Passivity of Series Damped Elastic Actuation under Velocity-Sourced Impedance Control

Series elastic actuation (SEA) is a widely-used interaction control approach that relies on an intentionally introduced compliant element between the actuator and the end-effector and the utilization of the model of this compliant element in closed-loop force control to achieve high interaction performance. Velocity-sourced impedance control (VSIC) is the most commonly employed controller for SEA due to its rendering performance, robustness, and ease of tuning. The necessary and sufficient conditions for the frequency-domain passivity of SEA under VSIC have been extensively studied in the literature, establishing the range of passively renderable impedances. In this study, we advocate the addition of physical damping in parallel to the series elastic element in SEA and provide sufficient conditions for the passivity of series damped elastic actuation (SDEA) under VSIC while rendering null space, linear spring, and Voigt model virtual environments. We rigorously prove that SDEA can extend the range of impedances that can be passively rendered with SEA and improve the control performance of the system thanks to the physical damping in parallel to the compliant element. Furthermore, we show the necessity of a physical dissipative element parallel to the series elastic component to render Voigt models and the necessity of the integral gain of the motion controller to render virtual environments modeled by a linear spring.