Elongation of Curvature-Bounded Path

TL;DR

This paper develops explicit conditions and strategies for elongating shortest curvature-bounded paths between two points to meet desired lengths, aiding mission planning for nonholonomic vehicles.

Contribution

It establishes verifiable existence conditions and elongation methods for curvature-bounded paths, with practical applications demonstrated in multi-vehicle formation planning.

Findings

Existence conditions for curvature-bounded path elongation are numerically verifiable.

Elongation strategies enable paths to meet specified lengths when conditions are satisfied.

Application to multi-vehicle formation shows practical effectiveness.

Abstract

The paper is concerned with elongating the shortest curvature-bounded path between two oriented points to an expected length. 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, the explicit conditions for the existence of curvature-bounded paths joining two oriented points with an expected length are established by applying the properties of the reachability set of curvature-bounded paths. 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 in the paper to get curvature-bounded paths with expected lengths. Finally, some examples of minimum-time path planning for multiple fixed-wing aerial vehicles to cooperatively achieve a triangle-shaped flight formation are presented, illustrating and verifying the developments of the paper.