Manifold-constrained Hamilton-Jacobi Reachability Learning for Decentralized Multi-Agent Motion Planning

TL;DR

This paper introduces a novel decentralized motion planning framework that incorporates manifold constraints through Hamilton-Jacobi reachability learning, enabling safe, task-aware multi-agent navigation in complex environments.

Contribution

It presents a new manifold-constrained HJR learning method that effectively integrates task-specific safety conditions into decentralized multi-agent motion planning.

Findings

Outperforms existing constrained motion planners in safety and efficiency.

Operates effectively in high-dimensional multi-agent manipulation tasks.

Demonstrates real-time applicability in complex, dynamic environments.

Abstract

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 .