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RoboFL: Federated Expert Assembly for World Action Models
Rongyu Zhang, Ruizhi Fan, Yunfan Lou, Hengyu Fang, Shenli Zheng, Chenrui Wu, Yili Jin, Li Du, Dan Wang, Yuan Du, Shanghang Zhang
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Abstract
Abstract:Vision-language-action and world-action models are increasingly popular, yet remain bottlenecked by physical interaction data that is scarce, institutionally siloed, and task-heterogeneous. A natural federated solution is to let each client adapt a shared foundation model through parameter-efficient fine-tuning, avoiding the exchange of full-model updates. However, federating these adapters is nontrivial, as naive aggregation can entangle incompatible updates, while incorporating MoE-style routing into federated aggregation may dilute specialization and destabilize expert selection. We present RoboFL, which instantiates MoSAIC (Mixture of Slotted Adapters) for federated world-action learning. MoSAIC directly installs locally trained LoRA adapters as the expert branches of a server MoE. Server-side routers learn token assignments over these prior-informed branches while jointly refining routing and expert parameters. Foresight-to-Action Routing Distillation (FARD) aligns routing across the model's three paths, while Path-Consensus Expert Aggregation (PCEA) converts complete expert updates into a compact global adapter for personalized redistribution. Experiments on RoboTwin 2.0, RLBench, and a real-world Franka robot arm show the superiority of RoboFL with structured expert assembly, as it outperforms centralized PEFT InternVLA-A1 by 12.23% on the Franka arm, while reducing per-round client communication by up to 86.81% relative to MoE-based federated VLA baselines.
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- Source: https://arxiv.org/abs/2609.34968v1
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ROBOFL: FEDERATED EXPERT ASSEMBLY FOR WORLD ACTION MODELS Rongyu Zhang ∗ Nanjing University Ruizhi Fan ∗ Nanjing University Yunfan Lou Peking University Hengyu Fang Nanjing University Shenli Zhang Nanjing University Chenrui Wu Simon Fraser University Yili Jin Simon Fraser University Li Du Nanjing University Dan Wang Hong Kong University of Science and Technology Yuan Du † Nanjing University Shanghang Zhang † Peking University ‡ RoboFL Conventional Federated LoRA WAMs RoboFL with MoSAIC task-siloed local data raw trajectories remain local Representative institution World-Action Model Understanding visual tokens language tokens Generation future latent tokens Action robot state noisy action time / noise Shared self-attention LoRA 1 Federated aggregation Server-side MoSAIC mixed-task server data server-only router Slotted LoRA Experts slot 1slot 2slot 3 local specialization preserved MoSAIC conversion Global LoRA adapter Grasping LoRA Placement LoRA Tool Interaction LoRA Articulated Objects LoRA LoRA 2 LoRA E Institution 1Institution 2 Institution 3 Institution E slot E Train with LoRA, inference with LoRA ❌Train with LoRA, inference with MoE ✅ Upload Download RoboTwin 2.0 Simulation InternVLA-LoRA FedVLAFogreVLA RLBenchRoboTwin 2.0Franka Research 3 Real-world Franka RoboFL Figure 1:From federated parameter averaging to prior-informed expert assembly. Left: Aggregating independently trained LoRA-MoE models can dilute local specialization and introduce inconsistent routing across heterogeneous clients. Middle: ROBOFL organizes institutions into task silos and directly installs their task-trained LoRA into the expert branches of a server MoE. Right: ROBOFL is evaluated in the RoboTwin 2.0 and RLBench simulator, and on a real-world Franka robot. ABSTRACT Vision-language-action and world-action models are increasingly popular, yet remain bottlenecked by physical interaction data that is scarce, institutionally siloed, and task-heterogeneous. A natural federated solution is to let each client adapt a shared foundation model through parameter-efficient fine-tuning, avoiding the exchange of full-model updates. However, federating these adapters is nontrivial, as naive aggregation can entangle incompatible updates, while incorporating MoE- style routing into federated aggregation may dilute specialization and destabilize expert selection. We present ROBOFL, which instantiates MOSAIC (Mixture of Slotted Adapters) for federated world-action learning. MoSAIC directly installs locally trained LoRA adapters as the expert branches of a server MoE. Server-side routers learn token assignments over these prior-informed branches while jointly refining routing and expert parameters. Foresight-to-Action Routing Distillation (FARD) aligns routing across the model’s three paths, while Path-Consensus Expert Aggregation (PCEA) converts complete expert updates into a compact global adapter for personalized redistribution. Experiments on RoboTwin 2.0, RLBench, and a real-world Franka robot arm show the superiority of ROBOFL with structured expert assembly, as it outperforms centralized PEFT InternVLA-A1 by 12.23% on the Franka arm, while reducing per-round client communication by up to 86.81% relative to MoE-based federated VLA baselines. ∗ Equal contributions. † Corresponding authors. ‡ State Key Laboratory of Multimedia Information Processing, School of Computer Science, Peking University 1 arXiv:2609.34968v1 [cs.RO] 28 Sep 2026 1INTRODUCTION Vision-language-action (VLA) models (Brohan et al., 2023; Driess et al., 2023; Ghosh et al., 2024; Kim et al., 2025; Black et al., 2025) and world-action models (WAMs) (Cai et al., 2026; Bi et al., 2026; Ye et al., 2026b) unify perception, language understanding, future prediction, and control in a single policy. Their progress has been driven by broader multimodal and multi-robot training, flow- based action generation, and future-state modeling. However, general-purpose embodied intelligence remains constrained by real interaction data. Unlike web data, robot demonstrations require hardware, expert teleoperation, repeated resets, safety monitoring, and synchronized multimodal sensing. They are expensive to collect, especially for contact-rich, long-horizon, and multi-embodiment tasks, making high-quality trajectories both scarce and valuable (Wu et al., 2025; Luo et al., 2025b). This data bottleneck is compounded by privacy and ownership constraints. Robot trajectories can expose private environments, user routines, and proprietary procedures, and their substantial acquisition cost makes them valuable institutional assets that owners are reluctant to share. Federated learning (FL) (McMahan et al., 2017; Kairouz et al., 2021) therefore provides a natural infrastructure for large-scale embodied training, letting institutions contribute complementary experience without centralizing raw data. This task-silo setting is practical rather than artificial: an institution typically owns the hardware, expertise, and suite of tasks for a focused family of manipulation tasks, so disjoint silos arise directly from existing practice. The resulting federation is nevertheless highly heterogeneous: client task families are largely disjoint and uneven in size, so each client optimizes over a different label distribution, and the aggregate problem is strongly non-IID. Under such task-level skew, local optima drift apart, and naive averaging blends transformations that are valid only within their own families. The objective is thus to combine complementary task-specific capabilities into a broadly competent policy without exposing or erasing their source. Mixture-of-Experts (MoE) (Jacobs et al., 1991; Shazeer et al., 2017; Fedus et al., 2022) provides a natural representation for such task diversity, combining specialized experts with a shared backbone and input-dependent routing. For example, FedVLA (Miao et al., 2025) trains dual-gating MoE models on clients and aggregates their aligned-MoE trunk parameters for performance enhancement. Yet a modular architecture does not, by itself, ensure coherent federated learning. When each client trains its own MoE on a narrow task distribution, the corresponding expert branches can acquire distinct specializations, while the routers learn assignments shaped by local task frequencies. Averaging these expert updates can dilute task-specific knowledge, and aggregating the routers can disrupt the assignments that make that knowledge useful, leading to performance degradation as shown in Section 4. The key is therefore to separate local specialization from the learning of a shared routing policy. To address this gap, we propose ROBOFL, a federated framework that combines a task-silo protocol with server-side expert assembly as shown in Figure 1. Designed for communication-constrained FL settings, ROBOFL leverages parameter-efficient fine-tuning (PEFT) (Hu et al., 2022; Wu et al., 2024) to enable clients to exchange compact LoRA adaptations rather than full model updates (Miao et al., 2025; Zhou et al., 2026). Specifically,➊each institution trains a single LoRA adapter on a focused family of tasks and uploads only its adaptation parameters to the server.