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). In the design of pHRI systems, safety is an imperative design criterion that limits interaction performance, since there exists a fundamental trade-off between the stability robustness and rendering performance. The safety of interaction necessitates coupled stability to ensure 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 certain basic environments, and the necessary and sufficient conditions for such passive terminations have been derived. In this study, we extend the one-port passivity analyzes provided in the literature and provide the necessary and sufficient condition for two-port passivity of SEA under velocity-sourced impedance control  . Based on the newly established conditions, we derive non-conservative passivity bounds for a virtual coupler . We also prove the need for a physical damping term in parallel to the series elastic element to ensure two-port passivity , even when a virtual coupler is present. Finally, we validate our theoretical results through numerical simulations and by reproducing one-port passivity results as special cases of our results that correspond to appropriate one-port terminations .
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. In this study, we provide the necessary and sufficient conditions for two-port passivity of series damped elastic actuation under velocity-sourced impedance control within the frequency-domain passivity framework . Based on the newly established conditions, we derive non-conservative passivity bounds for a virtual coupler and rigorously prove the necessity of a dissipative element parallel to the series elastic component and the necessity of a virtual coupler with dissipation for the absolute stability and two-port passivity of the system. The additional dissipative elements in the physical filter and the virtual coupler enable the system to render virtual stiffness values higher than that can be rendered using a pure SEA. Our results extend earlier studies on coupled stability by presenting the necessary and sufficient conditions for all passive terminations. We validate our results through a set of physical experiments and systematic numerical simulations .
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that limits interaction performance,
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the
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coupled stability to ensure
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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 certain basic environments, and the necessary and sufficient conditions for such passive terminations have been derived. In
In
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extend the one-port passivity analyzes provided in the literature and
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condition
conditions
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SEA
series damped elastic actuation
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within the frequency-domain passivity framework
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. We also prove the need for a physical damping term in
and rigorously prove the necessity of a dissipative element
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element to ensure
component and the necessity of a virtual coupler with dissipation for the absolute stability and
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, even when a virtual coupler is present. Finally, we validate our theoretical results through numerical simulations and by reproducing one-port passivity results as special cases of our results that correspond to appropriate one-port terminations
of the system. The additional dissipative elements in the physical filter and the virtual coupler enable the system to render virtual stiffness values higher than that can be rendered using a pure SEA. Our results extend earlier studies on coupled stability by presenting the necessary and sufficient conditions for all passive terminations. We validate our results through a set of physical experiments and systematic numerical simulations