Topological maps are more suitable than metric maps for robotic exploration tasks. However, real-time updating of accurate and detail-rich environmental topological maps remains a challenge. This paper presents a topological map updating method based on the Generalized Voronoi Diagram (GVD). First, the newly observed areas are denoised to avoid low-efficiency GVD nodes misleading the topological structure. Subsequently, a multi-granularity hierarchical GVD generation method is designed to control the sampling granularity at both global and local levels. This not only ensures the accuracy of the topological structure but also enhances the ability to capture detail features, reduces the probability of path backtracking, and ensures no overlap between GVDs through the maintenance of a coverage map, thereby improving GVD utilization efficiency. Second, a node clustering method with connectivity constraints and a connectivity method based on a switching mechanism are designed to avoid the generation of unreachable nodes and erroneous nodes caused by obstacle attraction. A special cache structure is used to store all connectivity information, thereby improving exploration efficiency. Finally, to address the issue of frontiers misjudgment caused by obstacles within the scope of GVD units, a frontiers extraction method based on morphological dilation is designed to effectively ensure the reachability of frontiers. On this basis, a lightweight cost function is used to assess and switch to the next viewpoint in real time. This allows the robot to quickly adjust its strategy when signs of path backtracking appear, thereby escaping the predicament and increasing exploration flexibility. And the performance of system for exploration task is verified through comparative tests with SOTA methods.

Spatial reasoning is a key capability in the field of artificial intelligence, especially crucial in areas such as robotics, computer vision, and natural language understanding. However, evaluating the ability of multimodal large language models(MLLMs) in complex spatial reasoning still faces challenges, particularly in scenarios requiring multi-step reasoning and precise mathematical constraints. This paper introduces ORIGAMISPACE, a new dataset and benchmark designed to evaluate the multi-step spatial reasoning ability and the capacity to handle mathematical constraints of MLLMs through origami tasks. The dataset contains 350 data instances,each comprising a strictly formatted crease pattern (CP diagram), the Compiled Flat Pattern, the complete Folding Process, and the final Folded Shape Image. We propose four evaluation tasks: Pattern Prediction, Multi-step Spatial Reasoning, Spatial Relationship Prediction, and End-to-End CP Code Generation. For the CP code generation task, we design an interactive environment and explore the possibility of using reinforcement learning methods to train MLLMs. Through experiments on existing MLLMs, we initially reveal the strengths and weaknesses of these models in handling complex spatial reasoning tasks.

Recent progress in Vision-Language-Action (VLA) models has enabled embodied agents to interpret multimodal instructions and perform complex tasks. However, existing VLAs are mostly confined to short-horizon, table-top manipulation, lacking the memory and reasoning capability required for long-horizon mobile manipulation, where agents must coordinate navigation and manipulation under changing spatial contexts. In this work, we present EchoVLA, a memory-aware VLA model for long-horizon mobile manipulation. EchoVLA incorporates a synergistic declarative memory inspired by the human brain, consisting of a scene memory that maintains a collection of spatial-semantic maps and an episodic memory that stores task-level experiences with multimodal contextual features. During both training and inference, the two memories are individually stored, updated, and retrieved based on current observations, task history, and instructions, and their retrieved representations are fused via coarse- and fine-grained attention to guide mobile-arm diffusion policies. To support large-scale training and evaluation, we further introduce MoMani, an automated benchmark that generates expert-level long-horizon trajectories through multimodal large language model (MLLM)-guided planning and feedback-driven refinement, supplemented with real-robot demonstrations. Experiments in simulated and real-world settings show that EchoVLA improves long-horizon performance, reaching 0.52 SR on manipulation/navigation and 0.31 on mobile manipulation, exceeding $π_{0.5}$ by +0.08 and +0.11.

