Physics-based modeling and data representation of pairwise interactions among pedestrians

Abstract

The possibility to understand and to quantitatively model the physics of the interactions between pedestrians walking in crowds has compelling relevant applications, e.g. related to the efficient design and the safety of civil infrastructures. In this work we study pedestrian-pedestrian interactions from observational experimental data in diluted pedestrian crowds. While in motion, pedestrians continuously adapt their walking paths trying to preserve mutual comfort distances and to avoid collisions. In mathematical models this behavior is typically modeled via "social" interaction forces.Leveraging on a high-quality, high-statistics dataset -composed of few millions of real-life trajectories acquired from state of the art observational experiments (about 6 months of high-resolution pedestrian tracks acquired in a train station) -we develop a quantitative model capable of addressing interactions in the case of binary collision avoidance. We model interactions in terms of both long-range (sight based) and short-range (hard-contact avoidance) forces, which we superimpose to our Langevin model for non-interacting pedestrian motion [Corbetta et al. Phys. Rev. E 95, 032316, 2017] (here further tested and extended). The new model that we propose here features a Langevin dynamics with "fast" random velocity fluctuations that are superimposed to the "slow" dynamics of a hidden model variable: the "intended" walking path. In case of interactions, social forces may act both on the intended path and on the actual walked path. The model is capable of reproducing quantitatively relevant statistics of the collision avoidance motion, such as the statistics of the side displacement and of the passing speed. Rare occurrences of actual bumping events are also recovered.Furthermore, comparing with large datasets of real-life tracks involves an additional computational challenge so far neglected: identifying automatically, within a database containing very heterogeneous conditions, only the relevant events corresponding to binary avoidance interactions. In order to tackle this challenge, we propose a novel and general approach based on a graph representation of pedestrian trajectories, which allows us to effectively operate complexity reduction for efficient data classification and selection.

Monitoring physical distancing for crowd management: Real-time trajectory and group analysis

“…[ 35 , 36 ]). In [ 19 , 37 ], graphs have also been used to address big-data analyses and representation of pedestrian dynamics aiming at efficient data searches.…”

“…In this section, we describe our scalable framework to characterize pedestrians pairwise distances, identify family-groups and distance offenders. Our approach is a substantial evolution of the graph approach presented by some of the authors in [ 19 , 37 ], which not only does enable to tackle, in real-time, relevant questions connected to Covid-19 safety measures, but unlocks the automation of relevant pedestrian dynamics aspects as the detection of groups. Relevant differences with the previous works [ 19 , 37 ] are postponed after the approach description.…”

“…In [ 19 , 37 ] some of the authors leveraged on a similar interaction network to build a scalable representation and search tool for high-statistics real-life pedestrian tracking data. The aim there was to tackle fundamental issues about the physics of pedestrian dynamics (e.g., mechanics of pairwise avoidance, statistical observables of undisturbed pedestrian motion), which requires extracting pertinent data from databases with few million real-life trajectories.…”

Age Factor and Pedestrian Speed on Sidewalks

“…Other studies are related to different scientific fields or use different populations or variables, e.g., sports medicine [14], social and planning studies [15,16], disabilities [17] or hilly urban areas [18]. Clearly the consequence is different methods, study sampling [14], walking experience [15], "social" interaction forces [16]. Also, for these studies, when the number of parameters increase, they are usually analyzed separately.…”

Micro- and macroscopic modeling of crowding and pushing in corridors

“…Different calibration techniques have been used for the social force model, see [19,29] and CA approaches, see [35,36]. Nowadays a large amount of data is publicly available -for example the database containing data for a multitude of experimental setups at the Forschungszentrum in Jülich, or data collected in a Dutch railway stations over the course of one year, see [10]. However, many mathematical questions concerning the calibration of macroscopic and meanfield models from individual trajectories are still open.…”