Effect of Inherent Damping of the Series Elastic Element on Rendering Performance and Passivity of Interaction Control

Abstract We study a realistic model of series elastic actuation (SEA) under velocity-sourced impedance control (VSIC), where the inherent damping of the series elastic element is considered during the analysis, even when only the elasticity of the series damped elastic element is used to estimate the interaction forces. We establish a fundamental rendering limitation when the viscous damping of the physical filter is considered in the plant model and prove that passive rendering of stiffness levels that are higher than the stiffness of the physical filter, as well as passive rendering of Voigt models whose damping levels exceed the physical damping of the plant, are possible. We introduce passive physical equivalents of the closed-loop SEA systems with inherent series damping while rendering Kelvin-Voigt, spring, and null impedance models to provide an intuitive understanding of the passivity bounds and to enable rigorous comparisons of rendering performance among various closed-loop systems with different plant models (including or omitting the series damping) and/or controllers (utilizing different interaction force estimates). We present a comprehensive set of experiments to verify our results and demonstrate the effect of including/omitting the damping of the physical filter in the model of SEA.