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LifelongCrossNav: Persistent 3D Semantic Memory for Cross-Floor Multi-Object Navigation
Zehui Li, Zihao Sun, Jiawei Xu, Zheqi He, Xiaoqiang Zhang, Jing-Shu Zheng, Lu Liu, Dahui Gao, Xiuwan Chen
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 90%
Last extracted: 8/10/2026, 4:11:11 AM
Summary
LifelongCrossNav is a framework for sequential multi-object ObjectNav in unknown multi-floor indoor environments. It utilizes a shared sparse 3D semantic voxel memory to accumulate geometric structure, traversability states, and vision-language features, enabling persistent search across floors. The system integrates support-aware 3D traversability mapping, stair-specific perception, and a unified navigation policy. The authors also introduce HM3D-MFMON, a benchmark for sequential Multi-Floor Multi-Object Navigation built on HM3D scenes, demonstrating that LifelongCrossNav outperforms planar persistent semantic-map baselines.
Entities (10)
Relation Signals (6)
HM3D-MFMON → builton → HM3D
confidence 95% · HM3D-MFMON, a benchmark for sequential Multi-Floor Multi-Object Navigation built on HM3D scenes
LifelongCrossNav → uses → 3D Semantic Voxel Memory
confidence 95% · LifelongCrossNav... continuously maintaining a shared sparse 3D semantic voxel memory.
LifelongCrossNav → supports → cross-floor navigation
confidence 92% · To support persistent search across floors, LifelongCrossNav combines support-aware 3D traversability mapping, stair-specific perception
LifelongCrossNav → outperforms → planar persistent semantic-map baseline
confidence 90% · LifelongCrossNav consistently outperforms a representative planar persistent semantic-map baseline on HM3D-MFMON
SED → usedin → LifelongCrossNav
confidence 85% · We adopt SED-based dense vision-language encoding... LifelongCrossNav stores goal-independent vision-language features
YOLOv7 → usedin → LifelongCrossNav
confidence 85% · we employ YOLOv7... for the six HM3D ObjectNav target categories
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Abstract
Abstract:Object-goal navigation has made substantial progress in semantic perception and exploration, yet persistent memory for multi-object navigation and cross-floor navigation are still commonly addressed separately. We present LifelongCrossNav, a framework for sequential multi-object ObjectNav in unknown multi-floor indoor environments. Within each episode, the agent receives an ordered sequence of object-goal queries while continuously maintaining a shared sparse 3D semantic voxel memory. This memory incrementally accumulates geometric structure, traversability states, and vision-language features, allowing subsequent object-goal queries to retrieve previously acquired scene information without rebuilding the map. To support persistent search across floors, LifelongCrossNav combines support-aware 3D traversability mapping, stair-specific perception, and direction-aware stair traversal. A unified navigation policy coordinates same-floor frontier exploration, live and historical point-of-interest retrieval, stair navigation, and target-object search and approach. We further introduce HM3D-MFMON, a benchmark for sequential Multi-Floor Multi-Object Navigation built on HM3D scenes, including a dedicated subset in which completing the full sequence of object-goal subtasks requires at least one floor transition. Experimental results show that LifelongCrossNav consistently outperforms a representative planar persistent semantic-map baseline on HM3D-MFMON, demonstrating that persistent 3D semantic memory and cross-floor traversability modeling effectively support sequential multi-object navigation in multi-floor environments. Project page: this https URL.
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- Source: https://arxiv.org/abs/2608.07079v1
- Canonical: https://arxiv.org/abs/2608.07079v1
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LifelongCrossNav: Persistent 3D Semantic Memory for Cross-Floor Multi-Object Navigation Zehui Li1,*, Zihao Sun1,*, Jiawei Xu1, Zheqi He2,†, Xiaoqiang Zhang1,†, Jing-Shu Zheng2, Lu Liu2, Dahui Gao2, Xiuwan Chen1 Abstract Object-goal navigation has made substantial progress in semantic perception and exploration, yet persistent memory for multi-object navigation and cross-floor navigation are still commonly addressed separately. We present LifelongCrossNav, a framework for sequential multi-object ObjectNav in unknown multi-floor indoor environments. Within each episode, the agent receives an ordered sequence of object-goal queries while continuously maintaining a shared sparse 3D semantic voxel memory. This memory incrementally accumulates geometric structure, traversability states, and vision-language features, allowing subsequent object-goal queries to retrieve previously acquired scene information without rebuilding the map. To support persistent search across floors, LifelongCrossNav combines support-aware 3D traversability mapping, stair-specific perception, and direction-aware stair traversal. A unified navigation policy coordinates same-floor frontier exploration, live and historical point-of-interest retrieval, stair navigation, and target-object search and approach. We further introduce HM3D-MFMON, a benchmark for sequential Multi-Floor Multi-Object Navigation built on HM3D scenes, including a dedicated subset in which completing the full sequence of object-goal subtasks requires at least one floor transition. Experimental results show that LifelongCrossNav consistently outperforms a representative planar persistent semantic-map baseline on HM3D-MFMON, demonstrating that persistent 3D semantic memory and cross-floor traversability modeling effectively support sequential multi-object navigation in multi-floor environments. Project page: https://flageval-baai.github.io/LifelongCrossNavPage. 