## 3 Experimental Studies and Results
### Experiments 3: The Robot Listens to a Story  
One of the key characteristics of social gaze is the ability to change the gaze direction following the addressee. To simulate the responsive gaze of the robot, we decided to examine a situation in which a person tells the robot a story and the robot acts as an active listener by demonstrating different modes of responsive gaze. The purpose of the new experiment was to study the effect of a robot's responsive gaze on its attractiveness to the user. In this experiment, two robots reacted to the communicative actions of a human in two different modes. In one case, the robot directed its gaze at the user; in the second case, it demonstrated side gaze, which is typical for the condition of thoughtfulness or when regulated by a politeness strategy to avoid face threatening acts aimed at the addressee [8; 38]--video is provided within the Supplementary Materials. Within the experiment, subjects had to tell two robots stories following a list of pictures by [PERSON] (Figure 5; see more about his artwork at [[https://en.wikipedia.org/wiki/[PERSON]](https://en.wikipedia.org/wiki/[PERSON])]([https://en.wikipedia.org/wiki/[PERSON]](https://en.wikipedia.org/wiki/[PERSON])), accessed on 1 October 2021). Each picture was represented as a stack of cards in random order. A total set of six stories was used; each subject had to tell three stories to each robot, switching to the other robot after each story. A total of 46 subjects participated in the experiment (mean age of 27 years, 33 females). Before the experiment, the F-2 robots were introduced to the subjects. The respondents were told that the developers were currently trying to train the robot to follow the story narrated by a human. The main purpose of the study, which was to investigate the effect of the robot's responsive gaze, was not included in the introduction. We examined the following hypotheses: (a) the robot is perceived as more attractive if it establishes gaze contact with the user; (b) respondents with a high level of emotional intelligence better distinguish the behavioral patterns of the robots. The orientation of the user's attention was roughly identified automatically by the orientation of the user's face and was recognized by a computer vision component based on OpenCV. This system was chosen as a possible \"built-in\" solution for emotional companion robots, allowing us to avoid the calibration typical for eye-tracker experiments, and thus, maintain more natural communication with the robots. To find a vector of the human face orientation that we interpret as a gaze vector, we built an approximate 3D model of human facial landmarks and developed the following steps. Human faces are detected within the camera video frames using a linear SVM classifier based on an advanced version of HoG features [39] implemented in the Dlib library. The image intensity histogram is normalized inside a box bounding the face. Then, landmarks of the found face are detected using an Ensemble of Regression Trees approach described in [40] and implemented in the Dlib library. These 2D landmarks' positions and 3D coordinates of the corresponding model points are used to solve a perspective-n-point (PnP) problem using the method suggested in [41] an implemented in the OpenCV library. Solving the PnP problem provides the orientation of the human face in 3D with respect to the camera. Next, a 3D gaze vector is built starting between the human's eyes and using the calculated face orientation, and the vector's coordinates are stabilized using a simple Kalman filter, assuming these coordinates to be independent. Then, a constant offset is added to the gaze vector's endpoint to make the vector point at the camera when the human is looking directly at the robot. The angle between the gaze vector and the direction from the camera center to the human's nose bridge provides information on if the human is looking at the robot. The procedure of the experiment was as follows.