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Intruder alert! Optimization models for solving the mobile robot graph-clear problem. (English) Zbl 1402.90102
Summary: 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.
MSC:
90C11 Mixed integer programming
91A24 Positional games (pursuit and evasion, etc.)
90C59 Approximation methods and heuristics in mathematical programming
Software:
NetworkX
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[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] Beldiceanu, N., & Demassey, S. Global constraint catalog. http://sofdem.github.io/gccat/ (2014), accessed: 2017-11.
[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] Chung, TH; Hollinger, GA; Volkan, I, Search and pursuit-evasion in mobile robotics, Autonomous Robot, 4, 299-316, (2011)
[5] Fomin, FV; Thilikos, DM, An annotated bibliography on guaranteed graph searching, Theoretical Computer Science, 399, 236-245, (2008) · Zbl 1160.68007
[6] Fusy, E, Uniform random sampling of planar graphs in linear time, Random Structures & Algorithms, 35, 464-522, (2009) · Zbl 1201.05096
[7] Garey, M.R., & Johnson, D.S. (1979). Computers and intractability Vol. 174. Freeman: San Francisco.
[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] Kirousis, LM; Papadimitriou, CH, Searching and pebbling, Theoretical Computer Science, 47, 205-218, (1986) · Zbl 0616.68064
[10] Kolling, A., & Carpin, S. (2007). Detecting intruders in complex environments with limited range mobile sensors. Robot Motion and Control, 417-425.
[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] 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] 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] Kolling, A; Carpin, S, Pursuit-evasion on trees by robot teams, IEEE Transactions on Robotics, 26, 32-47, (2010)
[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] 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] Laurière, JL, A language and a program for stating and solving combinatorial problems, Artificial Intelligence, 10, 29-127, (1978) · Zbl 0374.68060
[18] Liu, JNK; Wang, M; Feng, B, 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, 97-105, (2005)
[19] Parker, LE, Distributed algorithms for multi-robot observation of multiple moving targets, Autonomous robots, 12, 231-255, (2002) · Zbl 1012.68643
[20] Parsons, T.D. (1978). Pursuit-evasion in a graph. In Theory and applications of graphs (pp. 426-441): Springer. · Zbl 0379.05026
[21] Qu, H; Kolling, A; Veres, SM, Formulating robot pursuit-evasion strategies by model checking, IFAC Proceedings, 47, 3048-3055, (2014)
[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] 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] 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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