Optimal Geodesic Curvature Constrained Dubins’ Paths on a Sphere

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