Optimal Control of Human Balance Models With Reflex Delay

Abstract

Falls are the leading cause of injury-related deaths among the elderly, and scientists are increasingly interested in understanding the mechanism of human balance control. A single inverted pendulum is used to model the musculoskeletal dynamics of the human body with an ankle torque. There is a brief period of time between detecting a problem in proper positioning and applying torque to correct it. We present a mathematical optimal control model with delay for identifying human balance postural dynamics considering humans as a single inverted pendulum with an ankle torque. The equation of motion is a second-order delay differential equation, and it is solved numerically. Optimal feedback gains obtained from the optimal control problem with linear quadratic regulator function vary in time for a short period of time before becoming constant. These optimal feed- back gains are time and delay-dependent to compensate for the effect of the delay. We provide numerical simulations for different parameter values and scenarios to investigate human postural dynamics’ stability and demonstrate the model’s capabilities. Finally, we extend our study by investigating the dynamics of ankle and hip movement in response to perturbations using a double-inverted pendulum.