Dynamic simulation of human motion: numerically efficient inclusion of muscle physiology by convex optimization

Determining the muscle forces that underlie some experimentally observed human motion, is a challenging biomechanical problem, both from an experimental and a computational point of view. No non-invasive method is currently available for experimentally measuring muscle forces. The alternative of computing them from the observed motion is complicated by the inherent overactuation of the human body: it has many more muscles than strictly needed for driving all the degrees of freedom of the skeleton. As a result, the skeleton’s equations of motion do not suffice to determine the muscle forces unambiguously. Therefore, muscle force determination is often reformulated as a (large-scale) optimization problem. Generally, the optimization approaches are classified according to the formalism, inverse or forward, adopted for solving the skeleton’s equations of motion. Classical inverse approaches are fast but do not take into account the constraints imposed by muscle physiology. Classical forward approaches, on the other hand, do take the muscle physiology into account but are extremely costly from a computational point of view. The present paper makes a double contribution. First, it proposes a novel inverse approach that results from including muscle physiology (both activation and contraction dynamics) in the inverse dynamic formalism. Second, the efficiency with which the corresponding optimization problem is solved is increased by using convex optimization techniques. That is, an approximate convex program is formulated and solved in order to provide a hot-start for the exact nonconvex program. The key element in this approximation is a (global) linearization of muscle physiology based on techniques from experimental system identification. This approach is applied to the study of muscle forces during gait. Although the results for gait are promising, experimental study of faster motions is needed to demonstrate the full power and advantages of the proposed methodology, and therefore is the subject of subsequent research.