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.

This paper presents an analytical methodology and experimental study to identify quantitatively the zero-potential-energy (ZP) motion due to the stiffness matrices in Cartesian impedance control of redundant manipulators. This mode of motion, analogous to the rigid-body mode in classic mechanical systems, shows up as a result of the redundancy of the robot and creates a steady-state deviation from its initial configuration after it reaches equilibrium when subject to a perturbation, because of the principle of least energy for dynamic systems. We determine such ZP motion(s) by utilizing a vibration-based closed-form solution recently developed. We identify and provide experimental validation of the existence of the ZP motions on a 7 DoF Panda robot.