# Optimization of Actuator Stiffness and Actuation Timing of a Passive Ankle Exoskeleton: A Case Study Using a Musculoskeletal Modeling Approach

## TL;DR

This study uses a musculoskeletal model to find the best stiffness and timing for a passive ankle exoskeleton to reduce walking energy costs.

## Contribution

The study introduces a novel approach using OpenSim to optimize passive ankle exoskeleton parameters for energy efficiency.

## Key findings

- The greatest energy reduction of -2.67% was found at 15% stance timing and 5.5 kN/m stiffness.
- A quadratic relationship between stiffness and energy consumption was confirmed with R2 = 0.99.
- Optimal stiffness of ~5.5 kN/m minimizes energy cost during walking.

## Abstract

Objective: A modeling and simulation tool, OpenSim, was used to determine the optimal relationship between actuator stiffness and actuation timing of a passive ankle exoskeleton for reducing metabolic costs during walking. We hypothesized that the absolute minimum in total metabolic cost would exist at an actuation timing of 15% of stance and at a spring stiffness of 7.5 kN/m. We also hypothesized that a local minimum in total metabolic cost would exist at an actuation timing of 50% of stance. Methods: Bilateral kinematics and kinetics data were collected on a healthy male walking overground wearing his regular tennis shoe. The passive ankle exoskeleton geometry and the spring actuator were integrated into the OpenSim model. Simulations were performed for every combination of 25 spring stiffnesses ranging from 5.5 kN/m to 17.5 kN/m (increments of 0.5 kN/m) and 10 actuation timings ranging from 15% to 60% of stance (increments of 5%). Total energy expenditure was calculated as the sum of the energy expenditure of all the muscles in the model. Results: The greatest reduction in energy consumption (−2.67%) was observed at an actuation timing of approximately 15% of the stance phase with a spring stiffness of ~5.5 kN/m. A quadratic relationship between spring stiffness and energy consumption was identified (R2 = 0.99), with an optimal stiffness of approximately 5.5 kN/m minimizing the energy cost. Conclusions: Our findings suggest that OpenSim effectively predicts optimal exoskeleton parameters, supporting personalized assistance to improve energy efficiency and rehabilitation outcomes.