Receding Horizon Planning for Dubins Traveling Salesman Problems

In this paper we study the problem of finding the shortest global path of nonholonomic vehicles given a set of ordered waypoints. We represent the nonholonomic motion constraints using Dubins´ model. Many approaches for this problem piece together smooth trajectories by considering the solution of consecutive two-point optimal trajectories, enforcing smoothness at waypoints by requiring continuity of the vehicle state between segments. In this paper, we extend the two point optimal Dubins path solution to consider three consecutive waypoints, with several variations. We use this solution in a receding horizon approach to compute a smooth path through the sequence of waypoints. We compare our approach to alternative algorithms based on two- and three-point solutions, and show the advantage of our receding horizon algorithm over these alternatives. We also consider the problem when the set of waypoints is specified, but not the order. For these problems, we compute the order using an approximate traveling salesman problem solution based on straight line distances, and then solve for a smooth path using the receding horizon algorithm. Our experimental results show that this is superior to alternative approaches proposed in the literature