A Robotic Eye Gaze Mirroring System for Human–Robot Interaction: Evaluating Response Time Across Proxemic Distances

Robots are increasingly becoming part of everyday social environments. Among the different types of communication cues, eye gaze in the context of human–robot interactions (HRIs) fosters connection and engagement. Although gaze behavior has been extensively studied, most existing research assumes a fixed interaction distance and often does not account for variations in proxemic distance that influence the perceptions of gaze. While prior studies have developed robotic eye gaze systems capable of producing natural gaze behaviors, these systems are usually evaluated at fixed interaction distances. Comparatively, less attention has been given to measuring the impact of proxemic distance on gaze mirroring. This study introduces a gaze mirroring system that integrates 3D robotic eyes with a mobile robot to track human gaze across various proxemic distances. This paper presents the system’s mechanical design and implementation, as well as the evaluation of its tracking performance. Experiments on the system were conducted across Hall’s proxemic zones, intimate, personal, and social, under static, teleoperated, and integrated movement conditions. The results demonstrate that the proposed system achieves highly efficient tracking with response times that fall within established thresholds for natural gaze timing in human–robot interaction.