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A Clustering Approach to Path Planning for Groups

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Computational Science and Its Applications – ICCSA 2017 (ICCSA 2017)

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Abstract

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.

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References

  1. Jain, A.K., Dubes, R.C.: Algorithms for Clustering Data. Prentice-Hall Inc., Upper Saddle River (1988)

    MATH  Google Scholar 

  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. 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)

    Article  Google Scholar 

  4. Bonabeau, E.: Agent-based modeling: methods and techniques for simulating human systems. Proc. Nat. Acad. Sci. 99(suppl 3), 7280–7287 (2002)

    Article  Google Scholar 

  5. Bretti, G., Natalini, R., Piccoli, B.: A fluid-dynamic traffic model on road networks. Arch. Comput. Methods Eng. 14(2), 139–172 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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)

    Article  Google Scholar 

  8. Darken, C.J., Burgess, R.G.: Realistic human path planning using fluid simulation (2004)

    Google Scholar 

  9. Dubes, R., Jain, A.K.: Clustering methodologies in exploratory data analysis. Adv. Comput. 19, 113–228 (1980)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. Floyd, R.W.: Algorithm 97: shortest path. Commun. ACM 5(6), 345 (1962)

    Article  Google Scholar 

  13. Glowinski, R., Ciarlet, P., Lions, J.: Handbook of numerical analysis: Numerical methods for fluids (2003)

    Google Scholar 

  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. 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. 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. 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)

    Article  Google Scholar 

  18. Hughes, R.L.: A continuum theory for the flow of pedestrians. Transp. Res. Part B Methodological 36(6), 507–535 (2002)

    Article  Google Scholar 

  19. Jain, A.K., Murty, M.N., Flynn, P.J.: Data clustering: a review. ACM Comput. Surv. (CSUR) 31(3), 264–323 (1999)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  21. King, B.: Step-wise clustering procedures. J. Am. Stat. Assoc. 62(317), 86–101 (1967)

    Article  Google Scholar 

  22. Koenig, S., Likhachev, M.: D* lite. In: AAAI/IAAI, pp. 476–483 (2002)

    Google Scholar 

  23. Koenig, S., Likhachev, M., Furcy, D.: Lifelong planning A*. Artif. Intell. 155(1), 93–146 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. 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. 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. Metoyer, R.A., Hodgins, J.K.: Reactive pedestrian path following from examples. Vis. Comput. 20(10), 635–649 (2004)

    Article  Google Scholar 

  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. 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. 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. Rasmussen, E.M.: Clustering algorithms. Inf. Retrieval Data Struct. Algorithms 419, 442 (1992)

    Google Scholar 

  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. 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. 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. 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. 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. 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. Stentz, A., et al.: The focussed D* algorithm for real-time replanning. In: IJCAI, vol. 95, pp. 1652–1659 (1995)

    Google Scholar 

  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. 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. Szkandera, J., Kolingerová, I., Maňák, M.: Path planning for groups on graphs. Procedia Comput. Sci. 108, 2338–2342 (2017)

    Article  Google Scholar 

  43. Treuille, A., Cooper, S., Popović, Z.: Continuum crowds. ACMTrans. Graph. (TOG) 25, 1160–1168 (2006). ACM

    Article  Google Scholar 

  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. Warshall, S.: A theorem on boolean matrices. J. ACM 9(1), 11–12 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  46. Žalik, K.R., Žalik, B.: A sweep-line algorithm for spatial clustering. Adv. Eng. Softw. 40(6), 445–451 (2009)

    Article  MATH  Google Scholar 

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Acknowledgement

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.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Faculty of Applied Sciences, University of West Bohemia, Univerzitni 8, 30614, Plzen, Czech Republic

    Jakub Szkandera, Ondřej Kaas & Ivana Kolingerová

  2. New Technologies for the Information Society, Univerzitni 8, 30614, Plzen, Czech Republic

    Jakub Szkandera, Ondřej Kaas & Ivana Kolingerová

Authors
  1. Jakub Szkandera
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  2. Ondřej Kaas
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  3. Ivana Kolingerová
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Corresponding author

Correspondence to Jakub Szkandera .

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Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Italy

    Beniamino Murgante

  3. Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Trieste, Trieste, Italy

    Giuseppe Borruso

  5. Polytechnic University of Bari, Bari, Italy

    Carmelo M. Torre

  6. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  7. Monash University, Clayton, Victoria, Australia

    David Taniar

  8. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  9. Saint Petersburg State University, Saint Petersburg, Russia

    Elena Stankova

  10. University of Trieste, Trieste, Italy

    Alfredo Cuzzocrea

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Szkandera, J., Kaas, O., Kolingerová, I. (2017). A Clustering Approach to Path Planning for Groups. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2017. ICCSA 2017. Lecture Notes in Computer Science(), vol 10405. Springer, Cham. https://doi.org/10.1007/978-3-319-62395-5_32

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  • DOI: https://doi.org/10.1007/978-3-319-62395-5_32

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