Intruder alert! Optimization models for solving the mobile robot graph-clear problem

Abstract

We develop optimization approaches to the graph-clear problem, a pursuit-evasion problem where mobile robots must clear a facility of intruders. The objective is to minimize the number of robots required. We contribute new formal results on progressive and contiguous assumptions and their impact on algorithm completeness. We present mixed-integer linear programming and constraint programming models, as well as new heuristic variants for the problem, comparing them to previously proposed heuristics. Our empirical work indicates that our heuristic variants improve on those from the literature, that constraint programming finds better solutions than the heuristics in run-times reasonable for the application, and that mixed-integer linear programming is superior for proving optimality. Given their performance and the appeal of the model-and-solve framework, we conclude that the proposed optimization methods are currently the most suitable for the graph-clear problem.

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Notes

  1. 1.

    The definition of path used in the graph-clear literature is a generalization of the classical definition in that it is permitted to start or end on an edge.

  2. 2.

    The distinction between single vs. multiple targets makes no difference in our context.

  3. 3.

    In this paper we consider only the GCP that minimizes the number of robots used.

  4. 4.

    Although implemented in Python (which is in practice slower than C++), the implemented polynomial-time heuristics run in less than a second.

References

  1. 1.

    Barrière, L., Flocchini, P., Fraigniaud, P., Santoro, N. (2002). Capture of an intruder by mobile agents. In Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures (pp. 200–209).

  2. 2.

    Beldiceanu, N., & Demassey, S. Global constraint catalog. http://sofdem.github.io/gccat/ (2014), accessed: 2017-11.

  3. 3.

    Booth, K.E.C., Nejat, G., Beck, J.C. (2016). A constraint programming approach to multi-robot task allocation and scheduling in retirement homes. In International conference on principles and practice of constraint programming (pp. 539–555): Springer.

  4. 4.

    Chung, T.H., Hollinger, G.A., Volkan, I. (2011). Search and pursuit-Evasion in mobile robotics. Autonomous Robot, 4(31), 299–316.

    Article  Google Scholar 

  5. 5.

    Fomin, F.V., & Thilikos, D.M. (2008). An annotated bibliography on guaranteed graph searching. Theoretical Computer Science, 399(3), 236–245.

    MathSciNet  Article  MATH  Google Scholar 

  6. 6.

    Fusy, E. (2009). Uniform random sampling of planar graphs in linear time. Random Structures & Algorithms, 35(4), 464–522.

    MathSciNet  Article  MATH  Google Scholar 

  7. 7.

    Garey, M.R., & Johnson, D.S. (1979). Computers and intractability Vol. 174. Freeman: San Francisco.

    Google Scholar 

  8. 8.

    Hagberg, A., Swart, P., S Chult, D. (2008). Exploring network structure, dynamics, and function using NetworkX. Tech. rep., Los Alamos National Laboratory (LANL).

  9. 9.

    Kirousis, L.M., & Papadimitriou, C.H. (1986). Searching and pebbling. Theoretical Computer Science, 47, 205–218.

    MathSciNet  Article  MATH  Google Scholar 

  10. 10.

    Kolling, A., & Carpin, S. (2007). Detecting intruders in complex environments with limited range mobile sensors. Robot Motion and Control, 417–425.

  11. 11.

    Kolling, A., & Carpin, S. (2007). The graph-clear problem: definition, theoretical properties and its connections to multirobot aided surveillance. In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (pp. 1003–1008).

  12. 12.

    Kolling, A., & Carpin, S. (2008). Extracting surveillance graphs from robot maps. In Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (pp. 2323–2328).

  13. 13.

    Kolling, A., & Carpin, S. (2008). Multi-robot surveillance: an improved algorithm for the graph-clear problem. In Proceedings of the IEEE International Conference on Robotics and Automation (pp. 2360–2365).

  14. 14.

    Kolling, A., & Carpin, S. (2010). Pursuit-evasion on trees by robot teams. IEEE Transactions on Robotics, 26(1), 32–47.

    Article  Google Scholar 

  15. 15.

    Kolling, A., & Carpin, S. (2010). Solving pursuit-evasion problems with graph-clear: an overview. In Proceedings of the IEEE International Conference on Robotics and Automation. Workshop: Search and Pursuit/Evasion in the Physical World: Efficiency, Scalability, and Guarantees (pp. 27–32).

  16. 16.

    Korsah, G.A., Kannan, B., Browning, B., Stentz, A., Dias, M.B. (2012). xBots: an approach to generating and executing optimal multi-robot plans with cross-schedule dependencies. In Proceedings of the IEEE International Conference on Robotics and Automation (pp. 115–122).

  17. 17.

    Laurière, J.L. (1978). A language and a program for stating and solving combinatorial problems. Artificial Intelligence, 10(1), 29–127.

    MathSciNet  Article  MATH  Google Scholar 

  18. 18.

    Liu, J.N.K., Wang, M., Feng, B. (2005). IBOtguard: an internet-based intelligent robot security system using invariant face recognition against intruder. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 35 (1), 97–105.

    Article  Google Scholar 

  19. 19.

    Parker, L.E. (2002). Distributed algorithms for multi-robot observation of multiple moving targets. Autonomous robots, 12(3), 231–255.

    Article  MATH  Google Scholar 

  20. 20.

    Parsons, T.D. (1978). Pursuit-evasion in a graph. In Theory and applications of graphs (pp. 426–441): Springer.

  21. 21.

    Qu, H., Kolling, A., Veres, S.M. (2014). Formulating robot pursuit-evasion strategies by model checking. IFAC Proceedings, 47(3), 3048–3055.

    Article  Google Scholar 

  22. 22.

    Qu, H., Kolling, A., Veres, S.M. (2015). Computing time-optimal clearing strategies for pursuit-evasion problems with linear programming. In Conference towards autonomous robotic systems (pp. 216–228): Springer.

  23. 23.

    Shimosasa, Y., Kanemoto, J., Hakamada, K., Horii, H., Ariki, T., Sugawara, Y., Kojio, F., Kimura, A., Yuta, S. (1999). Security service system using autonomous mobile robot. In Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, (Vol. 4 pp. 825–829).

  24. 24.

    Van Hentenryck, P., & Carillon, J.P. (1988). Generality versus specificity: an experience with AI and OR techniques. In National conference on artificial intelligence (AAAI) (pp. 660–664).

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Acknowledgements

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). M.P. Castro is funded by the Comisión Nacional de Investigación Científica y Tecnológica (CONICYT, Becas Chile). M. Morin is funded by the Fonds de Recherche du Québec – Nature et Technologies (FRQNT).

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Correspondence to Michael Morin.

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This article belongs to the Topical Collection: Integration of Constraint Programming, Artificial Intelligence, and Operations Research

Guest Editor: Willem-Jan van Hoeve

‡ Margarita P. Castro and Kyle E.C. Booth equally contributing authors.

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Morin, M., Castro, M.P., Booth, K.E.C. et al. Intruder alert! Optimization models for solving the mobile robot graph-clear problem. Constraints 23, 335–354 (2018). https://doi.org/10.1007/s10601-018-9288-3

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Keywords

  • Pursuit-evasion
  • Graph-clear problem
  • Constraint programming
  • Mixed-integer linear programming
  • Optimization
  • Mobile robotics