➋The server assigns the uploaded adapters to fixed expert slots and composes them into a layer-wise MoE, where a router is trained to select among task-specialized LoRA experts.➌After server-side routing and expert refinement, the resulting expert updates are converted into a compact global adapter and blended with each client-associated expert before the next communication round. This procedure yields a Mixture-of-Slotted-Adapters with integration and conversion (MOSAIC). By separating local expert formation from global router learning, ROBOFL enables the router to build on task-trained capabilities rather than on initially unspecialized branches. The fixed client- to-slot mapping preserves parameter correspondence across rounds, while still allowing flexible token-to-expert assignments. This design supports more stable routing without imposing multi-expert training or communication on clients: local training and exchanged adapters retain the footprint of single-adapter fine-tuning, while routing and multi-expert optimization remain on the server. In addition, contemporary WAMs (Cai et al., 2026; Bi et al., 2026; Ye et al., 2026b) use aligned mixture-of-transformers (MoT) architectures (Liang et al., 2024) whose understanding, visual fore- sight, and action paths provide complementary evidence about the same interaction. Such a three-path structure of WAMs offers an additional source of guidance for this assembly process. MOSAIC 2 exploits this structure to inform both expert selection and adapter conversion. Therefore, we propose Foresight-to-Action Routing Distillation (FARD), which distills reliable routing consensus between the understanding and generation paths into the action router, using a detached teacher to guide expert selection for action generation. In addition, Path-Consensus Expert Aggregation (PCEA) uses detached consensus across all three paths to weight complete server-refined LoRA updates and reconstruct a rank-constrained global adapter. Together, these mechanisms use agreement across what the model understands, predicts, and executes to guide which experts it activates during server training and how it consolidates their knowledge for subsequent client training. Finally, we evaluate ROBOFL on RoboTwin 2.0 (Mu et al., 2025), RLBench (James et al., 2020), and a real-world Franka robot arm against centralized PEFT WAMs, as well as FL-based VLA methods, as shown on the right side of Figure 1. Experiments across simulation and the real world show that ROBOFL outperforms existing federated VLA methods and, in certain scenarios, even centralized PEFT WAMs, as it attains 83.12% overall on RoboTwin 2.0, 4.2% above federated averaging and 1.52% above centralized InternVLA-A1, reaches 59.17% against 46.94% for centralized InternVLA on six real-world Franka tasks, and cuts client communication by up to 86.81% against MoE-based federated VLA baselines. Our contributions are summarized as follows. 1. Task-siloed federated expert assembly. We propose ROBOFL with MOSAIC to assemble client-trained LoRA adapters into a server-routed MoE, keeping raw trajectories local and retaining single-adapter client training and communication. 2.Foresight-guided action routing. We introduce FARD to distill reliable understanding- generation routing consensus into the action router for MoT-based world action models. 3.Path-consensus adapter conversion. We introduce PCEA to aggregate complete server- refined expert updates using three-path consensus and reconstruct a rank-constrained global adapter for personalized redistribution. 2RELATED WORKS Vision-language-action and world-action models.VLA models connect multimodal knowledge to robot control, from RT-2 (Brohan et al., 2023) and PaLM-E (Driess et al., 2023) to multi-robot policies such as Octo (Ghosh et al., 2024) and OpenVLA (Kim et al., 2025). Subsequent work advances flow-based control (Black et al., 2025), dual-system architectures (Bjorck et al., 2025), action tokenization (Pertsch et al., 2025), spatial representations (Qu et al., 2025), and efficient adaptation (Zhang et al., 2026). Cosmos (Agarwal et al., 2025) and recent WAMs (Ye et al., 2026a; Li et al., 2026) further exploit future-state prediction. These systems generally assume centralized training rather than assembling future-aware policies from institutionally distributed task data. VLA and WAMs with MoE and FL.MoE models (Fedus et al., 2022; Zhang et al., 2025) support specialized computation, including expert selection and weighting decoupled in AdaMoE (Shen et al., 2025), force-aware routing in ForceVLA (Yu et al., 2025), and layer-wise activation in MoLe- VLA (Zhang et al., 2026). FLAME (Betran et al., 2025) benchmarks robotic FL, while FedVLA (Miao et al., 2025) combines federated training with dual-gating MoE and ForgeVLA (Zhou et al., 2026) addresses unannotated vision-action logs through instruction recovery, contrastive planning, and adaptive aggregation. Training MoE routers on narrow client distributions can nevertheless produce inconsistent expert assignments. ROBOFL separates local adapter specialization from server-side routing and jointly refines uploaded experts and module-specific routers on server data. Federated PEFT and MoE. LoRA (Hu et al., 2022) provides compact low-rank updates for federated adaptation. FLoRA (Wang et al., 2024), FRLoRA (Yan et al., 2025), FedSA-LoRA (Guo et al., 2025), and LoRA-A2 (Koo et al., 2025) study low-rank aggregation and sharing, while FedFisher (Jhunjhunwala et al., 2024) addresses one-shot aggregation. Mixture of LoRA Experts routes among adapters (Wu et al., 2024), FedMoE (Mei et al., 2024) integrates client-specific sub- MoEs, and pFedMoAP (Luo et al., 2025a) exchanges prompt experts for personalization. In contrast, ROBOFL installs single-adapter client updates as server MoE experts without federating selection routers, then uses cross-path consensus to convert complete expert updates into compact adapters for personalized redistribution. 3 RoboFL FARD: Cross-Path Routing Alignment MoSAIC-PCEA: Server-Side Expert Aggregation synchronized multi-view observation left wrist camerahead cameraright wrist camera language instruction Pickupthecan [EOS] visual observation noisy action ... time / noise t 1 t 2 ... t n Understanding Encoder + Tokenizer ... Generation Encoder ... Action Encoder ... Unified Masked Self-Attention Foresight Consensus Understanding Path (MoSAIC) Generation Path (MoSAIC) Action Path (MoSAIC) ... Router U ... Router A MoSAIC Router Adapter Slotting local specialization preserved Upload LoRA Articulated Object Task-Specialized LoRA Grasping and Movement Task-Specialized LoRA Alignment and contact Task-Specialized LoRA Rotate and Locate Task-Specialized LoRA Expert Slot 1 Expert Slot 2 Expert Slot 3 Expert Slot E ... Mixed-Task Server Data ... Server-Only Router ... 0.62 0.18 0.07 0.13 one router connects the expert adapters ... PCEA Path-Consensus Expert Aggregation consensus weights ... × ... � � =(( � � + � � + � � )/3) 2 � � � � FARD � � = � � � � � � � � � � � �=�×� H e l l i n g e r B a r y c e n t e r Router G � � Figure 2: Overview of ROBOFL. Left: Modality-specific tokens interact through unified masked self-attention, while FARD distills detached understanding-generation consensus into action routing. Right: MOSAIC installs task-trained LoRA adapters as server MoE experts and jointly refines routers and experts. PCEA aggregates complete expert updates using three-path consensus to form a rank-constrained global adapter, which is blended with each server-refined client expert. 