Journal of Intelligent & Robotic Systems

, Volume 65, Issue 1–4, pp 265–282 | Cite as

Path Planning for UAVs Under Communication Constraints Using SPLAT! and MILP



We will in this paper address the problem of offline path planning for Unmanned Aerial Vehicles (UAVs). Our goal is to find paths that meet mission objectives, are safe with respect to collision and grounding, fuel efficient and satisfy criteria for communication. Due to the many nonconvex constraints of the problem, Mixed Integer Linear Programming (MILP) will be used in finding the path. Approximate communication constraints and terrain avoidance constraints are used in the MILP formulation. To achieve more accurate prediction of the ability to communicate, the path is then analyzed in the radio propagation toolbox SPLAT!, and if the UAVs are not able to communicate according to design criteria for bandwidth, constraints are modified in the optimization problem in an iterative manner. The approach is exemplified with the following setup: The path of two UAVs are planned so they can serve as relay nodes between a target without line of sight to the base station.


Path planning Mixed integer linear programming Communication constraints Unmanned aerial vehicles 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Purvis, K., Astrom, K., Khammash, M.: Estimation and optimal configurations for localization using cooperative uavs. IEEE Trans. Control Syst. Technol. 16(5), 947–958 (2008)CrossRefGoogle Scholar
  2. 2.
    Frew, E.W., Brown, T.X.: Networking issues for small unmanned aircraft systems. J. Intell. Robot. Syst. 54, 21–37 (2008)CrossRefGoogle Scholar
  3. 3.
    Ruz, J.J., Arévalo, O., Pajares, G., de la Cruz, J.M.: UAV trajectory planning for static and dynamic environments. In: Lam, T.M. (ed.) Aerial Vehicles, InTech, pp. 581–600 (2009)Google Scholar
  4. 4.
    Henkel, D., Brown, T.X.: On controlled node mobility in delay-tolerant networks of unmanned aerial vehicles. In: Proc. of International Symposium on Advanced Radio Technologies (2006)Google Scholar
  5. 5.
    Hogie, L., Bouvry, P., Guinand, F.: An overview of MANET simulators. In: Proc. of the First International Workshop on Methods and Tools for Coordinating, Distributed and Mobile Systems (2006)Google Scholar
  6. 6.
    Durham, C.M., Andel, T.R., Hopkinson, K.M., Kurkowski, S.H.: Evaluation of an OPNET model for unmanned aerial vehicle (UAV) networks. In: Proc. of the Spring Simulation Multiconference (2009)Google Scholar
  7. 7.
    Stepanov, I., Herrscher, D., Rothermel, K.: On the impact of radio propagation models on MANET simulation results. In: IFIP International Conference on Mobile and Wireless Communications Networks (2005)Google Scholar
  8. 8.
    Schmitz, A., Wenig, M.: The effect of the radio wave propagation model in mobile ad hoc networks. In: Proc. of the 9th ACM International Symposium on Modeling Analysis and Simulation of Wireless and Mobile Systems (2006)Google Scholar
  9. 9.
    Dhoutaut, D., Régis, A., Spies, F.: Impact of radio propagation models in vehicular ad hoc networks simulations. In: VANET ’06: Proc. of the 3rd International Workshop on Vehicular Ad Hoc Networks, pp. 40–49. ACM, New York (2006)CrossRefGoogle Scholar
  10. 10.
    Ukrainsky, O., Zebrowitz, H., Hein, C., Cortese, A., Rubin, A., Poon, C., Bard, A., Reyes, H.: An open environment for rapid embedded planning of on-the-move communications networks using multi-level abstraction. In: Military Communications Conference, pp. 2631–2636 (2005)Google Scholar
  11. 11.
    McGraw, R.M., Shao, G., Mumme, D., MacDonald, R.: Design of an agent-based course of action (coa) analysis with radio effects toolbox. Int. J. Intell. Control Syst. 14, 104–114 (2009)Google Scholar
  12. 12.
    Burdakov, B., Doherty, P., Holmberg, K., Kvarnström, J., Olsson, P.-M.: Positioning unmanned aerial vehicles as communication relays for surveillance tasks. In: Robotics Science and Systems, Online Proceedings (2009)Google Scholar
  13. 13.
    Han, Z., Swindlehurst, A., Liu, K.: Optimization of MANET connectivity via smart deployment/movement of unmanned air vehicles. IEEE Trans. Veh. Technol. 58(7), 3533–3546 (2009)CrossRefGoogle Scholar
  14. 14.
