Supplementary Materials: Reparametrization of 3D CSC Dubins Paths Enabling 2D Search

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School of Engineering and Applied Science::General Robotics, Automation, Sensing and Perception Laboratory::Lab Papers (GRASP)
School of Engineering and Applied Science::Department of Mechanical Engineering & Applied Mechanics::Departmental Papers (MEAM)
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Mechanical Engineering
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Robotics, Path Planning, Dubins Path, Dynamics
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2024
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Ling Xu
Yuliy Baryshnikov
Cynthia Sung
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Abstract

This paper addresses the Dubins path planning problem for vehicles in 3D space. In particular, we consider the problem of computing CSC paths – paths that consist of a circular arc (C) followed by a straight segment (S) followed by a circular arc (C). These paths are useful for vehicles such as fixed-wing aircraft and underwater submersibles that are subject to lower bounds on turn radius. We present a new parameterization that reduces the 3D CSC planning problem to a search over 2 variables, thus lowering search complexity, while also providing gradients that assist that search. We use these equations with a numerical solver to explore numbers and types of solutions computed for a variety of planar and 3D scenarios. Our method successfully computes CSC paths for the large majority of test cases, indicating that it could be useful for future generation of robust, efficient curvature-constrained trajectories.

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2024-10-08
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This is the supplementary materials for a paper presented at The 16th International Workshop on the Algorithmic Foundations of Robotics (WAFR 2024). The WAFR proceedings will be published (as a special issue of Springer Proceedings in Advanced Robotics) without the supplementary materials, so we are hosting the materials here.
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