Optimal Geodesic Curvature Constrained Dubins' Paths on a Sphere Institutional Repository Document

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.

Darbha, S., Pavan, A., Rajagopal, K. R., Rathinam, S., Casbeer, D. W., & Manyam, S. G.

Darbha, Swaroop||Pavan, Athindra||Rajagopal, KR||Rathinam, Sivakumar||Casbeer, David W||Manyam, Satyanarayana G

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