Optimal 3D arm strategies for maximizing twist rotation during somersault of a rigid-body model

Abstract

Looking for new arm strategies for better twisting performances during a backward somersault is of interest for the acrobatic sports community while being a complex mechanical problem due to the nonlinearity of the dynamics involved. As the pursued solutions are not intuitive, computer simulation is a relevant tool to explore a wider variety of techniques. Simulations of twisting somersaults have mainly been realized with planar arm motions. The aim of this study was to explore the outcomes of using 3D techniques, with the demonstration that increasing the fidelity of the model does not increase the level of control complexity on the real system. Optimal control was used to maximize twists in a backward straight somersault with both types of models. A multistart approach was used to find large sets of near-optimal solutions. The robustness of these solutions was then assessed by modeling kinematic noise during motion execution. The possibility of using quaternions for representing orientations in this numerical optimization problem was discussed. Optimized solutions showed that 3D techniques generated about two additional twists compared to 2D techniques. The robustness analysis revealed clusters of highly twisting and stable 3D solutions. This study demonstrates the superiority of 3D solutions for twisting in backward somersault, a result that can help acrobatic sports athletes to improve their twisting performance.