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arXiv · 2603.28993

Collisionless Multi-Agent Path Planning in the Hamilton-Jacobi Formulation

Christian Parkinson·Adan Baca·Huy Nguyen
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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.

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Christian Parkinson, Adan Baca, Huy Nguyen. 2026-03-30. Collisionless Multi-Agent Path Planning in the Hamilton-Jacobi Formulation. https://arxiv.org/abs/2603.28993

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