This study addresses the challenge of ensuring pedestrian safety in shared spaces during human-robot interactions. As mobile robots become increasingly integrated into public environments, there is a need to better understand how pedestrians perceive robots in proximity. This research explores the effects of robot lateral distance, robot velocity, and pedestrian state on pedestrian perception, with a particular focus on proximity zones during human-robot interactions. Conducted in a virtual reality environment with a within-subject design, the study measured perceived danger through button presses and visualized proximity zones using contour density plots. Findings reveal that increasing lateral distance significantly decreases button press likelihood, particularly beyond 160 cm. Robot velocities of 1 mls and 1.5 mls showed no significant difference, suggesting pedestrians perceive them similarly due to their alignment with average walking speed. Proximity zones were consistently wider and denser on the left than the right, highlighting spatial asymmetry in perception. These results provide quantitative and visual insights for designing mobile robots in shared spaces. Future research should examine environmental and group dynamics and robot design to enhance safety and public acceptance in human-robot interactions.