## 1 Introduction
Together, these studies suggest that the challenge of HRI-enabled autism diagnosis is ongoing, and no final technological solution is yet available. It is also worth noting that the availability of a stable technology, i.e., the construction of a social robot for diagnosing autism, is hampered by several technological constraints, in particular those related to the difficulty in designing specific sensors. In conclusion, the literature clearly shows that the challenges associated with the design of an HRI-enabled ASD diagnosis tool is of interest to several international groups of researchers and is dependent on the technology readiness level of social robots. A 'top-down' approach to the robotic system design process was also applied by [14; 15; 17]. The approach adopted by these authors is as follows: First, a set of features to be detected by the robotic system for the purposes of autism diagnosis is identified. Next, user requirements are defined, along with the system specification. Alpha-version components of the system are then selected. Finally, a small-scale study is carried out to evaluate selected aspects of the final diagnostic system. However, none of these studies have ended up with a fully functioning diagnostic system for autism. Consequently, no satisfactory solutions exist due to the discrepancy between user requirements and currently available technology. Hence, in our research we apply the 'bottom-up' approach instead. In particular, we focus on primarily one symptom of autism, i.e., turn-taking deficits. On the basis of currently available technology, we have designed a dyadic game between an interactive robot and preschool children which aims to elicit a variety of turn-taking behaviors that are subsequently assessed by a specialist observer. It is important to note that turn-taking has attracted considerable attention in recent research on robotics and autism therapy. For instance, [PERSON] et al. [16] argue that the phenomenon of turn-taking is a central design issue in applying socially assistive robots (SAR) in autism research. This phenomenon has also been the focus of several other studies by [PERSON] [33], [PERSON] and [PERSON] [32], [PERSON] et al. [34] and [PERSON] [35]. The latter article does not focus on the use of robots but suggests that tablet devices can be themselves effective tools for supporting turn-taking behaviors in children with autism. [PERSON] and [PERSON] [35] conducted studies based on a virtual character implemented in the iTake Turns\({}^{\copyright. }\) app, but this game has some potential to be ported to a robot such as NAO. In terms of using robots to diagnose turn-taking deficits, there is an important issue concerning the availability of existing robots that can diagnose interactive behaviors in conditions similar to those in the everyday social environment of a child. A variety of robots have been used in autism research. [PERSON] et al. [16], [PERSON] et al. [25] and [PERSON] et al. [36] provided a representative overview of well-known robotic technology and platforms for these purposes. There are also a number of initiatives which were not taken into account in the aforementioned works, such as those of [37; 38]. There are only two humanoid robots in this group that are able to move around and are also commercially available: NAO([[https://www.softbankrobotics.com/emea/en/nao](https://www.softbankrobotics.com/emea/en/nao)]([https://www.softbankrobotics.com/emea/en/nao](https://www.softbankrobotics.com/emea/en/nao)), accessed on 1 May 2022) and ZENO ([[https://www.hansonrobotics.com/zeno/](https://www.hansonrobotics.com/zeno/)]([https://www.hansonrobotics.com/zeno/](https://www.hansonrobotics.com/zeno/)), accessed on 1 May 2022). NAO is an older design, but to date, it is the most widely used robot (see, e.g., [PERSON] et al. [25], [PERSON] [32], [PERSON] et al. [27], Bernardo [31]). For this reason, the NAO robot was chosen for use in this study. From a robotic perspective, the research problem outlined in this study can be formulated as follows.