Optimal Trajectories of Curvature Constrained Motion in the Hamilton–Jacobi Formulation

Abstract

We propose a PDE approach for computing time-optimal trajectories of a vehicle which travels under certain curvature constraints. We derive a class of Hamilton---Jacobi equations which models such motions; it unifies two well-known vehicular models, the Dubins' and Reeds---Shepp's cars, and gives further generalizations. Numerical methods (finite difference for the Reeds---Shepp's car and semi-Lagrangian for the Dubins' car) are investigated for two-dimensional domains and surfaces.