Effect of Reduced-Order Modelling on Passivity and Rendering Performance Analyses of Series Elastic Actuation

We study reduced-order models of series elastic actuation under velocity-sourced impedance control, where the inner motion controller is assumed to render the system into an ideal motion source within a control bandwidth and replaced by a low-pass filter. We present necessary and sufficient conditions for the passivity of this system and prove that the passivity results obtained through the reduced-order model may violate the passivity of the full-order model. To enable safe use of the reduced-order model, we derive conditions under which the passivity bounds of the reduced-order model guarantee the passivity of the full-order system. Moreover, we synthesize passive physical equivalents of closed-loop systems while rendering Kelvin-Voigt, linear spring, and null impedance models to provide rigorous comparisons of the passivity bounds and rendering performance among the full- and reduced-order models. We verify our results through a comprehensive set of simulations and experiments.