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

We establish the necessary and sufficient conditions for the frequency domain passivity of series (damped) elastic actuation (S(D)EA) while rendering null impedance and ideal springs under velocity sourced impedance control (VSIC). We introduce 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 plants dynamics (e.g., SEA and SDEA) and different cascaded controller architectures (e.g., P-P and P-PI) on the system performance. We show that passive physical equivalents establish a natural means for effective impedance analysis. We provide experimental validations of our theoretical results and evaluate the haptic rendering performance of S(D)EA under VSIC.