Stability of Human Balance During Quiet Stance With Physiological and Exoskeleton Time Delays

Abstract

Human balance with exoskeleton assistance is studied using an inverted pendulum model, considering time delays in the muscle reflexes and the exoskeleton controller. The model includes two motors at the ankle joint whose maximum torques depend on the joint angle and angular velocity, reflecting the combined moment-generating capacity of all plantarflexor and dorsiflexor muscles. These “muscle-like” motors obey a proportional–derivative (PD) reflex control law where the angle and angular velocity of the ankle joint are subject to feedback delays. The stability of this system is analyzed using Galerkin projection to convert the governing neutral delay differential equation into a system of first-order ordinary differential equations (ODEs) and computing the eigenvalues of the ODE system. The stability analysis is then repeated with exoskeleton torques included at the ankle joint. The exoskeleton torques are assumed to obey a PD control law as well but with a unique state feedback delay. Stability charts reveal that the area of the stability region always increases as the exoskeleton delay decreases, but the area may decrease as the physiological delay decreases. The presented analytical framework enables investigation of the effect of control gains and time delays on the stability of a combined human–exoskeleton system.