A Fundamental Limitation of Passive Spring Rendering With Series Elastic Actuation

We establish a fundamental limitation of stiffness rendering with series elastic actuation by rigorously proving that no causal controller can passively render virtual stiffness levels that are higher than the stiffness of the physical series elastic element. To relax this bound, we propose the addition of a viscous damping term parallel to the elastic element to form series damped elastic actuation (SDEA). We show that there exist LTI controllers for SDEA that can relax the passivity bound on the virtual stiffness, and derive the necessary and sufficient conditions for the passive stiffness rendering with SDEA under such a controller. We experimentally verify the relaxed passive stiffness rendering bounds for SDEA, by studying the coupled stability of interactions with most destabilizing environments.