Three-Link Inverted Pendulum for Human Balance Analysis: A Preliminary Study

Abstract

Quiet standing was, for many years, studied as a single inverted pendulum, based on the principle that the ankle joint is the most important joint of this movement. However, studies show that hip and knee joints perform, as well, an important role in quiet standing. The aim of this paper is to present a three-segment-inverted pendulum model, using Lagrange's dynamics, to study human quiet stance in the sagittal plane and, therefore, allow, in future work, its appliance to a lower-limb exoskeleton. As a preliminary study, lower limb kinematic and dynamic data were recorded from 15 healthy subjects while balancing using an optical motion capture system. The center-of-pressure (CoP) was calculated with reference to the ankle joint and the projection of the center-of-mass (CoM) in the sagittal plane was estimated, using the positions given by the mathematical model. The contributions of each joint to the estimated projection of CoM and CoP were also investigated. Finally, a correlation between joints kinematics and kinetics was also made. The first results show a good relationship between estimated CoM and CoP and between joints, supporting the theory that, together, the three joints control the body CoM and, thus, allow postural control.