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The Velocity Assignment Problem for Conflict Resolution with Multiple Aerial Vehicles Sharing Airspace

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Abstract

Efficient conflict resolution methods for multiple aerial vehicles sharing airspace are presented. The problem of assigning a velocity profile to each aerial vehicle in real time, such that the separation between them is greater than a given safety distance, is considered and the total deviation from the initial planned trajectory is minimized. The proposed methods involve the use of appropriate airspace discretization. In the paper it is demonstrated that this aerial vehicle velocity assignment problem is NP-hard. Then, the paper presents three different collision detection and resolution methods based on speed planning. The paper also presents simulations and studies for several scenarios.

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References

  1. Sesar consortium website: http://www.eurocontrol.int/sesar/public/subsite_homepage/homepage.html. Accessed 25 Jan 2012

  2. Maza, I., Caballero, F., Capitan, J., Martinez-de Dios J., Ollero, A.: A distributed architecture for a robotic platform with aerial sensor transportation and self-deployment capabilities. J. Field Robot. (JFR) 28(3), 303–328 (2011)

    Article  Google Scholar 

  3. Cobano, J.A., Martínez-de Dios, J.R., Conde, R., Sánchez-Matamoros, J.M., Ollero, A.: Data retrieving from heterogeneous wireless sensor network nodes using UAVs. J. Intell. Robot. Syst. 60(1), 133–151 (2010)

    Article  MATH  Google Scholar 

  4. Kuchar, J.K., Yang, L.C.: A review of conflict detection and resolution modeling methods. IEEE Trans. Intell. Transp. Syst. 1, 179–189 (2000)

    Article  Google Scholar 

  5. Hu, J., Prandini, M., Nilim, A., Sastry, S.: Optimal coordinated maneuvers for threedimensional aircraft conflict resolution. AIAA J. Guid. Control Dyn. 25(5), 888–900 (2002)

    Article  Google Scholar 

  6. Pallottino, L., Feron, E., Bicchi, A.: Conflict resolution problems for air traffic management systems solved with mixed integer programming. IEEE Trans. Intell. Transp. Syst. 3, 3–11 (2002)

    Article  Google Scholar 

  7. Ehrmanntraut, R.: The potential of speed control. In: 23rd Digital Avionics Systems Conference, vol. 1, pp. 3.E.3-1–3.E.7 (2004)

  8. Erzberger, H.: Automated conflict resolution for air traffic control. In: Proceeding International Congress Aeronautical Sciences, pp. 179–189 (2006)

  9. Carbone, C., Ciniglio, U., Corraro, F., Luongo, S.: A novel 3rd geometric algorithm for aircraft autonomous collision avoidance. In: 45th IEEE Conference on Decision and Control, pp. 1580–1585 (2006)

  10. Crück, E., Lygeros, J.: Subliminal air traffic control: human friendly control of a multi-agent system. In: American Control Conference, pp. 462–467 (2007)

  11. Vela, A., Solak, S., Singhose, W., Clarke, J.P.: A mixed integer program for flight-level assignment and speed control for conflict resolution. In: Proceedings of the 48th IEEE Conference on Decision and Control, 2009 Held Jointly with the 28th Chinese Control Conference, CDC/CCC 2009, pp. 5219–5226 (2009)

  12. Christodoulou, M.A., Kodaxakis, S.G.: Automatic commercial aircraft-collision avoidance in free flight: the three-dimensional problem. IEEE Trans. Intell. Transp. Syst. 7(2), 242–249 (2006)

    Article  Google Scholar 

  13. Vivona, R., Karr, D., Roscoe, D.: Pattern-based genetic algorithm for airborne conflict resolution. In: AIAA Guidance, Navigation and Control Conference and Exhibit. Keystone, Colorado (2006)

  14. Bicchi, A., Pallottino, L.: On optimal cooperative conflict resolution for air traffic management systems. IEEE Trans. Intell. Transp. Syst. 1, 221–231 (2000)

    Article  Google Scholar 

  15. Tomlin, C., Mitchell, I., Ghosh, R.: Safety verification of conflict resolution manoeuvres. IEEE Trans. Intell. Transp. Syst. 2, 110–120 (2001)

    Article  Google Scholar 

  16. Lecchini, A., Glover, W., Lygeros, J., Maciejowski, J.: Monte carlo optimization for conflict resolution in air traffic control. IEEE Trans. Intell. Transp. Syst. 7, 470–482 (2006)

