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

Non-prehensile Planar Manipulation via Trajectory Optimization with Complementarity Constraints