Pedestrians walking in crowds show complex dynamics and stunning collective motion.
The investigation of the underlining behaviors from single individuals to large-scale interactions is the topic of our research.
The typical questions we challenge ourselves with are
Can we write quantitative models for the behavior of pedestrians walking in crowds?
Are pedestrian crowds moving like fluid flows?
Answers to these questions has primary impact in engineering, as they enable accurate evacuation simulations, crowd management and interactive built environments.
Figure 1: The main walkway of Eindhoven Train Station. Four overhead Kinect sensors record continuously the traffic flow.
High statistics measurements
Walking individuals have an intrinsically random behavior. A quantitative prediction of walking trajectories is thus impossible. Nevertheless, we expect walking pedestrians to exhibit universal features at the statistical level. In other words, we expect the distributions of position, velocity or acceleration to describe the dynamics.
Comparison with measurements is paramount to shed light on this aspect. Hence, we perform extensive and highly accurate experimental measurements of pedestrian trajectories. To explore the statistical portrait including the rare events we perform 24/7 automatic data acquisition on a yearly basis. We established different measurement locations within TU/e [1, 2] and at Eindhoven Train Station (cf. Figure 1 and 2).
Figure 2: A depth map reconstructed from the recordings of four Kinect sensors. Darker pixels are closer to the plane of the cameras. Pedestrian trajectories and bodies orientation are estimated via an ad hoc method.
3D-range sensors for accurate tracking
To measure pedestrian trajectories accurately we employ an ad hoc technique utilizing multiple overhead Microsoft Kinect 3D-range sensors [1,2]. 3D-range sensors deliver depth maps that associate to each point its distance with the camera plane (cf. Figure 2). We perform pedestrian segmentation via clusterization algorithms applied on the 3D data. Thus, analyzing each cluster pedestrian we identify the head, which we track as a particle in a flow.
Quantitative modeling
We derive Langevin-like stochastic particle models to reproduce the dynamics of pedestrians. We deduce potentials in space and velocity to mimic and explain the observed non-Gaussian fluctuations up to rare events [1].
References
2017
Alessandro Corbetta; Chung-min Lee; Roberto Benzi; Adrian Muntean; Federico Toschi
@article{Corbetta_PRE_2017,
title = {Fluctuations around mean walking behaviours in diluted pedestrian flows},
author = {Alessandro Corbetta and Chung-min Lee and Roberto Benzi and Adrian Muntean and Federico Toschi},
url = {https://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.032316},
year = {2017},
date = {2017-03-15},
journal = {Physical Review E},
volume = {95},
pages = {032316},
abstract = {Understanding and modeling the dynamics of pedestrian crowds can help with designing and increasing the safety of civil facilities. A key feature of a crowd is its intrinsic stochasticity, appearing even under very diluted conditions, due to the variability in individual behaviors. Individual stochasticity becomes even more important under densely crowded conditions, since it can be nonlinearly magnified and may lead to potentially dangerous collective behaviors. To understand quantitatively crowd stochasticity, we study the real-life dynamics of a large ensemble of pedestrians walking undisturbed, and we perform a statistical analysis of the fully resolved pedestrian trajectories obtained by a yearlong high-resolution measurement campaign. Our measurements have been carried out in a corridor of the Eindhoven University of Technology via a combination of Microsoft Kinect 3D range sensor and automatic head-tracking algorithms. The temporal homogeneity of our large database of trajectories allows us to robustly define and separate average walking behaviors from fluctuations parallel and orthogonal with respect to the average walking path. Fluctuations include rare events when individuals suddenly change their minds and invert their walking directions. Such tendency to invert direction has been poorly studied so far, even if it may have important implications on the functioning and safety of facilities. We propose a model for the dynamics of undisturbed pedestrians, based on stochastic differential equations, that provides a good agreement with our field observations, including the occurrence of rare events.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Understanding and modeling the dynamics of pedestrian crowds can help with designing and increasing the safety of civil facilities. A key feature of a crowd is its intrinsic stochasticity, appearing even under very diluted conditions, due to the variability in individual behaviors. Individual stochasticity becomes even more important under densely crowded conditions, since it can be nonlinearly magnified and may lead to potentially dangerous collective behaviors. To understand quantitatively crowd stochasticity, we study the real-life dynamics of a large ensemble of pedestrians walking undisturbed, and we perform a statistical analysis of the fully resolved pedestrian trajectories obtained by a yearlong high-resolution measurement campaign. Our measurements have been carried out in a corridor of the Eindhoven University of Technology via a combination of Microsoft Kinect 3D range sensor and automatic head-tracking algorithms. The temporal homogeneity of our large database of trajectories allows us to robustly define and separate average walking behaviors from fluctuations parallel and orthogonal with respect to the average walking path. Fluctuations include rare events when individuals suddenly change their minds and invert their walking directions. Such tendency to invert direction has been poorly studied so far, even if it may have important implications on the functioning and safety of facilities. We propose a model for the dynamics of undisturbed pedestrians, based on stochastic differential equations, that provides a good agreement with our field observations, including the occurrence of rare events.
@article{Corbetta_TRP14,
title = {High statistics measurements of pedestrian dynamics},
author = {Alessandro Corbetta and Luca Bruno and Adrian Muntean and Federico Toschi},
url = {http://www.sciencedirect.com/science/article/pii/S2352146514000490},
doi = {10.1016/j.trpro.2014.09.013},
year = {2014},
date = {2014-10-24},
journal = {Transportation Research Procedia},
volume = {2},
pages = {96-104},
abstract = {Aiming at a quantitative understanding of basic aspects of pedestrian dynamics, extensive and high-accuracy measurements of real-life pedestrian trajectories have been performed. A measurement strategy based on Microsoft KinectTM has been used. Specifically, more than 100.000 pedestrians have been tracked while walking along a trafficked corridor at the Eindhoven University of Technology, The Netherlands. The obtained trajectories have been analyzed as ensemble data.
The main result consists of a statistical descriptions of pedestrian characteristic kinematic quantities such as positions and fundamental diagrams, possibly conditioned to the local crowd flow (e.g. co-flow or counter-flow).
Aiming at a quantitative understanding of basic aspects of pedestrian dynamics, extensive and high-accuracy measurements of real-life pedestrian trajectories have been performed. A measurement strategy based on Microsoft KinectTM has been used. Specifically, more than 100.000 pedestrians have been tracked while walking along a trafficked corridor at the Eindhoven University of Technology, The Netherlands. The obtained trajectories have been analyzed as ensemble data.
The main result consists of a statistical descriptions of pedestrian characteristic kinematic quantities such as positions and fundamental diagrams, possibly conditioned to the local crowd flow (e.g. co-flow or counter-flow).
