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This technical note studies the following version of the Traveling Salesperson Problem (TSP) for a double integrator with bounded velocity and bounded control inputs: given a set of points in Ropfd, find the fastest tour over the point set. We first give asymptotic bounds on the time taken to complete such a tour in the worst case. Then, we study a stochastic version of the TSP for a double integrator in Ropf2 and Ropf3, where we propose novel algorithms that asymptotically perform within a constant factor of the optimal strategy with probability one. Lastly, we study a dynamic TSP in Ropf2 and Ropf3 , where we propose novel stabilizing algorithms whose performances are within a constant factor from the optimum.