## 4 Experimental Setup
### User Behavior Tracking  
The UBT system was developed to measure user engagement during the interaction and analyze user attention and distraction time. This system aimed to complement self-reported engagement measures by providing a detailed dataset on attentional dynamics during the HRI to understand how the robot's responsive behavior influenced user attention and engagement.  
The logs contained the following variables related to user behavior. For each one, the timestamp of the interaction was recorded:  
* Head Pose Orientation: To determine the attentional focus of the user, the direction of their head was recorded at each sampling interval to identify whether the user was looking at either the robot or the game, or elsewhere, for example, toward a distractor.
* Distractor Activation Time: Events were timestamped according to the onset of visual or auditory distractors.
* Type of Distractor: Each distractor was categorized as visual-animated images on a side monitor or audio-recorded sounds played through speakers.  
The UBT sampling rate was set to 0.16 s (due to the camera's 6 FPS setting) as a compromise between accurate head orientation tracking and the need to maintain smooth performance for both the system and the robot. From the raw telemetry data, several measures were derived to characterize the user's interaction dynamics:  
* Total Number of Distractions (\(N_{d}\)): A distraction is defined as when the participant's head orientation shifted away from the robot or the game area toward a distractor and remained in that position for at least a minimum duration. Consecutive samples with distracted orientation were treated as part of the same distraction event.
* Total Distraction Time (\(T_{d}\)): Also derived from the head pose orientation data and timestamps, the cumulative time the user's head direction indicated distraction (e.g., not looking at the robot).
* Total Interaction Time (\(T_{i}\)): The duration from the first timestamp that marks the start of the game to the final timestamp when the robot concluded the interaction.  
To determine whether the user was distracted, we set a minimum duration threshold of 1.5 s for their head to remain oriented away from the robot or the game. This value was defined empirically, considering the average human reaction time to stimuli (between 250-500 ms) [56], and accounting for Hick's Law [57], which states that reaction time increases with the number and complexity of stimuli. In our case, the interaction included concurrent multimodal elements, such as the robot's movements and speech, the tablet interface, and external visual or auditory distractors, which justified a longer window. Moreover, the threshold helps to avoid false positives from brief saccadic eye or head movements, which typically last under 200 ms [58], ensuring that only sustained attentional shifts are classified as genuine distractions.  
Distraction time is computed cumulatively over all time steps in which the head pose classifier does not return the \"frontal\" label. This label is assigned when the estimated yaw angle lies within \(\pm\)15\({}^{\circ}\) and the pitch angle within \(\pm\)10\({}^{\circ}\), corresponding to the user roughly facing forward. Any orientation falling outside these angular limits is interpreted as an attentional shift and is included in the distraction time calculation.