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Autonomous Agents and Multi-Agent Systems

, Volume 32, Issue 3, pp 387–416 | Cite as

Spice: a cognitive agent framework for computational crowd simulations in complex environments

  • Peter M. Kielar
  • André Borrmann
Article
  • 188 Downloads

Abstract

Pedestrian behavior is an omnipresent topic, but the underlying cognitive processes and the various influences on movement behavior are still not fully understood. Nonetheless, computational simulations that predict crowd behavior are essential for safety, economics, and transport. Contemporary approaches of pedestrian behavior modeling focus strongly on the movement aspects and seldom address the rich body of research from cognitive science. Similarly, general purpose cognitive architectures are not suitable for agents that can move in spatial domains because they do not consider the profound findings of pedestrian dynamics research. Thus, multi-agent simulations of crowd behavior that strongly incorporate both research domains have not yet been fully realized. Here, we propose the cognitive agent framework Spice. The framework provides an approach to structure pedestrian agent models by integrating concepts of pedestrian dynamics and cognition. Further, we provide a model that implements the framework. The model solves spatial sequential choice problems in sufficient detail, including movement and cognition aspects. We apply the model in a computer simulation and validate the Spice approach by means of data from an uncontrolled field study. The Spice framework is an important starting point for further research, as we believe that fostering interdisciplinary modeling approaches will be highly beneficial to the field of pedestrian dynamics.

Keywords

Spatial sequential choice Cognitive agent Multi-agent simulation Pedestrian dynamics Crowd simulation 

Notes

Acknowledgements

This work was partially supported by the Federal Ministry for Education and Research (Bundesministerium für Bildung und Forschung, BMBF), project MultikOSi, under Grant FKZ 13N12823. We would like to thank Prof. Hölscher, Chair of Cognitive Sciences at the ETH-Zürich and his team for fruitful discussions. Also, we thank our student assistants for contributing to the pedestrian simulation framework MomenTUM.

Supplementary material

Supplementary material 1 (mp4 15193 KB)

