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

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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.

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Acknowledgement

This work was supported by the Mitacs Acceleration grant #IT11976 and by the Institut National du Sport du Québec.

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Authors and Affiliations

  1. Laboratoire de Simulation et Modélisation du Mouvement, Faculté de Médecine, Université de Montréal, Laval, QC, Canada

    François Bailly, Eve Charbonneau & Mickael Begon

  2. AgroParisTech, Paris, France

    Loane Danès

Authors
  1. François Bailly
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  2. Eve Charbonneau
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  3. Loane Danès
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  4. Mickael Begon
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Correspondence to François Bailly.

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Appendix

Appendix

Table 4 Summary table of the kinematics and kinetics bounds enforced by the optimization problem at the start, during the skill, and at the end of it. − stands for infinite bounds
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figure 8

Right and left arm abd/adduction (elevation) of the most-twisting 2D solution (2.94 twists) without penalization on the hand trajectory

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Fig. 9
figure 9

Right and left arm abd/adduction (elevation) and elevation change of plane of the most-twisting 3D solution (4.90 twists) without penalization on the hand trajectory

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Fig. 10
figure 10

Right and left arm abd/adduction (elevation) and elevation change of plane of another 3D solution (3.10 twists) with penalization on the hand trajectory

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Fig. 11
figure 11

Initial guesses of each optimization variable for the 3D and 2D models. Empty field means initialization to 0

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Bailly, F., Charbonneau, E., Danès, L. et al. Optimal 3D arm strategies for maximizing twist rotation during somersault of a rigid-body model. Multibody Syst Dyn 52, 193–209 (2021). https://doi.org/10.1007/s11044-020-09759-5

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  • DOI: https://doi.org/10.1007/s11044-020-09759-5

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