Coupled stability and performance of interaction control through series viscoelastic actuation

Official URL: https://risc01.sabanciuniv.edu/record=b2586056_(Table of contents)

Series Elastic Actuation (SEA) is a widely-used approach for interaction control as it enables high fidelity and robust force control, improving the safety of physical human-robot interaction (pHRI). Safety is an imperative design criterion for pHRI that limits the interaction performance since there exists a fundamental trade-off between stability robustness and rendering performance. The safety of interaction necessitates the closed-loop stability of a pHRI system when coupled to a wide range of unknown operators and environments. The frequency-domain passivity framework provides powerful analysis tools to study the coupled stability of linear time-invariant systems. In the literature, coupled stability of one-port models of SEA has been studied for various controllers while rendering basic environments, and the necessary and sufficient conditions for such passive terminations have been derived. In this study, we advocate the addition of physical damping in parallel to the compliant element in SEA and provide sufficient conditions for the passivity of series damped elastic actuation (SDEA) under velocity-sourced impedance control (VSIC) while rendering virtual environments with null space, linear spring, or Kelvin-Voigt (KV) models. We show the necessity of a physical dissipative element parallel to the series elastic component to render KV models and discuss the effect of an integral controller while rendering virtual environments modeled by a linear spring. Furthermore, we rigorously prove that SDEA can extend the range of impedances that can be passively rendered with SEA and improve the control performance of the system thanks to the physical damping in parallel to the compliant element. We further extend our results to study the two-port passivity of SDEA under VSIC. We cascade a virtual coupler between the virtual environment and the controlled SDEA and study the coupled stability of SDEA under VSIC for all passive terminations. In particular, we introduce an analysis method based on Sturm’s Theorem and provide the necessary and sufficient conditions for the two-port passivity of SDEA under VSIC within the frequency-domain passivity framework. We prove the necessity of additional dissipative elements in the physical filter and the virtual coupler for the two-port passivity of the system. Based on the newly established conditions, we derive non-conservative passivity bounds for the virtual coupler elements. We also show that these dissipative elements enable SDEA to display stiffer virtual environments than those can be passively rendered with an SEA. Finally, we validate our results through a set of physical experiments and systematic numerical simulations.