When simulating human movements it is frequently desirable to optimise multiple phase movements where the phases represent, e.g., different contact conditions. The different constraints are usually acting in parts of the movements and their time durations are in most cases unknown. Therefore a multiple phase free-time optimisation method is formulated in this work, with phase times included as variables. Through a temporal finite element approach, a discrete representation is derived and a nonlinear optimisation algorithm solves for the rather high number of variables (similar to 6000) and constraints (similar to 15000) in the presented numerical problem. A four degrees of freedom test problem, representing a standing high jump, is solved in order to test some basic aspects. A more realistic problem shows its performance in its intended applications, biomechanical simulations. This is a sagittal eight degrees of freedom model for a human backward somersault, including preparing movement, flight phase and landing. The numerical performance as well as some application specific results are discussed. The method description is general and applicable to other movements in its presented format.
QC 20140108