# Dynamic Proxemic Model for Human-Robot Interactions Using the Golden Ratio
## 6 Results and Discussion
The confidence intervals of the Go1 for both scenarios were leaning towards the robot stopping too close, i.e., a value of 1.0, but still just below a value pf 2.0 (comfortable distance). These findings suggest that the majority of participants perceived the robot's \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & **Go1 Mean** & **Go1** & \begin{tabular}{c} **Scout Mini** \\ **SD** \\ \end{tabular} & \begin{tabular}{c} **Scout Mini** \\ **Mean** \\ \end{tabular} & \begin{tabular}{c} **Scout Mini SD** \\ \end{tabular} & \
\begin{tabular}{c} **\(p\)-Value** \\ **Scenarios 1** \\ \end{tabular} &
\begin{tabular}{c} **\(p\)-Value** \\ **Go1/Scout** \\ **Mini 2** \\ \end{tabular} \\ \hline Distance— & 1.815 \(\pm\) & 0.456 & 2.055 \(\pm\) 0.206 & 0.416 & 0.064 & 0.399/0.332 \\ Distance— & 1.842 \(\pm\) & 0.436 & 2.000 \(\pm\) 0.170 & 0.343 & 0.183 & \\ Scenario 2 & 0.143 & & & & & \\ Speed— & 2.105 \(\pm\) & 0.559 & 2.055 \(\pm\) 0.317 & 0.639 & 0.768 & **0.046**/0.270 \\ Scenario 1 & 0.183 & & & & & \\ Speed— & 1.921 \(\pm\) & & & & & \\ Scenario 2 & 0.117 & & & & & \\ \hline \hline \end{tabular}  
* Two-tailed \(p\)-value of the T-test used to compare Go1 with Scout Mini for each scenario. 2 One-tailed \(p\)-value of the T-test used to compare scenario 1 with scenario 2 for each robot.  
\end{table} 
Table 3: Comparison of Go1 and Scout Mini results. stopping distance as pleasant, although some individuals rated the proximity as quite close during interactions with the Go1 robot. In analysing the robot's approach speed, a statistically significant difference was observed between scenarios 1 and 2 for the Go1. In scenario 1, where the person stood still while the robot approached, the participants generally found the speed of the Go1 to be agreeable, although leaning towards being slower (mean = 2.105). In contrast, scenario 2, which involved both the robot and the person moving towards each other, was also perceived as pleasant but with a tendency for quicker robot movement (mean = 1.921) (see Figure 12). This statistical difference arose from the varying dynamics between the scenarios, making it plausible. Nonetheless, both means are quite close to 2.0. The findings for the Scout Mini were very similar to those of the Go1, showing no statistically significant differences. The mean values for the Scout Mini were closer to the ideal value of 2.0 compared to the Go1, though they exhibited a larger confidence interval. This was due to the smaller number of participants. The overall results show that the interactions with both robots were rated positively, with a slight advantage for the Scout Mini, whose results were closer to the ideal value of 2.0. Both speed and distance were rated very close to the ideal value, with no significant differences between the robots. The Scout Mini robot was measured to be less noisy and, therefore, probably less invasive than the Go1. This finding suggests the suitability and universality of the proposed model based on the golden ratio and the speed profile fitted to it using a 2D Gaussian function. Hence, it can be concluded that the experimental proof of  
Figure 11: Comparison of mean values of stopping distances with confidence interval between scenarios 1 and 2 for Go1 and Scout Mini robots. Figure 12: Comparison of mean values of approaching speed with confidence interval between scenarios 1 and 2 for Go1 and Scout Mini robots. concept of the proposed methodology confirms the pleasant experience of the motion of the approaching robot. Subjective perception of the robots was assessed using the modified GQS questionnaire on a 5-point Likert scale. The data was statistically processed and compared between the two robots. Overall, both robots were perceived positively, with slightly higher values for the Scout Mini robot (see Figure 13). The only exception was question 3.4, focused on the Animacy dimension, where the Go1 received a higher rating (see Figure 14).