Nonlinear Optimal Control of Planar Musculoskeletal Arm Model With Minimum Muscles Stress Criterion

Abstract

In this paper, the optimal performance of a planar humanlike musculoskeletal arm is investigated during reaching movements employing an optimal control policy. The initial and final states (position and velocity) are the only known data of the response trajectory. Two biomechanical objective functions are taken into account to be minimized as the central nervous system (CNS) strategy: (1) a quadratic function of muscle stresses (or forces), (2) total time of movement plus a quadratic function of muscle stresses. A two-degress of freedom (DOF) nonlinear musculoskeletal arm model (for planar movements) with six muscle actuators and four state variables is used in order to evaluate the proposed optimal policy, while the constraints of the arm motion and muscle forces are considered mathematically. The nonlinear differential equations of this optimal control problem with the first objective function are solved using the method of variation of extremals (VE). For the second objective function, a modified version of the VE method is employed. Accordingly, the optimal total time of the motion is predicted via the second objective function in addition to the optimal trajectory and forces that are also predicted using the first objective function. The influence of the motion time duration on the optimal trajectory is shown and discussed. Finally, the obtained optimal trajectories are compared to the experimental trajectories of the human arm movements.