Design of Damping Matrices for Cartesian Impedance Control of Robotic Manipulators

Impedance control of robotic manipulators has been widely used in manipulation tasks for controlling the interaction behavior between a robotic end-effector and the environment. One of the main challenges in the implementation of impedance control schemes (even in “purely” stiffness control) is the choice of appropriate damping factors of the Cartesian damping matrix for the intended task. Although most tasks are described in the end-effector (or task) space, the required torques for the controller must be applied in the robot joint space. Thus, the attempt to control the end effector dynamics gives rise to dynamic behaviors in the joint space. We show that by analyzing the vibratory dynamics of the robot in joint space and planning out the suppression of the vibration modes of each of the robot joints, we can search for the Cartesian damping matrix parameters in a principled manner. Our method is especially useful for redundant robots and the main contribution of this paper is a novel, general, analytical, and practical method to determine the damping factors. We present experimental results on initial implementation of our algorithm on a 7-DoF robot arm.