A computationally efficient method for solving the redundant problem in biomechanics

Determining the optimal set of musculotendon forces with which to produce a forward dynamic simulation of movement typically involves a huge investment of time and computational resources. A new, computationally efficient method is proposed that simultaneously achieves the desired trajectory and the dynamically optimized set of muscle stresses, and hence forces, according to the maximal endurance criterion function of Crowninshield and Brand (1981). Muscle-induced accelerations of the system resulting from unit stress contractions of individual muscles are superposed via the new pseudoinverse method to yield the desired motion trajectory. The method is tested on a control problem involving a five degree-of-freedom (DOF), 30 muscle, upper extremity model, which incorporates a dual rigid-body forearm to represent pronation and supination more adequately. The pseudoinverse method delivered the desired motion to within 0.25 degrees for each DOF during a three-second simulation. It is anticipated that the methodology can be easily and accurately applied to other highly redundant optimal control problems in biomechanics.