Social aspects of collision avoidance: a detailed analysis of two-person groups and individual pedestrians.

Pedestrian groups are commonly found in crowds but research on their social aspects is comparatively lacking. To fill that void in literature, we study the dynamics of collision avoidance between pedestrian groups (in particular dyads) and individual pedestrians in an ecological environment, focusing in particular on (i) how such avoidance depends on the group's social relation (e.g. colleagues, couples, friends or families) and (ii) its intensity of social interaction (indicated by conversation, gaze exchange, gestures etc). By analyzing relative collision avoidance in the "center of mass" frame, we were able to quantify how much groups and individuals avoid each other with respect to the aforementioned properties of the group. A mathematical representation using a potential energy function is proposed to model avoidance and it is shown to provide a fair approximation to the empirical observations. We also studied the probability that the individuals disrupt the group by "passing through it" (termed as intrusion). We analyzed the dependence of the parameters of the avoidance model and of the probability of intrusion on groups' social relation and intensity of interaction. We confirmed that the stronger social bonding or interaction intensity is, the more prominent collision avoidance turns out. We also confirmed that the probability of intrusion is a decreasing function of interaction intensity and strength of social bonding. Our results suggest that such variability should be accounted for in models and crowd management in general. Namely, public spaces with strongly bonded groups (e.g. a family-oriented amusement park) may require a different approach compared to public spaces with loosely bonded groups (e.g. a business-oriented trade fair).

Intrinsic group behaviour II: On the dependence of triad spatial dynamics on social and personal features; and on the effect of social interaction on small group dynamics.

In a follow-up to our work on the dependence of walking dyad dynamics on intrinsic properties of the group, we now analyse how these properties affect groups of three people (triads), taking also in consideration the effect of social interaction on the dynamical properties of the group. We show that there is a strong parallel between triads and dyads. Work-oriented groups are faster and walk at a larger distance between them than leisure-oriented ones, while the latter move in a less ordered way. Such differences are present also when colleagues are contrasted with friends and families; nevertheless the similarity between friend and colleague behaviour is greater than the one between family and colleague behaviour. Male triads walk faster than triads including females, males keep a larger distance than females, and same gender groups are more ordered than mixed ones. Groups including tall people walk faster, while those with elderly or children walk at a slower pace. Groups including children move in a less ordered fashion. Results concerning relation and gender are particularly strong, and we investigated whether they hold also when other properties are kept fixed. While this is clearly true for relation, patterns relating gender often resulted to be diminished. For instance, the velocity difference due to gender is reduced if we compare only triads in the colleague relation. The effects on group dynamics due to intrinsic properties are present regardless of social interaction, but socially interacting groups are found to walk in a more ordered way. This has an opposite effect on the space occupied by non-interacting dyads and triads, since loss of structure makes dyads larger, but causes triads to lose their characteristic V formation and walk in a line (i.e., occupying more space in the direction of movement but less space in the orthogonal one).

Identification of social relation within pedestrian dyads.

This study focuses on social pedestrian groups in public spaces and makes an effort to identify the type of social relation between the group members. As a first step for this identification problem, we focus on dyads (i.e. 2 people groups). Moreover, as a mutually exclusive categorization of social relations, we consider the domain-based approach of Bugental, which precisely corresponds to social relations of colleagues, couples, friends and families, and identify each dyad with one of those relations. For this purpose, we use anonymized trajectory data and derive a set of observables thereof, namely, inter-personal distance, group velocity, velocity difference and height difference. Subsequently, we use the probability density functions (pdf) of these observables as a tool to understand the nature of the relation between pedestrians. To that end, we propose different ways of using the pdfs. Namely, we introduce a probabilistic Bayesian approach and contrast it to a functional metric one and evaluate the performance of both methods with appropriate assessment measures. This study stands out as the first attempt to automatically recognize social relation between pedestrian groups. Additionally, in doing that it uses completely anonymous data and proves that social relation is still possible to recognize with a good accuracy without invading privacy. In particular, our findings indicate that significant recognition rates can be attained for certain categories and with certain methods. Specifically, we show that a very good recognition rate is achieved in distinguishing colleagues from leisure-oriented dyads (families, couples and friends), whereas the distinction between the leisure-oriented dyads results to be inherently harder, but still possible at reasonable rates, in particular if families are restricted to parent-child groups. In general, we establish that the Bayesian method outperforms the functional metric one due, probably, to the difficulty of the latter to learn observable pdfs from individual trajectories.

Intrinsic group behaviour: Dependence of pedestrian dyad dynamics on principal social and personal features.

