Compared to rigid actuators, series elastic actuators (SEAs) offer a potential reduction of motor energy consumption and peak power, though these benefits are highly dependent on the design of the torque-elongation profile of the elastic element. In the case of linear springs, natural dynamics is a traditional method for this design, but it has two major limitations—arbitrary load trajectories are difficult or impossible to analyze and it does not consider actuator constraints. Parametric optimization is also a popular design method that addresses these limitations, but solutions are only optimal within the space of the parameters. To overcome these limitations, we propose a nonparametric convex optimization program for the design of the nonlinear elastic element that minimizes energy consumption and peak power for an arbitrary periodic reference trajectory. To obtain convexity, we introduce a convex approximation to the expression of peak power; energy consumption is shown to be convex without approximation. The combination of peak power and energy consumption in the cost function leads to a multiobjective convex optimization framework that comprises the main contribution of this paper. As a case study, we recover the elongation-torque profile of a cubic spring, given its natural oscillation as the reference load. We then design nonlinear SEAs for an ankle prosthesis that minimize energy consumption and peak power for different trajectories and extend the range of achievable tasks when subject to actuator constraints.

中文翻译：

---

最小化串联弹性执行器的能耗和峰值功率：弹性元件设计的凸优化框架

与刚性执行器相比，串联弹性执行器（SEA）可以降低电动机的能耗和峰值功率，尽管这些好处在很大程度上取决于弹性元件的扭矩-伸长曲线的设计。对于线性弹簧，自然动力学是此设计的传统方法，但它有两个主要限制-任意载荷轨迹很难或无法分析，并且没有考虑执行器约束。参数优化也是解决这些限制的一种流行的设计方法，但是解决方案仅在参数空间内是最佳的。为了克服这些限制，我们提出了一种用于非线性弹性元件设计的非参数凸优化程序，该程序可将任意周期性参考轨迹的能耗和峰值功率降至最低。为了获得凸性，我们在峰值功率的表达式中引入了一个凸近似。能量消耗显示为凸形，没有近似值。成本函数中峰值功率和能耗的组合导致了一个多目标凸优化框架，该框架包含了本文的主要贡献。作为案例研究，我们将立方弹簧的自然振动作为参考载荷，恢复了其伸长扭矩曲线。