Abstract
Consider a finite set of targets, with each target assigned a relative deadline, and each pair of targets assigned a fixed transit flight time. Given a flock of identical UAVs, can one ensure that every target is repeatedly visited by some UAV at intervals of duration at most the target’s relative deadline? The Cyclic-Routing UAV Problem (cr-uav) is the question of whether this task has a solution.
This problem can straightforwardly be solved in PSPACE by modelling it as a network of timed automata. The special case of there being a single UAV is claimed to be NP-complete in the literature. In this paper, we show that the cr-uav Problem is in fact PSPACE-complete even in the single-UAV case.
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Keywords
- Unmanned Aerial Vehicle
- Travelling Salesman Problem
- Mixed Integer Linear Programming
- Decision Version
- Satisfying Assignment
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Alighanbari, M., Kuwata, Y., How, J.: Coordination and control of multiple uavs with timing constraints and loitering. In: Proceedings of ACC 2003, vol. 6, pp. 5311–5316. IEEE Press (2003)
Alur, R.: Timed automata. In: NATO-ASI Summer School on Verification of Digital and Hybrid Systems. Springer (1998), http://www.cis.upenn.edu/~alur/Nato97.ps
Basilico, N., Gatti, N., Amigoni, F.: Developing a deterministic patrolling strategy for security agents. In: Proceedings of WI-IAT 2009, pp. 565–572. IEEE Computer Society Press (2009)
Basilico, N., Gatti, N., Amigoni, F.: Patrolling security games: Definition and algorithms for solving large instances with single patroller and single intruder. Artificial Intelligence 184-185, 78–123 (2012)
Böckenhauer, H.J., Hromkovic, J., Kneis, J., Kupke, J.: The parameterized approximability of TSP with deadlines. Theory Comput. Syst 41(3), 431–444 (2007), http://dx.doi.org/10.1007/s00224-007-1347-x
Crama, Y., Van De Klundert, J.: Cyclic scheduling of identical parts in a robotic cell. Operations Research 45(6), 952–965 (1997)
Drucker, N., Penn, M., Strichman, O.: Cyclic routing of unmanned air vehicles. Tech. Rep. IE/IS-2014-02, Faculty of Industrial Engineering and Management, Technion (2010), http://ie.technion.ac.il/tech_reports/1393234936_AUVSI-Abstract-31Aug2010-submitted.pdf
Feinberg, E.A., Curry, M.T.: Generalized pinwheel problem. Mathematical Methods of Operations Research 62(1), 99–122 (2005)
Henzinger, T.A., Manna, Z., Pnueli, A.: What good are digital clocks? In: Kuich, W. (ed.) ICALP 1992. LNCS, vol. 623, pp. 545–558. Springer, Heidelberg (1992)
Ho, H.M., Ouaknine, J.: The cyclic-routing UAV problem is PSPACE-complete. CoRR abs/1411.2874 (2014), http://arxiv.org/abs/1411.2874
Jain, M., Kardes, E., Kiekintveld, C., Ordóñez, F., Tambe, M.: Security games with arbitrary schedules: A branch and price approach. In: Proceedings of AAAI 2010, pp. 792–797. AAAI Press (2010)
Kats, V., Levner, E.: Minimizing the number of robots to meet a given cyclic schedule. Annals of Operations Research 69, 209–226 (1997)
Las Fargeas, J., Hyun, B., Kabamba, P., Girard, A.: Persistent visitation under revisit constraints. In: Proceedings of ICUAS 2013, pp. 952–957. IEEE Press (2013)
Marathe, M.V., Hunt III, H.B., Stearns, R.E., Radkakrishnan, V.: Complexity of hierarchically and 1-dimensional periodically specified problems. In: Satisfiability Problem: Theory and Applications. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 35, pp. 225–260. DIMACS (1997)
Orlin, J.B.: The complexity of dynamic languages and dynamic optimization problems. In: Proceedings of STOC 1981, pp. 218–227. ACM Press (1981)
Orlin, J.B.: Minimizing the number of vehicles to meet a fixed periodic schedule: An application of periodic posets. Operations Research 30(4), 760–776 (1982)
Richards, A., How, J.P.: Aircraft trajectory planning with collision avoidance using mixed integer linear programming. In: Proceedings of ACC 2002, vol. 3, pp. 1936–1941. IEEE Press (2002)
Savelsbergh, M.W.: Local search in routing problems with time windows. Annals of Operations Research 4(1), 285–305 (1985)
Sundar, K., Rathinam, S.: Route planning algorithms for unmanned aerial vehicles with refueling constraints. In: Proceedings of ACC 2012, pp. 3266–3271. IEEE Press (2012)
Tsai, J., Kiekintveld, C., Ordonez, F., Tambe, M., Rathi, S.: IRIS—a tool for strategic security allocation in transportation networks. In: Tambe, M. (ed.) Security and Game Theory: Algorithms, Deployed Systems, Lessons Learned. Cambridge University Press (2009)
Unmanned air vehicle systems association, http://www.uavs.org/
Wollmer, R.D.: An airline tail routing algorithm for periodic schedules. Networks 20(1), 49–54 (1990)
Yang, G., Kapila, V.: Optimal path planning for unmanned air vehicles with kinematic and tactical constraints. In: Proceedings of CDC 2002, vol. 2, pp. 1301–1306. IEEE Press (2002)
Zhao, W., Ammar, M.H., Zegura, E.W.: A message ferrying approach for data delivery in sparse mobile ad hoc networks. In: Proceedings of MobiHoc 2004, pp. 187–198. ACM Press (2004)
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Ho, HM., Ouaknine, J. (2015). The Cyclic-Routing UAV Problem is PSPACE-Complete. In: Pitts, A. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2015. Lecture Notes in Computer Science(), vol 9034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46678-0_21
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