3METHOD 3.1PRELIMINARY Three-Path World-Action Architecture.ROBOFL is built on a three-path world-action architec- ture, in which the understanding (U), generation (G), and action (A) paths are coupled through unified masked self-attention.Uencodes current images and instructions with Qwen3-VL.Gprocesses Cosmos-tokenized past and current frames to predict future-frame latents.Areceives a projected state token, followed by noisy action tokens fused with a time embedding. At each aligned layer, path-specific queries, keys, and values are concatenated along the token dimension for joint attention, then split for path-specific output projections and MLPs. Thus, the paths share the attention computa- tion, not projection or MLP weights. The block-causal mask orders tokens asU | G| state| actions: each block attends to itself and preceding blocks, subject to padding masks. Action tokens attend bidirectionally within a chunk and use U/G hidden context, not decoded future images. At matching layer/projectionm, letq P m,b ∈ R E be the sample-wise mean of the full pre-top-krouter probabilities for pathP ∈ U,G,A. Specifically, pooling masks out invalid observations and language positions in the understanding pathUand invalid visual positions in the generation pathG. InA, it includes all action positions, excluding the state token but not action padding. Cross-path comparisons use samples with valid pooled distributions in all three paths. Flow-Matching Action Policy. For a demonstrated action chunka∈ R H×d a , noiseε∼N (0,I), and time t∼ p time , the action path predicts the conditional velocity x t = (1− t)a + tε, u t = ε− a, L action = E a,ε,t [MSE valid (v θ (x t ,t,c),u t )], (1) wherecdenotesU/Gcontext and the robot state, and MSE averages over actual action dimensions and non-padded steps when padding labels are available. At inference, explicit Euler integration proceeds fromx 1 ∼ N (0,I)att = 1tot = 0. The generation lossL gen is the MSE between predicted and target future Cosmos latents over valid views. 4 3.2MOSAIC: MIXTURE OF SLOTTED ADAPTERS As shown in Figure 2, each of theKclients trains a standard LoRA adapter for each layer on its private task-family datasetD k . The server maintainsE = K > 1complete expert branches and one selection router per adapted projection. A slot identifies a client-associated LoRA adapter within a module, not a separate model. Adapter Slotting. In roundτ, clientkuploads its adapter factors, which directly overwrite slotk at each adapted module m: (A τ,0 m,k ,B τ,0 m,k )← (A loc,τ m,k ,B loc,τ m,k ).(2) No averaging occurs during installation. Client-to-slot identities remain fixed without restricting token assignments, and expert factors are refreshed each round, while selection routers persist only on the server. The protocol exchanges parameters, not raw trajectories. Routed Expert Integration. For token representation z, the adapted projection is, omitting bias, h m (z) = W 0 m z + γ m E X e=1 π m,e (z)B m,e A m,e z, γ m = α m /r,(3) whereW 0 m is frozen andπ m contains renormalized top-k route weights, distinct from the dense probabilities pooled intoq P m . The server jointly refines selection routers and both expert factors on mixed-task server data, starting from task-trained adapters. Path indices on weights are suppressed while each path retains its own parameters. Uploaded shared action-head weights are uniformly averaged across clients, refined at the server, and copied back to all clients. Global Adapter Conversion.Let∆W srv,τ m,e = γ m B srv,τ m,e A srv,τ m,e denote the complete server-refined adapter residual relative to the frozen backbone. PCEA converts these updates into a rank-constrained global adapter using detached routing evidence, as detailed below. This static conversion prepares client parameters rather than guaranteeing equivalence to the input-dependent MoE. Personalized Adapter Redistribution. Client k receives standard LoRA factors representing ∆W init,τ+1 m,k = Π r 1 2 ∆W srv,τ m,k + 1 2 ∆W glob,τ m ,(4) whereΠ r is a truncated SVD approximation of rank at mostr. The client-specific component is the post-server expert, not the original upload, which enables personalized parameter aggregation. 3.3FARD: FORESIGHT-TO-ACTION ROUTING DISTILLATION FARD uses understanding-generation agreement to guide action routing. For each valid module- sample pair (m,b), define the geometric-mean teacher and its reliability: a m,b = X e q q U m,b,e q G m,b,e , q UG m,b = q q U m,b q G m,b a m,b , r m,b = a m,b " 1− H(q UG m,b ) logE # + . (5) Thus, reliability combines path agreement with teacher concentration, so that unreliable routing signals are down-weighted during training. For valid samplesV m , the loss is L FARD = mean m " 1 |V m | X b∈V m sg(r m,b )D JS sg(q UG m,b ),q A m,b # ,(6) averaged over modules with nonemptyV m (zero if none). Heresgstops gradients while entropy and JS use natural logarithms, with numerical probability floors omitted for clarity. Gradients pass 5 through the action-distribution argument, not the teacher or reliability, and upstreamU/Gparameters can still receive indirect gradients through joint attention. The overall server objective therefore minimizes L MoSAIC =L action + λ gen L gen + λ aux L aux + λ (τ) FARD L FARD ,(7) whereL aux denotes the module-level auxiliary load-balancing loss averaged over theEexperts of each module, and λ (τ) FARD follows the round-wise warmup schedule. 3.4PCEA: PATH-CONSENSUS EXPERT AGGREGATION PCEA weights complete expert updates rather than averaging their factors, since, in general, X e ω e B e A e ̸= X e ω e B e ! X e ω e A e ! .(8) During server training, it collects detached, unnormalized Hellinger-barycenter evidence: g m,b,e = q q U m,b,e + q q G m,b,e + q q A m,b,e 3 2 .(9) Summing the valid sample occurrences across server steps and ranks within a round gives: s m,e = X b g m,b,e , w m,e = s m,e P j s m,j , ̄a m = P e s m,e N m ,(10) whereN m counts sample occurrences. The evidence retains its agreement mass rather than being normalized per sample. For observed module tripletsM, PCEA computes agreement-weighted global weights and a Hellinger midpoint: ̄w e = P m∈M ̄a m w m,e P m∈M ̄a m , ew m,e = ( √ w m,e + √ ̄w e ) 2 P j ( √ w m,j + √ ̄w j ) 2 .(11) MatchedU/G/Amodules share these weights. Eligible unobserved modules use ̄w, and PCEA requires nonempty evidence. The unmatched state-projection adapter is aggregated uniformly. For each physical module’s own post-server factors, conversion gives: ∆W glob,τ m = Π r X e ew m,e ∆W srv,τ m,e ! .(12) Implementation uses QR reduction on the stacked weighted factors, followed by a small SVD. FARD guides routing during server training, while PCEA consolidates the updates for client training. 4EXPERIMENTS 4.1EXPERIMENTAL SETTINGS Evaluation Protocol. We evaluate ROBOFL under the task-silo protocol on RoboTwin 2.0 (Mu et al., 2025), RLBench (James et al., 2020) and Franka robots 1 . We partition the 50 tasks into 8 client task-family groups and 1 server residual group for RoboTwin 2.0random, and split the 8 RLBench tasks into 4 client partitions and 1 server partition, with 6 tasks distributed across the four clients and 2 tasks retained on the server. As for real-world applications, we partition 6 manipulation tasks into 4 clients and 1 server for Franka, creating an extreme non-IID data scenario. 1 Full task settings and evaluation results are shown in the Appendix. 6 Table 1: RoboTwin 2.0 success rates on a 25-task challenging subset under random condition (selected as tasks where FedAvg < 80%). Overall reports performance on all 50 tasks. Method beat ham. rank size hand blo. hang mug lift pot move can move sta. pick div. pick dual place L place R bread ski. can basket CENTRALIZED TRAINING INTERNVLA73786227327653687485847960 MOTUS82866020408648708085808069 FEDERATED LEARNING(LORA/MOE) FEDAVG75745224336739697779797472 FEDMOE69714221345734617084806664 FORGEVLA75835735408344678287827868 FEDVLA73856126338545628480827774 ROBOFL78927330248750728487838082 Method dual shoe mouse pad place bas. place sca. press sta. bottles dus. put cab. rotate QR scan obj stack bow. stamp seal turn swi.Overall CENTRALIZED TRAINING INTERNVLA64708281749068776486684381.60 MOTUS73647973728967876577664580.96 FEDERATED LEARNING(LORA/MOE) FEDAVG67567975757768795879574878.92 FEDMOE60547569747962733178603875.12 FORGEVLA70598077788361776975595280.70 FEDVLA71537075758460757080655179.32 ROBOFL74587274749068817486705383.12 Federated Optimization. All experiments initialize from the pretrained InternVLA-A1-3B check- point, use full client participation,100communication rounds, and one local epoch. Client and server steps are500/200/300(RoboTwin / RLBench / Franka); client batch size is32, and server batch size is8/16/16. Both optimizers are AdamW with learning rate1× 10 −4 , betas(0.9, 0.95), epsilon 10 −8 , weight decay0.01, and gradient-norm clipping at1.0, using cosine decay from1× 10 −4 to 1× 10 −5 over 50,000/20,000/30,000 decay steps and 2,500/400/600 warmup steps. MoSAIC Configuration. MoSAIC uses eight expert branches per adapted module with top-4 server-side routing for RoboTwin 2.0, and four expert branches per adapted module with top-2server- side routing for RLBench and the real-world applications. Each expert uses rankr = 16, LoRA parameterα = 32(effective scalingα/r = 2), and dropout0.05. The generation and load-balancing coefficients areλ gen = 0.01andλ aux = 0.001. FARD usesλ FARD = 0.01with a10-round warmup. Baselines. We compare against InternVLA-A1 (Cai et al., 2026) and Motus (Bi et al., 2026), which are centralized PEFT references; FedAvg (McMahan et al., 2017) performs standard weight averaging; FedMoE (Mei et al., 2024) uses client-specific expert sub-MoEs; FedVLA (Miao et al., 2025) combines instruction-oriented scene parsing, dual-gating MoE, and expert-driven aggregation; and ForgeVLA (Zhou et al., 2026) targets heterogeneous federated robot data with weak or missing language supervision. We adapt them to the same FL-PEFT with Kaiming-random-initialized adapter. 