# Dynamic Proxemic Model for Human-Robot Interactions Using the Golden Ratio
## 7 Conclusions and Future Work  
This study introduced a dynamic proxemic model for human-robot interactions (HRIs) based on geometric scaling using the golden ratio. The proposed approach integrates ISO-compliant safety boundaries with adaptive comfort zones, enabling socially aware robot behaviour in environments shared with untrained and unpredictable human users. The experimental results indicate that this method maintains compliance with safety standards and also supports the subjective experience of human participants in terms of comfort and predictability. The aim of the experiment was to perform an initial proof of concept of the proposed methodology. The experiment investigated robot motion pleasantness, which is a major component that is affected by the proposed methodology. The experiment showed that the movement of both robots was pleasing to the subjects, which means that initial impressions were positive and more thorough testing of the suitability of the proposed methodology will be carried out in future research. Through real-time implementation on two mobile robotic platforms, the developed system demonstrated its flexibility, portability, and computational efficiency. The experimental results from two interaction scenarios show that the participants generally perceived the robot's behaviour as comfortable, predictable, and safe. The golden ratio provided an intuitive and aesthetically grounded mechanism for defining human-centred spatial boundaries, while the 2D Gaussian velocity profile enabled smooth and context-sensitive robot motion. Subjective feedback confirmed the model's acceptance, although the results also reveal that robots' morphology and acoustic characteristics can significantly influence user perception, confirming the need to consider hardware design in proxemics-aware systems. Despite using the same settings, the wheeled robot Scout Mini received more favourable ratings than the quadruped Go1, primarily due to lower noise levels and a more familiar movement profile. Based on the promising results of this study, several future directions can further enhance the proposed dynamic proxemic model. First, it is important to extend experimental validation beyond physical interaction by exploring how users respond to robot behaviour across broader comfort zones, including social and public distances. With this, it is also important to extend number of participants in different interaction scenarios and environments (such as corridor/open space, approaching the person from the side vs. the front, different tasks such as pick up from/put down on the robot, etc.). Future research should also incorporate additional sensory inputs, such as a person's gaze direction, body posture, age, or gender to improve the robot's ability to interpret human intent and adapt its behaviour accordingly. Another area for development is group interaction, where the model must account for multiple individuals simultaneously, requiring more complex spatial reasoning and prioritisation strategies. Personalisation based on user-specific attributes, such as age or familiarity with robots (habituation), could further refine comfort zone adaptation and increase user acceptance. These personalised interactions could be achieved by varying extension parameters for comfort zones and robot velocity. These personalisations are also important for different types of robots. For example, a small, cute, and quiet robot will likely be better received than a tall, loud, and industrial-looking one. Robots that are better received may be able to move faster and closer to people than those that are not. However, this is also a topic for future research, as covering such a variety of robot types would be time- and resource-intensive. As mentioned, long-term studies involving repeated interactions will be valuable in understanding how user perceptions evolve over time and how the model supports sustained, comfortable engagement in real-world settings, because with higher familiarity, comfort distance tends to decrease.