Time-Optimal Paths for Simple Cars with Moving Obstacles in the Hamilton-Jacobi Formulation

TL;DR

This paper introduces a novel Hamilton-Jacobi-Bellman formulation for time-optimal path planning of rectangular nonholonomic vehicles navigating through moving obstacles, extending previous models that only considered stationary obstacles and point vehicles.

Contribution

The work presents the first HJB-based approach that incorporates moving obstacles and vehicle shape, using a dynamic programming principle and finite difference scheme.

Findings

Effective path planning demonstrated with synthetic examples

First HJB formulation for moving obstacles in vehicle path planning

Handles rectangular vehicle shape in dynamic environments

Abstract

We consider the problem of time-optimal path planning for simple nonholonomic vehicles. In previous similar work, the vehicle has been simplified to a point mass and the obstacles have been stationary. Our formulation accounts for a rectangular vehicle, and involves the dynamic programming principle and a time-dependent Hamilton-Jacobi-Bellman (HJB) formulation which allows for moving obstacles. To our knowledge, this is the first HJB formulation of the problem which allows for moving obstacles. We design an upwind finite difference scheme to approximate the equation and demonstrate the efficacy of our model with a few synthetic examples.