Potential for the dynamics of pedestrians in a socially interacting group

Abstract

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.

Age and Group-driven Pedestrian Behaviour: from Observations to Simulations

“…Recent empirical contributions [11,12] clearly showed that pedestrian flows in urban crowded scenarios are characterised by the preponderant presence of groups: social units featured by common goals and variable strength of membership. In particular, the granulometric distribution of pedestrian flows is strongly affected by two-members groups (dyads), which represent the most frequent and basic interacting elements of crowds [3].…”

Frame vs. Trajectory Analyses of Pedestrian Dynamics Asymmetries in a Staircase Landing

“…In many occasions, nonetheless, when aiming at understanding the dynamics, a (possibly implicit) preliminary data screening is applied to ensure the aggregation and analysis just of occurrences of similar (homogeneous) flow conditions. In fact, we expect that pedestrians walking isolated from peers will exhibit a different dynamics than pedestrians walking in groups [23]. Thus, drawing statistics of data inclusive of these two heterogeneous flow conditions unavoidably yields ambiguous statistics.…”

“…Conventionally, manual data selection and annotation has been exclusively employed, e.g. to select groups in [23], to classify walking patterns in [24], or to isolate people waiting in [25]. Although manual annotation is certainly a possibility for processing data acquired in laboratories or in real-life at small scales, it may become prohibitively time consuming when dealing with extensive real-life recordings.…”

Parsimony versus Reductionism: How Can Crowd Psychology be Introduced into Computer Simulation?

“…Hence, in order to accurately simulate different types of crowds, While the importance of crowd psychology for engineering has been noted (Aguirre, El-Tawil, Best, Gill, & Fedorov, 2011;Sime, 1995), theories of crowd psychology have only been minimally incorporated into mathematical modelling and computer simulations, and from a psychological point of view, these are out-dated (Templeton, Drury, & Philippides, 2015). A more promising direction of research are proxemics (Baum & Paulus, 1987;Hall, 1966), which describe the social distances individuals keep from one another and has been used for the study of crowd behaviour (Costa, 2010;von Sivers & Köster, 2015;Zanlungo, Ikeda, & Kanda, 2014). Although there have been some attempts to introduce small groups within the larger crowd behaviour to simulation models such as families, friends or other predefined groups (Köster, Seitz, Treml, Hartmann, & Klein, 2011;Moussaïd, Perozo, Garnier, Helbing, & Theraulaz, 2010;Singh et al, 2009;Yang, Zhao, Li, & Fang, 2005), these models do not consider the social structure or dynamic of the whole crowd (for a comprehensive review, see (Templeton et al, 2015)).…”