## 2 Methods
### Robustness Analysis of the Optimal Solutions  
To simulate intra-athlete technique variability, noise was added to right and left arm kinematics as in [13]. Specifically, Gaussian noise (centered on zero with standard deviation of \(15^{\circ}\)) was added  
\begin{table}
\begin{tabular}{c c c c} \hline  & **Start** & **Skill** & **End** \\  & \(\mathbf{t=0}\) & \(\mathbf{0<t<T}\) & \(\mathbf{t=T}\) \\ \hline \multirow{4}{*}{\([\mathrm{m}]\)} & Standing position on the trampoline & Reasonable tilt & Landing position on the trampoline \\  & \(-1.0\times 10^{-4}\leq\ q_{1-3}\leq 1.0\times 10^{-4}\) & & \(-0.1\leq\ q_{1-3}\leq 0.1\) \\  & \(-6\times 10^{-3}\leq\ q_{4-6}\leq 6\times 10^{-3}\) & \(-45\leq\ q_{5}\leq 45\) & \(350\leq\ q_{4}\leq 370\) \\  & & \(-15\leq\ q_{5}\leq 15\) \\ \hline \multirow{4}{*}{\([\mathrm{\SIUnitSymbolDegree}]\)} & Arms upward & Realist arm amplitudes & Arms upward \\  & \(q_{7,8}=160\) & \(0\leq\ q_{7,8}\leq 180\) & \(155\leq\ q_{7,8}\leq 166\) \\  & \(-6\times 10^{-3}\leq\ q_{9,10}\leq 6\times 10^{-3}\) & \(-45\leq\ q_{9,10}\leq 135\) & \\ \hline \multirow{4}{*}{\([\mathrm{m/s}]\)} & Realistic ejection velocities & \multirow{4}{*}{\([\mathrm{m/s}]\)} \\  & \(-10\leq\ q_{1,2}\leq 10\) & & \\  & \(-5.9\leq\ q_{3}\leq 6.1\) & & \\ \([\mathrm{\SIUnitSymbolDegree}/\mathrm{s}]\) & \(-6\times 10^{-3}\leq\ q_{5,6}\leq 6\times 10^{-3}\) & & \\ \hline \multirow{4}{*}{\([\mathrm{\SIUnitSymbolDegree}/\mathrm{s}]\)} & Null velocity at each arm DoF & Arm velocities & Arm velocities \\  & \(-6\times 10^{-3}\leq\ q_{7-10}\leq 6\times 10^{-3}\) & \(-5730\leq\ q_{7-10}\leq 5730\) & \(-5730\leq\ q_{7-10}\leq 5730\) \\ \hline \multirow{4}{*}{\([\mathrm{Nm}]\)} & Arm torques & Arm torques & Arm torques \\  & \(-100\leq\tau_{1-4}\leq 100\) & \(-100\leq\tau_{1-4}\leq 100\) & \(-100\leq\tau_{1-4}\leq 1004\) \\ \hline \end{tabular}
\end{table}
Table 1: Constraints applied to the model through the simulation.  
to the shoulder joint angles at a randomly chosen node of the first half of the skill. For the first half of the movement, the body's kinematics were simulated consistently with these noisy arm trajectories. The second half of the movement was then optimized to match the optimal performance, i.e., the number of twist rotations. Bounds on the second half of the skill were kept unchanged from Section 2.3. Each technique was perturbed 100 times; the convergence rate, the kinematics and the number of twists generated were compared between techniques to assess robustness.  
The robustness was first characterized by the differences in the number of twists between the optimal solutions and the perturbed ones; the mean and standard deviation are reported (\(\Delta_{perf}\pm\sigma_{perf}\)). Robust techniques should still generate the same number of twists. To assess the magnitude of the arm kinematic changes required from the original technique, the root mean square (RMS) values were computed for the second half of the optimal technique and the reoptimized ones; the median and the median absolute deviation are reported (\(\Delta_{kin}\pm\sigma_{kin}\)). The \(\Delta_{kin}\) score adds some perspective to the robustness score, as when \(\Delta_{kin}\) gets smaller, \(\Delta_{perf}\) becomes more reliable. Robustness score should also be mitigated by the convergence rate, as a low convergence rate indicates that other local minima are hard to find in the region of the optimal solution, leading to important drops in performance in cases of kinematic variability. Techniques with small \(\Delta_{perf}\), \(\sigma_{perf}\) and \(\Delta_{kin}\) and a high convergence rate were considered robust, because they can be executed by athletes with different deviations from the optimal solution and still yield approximately the same outcome in terms of twist rotation, with minimal changes in arm kinematics.