Spring-loaded inverted pendulum goes through two contractionextension cycles during the single-support phase of walking

Abstract

Despite the overall complexity of legged locomotion, the motion of the center ofmass (COM) itself is relatively simple, and can be qualitatively described by simple mechanical models. In particular, walking can be qualitatively modeled by a simple model in which each leg is described by a spring-loaded inverted pendulum(SLIP). However, SLIP hasmany limitations and is unlikely to serve as a quantitative model. As a first step to obtaining a quantitative model for walking, we explored the ability of SLIP tomodel the single-support phase ofwalking, and found that SLIP has two limitations. First, it predicts larger horizontal ground reaction forces (GRFs) than empirically observed. A new model - angular and radial spring-loaded inverted pendulum (ARSLIP) - can overcome this deficit. Second, although the leg spring (surprisingly) goes through contraction-extension-contraction-extensions (CECEs) during the single-support phase of walking and can produce the characteristic M-shaped vertical GRFs, modeling the single-support phase requires active elements. Despite these limitations, SLIP as a model provides important insights. It shows that the CECE cycling lengthens the stance duration allowing the COMto travel passively for longer, and decreases the velocity redirection between the beginning and end of a step.