Sixteen task videos provide recorded manipulation sequences. Tasks 04, 06, 08, and 11 appear in Figure 4; Figures 8–10 cover the twelve other recorded tasks. Each row contains four chronologically ordered frames from one video: initial configuration, task-specific intermediate events, and a visible terminal configuration. Selection follows actions rather than equal time intervals; timestamps are source-video times. Task 15 places a hamburger in a takeaway box and closes the lid; its final frame shows both arms returned. Task 16 packs a phone into its box and fits the lid. This supplementary task is excluded from the fifteen-task main comparison. All 64 frames are decoded directly from the sixteen original videos at the reported timestamps. Tight opaque masks cover incidental packaging and equipment text, including chest branding; additional masks cover the visible torso while preserving foreground arms and hands. Task-defining numerals and mahjong symbols, timestamps, and stage labels are retained. Original cloth marks, object details, and robot poses are retained. Display frames are downsampled and JPEG-compressed; no generative editing or inpainting is applied. Original videos and unmasked extracted frames are retained. Supplementary phone packing.For packing a phone into its box and closing the lid, the supplied results report SRs of 5% forπ 0.5 and 85% for Ours. HPOST-TRAINING IMPLEMENTATION AND EVALUATION Agent implementation and experimental workflow.Completed task results and failure evidence are supplied to an improvement agent based on Claude Opus 5 or GPT 5.6 Sol. The agent returns 27 RAP-WAM: Predictive Rehearsal and Action Perturbations 1.0 s13.9 s26.8 s31.1 s 1.0 s9.9 s25.5 s32.2 s 1.1 s11.3 s26.5 s36.6 s 0.7 s10.5 s17.0 s23.5 s 01 Cover the largest and smallest circles Initial configurationCovering the first targetCovering the second targetBoth targets covered 02 Unpack the cake and place it in a bowl Initial configurationOpening the packageTransferring the cakeCake in bowl 03 Place fruits on a tray Initial configurationFirst placementFurther placementsFinal configuration 05 Nest three bowls Initial configurationFirst bowl nestedSecond bowl alignedFinal configuration Figure 8: Additional recorded task sequences (I). Tasks 01, 02, 03, and 05 show circle-size selection, cake unpacking and placement, fruit placement, and bowl nesting. Frames are event- aligned within each source video; torsos and incidental text are masked before display downsampling and compression. a post-training proposal specifying the parent policy, target behaviors, training-data allocation, and parameter-update scope. Training produces a candidate for task-level evaluation. Improved task capa- bilities enter the repertoire; unsuccessful candidates are excluded from active execution. Evaluation outcomes feed the next proposal, linking policy learning to repeated experimental decisions. Evaluation object. The full system combines task-specialized policies developed on the RAP- WAM substrate. Its task-to-policy assignment is part of the evaluated system specification. SR and Score for a task refer to the same policy execution record; parameters and within-episode action fragments are not averaged across policies. The numerical source manifest preserves task identities, policy identities, and original summary paths. Aggregation. The complete system has Generalization SR/Score of 10.50/14.375, Precision 21.0255/28.6617, Long-Horizon 36.5000/48.4318, Memory 9.3333/10.3167, and Open 0.75/1.1625. Applying Equation 12 gives 15.6218% SR and 20.5895 Score, rounded to 15.62% and 20.59 in the main text. Table 1 shows Generalization’s standard and random columns separately, recon- structed from the corresponding task-policy records. The local base comparison uses identical capability denominators. Inference configuration.Evaluation uses 30 denoising steps, replanning every eight actions, nine- step Savitzky–Golay smoothing, and four-action boundary blending. Each task assignment identifies the policy architecture, checkpoint, normalizer, and inference path. Component comparisons. Separating policy learning from agentic decision-making requires matched data, training compute, interaction counts, and retry budgets. The relevant comparisons are continued training without agent-guided intervention, refinement with history reset, and the 28 RAP-WAM: Predictive Rehearsal and Action Perturbations 0.9 s8.5 s16.0 s27.4 s 0.8 s7.4 s14.1 s24.0 s 0.4 s6.1 s10.0 s13.8 s 0.8 s13.5 s21.5 s27.5 s 0.8 s7.9 s15.9 s21.1 s 0.8 s5.3 s9.6 s13.8 s 0.3 s8.5 s17.0 s22.7 s 07 Place three cans on a tray Initial configurationFirst can placedSecond can placedThree cans on tray 09 Place food in separate dishes Initial configurationFirst item placedSecond item placedFinal configuration 10 Place a can on a coaster Initial configurationCan graspedCan alignedCan released 12 Align disposable towels and place a thick towel on top InitialAlign disposable towelsMove thick towelThick towel on top 13 Arrange a pair of shoes InitialReorient first shoeAlign second shoeArms returned 14 Mahjong kong formation InitialFirst tile revealedFurther tiles revealedArms returned 15 Pack a hamburger and close the box InitialPlace burger in boxClose the lidArms returned Figure 9: Additional recorded task sequences (I). Tasks 07, 09, and 10 show can placement, food placement, and coaster placement. Task 12 aligns disposable towels and places a thick towel on top; the torso and packaging text are masked; the recorded scene is otherwise retained. Tasks 13 and 14 show shoe organization and mahjong kong formation. Task 15 places a hamburger in a box and closes its lid, ending with both arms returned. Timestamps and frame-selection conventions follow Figure 8. complete feedback loop. Removing response-based credit tests the local learning rule; resetting experiment history tests the role of cross-round evidence. The reported system comparison eval- uates the combined procedure. 