Dynamic response of redundant robot manipulators under impedance control with null-space control

Abstract

A methodology for impedance control based on mechanical vibration theory was presented to select stiffness and damping to meet the desired dynamic response using modal analysis. This methodology provided profound insights into how changes in stiffness and damping matrices influence a robot’s dynamic response under impedance control, by determining natural frequencies and damping ratios in the modal space. In this paper, our analytical and experimental results challenge the claim of a recent paper stating that the use of a null-space projection does not affect the outcomes, which appears to be a claim that is valid based only on their specific choice of stiffness and damping matrices and robot configuration. Through experiments using a 7-DOF Franka Emika Panda robot, we demonstrate the influence of both stiffness/damping matrices and the weighting matrix of null-space control on the responses of robot manipulators with degrees of redundancy performing primary and secondary tasks. We also introduce and show insights of the benefits of switching between the statically and the dynamically consistent projection matrices, contributing to the broader understanding of the dynamic response of redundant robotic manipulators.