An analysis of the motion planning problem for a spherical rolling robot driven by internal rotors

The paper deals with the motion planning for a spherical rolling robot actuated by internal rotors that are placed on orthogonal axes. It is shown that if the robot is actuated by three rotors, any feasible kinematic trajectory is dynamically realizable. For the case of two rotors the conditions of controllability and dynamic realizability of a feasible kinematic trajectory are established. It is shown that in moving the robot by tracing straight lines and circles in the contact plane the dynamically realizable trajectories are not represented by the circles on the sphere, which is a feature of the kinematic model of pure rolling. The dynamic motion planning problem is then formulated in the optimal control settings, and the properties of the optimal trajectories are illustrated under simulation.