Necessary and Sufficient Conditions for Passivity of Velocity-Sourced Impedance Control of Series Elastic Actuators

Series Elastic Actuation (SEA) has become prevalent in applications involving physical human-robot interaction as it provides considerable advantages over traditional stiff actuators in terms of stability robustness and fidelity of force control. Several impedance control architectures have been proposed for SEA. Among these alternatives, the cascaded controller with an inner-most velocity loop, an intermediate torque loop and an outer-most impedance loop is particularly favoured for its simplicity, robustness, and performance. In this paper, we derive the \emph{necessary and sufficient conditions} to ensure the passivity of this cascade-controller architecture for rendering two most common virtual impedance models. Based on the newly established passivity conditions, we provide non-conservative design guidelines to haptically display a null impedance and a pure spring while ensuring the passivity of interaction. We also demonstrate the importance of including physical damping in the actuator model during derivation of passivity conditions, when integral controllers are utilized. In particular, we show the adversary effect of physical damping on system passivity.