In this article, the candidate optimal paths for a Dubins vehicle on a sphere are analytically derived. In particular, the arc angles for segments in CGC, CCC, CCCC, and CCCCC paths, which have previously been shown to be optimal depending on the turning radius r of the vehicle by Kumar \textit{et al.}, are analytically derived. The derived expressions are used for the implementation provided in https://github.com/DeepakPrakashKumar/Motion-planning-on-sphere.
@article{arxiv.2504.11832,
title = {Generation of Paths for Motion Planning for a Dubins Vehicle on Sphere},
author = {Deepak Prakash Kumar and Swaroop Darbha and Satyanarayana Gupta Manyam and David Casbeer},
journal= {arXiv preprint arXiv:2504.11832},
year = {2025}
}