On Motion Planning for Ball-Plate Systems With Limited Contact Area

The paper deals with motion planning for rolling-based systems with limited contact area. In a simplified formulation, the driving principle for such systems is based on controlling the position of the center of mass of the object, exploiting non-holonomic rolling constraint to propel the hemisphere. Two geometric algorithms for motion planning are formulated, analyzed, and tested under simulation. The simulation results show the possibility of moving the system to the desired configurations by steering the contact point on the hemisphere by generalized figure eights represented by circles and Viviani´s curves.