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On the point-to-point and traveling salesperson problems for Dubins' vehicle

In this paper we study the length of optimal paths for Dubins' vehicle, i.e., a vehicle constrained to move forward along paths of bounded curvature. First, we obtain an upper bound on the optimal length in the point-to-point problem. Next, we consider the corresponding traveling salesperson problem (TSP). We provide an algorithm with worst-case performance within a constant factor approximation of the optimum. We also establish an asymptotic bound on the worst-case length of the Dubins' TSP.