Optimal motor control strategies and a hybrid approach to stress analysis in skeletal systems

This work relates musculotendon dynamics and neurological controls to a continuum analysis of bone in order to show how the effects of muscular control affect the development of stress and strain in skeletal members. This is achieved by incorporating standard Hill-type models of musculotendon actuators into mathematical models of human motion in which the human body is modeled as an ensemble of articulating segments. The join torques and reaction forces as predicted by this analysis are incorporated into a stress analysis of the segmental links by utilizing an approach in which the equations of motion for the segmental links are derived as a hybrid parameter system. This method accounts for both the rigid body motions of the articulating links and the elastic deformations that represent the continuum effects in the bone. The effect of optimal control strategies upon stress development are also investigated. In particular, neural controls for the musculotendon actuators are derived by formulating a linear quadratic regulator problem in order to investigate control strategies that stabilize the musculoskeletal system about a nominal trajectory. Strategies that are considered correspond to controlling join positions, regulating muscle lengths or tendon stiffness, and full-state feedback control.