Minimizing Energy Consumption and Peak Power of Series Elastic Actuators: a Convex Optimization Framework for Elastic Element Design

TL;DR

This paper introduces a convex optimization framework for designing nonlinear elastic elements in Series Elastic Actuators to minimize energy consumption and peak power across arbitrary trajectories, overcoming limitations of traditional methods.

Contribution

It presents a novel non-parametric convex optimization approach for elastic element design that handles arbitrary load trajectories and actuator constraints.

Findings

Convex approximation of peak power enables joint optimization with energy consumption.

The framework successfully designs nonlinear SEAs for prosthetic ankle applications.

Results extend the range of achievable tasks with energy-efficient actuator designs.

Abstract

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 non-parametric 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.