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Optimal estimation of complex aerial movements using dynamic optimisation.

André Venne1, François Bailly2, Eve Charbonneau1

  • 1Laboratoire de Simulation et Modélisation du Mouvement, Université de Montréal, QC, Canada.

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Dynamic optimization accurately estimates dynamically consistent joint kinematics and kinetics for complex aerial movements like trampoline somersaults, ensuring momentum conservation.

Keywords:
Dynamic optimizationaerial acrobaticsinitial conditionsinverse dynamicsoptimal control

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Area of Science:

  • Biomechanics
  • Sports Science
  • Robotics

Background:

  • Traditional inverse kinematics and inverse dynamics methods struggle to ensure dynamical consistency in complex aerial motions, particularly those dependent on initial states.
  • Estimating dynamically consistent full-body motion from experimental data is crucial for understanding and improving athletic performance in aerial sports.

Purpose of the Study:

  • To develop and validate a dynamic optimization algorithm for estimating dynamically consistent joint kinematics and kinetics in complex aerial movements.
  • To compare the proposed dynamic optimization method with traditional Extended Kalman Filter (EKF) followed by inverse dynamics approaches.

Main Methods:

  • A 42-degrees-of-freedom biomechanical model with 95 markers was personalized for elite trampoline athletes.
  • Dynamic optimization was employed to estimate joint angles, velocities, and torques by tracking experimental marker positions during twisting somersaults.
  • Key metrics including kinematics, kinetics, angular and linear momenta, and marker tracking differences were analyzed and compared between methods.

Main Results:

  • The dynamic optimization approach successfully conserved angular and horizontal linear momentum, consistent with free-fall dynamics.
  • Marker tracking differences were lower when dynamic optimization tracked experimental markers (36 ± 11 mm) compared to tracking EKF joint angles (49 ± 9 mm), though higher than EKF alone (17 ± 4 mm).
  • Estimated joint angles were similar to EKF results, while joint torques were smoother, indicating improved dynamical consistency.

Conclusions:

  • Dynamic optimization provides a robust method for estimating dynamically consistent joint kinematics and kinetics in complex aerial rigid-body movements.
  • This approach adheres to the physical principles governing free-fall dynamics while maintaining close proximity to experimental 3D marker data.
  • The findings suggest dynamic optimization is a valuable tool for analyzing high-level athletic performance in sports like trampoline.