Optimal forward twisting pike somersault without self-collision.

In acrobatic sports, twisting fast before piking allows athletes to enlarge their scoring potential. Since planning the arm and hip movements to twist fast is unintuitive, optimal control appears as a powerful and risk-free tool. To our knowledge, predictive simulations of human motion did not include self-collision avoidance constraints resulting potentially in unrealistic solutions. Our objective was to generate innovative and realistic twisting techniques for forward somersaults ending in pike position by solving an optimal control problem including non-collision constraints. Optimal techniques for one, two, or three twists before piking were generated by minimising the duration of the twisting and piking phases. The model was composed of five segments with one degree of freedom at the chest and two at the hips and shoulders. We explored local minima using a multi-start approach. Solutions were further analysed to assess the impact of non-collision constraints, the segments' contribution to twist creation, and their stability. For each desired number of twists, one relevant solution was chosen. Optimisation showed that trampolinists could attempt new acrobatics: forward triple twisting somersault ending in pike position. This research also shows that non-collision constraints strongly modify the optimal techniques without impairing significantly their performance.

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.