Generation of Paths for Motion Planning for a Dubins Vehicle on Sphere

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 $\mathit{\text{et}}\mathit{\text{al.}}$, are analytically derived. The derived expressions are used for the implementation provided in https://github.com/DeepakPrakashKumar/Motion-planning-on-sphere.