An Optimal Control Model for Human Postural Regulation

Abstract

Human upright stance is inherently unstable without a balance control scheme. Many biological behaviors are likely to be optimal with respect to some performance measure that involves energy. It is reasonable to believe that the human is (unconsciously) optimizing some performance measure as he regulates his balance posture. In experimental studies, a notable feature of postural control is a small constant sway. Specifically, there is greater sway than would occur with a linear feedback control without delay. A second notable feature of the human postural control is that the response to perturbations varies with their amplitude. Small disturbances produce motion only at the ankles with the hip and knee angles unchanging. Large perturbation evoke ankle and hip angular movement only. Still larger perturbation result in movement of all three joint angles.

Inspired by these features, a biomechanical model resembling human balance control is proposed. The proposed model consists of three main components which are the body dynamics, a sensory estimator for delay and disturbance, and an optimal nonlinear control scheme providing minimum required corrective response. The human body is modeled as a multiple segment inverted pendulum in the sagittal plane and controlled by ankle and hip joint torques. A series of nonlinear optimal control problems are devised as mathematical models of human postural control during quiet standing. Several performance criteria that are high even orders in the body state or functions of these states (such as joint angle, Center of Pressure COP or Center of Mass COM) and quadratic in the joint control are utilized.

This objective function provides a trade-off between the allowed deviations of the position from its nominal value and the neuromuscular energy required to correct for these deviations. Note that this performance measure reduces the actuator energy used by penalizing small postural errors very lightly. By using the Model Predictive Control (MPC) technique, the discrete-time approximation to each of these problems can be converted into a nonlinear programming problem and then solved by optimization methods. The solution gives a control scheme that agrees with the main features of the joint kinematics and its coordination process. The derived model is simulated for different scenarios to validate and test the performance of the proposed postural control architecture.