Recent Vision-Language-Action (VLA) models have shown impressive flexibility and generalization, yet their deployment in robotic manipulation remains limited by heavy computational overhead and inference latency. In this work, we present ActDistill, a general action-guided self-derived distillation framework that transfers the action prediction capability of any existing VLA model to a lightweight counterpart. Unlike previous efficiency strategies that primarily emphasize vision-language correlations, ActDistill leverages action priors to guide knowledge transfer and model compression, achieving action-oriented efficiency for VLA models. Specifically, we employ a well-trained VLA model as the teacher and introduce a graph-structured encapsulation strategy to explicitly model the hierarchical evolution of action prediction. The student model, derived from the graph-encapsulated teacher, is further equipped with a dynamic router that adaptively selects computation paths based on action prediction demands, guided by hierarchical graph-informed supervision to ensure smooth and efficient evolution. During inference, graph-related auxiliary components are removed, allowing the student to execute only dynamically routed layers and predict high-precision actions with minimal computation and latency. Experiments on embodied benchmarks demonstrate that ActDistill achieves comparable or superior performance to full-scale VLA models while reducing computation by over 50% with up to 1.67 speedup, thereby establishing a general paradigm toward efficient embodied intelligence. Source codes can be found at https://github.com/

Incorporating spatial information, particularly those influenced by climate, weather, and demographic factors, is crucial for improving underwriting precision and enhancing risk management in insurance. However, spatial data are often unstructured, high-dimensional, and difficult to integrate into predictive models. Embedding methods are needed to convert spatial data into meaningful representations for modelling tasks. We propose a novel multi-view contrastive learning framework for generating spatial embeddings that combine information from multiple spatial data sources. To train the model, we construct a spatial dataset that merges satellite imagery and OpenStreetMap features across Europe. The framework aligns these spatial views with coordinate-based encodings, producing low-dimensional embeddings that capture both spatial structure and contextual similarity. Once trained, the model generates embeddings directly from latitude-longitude pairs, enabling any dataset with coordinates to be enriched with meaningful spatial features without requiring access to the original spatial inputs. In a case study on French real estate prices, we compare models trained on raw coordinates against those using our spatial embeddings as inputs. The embeddings consistently improve predictive accuracy across generalised linear, additive, and boosting models, while providing interpretable spatial effects and demonstrating transferability to unseen regions.

Video Models have achieved remarkable success in high-fidelity video generation with coherent motion dynamics. Analogous to the development from text generation to text-based reasoning in language modeling, the development of video models motivates us to ask: Can video models reason via video generation? Compared with the discrete text corpus, video grounds reasoning in explicit spatial layouts and temporal continuity, which serves as an ideal substrate for spatial reasoning. In this work, we explore the reasoning via video paradigm and introduce VR-Bench -- a comprehensive benchmark designed to systematically evaluate video models' reasoning capabilities. Grounded in maze-solving tasks that inherently require spatial planning and multi-step reasoning, VR-Bench contains 7,920 procedurally generated videos across five maze types and diverse visual styles. Our empirical analysis demonstrates that SFT can efficiently elicit the reasoning ability of video model. Video models exhibit stronger spatial perception during reasoning, outperforming leading VLMs and generalizing well across diverse scenarios, tasks, and levels of complexity. We further discover a test-time scaling effect, where diverse sampling during inference improves reasoning reliability by 10--20%. These findings highlight the unique potential and scalability of reasoning via video for spatial reasoning tasks.

Vision-Language-Action (VLA) models have emerged as a promising framework for enabling generalist robots capable of perceiving, reasoning, and acting in the real world. These models usually build upon pretrained Vision-Language Models (VLMs), which excel at semantic understanding due to large-scale image and text pretraining. However, existing VLMs typically lack precise spatial understanding capabilities, as they are primarily tuned on 2D image-text pairs without 3D supervision. To address this limitation, recent approaches have incorporated explicit 3D inputs such as point clouds or depth maps, but this necessitates additional depth sensors or pre-trained depth estimation models, which may yield defective results. In contrast, our work introduces a plug-and-play module that implicitly incorporates 3D geometry features into VLA models by leveraging an off-the-shelf visual geometry foundation model. This integration provides the model with depth-aware visual representations, improving its ability to understand the geometric structure of the scene and the spatial relationships among objects from RGB images alone. We evaluate our method on a set of spatially challenging tasks in both simulation and the real world. Extensive evaluations show that our method significantly improves the performance of state-of-the-art VLA models across diverse scenarios.