29 RAP-WAM: Predictive Rehearsal and Action Perturbations 16 Pack a phone into its box 0.3 s Initial 29.0 s Position the phone 53.6 s Fit the lid 61.5 s Arms returned Figure 10: Additional recorded task sequence (I). Task 16 packs a phone into its box and fits the lid. The four original-video frames show the initial configuration, phone positioning, lid placement, and the final configuration with both arms returned. Torso and incidental packaging and equipment text are masked; timestamps refer to the source video. Post-training implementation. In the continuation experiment with demonstration replay, we start from base step 742500, updating all action-generating parameters with AdamW and cosine decay. Learning-rate warmup lasts 2,000 updates; rehearsal, state-substitution, and credit schedules restart over 5,000 updates. Its immutable demonstration sampler uses 50% natural replay, 20% task-balanced replay, 15% reliable failure-boundary windows, and 15% late-progress windows. The source covers 35 training tasks; failure-boundary evidence is available for 21. Five virtual epochs correspond to ten source-dataset equivalents, with a final training step of 145,585. The final repertoire uses intermediate checkpoints at 12,500, 25,000, and 50,000 steps; the last training checkpoint is not automatically the retained policy for every task. Task-level improvement. The final assignment retains the base for 14 of 42 tasks and uses 16 specialist checkpoints for the other 28, drawing on 30 recorded candidate identities. Nine specialists are obtained within 5,000 additional optimization steps, indicating that useful task-specific refinements can emerge from short training runs. Success improves on 24 tasks; four other substitutions improve Score at unchanged SR. The capability-balanced SR gain is 2.7697 percentage points, from 12.8520% to 15.6218%. These checkpoint budgets describe the retained solutions; total development cost also includes longer training branches and candidate evaluation. The base serves 14 tasks, while 16 other checkpoint identities serve 28. Different specialists serve dif- ferent capability groups. Assignments use the observed evaluation results, as specified in Appendix H. Evaluation scope. The RAP-WAM base and post-trained repertoire use no external embodied pretraining. Task-policy selection uses observed evaluation results; the reported evidence does not include an independent held-out policy-selection test. Runs also differ in RNG and live-VAE metadata, so they are not paired stochastic replicates. This RoboDojo comparison evaluates integrated simulation performance. Real-robot results are reported separately in Figure 4. Replay-intervention parameter values.The sampler usesτ rel = 0.15,b min = 0.08,b max = 0.22, κ = 0.5,τ boundary = 0.30,K fallback = 128, andτ late = 0.65. The replay proportions are (0.50, 0.20, 0.15, 0.15)in the order used in Section 3.4, giving2Nvirtual windows. Learning rates areη backbone = 10 −5 andη interface = 3× 10 −5 . AdamW uses betas(0.9, 0.95)and weight decay 10 −4 for decayed parameter groups, with zero decay for the excluded groups; warmup lasts 2,000 optimizer steps, followed by cosine decay. Candidate checkpoints are saved every 2,500 steps. These values instantiate the replay intervention used in the experiments. Execution evidence to a training distribution. For each task, the execution profile records the fraction of failed episodes with positive partial-completion scores, together with a centerc t and quartilesq 25,t ,q 75,t . Boundary replay is enabled for eligible tasks whose positive-failure fraction reaches a reliability thresholdτ rel . A demonstration window at offsetkhas normalized progress p = k/ max(1,L − H), withp = 1if no offset range is available;Lis episode length and Hthe required sequence span. Setb t = clip(b min + κ(q 75,t − q 25,t ),b min ,b max )and proximity w = exp[−(p− c t ) 2 /(2b 2 t )] . The boundary pool contains windows withw ≥ τ boundary ; an empty pool falls back to theK fallback highest-proximity windows, capped by the available count. The 30 RAP-WAM: Predictive Rehearsal and Action Perturbations GeneralizationPrecisionLong-Horizon MemoryOpen Base P01 P02 P03 P04 P05 P06 P07 P08 P09 P10 P11 P12 P13 P14 P15 P16 2237 11 2 1 11 11 11 12 2 11 1 11 11 1 11 1 1 Cell values: assigned task count Figure 11: Task assignments in the retained repertoire. Each cell counts tasks assigned to the base or a retained specialist within one capability group; blank cells denote zero assignments. P01–P16 identify existing checkpoints, with identities recorded in the accompanying manifest. This is the final repertoire snapshot, not an iteration history or a policy-removal experiment. late-progress pool usesp≥ τ late . This transfers a task-level score profile to demonstration progress as a sampling heuristic, rather than estimating a physical failure time. Continued training and candidate generation. The training distribution combines natural re- play, task-balanced replay, boundary replay, and late-progress replay with nonnegative proportions α natural ,α balanced ,α boundary ,α late summing to one. A virtual epoch preserves one complete pass over the source windows and adds the other pools in these proportions. Additional samples are balanced across eligible tasks and drawn uniformly within each task pool, with replacement only when the requested count exceeds pool size. Images and action labels remain unchanged. The selected parent is then optimized using the existing RAP-WAM objectives. The backbone and action interface use separate learning ratesη backbone andη interface ; the latter covers the action head, action/state encoders, query tokens, and projections. The optimizer runs within a specified update budget, saving candidates at a prescribed interval for evaluation. The replay-intervention parameter values above specify the thresholds, mixture proportions, optimizer configuration, and checkpoint schedule. Per-task episode accounting. All reported aggregates use the same 42-task definition. Each task uses its valid evaluated layouts; the evaluation records contain 49 for Deposit coin and 44 for Fill egg holder, shared by the base and candidate policies. The source summaries and per-layout records were cross-checked; duplicate records were counted once. Candidate