# Social Distance in Interactions between Children with Autism and Robots
## 1 Introduction  
In recent years, there has been increasing attention on non-industrial robots called \"service robots\" in the welfare and humanities fields. This technology differs from industrial robots that perform assembly and other tasks in factories to replace human labor. With recent technological advancements, in 2015, domestic robots were introduced for home use in Japan and other countries with expectations for future expansion [1]. Service robots can be used to simulate social interactions with individuals who may be experiencing social anxiety, difficulties in communicating, or reading social cues. These robots can be designed to interact with humans and communicate in a simulated natural manner without generating fear or anxiety in humans [2]. To achieve this, there is a field of research called \"human-robot interaction (HRI)\". HRI assumes that humans can coexist with robots in daily life and that robots can support humans in daily life activities without harm. This requires robots to have the ability read human emotions. Robot technology research actively conducts practical applications of mental care robots that assist people in medical, long-term care, and welfare settings [3]. Socially assistive robots are one branch of this research field and some studies have focused on robot-assisted autism therapy [4]. In 2016, 1 in 54 children (aged 8 years) in the United States were diagnosed with autism spectrum disorder (ASD) [5], and the prevalence has been increasing [6]. In Japan, a recent report estimated the prevalence of children (aged 6-9 years) with neurodevelopmental disorders, including autism at 1.9% according to parents' ratings and 9.3% according to teachers' ratings [7]. Other studies have shown that Japan is also witnessing a surge in the number of children with autism [8]. Therefore, the social demand for effective programs to support the development of children with autism is extremely high. To address this problem, robot therapy is now used for children with autism [4, 9]. This has proven to beeffective because children with autism face difficulty in reading facial expressions and since robots have simpler structures and expressions compared to humans, they can be easily interpreted by children with autism [10; 11]. Studies surrounding robot-assisted autism therapy have focused not only on facial expressions, but other social skills [12]. This leads to more positive communication.  
In this study, we focus on social distance as an evaluation measure of robot therapy. Social distance depends on the nature of the relationship between people and their environment or on interpersonal relationships [13]. As such, this study suggests an automatic estimating program of social distance during robot-assisted autism therapy. Moreover, this study explores the correlation between the social responsiveness of children with autism and the detected social distance. The remainder of this article is organized as follows. Section 2 describes the developed programs to estimate social distance in natural HRI environments. Section 3 describes the experiments that featured children with autism interacting with a robot. Section 4 discusses the impact of the developed programs and social distance between children with autism and the robot, as well as the correlation between social responsiveness and distance. Section 5 describes some unanticipated findings and the limitations of this study. Section 6 provides the conclusions of this study.