The Traveling Salesman Problem for the Reeds-Shepp Car and the Differential Drive Robot

In this paper we consider variations on the traveling salesman problem for the Reeds-Shepp car and differential drive robot. We consider the problem of finding the shortest path compatible with the dynamics of such models through a set of points. We present algorithms that asymptotically perform within a deterministic constant factor of the optimum, for any distribution of points. In addition, we consider a version of such problems in which the target points are dynamically generated by a stochastic process with uniform spatial density. In such a case, the objective will be to minimize the expected waiting time between the appearance of a target and the time it is visited by the vehicle. We present algorithms that (i) ensure stability of the system, for all target generation rates, and (ii) provably perform within a constant factor of the optimum