September  2015, 10(3): 559-578. doi: 10.3934/nhm.2015.10.559

Keep right or left? Towards a cognitive-mathematical model for pedestrians

1. 

Rutgers University, Department of Psychology, Camden, NJ 08102, United States, United States

2. 

Équipe M2N - EA 7340, Conservatoire National des Arts et Métiers, Paris

3. 

Joseph and Loretta Lopez Chair Professor of Mathematics, Department of Mathematical Sciences and Program Director, Center for Computational and Integrative Biology, Rutgers University - Camden, 311 N 5th Street, Camden, NJ 08102

Received  March 2015 Revised  May 2015 Published  July 2015

In this paper we discuss the necessity of insight in the cognitive processes involved in environment navigation into mathematical models for pedestrian motion. We first provide a review of psychological literature on the cognitive processes involved in walking and on the quantitative one coming from applied mathematics, physics, and engineering. Then, we present a critical analysis of the experimental setting for model testing and we show experimental results given by observation. Finally we propose a cognitive model making use of psychological insight as well as optimization models from robotics.
Citation: Mary J. Bravo, Marco Caponigro, Emily Leibowitz, Benedetto Piccoli. Keep right or left? Towards a cognitive-mathematical model for pedestrians. Networks & Heterogeneous Media, 2015, 10 (3) : 559-578. doi: 10.3934/nhm.2015.10.559
References:
[1]

G. Arechavaleta, J.-P. Laumond, H. Hicheur and A. Berthoz, An optimality principle governing human walking,, Robotics, 24 (2008), 5.  doi: 10.1109/TRO.2008.915449.  Google Scholar

[2]

N. Bellomo and C. Dogbe, On the modeling of traffic and crowds: A survey of models, speculations, and perspectives,, SIAM Review, 53 (2011), 409.  doi: 10.1137/090746677.  Google Scholar

[3]

E. M. Cepolina and N. Tyler, Understanding Capacity Drop for designing pedestrian environments,, in Proceedings of the 6th International Walk21 Conference, (2005), 1.   Google Scholar

[4]

Y. Chitour, F. Jean and P. Mason, Optimal control models of goal-oriented human locomotion,, SIAM Journal on Control and Optimization, 50 (2012), 147.  doi: 10.1137/100799344.  Google Scholar

[5]

F. Chittaro, F. Jean and P. Mason, On inverse optimal control problems of human locomotion: Stability and robustness of the minimizers,, Journal of Mathematical Sciences, 195 (2013), 269.  doi: 10.1007/s10958-013-1579-z.  Google Scholar

[6]

R. Conroy-Dalton, The secret is to follow your nose: Route path selection and angularity,, in 3rd International Space Syntax Symposium, (2003), 1.   Google Scholar

[7]

E. Cristiani, B. Piccoli and A. Tosin, Multiscale Modeling of Pedestrian Dynamics,, MS&A: Modeling, (2014).  doi: 10.1007/978-3-319-06620-2.  Google Scholar

[8]

W. Daamen and S. Hoogendoorn, Experimental research of pedestrian walking behavior,, Transportation Research Record: Journal of the Transportation Research Board, 1828 (2003), 20.  doi: 10.3141/1828-03.  Google Scholar

[9]

J. M. Dabbs Jr and N. A. Stokes III, Beauty is power: The use of space on the sidewalk,, Sociometry, (): 551.   Google Scholar

[10]

E. Goffman, Relations in Public: Microstudies of the Social Order,, 1971., ().   Google Scholar

[11]

R. G. Golledge, Human wayfinding and cognitive maps,, in Wayfinding Behavior: Cognitive Mapping and Other Spatial Processes, (1999), 5.   Google Scholar

[12]

H. L. Golson and J. M. Dabbs, et al., Line-following tendencies among pedestrians: A sex difference,, Personality And Social Psychology Bulletin, 1 (1974), 16.  doi: 10.1177/014616727400100106.  Google Scholar

[13]

D. Helbing, Boltzmann-like and boltzmann-fokker-planck equations as a foundation of behavioral models,, Physica A: Statistical Mechanics and its Applications, 196 (1993), 546.  doi: 10.1016/0378-4371(93)90034-2.  Google Scholar

[14]

D. Helbing, L. Buzna, A. Johansson and T. Werner, Self-organized pedestrian crowd dynamics: Experiments, simulations, and design solutions,, Transportation Science, 39 (2005), 1.  doi: 10.1287/trsc.1040.0108.  Google Scholar

[15]

