  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.
