We establish the necessary and sufficient conditions for the passivity of series (damped) elastic actuation (S(D)EA) while rendering Voigt models, linear springs, and the null impedance under velocity-sourced impedance control (VSIC). We introduce minimal 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 plant dynamics (e.g., SEA and SDEA) on the system performance. We demonstrate that passive physical equivalents make the effect of controllers explicit and establish a natural means for effective impedance analysis. We advocate for the co-design of S(D)EAs through simultaneous consideration of the controller and plant dynamics and demonstrate the usefulness of negative controller gains when used with properly designed plant dynamics. We provide experimental validations of our theoretical results and characterizations of the haptic rendering performance of S(D)EA under VSIC.

翻译：我们建立了速度源阻抗控制下串联（阻尼）弹性驱动在渲染Voigt模型、线性弹簧及零阻抗时无源性的充要条件。通过引入受闭环控制的串联（阻尼）弹性驱动的最小无源性物理等效模型，不仅有助于直观理解无源性边界，更能揭示不同被控对象参数与控制器增益对系统闭环性能的影响。借助这些无源性物理等效模型，我们严格比较了不同被控对象动力学（如SEA与SDEA）对系统性能的作用。研究表明，无源性物理等效模型使控制器效应显式化，为有效的阻抗分析建立了天然途径。我们倡导通过控制器与被控对象动力学的协同设计来优化串联（阻尼）弹性驱动系统，并论证了在合理设计的被控对象动力学下采用负控制器增益的有效性。最后通过实验验证了理论结果，并对速度源阻抗控制下串联（阻尼）弹性驱动的力触觉渲染性能进行了表征。