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

2025-11-05

AI Summary

This work addresses safe, real-time navigation for multi-robot systems operating under task-defined manifold constraints (e.g., maintaining a cup upright) in dynamic environments. Methodologically, it introduces a Hamilton–Jacobi (HJ) reachability learning framework integrated with manifold constraints: it formulates task-aware safety as a learnable value function, approximates the HJ partial differential equation solution via deep neural networks, and computes decentralized control-invariant sets directly on the manifold space; multi-agent coordination is achieved through distributed trajectory optimization. The key contributions are: (i) overcoming the long-standing challenge of jointly modeling high-dimensional manifold constraints and dynamic obstacle avoidance; (ii) enabling task generalization and real-time planning; and (iii) demonstrating significant performance gains over conventional constrained planning methods in both simulation and physical experiments—highlighting strong practicality and scalability.

Technology Category

• Intelligent Robots: Multi-Robot Systems
• Multiagent Systems: Multiagent Planning
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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 .

Problem

• Safe multi-agent motion planning under task-induced manifold constraints
• Decentralized planning for robots navigating dynamic environments with constraints
• Incorporating task-aware safety conditions into trajectory optimization without policy assumptions

Innovation

• Manifold-constrained Hamilton-Jacobi reachability learning framework
• Decentralized trajectory optimization with safety integration
• Generalizes across diverse high-dimensional manipulation tasks