Discrete approaches for crowd movement modelling

This article is devoted to the modelling of the movements of an assembly of particles. Our aim is to develop a model capable of reproducing the behavior of a crowd of people in walking situations (free motion, emergency evacuation, etc.). The final model must be able to handle local interactions such as pedestrian-pedestrian and pedestrian-obstacle in order to reproduce the global dynamic of pedestrian traffic. Three already existing discrete methods, originally proposed to simulate a granular assembly, are first analyzed and compared. These methods are able to manage collisions between rigid particles. They are then adapted for representing pedestrians together with their willingness to move. Their numerical implementation allows for the performance of simulations in various specific configurations.

[1]  Y. Kishino,et al.  Disc Model Analysis of Granular Media , 1988 .

[2]  Christer Ericson,et al.  Real-Time Collision Detection , 2004 .

[3]  J. Moreau,et al.  Unilateral Contact and Dry Friction in Finite Freedom Dynamics , 1988 .

[4]  B. D. Hankin,et al.  Passenger Flow in Subways , 1958 .

[5]  Mathieu Renouf,et al.  Optimisation numérique et calcul parallèle pour l'étude de milieux divisés bi- et tridimensionnels. (Numerical Optimisation and Parallel Computing applied to the simulation of 2D/3D discrete element) , 2004 .

[6]  Stefano Dal Pont,et al.  THEORETICAL APPROACH TO AND NUMERICAL SIMULATION OF INSTANTANEOUS COLLISIONS IN GRANULAR MEDIA USING THE A-CD 2 METHOD , 2008 .

[7]  L. F. Henderson,et al.  The Statistics of Crowd Fluids , 1971, Nature.

[8]  Juliette Venel,et al.  Modelisation Mathematique des Mouvements de Foule , 2005 .

[9]  S. Dal Pont,et al.  A theory for multiple collisions of rigid solids and numerical simulation of granular flow , 2006 .

[10]  Pierre Argoul,et al.  Modelling crowd-structure interaction , 2010 .

[11]  Vincent Richefeu,et al.  Contact dynamics as a nonsmooth discrete element method , 2009 .

[12]  C. Brooks.  Computer simulation of liquids , 1989 .

[13]  Kardi Teknomo,et al.  Application of microscopic pedestrian simulation model , 2006 .

[14]  Soraia Raupp Musse,et al.  Using computer vision to simulate the motion of virtual agents , 2007, Comput. Animat. Virtual Worlds.

[15]  Michel Saint Jean,et al.  The non-smooth contact dynamics method , 1999 .

[16]  Craig W. Reynolds.  Flocks, herds, and schools: a distributed behavioral model , 1987, SIGGRAPH.

[17]  R. Luciano,et al.  Stress-penalty method for unilateral contact problems: mathematical formulation and computational aspects , 1994 .

[18]  Edward Ott,et al.  Theoretical mechanics: Crowd synchrony on the Millennium Bridge , 2005, Nature.

[19]  Michael Gleicher,et al.  Scalable behaviors for crowd simulation , 2004, Comput. Graph. Forum.

[20]  D. Helbing.  Traffic and related self-driven many-particle systems , 2000, cond-mat/0012229.

[21]  Pierre-Etienne Gautier,et al.  Modelling ballast behaviour under dynamic loading. Part 1: A 2D polygonal discrete element method approach , 2006 .

[22]  Helbing,et al.  Social force model for pedestrian dynamics. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[23]  Pierre Argoul,et al.  Modeling the lateral pedestrian force on a rigid floor by a self-sustained oscillator , 2010 .

[24]  Laetitia Paoli,et al.  Time discretization of vibro‐impact , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[25]  Sébastien Paris,et al.  Pedestrian Reactive Navigation for Crowd Simulation: a Predictive Approach , 2007, Comput. Graph. Forum.

[26]  P. Cundall.  A computer model for simulating progressive, large-scale movements in blocky rock systems , 1971 .

[27]  M. Frémond.  Rigid bodies collisions , 1995 .

[28]  Bertrand Maury,et al.  A time-stepping scheme for inelastic collisions , 2006, Numerische Mathematik.

[29]  Hubert Ludwig Kluepfel,et al.  A Cellular automaton model for crowd movement and egress simulation , 2003 .

[30]  Victor J. Blue,et al.  Cellular Automata Microsimulation of Bidirectional Pedestrian Flows , 1999 .

[31]  V. Brunel,et al.  Ecole Nationale des Ponts et Chausses , 2009 .

[32]  Pierre Argoul,et al.  Lateral Vibration of Footbridges under Crowd-Loading: Continuous Crowd Modeling Approach , 2007 .

[33]  Lubos Buzna,et al.  Self-Organized Pedestrian Crowd Dynamics: Experiments, Simulations, and Design Solutions , 2005, Transp. Sci..

[34]  Dirk Helbing,et al.  Simulating dynamical features of escape panic , 2000, Nature.

[35]  D. Helbing,et al.  The Walking Behaviour of Pedestrian Social Groups and Its Impact on Crowd Dynamics , 2010, PloS one.

[36]  Roux,et al.  Force Distributions in Dense Two-Dimensional Granular Systems. , 1996, Physical review letters.

[37]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[38]  Ron Kimmel,et al.  Fast Marching Methods for Computing Distance Maps and Shortest Paths , 1996 .

[39]  Joanna Bodgi.  Synchronisation piétons-structure : application aux vibrations des passerelles souples , 2008 .