|Global Formulation and Motion Planning for a Sphere Rolling on a Smooth Surface
Muhammad Rehan and Mahmut Reyhanoglu*
International Journal of Control, Automation, and Systems, vol. 16, no. 6, pp.2709-2717, 2018
Abstract : "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."
Global formulation, kinematics, nonholonomic, nonlinear.