Optimal estimation of complex aerial movements using dynamic optimisation

When estimating full-body motion from experimental data, inverse kinematics followed by inverse dynamics does not guarantee dynamical consistency of the resulting motion, especially in movements where the trajectory depends heavily on the initial state, such as in free-fall. Our objective was to estimate dynamically consistent joint kinematics and kinetics of complex aerial movements. A 42-degrees-of-freedom model with 95 markers was personalised for five elite trampoline athletes performing various backward and forward twisting somersaults. Using dynamic optimisation, our algorithm estimated joint angles, velocities and torques by tracking the recorded marker positions. Kinematics, kinetics, angular and linear momenta, and marker tracking difference were compared to results of an Extended Kalman Filter (EKF) followed by inverse dynamics. Angular momentum and horizontal linear momentum were conserved throughout the estimated motion, as per free-fall dynamics. Marker tracking difference went from 17 ± 4 mm for the EKF to 36 ± 11 mm with dynamic optimisation tracking the experimental markers, and to 49 ± 9 mm with dynamic optimisation tracking EKF joint angles. Joint angles from the dynamic optimisations were similar to those of the EKF, and joint torques were smoother. This approach satisfies the dynamics of complex aerial rigid-body movements while remaining close to the experimental 3D marker dataset.