Curvature-constrained path elongation with expected length for Dubins vehicle

Path elongation is a basic means of adjusting the time for a curvature-constrained vehicle to reach its destination, which is very common in the maneuvering control of high-speed vehicles or the coordinated control of their fleet. This paper studies the path elongation problem of a Dubins vehicle which moves in a two-dimensional plane and is subject to a maximum curvature. The aim of the paper is to answer the following question arising from the path elongation of Dubins vehicles: Can a Dubins vehicle reach a given destination by path elongation with a predefined path length? It is discovered and proved by theoretical analysis that, when the destination point is located in a special region, there is a special length interval for which no proper path exists. For all realizable length intervals, we provide an example of feasible path patterns for expected elongation. The results provide ideal reference trajectories with expected length for Dubins vehicles to follow for the sake of accurate arrival-time control.