Non-prehensile Planar Manipulation via Trajectory Optimization with Complementarity Constraints

Contact adaption is an essential capability when manipulating objects. Two key contact modes of non-prehensile manipulation are sticking and sliding. This paper presents a Trajectory Optimization (TO) method formulated as a Mathematical Program with Complementarity Constraints (MPCC), which is able to switch between these two modes. We show that this formulation can be applicable to both planning and Model Predictive Control (MPC) for planar manipulation tasks. We numerically compare: (i) our planner against a mixed integer alternative, showing that the MPCC planer converges faster, scales better with respect to time horizon, and can handle environments with obstacles; (ii) our controller against a state-of-the-art mixed integer approach, showing that the MPCC controller achieves better tracking and more consistent computation times. Additionally, we experimentally validate both our planner and controller with the KUKA LWR robot on a range of planar manipulation tasks.