Simulations of human movements through temporal discretization and optimization

Sammanfattning: Study of physical phenomena by means of mathematical models is common in various branches of engineering and science. In biomechanics, modelling often involves studying human motion by treating the body as a mechanical system made of interconnected rigid links. Robotics deals with similar cases as robots are often designed to imitate human behavior. Modelling human movements is a complicated task and, therefore, requires several simplifications and assumptions. Available computational resources often dictate the nature and the complexity of the models. In spite of all these factors, several meaningful results are still obtained from the simulations.One common problem form encountered in real life is the movement between known initial and final states in a pre-specified time. This presents a problem of dynamic redundancy as several different trajectories are possible to achieve the target state. Movements are mathematically described by differential equations. So modelling a movement involves solving these differential equations, along with optimization to find a cost effective trajectory and forces or moments required for this purpose.In this study, an algorithm developed in Matlab is used to study dynamics of several common human movements. The main underlying idea is based upon temporal finite element discretization, together with optimization. The algorithm can deal with mechanical formulations of varying degrees of complexity and allows precise definitions of initial and target states and constraints. Optimization is carried out using different cost functions related to both kinematic and kinetic variables.Simulations show that generally different optimization criteria give different results. To arrive on a definite conclusion on which criterion is superior over others it is necessary to include more detailed features in the models and incorporate more advanced anatomical and physiological knowledge. Nevertheless, the algorithm and the simplified models present a platform that can be built upon to study more complex and reliable models.