### LANS Publications

# "Optimal Control of Multiple Robot Systems with Friction using MPCC"

J. Peng, M. Anitescu, and S. Akella

Preprint ANL/MCS-P1157-0404

Preprint Version: [pdf]

This paper studies optimal control of multiple robot systems with frictional contact. The robots have nonlinear dynamics, which may arise from the robot body dynamics, friction between robot and environment, and friction between robot and robot. Nonpenetration constraints between robots are imposed, and the robots are assumed rigid. The problem is modeled as a mathematical program with complementarity constraints (MPCC). The MPCC model is solved using its elastic mode, which is a well-behaved nonlinear programming problem. Preliminary results with this approach are illustrated on example problems. The main contributions of this paper are: (1) a novel optimal control model that can deal with friction in the multiple robot system; (2) application of a new mathematical programming algorithm to solve the MPCC model effectively. The coordination model has potential applications in robot systems with friction, such as multi-finger manipulation, manipulation with ropes, and multi-robot pushing coordination.