1 Introduction Object-Goal Navigation (ObjectNav) requires an embodied agent to explore an unseen environment and navigate to an instance of a specified object category. Recent advances in open-vocabulary perception, semantic mapping, and frontier-based exploration have substantially improved target search in unseen scenes (Duan et al. 2022; Sun et al. 2025; Liu et al. 2025). However, most existing studies remain centered on single-object navigation in planar or single-floor environments, whereas real indoor agents may need to search for multiple objects in sequence and move between floors, as illustrated in Fig. 1. Figure 1: Conceptual illustration of sequential multi-object ObjectNav in a multi-floor environment. The agent navigates from Start to Goal 1 (TV), Goal 2 (bed), and Goal 3 (toilet) in order. The colored trajectories denote consecutive object-goal subtasks, including cross-floor traversal through the staircase. Existing research largely addresses these requirements separately. Cross-floor methods model stairs, floor transitions, or floor-level reasoning, but generally consider only one object goal (Gong et al. 2026; Zheng et al. 2026). Multi-object navigation instead retains environmental information across a sequence of object goals (Wani et al. 2020; Busch et al. 2025). In this setting, the agent receives only the current object goal, and the next one is revealed after the current object-goal subtask is completed. We use lifelong to denote this within-episode setting, in which the environment and accumulated memory persist across sequential object-goal subtasks. Nevertheless, existing multi-object methods primarily rely on planar representations or avoid goal sequences that require stair traversal. Planar maps may collapse vertically overlapping spaces, while single-object cross-floor methods need not preserve queryable semantic observations for future object goals. A unified solution must therefore support both vertical traversability and persistent semantic memory. To address this gap, we present LifelongCrossNav, a framework for sequential multi-object ObjectNav in unknown multi-floor indoor environments. It maintains a shared sparse 3D voxel representation that combines support-aware geometry with goal-independent vision-language features. The stored features can be re-queried when a new object goal is issued, while a unified navigation policy coordinates same-floor exploration, stair traversal, semantic retrieval, and final target-object approach through mode-aware 3D planning. We further introduce HM3D-MFMON, a benchmark for sequential multi-object navigation in multi-floor HM3D scenes. To handle multiple valid target object instances and agent-dependent subtask starting positions, we adopt a post-hoc stage-wise shortest-path protocol and conditional metrics that evaluate agents reaching each successive object-goal subtask. Our contributions are threefold: • We introduce HM3D-MFMON, comprising 927 three-goal episodes from 36 multi-floor HM3D scenes, including 288 Cross-Floor-Required episodes, together with a post-hoc evaluation protocol for multi-instance sequential navigation. • We propose LifelongCrossNav, which unifies support-aware 3D voxel mapping, persistent vision-language memory, stair-aware navigation, and historical semantic retrieval in a closed-loop system. • Experiments demonstrate improved multi-object and cross-floor navigation over a persistent planar semantic-memory baseline, while History POIs improve path efficiency for later object goals. 2 Related Work Open-Vocabulary Semantic Navigation Early ObjectNav methods combined semantic perception with explicit spatial memory. Goal-Oriented Semantic Exploration, for example, projects object detections into a semantic map and uses frontier-based exploration for long-horizon navigation (Batra et al. 2020; Chaplot et al. 2020). More recent methods use pretrained vision-language models to support zero-shot or open-vocabulary target search. ZSON aligns object goals with visual observations through multimodal goal embeddings, while VLFM scores exploration frontiers using vision-language relevance (Majumdar et al. 2022; Yokoyama et al. 2024). OpenFMNav and SG-Nav further incorporate foundation models or online 3D scene graphs for semantic reasoning (Kuang et al. 2024; Yin et al. 2024). These methods improve generalization to unseen object categories, but they primarily evaluate single-object navigation and do not focus on retaining semantic memory across successive object goals. Multi-Object Navigation and Persistent Memory Multi-object navigation extends ObjectNav from one object goal to an ordered sequence of object goals within the same environment. MultiON introduced this setting to evaluate semantic mapping and memory over successive target searches (Wani et al. 2020). GOAT-Bench further studies lifelong navigation with object-category, image, and language goals, emphasizing the reuse of experience without resetting the environment (Khanna et al. 2024). OneMap addresses zero-shot multi-object navigation by maintaining a reusable open-vocabulary feature map that can be queried again when a new object goal is issued (Busch et al. 2025). These works demonstrate that persistent scene memory can reduce repeated exploration and improve later-goal efficiency. However, their navigation representations are primarily planar or bird’s-eye-view maps and do not explicitly model stairs, vertically overlapping spaces, or traversable connections between floors. Cross-Floor Navigation and 3D Representation Cross-floor ObjectNav considers environments in which the agent and a target object instance may lie on different floors. MFNP uses multimodal reasoning and floor-transition policies for multi-floor target search (Zhang et al. 2025a), while ASCENT combines a multi-floor spatial abstraction with stair-aware, coarse-to-fine exploration (Gong et al. 2026). TravExplorer instead maintains a unified traversability-aware 3D representation of floors, stairs, and landings, allowing cross-floor paths to be planned directly through connected support surfaces (Zheng et al. 2026). Related 3D semantic mapping work, such as BeliefMapNav, shows that voxel maps can also organize object-location priors, online observations, and semantic uncertainty (Zhou et al. 2025). 3 Method Task Formulation Each episode is defined by an ordered sequence of K object goals (g1,…,gK)(g_1,…,g_K). Following sequential multi-object navigation, the agent receives only the current object goal gkg_k; the next object goal gk+1g_k+1 is revealed and activated only after the current object-goal subtask has been successfully completed (Wani et al. 2020). At each time step t, the agent receives an egocentric RGB observation ItI_t, a depth observation DtD_t, the 6-DoF camera pose TtT_t, and the current object goal gkg_k. The discrete action space contains MoveForward, TurnLeft, TurnRight, LookUp, LookDown, and Stop. MoveForward advances the agent by 0.250.25 m, while turning and camera pitch actions change the corresponding orientation by 30∘30 . A subtask is successful when the agent issues Stop within the success threshold of a valid target object instance. Within an episode, LifelongCrossNav retains the 3D geometric map, stair states, and goal-independent vision-language voxel features across object goals. When a new object goal is issued, its text embedding and query-conditioned similarity field are recomputed, while the POIs, navigation path, and goal-verification states associated with the previous object goal are reinitialized. An overview of LifelongCrossNav