The increasing presence of robots in human environments requires them to exhibit socially appropriate behavior, adhering to social norms. A critical aspect in this context is the concept of personal space, a psychological boundary around an individual that influences their comfort based on proximity. This concept extends to human-robot interaction, where robots must respect personal space to avoid causing discomfort. While much research has focused on modeling personal space in two dimensions, almost none have considered the vertical dimension. In this work, we propose a novel three-dimensional personal space model that integrates both height (introducing a discomfort function along the Z-axis) and horizontal proximity (via a classic XY-plane formulation) to quantify discomfort. To the best of our knowledge, this is the first work to compute discomfort in 3D space at any robot component's position, considering the person's configuration and height.

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Deploying robots in human environments requires effective social robot navigation. This article focuses on proxemics, proposing a new taxonomy and suggesting future directions through an analysis of state-of-the-art studies and the identification of research gaps. The various factors that affect the dynamic properties of proxemics patterns in human-robot interaction are thoroughly explored. To establish a coherent proxemics framework, we identified and organized the key parameters and attributes that shape proxemics behavior. Building on this framework, we introduce a novel approach to define proxemics in robot navigation, emphasizing the significant attributes that influence its structure and size. This leads to the development of a new taxonomy that serves as a foundation for guiding future research and development. Our findings underscore the complexity of defining personal distance, revealing it as a complex, multi-dimensional challenge. Furthermore, we highlight the flexible and dynamic nature of personal zone boundaries, which should be adaptable to different contexts and circumstances. Additionally, we propose a new layer for implementing proxemics in the navigation of social robots.

Personal space, also known as peripersonal space, is crucial in human social interaction, influencing comfort, communication, and social stress. Estimating and respecting personal space is essential for enhancing human-computer interaction (HCI) and smart environments. Personal space preferences vary due to individual traits, cultural background, and contextual factors. Advanced multimodal sensing technologies, including eye-tracking and wristband sensors, offer opportunities to develop adaptive systems that dynamically adjust to user comfort levels. Integrating physiological and behavioral data enables a deeper understanding of spatial interactions. This study develops a sensor-based model to estimate comfortable personal space and identifies key features influencing spatial preferences. Our findings show that multimodal sensors, particularly eye-tracking and physiological wristband data, can effectively predict personal space preferences, with eye-tracking data playing a more significant role. An experimental study involving controlled human interactions demonstrates that a Transformer-based model achieves the highest predictive accuracy (F1 score: 0.87) for estimating personal space. Eye-tracking features, such as gaze point and pupil diameter, emerge as the most significant predictors, while physiological signals from wristband sensors contribute marginally. These results highlight the potential for AI-driven personalization of social space in adaptive environments, suggesting that multimodal sensing can be leveraged to develop intelligent systems that optimize spatial arrangements in workplaces, educational institutions, and public settings. Future work should explore larger datasets, real-world applications, and additional physiological markers to enhance model robustness.

Service robots that work alongside humans in a shared environment need a navigation system that takes into account not only physical safety but also social norms for mutual cooperation. In this paper, we introduce a motion planning system that includes human states such as positions and velocities and their personal space for social-aware navigation. The system first extracts human positions from the LiDAR and the RGB-D camera. It then uses the Kalman filter to fuse that information for human state estimation. An asymmetric Gaussian function is then employed to model human personal space based on their states. This model is used as the input to the dynamic window approach algorithm to generate trajectories for the robot. Experiments show that the robot is able to navigate alongside humans in a dynamic environment while respecting their physical and psychological comfort.

There are many entities that disseminate in the physical space - information, gossip, mood, innovation etc. Personal spaces are also entities that disperse and interplay. In this work we study the emergence of configurations formed by participants when choosing a place to sit in a rectangular auditorium. Based on experimental questionnaire data we design several models and assess their relevancy to a real time-lapse footage of lecture hall being filled up. The main focus is to compare the evolution of entropy of occupied seat configurations in time. Even though the process of choosing a seat is complex and could depend on various properties of participants or environment, some of the developed models can capture at least basic essence of the real processes. After introducing the problem of seat selection and related results in close research areas, we introduce preliminary collected data and build models of seat selection based on them. We compare the resulting models to the real observational data and discuss areas of future research directions.