selection uses observed SR first and Score to break ties, with both metrics taken from one policy. Deposit coin uses P07 at 12,500 post-training steps (5/49 successes, Score 14.6939); Fill egg holder retains the base (0/44, Score 12.9545). Metrics are computed directly over these valid episodes. The unified base aggregate is 12.8520% SR / 17.8602 Score, and the system aggregate is 15.6218% / 20.5895, a gain of 2.7697 percentage points and 2.7293 Score. The base has the highest aggregate SR and Score among the individual checkpoints in this candidate pool. Nevertheless, refinements improve subsets of tasks while regressing on others. The retained assignment combines these local gains and reaches 15.62% SR and 20.59 Score. This distinguishes a task-specialized improvement from a universal improvement of one checkpoint. All candidate results 31 RAP-WAM: Predictive Rehearsal and Action Perturbations 111315 Average SR (%) 16 18 20 Average Score 15.62 / 20.59 12.85 / 17.86 Retained specialist Other candidate Base Task-conditioned system 201001020 Task count P08 U06 P09 U07 P16 P11 P06 P02 U09 U01 U05 P01 P03 P05 P04 P12 U12 U13 P10 P14 P13 U04 P15 U10 U02 U03 U11 U08 P07 Lower SRHigher SR (a) Policy-level performance(b) Candidate task-wise changes Figure 12: Why retain task specialists? (a) All 30 candidate checkpoint identities, evaluated using the same 42-task aggregation. Filled blue circles are retained specialists, open circles other candidates, the square is the base, and the diamond is the task-conditioned system. Axis origins are truncated to display the observed range. (b) For each of the 29 non-base candidates, tasks with lower SR (left) or higher SR (right) relative to the base; unchanged tasks are omitted from the bars. Candidates are ordered by average SR, with Score breaking ties. P identifiers match Figure 11; U identifiers denote unused candidates. are shown, including candidates excluded from the repertoire. The comparison uses the observed results involved in policy selection; the system point is reconstructed from its task assignments, rather than an independent validation or evidence that the same gains persist under new seeds. Inference metadata differences are described in Appendix H. H.1POST-TRAINING AND POLICY-RETENTION DETAILS Building on execution-feedback approaches (Xiao et al., 2026; Lu et al., 2026), the outer improve- ment loop uses experiment results to guide continued training, retain useful task specializations, and combine them through task-conditioned execution. Its stateX r = (B r ,g r ,H r )contains the policy repertoire, task assignment, and experiment history; the repertoire initially contains RAP-WAM. Train- ing creates candidates, while evaluation and retention determine which capabilities remain available. From execution evidence to continued training. At roundr, completed experimental results are supplied to a language-model-based improvement agent. Its inputF r contains task outcomes, execution trajectories, and available model diagnostics; the agent uses these results to design the next post-training procedure. The agent compares weak task behavior with previous interventions inH r to formulate a hypothesis about a learning bottleneck. It then specifiesu r : the parent policy, 32 RAP-WAM: Predictive Rehearsal and Action Perturbations target tasks or execution phases, the data or training-code change, and the trainable parameter set. This is a decision about the learning procedure; the policy optimizer carries out the resulting update: The intervention and optimization are defined by Equation 10. Agent-guided refinement yields multiple task specializations with only a few thousand fine-tuning steps, reusing existing policies and demonstrations. The operatorU RAP updates designated parameters from a parent checkpoint while preserving that policy. The replay intervention below instantiates this process; implementation details and workflow provenance appear in Appendix H. Evidence-guided continued training. The intervention mixes ordinary, task-balanced, failure- boundary, and late-progress demonstrations:q r = P j∈natural,balanced,boundary,late α j q j , with α j ≥ 0and P j α j = 1. Boundary windows are selected by proximity to a score-derived task profile; reliability thresholds and fallback rules handle weak evidence or empty pools. Ordinary replay maintains demonstration coverage. All pools retain recorded observations and action targets. Training optimizes the RAP-WAM objectives from the parent checkpoint, with intermediate checkpoints evaluated as candidates. Appendix H specifies window selection, optimizer settings, and budgets. The score-to-progress mapping is a sampling heuristic, not a measurement of physical failure time. Retention and task-conditioned composition.Task-wise comparison with the current assignment g r produces a result vectorE r of success, partial completion, and observed failures. LetC r contain the tasks on which the candidate is accepted. The comparison retains a task-level change vector ∆ t = (∆SR t , ∆Score t )relative to the incumbent on each task, so improvements and regressions are not hidden by an aggregate mean. Both metrics must come from the same candidate execution record. Their assignments switch to the candidate; other tasks retain their policies. A candidate with an accepted improvement enters the repertoire; ifC r = ∅, it is discarded from the active policy set andg r is unchanged: B r+1 = Retain(B r ,π + r ,C r ), g r+1 = Assign(B r+1 ,C r ,g r ), H r+1 =H r ∪(F r ,u r ,E r ,C r ). (29) The base and previously useful policies remain available. For tasktand observation historyo ≤k , the system executes a k ∼ π g r (t) (·| o ≤k ,t).