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

We introduce minimal passive physical realizations of series (damped) elastic actuation (S(D)EA) under closed-loop control to determine the effect of different plant parameters and controller gains on the closed-loop performance of the system and to establish an intuitive understanding of the passivity bounds. Furthermore, we explicitly derive the feasibility conditions for these passive physical equivalents and compare them to the necessary and sufficient conditions for the passivity of S(D)EA under velocity-sourced impedance control (VSIC) to establish their relationship. 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 controller gains explicit and establish a natural means for effective impedance analysis. We also show that passive physical equivalents promote co-design thinking by enforcing simultaneous and unbiased consideration of (possibly negative) controller gains and plant parameters. We demonstrate the usefulness of negative controller gains when coupled with properly designed plant dynamics. Finally, we provide experimental validations of our theoretical passivity results and comprehensive characterizations of the haptic rendering performance of S(D)EA under VSIC.