Dynamic Proxemic Model for Human–Robot Interactions Using the Golden Ratio

Abstract

This paper presents a novel approach to determine dynamic safety and comfort zones in human–robot interactions (HRIs), with a focus on service robots operating in dynamic environments with people. The proposed proxemic model leverages the golden ratio-based comfort zone distribution and ISO safety standards to define adaptive proxemic boundaries for robots around humans. Unlike traditional fixed-threshold approaches, this novel method proposes a gradual and context-sensitive modulation of robot behaviour based on human position, orientation, and relative velocity. The system was implemented on an NVIDIA Jetson Xavier NX platform using a ZED 2i stereo depth camera Stereolabs, New York, USA and tested on two mobile robotic platforms: Go1 Unitree, Hangzhou, China (quadruped) and Scout Mini Agilex, Dongguan, China (wheeled). The initial verification of proposed proxemic model through experimental comfort validation was conducted using two simple interaction scenarios, and subjective feedback was collected from participants using a modified Godspeed Questionnaire Series. The results show that the participants felt comfortable during the experiments with robots. This acceptance of the proposed methodology plays an initial role in supporting further research of the methodology. The proposed solution also facilitates integration into existing navigation frameworks and opens pathways towards socially aware robotic systems.