is shown in Fig. 2. Figure 2: Overview of LifelongCrossNav. Given RGB-D observations, the agent pose, and the current goal text, the system jointly updates a support-aware 3D voxel map and persistent 3D semantic memory. The geometric branch constructs multi-floor traversability from observed surfaces, ray-cast free space, and semantic-geometric stair evidence, while the semantic branch lifts and fuses goal-independent vision-language features into 3D surface voxels. The unified navigation policy selects among Basic Frontiers, Stair Frontiers, History POIs, and Live POIs and performs mode-aware 3D planning for basic exploration, stair exploration, POI navigation, and final object approach. After the current object goal is completed, the accumulated environmental memory is retained and the next object goal is activated. Support-Aware 3D Voxel Mapping LifelongCrossNav represents the environment using a sparse 3D voxel map. In contrast to planar projection, this representation preserves height and distinguishes vertically overlapping rooms, corridors, landings, and staircases. Inspired by traversability-aware ray-casting approaches (Zheng et al. 2026), the map combines RGB-D geometry, vertical support relationships, and stair-semantic evidence to represent executable connections across floors. RGB-D Projection and Sparse Voxelization. Valid depth pixels are back-projected into the camera coordinate system, transformed into the world frame using the 6-DoF camera pose, and quantized into sparse voxels. Depth-ray endpoints provide observed surface evidence, whereas intermediate ray locations provide free-space evidence. Only observed voxels and locally inferred navigation states are stored, allowing the map to grow incrementally with the explored space. Support-Aware Voxel Types. The navigation map abstracts the observed space into four functional voxel types: Occupied, Traversable, Stair, and Unsupported. Occupied voxels represent observed surfaces, including walls, furniture, floors, and stair candidates that have not yet been confirmed. For each ray-observed free-space voxel, the system searches downward within a local vertical range. Free space with reliable support is classified as Traversable, whereas free space without observed support is classified as Unsupported and provides geometric evidence for potential downward transitions. Stair voxels represent stair surfaces confirmed jointly by semantic and geometric observations. SegFormer-B2 (Xie et al. 2021) extracts a pixel-level stair mask, which is lifted into 3D using depth and camera pose and verified through local height variation, step trends, spatial continuity, and support relationships. Stair voxels are updated only after the system enters Stair Explore, where they form an explicit traversable connection between floors. Persistent 3D Semantic Memory LifelongCrossNav stores goal-independent vision-language features in the same sparse 3D coordinate system and re-queries them whenever the active object goal changes. Dense Vision-Language Feature Encoding. We adopt SED-based dense vision-language encoding (Xie et al. 2024). Given the current RGB observation, the encoder produces a 24×24×76824× 24× 768 spatial feature map aligned with the CLIP text-embedding space. The feature map is bilinearly upsampled to the depth resolution, and each valid depth pixel is associated with a local-contextual visual feature. Feature Lifting and Cumulative Fusion. Pixel features are lifted to the 3D surface voxels reached by their corresponding depth rays. Features are assigned only to observed surfaces and are not propagated through free-space voxels. When multiple pixels in the same frame are quantized into voxel v, their features are aggregated using observation-quality weights: ¯(t)=∑p∈qpp∑p∈qp+ϵ, f_v^(t)= _p _vq_pf_p _p _vq_p+ε, (1) where P_v is the set of pixels assigned to voxel v, pf_p is the corresponding visual feature, and qpq_p reflects the observation quality. Let (t−1)F_v^(t-1) and C(t−1)C_v^(t-1) denote the stored feature and accumulated confidence, and let c(t)c_v^(t) denote the confidence of the current per-frame observation. Multi-view observations are fused using a cumulative weighted average: (t) _v^(t) =C(t−1)(t−1)+c(t)¯(t)C(t−1)+c(t), = C_v^(t-1)F_v^(t-1)+c_v^(t) f_v^(t)C_v^(t-1)+c_v^(t), (2) C(t) C_v^(t) =C(t−1)+c(t). =C_v^(t-1)+c_v^(t). Query-Conditioned 3D Retrieval. When an object goal is activated, its text embedding is compared with the stored surface-voxel features using cosine similarity. The resulting responses form a query-conditioned 3D similarity field without rebuilding the geometric or semantic map. High-response historical regions are grouped using 3D neighborhood clustering, after which the Top-K candidates are retained as History POIs and assigned nearby reachable navigation positions. Unified Navigation Policy The unified policy selects navigation targets from Basic Frontiers, Stair Frontiers, History POIs, and Live POIs. These candidates support three navigation modes: Basic Explore, Stair Explore, and POI Navigation. Candidate Navigation Points. Basic Frontiers denote the three planar candidate types used during ordinary exploration, as shown in Fig. 3. Traversable Frontiers are formed at boundaries between Traversable voxels and unknown space. Descend Frontiers are extracted near boundaries between Traversable and Unsupported voxels and indicate potential downward transitions. Ascent Frontiers are generated from stair-semantic evidence, RGB-D step geometry, and multi-frame consistency, with their navigation positions remaining on the current exploration plane near a potential ascending entrance. Figure 3: Basic Frontier types and their default priority: ① Traversable, ② Descend, and ③ Ascent. The dashed staircase denotes unexplored cross-floor structure. Stair Frontiers are direction-aware advancing boundaries extracted from the currently confirmed stair-voxel cluster. Their heights change with the observed staircase, allowing the agent to continue exploring upward or downward within the stair structure. History POIs are obtained by querying the persistent vision-language voxel memory with the current goal text, thereby supporting semantic retrieval beyond a fixed detector label set. Live POIs are generated through a configurable target-detection interface. Following OneMap (Busch et al. 2025), we employ YOLOv7 (Wang et al. 2023) for the six HM3D ObjectNav target categories, which are covered by MS-COCO, and switch to YOLO-World (Cheng et al. 2024) for queries outside this category set. MobileSAM (Zhang et al. 2023) extracts the detected-object mask, while depth and pose recover its 3D location. Hierarchical Mode Switching and 3D Planning. Reliable