The Equivalence of Second-Order Impedance Control and Proportional Gain Explicit Force Control

Abstract

This paper discusses the essential equivalence o f s e cond order impedance c ontrol with force f e edback and proportional gain explicit force c ontrol with force f e edforward. This is rst done analytically by reviewing each control method and showing how they mathematically correspond for constrained manipulator control. For sti environments the correspondence is exact. However, even for softer environments similar response of the system is indicated. Next, the results of an implementation of these control schemes on the CMU DD Arm II are p r esented, con rming the predictions of the analysis. These results experimentally demonstrate that proportional gain force c ontrol and impedance control, with and without dynamics compensation, have equivalent response to commanded force t r ajectories.

Predictive Force Control of Robot Manipulators in Nonrigid Environments

“…The impedance control goal is to oblige the manipulator to follow the reference or target impedance. As shown by (Volpe & Khosla, 1995) a good impedance relation is achieved with a linear model of second order. The complete form of a second order type impedance control model, which is valid for free or constrained motion, is given by:…”

Comment on "The Equivalence of Second-Order Impedance Control and Proportional Gain Explicit Force Control"

“…Analyzing this one controller led the authors to &dquo;question the value of impedance control as a unified controller for motion through, and constrained interaction with, the environment&dquo; (Volpe and Khosla 1995). Throughout their several papers on this topic, they assume a stiff environment, and hence no significant work can be exchanged between' robot and workpiece in the direction normal to the surface of the environment.…”

“…In a series of papers, Volpe and Khosla (1993a, 1993b, 1995 demonstrate that one form of an impedance controller is equivalent to proportional gain explicit force control in certain interaction situations. They then use this equivalence to compare the performance of impedance control with other forms of explicit force control.…”

Energy-based and biomimetic robotics

“…Often, this specific implementation and choice has been considered in literature as "The impedance control approach," instead of the much more general causality and portbehaviour argument mentioned before. A characteristic example of this debate was published in [161] and the reaction by [167].…”

“…The main drawback is that force control is only possible if there is contact between the manipulator and the environment. In some cases there is an equivalence between force control and impedance control: if the manipulator does not move-for instance with an infinitely stiff environment-thenẋ = 0 in (2.22) and F is constant; [161]. However, there is again a clear distinction: impedance control determines the dynamic interaction behaviour of the manipulator and the observed equivalence only holds in some very specific cases; [167].…”