How Leg Stiffness Affects Energy Economy in Hopping

TL;DR

This study investigates how leg stiffness influences energy efficiency in hopping robots, finding that variable stiffness can significantly improve energy economy across different speeds.

Contribution

It provides a detailed numerical analysis showing that variable leg stiffness enhances energy efficiency compared to fixed stiffness in hopping robots.

Findings

Variable stiffness improves energy efficiency by up to 20%.

On average, variable stiffness yields a 6.8% energy saving.

Optimal control solutions depend on speed and stiffness parameters.

Abstract

In the fields of robotics and biomechanics, the integration of elastic elements such as springs and tendons in legged systems has long been recognized for enabling energy-efficient locomotion. Yet, a significant challenge persists: designing a robotic leg that perform consistently across diverse operating conditions, especially varying average forward speeds. It remains unclear whether, for such a range of operating conditions, the stiffness of the elastic elements needs to be varied or if a similar performance can be obtained by changing the motion and actuation while keeping the stiffness fixed. This work explores the influence of the leg stiffness on the energy efficiency of a monopedal robot through an extensive parametric study of its periodic hopping motion. To this end, we formulate an optimal control problem parameterized by average forward speed and leg stiffness, solving it numerically using direct collocation. Our findings indicate that, compared to the use of a fixed stiffness, employing variable stiffness in legged systems improves energy efficiency by 20 % maximally and by 6.8 % on average across a range of speeds.