Non-prehensile Planar Manipulation via Trajectory Optimization with Complementarity Constraints

TL;DR

This paper introduces a trajectory optimization method using complementarity constraints for non-prehensile planar manipulation, enabling mode switching between sticking and sliding, with demonstrated advantages in planning and control tasks.

Contribution

The paper presents a novel MPCC-based trajectory optimization approach for non-prehensile manipulation that outperforms mixed integer methods in speed, scalability, and robustness.

Findings

Faster convergence of the MPCC planner compared to mixed integer methods.

Better tracking and consistent computation times with the MPCC controller.

Successful experimental validation on a KUKA LWR robot.

Abstract

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.