NeHMO: Neural Hamilton-Jacobi Reachability Learning for Decentralized Safe Multi-Arm Motion Planning

Safe multi-arm motion planning is a challenging problem in robotics due to its high dimensionality, coupled configuration space, and complex collision constraints. Centralized planners are capable of coordinating all arms but often face scalability limitations, restricting applicability in real-time settings. On the other hand, decentralized methods are scalable and recent deep learning-based approaches have shown promising results. However, these depend on accurate behavior prediction or coordination protocols and may fail when other arms act unpredictably. To address these challenges, we introduce a neural Hamilton-Jacobi Reachability (HJR) learning-based approach to approximate a safety value function that captures worst-case inter-arm safety constraints. We further develop a decentralized trajectory optimization framework that uses the learned HJR representation for real-time planning. The proposed method is scalable and data-efficient, generalizes across multi-manipulator systems, and outperforms state-of-the-art baselines on challenging multi-arm motion planning tasks.

Safe multi-agent motion planning (MAMP) under task-induced constraints is a critical challenge in robotics. Many real-world scenarios require robots to navigate dynamic environments while adhering to manifold constraints imposed by tasks. For example, service robots must carry cups upright while avoiding collisions with humans or other robots. Despite recent advances in decentralized MAMP for high-dimensional systems, incorporating manifold constraints remains difficult. To address this, we propose a manifold-constrained Hamilton-Jacobi reachability (HJR) learning framework for decentralized MAMP. Our method solves HJR problems under manifold constraints to capture task-aware safety conditions, which are then integrated into a decentralized trajectory optimization planner. This enables robots to generate motion plans that are both safe and task-feasible without requiring assumptions about other agents' policies. Our approach generalizes across diverse manifold-constrained tasks and scales effectively to high-dimensional multi-agent manipulation problems. Experiments show that our method outperforms existing constrained motion planners and operates at speeds suitable for real-world applications. Video demonstrations are available at https://youtu.be/RYcEHMnPTH8 .

Decentralized multi-robot motion planning requires each robot to generate collision-free trajectories from local observations, without global sensing or reliable communication. However, most existing planners, whether classical or learning-based, generate trajectories from a static snapshot of the local observation, which limits their ability to anticipate the future behavior of neighboring robots. This limitation is critical as the number of robots increases and the environment becomes more cluttered. To overcome this challenge, this paper introduces Simulation-Informed Diffusion (SID), a decentralized framework built on constraint-aware diffusion models (CADM). SID first uses CADM to simulate the future trajectories of neighboring robots from their currently observed states, and then uses the same CADM to plan each robot's own trajectory under safety constraints informed by these simulations. Crucially, the accurate simulation of neighbors enables a minimal communication scheme that triggers coordination only when necessary in highly congested scenarios. Experiments across diverse environments show that SID consistently outperforms baseline methods in terms of planning effectiveness and constraint satisfaction, and scales to scenarios with 108 robots and 160 obstacles.