## 6 Preliminary System Validation
### Preliminary Results
#### 6.2.2 Path Trace Comparison  
In order to quantify the above-mentioned differences, the recorded trajectories were analysed using the Python-based Dynamic Time Warping (DTW) algorithm [51]. This algorithm provides a distance factor that represents the cumulative difference between two time series that are expected to be similar [52]. DTW allows for a good fit even when there is a lag in speed or time, making it suitable for comparing the traces in this experiment. Hence, the variation in the \([x,y]_{p}\) position of the participant's traces was compared regarding the \([x,y]_{ref}\) reference position given by the central line. DTW allows us to compare the differences without considering the drawing speed.  
Table 2 summarises the obtained DTW distances for the data captured with tablet-based and robot-based systems. The results are grouped for both the right and left hands, showing the scores for each participant's attempt. Since the DTW output is the remaining cumulative distance between the reference and the query time series, in this study, the DTW factor is used to compare the differences between the drawing traces (query) and the central line of paths (reference). Hence, in the scope of this paper, DTW provides the cumulative deviation from the central line in drawing tasks, regardless of the time spent. The greater  
Figure 10: Trajectories captured with the tablet-based and robot-based systems for the right (orange lines) and left (blue lines) hands.  
the deviation from the central reference line, the higher the DTW factor, suggesting worse performance in drawing. The reference line was implemented using interpolation methods with several partial functions, combining various linear and B-spline functions.  
As shown in the position plots, higher DTW values were obtained for traces gathered by the robot-based system. The DTW values for the tablet-based system ranged from 2.73 to 3.84, while the DTW values for the robot-based system ranged from 7.42 to 14.37. These results show that the participants achieved better performance with the tablet than with the robot, suggesting better fine motor coordination than gross motor coordination. In other words, the results suggest that participants performed better when the demand for interjoint coordination was lower. Additionally, when sorting the DTW results according to the dominant and non-dominant hands, it can be seen that higher DTW scores were obtained for the non-dominant hand, indicating a major trace deviation from the central path line. Figure 11 shows a bar plot grouping the DTW scores for each participant's attempts using the tablet-based and robotic-based systems, comparing the performance of the dominant hand (DH) and non-dominant hand (NDH).  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline  & \multicolumn{2}{c}{**DTW: Table**} & \multicolumn{2}{c}{**DTW: Robot**} \\  & **RH \({}^{\ddagger}\)** & **LH \({}^{\ddagger}\)** & **RH** & **LH** \\ \hline P1\_attempt\_1 & 3.02 & 3.05 & 11.23 & 9.77 \\ P1\_attempt\_2 & 2.73 & 3.12 & 12.10 & 9.10 \\ P2\_attempt\_1 & 3.84 & 3.23 & 11.04 & 9.81 \\ P2\_attempt\_2 & 3.13 & 3.27 & 11.02 & 9.46 \\ P3\_attempt\_1 & 3.47 & 3.21 & 8.53 & 9.10 \\ P3\_attempt\_2 & 2.99 & 3.21 & 9.32 & 8.61 \\ P4\_attempt\_1 & 2.58 & 3.27 & 9.54 & 9.78 \\ P4\_attempt\_2 & 2.89 & 2.99 & 9.17 & 9.01 \\ P5\_attempt\_1 & 3.33 & 3.30 & 9.66 & 8.55 \\ P5\_attempt\_2 & 2.94 & 2.82 & 8.09 & 7.42 \\ P6\_attempt\_1 & 3.14 & 3.11 & 14.37 & 12.44 \\ P6\_attempt\_2 & 3.18 & 3.15 & 12.14 & 11.48 \\ \hline \hline \end{tabular} \({}^{\dagger}\) Right hand; \({\ddagger}\) Left hand.  
\end{table}
Table 2: DTW values for trajectories captured using the tablet-based and robot-based systems.  
Figure 11: Normalised DTW values comparing the performance of the dominant and non-dominant hands.