A Three-Dimensional Mass-Spring Walking Model Could Describe the Ground Reaction Forces

Huiqi Liang,Wenbo Xie,Changhui Cui,Zhiqiang Zhang,Peizi Wei,Alessandro Lo Schiavo

doi:10.1155/2021/6651715

Abstract

The oscillatory behavior of the center of mass (CoM) and the ground reaction forces (GRFs) of walking people can be successfully explained by a 2D spring-loaded inverted pendulum (SLIP) model. However, the application of the 2D model is just restricted to a two-dimensional plane as the model fails to take the GRFs in the lateral direction into consideration. In this article, we simulated the gait cycle with a nonlinear dynamic model—a three-dimensional bipedal walking model—that compensated for defects in the 2D model. An experiment was conducted to compare the simulation results with the experimental data, which revealed that the experimental data of the ground reaction forces were in good agreement with the results of numerical simulation. A correlation analysis was also conducted between several initial dynamic parameters of the model. Through an examination of the impact of 3D dynamic parameters on the peaks of GRFs in three directions, we found that the 3D parameters had a major effect on the lateral GRFs. These findings demonstrate that the characteristics of human walking can be interpreted from a simple spring-damper system.

Highlights

Many mathematical models for dynamic systems in the field of engineering science are formulated as nonlinear differential equations
One of the typical passive models that deserves particular attention is the bipedal spring-loaded inverted pendulum (SLIP) model, in which the legs are equivalent to springs, and the ground reaction forces (GRFs) is generated through the alternation of the front and rear legs [9, 22,23,24]. e control strategy to guarantee the stability of walking robots based on the SLIP model has been widely studied and successfully applied [25,26,27,28,29,30,31]
Discussion e application of the conventional SLIP model is restricted to a two-dimensional plane, and the model can only predict the trajectory of center of mass (CoM) and the corresponding values of GRF in the vertical and longitudinal directions [11, 22] in the human walking process

Summary

Introduction

Many mathematical models for dynamic systems in the field of engineering science are formulated as nonlinear differential equations. Human walking models derived mathematically are widely used in many engineering fields, such as gait analysis [4,5,6,7,8,9,10,11], human walking assistance [12, 13], motion stability control of robots [14,15,16,17,18], and response prediction of civil structures induced by pedestrians [19,20,21]. A variety of kinetic models, both passive and active ones, are developed from nonlinear differential equations to study the kinetic phenomenon in human walking. Li et al [35] proposed an actuated dissipative spring-mass model that mimicked

Methods

Findings

Discussion

Conclusion