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On Confinement of the Initial Location of an Intruder in a Multi-robot Pursuit Game

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Abstract

Research in multi-robot pursuit-evasion demonstrates that three pursuers are sufficient to capture an intruder in a polygonal environment. However, this result requires the confined of the initial location of the intruder within the convex hull of the locations of the pursuers. In this study, we extend this result to alleviate this convexity through the application of a set of virtual goals that are independent of the locations of the pursuers. These virtual goals are solely calculated using the location information of the intruder such that whose locations confine the intruder within their convex hull at every execution cycle. We propose two strategies to coordinate the pursuers. They are the agents votes maximization and the profile matrix permutations strategies. We consider the time, the energy expended, and the distance traveled by the pursuers as metrics to analyze the performance of these strategies in contrast to three different allocation strategies. They are the probabilistic, the leader-follower, and the prioritization coordination strategies.

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References

  1. Chung, T.H., Hollinger, G.A.: Search and pursuit-evasion in mobile robotics. Auton. Robots 31, 299–316 (2011)

    Article  Google Scholar 

  2. Basar, T., Olsder, G.J.: Dynamic Noncooperative Game Theory. Society for Industrial Mathematics, Philadelphia(1999)

    MATH  Google Scholar 

  3. Kim, T.H., Sugie, T.: Cooperative control for target-capturing task based on a cyclic pursuit strategy. Automatica 43(8), 1426–1431 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Guo, J., Yan, G., Lin, Z.: Cooperative control synthesis for moving-target-enclosing with changing topologies. In: IEEE International Conference on Robotics and Automation (ICRA10) (2010)

  5. Undeger, C., Polat, F.: Multi-agent real-time pursuit. Auton. Agent. Multi-Agent Syst. 21, 69–107 (2010)

    Article  Google Scholar 

  6. Nowakowski, R., Winkler, P.: Vertex-to-vertex pursuit in a graph. Discrete Math. 43(2–3), 235–239 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  7. Aigner, M., Fromme, M.: A game of cops and robbers. Discrete Appl. Math. 8(1), 1–12 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  8. Isler, V., Karnad, N.: The role of information in the coprobber game. Theor. Comp. Sci. 3(399), 179–190 (2008). Special issue on graph searching

    Article  MathSciNet  Google Scholar 

  9. Jankovic, V.: About a man and lions. Mat. Vesn. 2, 359–361 (1978)

    MathSciNet  Google Scholar 

  10. Kopparty, S., Ravishankar, C.V.: A framework for pursuit evasion games in R n . Inf. Process. Lett. 96(3), 114–122 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Isler, V., Kannan, S., Khanna, S.: Randomized pursuit-evasion in a polygonal environment. IEEE Trans. Robot. 21(5), 875–884 (2005)

    Article  Google Scholar 

  12. Bopardikar, S.D., Bullo, F., Hespanha, J.P.: Sensing limitations in the Lion and Man problem. In: IEEE American Control Conference (2007)

  13. Thunberg, J., Ogren, P.: An iterative mixed integer linear programming approach to pursuit evasion problems in polygonal environment. In: International Conference on Robotics and Automation (ICRA) (2010)

  14. Alspach, B.: Searching and sweeping graphs: a brief survey. Matematiche 59, 5–37 (2004)

    MathSciNet  MATH  Google Scholar 

  15. Fomin, F.V., Thilikos, D.M.: An annotated bibliography on guaranteed graph searching. Theor. Comp. Sci. 399(3), 236–245 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Levy, R., Rosenschein, J.: A game theoretic approach to the pursuit problem. In: 11th International Workshop on Distributed Artificial Intelligence (1992)

  17. Harmati, I., Skrzypczyk, K.: Robot team coordination for target tracking using fuzzy logic controller in game theoretic framework. Robot. Auton. Syst. 57, 75–86 (2009)

    Article  Google Scholar 

  18. Shoham, Y., Brown, K.L.: Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations (2009)

  19. Keshmiri, S., Payandeh, S.: Multi-robot target pursuit: towards an opportunistic control architecture. In: 8th International Multi-Conference on Systems, Signals & Devices (SSD11) (2011)

  20. Koopman, B.O.: The theory of search. Part I. Kinematic bases. Oper. Res. 4(5), 324–346 (1956)

    Article  MathSciNet  Google Scholar 

  21. Koopman, B.O.: The theory of search. Part II. Target detection. Oper. Res. 4(5), 503–531 (1956)

    Article  MathSciNet  Google Scholar 

  22. Assaf, D., Zamir, S.: Optimal sequential search: a Bayesian approach. Ann. Stat. 13(3), 1213–1221 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  23. Washburn, A.R.: Search for a moving target: the FAB algorithm. Oper. Res. 31(4), 739–751 (1983)

    Article  MATH  Google Scholar 

  24. Kupitz, Y., Martini, H.: Geometric aspects of the generalized fermat-torricelli problem. Bolyai Soc. Math. Stud. 6, 55–129 (1997)

    MathSciNet  Google Scholar 

  25. Boltyanski, V., Martini, H., Soltan, V.: Geometric Methods and Optimization Problems. Kluwer Academic Publishers, Boston (1999)

    MATH  Google Scholar 

  26. Charniak, E.: Bayesian network without tears. AI Mag. 12, 50–63 (1991)

    Google Scholar 

  27. Thrun, S., Fox, D., Burgard, W., Dellaert, F.: Robust monte carlo localization for mobile robots. Artif. Intell. 128, 99–141 (2001)

    Article  MATH  Google Scholar 

  28. Borenstein, J., Everett, B., Feng, L.: Navigating Mobile Robots: Systems and Techniques. Wellesley, MA (1996)

  29. Chung, C.F., Furukawa, T.: Coordinated pursuer control using particle filters for autonomous search-and-capture. Robot. Auton. Syst. 57, 700–711 (2009)

    Article  Google Scholar 

  30. Furukawa, T., Bourgault, F., Lavis, B., Durrant-Whyte, H.F.: Recursive bayesian search-and-tracking using coordinated uavs for lost targets. In: IEEE International Conference on Robotics and Automation (ICRA06) (2006)

  31. Amigoni, F., Basilico, N., Gatti, N., Saporiti, A., Troiani, S.: Moving game theoretical patrolling strategies from theory to practice: an usarsim simulation. In: IEEE International Conference on Robotics and Automation (ICRA10) (2010)

  32. Mei, Y., Lu, Y.H., Hu, Y.C., Lee, C.: A case study of mobile robot’s energy consumption and conservation techniques. In: 12th International Conference on Advanced Robotics (ICAR05) (2005)

  33. Thrun, S., Fox, D., Burgard, W., Dellaert, F.: Robust monte carlo localization for mobile robots. Artif. Intell. 128, 99–141 (2001)

    Article  MATH  Google Scholar 

  34. Thrun, S., Burgard, W., Fox, D.: Probabilistic Robotics. The MIT Press, Cambridge, MA (2006)

    Google Scholar 

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Authors and Affiliations

  1. Experimental Robotics Laboratory, School of Engineering Science, Simon Fraser University, Burnaby, BC, Canada

    Soheil Keshmiri & Shahram Payandeh

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  1. Soheil Keshmiri
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  2. Shahram Payandeh
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Correspondence to Soheil Keshmiri.

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Keshmiri, S., Payandeh, S. On Confinement of the Initial Location of an Intruder in a Multi-robot Pursuit Game. J Intell Robot Syst 71, 361–389 (2013). https://doi.org/10.1007/s10846-012-9792-4

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  • DOI: https://doi.org/10.1007/s10846-012-9792-4

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