This study addresses the challenge of integrating social norms into robot navigation, which is essential for ensuring that robots operate safely and efficiently in human-centric environments. Social norms, often unspoken and implicitly understood among people, are difficult to explicitly define and implement in robotic systems. To overcome this, we derive these norms from real human trajectory data, utilizing the comprehensive ATC dataset to identify the minimum social zones humans and robots must respect. These zones are integrated into the robot' navigation system by applying barrier functions, ensuring the robot consistently remains within the designated safety set. Simulation results demonstrate that our system effectively mimics human-like navigation strategies, such as passing on the right side and adjusting speed or pausing in constrained spaces. The proposed framework is versatile, easily comprehensible, and tunable, demonstrating the potential to advance the development of robots designed to navigate effectively in human-centric environments.

Mobile robots are being used on a large scale in various crowded situations and become part of our society. The socially acceptable navigation behavior of a mobile robot with individual human consideration is an essential requirement for scalable applications and human acceptance. Deep Reinforcement Learning (DRL) approaches are recently used to learn a robot's navigation policy and to model the complex interactions between robots and humans. We propose to divide existing DRL-based navigation approaches based on the robot's exhibited social behavior and distinguish between social collision avoidance with a lack of social behavior and socially aware approaches with explicit predefined social behavior. In addition, we propose a novel socially integrated navigation approach where the robot's social behavior is adaptive and emerges from the interaction with humans. The formulation of our approach is derived from a sociological definition, which states that social acting is oriented toward the acting of others. The DRL policy is trained in an environment where other agents interact socially integrated and reward the robot's behavior individually. The simulation results indicate that the proposed socially integrated navigation approach outperforms a socially aware approach in terms of distance traveled, time to completion, and negative impact on all agents within the environment.

Predicting the trajectory of pedestrians in crowd scenarios is indispensable in self-driving or autonomous mobile robot field because estimating the future locations of pedestrians around is beneficial for policy decision to avoid collision. It is a challenging issue because humans have different walking motions, and the interactions between humans and objects in the current environment, especially between humans themselves, are complex. Previous researchers focused on how to model human-human interactions but neglected the relative importance of interactions. To address this issue, a novel mechanism based on correntropy is introduced. The proposed mechanism not only can measure the relative importance of human-human interactions but also can build personal space for each pedestrian. An interaction module including this data-driven mechanism is further proposed. In the proposed module, the data-driven mechanism can effectively extract the feature representations of dynamic human-human interactions in the scene and calculate the corresponding weights to represent the importance of different interactions. To share such social messages among pedestrians, an interaction-aware architecture based on long short-term memory network for trajectory prediction is designed. Experiments are conducted on two public datasets. Experimental results demonstrate that our model can achieve better performance than several latest methods with good performance.

The objective of this work is to expand upon previous works, considering socially acceptable behaviours within robot navigation and interaction, and allow a robot to closely approach static and dynamic individuals or groups. The space models developed in this dissertation are adaptive, that is, capable of changing over time to accommodate the changing circumstances often existent within a social environment. The space model's parameters' adaptation occurs with the end goal of enabling a close interaction between humans and robots and is thus capable of taking into account not only the arrangement of the groups, but also the basic characteristics of the robot itself. This work also further develops a preexisting approach pose estimation algorithm in order to better guarantee the safety and comfort of the humans involved in the interaction, by taking into account basic human sensibilities. The algorithms are integrated into ROS's navigation system through the use of the $costmap2d$ and the $move\_base$ packages. The space model adaptation is tested via comparative evaluation against previous algorithms through the use of datasets. The entire navigation system is then evaluated through both simulations (static and dynamic) and real life situations (static). These experiments demonstrate that the developed space model and approach pose estimation algorithms are capable of enabling a robot to closely approach individual humans and groups, while maintaining considerations for their comfort and sensibilities.