Dynamic optimization: inverse analysis for the Yurchenko layout vault in womenʹs artistic gymnastics

The use of dynamic optimization to compute the trajectory of joint torques is not popular due to the large amount of computation required, the choice of initial “guesstimates” of torque values and the mathematical sophistication required to understand the technique. Modern optimal control algorithms circumvent most of these objections to the method. It is our aim to demonstrate that the dynamic optimization technique is feasible for complex movements, using the Yurchenko layout vault as an example. A dynamic optimization method to compute joint torques so that the histories of the angular orientations of the model segments closely approximate the corresponding observed angular coordinate histories is demonstrated with the Yurchenko layout vault using an optimal control package. The objective function used is a measure of distance of fitted segment angles to the data, plus the distance of the fitted whole body centre of mass (CM), from the whole body CM computed from the data. Including the CM into the objective function, facilitates the optimization process so as to obtain a set of torques which reproduced the data. The paper shows that the approach works well for the task examined, that is, where the dynamics of the system change during a movement (impact to postflight).