current target evidence and reachable POIs are prioritized over unexplored geometric candidates. When no valid semantic candidate is available, Basic Explore first visits Traversable Frontiers on the current floor. Descend and Ascent Frontiers are considered only after no reachable ordinary frontier remains. Once a stair entrance has been verified, the policy activates Stair Explore and follows Stair Frontiers until a new landing is reached. An active stair session retains control so that stair traversal is not interrupted by ordinary frontiers or unrelated semantic candidates. All modes use a common 3D A* planner but differ in admissible voxel types and graph connectivity. Basic Explore uses a strict 26-neighbor graph over the current traversable region. POI Navigation uses the regular graph together with previously established stair connectivity when the selected POI lies on another floor. Stair Explore admits confirmed Stair voxels and expands the endpoint neighborhood within a fixed physical radius to connect staircase observations that may be sparse in the voxel map. Final Target-Object Approach and Verification. Once stable target-object evidence is obtained, the detected mask is projected into 3D and a nearby safe observation position is selected. During the approach, the system updates the detection and verifies the target object using detection confidence, mask quality, visibility, viewing direction, and 3D distance. Reaching either a History POI or a Live POI does not by itself complete the subtask; a current target-object observation must still pass the verification criteria. After successful verification, the next object goal is activated while the geometric map, stair structure, and goal-independent semantic memory are retained. If verification fails, the system returns to candidate selection and continues exploration. 4 Experimental Setup HM3D-MFMON Benchmark We construct HM3D-MFMON from HM3D v0.2 and its semantic annotations (Ramakrishnan et al. 2021; Yadav et al. 2023). HM3D provides semantically annotated indoor scenes with realistic multi-floor layouts and navigable stair connections, while remaining compatible with established Habitat ObjectNav protocols. Following the sequential task formulation of MultiON (Wani et al. 2020), each episode contains three sequentially issued object goals. The agent receives only the current object goal and is informed of the next one after successfully completing the current object-goal subtask. HM3D-MFMON includes six target object categories: chair, bed, toilet, plant, sofa, and tv_monitor. All valid instances of the current target object category are retained, and reaching any instance that satisfies the success criterion completes the corresponding subtask. We select 36 HM3D scenes with valid multi-floor structures and stair connectivity and generate 927 three-goal episodes. By verifying target-instance distributions and navigable connectivity, we identify a Cross-Floor-Required (CFR) subset of 288 episodes whose complete object-goal sequences cannot be completed without at least one floor transition. Post-hoc Multi-Object Evaluation Protocol Post-hoc Stage-Wise Shortest-Path Evaluation. In standard single-object ObjectNav, the episode start and target object category are fixed, allowing the shortest geodesic distance to the nearest valid target instance to be computed before navigation (Batra et al. 2020). This assumption does not directly extend to sequential multi-object navigation with multiple valid instances. The start of a later subtask depends on the target object instance selected for the previous object goal and on the position from which that subtask was completed. A globally optimized route over the complete object-goal sequence could resolve this ambiguity, but such a route uses future object goals that have not yet been issued. It may therefore favor a non-nearest instance of the current target category solely because that instance is closer to a future goal, violating the causal information constraint of the sequential task. Figure 4 illustrates the difference between such an oracle route and the proposed stage-wise evaluation. Figure 4: Post-hoc stage-wise shortest-path evaluation. A globally optimized route may depend on future object goals that are unavailable to the agent. For episode i, let i,kstartx^start_i,k denote the actual agent position when the k-th object goal gi,kg_i,k is activated. For the first subtask, this is the episode start; for later subtasks, it is obtained from the executed trajectory after the preceding object goal has been completed. Let i(gi,k)X_i(g_i,k) denote the valid navigable observation positions associated with all instances of the current target object category. We compute the stage-wise reference distance as di,k∗=min∈i(gi,k)dgeo(i,kstart,),d^*_i,k= _x _i(g_i,k)d_geo (x^start_i,k,x ), (3) where dgeod_geo denotes geodesic distance on the navigation mesh. This reference depends only on the actual stage start, the current object goal, and its valid target instances; it does not use future object goals. Different agents can therefore be evaluated using shortest paths consistent with the target object instances selected during their preceding subtasks. Per-Goal and Sequence-Level Metrics. Let SRi,k∈0,1SR_i,k∈\0,1\ indicate whether episode i successfully completes its k-th object-goal subtask, and let li,kl_i,k denote the path length executed during that subtask. Its per-goal path efficiency is SPLi,k=SRi,kdi,k∗max(di,k∗,li,k).SPL_i,k=SR_i,k d^*_i,k (d^*_i,k,l_i,k ). (4) For stage-wise dataset aggregation, an unexecuted subtask is assigned zero SR and SPL, while it remains distinguishable from an executed failure in the recorded episode results. Following MultiON (Wani et al. 2020), we report sequence-level Success Rate (SR), Success weighted by Path Length (SPL), Progress Rate (PR), and Progress weighted by Path Length (PPL). PR measures the fraction of completed object goals, while PPL weights the successfully completed prefix by its path efficiency. Stage-Wise Conditional Evaluation. Sequence-level metrics do not reveal how performance changes across successive object goals. Inspired by the stage-wise analysis of semantic-memory reuse in OneMap (Busch et al. 2025), we therefore report Conditional SR and Conditional SPL for each object-goal index. Under our sequential termination protocol, the k-th subtask is executed only when all preceding object goals have been completed. By defining SRi,0=1SR_i,0=1, the number of episodes that reach stage k is ∑i=1NSRi,k−1 _i=1^NSR_i,k-1. Conditional performance is therefore SRkcond=∑i=1NSRi,k∑i=1NSRi,k−1,SRi,0=1,SR^cond_k= _i=1^NSR_i,k _i=1^NSR_i,k-1, _i,0=1, (5) and