Feedback gains for correcting small perturbations to standing posture

A dynamical model of the neuromusculoskeletal mechanics of a cat hind limb has been developed and used to investigate the feedback regulation of standing posture under small perturbations. The model is a three-joint limb, moving only in the sagittal plane and driven by ten musculotendon actuators each having response dynamics dependent on activation kinetics and muscle kinematics. Under small perturbations the nonlinear postural regulation mechanism is approximately linear, and sensors that could provide state feedback exist. 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, a combination of muscle lengths and velocities, joint angles and velocities, and motoneuron activities. Thus the feedback gain matrices computed can be related to the spinal neural circuits. It is shown that a strategy of regulating all the states leads to controllers that best mimic the externally measured behavior of real cats