A Numerical Procedure for Inferring from Experimental Data the Optimization Cost Functions Using a Multibody Model of the Neuro-Musculoskeletal System

We propose a computational procedure for inferring the cost functions that, according to the Principle of Optimality, underlie experimentally observed motor strategies. In the current use of optimization-based mathematical models of neuro-musculoskeletal systems, the cost functions are not known a-priori, since they can not be directly observed or measured on the real bio-system. Consequently, cost functions need to be hypothesized for any given motor task of interest, based on insight into the physical processes that govern the problem. This work tries to overcome the need to hypothesize the cost functions, extracting this non-directly observable information from experimental data. Optimality criteria of observed motor tasks are here indirectly derived using: (a) a mathematical model of the bio-system; and (b) a parametric mathematical model of the possible cost functions, i.e. a search space constructed in such a way as to presumably contain the unknown function that was used by the bio-system in the given motor task of interest. The cost function that best matches the experimental data is identified within the search space by solving a nested optimization problem. This problem can be recast as a non-linear programming problem and therefore solved using standard techniques. The methodology is here formulated for both static and dynamic problems, and then tested on representative examples.