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

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.

[1]  Franck Barbier,et al.  Local versus global optimal sports techniques in a group of athletes , 2015, Computer methods in biomechanics and biomedical engineering.

[2]  Karen Leung,et al.  The Diver with a Rotor , 2015, 1510.02978.

[3]  Michael J. Hiley,et al.  The mechanics of the backward giant circle on the high bar , 2000 .

[4]  John L. Crassidis,et al.  Geometric Integration of Quaternions , 2012 .

[5]  Martin L. Felis.  RBDL: an efficient rigid-body dynamics library using recursive algorithms , 2017, Auton. Robots.

[6]  Guy Bessonnet,et al.  A Parametric Optimization Approach to Walking Pattern Synthesis , 2005, Int. J. Robotics Res..

[7]  Michael Boyle,et al.  The Integration of Angular Velocity , 2016, 1604.08139.

[8]  S. Sathiya Keerthi,et al.  Optimal control of a somersaulting platform diver: a numerical approach , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[9]  Jaco F Schutte,et al.  Evaluation of a particle swarm algorithm for biomechanical optimization. , 2005, Journal of biomechanical engineering.

[10]  M. R. Yeadon,et al.  Twist limits for late twisting double somersaults on trampoline. , 2017, Journal of biomechanics.

[11]  Katja Mombaur,et al.  Modeling and optimal control of human platform diving with somersaults and twists , 2011, Optimization and Engineering.

[12]  C. Frohlich.  The physics of somersaulting and twisting. , 1980, Scientific American.

[13]  Moritz Diehl,et al.  CasADi: a software framework for nonlinear optimization and optimal control , 2018, Mathematical Programming Computation.

[14]  Maurice R Yeadon,et al.  The control of twisting somersaults. , 2014, Journal of biomechanics.

[15]  Michael J. Hiley,et al.  Investigating optimal technique in a noisy environment: application to the upstart on uneven bars. , 2013, Human movement science.

[16]  Holger R. Dullin,et al.  Twisting Somersault , 2016, SIAM J. Appl. Dyn. Syst..

[17]  David G. Lloyd,et al.  A Predicted Optimal Performance of the Yurchenko Layout Vault in Women's Artistic Gymnastics , 2003 .

[18]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[19]  Anil V. Rao,et al.  Evaluation of Direct Collocation Optimal Control Problem Formulations for Solving the Muscle Redundancy Problem , 2016, Annals of Biomedical Engineering.

[20]  J. Lackner,et al.  Coordinated turn-and-reach movements. I. Anticipatory compensation for self-generated coriolis and interaction torques. , 2003, Journal of neurophysiology.

[21]  P. Crouch,et al.  Numerical integration of ordinary differential equations on manifolds , 1993 .

[22]  Stephen J. Wright.  Interior point methods for optimal control of discrete time systems , 1993 .

[23]  Richard R Neptune,et al.  Modular control of human walking: a simulation study. , 2009, Journal of biomechanics.

[24]  M. Yeadon.  The simulation of aerial movement--II. A mathematical inertia model of the human body. , 1990, Journal of biomechanics.

[25]  Antonie J van den Bogert,et al.  Implicit methods for efficient musculoskeletal simulation and optimal control. , 2011, Procedia IUTAM.

[26]  Jt Johan Padding,et al.  Improved quaternion-based integration scheme for rigid body motion , 2016, Acta Mechanica.

[27]  Guy Bessonnet,et al.  Energetic versus sthenic optimality criteria for gymnastic movement synthesis , 2006 .

[29]  Farzad Towhidkhah,et al.  Optimization of Barbell Trajectory During The Snatch Lift Technique By Using Optimal Control Theory , 2008 .

[30]  Leng-Feng Lee,et al.  Generating optimal control simulations of musculoskeletal movement using OpenSim and MATLAB , 2016, PeerJ.

[31]  Roy Featherstone,et al.  Rigid Body Dynamics Algorithms , 2007 .

[32]  Sameer Nagda,et al.  Defining functional shoulder range of motion for activities of daily living. , 2012, Journal of shoulder and elbow surgery.

[33]  R R Neptune,et al.  Simulated parallel annealing within a neighborhood for optimization of biomechanical systems. , 2005, Journal of biomechanics.