S. Sundar et Z. Shiller, OPTIMAL OBSTACLE AVOIDANCE BASED ON THE HAMILTON-JACOBI-BELLMAN EQUATION, IEEE transactions on robotics and automation, 13(2), 1997, pp. 305-310
This paper solves the on-line obstacle avoidance problem using the Ham
ilton-Jacobi-Bellman (HJB) theory. Formulating the shortest path probl
em as a time optimal control problem, the shortest paths are generated
by following the negative gradient of the return function, which is t
he solution of the HJB equation. To account for multiple obstacles, we
avoid obstacles optimally one at a time. This is equivalent to follow
ing the pseudoreturn function, which is an approximation of the true r
eturn function for the multi-obstacle problem. Paths generated by this
method are near-optimal and guaranteed to reach the goal, at which th
e pseudoreturn function is shown to have a unique minimum. The propose
d method is computationally very efficient, and applicable for on-line
applications. Examples for circular obstacles demonstrate the advanta
ges of the proposed approach over traditional path planning methods.