D. Helbing and P. Molnar, Social force model for pedestrian dynamics,, Physical Review E, 51 (1995).  doi: 10.1103/PhysRevE.51.4282.  Google Scholar

[16]

D. Helbing, P. Molnar, I. J. Farkas and K. Bolay, Self-organizing pedestrian movement,, Environment and Planning B, 28 (2001), 361.  doi: 10.1068/b2697.  Google Scholar

[17]

S. P. Hoogendoorn and P. H. Bovy, State-of-the-art of vehicular traffic flow modelling,, Proceedings of the Institution of Mechanical Engineers, 215 (2001), 283.   Google Scholar

[18]

T. Ishikawa, H. Fujiwara, O. Imai and A. Okabe, Wayfinding with a gps-based mobile navigation system: A comparison with maps and direct experience,, Journal of Environmental Psychology, 28 (2008), 74.  doi: 10.1016/j.jenvp.2007.09.002.  Google Scholar

[19]

T. Ishikawa and D. R. Montello, Spatial knowledge acquisition from direct experience in the environment: Individual differences in the development of metric knowledge and the integration of separately learned places,, Cognitive Psychology, 52 (2006), 93.  doi: 10.1016/j.cogpsych.2005.08.003.  Google Scholar

[20]

A. Johansson, D. Helbing and P. K. Shukla, Specification of the social force pedestrian model by evolutionary adjustment to video tracking data,, Advances in Complex Systems, 10 (2007), 271.  doi: 10.1142/S0219525907001355.  Google Scholar

[21]

H. S. Jung and H.-S. Jung, Survey of korean pedestrians' natural preference for walking directions,, Applied Ergonomics, 44 (2013), 1015.  doi: 10.1016/j.apergo.2013.04.003.  Google Scholar

[22]

A. Lachapelle and M.-T. Wolfram, On a mean field game approach modeling congestion and aversion in pedestrian crowds,, Transportation Research Part B: Methodological, 45 (2011), 1572.  doi: 10.1016/j.trb.2011.07.011.  Google Scholar

[23]

R. Lloyd and C. Heivly, Systematic distortions in urban cognitive maps,, Annals of the Association of American Geographers, 77 (1987), 191.  doi: 10.1111/j.1467-8306.1987.tb00153.x.  Google Scholar

[24]

K. Mombaur, J.-P. Laumond and E. Yoshida, An optimal control-based formulation to determine natural locomotor paths for humanoid robots,, Advanced Robotics, 24 (2010), 515.  doi: 10.1163/016918610X487090.  Google Scholar

[25]

K. Mombaur, A. Truong and J.-P. Laumond, From human to humanoid locomotion-an inverse optimal control approach,, Autonomous Robots, 28 (2010), 369.  doi: 10.1007/s10514-009-9170-7.  Google Scholar

[26]

D. R. Montello, The perception and cognition of environmental distance: Direct sources of information,, in Spatial Information Theory A Theoretical Basis for GIS, 1329 (1997), 297.  doi: 10.1007/3-540-63623-4_57.  Google Scholar

[27]

M. Moussaīd, D. Helbing and G. Theraulaz, How simple rules determine pedestrian behavior and crowd disasters,, Proceedings of the National Academy of Sciences, 108 (2011), 6884.   Google Scholar

[28]

J. Ondřej, J. Pettré, A.-H. Olivier and S. Donikian, A synthetic-vision based steering approach for crowd simulation,, in ACM Transactions on Graphics (TOG), 29 (2010).   Google Scholar

[29]

E. Papadimitriou, G. Yannis and J. Golias, A critical assessment of pedestrian behaviour models,, Transportation Research Part F: Traffic Psychology and Behaviour, 12 (2009), 242.  doi: 10.1016/j.trf.2008.12.004.  Google Scholar

[30]

T. Rosenbloom, Crossing at a red light: Behaviour of individuals and groups,, Transportation Research Part F: Traffic Psychology and Behaviour, 12 (2009), 389.  doi: 10.1016/j.trf.2009.05.002.  Google Scholar

[31]

J. van den Berg, S. Patil, J. Sewall, D. Manocha and M. Lin, Interactive navigation of multiple agents in crowded environments,, in Proceedings of the 2008 symposium on Interactive 3D graphics and games, (2008), 139.   Google Scholar

[32]

D. Vickers, P. Bovet, M. D. Lee and P. Hughes, The perception of minimal structures: Performance on open and closed versions of visually presented euclidean travelling salesperson problems,, Perception-London, 32 (2003), 871.  doi: 10.1068/p3416.  Google Scholar

