Semi-Infinite Programming with Complementarity Constraints for Pose Optimization with Pervasive Contact

This paper presents a novel computational model to address the problem that contact is an infinite phenomena involving continuous regions of interaction. The problem is cast as a semi-infinite program with complementarity constraints (SIPCC). Rather than pre-discretize contacting surfaces into a finite number of contact points, we use semi-infinite programming (SIP) techniques that operate on the underlying continuous geometry, but dynamically determine a finite number of constraints that are most relevant to solving the problem. Then we solve the series of problems whose solutions converge toward one that contains a true optimum of the original SIPCC. We apply the model to a grasping pose optimization problem for a gripper and a humanoid robot, and our model enables the robots to find a feasible pose to hold (non-)convex objects while ensuring force and torque balance.