References

  1. 1.
    AlGadhi, S. A. H., & Mahmassani, H. (1991). Simulation of crowd behavior and movement: Fundamental relations and application. Transportation Research Record, 1320, 260–268.Google Scholar
  2. 2.
    Allik, J., & Tuulmets, T. (1991). Occupancy model of perceived numerosity. Perception & Psychophysics, 49(4), 303–314.CrossRefGoogle Scholar
  3. 3.
    Alonso-Marroquín, F., Busch, J., Chiew, C., Lozano, C., & Ramírez-Gómez, Á. (2014). Simulation of counterflow pedestrian dynamics using spheropolygons. Physical Review E, 90(6), 063305.CrossRefGoogle Scholar
  4. 4.
    Anderson, J. R. (1983). A spreading activation theory of memory. Journal of Verbal Learning and Verbal Behavior, 22(3), 261–295.MathSciNetCrossRefGoogle Scholar
  5. 5.
    Anderson, J. R. (1993). Problem solving and learning. American Psychologist, 48(1), 35.CrossRefGoogle Scholar
  6. 6.
    Anderson, J. R. (2010). Cognitive psychology and its implications (7th ed.). New York: Worth Publishing.Google Scholar
  7. 7.
    Anderson, J. R., Matessa, M., & Lebiere, C. (1997). ACT-R: A theory of higher level cognition and its relation to visual attention. Human-Computer Interaction, 12, 439–462.CrossRefGoogle Scholar
  8. 8.
    Anderson, J. R., & Schooler, L. J. (1991). Reflections of the environment in memory. Psychological Science, 2(6), 396–408.CrossRefGoogle Scholar
  9. 9.
    Arentze, T. A., Ettema, D., & Timmermans, H. J. (2011). Estimating a model of dynamic activity generation based on one-day observations: method and results. Transportation Research Part B: Methodological, 45(2), 447–460.CrossRefGoogle Scholar
  10. 10.
    Arentze, T. A., & Timmermans, H. J. (2011). A dynamic model of time-budget and activity generation: Development and empirical derivation. Transportation Research Part C: Emerging Technologies, 19(2), 242–253.CrossRefGoogle Scholar
  11. 11.
    Aumann, Q., & Kielar, P. M. (2016). A modular routing graph generation method for pedestrian simulation. In 28. Forum Bauinformatik (pp. 241–253).Google Scholar
  12. 12.
    Baddeley, A. D., & Hitch, G. (1974). Working memory. Psychology of Learning and Motivation, 8, 47–89.CrossRefGoogle Scholar
  13. 13.
    Balke, T., & Gilbert, N. (2014). How do agents make decisions? A survey. Journal of Artificial Societies and Social Simulation, 17(4), 13.CrossRefGoogle Scholar
  14. 14.
    Bandini, S., Rubagotti, F., Vizzari, G., & Shimura, K. (2011). An agent model of pedestrian and group dynamics: Experiments on group cohesion. In Congress of the Italian association for artificial intelligence (pp. 104–116).Google Scholar
  15. 15.
    Benedikt, M. L. (1979). To take hold of space: Isovists and isovist fields. Environment and Planning B: Planning and design, 6(1), 47–65.CrossRefGoogle Scholar
  16. 16.
    Bierlaire, M., & Robin, T. (2009). Pedestrians choices. In H. Timmermans (Ed.), Pedestrian behavior. Models, data collection and applications (pp. 1–26). Bingley: Emerald Group Publishing.Google Scholar
  17. 17.
    Blue, V. J., & Adler, J. L. (2001). Cellular automata microsimulation for modeling bi-directional pedestrian walkways. Transportation Research Part B: Methodological, 35(3), 293–312.CrossRefGoogle Scholar
  18. 18.
    Borgers, A., & Timmermans, H. (2014). Indices of pedestrian behavior in shopping areas. Procedia Environmental Sciences, 22, 366–379.CrossRefGoogle Scholar
  19. 19.
    Borgers, A. W. J., & Timmermans, H. J. P. (1986). A model of pedestrian route choice and demand for retail facilities within inner-city shopping areas. Geographical Analysis, 18(2), 115–128.CrossRefGoogle Scholar
  20. 20.
    Bresenham, J. E. (1965). Algorithm for computer control of a digital plotter. IBM Systems journal, 4(1), 25–30.CrossRefGoogle Scholar
  21. 21.
    Canca, D., Zarzo, A., Algaba, E., & Barrena, E. (2013). Macroscopic attraction-based simulation of pedestrian mobility: A dynamic individual route-choice approach. European Journal of Operational Research, 231(2), 428–442.CrossRefGoogle Scholar
  22. 22.
    Chu, M. L., & Law, K. (2013). Computational framework incorporating human behaviors for egress simulations. Journal of Computing in Civil Engineering, 27(6), 699–707.CrossRefGoogle Scholar
  23. 23.
