Operational Space Inertia for Closed Chain Robotic Systems

Abstract

Operational space modeling and control are important techniques for robot manipulation. A key element of operational space control is the operational space inertia matrix (OSIM). The OSIM matrix represents a mapping between endeffector spatial forces and spatial accelerations and is configurationdependent. In the case of multiple endeffectors, the OSIM also encapsulates the dynamics cross coupling between the endeffectors. The rich structure of the OSIM for tree systems has been exploited by researchers for analysis and the development of loworder computational algorithms. Extending such techniques to the OSIM for closedchain robotic systems is the focus of this short paper. We derive explicit analytical expressions for the closedchain OSIM that reveals its close relationship to an extended treesystem OSIM.