Optimal obstacle avoidance based on the Hamilton-Jacobi-Bellman equation

This paper presents a method for generating shortest paths in cluttered environments, based on the Hamilton-Jacobi-Bellman (HJB) equation. Formulating the shortest obstacle avoidance problem as a time optimal control problem, the shortest paths are generated by following the negative gradient of the return function, which satisfies the HJB equation. A method to generate near-optimal paths is also presented, based on a psuedo return function. Paths generated by this method are guaranteed to reach the goal, at which the psuedo return function is shown to have a unique minimum. The computation required to generate the near-optimal paths is substantially lower than those of traditional potential field methods, making it applicable to on-line obstacle avoidance. Examples with circular obstacles demonstrate close correlation between the near-optimal and optimal paths, and the advantages of the proposed approach over traditional potential field methods