Optimal control of human-like musculoskeletal arm: Prediction of trajectory and muscle forces

Optimal trajectory and muscle forces of a human‐like musculoskeletal arm are predicted for planar point‐to‐point movements using optimal control theory. The central nervous system (CNS) is modeled as an optimal controller that performs a reaching motion to final states via minimization of an objective function. For the CNS strategy, a cubic function of muscles stresses is considered as an appropriate objective function that minimizes muscles fatigue. A two‐DOF nonlinear musculoskeletal planar arm model with four states and six muscle actuators is used for the evaluation of the proposed optimal strategy. The nonlinear variational formulation of the corresponding optimal control problem is developed and solved using the method of variation of extremals. The initial and (desired) final states (position and velocity) are used as input kinematic information, while the problem constraints include the motion range of each joint, maximum allowable muscle tension, and stability requirements. The resulting optimal trajectories are compared with experimental data as well as those corresponding to recent researches on model predictions of human arm movements. It is demonstrated that the proposed optimal control strategy using minimum fatigue criterion is more realistic in prediction of motion trajectories in comparison with previous work that has utilized minimum joints' torque criterion. Accordingly, minimization of muscles fatigue is an effective biomechanical criterion for the CNS in prediction of point‐to‐point human arm motions.