Effect of Low-Pass Filtering on Passivity and Rendering Performance of Series Elastic Actuation

We study the effect of low-pass filtering on the passivity and performance of series elastic actuation (SEA) under velocity-sourced impedance control (VSIC) while rendering virtual linear springs and the null impedance. We analytically derive the necessary and sufficient conditions for the passivity of SEA under VSIC with filters in the loop. We demonstrate that low-pass filtered velocity feedback of the inner motion controller amplifies the noise at the outer force loop, necessitating the force controller also be equipped with low-pass filtering. We derive passive physical equivalents of the closed-loop systems to provide intuitive explanations of the passivity bounds and to rigorously compare the performance of controllers with and without low-pass filtering. We show that, while low-pass filtering improves the rendering performance by decreasing the parasitic damping effects and allowing for higher motion controller gains, it also introduces more strict bounds on the range of passively renderable stiffness. We experimentally verify the passive stiffness rendering bounds and performance improvements for SEA under VSIC with filtered velocity feedback.