# Social Distance in Interactions between Children with Autism and Robots
## 1 Introduction
### HRI and Social Distance  
The concept of interpersonal distance deals with how the distance between people during an interaction indicates the facets of the relationship between them. This is called the \"social distance\". In the proxemics theory, the space between people is determined by being aware of the other person's presence, and includes psychological and communicative properties [30]. Social distance consists of four types; close distance, individual distance, social distance, and public distance [31; 32]. In a close relationship, such as with a family member or an intimate partner, the distance between people is 0 m to 0.45 m, or within touching distance. Individual distance is usually the distance one maintains with friends, while social distance is around 1.2 m to 3.5 m when conversations are conducted not within touching distance. Public distance is the distance maintained in business negotiations or between an audience and a speaker in a public forum and is usually 3.5 m or more (SeeFigure 1). We implemented this theory into our robot to maintain personal distance during the interactions; however, this study does not use the function of keeping this specific distance between a human and robot.  
Although social distance is defined above, the size of one's preferred personal space varies. Introverts tend to have a larger personal space preference, for example. Invading one's desired personal space can cause discomfort and tension in social interactions. Social distance, therefore, extends in front of a person during social interactions. [PERSON] and [PERSON] conducted an experiment in which a robot advanced toward a participant in a standing or sitting position from a distance of 10 m, and when the participant did not want the robot to approach any further, they raised their hand and the robot stopped. It was found that it is easier to estimate the distance between the robot and the participant when the latter is in a sitting position; moreover, the distance increases in proportion to the speed of the moving robot [33]. [PERSON] and [PERSON] measured the distance between two humans by attaching a marker to the top of the participant's head and taking pictures with a camera mounted on the ceiling [34]. [PERSON] et al. measured the distance in a room using omnidirectional cameras installed in the corners and ceiling to measure the location of people from the images captured [35]. These two methods involved attaching devices to the participant or using a specific camera. [PERSON] et al. measured the comfort of participants during interactions with a social robot. In this study, the distance during interactions was divided into three zones: less than 1 m, 1 m to 3 m, and more than 3 m. Participants felt discomfort when the distance between them and the robot fell within 3 m [36]. As for social distance in HRI, [PERSON] and [PERSON] considered not only proxemics but also power relationships (such as a supervisor robot with a subordinate robot) and the nature of the task (such as a cooperating robot and a competing robot). This study showed that participants preferred to have more distance from the robot if the human and the robot were in a cooperative relationship [13]. [PERSON] et al. explored the acceptance of users toward robots when they are touched by the robot at an intimate distance. The results showed that people felt discomfort when physically contacted by the robots [37]. In these studies, however, in measuring the social distance of humans to robots in HRI, it cannot be said that natural communication is performed only by examining the appropriate social distance.  
Figure 1: Social distance and the interpersonal relationship by [PERSON] [31] and [PERSON] [32]. ‘A’ means an agent, either human or robot.