(30) The outer assignment selects a complete learned policy; credit coefficients govern supervision within policy training. Task-level comparison determines retention, with evaluation accounting specified in Appendix H. Closing the improvement loop.History retains interventions, task-wise outcomes, and acceptance decisions, including rejected candidates. Later rounds can revise unsuccessful hypotheses and continue from useful specialists. Each evaluation is supplied back to the agent to design the next post-training round. The resulting loop is evaluate, propose, train, re-evaluate, and retain or discard. Discarding a policy does not imply discarding the experimental evidence used for the next decision. IADDITIONAL RELATED WORK Generalist representations and action interfaces. OpenVLA adapts vision–language represen- tations to robot actions (Kim et al., 2024). G0.5 places reasoning and action in one autoregressive stream (Liu et al., 2026), while Xiaomi-Robotics-1 scales action-labeled pretraining (Xiaomi Robotics Team et al., 2026) and Hy-Embodied uses modality-specific computation with a flow-based action expert (Zhang et al., 2026). Spatial Forcing supplies geometric alignment targets (Li et al., 2026). Our model learns its action interface on the target data. Its loss-coefficient rule uses the joint model’s own outputs and existing future targets, rather than requiring an additional pretrained robot expert or geometric-label pipeline. Training with predicted inputs and adaptive supervision.Self Forcing trains video diffusion on self-generated context with sequence-level supervision (Huang et al., 2025). Our rehearsal instead supervises an adjacent recorded segment and retains its demonstration targets. Scheduled sampling and interactive imitation learning address discrepancies between recorded demon- stration inputs and histories produced by policy execution (Bengio et al., 2015; Ross et al., 2011). Our 33 RAP-WAM: Predictive Rehearsal and Action Perturbations adjacent-segment training replaces observed inputs with predictions while retaining recorded demon- stration targets; it neither collects new interactions nor inherits interactive data-aggregation guarantees. Prioritized replay and focal loss emphasize selected errors (Schaul et al., 2016; Lin et al., 2017); importance sampling targets estimator variance (Katharopoulos & Fleuret, 2018), and value-aware model learning uses decision structure (Farahmand et al., 2017). response-based credit combines persistent error with action response, and projects the same response into spatial and temporal su- pervision. RoboDojo and RoboTwin offer complementary manipulation benchmarks (Chen et al., 2026b; 2025); we report RoboDojo and real-robot task outcomes, alongside prediction diagnostics. Synthetic trajectories and joint world action pretraining. UWM couples video and action diffusion with independent modality timesteps (Zhu et al., 2025); DreamZero jointly models video and actions to transfer across tasks and embodiments (Ye et al., 2026b). Motus learns latent actions from optical flow (Bi et al., 2026), and MotuBrain extends joint modeling to multiview and cross- embodiment settings (MotuBrain Team et al., 2026). DreamGen generates synthetic task videos and recovers pseudo-actions using latent-action or inverse-dynamics models (Jang et al., 2025). Our rehearsal instead changes the conditioning context while retaining recorded demonstration targets; response-based credit then redistributes supervision within that training. These approaches provide architectural and data-generation context, not controlled evidence for the effect of our credit rule. JRECORDED AND PREDICTED FUTURES IN REAL-ROBOT TRAINING Figures 14–28 show one reproducible training example for 15 of the 16 real-robot tasks with external- view video sequences in Appendix G. Task 16 uses the completed Tencent Cloud phone-training run; its configuration, checkpoint, and sample identity were independently verified. Each example uses the final checkpoint of its audited task-training run. We select the median-length eligible continuous training segment and its middle legal two-chunk window, before inspecting predictions or attention. The archived exports used previously are replaced by these identified samples so that predictions and attention come from the same forward trajectory. Recorded targets belong to the same training sample as the prediction; the separately filmed external-view execution need not be the same episode. Each model receives only the conditioning observation and recorded current state at inference. There are no weight updates. The first column repeats the condition; offsetst + 1,t + 4,t + 8,t + 12,t + 16 index the sampled future sequence, not seconds. Prediction metrics.Every predicted frame is labeled with RGB SSIM (Wang et al., 2004); figure- level SSIM and LPIPS (Zhang et al., 2018) are arithmetic means over the five displayed future frames, excluding the condition. SSIM uses an11× 11Gaussian window withσ = 1.5, population covariance, and channel averaging, excluding a five-pixel image border. LPIPS uses the official AlexNet network, version 0.1, at native resolution with inputs mapped to[−1, 1]. Both metrics use decoded float images clipped to[0, 1], before privacy masks, quantization, or JPEG display compression. The orange dashed baseline (“Repeat current frame”) uses the current conditioning image itself as the prediction at every future position, without running the world model. For current imageI t and recorded futureI t+h , its plotted error isLPIPS(I t ,I t+h ). Thus it measures how much the recorded scene departs from remaining visually unchanged. Higher SSIM and lower LPIPS indicate closer images. We also retain metrics for all 16 predicted frames in the accompanying data. Attention and local error.The bottom strip shows the condition with a fixed task-region rectangle, predictive-query attention, mean absolute RGB prediction error over the five displayed future frames, and the horizon-wise LPIPS curve. Rectangles were marked from condition images and checked for visible task coverage, independently of attention magnitude; they are coarse task regions, not object segmentations, and do not track moving objects. Region SSIM and MAE use the same rectangle in each future frame. A read-only probe records the actual self-attention query/key tensors after normalization and rotary encoding, retaining the model’s additive mask and full softmax denominator. We average all 24 heads and 16 predictive-query rows at layers 10, 20, and 30, and denoising iterations 