Motion analysis of a spherical mobile robot

A path planning algorithm for a spherical mobile robot rolling on a plane is presented in this paper. The robot is actuated by two internal rotors that are fixed to the shafts of two motors. These are in turn mounted on the spherical shell in mutually orthogonal directions. The system is nonholonomic due to the nonintegrable nature of the rolling constraints. Further, the system cannot be converted into a chained form, and neither is it nilpotent nor differentially flat. So existing techniques of nonholonomic path planning cannot be applied directly to the system. The approach presented here uses simple geometrical notions and provides numerically efficient and intuitive solutions. We also present the dynamic model and derive motor torques for execution of the algorithm. Along the proposed paths, we achieve dynamic decoupling of the variables making the algorithm more suitable for practical applications.