On the construction of an optimal feedback control law for the shortest path problem for the Dubins car-like robot

Abstract

We derive a set of six basic formulas for computing feedback control steering the origin to any given terminal state and use them to construct an optimal feedback control law for the shortest path problem for the Dubins car-like robot. The construction of such an optimal feedback control law can be carried out without prior knowledge of the partition of the state space, while knowing the partition helps to simplify the process of constructing an optimal feedback controller.