# Leader-Follower Role Allocation for Physical Collaboration in Human Dyads
## 3 Results  
Determining the higher-performing and lower-performing subjectFFits' law models for each pair are shown in Figure 2 with subjects 1 and 2 not being yet determined as either the higher- or the lower-performing subject. How different sorting methods influence the subject being defined as a lower-performing or a higher-performing individual is shown in Table 1. Comparing the three sorting methods, results in Table 1 show that using any of the three sorting methods determine the same subject to be the higher-performing individual, with the exception of pair 2 and 4. Looking at Figure 3 however, the presented results suggest that predicting the leader of the dyad improves when using the sorting method based on maximum velocity. This can be seen in the decrease of the standard error of mean (SEM) for predicting the leader when using the velocity sorting method, as shown in the bottom plot in Figure 3. As stated in Section 2.4 a lower SEM shows that the results for determining the leader were more consistent throughout all pairs, which in extension means that the sorting method produces more accurate results. Based on these results, all further statistical analysis presented in this paper was performed on data sorted using the maximum velocity approach. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Sorting Method**} & \multicolumn{8}{c}{**Higher-Performing Individual (Subject)**} \\ \cline{2-9}  & **Pair 1** & **Pair 2** & **Pair 3** & **Pair 4** & **Pair 5** & **Pair 6** & **Pair 7** & **Pair 8** \\ \hline mean time & 2 & 2 & 1 & 2 & 2 & 2 & 2 \\ \hline max. velocity & 2 & 2 & 1 & 1 & 2 & 2 & 2 & 2 \\ \hline index of performance & 2 & 1 & 1 & 2 & 2 & 2 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Table showing which subject was defined as the higher-performing individual based on all sorting methods. The cells marked in gray show which sorting method produced a different higher-performing individual than the rest. Figure 2: Fitts’ law models of individual and collaborative tasks for each pair, independent of the sorting method used. Here, subjects are defined as subject 1 and subject 2 as they are not yet determined to be either higher-performing or the lower-performing subjects. Whether subject 1 or 2 is determined to be the higher-performing individual and the other as the lower-performing one can be found in Table 1 for different sorting methods. Determining the leader-follower dynamics:As stated in Section 2.4 (_Determining the leader-follower dynamics_), the leader of the dyad in collaboration was calculated based on the amount of the force applied to the robot by each partner during the overall task. Figure 4 represents the differences in the forces applied by the partner with a lower individual performance (\(F_{i}\)) and partner with a higher individual performance (\(F_{s}\)) in a collaborative task. Here, the values represent the average leading partner of the eight dyads including SEM for each target. Equation (3) defines positive values as equal to the partner with the higher individual performance (i.e., the subject with higher maximum velocity) leading the collaborative tasks, while negative differences equal to the partner with lower individual performance (i.e., the subject with lower maximum velocity) leading in the collaborative tasks. Equation (3) also tells us how much the leading partner influences the task movement based on the absolute value of the difference. Here, the higher the absolute values, the more  
Figure 3: (**a**) Leading subject for all targets based on each sorting method, where the values represent mean leader \(L[N]\) between the 8 pairs \(\pm\) SEM. The bottom plot (**b**) shows comparison between SEM of each sorting method for individual targets. dominant the leading partner was, while the values closer to 0 showcase that the amount of exerted force from both partners was close to equal.