On the motion planning problem for a spherical rolling robot driven by two rotors

The paper deals with the motion planning for a spherical rolling robot actuated by two internal rotors that are placed on orthogonal axes. The condition of controllability is derived and it is shown that the robot is controllable unless the contact trajectory goes along the equatorial line in the plane of the two rotors. The dynamic motion planning problem is then formulated, and an approach based on the nilpotentization of the originally non-nilpotent robot dynamics and on the three step motion panning strategy is explored. A nilpotent approximation is constructed and used for iterative steering of the rolling robot. The initial simulations show the feasibility of this approach.