Optimal control of multiple robot systems with friction using mpcc

This paper studies optimal control of multiple robot systems with frictional contact. The task is to move the robots into goal regions with specified velocities using external control forces. 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 by 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 a novel optimal control model that can deal with friction in the multiple robot system, and application of a new mathematical programming algorithm to solve the MPCC formulation. This optimal control model has potential applications in robot systems with friction, such as multifinger manipulation, manipulation with ropes, and multirobot pushing coordination.