4.2QUANTITATIVE RESULTS FOR SIMULATION Model Performance on RoboTwin 2.0. Table 1 reports the 25 RoboTwin 2.0 tasks on which FedAvg stays below 80%, since the remaining tasks are near-saturated and thus uninformative. ROBOFL attains the highest overall success rate of 83.12%, exceeding FedAvg by 4.20% and also surpassing centralized PEFT with InternVLA-A1 and Motus. This pattern matches MOSAIC’s design: retaining locally specialized adapters as expert branches and learning their input-dependent composition rather than immediately averaging them. Best or joint-best results on 15 displayed tasks show that the gains extend across tasks. Overall, ROBOFL delivers the strongest performance in 7 terms of single-adapter client cost, demonstrating that server-side expert assembly can outperform both federated averaging and centralized PEFT across heterogeneous task silos. Table 2: Average success rates (%) for eight RLBench tasks with 4-expert MoSAIC for ROBOFL. MethodInternVLAMotusForgeVLAFedVLAROBOFL Type Central-LoRAFL-LoRA FL-MoE LoRA→MoE SUCCESS52.7552.5034.2531.0041.25 Model Performance on RLBench. We further examine how ROBOFLperforms on RLBench with only eight tasks under a 4-client, 4-expert MoSAIC in Table 2. ROBOFL remains the best FL method at 41.25%, yet the margin over centralized PEFT reverses relative to RoboTwin, where ROBOFL also beats InternVLA-A1 and Motus. With fewer tasks and clients, each expert sees less complementary evidence for routed composition, so the advantage of structured expert assembly is smaller. These results suggest that ROBOFL is most effective in large-scale, task-heterogeneous regimes rather than in small, low-data suites. Table 3: Client resources and logical communication on RoboTwin 2.0. Communication combines upload and download per participating client per round. Method Adapters c / s Params (M) Comm. MiB Mem. GiB Success (%) FEDAVG1 / 140.85311.638.3378.92 FEDMOE4 / 8158.111,206.2811.4475.12 FORGEVLA1 / 140.85312.068.3380.70 FEDVLA8 / 8312.932,362.8515.5979.32 ROBOFL1 / 840.85311.638.3383.12 Client Resources and Communication. Table 3 compares adaptation resources at the client boundary, combining upload and download into a per-round communication total. With one rank-16 adapter per client, ROBOFL matches FedAvg’s40.85M train- able parameters and311.63MiB payload, while retaining eight server-side expert branches. Relative to MoE-based FL meth- ods FedMoE and FedVLA, client param- eters decrease by up to 86.95% and per- round communication by up to 86.81%, while RoboTwin 2.0’s success rates increase by 8 and 3.8 percentage points, respectively. Peak allocated GPU memory falls from15.59to8.33GiB in the standardized client-architecture mi- crobenchmark. These results demonstrate that ROBOFL achieves the best accuracy-efficiency trade- off: it attains the highest success rate with the same computational and communication overhead as single-adapter baselines, while remaining far below client-side MoE. 4.3ABLATION STUDIES > 80%≥ 90%≥ 95%= 100% Task success-rate criterion 0 10 20 30 40 Number of tasks (out of 50) 31 21 14 4 31 19 15 4 33 17 14 6 34 24 14 9 High-success task coverage RoboTwin / 50 tasks / 100 trials per task Counts are cumulative; 100% denotes 100 successes in 100 evaluation trials. Centralized LoRAvanilla MoSAIC+ FARD+ FARD + PCEA Figure 3: Success-threshold coverage on RoboTwin. Bars count tasks satisfying each success-rate criterion across 50 tasks with 100 trials per task. Influence of FARD and PCEA. We present a sequential ablation of FARD and PCEA, using vanilla MoSAIC as the base- line and centralized LoRA as an external reference under its own training schedule with RoboTwin 2.0, as shown in Figure 3. We evaluate PCEA on top of FARD be- cause its consensus-weighted conversion is designed to exploit the routing agreement. FARD alone increases the number of tasks exceeding80%success from31to33, but reduces coverage at≥ 90%from19to17. Adding PCEA raises these counts to34and 24, surpassing both vanilla MoSAIC and centralized LoRA at the latter threshold. Tasks with 100/100 successes likewise increase from4for both references to6with FARD and9with FARD+PCEA. At≥ 95%, however, both variants cover 14tasks versus15for vanilla MoSAIC. These results support combining routing distillation with expert conversion, potentially preserving coordinated task knowledge across federated rounds and supporting more consistent execution and broader coverage of high-success tasks. Routing Coupling and Intervention.We probe route-to-action coupling across 50 RoboTwin 2.0 tasks while holding the initial observation and robot state fixed. Instruction substitution changes only the language condition, whereas uniformized and scrambled controls intervene only on the action- 8 Table 4: Real-world applications with six single-arm Franka tasks SR (%) with three replicates. MethodType adjust bottle stamp seal stack cups screw bottle pour water test tube Mean± Avg. SD INTERNVLACENTRALIZED-LORA63.3353.3341.6731.6748.3343.3346.94± 7.80 FORGEVLAFL-LORA41.6731.6746.6728.3331.6733.3335.56± 7.03 FEDVLAFL-MOE43.3341.6733.3313.3340.0030.0033.61± 5.60 ROBOFLFL-LORA→MOE68.3366.6768.3336.6756.6758.3359.17± 7.61 adjust_bottle pour_water screw_bottle stack_cups stamp_seal test_tube Successful real-world rollouts; four chronological keyframes per task (initial scene, approach or contact, task progress, final state). Figure 5: Qualitative successful real-world Franka rollouts for each of six single-arm Franka tasks. router distribution. As shown in Figure 4, instruction swaps produce strong pooled route-to-action coupling, establishing that task semantics reach action generation through routing. 0.00000.00250.00500.00750.01000.01250.01500.0175 Mean route JSD from original instruction 0 20 40 60 80 100 Action chunk L2 from original instruction Routing displacement and action displacement across semantic and direct router probes Instruction-swap trends: matched ρ=0.832, mismatched ρ=0.800 Task family stacking ranking handover bottle manipulation transport place contact control open inspect Checkpoint FARD Vanilla RoboFL 0.000.010.020.030.04 action-route JSD 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 action L2 direct intervention Probe condition family-matched family-mismatched uniformized router scrambled router Filled/open: matched/mismatched instruction; squares/diamonds: direct action-router intervention. Routing Displacement and action displacement Figure 4: Route-to-action coupling under instruction swaps and direct action-router interventions. The inset magnifies the direct intervention regime. The direct intervention isolates the action router more strictly. Scrambling produces a larger routing displacement for FARD, yet a smaller action displacement than vanilla ROBOFL. Thus, FARD makes rout- ing more selective without making the re- sulting policy brittle. Together, the probes support FARD as a cross-path routing- alignment mechanism, while PCEA per- forms the corresponding path-consistent expert conversion. 