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arXiv · 2109.02125

Elongation of Curvature-Bounded Path

Zheng Chen·Kun Wang·Yang Lu
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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.

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Zheng Chen, Kun Wang, Yang Lu. 2021-09-05. Elongation of Curvature-Bounded Path. https://doi.org/10.1016/j.automatica.2023.110936

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