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

This paper discusses the essential equivalence of second order impedance control with force feedback and proportional gain explicit force control with force feedforward. 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 presented, con rming the predictions of the analysis. These results experimentally demonstrate that proportional gain force control and impedance control, with and without dynamics compensation, have equivalent response to commanded force trajectories.