## 2 Materials and Methods
### Theoretical Framework  
The theoretical framework of this study is based on five mechanisms that represent constructs in which distinct differences can be observed in human experiences with various robot representations: situativity, interactivity, agency, proxemics, and believability [7]. These mechanisms collectively contribute to understanding the dynamics of human-robot interaction, highlighting key dimensions in how users perceive and engage with robots.  
Situativity in robot-user interactions refers to how context influences a robot's behavior. This mechanism examines the degree to which a robot, designed for specific applications, can adapt to the user's environment. For instance, users might repurpose a robot for varied scenarios, affecting engagement and perceived realism. Unlike virtual agents limited to scripted settings, physical robots interact dynamically within user-defined physical spaces [7]. Both robots in this study are situated in the user's physical environment, though each is designed with different purposes. Differences in situativity impact how users perceive and interact with the robots; for example, one robot may be more suited for tasks requiring physical handling of objects, while the other may excel in tasks that involve mobility in different settings.  
Interactivity refers to the extent to which users can engage with the robot [7]. This mechanism focuses on the structure and evolution of interactions, both in physical and vir  
Figure 2: A remote user interacting through the Double 3 robot with one of the participants in the test.  
tual environments. Interactivity influences user satisfaction and the perceived intelligence of a robot. While interactions with virtual agents are often scripted and limited, physical robots allow for more user-directed engagement. In this study, both physical robots enable natural and intuitive interactions, though the specific capabilities of each vary. For instance, one robot may be better suited for tasks requiring physical assistance, while the other may excel in information retrieval.  
Agency denotes the degree to which a robot can act autonomously and influence its surroundings, as well as its perception as an independent entity with its own goals [7]. Agency affects users' trust and perceptions of the robot's competence. Physical robots are often seen as more flexible in acting independently due to their ability to impact the physical environment, while virtual agents are constrained by their lack of physical autonomy. In this study, both robots have physical forms and can move autonomously, though their specific behaviors differ. For example, one robot may be suited to tasks that require autonomous decision-making, while the other may be designed to follow a structured script.  
Proxemics refers to the spatial relationship between the user and the robot, addressing how a robot's proximity and behavior toward the user affect interaction and user behavior [7]. Proxemics influence user comfort and the perceived social presence of the robot. Physical robots can adjust proximity dynamically, while virtual agents are restricted by their virtual settings. In this study, both robots adhere to social norms for spatial relations, though each has unique capabilities. For example, one robot may be more appropriate for tasks that require close proximity, while the other may be designed for interaction at a distance.  
Believability refers to the degree to which a robot's appearance and behavior are perceived as realistic and convincing [7]. Believability affects user engagement and perceived social presence. Physical robots are often seen as more believable because of their tangible nature and ability to physically interact with users, unlike virtual agents. Both robots in this study, by virtue of their physical forms, can interact with users in natural ways, although design and functionality differences may affect perceived believability. For example, one robot may have a human-like appearance and behavior, while the other may adopt a more mechanical design.