Impedance Control on Redundant Manipulators With Zero-Potential-Energy Motions: Theory and Experimental Validation

This article presents an experimental study with theory to identify quantitatively the zero-potential-energy (ZP) motion in Cartesian impedance control of redundant manipulators, based on a new analytical methodology. This ZP mode of motion, analogous to the rigid-body mode in classic mechanical systems, is a result of the redundancy of the robot. When subject to an external perturbation under impedance control, a redundant robot will assume a new equilibrium configuration determined by the ZP motion, governed by the least-energy principle. Consequently, this creates a steady-state deviation from its initial configuration after a perturbation and reaches a new equilibrium. We determine such ZP motion(s) by utilizing a closed-form solution based on vibration theory. Experiments were conducted on a 7-degrees-of-freedom (DoF) redundant Panda robot to determine the new equilibrium after a perturbation. The experimental results are compared with the theoretical prediction of the ZP motions to validate the theoretical results of the zero-potential-energy motions due to stiffness in impedance control. Furthermore, we demonstrated that the ZP motion due to redundancy can be eliminated by removing the redundancy through experimental validation by employing the null-space control, as expected.