Journal of Global Optimization

, Volume 48, Issue 4, pp 511–531 | Cite as

Optimal placement of UV-based communications relay nodes

  • Oleg BurdakovEmail author
  • Patrick Doherty
  • Kaj Holmberg
  • Per-Magnus Olsson


We consider a constrained optimization problem with mixed integer and real variables. It models optimal placement of communications relay nodes in the presence of obstacles. This problem is widely encountered, for instance, in robotics, where it is required to survey some target located in one point and convey the gathered information back to a base station located in another point. One or more unmanned aerial or ground vehicles (UAVs or UGVs) can be used for this purpose as communications relays. The decision variables are the number of unmanned vehicles (UVs) and the UV positions. The objective function is assumed to access the placement quality. We suggest one instance of such a function which is more suitable for accessing UAV placement. The constraints are determined by, firstly, a free line of sight requirement for every consecutive pair in the chain and, secondly, a limited communication range. Because of these requirements, our constrained optimization problem is a difficult multi-extremal problem for any fixed number of UVs. Moreover, the feasible set of real variables is typically disjoint. We present an approach that allows us to efficiently find a practically acceptable approximation to a global minimum in the problem of optimal placement of communications relay nodes. It is based on a spatial discretization with a subsequent reduction to a shortest path problem. The case of a restricted number of available UVs is also considered here. We introduce two label correcting algorithms which are able to take advantage of using some peculiarities of the resulting restricted shortest path problem. The algorithms produce a Pareto solution to the two-objective problem of minimizing the path cost and the number of hops. We justify their correctness. The presented results of numerical 3D experiments show that our algorithms are superior to the conventional Bellman-Ford algorithm tailored to solving this problem.


Unmanned vehicles Global optimization Hop-restricted shortest paths Pareto solution Label correcting algorithms 


