Minimal Coordinate Formulation of Contact Dynamics in Operational Space

In recent years, complementarity techniques have been developed for modeling non-smooth contact and collision dynamics problems for multi-link robotic systems. In this approach, a linear complementarity problem (LCP) is set up using 6n non-minimal coordinates for a system with n links together with all the unilateral constraints and inter-link bilateral constraints on the system. In this paper, we use operational space dynamics to develop a complementarity formulation for contact and collision dynamics that uses minimal coordinates. The use of such non-redundant coordinates results in much smaller size LCP problems and the automatic enforcement of the inter-link bilateral constraints. Furthermore, we exploit operational space low-order algorithms to overcome some of the computational bottlenecks in using minimal coordinates.