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
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show all references

References:
[1]

Robotics, IEEE Transactions on, 24 (2008), 5-14. doi: 10.1109/TRO.2008.915449.  Google Scholar

[2]

SIAM Review, 53 (2011), 409-463. doi: 10.1137/090746677.  Google Scholar

[3]

in Proceedings of the 6th International Walk21 Conference, Zurich, 2005, 1-11. Google Scholar

[4]

SIAM Journal on Control and Optimization, 50 (2012), 147-170. doi: 10.1137/100799344.  Google Scholar

[5]

Journal of Mathematical Sciences, 195 (2013), 269-287. doi: 10.1007/s10958-013-1579-z.  Google Scholar

[6]

in 3rd International Space Syntax Symposium, Atlanta, 2003, 1-47. Google Scholar

[7]

MS&A: Modeling, Simulation and Applications, 12, Springer-Verlag, 2014. doi: 10.1007/978-3-319-06620-2.  Google Scholar

[8]

Transportation Research Record: Journal of the Transportation Research Board, 1828 (2003), 20-30. 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]

in Wayfinding Behavior: Cognitive Mapping and Other Spatial Processes, JHU Press, 1999, 5-45. Google Scholar

[12]

Personality And Social Psychology Bulletin, 1 (1974), 16-18. doi: 10.1177/014616727400100106.  Google Scholar

[13]

Physica A: Statistical Mechanics and its Applications, 196 (1993), 546-573. doi: 10.1016/0378-4371(93)90034-2.  Google Scholar

[14]

Transportation Science, 39 (2005), 1-24. doi: 10.1287/trsc.1040.0108.  Google Scholar

[15]

Physical Review E, 51 (1995), 4282. doi: 10.1103/PhysRevE.51.4282.  Google Scholar

[16]

Environment and Planning B, 28 (2001), 361-383. doi: 10.1068/b2697.  Google Scholar

[17]

Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 215 (2001), 283-303. Google Scholar

[18]

Journal of Environmental Psychology, 28 (2008), 74-82. doi: 10.1016/j.jenvp.2007.09.002.  Google Scholar

[19]

Cognitive Psychology, 52 (2006), 93-129. doi: 10.1016/j.cogpsych.2005.08.003.  Google Scholar

[20]

Advances in Complex Systems, 10 (2007), 271-288. doi: 10.1142/S0219525907001355.  Google Scholar

[21]

Applied Ergonomics, 44 (2013), 1015-1023. doi: 10.1016/j.apergo.2013.04.003.  Google Scholar

[22]

Transportation Research Part B: Methodological, 45 (2011), 1572-1589. doi: 10.1016/j.trb.2011.07.011.  Google Scholar

[23]

Annals of the Association of American Geographers, 77 (1987), 191-207. doi: 10.1111/j.1467-8306.1987.tb00153.x.  Google Scholar

[24]

Advanced Robotics, 24 (2010), 515-535. doi: 10.1163/016918610X487090.  Google Scholar

[25]

Autonomous Robots, 28 (2010), 369-383. doi: 10.1007/s10514-009-9170-7.  Google Scholar

[26]

in Spatial Information Theory A Theoretical Basis for GIS, Springer, 1329 (1997), 297-311. doi: 10.1007/3-540-63623-4_57.  Google Scholar

[27]

Proceedings of the National Academy of Sciences, 108 (2011), 6884-6888. Google Scholar

[28]

in ACM Transactions on Graphics (TOG), ACM, 29 (2010), p123. Google Scholar

[29]

Transportation Research Part F: Traffic Psychology and Behaviour, 12 (2009), 242-255. doi: 10.1016/j.trf.2008.12.004.  Google Scholar

[30]

Transportation Research Part F: Traffic Psychology and Behaviour, 12 (2009), 389-394. doi: 10.1016/j.trf.2009.05.002.  Google Scholar

[31]

in Proceedings of the 2008 symposium on Interactive 3D graphics and games, ACM, 2008, 139-147. Google Scholar

[32]

Perception-London, 32 (2003), 871-886. doi: 10.1068/p3416.  Google Scholar

[33]

People in Places: The Sociology of the Familiar, Praeger, New York, 1973, 35-48. Google Scholar

[34]

Physica A: Statistical Mechanics and its Applications, 387 (2008), 3281-3289. doi: 10.1016/j.physa.2008.01.107.  Google Scholar

[35]

PloS one, 7 (2012), e50720. doi: 10.1371/journal.pone.0050720.  Google Scholar

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