4, 8, and 16. We then display attention to the conditioning-time visual tokens. The spatial grid is7× 7, displayed without smoothing. Attention color is density relative to a uniform spatial distribution after conditioning on the displayed view, using a common0–4×scale; error uses a common[0, 0.15]scale. Values beyond either scale are clipped for display only. Region enrichment 34 RAP-WAM: Predictive Rehearsal and Action Perturbations is its fraction of attention divided by its fraction of image area; 1 denotes uniform allocation. Raw attention masses and layer/iteration maps are retained. Scope of the evidence. Across these 15 selected examples, mean SSIM is 0.879 versus 0.814 for persistence, and mean LPIPS is 0.018 versus 0.095. Under the fixed aggregation, 1 of 15 task regions have attention enrichment above 1. Thus these maps do not establish preferential attention to task objects or accurate object recognition. They are descriptive internal diagnostics, not causal explanations. The examples come from training data and different task checkpoints; they do not establish held-out prediction quality, task success, or the separate contribution of response-based credit or agentic refinement. Incidental text and visible background faces are masked at paired locations; task numerals and mahjong symbols remain. Display editing is limited to deterministic masking, display downsampling, and compression. Horizon-wise comparison.The fourth diagnostic panel in each task figure plots LPIPS over all 16 predicted frames, against the copy-condition baseline, using a common vertical scale within each domain. Figure 13 aggregates all 15 real-robot and 35 simulation windows with equal task and frame weights. Full-horizon mean LPIPS decreases by 81.8% for real robots and 86.3% for simulation, computed as one minus the ratio of the model and baseline grand means. Every task has a lower full-horizon mean, although individual frames can favor persistence; all frames and tasks are retained. These comparisons demonstrate improved future-image fidelity over repeating the current observation on the selected training windows. They do not isolate the contribution of response-based credit or compare against an independently trained base model. 1481216 Future-frame index 0.0 0.1 0.2 0.3 0.4 LPIPS (lower is better) Mean LPIPS reduction: 81.8% 15/15 task means improve Real robot (15 tasks) 1481216 Future-frame index 0.0 0.1 0.2 0.3 0.4 Mean LPIPS reduction: 86.3% 35/35 task means improve RoboDojo (35 tasks) World modelRepeat current frame Figure 13: Prediction error over the full future horizon. Solid blue curves show the world model. Dashed orange curves show the LPIPS between the unchanged current image and each recorded future frame: the current image is reused as the future prediction, without model inference. Lines are task means, and shaded bands show the 25th–75th percentiles across the selected task windows, not confidence intervals. Both panels use the same vertical scale. Relative reductions use all 16 frames; the condition is excluded. 35 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Recorded (GT) Predicted SSIM 0.859SSIM 0.870SSIM 0.868SSIM 0.873SSIM 0.872 Mean SSIM: 0.869 | LPIPS: 0.019 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.843 / LPIPS 0.049 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.00 0.15 0.30 ModelRepeat current frame ROI attention enrichment: 0.77x | ROI SSIM: 0.840 | ROI MAE: 0.024 04x00.15 Figure 14: Task 01: Cover the largest and smallest circles. Conditiont+1t+4t+8t+12t+16 Recorded (GT) Predicted SSIM 0.841SSIM 0.854SSIM 0.852SSIM 0.864SSIM 0.876 Mean SSIM: 0.857 | LPIPS: 0.024 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.775 / LPIPS 0.204 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.00 0.15 0.30 ModelRepeat current frame ROI attention enrichment: 0.54x | ROI SSIM: 0.855 | ROI MAE: 0.025 04x00.15 Figure 15: Task 02: Unpack the cake and place it in a bowl. 36 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Recorded (GT) Predicted SSIM 0.866SSIM 0.877SSIM 0.886SSIM 0.887SSIM 0.884 Mean SSIM: 0.880 | LPIPS: 0.013 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.833 / LPIPS 0.083 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.00 0.15 0.30 ModelRepeat current frame ROI attention enrichment: 0.68x | ROI SSIM: 0.856 | ROI MAE: 0.028 04x00.15 Figure 16: Task 03: Place fruits on a tray. Conditiont+1t+4t+8t+12t+16 Recorded (GT) Predicted SSIM 0.839SSIM 0.857SSIM 0.876SSIM 0.881SSIM 0.881 Mean SSIM: 0.867 | LPIPS: 0.023 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.727 / LPIPS 0.168 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.00 0.15 0.30 ModelRepeat current frame ROI attention enrichment: 0.74x | ROI SSIM: 0.849 | ROI MAE: 0.033 04x00.15 Figure 17: Task 04: Reorder three different types of bottles by height. 37 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Recorded (GT) Predicted SSIM 0.878SSIM 0.884SSIM 0.893SSIM 0.892SSIM 0.890 Mean SSIM: 0.887 | LPIPS: 0.015 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.787 / LPIPS 0.073 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.00 0.15 0.30 ModelRepeat current frame ROI attention enrichment: 0.64x | ROI SSIM: 0.849 | ROI MAE: 0.022 04x00.15 Figure 18: Task 05: Nest three bowls. Conditiont+1t+4t+8t+12t+16 Recorded (GT) Predicted SSIM 0.885SSIM 0.895SSIM 0.905SSIM 0.905SSIM 0.898 Mean SSIM: 0.897 | LPIPS: 0.012 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.887 / LPIPS 0.038 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.00 0.15 0.30 ModelRepeat current frame ROI attention enrichment: 0.82x | ROI SSIM: 0.850 | ROI MAE: 0.019 04x00.15 Figure 19: Task 06: Rearrange numbered blocks. 