Global Formulation and Motion Planning for a Sphere Rolling on a Smooth Surface
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This paper studies the motion planning problem for a rolling sphere on an arbitrary smooth manifold embedded in ℝ3. The sphere is allowed to roll on the surface without slipping or twisting. A mathematical model describing the kinematics of the sphere is developed in a geometric form so that the model is globally defined without singularities or ambiguities. An algorithm for constructing a path between specified initial and final configurations is presented. The algorithm utilizes the nonholonomic nature of the system. The theoretical results are specialized for two specific surfaces defined in ℝ3, namely a flat surface and the surface of a stationary sphere.
KeywordsGlobal formulation kinematics nonholonomic nonlinear
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