4.4REAL-WORLD APPLICATIONS WITH FRANKA Quantitative Analysis. Table 4 reports success rates on six single-arm Franka tasks. We report mean success rates over three evaluation rounds of 20 trials per task. ROBOFL attains the highest Overall success rate of 59.17%, exceeding centralized InternVLA by 12.23% and federated ForgeVLA and FedVLA by 23.61% and 25.56%. MoSAIC therefore extends beyond simulation: installing each client’s single LoRA as a routed server expert, rather than averag- 9 ing updates, preserves input-dependent specialization under real perception, contact, and hardware variability, even surpassing pooled centralized PEFT at the cost of a single adapter per client. Qualitative Analysis. Figure 5 shows successful rollouts on six Franka tasks. Execution follows the simulation’s three-phase structure: approach, sustained contact, and sequenced state change. This closed-loop coherence reflects the method’s design: task-trained experts remain distinct under server routing, while understanding-generation consensus guides action routing, so contact-rich behaviors remain input-dependent rather than averaging into generic motions. For example, adjust bottle task seats rather than strikes, screw bottle task sustains rotation through the cap. 5CONCLUSION We presented ROBOFL, a federated framework for learning world-action models from task-siloed robot data without centralizing raw trajectories. MOSAIC installs locally trained LoRA adapters as server MoE experts and jointly refines routing and expert parameters. Specifically, FARD aligns action routing with understanding-generation consensus and PCEA consolidates expert updates into a rank-constrained global adapter for personalized redistribution. Across simulation and real- robot experiments, their combination delivers the highest overall success rates among the evaluated federated methods while keeping client training at single-adapter cost. AI USE STATEMENT The authors used AI-based writing and coding assistants to help draft and polish portions of the text and to support the implementation and analysis scripts. All problem formulation, method design, experimental execution, data collection, and interpretation of results were carried out and verified by the authors, who take full responsibility for the content of this paper. ETHICS STATEMENT This work studies federated learning of world-action models for robotic manipulation. Experiments in simulation use the publicly released RoboTwin 2.0 and RLBench benchmarks, and the real-robot evaluations collect no personally identifiable information. The motivating concern of the paper is that robot trajectories can reveal private environments, user routines, or proprietary procedures, and that centralized pooling of such data may be undesirable. The proposed protocol keeps raw trajectories at each institution and exchanges only adaptation parameters, thereby reducing this exposure; however, we do not claim formal privacy guarantees, such as differential privacy or secure aggregation, and parameter updates may still leak information in adversarial settings. We therefore position the method as an architectural alternative to raw-data centralization rather than as a complete privacy solution. We also note that broad manipulation policies can be misused, and we follow the ICLR Code of Ethics in conducting and reporting this work. REPRODUCIBILITY STATEMENT We summarize the resources provided to support reproducibility. The full set of training and evaluation settings appears in Table 5 and Appendix A; the task-silo assignments for the eight RoboTwin 2.0 clients and the four RLBench clients are listed in Tables 6 and 8; and the observation, action, and optimization interfaces are specified in the same appendix. The client resources, logical communication accounting, and the architecture profiles behind the memory measurements are documented in Appendix A.1. The MoSAIC, FARD, and PCEA formulations, including the adapter slotting, router integration, personalized redistribution, and consensus-weighting rules, are given in the Method section and implemented as described in Appendix A.1. We plan to release the source code, launch configurations, and evaluation scripts as supplementary materials; these will include data preprocessing and normalization steps, evaluation packages for both benchmarks, and scripts used to generate the resource and ablation figures. Simulation results use a single fixed evaluation seed; real-robot results use a fixed scripted protocol with 20 trials per task. Differences below a few points, and per-task swings on the 8-task RLBench suite, should be read as descriptive rather than statistically established. 10 ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (62476011) and (625B2090), the Beijing Natural Science Foundation (L252060). REFERENCES Niket Agarwal, Arslan Ali, Maciej Bala, Yogesh Balaji, Erik Barker, Tiffany Cai, Prithvijit Chat- topadhyay, Yongxin Chen, Yin Cui, Yifan Ding, et al. Cosmos world foundation model platform for physical ai. arXiv preprint arXiv:2501.03575, 2025. Santiago Bou Betran, Alberta Longhini, Miguel Vasco, Yuchong Zhang, and Danica Kragic. Flame: A federated learning benchmark for robotic manipulation. In 2025 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), p. 2494–2500. IEEE, 2025. Hongzhe Bi, Hengkai Tan, Shenghao Xie, Zeyuan Wang, Shuhe Huang, Haitian Liu, Ruowen Zhao, Yao Feng, Chendong Xiang, Yinze Rong, et al. 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LoRA adapts the attention, MLP, and state projections. Clients upload complete LoRA factors together with the trainable action input/output projections and action-time MLP weights, while frozen backbone weights are excluded. Shared action-head weights are averaged uniformly and synchronized separately from expert conversion. Server MoE checkpoints are saved before global adapter conversion and personalized redistribution. Server participation and shared-compute assumption.ROBOFL lets the central server take part in training rather than act only as an aggregator. We regard this as a reasonable and common use of the decentralized setting: the server is typically the best-provisioned node, and federated methods routinely exploit server-side computation, for example through server-level adaptive op- timization (Reddi et al., 2021), distillation of the client ensemble on server or surrogate data (Lin et al., 2020; Chen & Chao, 2021), or data-free server-side generators (Zhu et al., 2021). Under this assumption, the server holds one residual task group and performs the routed expert-refinement stage on it, which enables a single shared router over task-trained experts; the alternative reading, in which the server has no data of its own, would leave the router without a common distribution to learn from. Crucially, this does not amount to centralized training: the server group covers only a small fraction of each benchmark (7/50,2/8, and2/6tasks on RoboTwin 2.0, RLBench, and Franka), so the bulk of the task distribution still resides with the clients. The server is also not given a disproportionate optimization budget: its per-round steps match the per-client local steps (500/200/300for the three scenarios), and its task group is comparable in size to the client partitions (3-8,1-2, and1task per client). Clients therefore continue to train a single adapter, and the additional routing and multi-expert computation remains on the server. Comparison Fairness with Centralized Training Baselines We treat centralized PEFT as a deliberately stronger reference than any federated method, not as an equal-budget competitor. A centralized run observes the union of all task families in a single optimizer, with no task silos, no non-IID client drift, and no communication rounds. That ROBOFL matches or exceeds this reference on RoboTwin 2.0 and Franka while operating under task-silo federated learning, and, consistent with its mechanism, trails it only on the low-data RLBench suite, where less complementary evidence exists for expert composition, is the intended empirical claim of Section 4. The comparison is also capacity-matched at the point of deployment. The entity that is trained, redistributed, and evaluated is a single rank-16 LoRA adapter per client, identical in family, rank, and scaling to the adapters used by federated averaging and by the centralized PEFT references. The eight-expert server MoE is a training-time construct that never leaves the server; clients never hold routers or multiple experts, and the deployed policy is the redistributed single adapter, not the server MoE. At the client boundary, ROBOFL is therefore indistinguishable from single-adapter FL in trainable parameters, communication, and memory (Table 3), and is far below client-side MoE methods. The reported gains consequently cannot be attributed to a larger deployed model or to additional client-side capacity: they follow from how task-specialized adapters are composed on the server under heterogeneity, not from giving the learned policy more parameters than its baselines. Notably, this advantage is obtained under an extreme non-IID, task-disjoint regime in which every client still trains and communicates a single adapter. Configuration. Table 5 summarizes the numerical settings. RLBench training entries marked† are launcher defaults, not reconstructed settings of the reported checkpoints. Task assignments and evaluation semantics are specified separately below. Last but not least, all the FL-based baselines follow the same training procedure as ROBOFL. 