## 1 Introduction
The variable degree of intentionality within the control of communicative cues is described as [PERSON]'s continuum [10; 11], where the unintentional and uncontrolled behavioral patterns stay at one end, while the controlled nonverbal signs, quite like the signs of natural language, are located at the other end. Departing from this point, the expressive possibilities of the gaze system are extensively studied within the theory of communication; a comprehensive review can be found in [12]. Gaze is also an important feature in the natural interfaces ofcompanion robots, and thus, it is widely implemented and evaluated within applied robotic systems, for example, in the robots Cog [13], Kismet [14], and Infanoid [15], and others. The attention of researchers and developers to artificial gaze systems is attracted by various features of the natural gaze. 1. **Gaze direction** is the primary object of study, and in applied systems, the direction of gaze is critical for effective interaction. At the same time, the perception of gaze is quite complex and may include the evaluation of the position of the eyes relative to the rotation of the head. For example, the gaze direction of a back-projected robot is perceived more naturally and precisely if its eyes are moving relative to the head and not fixed in the central position [16]. 2. Saccades, pupil dilatation, and ocular torsion constitute the micromovements within the gaze system. They are the main objects of studies regarding the psychology of attention but are not widely implemented in artificial interfaces. An extensive study on gaze micro-features, including eye saccades, eyelid micro-movements, and blinking, and their relation to the level of trust that they arouse in users, is represented in [17]. 3. Movements of eyelids and brows and blinking. Most virtual agents and even some physical robots are designed to blink and move their eyelids and eyebrows. In [18], the behavioral modes of a physical robot were compared, including non-blinking and blinking according to statistical models, and blinking according to physiological data. According to this study, a robot with a physiological blink seemed more intelligent to the respondents. In [19], the researchers varied the number of blinks performed by the agent. It was determined that respondents have a feeling that the agent is looking at them when the number of blinks of the agent exceeds the number of blinks of the respondent. Thus, eyebrows and eyelids combined can express numerous expressive and emotional patterns, which are widely studied in the field of the psychology of emotion and are also used within the existing interfaces of Kismet, Mertz, iCat, and others. 4. Responsive gaze is studied as the ability to reply to another's gaze by looking at the opponent and maintaining the balance of gazes during communication. This topic is extensively studied by [PERSON] and his colleagues with regard to human-robot interactions. In experimental studies, the researchers showed that the robot that responded with its gaze to the gaze of the interlocutor provided the subjects with the feeling of gaze contact and was evaluated as a more positive counterpart [19; 20]. 5. Joint attention is studied as the ability to concentrate on the object of interest of another person. A robot's ability to support joint attention with humans is considered an important feature for companion robots, as it makes them look more competent and socially interactive while solving spatial tasks with humans [21]. In a study from our lab, subjects learned to control a robotic device using the joint attention gaze patterns. The robot was prompted by a responsive gaze of a human and then followed the direction of the human gaze, simulating joint attention to select the location for the required action of the robot [22]. These studies on the superficial expressive patterns of gaze are combined with a major area, in which human gaze is used as a controller in interfaces to position a cursor, select objects, or navigate in the environment.