Being determined by human social behaviour, pedestrian group dynamics may depend on "intrinsic properties" such as the purpose of the pedestrians, their personal relation, gender, age, and body size. In this work we investigate the dynamical properties of pedestrian dyads (distance, spatial formation and velocity) by analysing a large data set of automatically tracked pedestrian trajectories in an unconstrained "ecological" setting (a shopping mall), whose apparent physical and social group properties have been analysed by three different human coders. We observed that females walk slower and closer than males, that workers walk faster, at a larger distance and more abreast than leisure oriented people, and that inter-group relation has a strong effect on group structure, with couples walking very close and abreast, colleagues walking at a larger distance, and friends walking more abreast than family members. Pedestrian height (obtained automatically through our tracking system) influences velocity and abreast distance, both growing functions of the average group height. Results regarding pedestrian age show that elderly people walk slowly, while active age adults walk at the maximum velocity. Groups with children have a strong tendency to walk in a non-abreast formation, with a large distance (despite a low abreast distance). A cross-analysis of the interplay between these intrinsic features, taking in account also the effect of an "extrinsic property" such as crowd density, confirms these major results but reveals also a richer structure. An interesting and unexpected result, for example, is that the velocity of groups with children increases with density, at least in the low-medium density range found under normal conditions in shopping malls. Children also appear to behave differently according to the gender of the parent.

Spatial-size scaling of pedestrian groups under growing density conditions.

We study the dependence on crowd density of the spatial size, configuration, and velocity of pedestrian social groups. We find that, in the investigated density range, the extension of pedestrian groups in the direction orthogonal to that of motion decreases linearly with the pedestrian density around them, both for two- and three-person groups. Furthermore, we observe that at all densities, three-person groups walk slower than two-person groups, and the latter are slower than individual pedestrians, the differences in velocities being weakly affected by density. Finally, we observe that three-person groups walk in a V-shaped formation regardless of density, with a distance between the pedestrians in the front and back again almost independent of density, although the configuration appears to be less stable at higher densities. These findings may facilitate the development of more realistic crowd dynamics models and simulators.

Potential for the dynamics of pedestrians in a socially interacting group.

We introduce a simple potential to describe the dynamics of the relative motion of two pedestrians socially interacting in a walking group. We show that the proposed potential, based on basic empirical observations and theoretical considerations, can qualitatively describe the statistical properties of pedestrian behavior. In detail, we show that the two-dimensional probability distribution of the relative distance is determined by the proposed potential through a Boltzmann distribution. After calibrating the parameters of the model on the two-pedestrian group data, we apply the model to three-pedestrian groups, showing that it describes qualitatively and quantitatively well their behavior. In particular, the model predicts that three-pedestrian groups walk in a V-shaped formation and provides accurate values for the position of the three pedestrians. Furthermore, the model correctly predicts the average walking velocity of three-person groups based on the velocity of two-person ones. Possible extensions to larger groups, along with alternative explanations of the social dynamics that may be implied by our model, are discussed at the end of the paper.

Deciphering the crowd: modeling and identification of pedestrian group motion.

Associating attributes to pedestrians in a crowd is relevant for various areas like surveillance, customer profiling and service providing. The attributes of interest greatly depend on the application domain and might involve such social relations as friends or family as well as the hierarchy of the group including the leader or subordinates. Nevertheless, the complex social setting inherently complicates this task. We attack this problem by exploiting the small group structures in the crowd. The relations among individuals and their peers within a social group are reliable indicators of social attributes. To that end, this paper identifies social groups based on explicit motion models integrated through a hypothesis testing scheme. We develop two models relating positional and directional relations. A pair of pedestrians is identified as belonging to the same group or not by utilizing the two models in parallel, which defines a compound hypothesis testing scheme. By testing the proposed approach on three datasets with different environmental properties and group characteristics, it is demonstrated that we achieve an identification accuracy of 87% to 99%. The contribution of this study lies in its definition of positional and directional relation models, its description of compound evaluations, and the resolution of ambiguities with our proposed uncertainty measure based on the local and global indicators of group relation.

A microscopic "social norm" model to obtain realistic macroscopic velocity and density pedestrian distributions.

We propose a way to introduce in microscopic pedestrian models a "social norm" in collision avoiding and overtaking, i.e. the tendency, shared by pedestrians belonging to the same culture, to avoid collisions and perform overtaking in a preferred direction. The "social norm" is implemented, regardless of the specific collision avoiding model, as a rotation in the perceived velocity vector of the opponent at the moment of computation of the collision avoiding strategy, and justified as an expectation that the opponent will follow the same "social norm" (for example a tendency to avoid on the left and overtake on the right, as proposed in this work for Japanese pedestrians). By comparing with real world data, we show that the introduction of this norm allows for a better reproduction of macroscopic pedestrian density and velocity patterns.