We address the problem of optimal path planning for a simple nonholonomic vehicle in the presence of obstacles. Most current approaches are either split hierarchically into global path planning and local collision avoidance, or neglect some of the ambient geometry by assuming the car is a point mass. We present a Hamilton-Jacobi formulation of the problem that resolves time-optimal paths and considers the geometry of the vehicle.
@article{arxiv.2005.03623,
title = {A Hamilton-Jacobi Formulation for Time-Optimal Paths of Rectangular Nonholonomic Vehicles},
author = {Christian Parkinson and Andrea L. Bertozzi and Stanley Osher},
journal= {arXiv preprint arXiv:2005.03623},
year = {2020}
}