On Traveling Salesperson Problems for a double integrator

In this paper we propose some novel path planning strategies for a double integrator with bounded velocity and bounded control inputs. First, we study the following version of the Traveling Salesperson Problem (TSP): given a set of points in Ropf
^d
, find the fastest tour over the point set for a double integrator. We first give asymptotic bounds on the time taken for to complete such a tour in the worst-case. Then, we study a stochastic version of the TSP for double integrator where the points are randomly sampled from a uniform distribution in a compact environment in Ropf
²
and Ropf
³
. We propose novel algorithms that perform within a constant factor of the optimal strategy with high probability. Second, we study a dynamic TSP: given a stochastic process that generates targets, is there a policy which guarantees that the number of unvisited targets does not diverge over time? If such stable policies exist, what is the minimum wait for a target? We propose novel stabilizing algorithms whose performances are within a constant factor from the optimum, in Ropf
²
as well as in Ropf
³
. We also argue that these algorithms give similar performances for a particular nonholonomic vehicle, the Dubins vehicle