We introduce minimal passive physical equivalents of series (damped) elastic actuation (S(D)EA) under closed-loop control to determine the effect of different plant parameters and controller gains on the closed-loop performance of the system and to help establish an intuitive understanding of the passivity bounds. Furthermore, we explicitly derive the feasibility conditions for these passive physical equivalents and compare them to the necessary and sufficient conditions for the passivity of S(D)EA under velocity sourced impedance control (VSIC) to establish their relationship. 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 controller gains explicit and establish a natural means for effective impedance analysis. We also show that passive physical equivalents promote co-design thinking by enforcing simultaneous and unbiased consideration of (possibly negative) controller gains and plant parameters. We demonstrate the usefulness of negative controller gains when coupled to properly designed plant dynamics. Finally, we provide experimental validations of our theoretical results and characterizations of the haptic rendering performance of S(D)EA under VSIC.

翻译：我们引入了闭环控制下串联（阻尼）弹性驱动器的极小无源物理等效模型，以确定不同对象参数和控制器增益对系统闭环性能的影响，并帮助建立对无源性边界的直观理解。此外，我们显式推导了这些无源物理等效模型的可行性条件，并将其与速度源阻抗控制下串联（阻尼）弹性驱动器无源性的充要条件进行比较，以建立它们之间的关系。通过无源物理等效模型，我们严格比较了不同对象动力学（例如，串联弹性驱动器和串联阻尼弹性驱动器）对系统性能的影响。我们证明，无源物理等效模型使控制器增益的影响显式化，并建立了进行有效阻抗分析的自然手段。我们还表明，无源物理等效模型通过强制同时且无偏地考虑（可能为负的）控制器增益和对象参数，促进了协同设计思维。我们展示了负控制器增益在与适当设计的对象动力学耦合时的有用性。最后，我们提供了理论结果的实验验证，以及速度源阻抗控制下串联（阻尼）弹性驱动器触觉渲染性能的表征。