Infimum of Path Length of Nonholonomic Vehicle with Finitely Bounded Curvature Radius

In this paper, we address the shortest path problem of point-to-point maneuver for a new nonholonomic wheeled vehicle. The vehicle performs forward-only motion which is adopted by Dubins car, while the curvature radius of its path is restricted to a finitely bounded interval which is different from that of Dubins car with a lower-bounded curvature radius. We first provide the infimum of the path length of the vehicle of point-to-point maneuver without a start or final orientation constraint. Then we study the infimum of the path length of the vehicle for point-to-point maneuver with a start and final orientation constraints. Next, we derive the explicit expressions for the candidate infimums. The infimum of the length path is the minimum of the candidates. Moreover, several examples are provided to verify the main results. The results in this paper extend the results on the existence of the shortest path of Dubins car to the new type of nonholonomic vehicles.