    Goldenberg, D.K., Lin, J., Morse, A.S., Rosen, B.E., Yang, Y.R. (2004) Towards mobility as a network control primitive. In: MobiHoc 04: Proc. of the 5th ACM International Symposium on Mobile Ad Hoc Networking and Computing, pp. 163–174. ACM PressGoogle Scholar
  15. 15.
    So, A., Liang, B.: Minimum cost configuration of relay and channel infrastructure in heterogeneous wireless mesh networks. In: Networking 2007. Ad Hoc and Sensor Networks, Wireless Networks, Next Generation Internet, pp. 275–286. Springer, Berlin/Heidelberg (2007)CrossRefGoogle Scholar
  16. 16.
    Dixon, C., Frew, E.W.: Decentralized extremum-seeking control of nonholonomic vehicles to form a communication chain. In: Advances in Cooperative Control and Optimization, pp. 311–322. Springer, Berlin/Heidelberg (2007)CrossRefGoogle Scholar
  17. 17.
    Moses Sathyaraj, B., Jain, L.C., Finn, A., Drake, S.: Multiple UAVs path planning algorithms: a comparative study. Fuzzy Optimization and Decision Making 7, 257–267 (2008)CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Williams, H.P.: Model Building in Mathematical Programming, 4th edn. Wiley, New York (1999). ISBN: 978-0471997887Google Scholar
  19. 19.
    Bemporad, A., Morari, M.: Control of systems integrating logic, dynamics, and constraints. Automatica 35, 407–427 (1999)CrossRefMATHMathSciNetGoogle Scholar
  20. 20.
    Richards, A., How, J.: Mixed-integer programming for control. In: Proc. of the American Control Conference (2005)Google Scholar
  21. 21.
    Chaudhry, A., Misovec, K., D’Andrea, R.: Low observability path planning for an unmanned air vehicle using mixed integer linear programming. In: Proc. of the 43rd IEEE Conference on Decision and Control (2004)Google Scholar
  22. 22.
    Bellingham, J.S.: Coordination and control of uav fleets using mixed-integer linear programming. Master’s thesis, Massachussetts Institute of Technology (2002)Google Scholar
  23. 23.
    Schouwenaars, T., Stubbs, A., Paduano, J., Feron, E.: Multivehicle path planning for nonline-of-sight communication. Journal of Field Robotics 23, 269–290 (2006)CrossRefGoogle Scholar
  24. 24.
    Alighanbari, M., Kuwata, Y., How, J.: Coordination and control of multiple uavs with timing constraints and loitering. In: Proc. of the American Control Conference, vol. 6, pp. 5311–5316 (2003)Google Scholar
  25. 25.
    Hao, Y., Davari, A., Manesh, A.: Differential flatness-based trajectory planning for multiple unmanned aerial vehicles using mixed-integer linear programming. In: Proceedings of the 2005 American Control Conference, pp. 104–109 (2005)Google Scholar
  26. 26.
    Kim, Y., Gu, D.-W., Postlethwaite, I.: Real-time optimal mission scheduling and flight path selection. IEEE Trans. Automat. Contr. 52(6), 1119–1123 (2007)CrossRefMathSciNetGoogle Scholar
  27. 27.
    Reinl, C., von Stryk, O.: Optimal control of multi-vehicle-systems under communication constraints using mixed-integer linear programming. In: Proc. of the International Conference on Robot Communication and Coordination (2007)Google Scholar
  28. 28.
    Branca, C., Fierro, R.: A hierarchical optimization algorithm for cooperative vehicle networks. In: Proc. of the American Control Conference, pp. 4225–4230 (2006)Google Scholar
  29. 29.
    Earl, M.G., D’Andrea, R.: Iterative MILP methods for vehicle-control problems. IEEE Trans. Robot. 21, 1158–1167 (2005)CrossRefGoogle Scholar
  30. 30.
    Vitus, M.P., Pradeep, V., Hoffmann, G.M., Waslander, S.L., Tomlin, C.J.: Tunnel MILP: path planning with sequential convex polytopes. In: Proc. of the AIAA Guidance, Navigation, and Control Conference (2008)Google Scholar
  31. 31.
    Kotz, D., Newport, C., Gray, R.S., Liu, J., Yuan, Y., Elliott, C.: Experimental evaluation of wireless simulation assumptions. In: Proc. of the 7th ACM Symposium on Modeling, Analysis and Simulation of Wireless and Mobile Systems, pp. 78–82 (2004)Google Scholar
  32. 32.
    Maglicane, J.: SPLAT! An RF signal propagation, loss and terrain analysis tool. Available online. Accessed 18 August 2010. (2010)
  33. 33.
    McMellen, J.: RF propagation modeling with SPLAT! for windows. Available online. Accessed 18 Aug 2010. (2010)
  34. 34.
    Longley, A.G., Rice, P.L.: Prediction of Tropospheric Radio Transmission Loss Over Irregular Terrain: a Computer Method. U.S. Goverment, Tech. Rep. (1968)Google Scholar
  35. 35.
