Modelling Proxemic Zone Shapes from Analytic and Simulated Motion Strategies

Abstract Autonomous robots need to navigate around and negotiate for space with humans. Proxemics is the study of zones of personal and social space which humans experience around themselves and others, and use to control spatial interactions. By formalizing proxemic zones, autonomous robots may interact similarly. This study shows how proxemic zones may be generated by kinetics and trust, with the social zone being the critical space in which a human must trust another agent to avoid collision under their possible future motions. Previous studies have formalized these kinematics but have assumed that zones are circular in shape and found only their radii. However the kinematics and trust concepts used to generate them enable models to take account of the heading and rotational kinematics involved. This is shown to result in new non-circular shapes for the proxemic zones, whose egg shapes match those which have been found empirically and assumed without prior theory by current practical robots. Numerical and approximate analytical solutions to describe the zone shapes and sizes are presented. Zones are shown to change shape and size in response to the properties of the other agent, and are shown to generalize to include the stopping distances taught to drivers and pedestrians as well as natural human body zones.