  Long-term non-prehensile planar manipulation is a challenging task for
planning and control, requiring determination of both continuous and discrete
contact configurations, such as contact points and modes. This leads to the
non-convexity and hybridness of contact optimization. To overcome these
difficulties, we propose a novel approach that incorporates human
demonstrations into trajectory optimization. We show that our approach
effectively handles the hybrid combinatorial nature of the problem, mitigates
the issues with local minima present in current state-of-the-art solvers, and
requires only a small number of demonstrations while delivering robust
generalization performance. We validate our results in simulation and
demonstrate its applicability on a pusher-slider system with a real Franka
Emika robot.
