Developing a hybrid method for solving optimal control problems of the musculoskeletal system of the human body: Combination of linear and angular actuators

Musculoskeletal modeling plays an important role in gaining insight into coordination of muscles during human movement. Optimal control can be an effectual method for solving muscle redundancy due to its accuracy; however, this technique suffers from high computational cost. Torque driven methods in which moments-instead of muscles-are considered as actuators of the musculoskeletal systems can reduce the redundancy of the system and the number of unknowns; consequently, it enhances the computational speed. Should we want to define the force of individual muscle(s), this approach is not sufficient. In this study, we provide a hybrid model including muscle-based and moment-based methods in order to compensate this limitation. To reach this goal, a 2-degree-of-freedom skeletal model was considered. Two different sets of actuators were assumed for this model. In the first one six musculotendon units were considered as the actuators of this model. A Hill-based muscle model in accompanied with a stiff tendon was employed to represent the musculotendon units. In the second problem, except for the 5th muscle, we summarized the effects of the musculotendon units into rotational actuators, i.e. torques. The results obtained from the hybrid model and the outcomes of the muscle-driven one, in terms of the joint trajectories, first derivative of joint trajectories and the magnitude of muscle force were compared to each other. While these results were equivalent to each other up to six significant figures, the results of the hybrid method were obtained more than five times faster than the outcomes of the muscle-driven method.