Minimizing Energy Consumption and Peak Power of Series Elastic Actuators: a Convex Optimization Framework for Elastic Element Design
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Series elastic actuators (SEAs) support the development of energy-efficient lightweight robotic systems that interact in uncertain environments. Compared to rigid actuators, SEAs offer a potential reduction of energy consumption and peak power, though these benefits are highly dependent on the design of the elastic element. The method of natural dynamics is traditionally used 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 non-parametric convex optimization problem for the design of the elastic element such that energy consumption and peak power are minimized for arbitrary periodic reference trajectories. 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 the present work. As a case study, we show the approach can recover the elongation-torque profile of a cubic spring when 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.
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