Damping Selection for Cartesian Impedance Control with Dynamic Response Modulation

This article presents an analytical method to modulate the dynamic response of a robotic manipulator interacting with its environment when performing impedance-related robotic tasks, through the choice of stiffness and damping parameters. By joint space analysis of vibration and experiments, we prove that in order to preserve a desired dynamic behavior of the robot in the Cartesian space, neither a stiffness nor damping matrix can be arbitrarily chosen; this choice has to meet the desired dynamic criteria for any given configuration. After mapping the parameters (matrices) into the joint space, we analyze the vibratory dynamics of the robot and identify the proper way of suppressing of the vibration modes by specific elements in the Cartesian damping matrix without need of trial and error. Our method is especially useful for redundant robots. We show and compare experimental results from two different 7 degrees of freedom robotic manipulators.