15 Table 5: Training and evaluation settings for the simulation and real-world scenarios. Execution horizon is specified independently of prediction length. SettingRoboTwin 2.0RLBenchFranka Optimization and adapters Pretrained checkpoint InternVLA-A1-3B Clients / experts8/ 84/ 44/ 4 Routing top-k422 Communi. rounds100100100 Local steps / round500200300 Local epochs111 Server steps / round500200300 Peak / final LR10 −4 / 10 −5 10 −4 / 10 −5 10 −4 / 10 −5 Warmup / decay steps 2,500/ 50,000400/ 20,000600/ 30,000 LoRA rank / α16/ 3216/ 3216/ 32 LoRA dropout0.050.050.05 λ gen /λ aux 0.01/ 0.0010.01/ 0.0010.01/ 0.001 Observation and action interface ViewsHead + two wristsFront + two masked slots External stand + wrist + masked slot Resolution224× 224224× 224224× 224 StateJoint configurationXYZ + Euler + gripperJoint + gripper ActionJoint-space offsets∆XYZ + absolute Euler + gripper Absolute joint targets History stride15115 Predicted chunk50850 Inference steps101010 Evaluation protocols Evaluated tasks5086 Trials / task1005020 Executed actions30850 InitializationRandomizedseed 42Operator reset A.2HYPERPARAMETER AND DESIGN CHOICES The non-obvious hyperparameters follow standard practice. The personalization coefficient 1 2 in Eq. 4 represents an equal global-local model interpolation, a standard personalization strategy with generalization guarantees (Mansour et al., 2020). The local term preserves client specialization, while the global term shares server-acquired knowledge, and fixing it avoids introducing a per-client hyperparameter. The auxiliary weights are kept small becauseL action remains the primary objective and only the magnitude of such weights matters: we useλ aux = 0.001(Kendall et al., 2018), with the load-balancing scale following the sparse-MoE convention (Shazeer et al., 2017; Fedus et al., 2022). FARD is likewise a routing regularizer based on detached Jensen-Shannon distillation (Hinton et al., 2015), soλ FARD = 0.01, and it is warmed up over10rounds because the reliability weight is uninformative before the action router stabilizes. Warmup is a standard variance-reduction device (Liu et al., 2020). A.3ROBOTWIN 2.0 Task-silo manifest. Table 6 lists the task-disjoint client and server assignments implemented by fedforesightcategory. Episodes remain within their assigned task partition, while the server residual group is used for routed optimization. 16 Table 6: Task assignments in the explicit eight-client task-silo implementation. Counts refer to tasks, not episodes or training frames. PartitionCountTasks Client 05 grabroller, pickdiversebottles, pickdualbottles, put bottlesdustbin, putobjectcabinet Client 17 placeobjectbasket, placebreadbasket, place breadskillet, placecanbasket, placecansplasticbox, placecontainerplate, placeemptycup Client 28 place a2bleft, placea2bright, placefan, placemousepad, placeobjectscale, placeobjectstand, placephonestand, placeshoe Client 36 stack blocksthree, stackblockstwo, stackbowlsthree, stackbowlstwo, blocksrankingrgb, blocksrankingsize Client 45 adjustbottle, liftpot, movepillbottlepad, move playingcardaway, movestaplerpad Client 53 beatblockhammer, pressstapler, stampseal Client 66 clickalarmclock, clickbell, turnswitch, openlaptop, openmicrowave, rotateqrcode Client 73 scanobject, shakebottle, shakebottlehorizontally Server7 placeburgerfries, placedualshoes, dumpbinbigbin, handoverblock, handovermic, hangingmug, movecanpot Observation and action interface. As shown in the Table 5, predicted joint-space offsets are converted to joint targets using the configuration at the start of each action queue. The evaluator truncates predictions using its execution-horizon argument, while prediction length does not determine the number of executed actions. Sampling and update accounting. Local training cycles through a shuffled frame-level loader, without task-balanced sampling. The epoch setting repeats the local-step loop rather than guaranteeing a full dataset traversal of the dataset. ForCclients,Krounds,Llocal steps,Erepetitions, andM server steps, the update counts areKLEper client,CKLEacross clients, andKMat the server. The schedule is given in Table 5. Batch-size conventions. Client batch size is per local update, while server batch size is per distributed rank. WithRserver ranks and per-rank batch sizeB srv , the effective server batch is RB srv . Client optimizer states are retained separately across rounds, while server optimizer state persists across expert replacement. Randomized initialization.As shown in Table 5, unstable or expert-unsuccessful candidate scenes are excluded before policy evaluation. Accepted trials therefore need not correspond to consecutive candidate seeds. The evaluator defaults to the unseen instruction split. A.4RLBENCH Task-silo manifest. Table 8 identifies the reported evaluation tasks, not client IDs. The training implementation provides task-disjoint bytask partitions with four clients and a separate server. Observation and action interface. See Table 5. Unlike RoboTwin, each queued translation increment is added to the current end-effector position, while the predicted Euler angles specify an absolute world-frame orientation. The resulting pose is executed by a motion planner. Stored translation labels are already relative while preprocessing must not subtract the state again. 17 Table 7: RoboTwin 2.0 task success rates (%) on the complementary 25 tasks not shown in Table 1. Best and second-best reported results are boldfaced and italicized. Method adjust bot. rank RGB click alarm click bell dump bin grab roller hand mic move pill move card open laptop open micro. bread bas. burger fries CENTRALIZED TRAINING INTERNVLA9991859198100958710098918799 MOTUS1009483909110081919792808193 FEDERATED LEARNING(LORA/MOE) FEDAVG999184939510089839890848298 FEDMOE1009176919410082809588658097 FORGEVLA1009085929410082919893828293 FEDVLA99888289929983839690788296 ROBOFL10095839697100929210090859093 Method cans box cont. plate empty cup place fan obj. stand phone stand place shoe shake bot. shake horiz. stack 3 blo. stack 2 blo. stack 2 bow.Overall CENTRALIZED TRAINING INTERNVLA9797100918894939997871009881.60 MOTUS97991008587939110010083999880.96 FEDERATED LEARNING(LORA/MOE) FEDAVG941001008684919310097849910078.92 FEDMOE8599100848991869999809910075.12 FORGEVLA9310010088859492100100811009980.70 FEDVLA891001008384909010098849510079.32 ROBOFL94100100909195951001008210010083.12 Table 8: RLBench evaluation manifest. Rows identify evaluation tasks, not federated clients. PartitionCountTasks Client 01 takeumbrellaoutofumbrellastand Client 12 closefridge, toiletseatdown Client 22 closelaptoplid, closebox Client 31 sweeptodustpan Server2 putrubbishinbin, phoneonbase Sampling and update accounting.The implementation uses the same shuffled-loader and update- counting conventions as RoboTwin. Table 5 records launcher defaults. Batch-size conventions. The same per-client-update and per-server-rank conventions apply as in RoboTwin for the independent-client configuration. A grouped-client distributed run also requires the number of ranks per client to determine the effective local batch size. Randomized initialization. Simulator resets use the variation and seed in Table 5, without RoboTwin’s expert-based candidate screening. Invalid actions and failures terminate the episode and count as failures. Expert actions and future observations are not supplied to the policy. BADDITIONAL EXPERIMENTAL DETAILS FOR REAL-WORLD FRANKA TASKS B.1IMPLEMENTATION DETAILS Task-silo manifest.Table 9 identifies the six reported single-arm Franka tasks and their client and server assignments. The implementation provides task-disjoint partitions among four clients and a separate server, with each client owning one task family and the server retaining the remaining two. Evaluation is performed via real-robot inference on the physical platform described in Appendix B.2. 