    Cowan, N. (2001). The magical number 4 in short-term memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences, 24(1), 87–114.CrossRefGoogle Scholar
  24. 24.
    de Sevin, E., & Thalmann, D. (2005). A motivational model of action selection for virtual humans. In International 2005 computer graphics (pp. 213–220).Google Scholar
  25. 25.
    Dai, J., Li, X., & Liu, L. (2013). Simulation of pedestrian counter flow through bottlenecks by using an agent-based model. Physica A, 392(9), 2202–2211.MathSciNetCrossRefGoogle Scholar
  26. 26.
    Danalet, A., Tinguely, L., de Lapparent, M., & Bierlaire, M. (2016). Location choice with longitudinal WiFi data. Journal of Choice Modelling, 18, 1–17.CrossRefGoogle Scholar
  27. 27.
    Dijkstra, J., Timmermans, H. J. P., & Jessurun, J. (2014). Modeling planned and unplanned store visits within a framework for pedestrian movement simulation. Transportation Research Procedia, 2, 559–566.CrossRefGoogle Scholar
  28. 28.
    Dong, X., Ben-Akiva, M. E., Bowman, J. L., & Walker, J. L. (2006). Moving from trip-based to activity-based measures of accessibility. Transportation Research Part A: Policy and Practice, 40(2), 163–180.Google Scholar
  29. 29.
    DOrazio, M., Spalazzi, L., Quagliarini, E., & Bernardini, G. (2014). Agent-based model for earthquake pedestrians evacuation in urban outdoor scenarios: Behavioural patterns definition and evacuation paths choice. Safety Science, 62, 450–465.CrossRefGoogle Scholar
  30. 30.
    Duives, D. C., Daamen, W., & Hoogendoorn, S. P. (2013). State-of-the-art crowd motion simulation models. Transportation Research Part C: Emerging Technologies, 37, 193–209.CrossRefGoogle Scholar
  31. 31.
    Dyer, J. R. G., Johansson, A., Helbing, D., Couzin, I. D., & Krause, J. (2009). Leadership, consensus decision making and collective behaviour in humans. Philosophical Transactions of the Royal Society of London B: Biological Sciences, 364(1518), 781–789.CrossRefGoogle Scholar
  32. 32.
    Förster, J., Liberman, N., & Friedman, R. S. (2007). Seven principles of goal activation: A systematic approach to distinguishing goal priming from priming of non-goal constructs. Personality and Social Psychology Review, 11(3), 211–233.CrossRefGoogle Scholar
  33. 33.
    Förster, J., Liberman, N., & Higgins, E. T. (2005). Accessibility from active and fulfilled goals. Journal of Experimental Social Psychology, 41(3), 220–239.CrossRefGoogle Scholar
  34. 34.
    Frith, C. D., & Frith, U. (2012). Mechanisms of social cognition. Annual Review of Psychology, 63, 287–313.CrossRefGoogle Scholar
  35. 35.
    Gärling, T. (1994). Processing of time constraints on sequence decisions in a planning task. European Journal of Cognitive Psychology, 6(4), 399–416.CrossRefGoogle Scholar
  36. 36.
    Gärling, T. (1995). Tradeoffs of priorities against spatiotemporal constraints in sequencing activities in environments. Journal of Environmental Psychology, 15(2), 155–160.CrossRefGoogle Scholar
  37. 37.
    Gärling, T. (1999). Human information processing in sequential spatial choice. In Wayfinding behavior: Cognitive mapping and other spatial processes (pp. 81–98).Google Scholar
  38. 38.
    Gärling, T., & Gärling, E. (1988). Distance minimization in downtown pedestrian shopping. Environment and Planning A, 20(4), 547–554.CrossRefGoogle Scholar
  39. 39.
    Gärling, T., Kwan, Mp, & Golledge, R. G. (1994). Computational-process modelling of household activity scheduling. Transportation Research Part B: Methodological, 28(5), 355–364.CrossRefGoogle Scholar
  40. 40.
    Gärling, T., Säisä, J., Book, A., & Lindberg, E. (1986). The spatiotemporal sequencing of everyday activities in the large-scale environment. Journal of Environmental Psychology, 6(4), 261–280.CrossRefGoogle Scholar
  41. 41.
    Gillner, S., & Mallot, H. A. (2007). These maps are made for walking—task hierarchy of spatial cognition. In Robotics and cognitive approaches to spatial mapping (pp. 181–201).Google Scholar
  42. 42.
    Graf, P., & Schacter, D. L. (1985). Implicit and explicit memory for new associations in normal and amnesic subjects. Journal of Experimental Psychology: Learning, Memory, and Cognition, 11(3), 501–518.Google Scholar
  43. 43.
    Hartmann, D. (2010). Adaptive pedestrian dynamics based on geodesics. New Journal of Physics, 12(4), 043032.CrossRefzbMATHGoogle Scholar
