A Novel Theoretical Framework for the Dynamic Stability Analysis, Movement Control, and Trajectory Generation in a Multisegment Biomechanical Model

Abstract

We consider a simplified characterization of the postural control system that embraces two broad components: one representing the musculoskeletal dynamics in the sagittal plane and the other representing proprioceptive feedback and the central nervous system (CNS). Specifically, a planar four-segment neuromusculoskeletal model consisting of the ankle, knee, and hip degrees-of-freedom (DOFs) is described in this paper. The model includes important physiological constructs such as Hill-type muscle model, active and passive muscle stiffnesses, force feedback from the Golgi tendon organ, muscle length and rate feedback from the muscle spindle, and transmission latencies in the neural pathways. A proportional-integral-derivative (PID) controller for each individual DOF is assumed to represent the CNS analog in the modeling paradigm. Our main hypothesis states that all stabilizing PID controllers for such multisegment biomechanical models can be parametrized and analytically synthesized. Our analytical and simulation results show that the proposed representation adequately shapes a postural control that (a) possesses good disturbance rejection and trajectory tracking, (b) is robust against feedback latencies and torque perturbations, and (c) is flexible to embrace changes in the musculoskeletal parameters. We additionally present detailed sensitivity analysis to show that control under conditions of limited or no proprioceptive feedback results in (a) significant reduction in the stability margins, (b) substantial decrease in the available stabilizing parameter set, and (c) oscillatory movement trajectories. Overall, these results suggest that anatomical arrangement, active muscle stiffness, force feedback, and physiological latencies play a major role in shaping motor control processes in humans.