    Löfberg, J.: Modeling and solving uncertain optimization problems in YALMIP. In: Proc. of IFAC World Congress (2008)Google Scholar
  36. 36.
    Lodi, A., and Linderoth, J.T.: MILP software. In: Encyclopedia for Operations Research. Wiley, New York (2011)Google Scholar
  37. 37.
    Yin, W.: Gurobi Mex: a MATLAB interface for Gurobi. Available online. Accessed 12 Dec 2010. (2010)
  38. 38.
    Farrell, J.A., Barth, M.: The Global Positioning Systems & Inertial Navigation. McGraw-Hill. ISBN: 0-07-022045-X (1998)Google Scholar
  39. 39.
    Fossen, T.I.: Marine Control Systems: Guidance, Navigation, and Control of Ships, Rigs and Underwater Vehicles. Marine Cybernetics (2002)Google Scholar
  40. 40.
    Culligan, K.F.: Online trajectory planning for uavs using mixed integer linear programming. Master’s thesis, Massachusetts Institute of Technology (2006)Google Scholar
  41. 41.
    Culligan, K., Valenti, M., Kuwata, Y., How, J.P.: Three-dimensional flight experiments using on-line mixed-integer linear programming trajectory optimization. In: Proc. of the American Control Conference (2007)Google Scholar
  42. 42.
    Luders, B.: Robust trajectory planning for unmanned aerial vehicles in uncertain environments. Master’s thesis, MIT (2008)Google Scholar
  43. 43.
    Schouwenaars, T., De Moor, B., Feron, E., How, J.: Mixed integer programming for multi-vehicle path planning. In: Proc. of the European Control Conference (2001)Google Scholar
  44. 44.
    Ma, C.S., Miller, R.H.: MILP optimal path planning for real-time applications. In: Proc. of the American Control Conference (2006)Google Scholar
  45. 45.
    Richards, A., How, J.P.: Aircraft trajectory planning with collision avoidance using mixed integer linear programming. In: Proc. of the American Control Conference (2002)Google Scholar
  46. 46.
    Kamal, W.A., Gu, D.-W., Postlethwaite, I.: MILP and its application in flight path planning. In: Proc. of the 16th IFAC World Congress (2005)Google Scholar
  47. 47.
    Kvasnica, M., Grieder, P., Baotić, M.: Multi-Parametric Toolbox (MPT). Available online. Accessed 13 Dec 2010. (2004)
  48. 48.
    Beard, R.W., Mc Lain, T.W.: Multiple UAV cooperative search under collision avoidance and limited range communication constraints. In: Proceedings of the 42nd IEEE Conference on Decision and Control, pp. 25–30 (2003)Google Scholar
  49. 49.
    Mitchell, I., Bayen, A.M., Tomlin, C.J.: A time-dependent Hamilton–Jacobi formulation of reachable sets for continuous dynamic games. IEEE Trans. Automat. Contr. 50, 947–957 (2005)CrossRefMathSciNetGoogle Scholar
  50. 50.
    Shengxiang, Z., Hailong, P.: Real-time optimal trajectory planning with terrain avoidance using MILP. In: Proc. of the International Symposium on Systems and Control in Aerospace and Astronautics (2008)Google Scholar
  51. 51.
    Sakhi, O.: Image and terrain modeling using incremental Delaunay triangulation. Available online. Accessed 22 Jan 2011. (2010)
  52. 52.
    Fischer, G.: Distance between a point and a triangle in 3d. Available online. Accessed 22 Jan 2011. (2009)
  53. 53.
    Fahlstrom, P.G., Gleason, T.J.: Introduction to UAV Systems (1998)Google Scholar
  54. 54.
    Frew, E.W., Dixon, C., Elston, J., Stachura, M.: Active sensing by unmanned aircraft systems in realistic communication environments. In: Proc. of the IFAC Workshop on Networked Robotics (2009)Google Scholar
  55. 55.
    de Ferranti, J.: Digital elevation data. Available online. Accessed 22 Jan 2011. (2005)
  56. 56.
    Hutter, F., Hoos, H.H., Stützle, T.: Automatic algorithm configuration based on local search. In: Proc. of the 22nd Conference on Artificial Intelligence (2007)Google Scholar
  57. 57.
    Cao, X.: An integer linear programming approach for topology design in owc networks. In: Proc. of the IEEE GLOBECOM Workshops, pp. 1–5 (2008)Google Scholar
  58. 58.
    Kiese, M., Hartmann, C., Vilzmann, R.: Optimality bounds of the connectivity of adhoc networks with beamforming antennas. In: Proc. of GLOBECOM (2009)Google Scholar
  59. 59.
    Magatão, L.: Mixed integer linear programming and constraint logic programming: towards a unified modeling framework. Ph.D. dissertation, The Federal Center of Technological Education of Paraná (2005)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Engineering CyberneticsO.S. Bragstads plass 2DTrondheimNorway

Personalised recommendations