Pedestrian dynamics: from pairwise interactions to large scale measurements

Transcription

1 Flowing Matter 16 January 14 th, 2016 Pedestrian dynamics: from pairwise interactions to large scale measurements Alessandro Corbetta Eindhoven University of Technology, NL with: Chung-Min Lee (CSULB), Jasper Meeusen (TU/e), Roberto Benzi (Rome 2), Adrian Muntean (Karlstad), Federico Toschi (TU/e) Centre for Analysis, Scientific computing and Applications

2 Crowd TU/e: Part II follow up to: Pedestrian dynamics: experiments and single pedestrian modeling by Chung-min Lee, Monday Today: Extensions + Present/Future directions

3 Introduction & Motivation Walking pedestrians: rich & complex dynamics Reliable models: relevant in science & technology Stochastic, nearly unpredictable motion Quantitative predictions? Interactions?

4 High statistics measurements approach Metaforum, TU/e Real-life setting 1y recording ~h24, ~2.2K people/day ~230K tracks dataset [Seer et al. 2014, Corbetta et al. 2014, Corbetta et al. 2015]

5 Single pedestrian dynamics Single pedestrian stochastic dynamics ẍ = r v K(v) r x V (x)+ẇ Statistics: small fluctuations u p u p Fluctuations around a preferred path Double-well velocity potential Captured inversion events

6 From individuals to crowds Statistical crowd behavior? Mutual interactions in diluted and dense crowds? Changes in statistics? Rare events in real crowds? e.g., in a train station?

7 From individuals to crowds Extended tracking system 4 Kinect signals merged ~3m x 9m area covered 24/7 measurements 6 months

8 Everyday dynamics 100K people/day (~scale of all TU/e ) Many different experiments Rarefied & dense σ =10sec σ =5min load hour

9 Modeling interactions Single pedestrian stochastic dynamics Statistics: Question:

10 Modeling interactions Single pedestrian stochastic dynamics Statistics: Question: Pairwise interaction kernel to get modified statistics? K = K( x, v, x, v,...)

11 Interaction in diluted conditions: avoidance Counter-flow Pedestrians encountering just another pedestrian in counterflow

12 Avoidance dynamics in pairs Avoidance => shift of positions to the relative right 2L ( ) 2R (!)

13 Average social force field

14 Perturbations in the dynamics Undisturbed ped vs. Pairs W τ (2Ls) W τ (2Lc) W τ (2Rs) W τ (2Rc) longitudinal velocity transversal fluctuations longitudinal velocity [m/s] longitudinal velocity [m/s] W n (2Ls) W n (2Lc) W n (2Rs) W n (2Rc) transversal velocity [m/s] transversal velocity [m/s]

15 Perturbations in the dynamics Undisturbed ped vs. Pairs W τ (2Ls) W τ (2Lc) W τ (2Rs) W τ (2Rc) longitudinal velocity transversal fluctuations longitudinal velocity [m/s] longitudinal velocity [m/s] Asymmetric variation of the dynamics wrt. single ped. Inner side more influenced! W n (2Ls) W n (2Lc) W n (2Rs) W n (2Rc) transversal velocity [m/s] transversal velocity [m/s] Larger perturbation Asymmetries?

16 Key aspects of the interaction Usual interaction Kernels [Helbing 95]: Radial avoidance + anisotropic intensity, Gaussian decay Longit. Transv. Curvilinear-distance-based lateral avoidance force K Longitudinal slow-downs to avoid imminent frontal collisions

17 Key aspects of the interaction Usual interaction Kernels [Helbing 95]: Radial avoidance + anisotropic intensity, Gaussian decay Longit. Transv. Curvilinear-distance-based lateral avoidance force K Longitudinal slow-downs to avoid imminent frontal collisions L 2R L white path 2L simulation mean path R white path 2R simulation mean path

18 Outlook Massive statistics from long-time real world measurements Modify/enrich undisturbed pedestrian model to include interactions Give insights on rare events Behavior in dense conditions Acknowledgements: Alex Liberzon, Ad Holten, Dutch National Railways, Intelligent Lighting Institute (Eindhoven)

19 References 1. A. Corbetta, L. Bruno, A. Muntean, F. Toschi, High Statistic Measurements of Pedestrian Dynamics, 2014, Transportation Research Procedia, S. Seer, N. Brandle and C. Ratti, Kinects and human kinetics: a new approach for studying pedestrian behavior, Transportation Research Part C: Emerging Technologies, 2014, 48 : A. Corbetta, A. Muntean, K. Vafayi, F. Toschi, Parameter Estimation of Social Forces in Pedestrian Dynamics models via a Probabilistic Method, 2015, Mathematical Biosciences and Engineering, 12 (2), The OpenPTV initiative, , 5. J. Willneff, A. Gruen, A new Spatio-Temporal Matching Algorithm for 3D-Particle Tracking Velocimetry, The 9 th of International Symposium on Transport Phenomena and Rotating Machinery, Honolulu, Hawaii, J. Willneff, A Spatio-Temporal Matching Algorithm for 3D Particle Tracking Velocimetry, PhD Thesis, ETH-Zurich, A. Corbetta, Multiscale pedestrian dynamics: physical analysis, modeling and applications, PhD Thesis, A. Corbetta, C. Lee, R. Benzi, A. Muntean, F. Toschi, Fluctuations and mean behaviours in diluted pedestrian flows, to be submitted