Passive Realizations of Series Elastic Actuation: Effects of Plant and Controller Dynamics on Haptic Rendering Performance

We establish the necessary and sufficient conditions for the passivity of series (damped) elastic actuation (S(D)EA) while rendering Voigt models, linear springs, and the null impedance under velocity-sourced impedance control (VSIC). We introduce minimal passive physical equivalents for S(D)EA under closed-loop control to help establish an intuitive understanding of the passivity bounds and to highlight the effect of different plant parameters and controller gains on the closed-loop performance of the system. Through the passive physical equivalents, we rigorously compare the effect of different plant dynamics (e.g., SEA and SDEA) on the system performance. We demonstrate that passive physical equivalents make the effect of controllers explicit and establish a natural means for effective impedance analysis. We advocate for the co-design of S(D)EAs through simultaneous consideration of the controller and plant dynamics and demonstrate the usefulness of negative controller gains when used with properly designed plant dynamics. We provide experimental validations of our theoretical results and characterizations of the haptic rendering performance of S(D)EA under VSIC.