Geometric algorithms for operational space dynamics and control

In this article we develop a geometric formulation of operational space dynamics and control based on standard results from the theory of Lie groups and Lie algebras. Beginning with the coordinate invariant formulation of robot dynamics presented in Park et al. (1995), we extend these results to develop the equations of motion in operational space coordinates. The resulting equations can be expressed in a recursive fashion for applications requiring computationally efficient algorithms, or can be expressed in terms of simple matrix factors in which the robot parameters appear transparently for applications involving high-level manipulation of the equations of motion. Further, our formulation of operational space dynamics and control is not bound to any specific choice of local reference frames to carry out the dynamic analysis