18 Table 9: Franka real-robot manifest. Rows identify evaluation tasks, not federated clients. PartitionCountTasks Client 01 stackcups Client 11 screw bottle Client 21 stampseal Client 31 testtube Server2 adjustbottle, pourwater Observation and action interface.See Table 5. Unlike RoboTwin, each action is an absolute joint target executed directly by the robot, while queued targets are not added to the state at the start of the action queue. The policy consumes the external stand and wrist views, with the third view slot masked. State and action are both eight-dimensional, and auxiliary tactile and wrench channels are not supplied to the policy. Sampling and update accounting.The implementation uses the same shuffled-loader and update- counting conventions as RoboTwin and RLBench. Table 5 records the schedule. Batch-size conventions. The same per-client-update and per-server-rank conventions apply as in RoboTwin and RLBench for the independent-client configuration. The client batch size is32per local update, while the server batch size is 16 per distributed rank. Evaluation protocol.Each method is evaluated in three rounds of 20 trials per task. Each real-robot trial is started and reset by the operator, which places the objects and fixtures in their nominal task configuration. The policy then executes in a closed loop on the physical robot, and a trial is scored as successful only if the task goal is reached; otherwise, the episode terminates and counts as a failure. B.2FRANKA SINGLE-ARM PLATFORM Robot and gripper. Figure 6 shows the hardware configuration for our Franka single-arm experi- ments. The platform consists of a Franka Research 3 manipulator equipped with a Robotiq 2F-85 gripper. The robot is mounted beside a tabletop workspace containing the objects and fixtures used in the manipulation tasks. Camera arrangement. Two RealSense D435i cameras provide complementary views of the workspace. One camera is mounted externally on a stand and faces the tabletop, providing an overview of the scene and object arrangement. The second camera is mounted on the robot wrist, providing a local view of the manipulation area as the arm moves. This configuration combines an external scene view with a close-range view of gripper-object interactions. Workspace and task objects.The workspace contains a perforated board and task-specific objects, including bottles, cups, a stamp and ink pad, glassware, and a test-tube rack. These objects support the six Franka tasks reported in the main text: adjust bottle, stamp seal, stack cups, screw bottle, pour water, and test tube. CADDITIONAL EXPERIMENTAL RESULTS C.1COMPLEMENTARY QUANTITATIVE ANALYSIS FOR ROBOTWIN 2.0 The complementary results explain the emphasis on challenging tasks in Table 1. Most reported scores on this subset exceed 90%, with many at or near 100%, leaving limited headroom to distinguish methods. The main table therefore focuses on a lower-success subset where FedAvg scores below 80%. This presentation makes ROBOFL’s improvements on difficult manipulation tasks more visible, rather than relying on comparisons among near-saturated results, while the appendix preserves complete task coverage. 19 Franka Research 3 RealSense D435i Robotiq 2F-85 RealSense D435i Figure 6: Franka single-arm experimental setup. The platform comprises a Franka Research 3, a Robotiq 2F-85 gripper, and two RealSense D435i cameras mounted on the wrist and an external stand, respectively. The tabletop contains the objects and fixtures used in the manipulation tasks. Table 10: Ablation of MOSAIC components on RoboTwin 2.0. All rows report overall success rates (%) on all 50 tasks with 100 trials per task. The three MOSAIC rows use the same federated pipeline and differ only in the server mechanism; FedAvg and FedMoE are external references. ConfigurationOverall FedAvg (averaged single adapter)78.92 FedMoE (client-side routed MoE)75.12 Vanilla MOSAIC (task-trained experts + routing)81.94 + FARD82.42 + FARD + PCEA (ROBOFL)83.12 Despite the higher success rates and reduced room for improvement, ROBOFL remains highly competitive, achieving best or joint-best results on 16 of the 25 tasks and 100% observed success on nine. Strong results across ranking, object placement, and bottle shaking show that its performance extends beyond the difficult cases highlighted in the main table. Together, the two subsets demonstrate that ROBOFL combines improvements on challenging tasks with strong performance on the more saturated portion of the benchmark. In addition, Table 10 reports the overall success rate of MOSAIC components on the full 50-task RoboTwin 2.0 benchmark. Installing task-trained adapters as expert branches with learned routing (vanilla MOSAIC) reaches 81.94%; adding routing distillation (FARD) raises this to 82.42%; and adding consensus-weighted conversion (PCEA) reaches 83.12%. The two external references put these numbers in context: federated averaging reaches 78.92%, while a client-side-routed LoRA-MoE (FedMoE) reaches 75.12%. Most of the gain, therefore, comes from retaining task-trained experts and learning their composition on the server (3.02% over FedAvg), with FARD and PCEA contributing smaller but consistent additional improvements (0.48% and 0.70%, respectively). FARD and PCEA mainly affect the distribution of high-success tasks as shown in Section 4.3. C.2QUANTITATIVE ANALYSIS FOR RLBENCH We further evaluate the methods in a lower-data, single-view RLBench setting with eight tasks and 50 trials per task. ROBOFL reaches41.25%, the best among federated methods, improving over FL baselines. Unlike RoboTwin, where ROBOFL also surpasses centralized PEFT, it trails centralized 20 Table 11: RLBench task success rates (%) on the 8-task single-view suite. Overall is the equally weighted mean across the eight tasks. Best and second-best results are boldfaced and italicized. Method put rubbish seat down draw umbrella close laptop sweep dustpan close fridge close box phone on base Overall CENTRALIZED TRAINING INTERNVLA601834626646865052.75 MOTUS442236587258923852.50 FEDERATED LEARNING(LORA/MOE) FEDAVG018224147292027.75 FEDMOE0121614226470825.75 FORGEVLA121432262070841634.25 FEDVLA61624123056802431.00 ROBOFL262432642450605041.25 InternVLA (52.75%) and Motus (52.50%) on RLBench. We hypothesize that the smaller single-view suite provides less task diversity and complementary evidence for expert composition, whereas centralized PEFT can directly pool all available examples. RoboTwin better represents the broad, task-heterogeneous distributed regime in which preserving specialized adapters is most valuable. These results therefore suggest that ROBOFL is particularly suited to large-scale distributed learning with complementary non-IID data. C.3QUALITATIVE ANALYSIS We visualize successful rollouts to examine whether the reported success rates correspond to sensible task behavior: approach and alignment, contact or grasp, and execution of the intended state change. Each task contributes four chronologically ordered keyframes from a single successful episode, and the frames are exported at their native resolution without cropping or enhancement. Because the evaluators record an observation before each executed action, the final frame may precede the release or contact that triggered the success flag, so visual inspection captures the executed behavior rather than confirming the terminal success event. RoboTwin 2.0. Figure 7 and 8 show one successful rollout for each of the 50 RoboTwin 2.0 tasks. Across these rollouts, the policy exhibits a consistent three-phase structure: an alignment phase in which the end effector approaches the target, a contact or grasp phase, and a transport or placement phase. Articulated and contact-rich tasks such as open microwave, close laptop lid, and rotate qrcode show the gripper establishing contact and then applying a sustained motion rather than a ballistic strike. Multi-object tasks such as the stacking and ranking families, place bread basket, place cans plasticbox, and place dual shoes involve sequential subgoals, in which the second object is manipulated only after the first has been positioned. The tasks that remain difficult in the quantitative results, notably hanging mug and lift pot, are also visually harder: they require precise two-sided or handle-based contact under substantial occlusion, and their successful rollouts show a slower, more tentative approach. The remaining failures in the report are therefore concentrated in fine-grained contact and long-horizon placement rather than in gross reaching or scene understanding. RLBench.Figure 9 shows successful rollouts for the eight-task single-view suite under the evalua- tion protocol of Table 5: front camera, variation 0, and an eight-action chunk queue. The rollouts reveal several recurring behaviors. Closing tasks, including close Box, close fridge, and close laptop lid, are executed as a short contact-and-push sequence: the gripper reaches the lid or door, establishes contact, and then drives it through its range in a single continuous motion. Grasping-and-relocation tasks such as put rubbish in bin and take umbrella out of umbrella stand show a descending approach and a closed grasp before the object is lifted clear. Tool-use and placement tasks, sweep to dustpan and phone on base, require the gripper to align with a narrow target region before the state change. 