  44. 44.
    Hartmann, D., & von Sivers, I. (2013). Structured first order conservation models for pedestrian dynamics. Networks and Heterogeneous Media, 8(4), 985–1007.MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    Helbing, D., Buzna, L., Johansson, A., & Werner, T. (2005). Self-organized pedestrian crowd dynamics: Experiments, simulations, and design solutions. Transportation Science, 39(1), 1–24.CrossRefGoogle Scholar
  46. 46.
    Helbing, D., Farkas, I., & Vicsek, T. (2000). Simulating dynamical features of escape panic. Nature, 407(6803), 487–490.CrossRefGoogle Scholar
  47. 47.
    Helbing, D., Johansson, A., & Al-Abideen, H. Z. (2007). Dynamics of crowd disasters: An empirical study. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 75(4), 1–7.CrossRefGoogle Scholar
  48. 48.
    Helbing, D., & Mukerji, P. (2012). Crowd disasters as systemic failures: Analysis of the Love Parade disaster. EPJ Data Science, 1(1), 1–40.CrossRefGoogle Scholar
  49. 49.
    Höcker, M., Berkhahn, V., Kneidl, A., Borrmann, A., & Klein, W. (2010). Graph-based approaches for simulating pedestrian dynamics in building models. In eWork and eBusiness in architecture, engineering and construction (pp. 389–394).Google Scholar
  50. 50.
    Hollmann, C. (2015). A cognitive human behaviour model for pedestrian behaviour simulation. Dissertation, University of Greenwich.Google Scholar
  51. 51.
    Hölscher, C., Tenbrink, T., & Wiener, J. M. (2011). Would you follow your own route description? Cognitive strategies in urban route planning. Cognition, 121(2), 228–247.CrossRefGoogle Scholar
  52. 52.
    Hoogendoorn, S. P., & Bovy, P. H. L. (2004). Pedestrian route-choice and activity scheduling theory and models. Transportation Research Part B: Methodological, 38(2), 169–190.CrossRefGoogle Scholar
  53. 53.
    Hoogendoorn, S. P., Bovy, P. H. L., & Daamen, W. (2001). Microscopic pedestrian wayfinding and dynamics modelling. In 1th international conference on pedestrian and evacuation dynamics (pp. 124–154).Google Scholar
  54. 54.
    Johansson, F., Peterson, A., & Tapani, A. (2015). Waiting pedestrians in the social force model. Physica A: Statistical Mechanics and its Applications, 419(419), 95–107.CrossRefGoogle Scholar
  55. 55.
    Jorgensen, C. J., & Lamarche, F. (2014). Space and time constrained task scheduling for crowd simulation. Technical Report hal-00940570, PI 2013.Google Scholar
  56. 56.
    Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica: Journal of the Econometric Society, 47, 263–291.CrossRefzbMATHGoogle Scholar
  57. 57.
    Kielar, P. M., Biedermann, D. H., & André, B. (2016). MomenTUMv2: A modular, extensible, and generic agent-based pedestrian behavior simulation framework. Technical Report TUM-I1643, Technische Universität Müchen.Google Scholar
  58. 58.
    Kielar, P. M., Biedermann, D. H., Kneidl, A., & Borrmann, A. (2017). A unified pedestrian routing model for graph-based wayfinding built on cognitive principles. Transportmetrica A: Transport Science.  https://doi.org/10.1080/23249935.2017.1309472.
  59. 59.
    Kielar, P. M., & Borrmann, A. (2016). Coupling spatial task solving models to simulate complex pedestrian behavior patterns. In 8th international conference on pedestrian and evacuation dynamics (pp. 229–235).Google Scholar
  60. 60.
    Kielar, P. M., & Borrmann, A. (2016). Modeling pedestrians interest in locations: A concept to improve simulations of pedestrian destination choice. Simulation Modelling Practice and Theory, 61, 47–62.CrossRefGoogle Scholar
  61. 61.
    Kielar, P. M., Handel, O., Biedermann, D. H., & Borrmann, A. (2014). Concurrent hierarchical finite state machines for modeling pedestrian behavioral tendencies. Transportation Research Procedia, 2, 584–593.CrossRefGoogle Scholar
  62. 62.
    Kieras, D. E., & Meyer, D. E. (1995). An overview of the EPIC architecture for cognition and performance with application to human-computer interaction. Technischer Bericht 5, University of Michigan.Google Scholar
  63. 63.
    Klüpfel, H. (2007). The simulation of crowd dynamics at very large events calibration, empirical data, and validation. In 3th international conference on pedestrian and evacuation dynamics (pp. 285–296).Google Scholar
  64. 64.
