# Dynamic Proxemic Model for Human-Robot Interactions Using the Golden Ratio
## 2 Related Work  
Proxemics, the study of personal spatial zones between people, can be interpreted and used for designing effective and safe human-robot interactions. Current research focuses on various factors affecting these interactions, including the size and appearance of the robot, its motion characteristics, and the dynamics of the environment [18]. For service robots to be truly useful to humans, they need to be socially acceptable to humans during their interactions. [PERSON] [15] defined five basic zones of human personal space during human-human interactions: intimate, close intimate, personal, social, and public zones. His research shows that the distance between the subjects interacting is very important and depends on factors such as the degree of familiarity between the subjects, the type and purpose of the interaction, or cultural differences (see Table 1). [PERSON] et al. [20] investigated whether humans adapt social zones to the size of the small humanoid robot NAO. Participants approached the robot at an average of 48 cm, which corresponds to the human personal zone according to [PERSON], and did not reflect the smaller size of the robot. The robot's response to space intrusion (leaning backwards) was often perceived as unkind. [PERSON] et al. [21] tested the interaction with the quadruped robot Spot. Humans maintained the smallest distance (1.13 m) when the robot moved forwards without eye contact. The greatest distance (1.33 m) was when it was stationary, indicating possible human uncertainty from sudden movement. [PERSON] et al. [22] showed that people preferred a greater distance from robots with negative emotions, an aggressive voice or a higher noise level. Appearance also mattered significantly--humanoid robots allowed closer contact. [PERSON] et al. [23] addressed adaptive robot navigation, where the robot estimates the intention of the interaction and adjusts its trajectory. When the person was uninterested, the robot maintained a distance of 3.6 m, and when interested, it approached \begin{table}
\begin{tabular}{c c c} \hline
**Range** & **Situation** & **Personal Space Zones** \\ \hline
0 to 0.15 m & Lower or close friend & Intimate Zone \\
0.15 m to 0.45 m & touching & Close Intimate Zone \\
0.45 m to 1.2 m & Conversation between & Personal Zone \\
1.2 m to 3.6 m & Conversation to non-friends & Social Zone \\
3.6 m+ & Public speech making & Public Zone \\ \hline \end{tabular} Most current studies of mobile robot proxemics are based on these zone classifications and attempt to apply them to human–robot interactions [19]. It turns out that the acceptability of robot proximity is not uniquely given but varies depending on the type of robot and its visual and motion characteristics, as shown in Table 2.  
\end{table} 
Table 1: [PERSON]’s proxemic zones [15]. \begin{table}
\begin{tabular}{c c c} \hline
**Robot** & **Measuring Points** & **Average** \\  & **Distance** & **Distance** \\ \hline  & Key points between the robot (head and torso) & \\  & and the human (head and waist). The distances & \\  & between these pairs were calculated, and the & 48 cm [20] \\  & shortest of them was taken as the current & \\  & interpersonal distance. & \\ \hline Boston Dynamics—Spot & Robot centre–top of the person’s head & 110 cm [21] \\ \hline MIRb mobile robot & & The highest was 122 cm \\   platform & Not specified & (angry) \\  & & The lowest was \\  & & 54 cm (sad) [22] \\ \hline FESTO Robotino robot & Not specified & Not specified [23] \\ \hline \end{tabular}
\begin{tabular}{c c} \hline  & The distances were measured between the closest \\  & parts of the human and robot bodies, i.e., \\  & without including arms or manipulators. & 57 cm [24] \\ \hline Double Robotics—Double 3 & Not specified & 104 cm [25] \\ \hline Care-O-bot® 3 & Shortest distance between person and \\  & robot & 92 cm [26] \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of average measured distances and measured points between different robots and people.