SPLkcond=∑i=1NSPLi,k∑i=1NSRi,k−1.SPL^cond_k= _i=1^NSPL_i,k _i=1^NSR_i,k-1. (6) Conditional metrics evaluate success and efficiency only among episodes that reach stage k. Conditional SPL is particularly useful for examining whether later object goals are reached more efficiently as geometric and semantic memory accumulates. For completeness, the stage-wise Global metrics average over all N episodes, with unexecuted subtasks contributing zero: SRkglobal=1N∑i=1NSRi,k,SPLkglobal=1N∑i=1NSPLi,k.SR^global_k= 1N _i=1^NSR_i,k, ^global_k= 1N _i=1^NSPL_i,k. (7) Under the sequential termination protocol, these metrics are directly related to their Conditional counterparts: SRkglobal=SRk−1globalSRkcond,SPLkglobal=SRk−1globalSPLkcond,SR0global=1. aligned SR^global_k&=SR^global_k-1SR^cond_k,\\ SPL^global_k&=SR^global_k-1SPL^cond_k, aligned ^global_0=1. (8) Global metrics additionally incorporate the probability of reaching stage k and are used only to distinguish stage-conditioned performance from preceding failures. We focus on Conditional SR and Conditional SPL in the main text and report Global results in the supplementary material. Sequence-level SR, SPL, PR, and PPL summarize complete and partial episode progress. Baselines and Evaluation Settings Multi-Object Navigation. For sequential multi-object navigation, OneMap serves as the primary baseline because it maintains a persistent open-vocabulary 2D semantic map that can be reused across successive object goals (Busch et al. 2025). OneMap and LifelongCrossNav are evaluated under the same task and evaluation settings described above. To isolate the effect of historical semantic retrieval, we additionally evaluate a variant denoted as w/o H-POI. This variant disables only History POI generation, while retaining the support-aware 3D voxel map, accumulated vision-language features, and all cross-floor navigation components. Single-Object Navigation. As an auxiliary evaluation, we follow the OneMap setting and evaluate LifelongCrossNav on the HM3D ObjectNav validation split, which contains 2,000 episodes over six target object categories (Yadav et al. 2023). We compare against representative task-specific, zero-shot, open-vocabulary, and floor-aware ObjectNav methods, including SGMT (Zhang et al. 2024), XGX (Wasserman et al. 2024), ZSON (Majumdar et al. 2022), VLFM (Yokoyama et al. 2024), SG-Nav (Yin et al. 2024), OpenFMNav (Kuang et al. 2024), OneMap (Busch et al. 2025), InstructNav (Long et al. 2025), ApexNav (Zhang et al. 2025b), BeliefMapNav (Zhou et al. 2025), MFNP (Zhang et al. 2025a), and ASCENT (Gong et al. 2026). Each episode contains one object goal, and performance is measured using standard SR and SPL. The experiments follow the six-category HM3D ObjectNav setting and therefore use YOLOv7 for target-object detection. All evaluations are conducted on a single NVIDIA RTX 5090 GPU. 5 Experimental Results Multi-Object Navigation Overall Performance. As shown in Table 1, LifelongCrossNav substantially improves sequence completion and partial progress over the planar semantic-memory baseline. Disabling History POI generation mainly reduces SPL and PPL, indicating that historical semantic retrieval mitigates repeated exploration during later object-goal subtasks. The slightly higher SR and PR of w/o H-POI are examined in the Failure Analysis. Stage-Wise Results on All Episodes. Figure 5 reports Conditional SR and Conditional SPL for the three sequential object goals. LifelongCrossNav maintains higher Conditional SR than OneMap throughout the sequence, showing that its 3D representation supports more object-goal subtasks involving vertical-space exploration. Both persistent-memory methods become more path-efficient on later goals, whereas the w/o H-POI variant remains nearly unchanged. This contrast shows that the later-stage efficiency gain arises primarily from reusing historical semantic observations rather than from geometric exploration alone. Cross-Floor-Required Evaluation. As shown in Table 2, OneMap can complete some preceding subtasks but cannot complete any full Cross-Floor-Required sequence. LifelongCrossNav achieves nonzero sequence success and stronger partial progress, demonstrating that persistent planar memory alone is insufficient when task completion requires explicit stair traversal and cross-floor connectivity. The stage-wise results in Fig. 6 show that OneMap cannot complete the remaining object-goal subtasks once cross-floor traversal becomes necessary. In the CFR subset, episodes that successfully reach later stages have already completed previous same-floor subtasks; therefore, the remaining target is more likely to require the unresolved floor transition. Without explicit stair representation and cross-floor connectivity, the planar semantic map cannot provide an executable solution for these cases. Method SR ↑ SPL ↑ PR ↑ PPL ↑ OneMap 16.83 6.95 33.69 14.03 w/o H-POI 29.77 8.46 48.54 14.91 LifelongCrossNav 29.13 9.64 48.40 16.70 Table 1: Overall multi-object navigation results on all 927 HM3D-MFMON episodes. Figure 5: Stage-wise conditional performance on all 927 HM3D-MFMON episodes. Unlike the trend over all episodes, Conditional SPL does not increase monotonically on the CFR subset because later goals may still require unseen-floor exploration and additional stair traversal. Nevertheless, the complete framework remains more efficient than both OneMap and w/o H-POI on later stages, indicating that historical semantic retrieval remains useful after floor transitions. Method SR ↑ SPL ↑ PR ↑ PPL ↑ OneMap 0.00 0.00 18.52 7.97 w/o H-POI 7.29 1.91 28.94 9.16 LifelongCrossNav 7.99 2.35 29.17 9.75 Table 2: Overall multi-object navigation results on the 288 Cross-Floor-Required episodes. Figure 6: Stage-wise conditional performance on the 288 Cross-Floor-Required episodes. Single-Object Navigation Method Zero-shot Multi-Floor LLM Reasoning SR ↑ SPL ↑ SGM × × × 60.2 30.8 XGX × × × 72.9 35.7 ZSON ✓ × × 25.5 12.6 VLFM ✓ × × 52.5 30.4 SG-Nav ✓ × ✓ 54.0 24.9 OpenFMNav ✓ × ✓ 54.9 24.4 OneMap ✓ × × 55.8 37.4 InstructNav ✓ × ✓ 58.0 20.9 ApexNav ✓ × ✓ 59.6 33.0 BeliefMapNav ✓ × ✓ 61.4 30.6 MFNP ✓ ✓ ✓ 58.3 26.7 ASCENT ✓ ✓ ✓ 65.4 33.5 LifelongCrossNav ✓ ✓ × 59.7 28.0 Table 3: Single-object navigation results on HM3D. Table 3 shows that LifelongCrossNav retains competitive single-object success without online LLM reasoning. Compared with OneMap, its higher SR but lower SPL reflects a multi-floor policy that prioritizes current-floor exploration before activating cross-floor candidates. Failure Analysis The slightly higher SR and PR of w/o H-POI in Table 1 do not constitute a reliable success advantage. Paired episode analysis attributes this difference to a limited number of outcome reversals after History