  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.
