Collisionless Multi-Agent Path Planning in the Hamilton-Jacobi Formulation
Abstract
We present a method for collisionless multi-agent path planning using the Hamilton-Jacobi-Bellman equation. Because the method is rooted in optimal control theory and partial differential equations, it avoids the need for hierarchical planners and is black-box free. Our model can account for heterogeneous agents and realistic, high-dimensional dynamics. We develop a grid-free numerical method based on a variational formulation of the solution of the Hamilton-Jacobi-Bellman equation which can resolve optimal trajectories even in high-dimensional problems, and include some practical implementation notes. In particular, we resolve the solution using a primal-dual hybrid gradient optimization scheme. We demonstrate the method's efficacy on path planning problems involving simple cars and quadcopter drones.
Cite
@article{arxiv.2603.28993,
title = {Collisionless Multi-Agent Path Planning in the Hamilton-Jacobi Formulation},
author = {Christian Parkinson and Adan Baca and Huy Nguyen},
journal= {arXiv preprint arXiv:2603.28993},
year = {2026}
}