38 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Recorded (GT) Predicted SSIM 0.851SSIM 0.864SSIM 0.871SSIM 0.875SSIM 0.875 Mean SSIM: 0.867 | LPIPS: 0.019 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.780 / LPIPS 0.105 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.00 0.15 0.30 ModelRepeat current frame ROI attention enrichment: 0.42x | ROI SSIM: 0.829 | ROI MAE: 0.035 04x00.15 Figure 20: Task 07: Place three cans on a tray. Conditiont+1t+4t+8t+12t+16 Recorded (GT) Predicted SSIM 0.892SSIM 0.898SSIM 0.908SSIM 0.907SSIM 0.914 Mean SSIM: 0.904 | LPIPS: 0.012 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.850 / LPIPS 0.063 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.00 0.15 0.30 ModelRepeat current frame ROI attention enrichment: 0.75x | ROI SSIM: 0.867 | ROI MAE: 0.023 04x00.15 Figure 21: Task 08: Cover the largest and smallest numbers. 39 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Recorded (GT) Predicted SSIM 0.884SSIM 0.895SSIM 0.903SSIM 0.906SSIM 0.908 Mean SSIM: 0.899 | LPIPS: 0.012 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.835 / LPIPS 0.094 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.00 0.15 0.30 ModelRepeat current frame ROI attention enrichment: 0.69x | ROI SSIM: 0.871 | ROI MAE: 0.019 04x00.15 Figure 22: Task 09: Place food in separate dishes. Conditiont+1t+4t+8t+12t+16 Recorded (GT) Predicted SSIM 0.830SSIM 0.848SSIM 0.859SSIM 0.860SSIM 0.861 Mean SSIM: 0.852 | LPIPS: 0.021 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.706 / LPIPS 0.123 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.00 0.15 0.30 ModelRepeat current frame ROI attention enrichment: 0.66x | ROI SSIM: 0.833 | ROI MAE: 0.024 04x00.15 Figure 23: Task 10: Place a can on a coaster. 40 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Recorded (GT) Predicted SSIM 0.872SSIM 0.881SSIM 0.893SSIM 0.876SSIM 0.854 Mean SSIM: 0.875 | LPIPS: 0.019 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.830 / LPIPS 0.095 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.00 0.15 0.30 ModelRepeat current frame ROI attention enrichment: 1.04x | ROI SSIM: 0.867 | ROI MAE: 0.018 04x00.15 Figure 24: Task 11: Insert a folding fan into an open-top vessel. Conditiont+1t+4t+8t+12t+16 Recorded (GT) Predicted SSIM 0.909SSIM 0.916SSIM 0.914SSIM 0.912SSIM 0.913 Mean SSIM: 0.913 | LPIPS: 0.016 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.812 / LPIPS 0.130 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.00 0.15 0.30 ModelRepeat current frame ROI attention enrichment: 0.84x | ROI SSIM: 0.892 | ROI MAE: 0.022 04x00.15 Figure 25: Task 12: Align disposable towels and place a thick towel on top. 41 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Recorded (GT) Predicted SSIM 0.866SSIM 0.871SSIM 0.878SSIM 0.880SSIM 0.850 Mean SSIM: 0.869 | LPIPS: 0.017 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.831 / LPIPS 0.098 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.00 0.15 0.30 ModelRepeat current frame ROI attention enrichment: 0.63x | ROI SSIM: 0.858 | ROI MAE: 0.019 04x00.15 Figure 26: Task 13: Arrange a pair of shoes. Conditiont+1t+4t+8t+12t+16 Recorded (GT) Predicted SSIM 0.883SSIM 0.896SSIM 0.901SSIM 0.910SSIM 0.909 Mean SSIM: 0.900 | LPIPS: 0.015 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.888 / LPIPS 0.031 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.00 0.15 0.30 ModelRepeat current frame ROI attention enrichment: 0.75x | ROI SSIM: 0.917 | ROI MAE: 0.026 04x00.15 Figure 27: Task 14: Mahjong kong formation. 42 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Recorded (GT) Predicted SSIM 0.868SSIM 0.860SSIM 0.855SSIM 0.851SSIM 0.824 Mean SSIM: 0.851 | LPIPS: 0.028 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.823 / LPIPS 0.065 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.00 0.15 0.30 ModelRepeat current frame ROI attention enrichment: 0.90x | ROI SSIM: 0.838 | ROI MAE: 0.022 04x00.15 Figure 28: Task 16: Pack a phone into its box. KRECORDED AND PREDICTED FUTURES IN ROBODOJO SIMULATION Figures 29–63 show one identified training example for each of the 35 RoboDojo training tasks (task IDs 00–34). All examples use the retained post-training checkpoint P09 (step 50,000) described in Appendix H. We preserve the training loader’s seed-42 validation exclusion, select the median-length eligible training episode per task, and use its middle legal two-chunk window. Task IDs are verified against dataset metadata, and the corresponding task-language embedding is explicitly supplied during inference. Each figure pairs the recorded future with a 16-frame prediction sampled using 16 denoising steps. Inputs are the conditioning image, current state, and task-language embedding. The 30-step setting in Appendix A applies to policy evaluation. The original head-and-two-wrist camera mosaic is retained; task numbers denote dataset IDs, not difficulty ranks. SSIM, LPIPS, the persistence baseline, and the fixed attention aggregation follow Appendix J. Global similarity metrics use the full original384× 320camera mosaic. The diagnostic bottom strip shows only the head view, the upper256× 320region; region metrics and attention enrichment are restricted to that view. The original attention grid is12× 10over the mosaic, with an8× 10head-view subgrid. It is displayed without smoothing across camera boundaries, with the same attention and error color scales as the real-robot figures. Region rectangles were marked from conditions and checked for visible task coverage, independently of attention magnitude. Across the 35 selected training examples, mean SSIM is 0.942 versus 0.828 for the copy-condition baseline, and mean LPIPS is 0.018 versus 0.134. SSIM improves on persistence in 34 of 35 examples and LPIPS in all 35. None of the 35 marked regions has attention enrichment above 1 under this fixed aggregation, so these maps do not support a claim of object-localized attention or object-recognition accuracy. Coverage of all training task types is not a held-out evaluation: one window per task cannot establish average trajectory fidelity, causal component gains, or rollout success. Incidental text is masked for display while task-defining numbers, letters, and mahjong symbols are retained; metrics are computed before masking and compression. 43 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.957SSIM 0.954SSIM 0.931SSIM 0.921SSIM 0.920 Mean SSIM: 0.937 | LPIPS: 0.017 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.736 / LPIPS 0.217 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.48x | ROI SSIM: 0.957 | ROI MAE: 0.011 04x00.15 Figure 29: RoboDojo task 00: Arrange numbers. Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.963SSIM 0.967SSIM 0.948SSIM 0.938SSIM 0.936 Mean SSIM: 0.951 | LPIPS: 0.015 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.786 / LPIPS 0.179 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.56x | ROI SSIM: 0.959 | ROI MAE: 0.011 04x00.15 Figure 30: RoboDojo task 01: Build a tower. 44 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.963SSIM 0.950SSIM 0.949SSIM 0.922SSIM 0.929 Mean SSIM: 0.943 | LPIPS: 0.017 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.864 / LPIPS 0.085 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.56x | ROI SSIM: 0.931 | ROI MAE: 0.016 04x00.15 Figure 31: RoboDojo task 02: Sort objects by category. Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.957SSIM 0.960SSIM 0.963SSIM 0.965SSIM 0.971 Mean SSIM: 0.963 | LPIPS: 0.009 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.848 / LPIPS 0.156 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.53x | ROI SSIM: 0.974 | ROI MAE: 0.007 04x00.15 Figure 32: RoboDojo task 03: Remember covered block colors. 45 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.961SSIM 0.949SSIM 0.940SSIM 0.937SSIM 0.933 Mean SSIM: 0.944 | LPIPS: 0.018 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.800 / LPIPS 0.181 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.49x | ROI SSIM: 0.951 | ROI MAE: 0.011 04x00.15 Figure 33: RoboDojo task 04: Insert a coin. Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.951SSIM 0.920SSIM 0.866SSIM 0.875SSIM 0.856 Mean SSIM: 0.894 | LPIPS: 0.043 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.713 / LPIPS 0.219 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.67x | ROI SSIM: 0.912 | ROI MAE: 0.021 04x00.15 Figure 34: RoboDojo task 05: Spell RoboDojo. 46 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.965SSIM 0.968SSIM 0.971SSIM 0.963SSIM 0.961 Mean SSIM: 0.966 | LPIPS: 0.007 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.916 / LPIPS 0.040 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.46x | ROI SSIM: 0.967 | ROI MAE: 0.010 04x00.15 Figure 35: RoboDojo task 06: Tighten color-matched screws. Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.939SSIM 0.925SSIM 0.911SSIM 0.882SSIM 0.871 Mean SSIM: 0.906 | LPIPS: 0.029 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.793 / LPIPS 0.181 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.60x | ROI SSIM: 0.797 | ROI MAE: 0.034 04x00.15 Figure 36: RoboDojo task 07: Store eggs and close the holder. 47 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.925SSIM 0.908SSIM 0.917SSIM 0.921SSIM 0.926 Mean SSIM: 0.919 | LPIPS: 0.030 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.783 / LPIPS 0.213 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.54x | ROI SSIM: 0.962 | ROI MAE: 0.009 04x00.15 Figure 37: RoboDojo task 08: Put pens into a holder. Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.931SSIM 0.906SSIM 0.904SSIM 0.902SSIM 0.908 Mean SSIM: 0.910 | LPIPS: 0.021 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.842 / LPIPS 0.092 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.48x | ROI SSIM: 0.806 | ROI MAE: 0.034 04x00.15 Figure 38: RoboDojo task 09: Fold clothes. 48 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.961SSIM 0.952SSIM 0.935SSIM 0.940SSIM 0.921 Mean SSIM: 0.942 | LPIPS: 0.019 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.890 / LPIPS 0.072 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.70x | ROI SSIM: 0.947 | ROI MAE: 0.012 04x00.15 Figure 39: RoboDojo task 10: Hang mugs. Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.959SSIM 0.956SSIM 0.957SSIM 0.954SSIM 0.955 Mean SSIM: 0.956 | LPIPS: 0.012 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.867 / LPIPS 0.060 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.56x | ROI SSIM: 0.947 | ROI MAE: 0.014 04x00.15 Figure 40: RoboDojo task 11: Recall object placement order. 49 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.943SSIM 0.951SSIM 0.958SSIM 0.957SSIM 0.957 Mean SSIM: 0.953 | LPIPS: 0.013 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.816 / LPIPS 0.136 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.50x | ROI SSIM: 0.908 | ROI MAE: 0.017 04x00.15 Figure 41: RoboDojo task 12: Insert a thick card. Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.951SSIM 0.954SSIM 0.958SSIM 0.955SSIM 0.954 Mean SSIM: 0.954 | LPIPS: 0.011 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.904 / LPIPS 0.063 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.45x | ROI SSIM: 0.958 | ROI MAE: 0.011 04x00.15 Figure 42: RoboDojo task 13: Place tubes in a rack. 50 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.967SSIM 0.969SSIM 0.970SSIM 0.933SSIM 0.948 Mean SSIM: 0.957 | LPIPS: 0.010 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.931 / LPIPS 0.037 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.58x | ROI SSIM: 0.957 | ROI MAE: 0.014 04x00.15 Figure 43: RoboDojo task 14: Form a mahjong kong. Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.924SSIM 0.920SSIM 0.902SSIM 0.907SSIM 0.870 Mean SSIM: 0.905 | LPIPS: 0.031 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.649 / LPIPS 0.312 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.68x | ROI SSIM: 0.951 | ROI MAE: 0.014 04x00.15 Figure 44: RoboDojo task 15: Toast bread. 51 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.979SSIM 0.979SSIM 0.981SSIM 0.981SSIM 0.981 Mean SSIM: 0.980 | LPIPS: 0.007 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.981 / LPIPS 0.010 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.79x | ROI SSIM: 0.979 | ROI MAE: 0.007 04x00.15 Figure 45: RoboDojo task 16: Match a remembered conveyor object. Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.935SSIM 0.902SSIM 0.908SSIM 0.916SSIM 0.924 Mean SSIM: 0.917 | LPIPS: 0.025 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.735 / LPIPS 0.217 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.75x | ROI SSIM: 0.954 | ROI MAE: 0.012 04x00.15 Figure 46: RoboDojo task 17: Organize a desk. 52 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.924SSIM 0.904SSIM 0.890SSIM 0.904SSIM 0.922 Mean SSIM: 0.909 | LPIPS: 0.034 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.752 / LPIPS 0.200 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.58x | ROI SSIM: 0.858 | ROI MAE: 0.022 04x00.15 Figure 47: RoboDojo task 18: Pack objects facing left. Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.917SSIM 0.909SSIM 0.925SSIM 0.931SSIM 0.936 Mean SSIM: 0.924 | LPIPS: 0.023 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.799 / LPIPS 0.175 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.56x | ROI SSIM: 0.883 | ROI MAE: 0.028 04x00.15 Figure 48: RoboDojo task 19: Play the xylophone. 53 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.968SSIM 0.958SSIM 0.955SSIM 0.954SSIM 0.924 Mean SSIM: 0.952 | LPIPS: 0.013 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.846 / LPIPS 0.129 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.49x | ROI SSIM: 0.932 | ROI MAE: 0.017 04x00.15 Figure 49: RoboDojo task 20: Assemble a stacking toy. Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.963SSIM 0.968SSIM 0.972SSIM 0.974SSIM 0.964 Mean SSIM: 0.968 | LPIPS: 0.007 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.891 / LPIPS 0.045 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.45x | ROI SSIM: 0.961 | ROI MAE: 0.011 04x00.15 Figure 50: RoboDojo task 21: Play tic-tac-toe. 54 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.942SSIM 0.950SSIM 0.960SSIM 0.968SSIM 0.963 Mean SSIM: 0.957 | LPIPS: 0.014 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.818 / LPIPS 0.194 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.47x | ROI SSIM: 0.958 | ROI MAE: 0.012 04x00.15 Figure 51: RoboDojo task 22: Plug in a charger. Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.909SSIM 0.922SSIM 0.925SSIM 0.923SSIM 0.916 Mean SSIM: 0.919 | LPIPS: 0.025 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.676 / LPIPS 0.262 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.54x | ROI SSIM: 0.929 | ROI MAE: 0.015 04x00.15 Figure 52: RoboDojo task 23: Pour balls into a vase. 55 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.975SSIM 0.971SSIM 0.973SSIM 0.972SSIM 0.972 Mean SSIM: 0.973 | LPIPS: 0.007 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.965 / LPIPS 0.013 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.56x | ROI SSIM: 0.937 | ROI MAE: 0.016 04x00.15 Figure 53: RoboDojo task 24: Pour liquid into a cup. Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.928SSIM 0.941SSIM 0.930SSIM 0.948SSIM 0.960 Mean SSIM: 0.942 | LPIPS: 0.017 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.671 / LPIPS 0.321 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.45x | ROI SSIM: 0.951 | ROI MAE: 0.012 04x00.15 Figure 54: RoboDojo task 25: Count button presses. 56 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.950SSIM 0.941SSIM 0.943SSIM 0.943SSIM 0.946 Mean SSIM: 0.944 | LPIPS: 0.018 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.880 / LPIPS 0.115 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.64x | ROI SSIM: 0.904 | ROI MAE: 0.015 04x00.15 Figure 55: RoboDojo task 26: Align a T-shaped block. Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.955SSIM 0.899SSIM 0.896SSIM 0.877SSIM 0.852 Mean SSIM: 0.896 | LPIPS: 0.054 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.674 / LPIPS 0.238 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.60x | ROI SSIM: 0.873 | ROI MAE: 0.022 04x00.15 Figure 56: RoboDojo task 27: Discard bottles. 57 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.966SSIM 0.923SSIM 0.905SSIM 0.940SSIM 0.868 Mean SSIM: 0.921 | LPIPS: 0.032 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.907 / LPIPS 0.081 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.56x | ROI SSIM: 0.834 | ROI MAE: 0.031 04x00.15 Figure 57: RoboDojo task 28: Order nesting dolls. Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.967SSIM 0.966SSIM 0.952SSIM 0.952SSIM 0.941 Mean SSIM: 0.955 | LPIPS: 0.012 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.926 / LPIPS 0.060 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.51x | ROI SSIM: 0.934 | ROI MAE: 0.012 04x00.15 Figure 58: RoboDojo task 29: Stack textured blocks. 58 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.969SSIM 0.962SSIM 0.963SSIM 0.963SSIM 0.959 Mean SSIM: 0.963 | LPIPS: 0.011 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.893 / LPIPS 0.077 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.52x | ROI SSIM: 0.949 | ROI MAE: 0.013 04x00.15 Figure 59: RoboDojo task 30: Stack bowls. Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.966SSIM 0.962SSIM 0.962SSIM 0.955SSIM 0.935 Mean SSIM: 0.956 | LPIPS: 0.012 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.831 / LPIPS 0.068 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.78x | ROI SSIM: 0.959 | ROI MAE: 0.011 04x00.15 Figure 60: RoboDojo task 31: Store headphones and a laptop. 59 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.961SSIM 0.968SSIM 0.972SSIM 0.959SSIM 0.943 Mean SSIM: 0.960 | LPIPS: 0.010 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.834 / LPIPS 0.102 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.54x | ROI SSIM: 0.954 | ROI MAE: 0.010 04x00.15 Figure 61: RoboDojo task 32: Swap T-shaped blocks. Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.964SSIM 0.966SSIM 0.969SSIM 0.970SSIM 0.959 Mean SSIM: 0.966 | LPIPS: 0.007 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.874 / LPIPS 0.045 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.45x | ROI SSIM: 0.955 | ROI MAE: 0.013 04x00.15 Figure 62: RoboDojo task 33: Swap blocks via an empty mat. 60 RAP-WAM: Predictive Rehearsal and Action Perturbations Conditiont+1t+4t+8t+12t+16 Simulation (GT) Predicted SSIM 0.968SSIM 0.956SSIM 0.954SSIM 0.955SSIM 0.953 Mean SSIM: 0.957 | LPIPS: 0.013 (SSIM higher / LPIPS lower is better) Repeat current frame: SSIM 0.890 / LPIPS 0.079 Condition + ROIQuery attentionMean pixel errorLPIPS vs. future frame 1816 0.000 0.225 0.450 ModelRepeat current frame ROI attention enrichment: 0.57x | ROI SSIM: 0.908 | ROI MAE: 0.017 04x00.15 Figure 63: RoboDojo task 34: Sweep blocks. 61