Optimal 3D arm strategies for maximizing twist rotation during somersault of a rigid-body model
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Optimal 3D arm strategies for maximizing twist rotation during somersault of a rigid-body model François Bailly1 Mickael Begon1
· Eve Charbonneau1 · Loane Danès2 ·
Received: 26 March 2020 / Accepted: 1 October 2020 © Springer Nature B.V. 2020
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. Keywords Rigid-body dynamics · Biomechanics · Optimal control · Numerical optimization · Sports performance
1 Introduction Twist rotations during aerial somersaults in acrobatic sports have been frequently studied in biomechanics [1–3]. Apart from contact techniques that involve a twisting angular
B F. Bailly
[email protected]
1
Laboratoire de Simulation et Modélisation du Mouvement, Faculté de Médecine, Université de Montréal, Laval, QC, Canada
2
AgroParisTech, Paris, France
F. Bailly et al.
momentum at takeoff, there exist two main categories of techniques, which have sparked researchers interest, namely aerial and cat-twist techniques [4]. Understanding the motor strategies underlying these approaches is an interesting challenge because they involve complex sequences of actions subject to highly nonlinear dynamics. Pure aerial techniques – as opposed to cat twists – are of particular interest in acrobatic sports since they can be performed using only arm motions, leaving the rest of the body in a straight configuration, which is often preferred for aesthetic reasons and simpler to model in simulation. In most of the acrobatic/artistic activities (trampoline, diving, gymnastics, freestyle skiing, etc.), the number of twists during somersaults is considered as a part of the sports performance. Looking for innovative arm strategies
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