[33]

M. Wolff, Notes on the behaviour of pedestrians,, People in Places: The Sociology of the Familiar, (1973), 35.   Google Scholar

[34]

L. Yang, J. Li and S. Liu, Simulation of pedestrian counter-flow with right-moving preference,, Physica A: Statistical Mechanics and its Applications, 387 (2008), 3281.  doi: 10.1016/j.physa.2008.01.107.  Google Scholar

[35]

F. Zanlungo, T. Ikeda and T. Kanda, A microscopic "social norm" model to obtain realistic macroscopic velocity and density pedestrian distributions,, PloS one, 7 (2012).  doi: 10.1371/journal.pone.0050720.  Google Scholar

show all references

References:
[1]

G. Arechavaleta, J.-P. Laumond, H. Hicheur and A. Berthoz, An optimality principle governing human walking,, Robotics, 24 (2008), 5.  doi: 10.1109/TRO.2008.915449.  Google Scholar

[2]

N. Bellomo and C. Dogbe, On the modeling of traffic and crowds: A survey of models, speculations, and perspectives,, SIAM Review, 53 (2011), 409.  doi: 10.1137/090746677.  Google Scholar

[3]

E. M. Cepolina and N. Tyler, Understanding Capacity Drop for designing pedestrian environments,, in Proceedings of the 6th International Walk21 Conference, (2005), 1.   Google Scholar

[4]

Y. Chitour, F. Jean and P. Mason, Optimal control models of goal-oriented human locomotion,, SIAM Journal on Control and Optimization, 50 (2012), 147.  doi: 10.1137/100799344.  Google Scholar

[5]

F. Chittaro, F. Jean and P. Mason, On inverse optimal control problems of human locomotion: Stability and robustness of the minimizers,, Journal of Mathematical Sciences, 195 (2013), 269.  doi: 10.1007/s10958-013-1579-z.  Google Scholar

[6]

R. Conroy-Dalton, The secret is to follow your nose: Route path selection and angularity,, in 3rd International Space Syntax Symposium, (2003), 1.   Google Scholar

[7]

E. Cristiani, B. Piccoli and A. Tosin, Multiscale Modeling of Pedestrian Dynamics,, MS&A: Modeling, (2014).  doi: 10.1007/978-3-319-06620-2.  Google Scholar

[8]

W. Daamen and S. Hoogendoorn, Experimental research of pedestrian walking behavior,, Transportation Research Record: Journal of the Transportation Research Board, 1828 (2003), 20.  doi: 10.3141/1828-03.  Google Scholar

[9]

J. M. Dabbs Jr and N. A. Stokes III, Beauty is power: The use of space on the sidewalk,, Sociometry, (): 551.   Google Scholar

[10]

E. Goffman, Relations in Public: Microstudies of the Social Order,, 1971., ().   Google Scholar

[11]

R. G. Golledge, Human wayfinding and cognitive maps,, in Wayfinding Behavior: Cognitive Mapping and Other Spatial Processes, (1999), 5.   Google Scholar

[12]

H. L. Golson and J. M. Dabbs, et al., Line-following tendencies among pedestrians: A sex difference,, Personality And Social Psychology Bulletin, 1 (1974), 16.  doi: 10.1177/014616727400100106.  Google Scholar

[13]

D. Helbing, Boltzmann-like and boltzmann-fokker-planck equations as a foundation of behavioral models,, Physica A: Statistical Mechanics and its Applications, 196 (1993), 546.  doi: 10.1016/0378-4371(93)90034-2.  Google Scholar

[14]

D. Helbing, L. Buzna, A. Johansson and T. Werner, Self-organized pedestrian crowd dynamics: Experiments, simulations, and design solutions,, Transportation Science, 39 (2005), 1.  doi: 10.1287/trsc.1040.0108.  Google Scholar

[15]

D. Helbing and P. Molnar, Social force model for pedestrian dynamics,, Physical Review E, 51 (1995).  doi: 10.1103/PhysRevE.51.4282.  Google Scholar

[16]

D. Helbing, P. Molnar, I. J. Farkas and K. Bolay, Self-organizing pedestrian movement,, Environment and Planning B, 28 (2001), 361.  doi: 10.1068/b2697.  Google Scholar

[17]

S. P. Hoogendoorn and P. H. Bovy, State-of-the-art of vehicular traffic flow modelling,, Proceedings of the Institution of Mechanical Engineers, 215 (2001), 283.   Google Scholar

[18]

