Feedback gains for correcting small perturbations to standing posture

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Abstract
A dynamical model of the neuro-musculo-skeletal mechanics of a cat hindlimb is developed to investigate the feedback regulation of standing posture under small perturbations. The model is a three-joint limb, moving only in the sagittal plane, driven by 10 musculotendon actuators, each with response dynamics dependent on activation kinetics and muscle kinematics. Under small perturbations, the nonlinear postural regulation mechanism is approximately linear. Sensors exist which could provide state feedback. Thus, the linear quadratic regulator is proposed as a model for the structure of the feedback controller for regulation of small perturbations. System states are chosen to correspond to the known outputs of physiological sensors: muscle forces (sensed by tendon organs), a combination of muscle lengths and velocities (sensed by spindle organs), joint angles and velocities (sensed by joint receptors), and motoneuron activities (sensed by Renshaw cells). Thus, the feedback gain matrices computed can be related to the spinal neural circuits. Several proposals for control strategy have been tested under this formulation. It is shown that a strategy of regulating all the states leads to controllers that best mimic the externally measured behavior of real cats.