POI retrieval changes the selected target-object instance or approach viewpoint. The category-wise distributions in Tables 4 and 5 further show that History POIs change the composition of navigation failures: they reduce failures caused by local planning, incomplete exploration, and unreachable candidates, but increase false target-object detections. Out-of-time failures remain broadly comparable between the two settings. Object Total Success Failure Misdetection Failure Stuck Failure OOT Failure Not Reached Failure All Explored chair 363 323 13 17 9 0 1 toilet 345 267 24 20 27 0 7 sofa 372 239 84 27 14 3 5 tv_monitor 291 180 30 16 50 14 1 plant 276 155 8 43 59 1 10 bed 356 182 163 3 3 4 1 Table 4: Object-wise outcome counts for LifelongCrossNav. Object Total Success Failure Misdetection Failure Stuck Failure OOT Failure Not Reached Failure All Explored chair 362 323 10 17 10 0 2 toilet 338 261 23 24 20 0 10 sofa 376 243 73 33 18 3 6 tv_monitor 290 174 28 23 48 13 4 plant 277 148 8 53 58 2 8 bed 358 201 133 8 9 6 1 Table 5: Object-wise outcome counts for w/o H-POI. The additional misdetections are concentrated primarily on bed. History POIs can direct the agent toward alternative object instances and approach viewpoints, from which YOLOv7 occasionally confuses beds with visually similar sofas. These false detections trigger unnecessary approaches and failed target verification, offsetting part of the navigation benefit gained from historical semantic retrieval. Outside bed, category-level success is generally preserved or improved, with a marginal reduction for sofa. In particular, the reductions in stuck and incomplete-exploration failures indicate that History POIs provide more informative navigation targets and reduce repeated geometric exploration. Their consistent gains in SPL, PPL, and later-stage Conditional SPL therefore provide clearer evidence of improved path efficiency, while also highlighting target verification as the main remaining source of error. 6 Conclusion In this work, we introduced LifelongCrossNav for sequential multi-object ObjectNav in unknown multi-floor environments. LifelongCrossNav combines support-aware 3D voxel mapping, persistent vision-language semantic memory across object goals, and a unified policy for planar exploration and stair navigation, enabling the agent to jointly exploit vertical structure, cross-floor connectivity, and historical semantic observations. 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Appendix A Computational Environment All reported experiments were conducted using the software and hardware environment summarized in Table 6. The CUDA version listed below refers to the runtime bundled with PyTorch, rather than the version reported by the host GPU driver. Appendix B Experimental Configuration Each HM3D-MFMON episode contains three sequential object-goal queries. The sparse geometric map and goal-independent SED/CLIP features persist across queries within the same episode. Query-conditioned similarity scores, POIs, active paths, frontier selections, and controller states are refreshed when the active object goal changes. All states are reset between independent episodes. Table 7 summarizes the frozen settings used for the reported experiments. The internal target-approach range is a policy parameter, whereas the evaluator success radius is used only for ground-truth success assessment. Appendix C Persistent 3D Semantic Memory Dense Feature Projection and Fusion For each RGB frame, the SED image encoder produces a spatial feature tensor tdense∈ℝ24×24×768.F_t^dense ^24× 24× 768. (9) The feature tensor is bilinearly interpolated to the depth resolution. Each valid depth pixel is then back-projected with the camera intrinsics and transformed into the global frame using the 6-DoF camera pose. Consequently, features are written only to observed surface voxels rather than being copied uniformly over free space. For pixel (u,v)(u,v), the observation quality is qt(u,v)= q_t(u,v)= [1−tanh(γ‖∇Dt(u,v)‖)] [1- \! (γ \|∇ D_t(u,v) \| ) ] (10) ×exp[−(d0−Dt(u,v))23σd2]. × \! [- (d_0-D_t(u,v))^23 _d^2 ]. Depth discontinuities and observations far from the preferred range therefore receive smaller weights. If voxel v has accumulated feature vt−1f_v^t-1 and confidence wvt−1w_v^t-1, the new observation is fused using vt _v^t =wvt−1vt−1+qvtv,obstwvt−1+qvt, = w_v^t-1f_v^t-1+q_v^tf_v,obs^tw_v^t-1+q_v^t, (11) wvt w_v^t =wvt−1+qvt. =w_v^t-1+q_v^t. This is a cumulative weighted average rather than an exponential moving average. The fused features and confidence values persist across object-goal subtasks within an episode. Query-Conditioned Retrieval For the active object-goal text q, the normalized text embedding qt_q is compared with every feature-bearing voxel: sq(v)=v⊤q‖v‖2‖q‖2.s_q(v)= f_v t_q\|f_v\|_2\|t_q\|_2. (12) The resulting 3D similarity field is query-dependent and is not part of the persistent memory itself. Spatially consistent high-similarity responses are clustered, and the four highest-ranked clusters form the initial History-POI candidate set. When the active object goal changes, the stored voxel features remain unchanged, whereas the similarity field and History POIs are recomputed for the new text query. Component Tested value OS Ubuntu 22.04, Linux 6.8 Python 3.10.20 PyTorch / torchvision 2.11.0+cu128 / 0.26.0+cu128 CUDA runtime used by PyTorch 12.8 GPU used for paper runs NVIDIA GeForce RTX 5090, 32 GB Habitat-Sim / Habitat-Lab 0.2.4 / 0.2.4 Transformers 4.26.1 OpenCV / NumPy 4.8.0 / 1.26.4 Detectron2 / timm 0.6 / 1.0.26 Rerun SDK 0.23.1 Table 6: Software and hardware environment used for the reported experiments. Group Parameter Value Group Parameter Value Sensor RGB/depth resolution 640×640640\!×\!640 Map Metric XY extent 60×6060\!×\!60 m Sensor Horizontal field of view 90∘90 Map Voxel resolution (XYZ) 0.10 m Sensor Camera height 0.88 m Map Indexed Z extent approx. ±30± 30 m Action Forward step 0.25 m Map Inflation radius 0.20 m Action Yaw/pitch increment 30∘30 Map Support search depth 0.40 m SED Encoder input 768×768768\!×\!768 SED Dense output 24×24×76824\!×\!24\!