Gaze and movement adaptation in response to delayed robotic movement during turn-taking.

While delays in human-robot encounters can harm perceptions of competence, they can also enhance engagement and relatability, making timing a crucial factor in the design of robot behaviors for effective human-robot interaction. Previous research has primarily focused on how robots' pauses or errors impact perceptions of competence, but it has not adequately addressed the complexity of timing in shaping social interactions. This study explored the effects of different delay conditions (no delay, short delay (4s), long delay (10s)) on human gaze behaviors and movements during a Tic-Tac-Toe game interactions with an Epi humanoid robot. We hypothesized that shorter delays would be interpreted as thinking pauses, increasing engagement, operationalized as directing gaze to the robot's hand or face, while longer delays would lead to distractions, i.e. gazing away from the robot and perhaps searching for cues in other places. Gaze indicates attentional focus, a common proxy for engagement in HRI. The results, however, indicated that the no delay condition prompted the highest levels of participants gazing at the robot's hand ('gaze to hand behavior'), with significantly more frequent gaze to hand behavior compared to both delay conditions. The duration of participants gazing at the robot's face ('face gaze') showed no significant differences, though trends suggested participants engaged more in face gaze in the no delay condition. Interestingly, during delay periods, participants spent significantly more time gazing at the robot's face and hands, suggesting a monitoring response to unexpected pauses. Additionally, positive pre-interaction impressions of the robot were linked to higher gaze to hand behavior, while increased face gaze was associated with lower fluency ratings, indicating compensatory behavior during perceived interaction difficulties. These findings suggest that delays reduce overall engagement regardless of duration, while they might increase engagement temporally while the delays take place. The results also highlight the complexity of gaze behaviors in human-robot interaction and suggest that gaze patterns can indicate participants' perceptions of the robot's performance.