# Dynamic Proxemic Model for Human-Robot Interactions Using the Golden Ratio
## 6 Results and Discussion
The numbering of the questions in Figure 14 is based on their labels, as shown in Figure 10.  
A paired t-test confirmed a statistically significant difference in favour of the Scout Mini (\(p=0.00031\)). The difference may be mainly influenced by the robot's emitted noise. In the experiment with the Go1 robot, the ambient noise level was measured to be 32 dB. The noise level measured near the moving robot increased to 75 dB, which corresponds to an increase of 45 dB. In contrast, the ambient noise level with the Scout Mini robot was 31 dB. With the passing robot, the noise increased to a value of 45 dB. Therefore, the increase in this case was 14 dB, which is considerably less than in the case of the Go1. Given the logarithmic dB scale, this is a significant difference that may affect the perception of safety, likability, and overall acceptance of the robot. Figure 14: Comparison of responses for each GQS question between Go1 and Scout Mini robots. Figure 13: Comparison of GQS dimension responses between Go1 and Scout Mini robots. In contrast to noise, the intelligence dimension (questions 2.1-2.4) was associated with the success of performing the given task (candy delivery). The Scout Mini scored higher in the intelligence dimension as well, indicating a higher subjective confidence in the robot's abilities. The comparison between the robots of different morphologies--Unitree Go1 (quadruped) and Scout Mini (wheeled)--demonstrates that while the underlying algorithm was consistent, the form factor and acoustic profile of the robot influenced user perception, according to the participants' statements. Specifically, the Scout Mini was consistently rated more positively in perceived safety and comfort, likely due to its lower noise levels and more familiar locomotion. This observation aligns with prior research [8,24], where anthropomorphism and auditory feedback were shown to affect human acceptance in HRIs. The overall result of the initial experiments suggests that the proposed proxemic model based on the golden ratio may be applicable. However, it should be noted that a number of additional experiments should be conducted in various different environments and situations in order to more thoroughly test the suitability of this model. The golden ratio-based scaling of comfort zones in combination with the Gaussian velocity profile allows for a continuous, non-abrupt modulation of robot behaviour, which users usually found to be natural and non-intrusive [26]. This could be a marked improvement over classical models, such as [PERSON]'s proxemic zones, which are discrete and symmetric. The application of anisotropic Gaussian velocity profiles further personalises the interaction, adapting robot motion based on the relative velocity and orientation of the human, thereby enhancing social awareness. However, some limitations remain. The evaluation was focused primarily on the inner layers of the comfort zone (physical interaction and near social distances). The outer layers (middle social, distant social, and public zones) were not rigorously tested, nor was group interaction considered. In addition to subjective evaluation, the age and gender of participants were also monitored, but due to the small number and diversity of the participants, the results are not statistically significant.