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  1. 1.
    Ahuja R.K., Magnanti T.L., Orlin J.B.: Network Flows: Theory, Algorithms, and Applications. Prentice-Hall, Englewood Cliffs, NJ (1993)Google Scholar
  2. 2.
    Anderson, S.O., Simmons, R., Goldberg, D.: Maintaining line of sight communications network between planetary rovers. In: Proceedings of the 2003 IEEE/RSJ International Conference of Intelligent Robots and Systems, pp. 2266–2272. IEEE (2003)Google Scholar
  3. 3.
    Anisi, D.A., Ögren, P., Hu, X.: Communication constrained multi-UGV surveillance. In: Proceedings of the 17th IFAC World Congress, Seoul, South Korea, 6–11 July 2008Google Scholar
  4. 4.
    Arkin, R.C., Diaz, J.: Line-of-sight constrained exploration for reactive multiagent robotic teams. In: 7th International Workshop on Advanced Motion Control, pp. 455–461 (2002)Google Scholar
  5. 5.
    Balakrishnan A., Altinkemer K.: Using a hop-constrained model to generate alternative communication network design. ORSA J. Comput. 4(2), 192–205 (1992)Google Scholar
  6. 6.
    Bellman R.: On a routing problem. Q. Appl. Math. 16(1), 87–90 (1958)Google Scholar
  7. 7.
    Ben-Moshe B., Carmi P., Katz M.J.: Approximating the visible region of a point on a terrain. GeoInformatica 12(1), 21–36 (2008)CrossRefGoogle Scholar
  8. 8.
    Bertsekas D.P.: Dynamic Programming and Optimal Control. Athena Scientific, Belmont, MA (1995)Google Scholar
  9. 9.
    Bertsekas D.P.: Network Optimization: Continuous and Discrete Models. Athena Scientific, Belmont, MA (1998)Google Scholar
  10. 10.
    Burdakov, O., Holmberg, K., Olsson, P.-M.: A dual ascent method for the hop-constrained shortest path problem with application to positioning of unmanned aerial vehicles. Technical Report LiTH-MAT-R-2008-07, Department of Mathematics, Linköping University (2008)Google Scholar
  11. 11.
    Burdakov, O., Doherty, P., Holmberg, K., Kvarnström, J., Olsson, P.-M.: Positioning unmanned aerial vehicles as communication relays for surveillance tasks. In: Proceedings of Robotics: Science and Systems, Seattle, USA (2009)Google Scholar
  12. 12.
    Cherkassky B.V., Goldberg A.V., Radzik T.: Shortest paths algorithms: theory and experimental evaluation. Math. Program. 73(2), 129–174 (1996)CrossRefGoogle Scholar
  13. 13.
    Choset H., Lynch K.M., Hutchinson S., Kantor G., Burgard W., Kavraki L.E., Thrun S.: Principles of Robot Motion: Theory, Algorithms, and Implementations. MIT Press, Cambridge, MA (2005)Google Scholar
  14. 14.
    Cormen T.H., Leiserson C.E., Rivest R.L., Stein C.: Introduction to Algorithms, 2nd edn. MIT Press/McGraw-Hill, Cambridge/New York (2001)Google Scholar
  15. 15.
    De Floriani L., Magillo P.: Algorithms for visibility computation on terrains: a survey. Environ. Plann. B Plann. Des. 30(5), 709–728 (2003)CrossRefGoogle Scholar
  16. 16.
    Doherty, P.: Advanced research with autonomous unmanned aerial vehicles. In: Proceedings on the 9th International Conference on Principles of Knowledge Representation and Reasoning (2004)Google Scholar
  17. 17.
    Doherty, P., Rudol, P.: A UAV search and rescue scenario with human body detection and geolocalization. In: 20th Australian Joint Conference on Artificial Intelligence (AI07) (2007)Google Scholar
  18. 18.
    Dumitrescu I., Boland N.: Improved preprocessing, labeling and scaling algorithms for the weight-constrained shortest path problem. Networks 42(3), 135–153 (2003)CrossRefGoogle Scholar
  19. 19.
    Dynia, M., Kutylowski, J., auf der Heide, F.M., Schrieb, J.: Local strategies for maintaining a chain of relay stations between an explorer and a base station. In: SPAA ’07: Proceedings of the Nineteenth Annual ACM Symposium on Parallel Algorithms and Architectures, pp. 260–269. ACM Press, New York, USA, 1 Jan 2007Google Scholar
  20. 20.
    Ford L.R. Jr, Fulkerson D.R.: Flows in Networks. Princeton University Press, Princeton, NJ (1962)Google Scholar
  21. 21.
    Fridman, A., Modi, J., Weber, S., Kam, M.: Communication-based motion planning. In: Proceedings of 41st Annual Conference on Information Sciences and Systems, pp. 382–387. IEEE (2007)Google Scholar
  22. 22.
    Ghosh S.K.: Visibility Algorithms in the Plane. Cambridge University Press, Cambridge, MA (2007)CrossRefGoogle Scholar
  23. 23.
    Guérin R., Orda A.: Computing shortest paths for any number of hops. IEEE/ACM Trans. Netw. 10(5), 613–620 (2002)CrossRefGoogle Scholar
  24. 24.
    LaValle S.M.: Planning Algorithms. Cambridge University Press, Cambridge, MA (2006)CrossRefGoogle Scholar
  25. 25.
    Lawler E.L.: Combinatorial Optimization: Networks and Matroids. Holt, Rinehart and Winston, New York (1976)Google Scholar
  26. 26.
    Leighton F.T., Rosenberg A.L.: Three-dimensional circuit layouts. SIAM J. Comput. 15(3), 793–813 (1986)CrossRefGoogle Scholar
  27. 27.
    Moitra A., Mattheyses R.M., DiDomizio V.A., Hoebel L.J., Szczerba R.J., Yamrom B.: Multivehicle reconnaissance route and sensor planning. IEEE Trans. Aerosp. Electron. Syst. 39(3), 799–812 (2003)CrossRefGoogle Scholar
  28. 28.
    Nagy G.: Terrain visibility. Comput. Graph. 18(6), 763–773 (1994)CrossRefGoogle Scholar
  29. 29.
    Obermeyer, K.J.: The VisiLibity library. (2008)
  30. 30.
    Pereira, G.A.S., Das, A.K., Kumar, V., Campos, M.F.M.: Decentralized motion planning for multiple robots subject to sensing and communication constraints. In: Proceedings of the Second Multi-Robot Systems Workshop, pp. 267–278. Kluwer Academic Press (2003)Google Scholar
  31. 31.
    Pezeshkian, N., Nguyen, H.G., Burmeister, A.: Unmanned ground vehicle radio relay deployment system for non-line-of-sight operations. In: Proceedings of IASTED International Conference on Robotics and Applications. ACTA Press (2007)Google Scholar
  32. 32.
    Pinkney, M.F.J., Hampel, D., DiPierro, S.: Unmanned aerial vehicle (uav) communications relay. In: Military Communications Conference MILCOM’96, vol. 1, pp. 45–51. IEEE (1996)Google Scholar
  33. 33.
    Pirkul H., Soni S.: New formulations and solution procedures for the hop constrained network design problem. Eur. J. Oper. Res. 148(1), 126–140 (2003)CrossRefGoogle Scholar
  34. 34.
    Schouwenaars T., Stubbs A., Paduano J., Feron E.: Multivehicle path planning for nonline-of-sight communication. J. Field Rob. 23(3–4), 269–290 (2006)CrossRefGoogle Scholar
  35. 35.
    Sridharan K., Priya T.K.: A hardware accelerator and fpga realization for reduced visibility graph construction using efficient bit representations. IEEE Trans. Ind. Electron. 54(3), 1800–1804 (2007)CrossRefGoogle Scholar
  36. 36.
    Stewart A.J.: Fast horizon computation at all points of a terrain with visibility and shading applications. IEEE Trans. Vis. Comput. Graph. 4(1), 82–93 (1998)CrossRefGoogle Scholar
  37. 37.
    Szczerba, R.J., Chen, D.Z., Klenk, K.S.: Minimum turns/shortest path problems: a framed-subspace approach. In: Proceedings of the 1997 IEEE International Conference on Systems, Man, and Cybernetics, vol. 1, pp. 398–403. IEEE (1997)Google Scholar
  38. 38.
    Szeszler, D.: Combinatorial algorithms in VLSI routing. PhD thesis, Budapest University of Technology and Economics (2005)Google Scholar
  39. 39.
    Tandy, C.R.V.: The isovist method of landscape survey. In: Murray, H.C. (ed.) Symposium on Methods of Landscape Analysis, pp. 9–10. Landscape Research Group, London (1967)Google Scholar
  40. 40.
    Turner A., Doxa M., O’Sullivan D., Penn A.: From isovists to visibility graphs: a methodology for the analysis of architectural space. Environ. Plann. B Plann. Des. 28, 103–121 (2001)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC. 2010

Authors and Affiliations

  • Oleg Burdakov
    • 1
    Email author
  • Patrick Doherty
    • 2
  • Kaj Holmberg
    • 1
  • Per-Magnus Olsson
    • 2
  1. 1.Department of MathematicsLinköping UniversityLinköpingSweden
  2. 2.Department of Computer and Information ScienceLinköping UniversityLinköpingSweden

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