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

TL;DR

This paper introduces a collisionless multi-agent path planning method based on the Hamilton-Jacobi-Bellman equation, capable of handling high-dimensional, heterogeneous agent dynamics without hierarchical planning.

Contribution

It develops a grid-free numerical approach using a variational formulation and primal-dual optimization, enabling efficient high-dimensional path planning.

Findings

Successfully plans paths for simple cars and quadcopters.

Avoids hierarchical planners by using a PDE-based optimal control approach.

Handles heterogeneous agents and realistic dynamics.

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.