An optimal control model for analyzing human postural balance

Abstract
The question posed in this study is whether optimal control and state estimation can explain selection of control strategies used by humans, in response to small perturbations to stable upright balance. To answer this question, a human sensorimotor control model, compatible with previous work by others, was assembled. This model incorporates linearized equations and full-state feedback with provision for state estimation. A form of gain-scheduling is employed to account for nonlinearities caused by control and biomechanical constraints. By decoupling the mechanics and transforming the controls into the space of experimentally observed strategies, the model is made amenable to the study of a number of possible control objectives. The objectives studied include cost functions on the state deviations, so as to control the center of mass, provide a stable platform for the head, or maintain upright stance, along with a cost function on control effort. Also studied was the effect of time delay on the stability of controls produced using various control strategies. An objective function weighting excursion of the center of mass and deviations from the upright stable position, while taking advantage of fast modes of the system, as dictated by inertial parameters and musculoskeletal geometry, produces a control that reasonably matches experimental data. Given estimates of sensor performance, the model is also suited for prediction of uncertainty in the response.

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