On Motion Planning for Robotic Manipulation with Rolling Contacts

Abstract The paper addresses the motion planning problem (MPP) arising in manipulation tasks where rigid bodies may roll on each other without slipping. In the planar case, where both the kinematics and dynamics of the system are considered, the MPP can be solved without quasi-static approximations. This result follows from the integrability of the kinematic constraints and the differential flatness property which allows to easily parameterize the set of feasible trajectories of the system. An extension to a three dimensional example is also presented using the Liouvillian property of the corresponding kinematic model.