A Clustering Approach to Path Planning for Groups

  • Jakub SzkanderaEmail author
  • Ondřej Kaas
  • Ivana Kolingerová
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10405)


The paper introduces a new method of planning paths for crowds in dynamic environment represented by a graph of vertices and edges, where the edge weight as well as the graph topology may change, but the method is also applicable to environment with a different representation. The utilization of clusterization enables the method to use the computed path for a group of agents. In this way a speed-up and memory savings are achieved at a cost of some path suboptimality. The experiments showed good behaviour of the method as to the speed-up and relative error.


Path planning Agent based model Graph representation Clustering 



This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic, project SGS-2016-013 Advanced Graphical and Computing Systems, and Czech Science Foundation, project 17-07690S.


  1. 1.
    Jain, A.K., Dubes, R.C.: Algorithms for Clustering Data. Prentice-Hall Inc., Upper Saddle River (1988)zbMATHGoogle Scholar
  2. 2.
    Ball, G.H., Hall, D.J.: Isodata, a novel method of data analysis and pattern classification. Technical report, DTIC Document (1965)Google Scholar
  3. 3.
    Baraldi, A., Blonda, P.: A survey of fuzzy clustering algorithms for pattern recognition. I. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 29(6), 778–785 (1999)CrossRefGoogle Scholar
  4. 4.
    Bonabeau, E.: Agent-based modeling: methods and techniques for simulating human systems. Proc. Nat. Acad. Sci. 99(suppl 3), 7280–7287 (2002)CrossRefGoogle Scholar
  5. 5.
    Bretti, G., Natalini, R., Piccoli, B.: A fluid-dynamic traffic model on road networks. Arch. Comput. Methods Eng. 14(2), 139–172 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Charikar, M., Guha, S.: Improved combinatorial algorithms for the facility location and k-median problems. In: 40th Annual Symposium on Foundations of Computer Science, 1999, pp. 378–388. IEEE (1999)Google Scholar
  7. 7.
    Chu, K., Lee, M., Sunwoo, M.: Local path planning for off-road autonomous driving with avoidance of static obstacles. IEEE Trans. Intell. Transp. Syst. 13(4), 1599–1616 (2012)CrossRefGoogle Scholar
  8. 8.
    Darken, C.J., Burgess, R.G.: Realistic human path planning using fluid simulation (2004)Google Scholar
  9. 9.
    Dubes, R., Jain, A.K.: Clustering methodologies in exploratory data analysis. Adv. Comput. 19, 113–228 (1980)CrossRefGoogle Scholar
  10. 10.
    Fang, Z., Zong, X., Li, Q., Li, Q., Xiong, S.: Hierarchical multi-objective evacuation routing in stadium using ant colony optimization approach. J. Transport Geogr. 19(3), 443–451 (2011)CrossRefGoogle Scholar
  11. 11.
    Fayyad, U., Piatetsky-Shapiro, G., Smyth, P.: From data mining to knowledge discovery in databases. AI Mag. 17(3), 37 (1996)Google Scholar
  12. 12.
    Floyd, R.W.: Algorithm 97: shortest path. Commun. ACM 5(6), 345 (1962)CrossRefGoogle Scholar
  13. 13.
    Glowinski, R., Ciarlet, P., Lions, J.: Handbook of numerical analysis: Numerical methods for fluids (2003)Google Scholar
  14. 14.
    Guy, S.J., Chhugani, J., Kim, C., Satish, N., Lin, M., Manocha, D., Dubey, P.: Clearpath: highly parallel collision avoidance for multi-agent simulation. In: Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 177–187. ACM (2009)Google Scholar
  15. 15.
    Guy, S.J., Kim, S., Lin, M.C., Manocha, D.: Simulating heterogeneous crowd behaviors using personality trait theory. In: Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pp. 43–52. ACM (2011)Google Scholar
  16. 16.
    Harabor, D., Botea, A.: Hierarchical path planning for multi-size agents in heterogeneous environments. In: 2008 IEEE Symposium On Computational Intelligence and Games, pp. 258–265. IEEE (2008)Google Scholar
  17. 17.
    Hart, P.E., Nilsson, N.J., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Trans. Syst. Sci. Cybern. 4(2), 100–107 (1968)CrossRefGoogle Scholar
  18. 18.
    Hughes, R.L.: A continuum theory for the flow of pedestrians. Transp. Res. Part B Methodological 36(6), 507–535 (2002)CrossRefGoogle Scholar
  19. 19.
    Jain, A.K., Murty, M.N., Flynn, P.J.: Data clustering: a review. ACM Comput. Surv. (CSUR) 31(3), 264–323 (1999)CrossRefGoogle Scholar
  20. 20.
    Jiang, H., Xu, W., Mao, T., Li, C., Xia, S., Wang, Z.: Continuum crowd simulation in complex environments. Comput. Graph. 34(5), 537–544 (2010)CrossRefGoogle Scholar
  21. 21.
    King, B.: Step-wise clustering procedures. J. Am. Stat. Assoc. 62(317), 86–101 (1967)CrossRefGoogle Scholar
  22. 22.
    Koenig, S., Likhachev, M.: D* lite. In: AAAI/IAAI, pp. 476–483 (2002)Google Scholar
  23. 23.
    Koenig, S., Likhachev, M., Furcy, D.: Lifelong planning A*. Artif. Intell. 155(1), 93–146 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Likhachev, M., Ferguson, D.I., Gordon, G.J., Stentz, A., Thrun, S.: Anytime dynamic A*: an anytime, replanning algorithm. In: ICAPS, pp. 262–271 (2005)Google Scholar
