Operational Space Inertia for Robots with Internal Loops

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. In the case of multiple end-effectors, the OSIM also encapsulates the dynamics cross-coupling between the end-effectors. The OSIM matrix is configuration dependent. The rich structure of the OSIM for tree systems has been exploited by researchers for analysis and the development of low order computational algorithms. Extending such techniques to the OSIM for closed-chain robotic systems is the focus of this short paper. We derive explicit analytical expressions for the closed-chain OSIM that reveals its close relationship to an extended tree-system OSIM.