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arXiv · 2203.16426

Optimal Geodesic Curvature Constrained Dubins' Paths on a Sphere

Swaroop Darbha·Athindra Pavan·K. R. Rajagopal·Sivakumar Rathinam·David W. Casbeer·Satyanarayana G. Manyam
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Abstract

In this article, we consider the motion planning of a rigid object on the unit sphere with a unit speed. The motion of the object is constrained by the maximum absolute value, $U_{max}$ of geodesic curvature of its path; this constrains the object to change the heading at the fastest rate only when traveling on a tight smaller circular arc of radius $r <1$, where $r$ depends on the bound, $U_{max}$. We show in this article that if $0 \frac{1}{2}$, while paths of the above type may cease to exist depending on the boundary conditions and the value of $r$, optimal paths may be concatenations of more than three circular arcs.

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Swaroop Darbha, Athindra Pavan, K. R. Rajagopal, Sivakumar Rathinam, David W. Casbeer, Satyanarayana G. Manyam. 2022-03-30. Optimal Geodesic Curvature Constrained Dubins' Paths on a Sphere. https://arxiv.org/abs/2203.16426

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