Abstract
Each person has their personal area which they do not want to share with others during social interactions. The size of this area usually depends on various factors such as their culture, personal traits, and acquaintanceship. The same applies to the case of human–robot interaction, especially when the robot is required to exhibit a certain level of social competence. Here, we propose a new robot navigation strategy to socially interact with people reflecting upon the social relationship between the robot and each person. To this end, we need a clear definition of interaction areas: (1) quality interaction area where people can be engaged in high-quality interactions with robots, and (2) private area not to be interfered with by the robot speech or action. A technical challenge in enhancing social human–robot interactions is how to enable robots to delineate the boundary of the two areas of each person. Specifically, the social force model (SFM) is designed by a fuzzy inference system, where the membership functions are optimized to give the robot the ability to navigate autonomously in the quality interaction area using a reinforcement learning algorithm. Finally, the proposed model was verified through simulations and experiments with a real robot that can generate a suitable SFM of each person, allowing the robot to maintain the quality of interaction with each person while keeping their private personal distance.

















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Acknowledgements
This work was supported by the EU-Japan coordinated R&D project on “Culture Aware Robots and Environmental Sensor Systems for Elderly Support” commissioned by the Ministry of Internal Affairs and Communications of Japan and EC Horizon 2020.
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Patompak, P., Jeong, S., Nilkhamhang, I. et al. Learning Proxemics for Personalized Human–Robot Social Interaction. Int J of Soc Robotics 12, 267–280 (2020). https://doi.org/10.1007/s12369-019-00560-9
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DOI: https://doi.org/10.1007/s12369-019-00560-9