Manifold-Constrained Hamilton-Jacobi Reachability Learning for Decentralized Multi-Agent Motion Planning
Qingyi Chen, Ruiqi Ni, Junyoung Kim, Ahmed H. Qureshi
AI summary
Problem
Existing decentralized multi-agent motion planners struggle to enforce task-induced manifold constraints while scaling to high-dimensional systems, often relying on centralized coordination or ignoring constraints entirely.
Approach
The method extends neural Hamilton-Jacobi reachability solvers to compute safety value functions intrinsically on constraint manifolds, which are then embedded into a decentralized receding-horizon trajectory optimizer for real-time collision avoidance.
Key results
- Theoretical extension of DeepReach to solve HJR under manifold constraints
- Decentralized trajectory planner ensuring safety and task compliance without assuming other agents' policies
- High accuracy in backward reachable set prediction compared to unconstrained baselines
- Successful generalization across object-carrying, cup-holding, and doorway-crossing tasks with real UR5 robots
Why it matters
Provides a scalable, real-time safety guarantee for multi-robot systems operating in constrained, dynamic environments like factories and service spaces.
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. Exper- iments show that our method outperforms existing constrained motion planners and operates at speeds suitable for real- world applications. Video demonstrations and source code are available at https://youtu.be/RYcEHMnPTH8 and https://github.com/qingyichen/hammar.