# Dynamic Proxemic Model for Human-Robot Interactions Using the Golden Ratio
## 6 Results and Discussion  
The experimental evaluation focused mainly on the perceived robot's motion towards the person and subsequently on the subjective comfort, perceived safety, and naturalness of robot behaviour during their approach using the proposed dynamic model. The data were analysed across the two scenarios and two robotic platforms using descriptive statistics and statistical hypothesis testing. The participants answered questions from the GQS and whether the robot approached too quickly, too slowly, or at a comfortable pace. Similarly, they evaluated if the robot stopped too close, too far, or at an appropriate distance. Answers were collected for each trial. The robot's approaching speed and stopping distance were crucial for the initial methodology evaluation. A total of 38 people (29 men and 9 women) participated in the experiment with the Go1 robot. The sample ranged in age from 7 to 70 years (mean = 32, SD = 13), with a median age of 28 years. For the Scout Mini, a total of 17 people participated (13 men and  
Figure 10: A sample of the questionnaire created for participants with the response values for the questions depicted, including the numerical labelling of the questions from the GQS. 4 women). The median age of the participants was 23 years, while the sample ranged from 21 to 41 years (mean = 26, SD = 6). All participants were European, mostly from the Czech Republic. The adults were employees, students, or family members of people working at the university. Additionally, ambient sound levels were recorded both with and without the presence of the robot, for both robotic platforms, to evaluate the impact of noise on user perception. The main goal was to determine how the participants perceived the robot's approaching speed and stopping distance in both scenarios (two questions at the bottom of the questionnaire (see Figure 10)). The ideal value, a pleasant feeling about the interaction, is interpreted in the results as a value of 2, i.e., the closer the mean value is to 2.0, the more pleasant the interaction was. From the acquired data, it was found that the stopping distance and approach speed of the robots were perceived as pleasant. Student's t-test showed no statistical significance of differences in the scenario ratings between the robots. This suggests that both robots were rated equally, and therefore, there was no difference in the perceived pleasantness of the approach speed and stopping distance between the robots. Differences between the scenarios for each robot proved to be statistically significant only for the perceived speed of the Go1 (\(p\) = 0.046), with a statistical significance of \(\alpha\) = 0.05 (see Table 3). In this case, the second scenario tended to be received better. This was most likely due to the person's ability to adjust the speed of their approach to the robot, as they were both in motion. The closest result to statistical significance between the Go1 and Scout Mini robots was the comparison of stopping distance pleasantness in scenario 1 (\(p\) = 0.064). A two-sample Student's t-test with equality of variances was used to determine the statistical significance of the differences between the scenarios for the robots, as the \(p\)-values of the F-tests for the variances came out greater than 0.05 for all comparisons. A comparison between scenarios by gender was also made with the same robot, but due to the very small number of females in the sample (9 females for the Go1 robot and 4 females for the Scout Mini robot), the comparison by gender cannot be considered meaningful. In Figure 11, we can see that all mean ratings for the robot stopping distance were close to the value of 2.0. As presented in Table 3, no statistically significant difference was found between the distances comparing robots or scenarios. However, when comparing robot stopping distances, the mean values were closer to 2.0 for the Scout Mini robot compared to the Go1.