  25. 25.
    Loscos, C., Marchal, D., Meyer, A.: Intuitive crowd behavior in dense urban environments using local laws. In: Theory and Practice of Computer Graphics, 2003 Proceedings, pp. 122–129. IEEE (2003)Google Scholar
  26. 26.
    MacQueen, J., et al.: Some methods for classification and analysis of multivariate observations. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Oakland, CA, USA, vol. 1, pp. 281–297 (1967)Google Scholar
  27. 27.
    Mao, T., Jiang, H., Li, J., Zhang, Y., Xia, S., Wang, Z.: Parallelizing continuum crowds. In: Proceedings of the 17th ACM Symposium on Virtual Reality Software and Technology, pp. 231–234. ACM (2010)Google Scholar
  28. 28.
    Metoyer, R.A., Hodgins, J.K.: Reactive pedestrian path following from examples. Vis. Comput. 20(10), 635–649 (2004)CrossRefGoogle Scholar
  29. 29.
    Meyerson, A.: Online facility location. In: 42nd IEEE Symposium on Foundations of Computer Science, 2001 Proceedings, pp. 426–431. IEEE (2001)Google Scholar
  30. 30.
    Okazaki, S., Matsushita, S.: A study of simulation model for pedestrian movement with evacuation and queuing. In: International Conference on Engineering for Crowd Safety, vol. 271 (1993)Google Scholar
  31. 31.
    Pellegrini, S., Ess, A., Schindler, K., Van Gool, L.: You’ll never walk alone: modeling social behavior for multi-target tracking. In: 2009 IEEE 12th International Conference on Computer Vision, pp. 261–268. IEEE (2009)Google Scholar
  32. 32.
    Rasmussen, E.M.: Clustering algorithms. Inf. Retrieval Data Struct. Algorithms 419, 442 (1992)Google Scholar
  33. 33.
    Rohlf, F.J.: 12 Single-link clustering algorithms. In: Krishnaiah, P.R., Kanal, L.N. (eds.) Handbook of Statistics, vol. 2, pp. 267–284. Amsterdam, North-Holland (1982)Google Scholar
  34. 34.
    Singh, S., Kapadia, M., Hewlett, B., Reinman, G., Faloutsos, P.: A modular framework for adaptive agent-based steering. In: Symposium on Interactive 3D Graphics and Games, pp. 141–150. ACM (2011)Google Scholar
  35. 35.
    Skála, J.: Algorithms for manipulation with large geometric and graphic data. Technical report, Technical Report DCSE/TR-2009-02, Department of Computer Science and Engineering, University of West Bohemia (2009)Google Scholar
  36. 36.
    Skála, J., Kolingerová, I.: Accelerating the local search algorithm for the facility location. In: Proceedings of the 12th WSEAS International Conference on Mathematical and Computational Methods in Science and Engineering, pp. 98–103. World Scientific and Engineering Academy and Society (WSEAS) (2010)Google Scholar
  37. 37.
    Sokal, R.: The principles of numerical taxonomy: twenty-five years later. In: Goodfellow, M., Jones, D., Priest, F.G. (eds.) Computer-Assisted Bacterial Systematics, vol. 15, p. 1. Academic Press, New York (1985)Google Scholar
  38. 38.
    Stentz, A.: Optimal and efficient path planning for partially-known environments. In: 1994 IEEE International Conference on Robotics and Automation, 1994 Proceedings, pp. 3310–3317. IEEE (1994)Google Scholar
  39. 39.
    Stentz, A., et al.: The focussed D* algorithm for real-time replanning. In: IJCAI, vol. 95, pp. 1652–1659 (1995)Google Scholar
  40. 40.
    Sun, X., Yeoh, W., Koenig, S.: Generalized fringe-retrieving A*: faster moving target search on state lattices. In: Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: Volume 1-Volume 1, pp. 1081–1088. International Foundation for Autonomous Agents and Multiagent Systems (2010)Google Scholar
  41. 41.
    Sun, X., Yeoh, W., Koenig, S.: Moving target D* lite. In: Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: Volume 1-Volume 1, pp. 67–74. International Foundation for Autonomous Agents and Multiagent Systems (2010)Google Scholar
  42. 42.
    Szkandera, J., Kolingerová, I., Maňák, M.: Path planning for groups on graphs. Procedia Comput. Sci. 108, 2338–2342 (2017)CrossRefGoogle Scholar
  43. 43.
    Treuille, A., Cooper, S., Popović, Z.: Continuum crowds. ACMTrans. Graph. (TOG) 25, 1160–1168 (2006). ACMCrossRefGoogle Scholar
  44. 44.
    Vadakkepat, P., Tan, K.C., Ming-Liang, W.: Evolutionary artificial potential fields and their application in real time robot path planning. In: Proceedings of the 2000 Congress on Evolutionary Computation, vol. 1, pp. 256–263. IEEE (2000)Google Scholar
  45. 45.
    Warshall, S.: A theorem on boolean matrices. J. ACM 9(1), 11–12 (1962)MathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    Žalik, K.R., Žalik, B.: A sweep-line algorithm for spatial clustering. Adv. Eng. Softw. 40(6), 445–451 (2009)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Jakub Szkandera
    • 1
    • 2
    Email author
  • Ondřej Kaas
    • 1
    • 2
  • Ivana Kolingerová
    • 1
    • 2
  1. 1.Department of Computer Science and Engineering, Faculty of Applied SciencesUniversity of West BohemiaPlzenCzech Republic
  2. 2.New Technologies for the Information SocietyPlzenCzech Republic

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