The Effect of Shapes in Input-State Linearization for Stabilization of Nonprehensile Planar Rolling Dynamic Manipulation

A control framework for nonprehensile planar rolling dynamic manipulation is derived in this letter. By rotating around the center of mass, the manipulator moves a part without grasping it but exploiting its dynamics. Given some assumptions on the shapes of both the object and the manipulator, a state transformation is found rendering the state-space system in a chain of integrators form without internal dynamics, allowing the possibility to exploit linear controls to stabilize the whole system. An analysis of the differential flatness property of the system is also provided. Simulations and experiments validate the derived framework.