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 non-linearity 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 multi-start 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 could help acrobatic sports athletes to improve their twisting performance.

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Musculoskeletal simulations are useful in biomechanics to investigate the causes of movement disorder, to estimate non-measurable physiological quantities or to study the optimality of human movement. We introduce bioptim, an easy-to-use Python framework for biomechanical optimal control, handling musculoskeletal models. Relying on algorithmic differentiation and the multiple shooting formulation, bioptim interfaces nonlinear solvers to quickly provide dynamically consistent optimal solutions. The software is both computationally efficient (C++ core) and easily customizable, thanks to its Python interface. It allows to quickly define a variety of biomechanical problems such as motion tracking/prediction, muscle-driven simulations, parameters optimization, multiphase problems, etc. It is also intended for real-time applications such as moving horizon estimation and model predictive control. Six contrasting examples are presented, comprising various models, dynamics, objective functions and constraints. They include data-driven simulations (i.e., a multiphase muscle driven gait cycle and an upper-limb real-time moving horizon estimation of muscle forces) and predictive simulations (i.e., a muscle-driven pointing task, a twisting somersault with a quaternion-based model, a position controller using external forces, and a multiphase torque-driven maximum-height jump motion).

Aerial twisting techniques are preferred by trampoline coaches for their balanced landings. As these techniques are not intuitive, computer simulation has been a relevant tool to explore a variety of techniques. Up to now, twisting somersaults were mainly simulated using arm abduction/adduction only (2D). Our objective was to explore more complex (3D) but still anatomically feasible arm techniques to find innovative and robust twisting techniques. The twist rotation was maximized in a straight backward somersault performed by a model including arm abduction/adduction with and without changes in the plane of elevation. A multi-start approach was used to find a series of locally optimal performances. Six of them were retained and their robustness was assessed by adding noise to the first half of the arm kinematics and then reoptimizing the second half of the skill. We found that aerial twist performance linearly correlates with the complexity of arm trajectory. Optimal techniques share a common strategy consisting of moving the arm in a plane formed by the twisting and angular momentum axes, termed as the best tilting plane. Overall, 3D techniques are simpler and require less effort than 2D techniques for similar twist performances. Three techniques which generate ∼3 aerial twists could be used by athletes because kinematic perturbations do not compromise the performance and the landing.

Musculoskeletal simulations are useful in biomechanics to investigate the causes of movement disorders, to estimate non-measurable physiological quantities or to study the optimality of human movement. We introduce Bioptim, an easy-to-use Python framework for biomechanical optimal control based on both direct multiple shooting and direct collocation, handling musculoskeletal models. Relying on algorithmic differentiation, Bioptim is fast and it interfaces several nonlinear solvers. The software is both computationally efficient (C++ core) and easily customizable, thanks to its Python interface. It allows to quickly define a variety of biomechanical problems such as motion tracking/prediction, muscle-driven simulations, parameters optimization, multiphase problems, etc. It is also intended for real-time applications such as moving horizon estimation and model predictive control.