ConstrainedStabilization on the n − Sphere ?

In this note, we solve the problem of constrained stabilization on the n−dimensional unit sphere by mapping it to a navigation problem on the Euclidean space R in the presence of spherical obstacles. As a consequence, any controller that was originally designed for navigating in Euclidean sphere worlds can be used to solve the stabilization problem on the n−sphere in the presence of conic constraints. A simulation example on the 2−sphere illustrates the effectiveness of the proposed approach.

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