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

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 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 elongationtorque 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.

Challenges and solutions for application and wider adoption of wearable robots

“…Moreover, springs offer the possibility to mechanically store energy when the actuator performs negative work and release it when positive work is required. As such, the average power flow through the actuator is reduced, resulting in an improvement in energy efficiency of the actuator (Hollander et al, 2006;Verstraten et al, 2017;Bolivar Nieto et al, 2019).…”

Computational design of energy-efficient legged robots: Optimizing for size and actuators

“…independent of the chosen trajectory). This holds for any conservative energy component (e.g elastic energy [15]), therefore is not a quantity that needs to be added to the cost function.…”

Natural Motion for Energy Saving in Robotic and Mechatronic Systems

“…Their use is demonstrated to be beneficial in compliant actuation, energy storage, interaction safety, in the absorption of contact shocks and in the reduction of the peak forces due to the impacts in bipedal walking robots [36,37]. Examples of SEA for minimizing energy consumption can be found in References [38,39]. In these works, a convex optimization problem is presented for the design of a SEA capable of energy regeneration such that energy consumption and peak power are minimized for arbitrary periodic reference trajectories.…”