A Jacobi-like acceleration for dynamic programming

The Hamilton-Jacobi-Bellman (HJB) equation provides a general method to solve optimal control problems. Since the HJB equation is a nonlinear partial differential equation, a closed form solution does not exist for the general case and various numerical procedures have been developed for its solution. Some recent approaches, after some simplifications, convert the problem into a fixed-point iteration. One problem related to the iteration is that its convergence speed is rather poor. We propose a Jacobi-like acceleration that allows to improve the convergence speed. As an application, we compute the minimum-time solution of a parking maneuver for a car-like vehicle with bounded velocity and steering angle.