Intruder alert! Optimization models for solving the mobile robot graph-clear problem
- 263 Downloads
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.
KeywordsPursuit-evasion Graph-clear problem Constraint programming Mixed-integer linear programming Optimization Mobile robotics
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).
- 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).Google Scholar
- 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.Google Scholar
- 7.Garey, M.R., & Johnson, D.S. (1979). Computers and intractability Vol. 174. Freeman: San Francisco.Google Scholar
- 8.Hagberg, A., Swart, P., S Chult, D. (2008). Exploring network structure, dynamics, and function using NetworkX. Tech. rep., Los Alamos National Laboratory (LANL).Google Scholar
- 10.Kolling, A., & Carpin, S. (2007). Detecting intruders in complex environments with limited range mobile sensors. Robot Motion and Control, 417–425.Google Scholar
- 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).Google Scholar
- 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).Google Scholar
- 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).Google Scholar
- 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).Google Scholar
- 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).Google Scholar
- 20.Parsons, T.D. (1978). Pursuit-evasion in a graph. In Theory and applications of graphs (pp. 426–441): Springer.Google Scholar
- 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.Google Scholar
- 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).Google Scholar
- 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).Google Scholar