Minimizing Energy Consumption and Peak Power of Series Elastic Actuators: a Convex Optimization Framework for Elastic Element Design
Minimizing Energy Consumption and Peak Power of Series Elastic Actuators: a Convex Optimization Framework for Elastic Element Design
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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
DOI：
10.1109/tmech.2019.2906887
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Gregg, Robert
中科院分区：
文献类型：
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作者：
Bolivar Nieto, Edgar Alberto;Rezazadeh, Siavash;Gregg, Robert
与刚性执行器相比，串联弹性执行器 (SEA) 可以降低电机能耗和峰值功率，尽管这些优势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，自然动力学是这种设计的传统方法，但它有两个主要局限性：任意载荷轨迹很难或不可能分析，并且它不考虑执行器约束。参数优化也是解决这些限制的流行设计方法，但解决方案仅在参数空间内才是最佳的。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，该程序可以最小化任意周期参考轨迹的能耗和峰值功率。为了获得凸性，我们对峰值功率的表达式引入凸近似；能量消耗在没有近似的情况下显示为凸的。成本函数中峰值功率和能耗的组合产生了多目标凸优化框架，该框架构成了本文的主要贡献。作为案例研究，我们恢复了立方弹簧的伸长扭矩曲线，并将其自然振荡作为参考载荷。然后，我们为踝关节假体设计非线性 SEA，最大限度地减少不同轨迹的能耗和峰值功率，并在受到执行器约束时扩展可实现的任务范围。
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.