Optimality in forward dynamics simulations

This paper discusses a methodology and an algorithm for the analysis of dynamics of bio-mechanical systems, and in particular of optimal movement patterns between initial and target configurations. The basic formulation utilizes a finite element time discretization and establishes a large set of equations in displacements and forces. These are solved simultaneously for the whole time interval considered. The algorithm allows different optimization criteria for the movement, based on either the smoothness of the movement or the minimization of needed controls or control rates. It is primarily aimed at musculoskeletal simulations with either the joint resultant moments or the redundant muscular tensions as unknowns. Kinetic and kinematic constraints can be introduced for the obtained movement. Examples show that the obtained results are strongly dependent on the optimality criterion used. Systematic usage of the algorithm can improve knowledge about optimal motion planning.