# Dynamic Proxemic Model for Human-Robot Interactions Using the Golden Ratio
## 2 Related Work
up to 1.2 m. When the robot was uncertain, it chose a compromised distance and approach angle. [PERSON] et al. [24] found that verbal interaction led to greater distances than physical interaction. Humanoid robots were perceived as more invasive than mechanical-looking ones. [PERSON] et al. [25] analysed communication with a telepresence robot. The average communication distance was 104 cm, with women choosing a greater distance than men. Also, previous experience with technology led to smaller distances. [PERSON] [26] showed that a higher robot approach speed increased the desired comfort distance (up to 1.25 m). Gradual deceleration and human positioning affected the accepted proximity. The distance decreased with habituation (people getting used to being approached by the robot). [PERSON] and [PERSON] [27] summarised the findings from 27 studies (1299 participants). Neither appearance nor gender had a statistically significant effect. Humans were more likely to approach robots than vice versa. However, methodological differences between studies make conclusions difficult. The review showed that the comfortable distance between humans and robots depends on many factors: appearance, behaviour, voice, speed of movement, context, and user experience. Although numerous studies have investigated human comfort in HRIs, there is still a lack of a unified and adaptable model that accounts for dynamic human behaviour, and there is no uniform methodology for determining these zones. Hall's proxemics is widely used but lacks portability to robots that do not exhibit human social signals. Therefore, there is a need to develop a specific methodology for robots, based on empirical data and respecting the variability of interactions and environments. For industrial robots, safety standards such as ISO 10218-1/2 [28; 29] and ISO 12100 [30] apply, which set out requirements for workplace safety, risk minimisation, and the positioning of safety features. These regulations provide a predictable environment and trained workers where risks and safety zones can be precisely defined. For collaborative robots, the ISO/TS 15066 [31] standard is used to supplement the above regulations with limits on forces, speeds, and other specifications necessary for safe human-robot collaboration. However, service robots can operate in non-industrial environments (homes, public spaces) where humans are not performing activities related to the production process for which they are trained, nor do they move exclusively within designated areas. In such situations, it is not possible to apply industry standards without modification; not only must physical safety be addressed, but also the person's comfort and reaction to the robot's approach. ISO 13482:2014 [5] specifies safety requirements for service robots, including those working in proximity to humans (e.g., care robots). This standard defines a safety zone in which the robot must stop to avoid a collision. However, no uniform methodology was found for determining the so-called comfort zone--the area in which humans feel comfortable. The comfort distance is influenced by many factors (appearance, speed of movement, situation, age of the human, etc.). Scientific research in this area is still in the validation phase and is not standardised. While safety zones can be established according to existing standards (e.g., ISO 13482, ISO 13855), comfort zones require further research and the design of a specific methodology for use in dynamic human environments. The optimal solution will involve a combination of both safety and comfort zones that adapt to real human behaviour. This study focuses on addressing these gaps in the research (the lack of uniform methodology for determining comfort zones in HRIs) and standards (no mention of personal comfort) by proposing a novel dynamic proxemic model based on the golden ratio, which allows for the continuous adaptation of comfort zones according to relative movement and human orientation, in combination with valid safety standards.