Dynamic Cartesian Coordinate Control of a Manipulator

An algorithm for the dyanamic control of a manipulator in Cartesian coordinates is presented. The desired acceleration of the end-effector is transformed into desired joint accelerations through the use of the Gram-Schmidt orthogonalization procedure. The recognition of singular conditions is part of the algorithm and appropriate action is taken when they occur. Given the desired joint accelerations, the Newton-Euler formulation of the manipulator dynamics is used to compute the required actuator torques/forces. A new notation is presented which simplifies the writing of the equations of the model as well as the control algorithm.