Analysis of the influence of coordinate and dynamic formulations on solving biomechanical optimal control problems

Predictive simulations are useful in biomechanics to determine the optimal trajectories between two mechanical states and their forces in an in-silico approach. To perform these predictions, optimal control problems are increasingly in use. However, the efficiency of their formulation is crucial: in order to converge to the same optimal solution, some formulations could take a higher number of iterations than others. The paper presents an analysis of how certain key factors affect the convergence of these simulations. We compare the convergence of several optimal control problems solved using a direct collocation method. Eight planar torque-driven models of a human skeleton are used with four different types of coordinates and two dynamic formulations. The results show that both the mass matrix of the multibody system and the Hessian matrix of the non-linear problem affect the convergence of the solution: there is a statistical significant relationship among the number of iterations and the conditioning of these two matrices. Moreover, the study shows that the optimal control problems formulated with absolute coordinates are the ones requiring the lowest number of iterations overall. These findings suggest that formulations leading to poor conditioning of mass and Hessian matrices should be avoided.Peer ReviewedPostprint (author's final draft