    Kneidl, A. (2015). How do people queue a study of different queuing models. In Proceedings of the 11th conference on traffic and granular flow.Google Scholar
  65. 65.
    Kneidl, A., Borrmann, A., & Hartmann, D. (2012). Generation and use of sparse navigation graphs for microscopic pedestrian simulation models. Advanced Engineering Informatics, 26(4), 669–680.CrossRefGoogle Scholar
  66. 66.
    Köster, G., Treml, F., & Gödel, M. (2013). Avoiding numerical pitfalls in social force models. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 87(6), 1–13.CrossRefGoogle Scholar
  67. 67.
    Kwak, J., Jo, H. H., Luttinen, T., & Kosonen, I. (2014). Modeling pedestrian switching behavior for attractions. Transportation Research Procedia, 2, 612–617.CrossRefGoogle Scholar
  68. 68.
    Laird, J. E. (2008). Extending the soar cognitive architecture. Frontiers in Artificial Intelligence and Applications, 171, 224–235.Google Scholar
  69. 69.
    Laird, J. E., Newell, A., & Rosenbloom, P. S. (1987). Soar: An architecture for general intelligence. Artificial Intelligence, 33(1), 1–64.CrossRefGoogle Scholar
  70. 70.
    Langley, P., Laird, J. E., & Rogers, S. (2009). Cognitive architectures: Research issues and challenges. Cognitive Systems Research, 10(2), 141–160.CrossRefGoogle Scholar
  71. 71.
    Lappe, M., Jenkin, M., & Harris, L. R. (2007). Travel distance estimation from visual motion by leaky path integration. Experimental Brain Research, 180(1), 35–48.CrossRefGoogle Scholar
  72. 72.
    Lewandowsky, S., & Farrell, S. (2010). Computational modeling in cognition: Principles and practice. Thousand Oaks, CA: Sage Publications.Google Scholar
  73. 73.
    Lewin, K., & Cartwright, D. (1952). Field theory in social science: Select theoretical papers (edited by Dorwin Cartwright). London: Tavistock.Google Scholar
  74. 74.
    Liddle, J., Seyfried, A., Klingsch, W., Rupprecht, T., Schadschneider, A., & Winkens, A. (2009). An experimental study of pedestrian congestions: influence of bottleneck width and length. arXiv preprint arXiv:0911.4350.
  75. 75.
    Lindberg, E. (2013). Adults’ memory representations of the spatial properties of their everyday physical environment. In The development of spatial cognition (p. 141).Google Scholar
  76. 76.
    Masicampo, E., & Ambady, N. (2014). Predicting fluctuations in widespread interest: Memory decay and goal-related memory accessibility in Internet search trends. Journal of Experimental Psychology: General, 143(1), 205–214.CrossRefGoogle Scholar
  77. 77.
    Moussaïd, M., Helbing, D., & Theraulaz, G. (2011). How simple rules determine pedestrian behavior and crowd disasters. Proceedings of the National Academy of Sciences, 108(17), 6884–6888.CrossRefGoogle Scholar
  78. 78.
    Moussaïd, M., Perozo, N., Garnier, S., Helbing, D., & Theraulaz, G. (2010). The walking behaviour of pedestrian social groups and its impact on crowd dynamics. PLoS ONE, 5(4), 1–7.CrossRefGoogle Scholar
  79. 79.
    Newell, A., Simon, H. A., et al. (1972). Human problem solving. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
  80. 80.
    Pan, X., Han, C. S., Dauber, K., & Law, K. H. (2007). A multi-agent based framework for the simulation of human and social behaviors during emergency evacuations. Ai & Society, 22(2), 113–32.CrossRefGoogle Scholar
  81. 81.
    Paris, S., & Donikian, S. (2009). Activity-driven populace: A cognitive approach to crowd simulation. IEEE Computer Graphics and Applications, 29(4), 34–43.CrossRefGoogle Scholar
  82. 82.
    Park, J. H., Rojas, F. A., & Yang, H. S. (2013). A collision avoidance behavior model for crowd simulation based on psychological findings. Computer Animation and Virtual Worlds, 24(3–4), 173–183.CrossRefGoogle Scholar
  83. 83.
    Pelechano, N., O’Brien, K., Silverman, B. G., & Badler, N. (2005). Crowd simulation incorporating agent psychological models, roles and communication. Center for Human Modeling and Simulation University of Pennsylvania.Google Scholar
  84. 84.
    Peters, C., & Ennis, C. (2009). Modeling groups of plausible virtual pedestrians. IEEE Computer Graphics and Applications, 29(4), 54–63.CrossRefGoogle Scholar
  85. 85.
    Phillips, F., & Layton, O. (2009). The traveling salesman problem in the natural environment. Journal of Vision, 9(8), 1145.CrossRefGoogle Scholar
