Simple motion planning algorithms for ball-plate systems with limited contact area

The paper deals with motion planning for rolling-based systems with limited contact area. To understand the problem we resort to a simplified quasi-static model in which the locomotion object is represented by a mass point. In this formulation, the driving principle is based on controlling the position of the center of mass of the object, exploiting nonholonomic rolling constraint to propel the hemisphere. Two motion planning algorithms are proposed. The algorithms are tested under simulation. The simulation results show the possibility of steering the locomotion system to the desired configurations by moving the center of mass through multiple generalized figure eights on the main hemisphere plane