Minimal Coordinates Formulation of Contact Dynamics

In recent years, complementarity techniques have been developed for modeling non-smooth dynamics arising from contact and collision problems for multi-link robotic systems. The commonly used complementarity approach sets up a linear complementarity problem (LCP) using non-minimal coordinates together with all the unilateral contact constraints and inter-link hinge and loop closure bilateral constraints on the system. In this paper, we develop a complementarity formulation that uses an operational space approach. It uses minimal coordinates resulting in a much smaller LCP problem whose size is independent of the number of bodies and the number of degrees of freedom in the system. Furthermore, we exploit operational space low-order algorithms to overcome key computational bottlenecks to obtain over an order of magnitude speed up in the solution procedure.