  86. 86.
    Rumbaugh, J., Jacobson, I., & Booch, G. (2004). Unified modeling language reference manual. London: The Pearson Higher Education.Google Scholar
  87. 87.
    Russell, S. J., Norvig, P., Canny, J. F., Malik, J. M., & Edwards, D. D. (2003). Artificial intelligence: A modern approach (Vol. 2). Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
  88. 88.
    Säisä, J., & Gärling, T. (1987). Sequential spatial choices in the large-scale environment. Environment and Behavior, 19(5), 614–635.CrossRefGoogle Scholar
  89. 89.
    Scheiner, J. (2014). The gendered complexity of daily life: effects of life-course events on changes in activity entropy and tour complexity over time. Travel Behaviour and Society, 1(3), 91–105.CrossRefGoogle Scholar
  90. 90.
    Seitz, M., Köster, G., & Pfaffinger, A. (2014). Pedestrian group behavior in a cellular automaton. Pedestrian and Evacuation Dynamics, 2012, 807–814.Google Scholar
  91. 91.
    Shao, W., & Terzopoulos, D. (2007). Autonomous pedestrians. Graphical Models, 69(5–6), 246–274.CrossRefGoogle Scholar
  92. 92.
    Taatgen, N. A., Lebiere, C., & Anderson, J. R. (2006). Modeling paradigms in ACT-R. In Cognition and multi-agent interaction: From cognitive modeling to social simulation (pp. 29–52). New York: Cambridge University Press.Google Scholar
  93. 93.
    Timmermans, H. J. P., van der Hagen, X., & Borgers, A. W. J. (1992). Transportation systems, retail environments and pedestrian trip chaining behaviour: Modelling issues and applications. Transportation Research Part B: Methodological, 26(1), 45–59.CrossRefGoogle Scholar
  94. 94.
    Tulving, E. (1972). Episodic and semantic memory. Organization of Memory. London: Academic, 381(4), 382–404.Google Scholar
  95. 95.
    Tulving, E. (1986). Episodic and semantic memory: Where should we go from here? Behavioral and Brain Sciences, 9(3), 573–577.CrossRefGoogle Scholar
  96. 96.
    Urbani, L. (2012). Commuters rail sations and pedestrians flows: The Hardbrücke station in Zurich, Switzerland. Procedia-Social and Behavioral Sciences, 53, 146–154.CrossRefGoogle Scholar
  97. 97.
    von Sivers, I., Seitz, M. J., & Köster, G. (2016). How do people search: A modelling perspective. In Proceedings of the 11th international conference of parallel processing and applied mathematics (pp. 487–496).Google Scholar
  98. 98.
    Wagner, N., & Agrawal, V. (2014). An agent-based simulation system for concert venue crowd evacuation modeling in the presence of a fire disaster. Expert Systems with Applications, 41(6), 2807–2815.CrossRefGoogle Scholar
  99. 99.
    Wang, R. F. (2004). Between reality and imagination: When is spatial updating automatic? Perception & Psychophysics, 66(1), 68–76.CrossRefGoogle Scholar
  100. 100.
    Wiener, J. M., Büchner, S. J., & Hölscher, C. (2009). Taxonomy of human wayfinding tasks: A knowledge-based approach. Spatial Cognition & Computation, 9(2), 152–165.CrossRefGoogle Scholar
  101. 101.
    Wijermans, N., Conrado, C., van Steen, M., Martella, C., & Li, J. (2016). A landscape of crowd-management support: An integrative approach. Safety Science, 86, 142–164.CrossRefGoogle Scholar
  102. 102.
    Wijermans, N., Jorna, R., Jager, W., van Vliet, T., & Adang, O. (2013). CROSS: Modelling crowd behaviour with social-cognitive agents. Journal of Artificial Societies and Social Simulation, 16(4), 1.CrossRefGoogle Scholar
  103. 103.
    Williams, L. (1978). Casting curved shadows on curved surfaces. ACM Siggraph Computer Graphics, 12(3), 270–274.MathSciNetCrossRefGoogle Scholar
  104. 104.
    Willingham, D. B., Nissen, M. J., & Bullemer, P. (1989). On the development of procedural knowledge. Journal of Experimental Psychology: Learning, Memory, and Cognition, 15(6), 1047.Google Scholar
  105. 105.
    Wolbers, T., & Hegarty, M. (2010). What determines our navigational abilities? Trends in Cognitive Sciences, 14(3), 138–146.CrossRefGoogle Scholar
  106. 106.
    Wooldridge, M. (2009). An introduction to multiagent systems (second ed.). New York: Wiley.Google Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Chair of Computational Modeling and SimulationTechnische Universität MünchenMunichGermany

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