21 adjust_bottlebeat_block_hammer blocks_ranking_ rgb blocks_ranking_ size click_alarmclockclick_bell dump_bin_bigbingrab_roller handover_blockhandover_mic hanging_muglift_pot move_can_pot move_pillbottle_ pad move_playingcard_ away move_stapler_pad open_laptopopen_microwave pick_diverse_ bottles pick_dual_bottles place_a2b_leftplace_a2b_right place_bread_ basket place_bread_ skillet place_burger_ fries place_can_basket place_cans_ plasticbox place_container_ plate place_dual_shoesplace_empty_cup place_fanplace_mouse_pad place_object_ basket place_object_ scale place_object_ stand place_phone_stand place_shoepress_stapler put_bottles_ dustbin put_object_ cabinet rotate_qrcodescan_object shake_bottle shake_bottle_ horizontally stack_blocks_ three stack_blocks_two stack_bowls_threestack_bowls_two stamp_sealturn_switch FARD+PCEAFARD-onlyvanilla LoRA-MoE (fallback)Four ordered keyframes per successful rollout; label is the RoboTwin 2.0 task. Figure 7: Qualitative RoboTwin 2.0 rollouts (part 1 of 2). Each row shows two tasks. Every task is labeled with its name and contributes four chronologically ordered keyframes from one successful rollout, illustrating approach, contact or grasp, and execution of the intended state change. Frames are exported at their native resolution without cropping or enhancement. C.4FAILURE ANALYSIS Despite the overall gains, we observe recurring failures in both simulation and hardware, as illustrated in Figures 10 and 11. 1) Incomplete Object Engagement: In lift pot and hanging mug the gripper topples or tilts the object instead of lifting or hanging it, and on Franka screw bottle never achieves threaded engagement. This suggests that a skill absent from every client family must be synthesized by expert composition, which can fall back to a blend of adjacent experts. 2) Stalled or Abandoned Motion: stamp seal hovers without pressing, scan object drifts away after approaching, and on Franka pour water and test tube stop short of the manipulation, consistent with weak understanding- generation consensus under self-occlusion leaving the router under-constrained. 3) Misplaced End State: put object cabinet drags the object instead of stowing it, and stack cups lands beside the base, indicating that rank-limited conversion attenuates the expert-specific component of a terminal motion. The RLBench failures in Figure 10 (bottom) differ, all ending in a motion-planning error (InvalidActionError) rather than a policy error. Overall, these cases highlight that skills absent from all clients, ambiguous routing, and lossy conversion remain the main bottlenecks, which we plan to instrument in future work. DSTATISTICAL REPORTING PROTOCOL Recent VLA and WAM work typically reports success rates over a fixed number of execution trials from a single training run rather than averaging over multiple training seeds on the simulation: for example, Motus evaluates each RoboTwin 2.0 task over100execution trials from one fine-tuned model (Bi et al., 2026), and comparable single-run protocols are used for InternVLA-A1 (Cai et al., 22 adjust_bottlebeat_block_hammer blocks_ranking_ rgb blocks_ranking_ size click_alarmclockclick_bell dump_bin_bigbingrab_roller handover_blockhandover_mic hanging_muglift_pot move_can_pot move_pillbottle_ pad move_playingcard_ away move_stapler_pad open_laptopopen_microwave pick_diverse_ bottles pick_dual_bottles place_a2b_leftplace_a2b_right place_bread_ basket place_bread_ skillet place_burger_ fries place_can_basket place_cans_ plasticbox place_container_ plate place_dual_shoesplace_empty_cup place_fanplace_mouse_pad place_object_ basket place_object_ scale place_object_ stand place_phone_stand place_shoepress_stapler put_bottles_ dustbin put_object_ cabinet rotate_qrcodescan_object shake_bottle shake_bottle_ horizontally stack_blocks_ three stack_blocks_two stack_bowls_threestack_bowls_two stamp_sealturn_switch FARD+PCEAFARD-onlyvanilla LoRA-MoE (fallback)Four ordered keyframes per successful rollout; label is the RoboTwin 2.0 task. Figure 8: Qualitative RoboTwin 2.0 rollouts (part 2 of 2). Each row shows two tasks. Every task is labeled with its name and contributes four chronologically ordered keyframes from one successful rollout, illustrating approach, contact or grasp, and execution of the intended state change. Frames are exported at their native resolution without cropping or enhancement. put_rubbish_ in_bin toilet_seat_ down take_umbrella_ out_of_umbrella_ stand close_laptop_ lid sweep_to_ dustpan close_fridge close_boxphone_on_base RLBench MoLe single-view, front camera, variation 0, chunk-queue 8; up to four ordered keyframes from a successful rollout; label gives task name and episode successes. Figure 9: Qualitative RLBench rollouts. Each row shows two tasks, each labeled with its name and the number of successful episodes out of 50, and includes up to four chronologically ordered keyframes from one successful rollout. All rollouts use the single-view interface with the front camera at variation 0 and the eight-action chunk-queue protocol. The displayed episode for each task was selected for visual clarity rather than being the longest or most representative rollout. 2026) and ForgeVLA (Zhou et al., 2026). We follow this convention: all simulation results are obtained from a single fixed training seed and a single evaluation seed, with100(RoboTwin 2.0) and 50(RLBench) trials per task, and the real-robot protocol is a fixed, scripted sequence. This keeps our results directly comparable to the benchmarks and baselines that we report. Multi-seed training with confidence intervals would strengthen the evidence for these smaller effects and is a natural direction for future work. 23 RoboTwin 2.0 failures hanging_muglift_pot place_mouse_pad put_object_ cabinet scan_objectstamp_seal RLBench failures put_rubbish_in_ bin toilet_seat_down phone_on_baseclose_laptop_lid Failed rollouts; four ordered keyframes per failure (initial scene, first attempt, visible deviation, final state); label gives task name and success count. Figure 10: Failure cases across benchmarks. RoboTwin 2.0 failures (top) and RLBench failures (bottom) contribute four chronologically ordered keyframes from one failed rollout: initial scene, first meaningful attempt, visible deviation, and final failing state. Because observations are recorded before actions and the video ends at the failure, the last frame shows the episode-terminated state. RoboFL on Franka: failed rollouts adjust_bottle pour_water screw_bottle stack_cups stamp_seal test_tube Failed real-world rollouts; four chronological keyframes per task (initial scene, first attempt, visible deviation, final state). Figure 11: Franka failure cases. Failed rollouts for six Franka tasks, with each row contributing four chronologically ordered keyframes (initial scene, first attempt, visible deviation, final state). ELIMITATIONS Our study has several limitations. First, all experiments use a single backbone (InternVLA-A1-3B) and one aligned MoT architecture. Second, we target task heterogeneity: clients differ in task distributions but share the embodiment, sensor suite, and action space, so cross-embodiment and cross-modal heterogeneity remain open questions. Finally, simulation results use a single evaluation seed, and the real-robot results use a fixed scripted protocol with 20 trials per task. 24