T. Ishikawa, H. Fujiwara, O. Imai and A. Okabe, Wayfinding with a gps-based mobile navigation system: A comparison with maps and direct experience,, Journal of Environmental Psychology, 28 (2008), 74.  doi: 10.1016/j.jenvp.2007.09.002.  Google Scholar

[19]

T. Ishikawa and D. R. Montello, Spatial knowledge acquisition from direct experience in the environment: Individual differences in the development of metric knowledge and the integration of separately learned places,, Cognitive Psychology, 52 (2006), 93.  doi: 10.1016/j.cogpsych.2005.08.003.  Google Scholar

[20]

A. Johansson, D. Helbing and P. K. Shukla, Specification of the social force pedestrian model by evolutionary adjustment to video tracking data,, Advances in Complex Systems, 10 (2007), 271.  doi: 10.1142/S0219525907001355.  Google Scholar

[21]

H. S. Jung and H.-S. Jung, Survey of korean pedestrians' natural preference for walking directions,, Applied Ergonomics, 44 (2013), 1015.  doi: 10.1016/j.apergo.2013.04.003.  Google Scholar

[22]

A. Lachapelle and M.-T. Wolfram, On a mean field game approach modeling congestion and aversion in pedestrian crowds,, Transportation Research Part B: Methodological, 45 (2011), 1572.  doi: 10.1016/j.trb.2011.07.011.  Google Scholar

[23]

R. Lloyd and C. Heivly, Systematic distortions in urban cognitive maps,, Annals of the Association of American Geographers, 77 (1987), 191.  doi: 10.1111/j.1467-8306.1987.tb00153.x.  Google Scholar

[24]

K. Mombaur, J.-P. Laumond and E. Yoshida, An optimal control-based formulation to determine natural locomotor paths for humanoid robots,, Advanced Robotics, 24 (2010), 515.  doi: 10.1163/016918610X487090.  Google Scholar

[25]

K. Mombaur, A. Truong and J.-P. Laumond, From human to humanoid locomotion-an inverse optimal control approach,, Autonomous Robots, 28 (2010), 369.  doi: 10.1007/s10514-009-9170-7.  Google Scholar

[26]

D. R. Montello, The perception and cognition of environmental distance: Direct sources of information,, in Spatial Information Theory A Theoretical Basis for GIS, 1329 (1997), 297.  doi: 10.1007/3-540-63623-4_57.  Google Scholar

[27]

M. Moussaīd, D. Helbing and G. Theraulaz, How simple rules determine pedestrian behavior and crowd disasters,, Proceedings of the National Academy of Sciences, 108 (2011), 6884.   Google Scholar

[28]

J. Ondřej, J. Pettré, A.-H. Olivier and S. Donikian, A synthetic-vision based steering approach for crowd simulation,, in ACM Transactions on Graphics (TOG), 29 (2010).   Google Scholar

[29]

E. Papadimitriou, G. Yannis and J. Golias, A critical assessment of pedestrian behaviour models,, Transportation Research Part F: Traffic Psychology and Behaviour, 12 (2009), 242.  doi: 10.1016/j.trf.2008.12.004.  Google Scholar

[30]

T. Rosenbloom, Crossing at a red light: Behaviour of individuals and groups,, Transportation Research Part F: Traffic Psychology and Behaviour, 12 (2009), 389.  doi: 10.1016/j.trf.2009.05.002.  Google Scholar

[31]

J. van den Berg, S. Patil, J. Sewall, D. Manocha and M. Lin, Interactive navigation of multiple agents in crowded environments,, in Proceedings of the 2008 symposium on Interactive 3D graphics and games, (2008), 139.   Google Scholar

[32]

D. Vickers, P. Bovet, M. D. Lee and P. Hughes, The perception of minimal structures: Performance on open and closed versions of visually presented euclidean travelling salesperson problems,, Perception-London, 32 (2003), 871.  doi: 10.1068/p3416.  Google Scholar

[33]

M. Wolff, Notes on the behaviour of pedestrians,, People in Places: The Sociology of the Familiar, (1973), 35.   Google Scholar

[34]

L. Yang, J. Li and S. Liu, Simulation of pedestrian counter-flow with right-moving preference,, Physica A: Statistical Mechanics and its Applications, 387 (2008), 3281.  doi: 10.1016/j.physa.2008.01.107.  Google Scholar

[35]

F. Zanlungo, T. Ikeda and T. Kanda, A microscopic "social norm" model to obtain realistic macroscopic velocity and density pedestrian distributions,, PloS one, 7 (2012).  doi: 10.1371/journal.pone.0050720.  Google Scholar

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