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

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. Leveraging on a high-quality, high-statistics data set, composed of several few millions 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 on our Langevin model for noninteracting pedestrian motion [Corbetta et al., Phys. Rev. E 95, 032316 (2017)] (here further tested and extended). The model that we propose here features a Langevin dynamics with fast random velocity fluctuations that are superimposed on the slow dynamics of a hidden model variable: the intended walking path. In the 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 data sets 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 general approach based on a graph representation of pedestrian trajectories, which allows us to effectively operate complexity reduction for efficient data classification and selection.