×\!768 Fusion Depth-gradient factor γ 0.20 Fusion Preferred depth d0d_0 1.0 m Fusion Depth scale σd _d 1.5 m History POI Retrieved clusters Top-4 History POI Blacklist cylinder 0.8 m XY, 0.6 m Z POI Live takeover radius 1.0 m Object YOLOv7 confidence 0.70 Object Secondary confidence 0.60 Object Found confidence 0.70 Object Minimum box area 1/641/64 image Object Minimum projected voxels 10 Object Target-approach range 1.30 m Stair SegFormer pixel threshold 0.25 Stair Minimum component area 80 px Stair Descent confirmation 0.48 Stair Geometry threshold 0.65 Frontier Normal minimum cluster 5 Frontier Init./descent minimum cluster 2 StairSem Session admission radius 2.5 m StairSem Arrival threshold 0.40 m Planner Normal graph 26-neighbor Planner StairSem edge radius 1.0 m Evaluation Episode action budget 1200 Evaluation Success radius 1.50 m Navmesh Agent height/radius 1.50/0.10 m Navmesh Maximum climb/slope 0.30 m/60∘60 Navmesh Cell size/height 0.03/0.05 m Dataset Goals/categories 3/6 Table 7: Frozen configuration used for the reported LifelongCrossNav experiments. Appendix D Support-Aware Voxel States The sparse map maintains seven operational voxel states. Surface states store observed geometry, while air states represent the volume occupied by the agent above a supporting surface. Table 8 summarizes their construction and planning roles. Voxel state Construction and geometric interpretation Pathable Targetable Planning role OCCUPIED Surface voxel produced by a valid RGB-D depth return. It represents walls, furniture, ordinary floors, and other observed geometry and may carry a semantic feature. No No Collision geometry and ordinary support. TRAVERSABLE Ray-observed free-space voxel whose first valid support within 0.40 m is OCCUPIED or reversible FAKE_STAIR. Yes Yes Primary state for same-floor navigation. TRAVERSABLE_STAIR Free-space voxel whose first valid support is STAIR or STAIR_EXPANDED. Yes Yes Robot occupancy above a confirmed stair surface. TRAVERSABLE_FAKE Ray-observed free-space voxel for which no valid support is found within the support-search depth. No No Marks unsupported air, drop-offs, or stair voids. STAIR Surface voxel accepted as stair geometry after semantic and 3D geometric verification. Yes Yes Confirmed stair body used during StairSem. STAIR_EXPANDED Neighboring OCCUPIED voxel assimilated into a confirmed stair component to improve sparse geometric continuity. Yes Yes Complements incomplete stair observations with a higher planning cost. FAKE_STAIR Rejected or reversible stair evidence retained instead of being immediately discarded. Fallback No High-cost temporary connection and reversible support state. Table 8: Operational voxel states and their roles in mapping and planning. Support Classification Depth returns are first inserted as OCCUPIED. Ray casting creates observed free-space samples, after which support is searched vertically below each sample. Let s(v)s(v) denote the first valid support type found below voxel v. We define the ordinary-support and stair-support sets as ord=OCCUPIED,FAKE_STAIRS_ord=\ OCCUPIED, FAKE\_STAIR\ and stair=STAIR,STAIR_EXPANDEDS_stair=\ STAIR, STAIR\_EXPANDED\, respectively. The derived air state is then determined by τair(v)=TRAVERSABLE,s(v)∈ord,TRAVERSABLE_STAIR,s(v)∈stair,TRAVERSABLE_FAKE,s(v)=∅. _air(v)= cases TRAVERSABLE,&s(v) _ord,\\ TRAVERSABLE\_STAIR,&s(v) _stair,\\ TRAVERSABLE\_FAKE,&s(v)= . cases (13) Accordingly, TRAVERSABLE represents supported free space above an ordinary or reversible surface, whereas TRAVERSABLE_STAIR denotes free space supported by confirmed stair geometry. In contrast, TRAVERSABLE_FAKE indicates observed free space for which no valid support is found within the support-search depth. It should therefore not be confused with FAKE_STAIR, which is a reversible surface state rather than an unsupported-air state. Stair-State Promotion During Basic Explore, SegFormer masks and RGB-D geometry may generate ascent or descent evidence, but ordinary OCCUPIED voxels are not immediately rewritten as confirmed stairs. After the corresponding stair entrance is reached and verified, the controller enters Stair Explore, implemented as the StairSem mode. Within StairSem, accepted surface voxels are promoted to STAIR; adjacent occupied cells may become STAIR_EXPANDED; rejected evidence is retained as FAKE_STAIR. Support-dependent air voxels are then reclassified locally. This delayed promotion prevents uncertain stair observations collected during ordinary exploration from directly changing the cross-floor planning graph. Appendix E Candidate Hierarchy and Navigation Modes Candidate Priority The controller considers four main candidate classes: t=tlive/history∪ℱttrav∪ℱtdesc∪ℱtasc.C_t=P_t^live/history _t^trav _t^desc _t^asc. (14) Their default selection priority is tlive/history≻ℱttrav≻ℱtdesc≻ℱtasc.P_t^live/history _t^trav _t^desc _t^asc. (15) Here, Basic Frontiers collectively refer to Traversable, Descend, and Ascent Frontiers used during ordinary exploration: • Traversable Frontier: the boundary between supported TRAVERSABLE voxels and genuine unknown space; • Descend Frontier: the boundary between supported traversable space and unsupported or fake-stair geometry; • Ascent Frontier: a semantic-geometric entrance proposal for an upward stair. The controller first explores reachable Traversable Frontiers on the current floor. Only after no reachable ordinary frontier remains does it consider Descend and Ascent Frontiers. Descend is attempted before ascent by default, although the order may be adapted according to the most recent successful floor-transition direction. A selected candidate is committed for a short grace period so that incremental map updates do not cause frequent target switching. Commitment is therefore a stability mechanism rather than an additional candidate class. A committed candidate is replaced only when it becomes invalid, unreachable, or is superseded by a higher-priority POI. Mode Definitions Table 9 summarizes the high-level modes and their planning behavior. Mode Navigation target Graph construction Main behavior and admissibility Exit condition Basic Explore Traversable, Descend, or Ascent Frontier Strict 26-neighbor graph; selected target remains on the current exploration level Prioritizes ordinary TRAVERSABLE space. Descend and ascent targets are entrance proposals; Basic Explore does not actively traverse an unconfirmed stair body. Valid POI, verified stair entrance, or exhausted candidates. POI Navigation Live POI or History POI Standard 26-neighbor 3D graph Navigates toward current or previously observed semantic evidence. Previously confirmed stair connections may be reused to reach a POI on another floor. POI arrival, invalidation, live-target takeover, or failure. Stair Explore / StairSem Directional Stair Frontier Pathable endpoints inside a 1.0 m physical 3D sphere Admits confirmed stair states and stair-supported air. The requested ascent or descent direction constrains vertical progress and suppresses unrelated platforms or neighboring stair flights. Stair-frontier arrival followed by multi-frame landing confirmation. Target Approach Observation viewpoint near a Live POI Local path planning and discrete view correction Refines the camera pose, target mask, and stopping decision. It does not initiate new cross-floor