Abstract:In this work, we investigate the partitioning and control problems on the 2−sphere, the set of all unit vectors in R 3. Specifically, we present a spherical-polytope-based partitioning for the 2−sphere and then propose a novel approach to construct a feedback control law over a given set of spherical polytopes. Instead of designing the control law directly on the sphere, we propose a smooth atlas on it based on the gnomonic projection. We further show that the gnomonic map projects the spherical polytopes to E… Show more
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