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arXiv · 2409.09954

Generalization of Optimal Geodesic Curvature Constrained Dubins' Path on Sphere with Free Terminal Orientation

Deepak Prakash Kumar·Swaroop Darbha·Satyanarayana Gupta Manyam·David Casbeer
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Abstract

In this paper, motion planning for a Dubins vehicle on a unit sphere to attain a desired final location is considered. The radius of the Dubins path on the sphere is lower bounded by $r$. In a previous study, this problem was addressed, wherein it was shown that the optimal path is of type $CG, CC,$ or a degenerate path of the same for $r \leq \frac{1}{2}.$ Here, $C = L, R$ denotes an arc of a tight left or right turn of minimum turning radius $r,$ and $G$ denotes an arc of a great circle. In this study, the candidate paths for the same problem are generalized to model vehicles with a larger turning radius. In particular, it is shown that the candidate optimal paths are of type $CG, CC,$ or a degenerate path of the same for $r \leq \frac{\sqrt{3}}{2}.$ Noting that at most two $LG$ paths and two $RG$ paths can exist for a given final location, this article further reduces the candidate optimal paths by showing that only one $LG$ and one $RG$ path can be optimal, yielding a total of seven candidate paths for $r \leq \frac{\sqrt{3}}{2}.$ Additional conditions for the optimality of $CC$ paths are also derived in this study.

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Deepak Prakash Kumar, Swaroop Darbha, Satyanarayana Gupta Manyam, David Casbeer. 2024-09-16. Generalization of Optimal Geodesic Curvature Constrained Dubins' Path on Sphere with Free Terminal Orientation. https://arxiv.org/abs/2409.09954

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