exploration. Valid found action, rejected detection, or return to exploration. Table 9: Navigation modes, target types, and mode-dependent planning behavior. During History-POI navigation, a new Live POI may take control only when its projected 3D location is spatially consistent with the active History-POI region. This prevents unrelated detections elsewhere in the scene from interrupting historical retrieval. Appendix F Type-Aware 3D A∗ Normal Graph Basic Explore and POI Navigation use a 26-neighbor graph. The heuristic is the 3D Euclidean distance from the current voxel to the goal: h(n)=(ix−gx)2+(iy−gy)2+(iz−gz)2.h(n)= (i_x-g_x)^2+(i_y-g_y)^2+(i_z-g_z)^2. (16) The transition cost is c(n,n′)=‖n−n′‖2+p(τn′),c(n,n )=\|n-n \|_2+p( _n ), (17) where p(τn′)p( _n ) is determined by the destination voxel state. The penalties favor stable supported air while preserving access to confirmed stair geometry. FAKE_STAIR remains available only as a costly fallback and is never selected as a navigation endpoint. Ordinary planning prioritizes non-inflated voxels. When a mode explicitly permits an inflated pathable endpoint, its transition cost is multiplied by two. If the agent is already inside an inflated pathable region, the planner may temporarily retain inflated states to allow the agent to leave that region; strict planning resumes afterward. StairSem Graph Sparse RGB-D observations may leave gaps larger than one voxel between successive stair surfaces. StairSem therefore replaces the fixed 26-neighbor relation with all existing pathable endpoints inside a 1.0 m physical sphere. This neighborhood is defined in metric 3D space rather than by a fixed voxel offset. Inflated TRAVERSABLE and TRAVERSABLE_STAIR endpoints may be used when necessary, whereas inflated STAIR, STAIR_EXPANDED, and FAKE_STAIR endpoints are rejected. If the final Stair Frontier is temporarily unreachable, intermediate session-local stair targets are tried in descending order of vertical progress. The expanded graph is deliberately permissive for incomplete stair observations. It verifies the stored endpoints of each edge but does not claim continuous swept-volume collision certification along every intermediate sample of a long edge. Destination voxel state Type penalty TRAVERSABLE 0 TRAVERSABLE_STAIR 0 STAIR 4 STAIR_EXPANDED 5 FAKE_STAIR 10 Table 10: Voxel-type penalties used by the 3D A∗ planner. Appendix G Evaluation Protocol and Additional Results Benchmark Summary HM3D-MFMON contains 927 three-goal episodes from 36 multi-floor HM3D scenes. The finalized Cross-Floor-Required (CFR) subset contains 288 episodes whose complete object-goal sequences require at least one floor transition. The first mandatory transition occurs at the first, second, or third object-goal subtask in 102, 101, and 85 episodes, respectively. Post-Hoc Stage-Wise Shortest Paths For stage k of episode i, the shortest-path denominator is recomputed from the actual beginning of that trajectory segment: di,k⋆=minv∈(qi,k)dgeo(xi,kstart,v),d_i,k = _v (q_i,k)d_geo (x_i,k^start,v ), (18) where (qi,k)V(q_i,k) contains the valid navigable viewpoints of all instances belonging to the requested object category. Let si,k∈0,1s_i,k∈\0,1\ denote stage success and let li,kl_i,k be the executed trajectory length. Stage-wise SPL is SPLi,k=si,kdi,k⋆max(di,k⋆,li,k).SPL_i,k=s_i,k d_i,k (d_i,k ,l_i,k). (19) This post-hoc protocol does not require the agent to know future object goals and avoids fixing later-stage shortest paths before the actual completion location of the preceding goal is known. Conditional and Global Metrics Unexecuted later goals are excluded from conditional denominators. Setting si,0=1s_i,0=1, the conditional metrics are SRkcond ^cond_k =∑i=1Nsi,k∑i=1Nsi,k−1, = _i=1^Ns_i,k _i=1^Ns_i,k-1, (20) SPLkcond ^cond_k =∑i=1Nsi,k−1SPLi,k∑i=1Nsi,k−1. = _i=1^Ns_i,k-1SPL_i,k _i=1^Ns_i,k-1. The corresponding global metrics use the complete episode set: SRkglobal ^global_k =1N∑i=1Nsi,k, = 1N _i=1^Ns_i,k, (21) SPLkglobal ^global_k =1N∑i=1Nsi,k−1SPLi,k. = 1N _i=1^Ns_i,k-1SPL_i,k. The two views are related by SRkglobal ^global_k =∑isi,k−1NSRkcond, = _is_i,k-1NSR^cond_k, (22) SPLkglobal ^global_k =∑isi,k−1NSPLkcond. = _is_i,k-1NSPL^cond_k. Conditional metrics isolate performance among episodes that reach stage k, whereas global metrics additionally preserve the cascade effect of earlier failures. For a three-goal episode, SR3globalSR^global_3 is equal to the episode-level SR because success at the third stage implies that all preceding goals have also been completed. History-POI Ablation Boundary The w/o H-POI variant disables only History-POI generation and selection. It retains the persistent SED feature map, cumulative feature fusion, Live POIs, support-aware voxel mapping, stair perception, and cross-floor planning. The ablation therefore measures the contribution of explicit historical semantic retrieval rather than removing the complete semantic-memory representation. Global Results on All Episodes Method Global SR ↑ Global SPL ↑ k=1k=1 k=2k=2 k=3k=3 k=1k=1 k=2k=2 k=3k=3 OneMap 54.58 29.67 16.83 23.46 13.54 9.14 w/o H-POI 70.33 45.52 29.77 25.26 18.06 11.64 LifelongCrossNav 70.33 45.74 29.13 25.26 22.71 15.82 Table 11: Stage-wise global performance on all 927 HM3D-MFMON episodes. All values are percentages. Method Global SR ↑ Global SPL ↑ k=1k=1 k=2k=2 k=3k=3 k=1k=1 k=2k=2 k=3k=3 OneMap 42.36 13.19 0.00 17.82 6.89 0.00 w/o H-POI 55.56 23.96 7.29 19.00 10.79 3.02 LifelongCrossNav 55.56 23.96 7.99 19.00 12.99 4.92 Table 12: Stage-wise global performance on the 288 CFR episodes. All values are percentages. The global results preserve the same efficiency trend observed with Conditional SPL. The complete framework maintains substantially higher later-stage Global SPL than w/o H-POI, showing that the efficiency improvement from historical retrieval remains visible after accounting for episodes that fail before reaching later goals. Global Results on Cross-Floor-Required Episodes The CFR results expose the effect of unresolved floor transitions. If OneMap reaches the third object goal, its first two goals have already been completed without requiring a floor transition. Because every CFR sequence contains at least one mandatory transition, the remaining third goal must then contain the unresolved cross-floor requirement. Without an executable stair representation, OneMap consequently obtains zero third-stage success. LifelongCrossNav retains nonzero third-stage Global SR and SPL by explicitly representing stair structures and cross-floor connectivity. The higher later-stage Global SPL of the complete framework relative to w/o H-POI further shows that historical semantic retrieval remains useful after floor transitions.