Elongation of curvature-bounded path

Abstract

The elongation of curvature-bounded paths to an expected length is fundamentally important to plan missions for nonholonomic-constrained vehicles in many practical applications, such as coordinating multiple nonholonomic-constrained vehicles to reach a destination simultaneously or performing a mission with a strict time window. In the paper, by applying the properties of the reachability set of curvature-bounded paths, the explicit conditions for the existence of curvature-bounded paths joining two oriented points with an expected length are established. These existence conditions are numerically verifiable, allowing readily checking the existence of curvature-bounded paths between two prescribed oriented points with a desired length. In addition, once the existence conditions are met, elongation strategies are provided to get curvature-bounded paths with the expected length. Finally, some examples of minimum-time path planning for multiple Dubins vehicles to cooperatively achieve a triangle-shaped formation are presented, illustrating and verifying the developments of the paper.