    Article  Google Scholar 

  17. Paielli, R.A., Erzberger, H.: Conflict probability estimation for free flight. AIAA J. Guid. Control Dyn. 20, 588–596 (1997)

    Article  MATH  Google Scholar 

  18. Hu, J., Pr, M., Sastry, S.: Aircraft conflict prediction in the presence of a spatially correlated wind field. IEEE Trans. Intell. Transp. Syst. 6, 326–340 (2005)

    Article  Google Scholar 

  19. Prandini, M., Hu, J., Lygeros, J., Sastry, S.: A probabilistic approach to aircraft conflict detection. IEEE Trans. Intell. Transp. Syst. 1, 199–220 (2000)

    Article  Google Scholar 

  20. Irvine, R.:A geometrical approach to conflict probability estimation. Air Traffic Control Q. 10, 85–113 (2002)

    Google Scholar 

  21. Bakker, G., Blom, H.: Conflict probability and incrossing probability in air traffic management. In: IEEE Conference on Decision and Control, pp. 2421–2426. Las Vegas (2002)

  22. Rebollo, J.J., Ollero, A., Maza, I.: Collision avoidance among multiple aerial robots and other non-cooperative aircraft based on velocity planning. In: 7th Conference on Mobile Robots. Albufeira, Portugal (2007)

  23. Richards, A., Bellingham, J., Tillerson, M., How, J.: Coordination and control of multiple uavs. In: AIAA Guidance, Navigation, and Control Conference and Exhibit. Monterey, CA (2002)

  24. Waslander, S., Inalhan, G., Tomlin, C.: Decentralized optimization via nash bargaining. Theory Algorithms Coop. Syst. 4, 565–585 (2004)

    Article  MathSciNet  Google Scholar 

  25. Kant, K., Zucker, S.: Toward efficient trajectory planning: the path-velocity decomposition. Int. J. Rob. Res. 5(3), 72–89 (1986)

    Article  Google Scholar 

  26. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1979)

    MATH  Google Scholar 

  27. Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B.: Sequencing and scheduling: algorithms and complexity. In: Graves, S.C., Rinnooy Kan, A.H.G., Zipkin, P.H. (eds.) Logistics of Production and Inventory. Handbooks in Operations Research and Management Science, vol. 4, ch. 9, pp. 445–522. Elsevier, Amsterdam (1993)

    Google Scholar 

  28. Sgall, J.: On-line scheduling—a survey. Lect. Notes Comput. Sci. 1442, 196–231 (1998). doi:10.1007/BFb00295701997

    Article  MathSciNet  Google Scholar 

  29. Aspvall, B., Plass, M.F., Tarjan, R.E.: A linear-time algorithm for testing the truth of certain quantified boolean formulas. Inf. Process. Lett. 8(3), 121–123 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  30. Project, T.C.: CGAL User and Reference Manual, 3.9th edn. CGAL Editorial Board (2011). http://www.cgal.org/Manual/3.9/doc_html/cgal_manual/packages.html

  31. McLain, T.W., Beard, R.W.: Coordination variables, coordination functions, and cooperative timing missions. J. Guid. Control Dyn. 28(1), 150–161 (2005)

    Article  Google Scholar 

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Authors and Affiliations

  1. Robotics, Vision and Control Group Engineering School, University of Seville, 41092, Seville, Spain

    D. Alejo, J. A. Cobano & A. Ollero

  2. Applied Mathematics II Department Engineering School, University of Seville, 41092, Seville, Spain

    J. M. Díaz-Báñez

  3. Escuela de Ingeniería Civil en Informática, Universidad de Valparaíso, 2340000, Valparaíso, Chile

    P. Pérez-Lantero

Authors
  1. D. Alejo
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  2. J. M. Díaz-Báñez
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  3. J. A. Cobano
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  4. P. Pérez-Lantero
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  5. A. Ollero
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Correspondence to J. A. Cobano.

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Alejo, D., Díaz-Báñez, J.M., Cobano, J.A. et al. The Velocity Assignment Problem for Conflict Resolution with Multiple Aerial Vehicles Sharing Airspace. J Intell Robot Syst 69, 331–346 (2013). https://doi.org/10.1007/s10846-012-9768-4

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  • DOI: https://doi.org/10.1007/s10846-012-9768-4

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