Recent advances in Multimodal Large Language Models (MLLMs) have significantly enhanced their capabilities; however, their spatial perception abilities remain a notable limitation. To address this challenge, multimodal data synthesis offers a promising solution. Yet, ensuring that synthesized data adhere to spatial common sense is a non-trivial task. Our approach addresses this critical gap by providing a systematic framework for generating spatially coherent data. In this work, we introduce SKG2DATA, a novel multimodal synthesis approach guided by spatial knowledge graphs, grounded in the concept of knowledge-to-data generation. SKG2DATA employs an automated pipeline for constructing Spatial Knowledge Graph (SKG) that effectively captures human-like spatial cognition, including directional and distance relationships. These structured representations then serve as precise guidance for our integrated synthesis pipeline, where a diffusion model generates spatially-consistent images while a MLLM produces corresponding textual descriptions. The automated construction of SKG enables scalable generation of diverse yet realistic spatial configurations, overcoming the limitations of manual data collection and annotation. Extensive experiments demonstrate that data synthesized from diverse types of spatial knowledge, including direction and distance, enhance the spatial perception and reasoning abilities of MLLMs markedly, albeit with a slight cost to their general capabilities. We hope that the idea of knowledge-based data synthesis can advance the development of spatial intelligence. Code is available at https://github.com/zjunlp/Knowledge2Data.

The success of foundation models in language has inspired a new wave of general-purpose models for human mobility. However, existing approaches struggle to scale effectively due to two fundamental limitations: a failure to use meaningful basic units to represent movement, and an inability to capture the vast diversity of patterns found in large-scale data. In this work, we develop MoveGPT, a large-scale foundation model specifically architected to overcome these barriers. MoveGPT is built upon two key innovations: (1) a unified location encoder that maps geographically disjoint locations into a shared semantic space, enabling pre-training on a global scale; and (2) a Spatially-Aware Mixture-of-Experts Transformer that develops specialized experts to efficiently capture diverse mobility patterns. Pre-trained on billion-scale datasets, MoveGPT establishes a new state-of-the-art across a wide range of downstream tasks, achieving performance gains of up to 35% on average. It also demonstrates strong generalization capabilities to unseen cities. Crucially, our work provides empirical evidence of scaling ability in human mobility, validating a clear path toward building increasingly capable foundation models in this domain.

While Visual Large Language Models (VLLMs) show great promise as embodied agents, they continue to face substantial challenges in spatial reasoning. Existing embodied benchmarks largely focus on passive, static household environments and evaluate only isolated capabilities, failing to capture holistic performance in dynamic, real-world complexity. To fill this gap, we present IndustryNav, the first dynamic industrial navigation benchmark for active spatial reasoning. IndustryNav leverages 12 manually created, high-fidelity Unity warehouse scenarios featuring dynamic objects and human movement. Our evaluation employs a PointGoal navigation pipeline that effectively combines egocentric vision with global odometry to assess holistic local-global planning. Crucially, we introduce the "collision rate" and "warning rate" metrics to measure safety-oriented behaviors and distance estimation. A comprehensive study of nine state-of-the-art VLLMs (including models such as GPT-5-mini, Claude-4.5, and Gemini-2.5) reveals that closed-source models maintain a consistent advantage; however, all agents exhibit notable deficiencies in robust path planning, collision avoidance and active exploration. This highlights a critical need for embodied research to move beyond passive perception and toward tasks that demand stable planning, active exploration, and safe behavior in dynamic, real-world environment.