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Conflict avoidance: \(0-1\) linear models for conflict detection & resolution. (English) Zbl 1276.90015

Summary: The Conflict Detection and Resolution Problem for Air Traffic Flow Management consists of deciding the best strategy for airborne aircraft so that there is guarantee that no conflict takes place, i.e., all aircraft maintain the minimum safety distance at every time instant. Two integer linear optimization models for conflict avoidance between any number of aircraft in the airspace are proposed, the first being a pure 0-1 linear which avoids conflicts by means of altitude changes, and the second a mixed 0-1 linear whose strategy is based on altitude and speed changes. Several objective functions are established. Due to the small elapsed time that is required for solving both problems, the approach can be used in real time by using state-of-the-art mixed integer linear optimization software.

MSC:

90B20 Traffic problems in operations research
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[1] Alonso-Ayuso A, Escudero LF, Martín-Campo FJ (2010) Collision avoidance in the ATM problem: a mixed integer linear optimization approach. IEEE Trans Intell Transp Syst 12:47–57 · doi:10.1109/TITS.2010.2061971
[2] Air Traffic Action Group (ATAG) (1999) European air traffic forecast 1985–2015. Geneva, Switzerland
[3] Christodoulou MA, Costoulakis C (2004) Nonlinear mixed integer programming for aircraft collision avoidance in free flight. In: IEEE Melecon, Dubrovnik (Croatia), vol 1, pp 327–330
[4] Christodoulou MA, Kodaxakis SG (2006) Automatic commercial aircraft-collision avoidance in free flight: the three-dimensional problem. IEEE Trans Intell Transp Syst 7(2):242–249 · doi:10.1109/TITS.2006.874684
[5] Etkin B, Reid LD (1996) Dynamics of flight: stability and control. Wiley, New York
[6] Hu J, Prandini M, Sastry S (2002) Optimal coordinated maneuvers for three dimensional aircraft conflict resolution. AIAA J Guid Control Dyn 25(5):888–900 · doi:10.2514/2.4982
[7] Hu J, Prandini M, Sastry S (2003) Optimal coordinated motions for multiple agents moving on a plane. SIAM J Control Optim 42(2):637–668 · Zbl 1046.65051 · doi:10.1137/S0363012901387562
[8] Hu J, Prandini M, Sastry S (2003) Probabilistic safety analysis in three dimensional aircraft flight. In: Proceedings of 42nd IEEE conference on decision and control, vol 5, pp 5335–5340
[9] Hu J, Prandini M, Sastry S (2005) Aircraft conflict prediction in the presence of a spatially correlated wind field. IEEE Trans Intell Transp Syst 6(3):326–340 · doi:10.1109/TITS.2005.853699
[10] Hull DG (2007) Fundamentals of airplane flight mechanics. Springer, Berlin · Zbl 1126.76001
[11] IBM ILOG COKEX (2009) User manual
[12] Jardin MR (2003a) Real-time conflict-free trajectory optimization. In: Fifth USA/Europe air trafic management RD seminar, Budapest (Hungary)
[13] Jardin MR (2003b) Toward real-time en route air traffic control optimization. PhD thesis, Stanford University (California)
[14] Jardin MR (2005) Grid-based strategic air traffic conflict detection. In: AIAA guidance, navigation, and control conference and exhibition
[15] Kuchar JK, Yang LC (2000) A review of conflict detection and resolution modeling methods. IEEE Trans Intell Transp Syst 1:179–189 · doi:10.1109/6979.898217
[16] Magister T (2002) Conflict detection and resolution in the vicinity of the top of descent point. Promet 14(6):269–275
[17] Magister T (2004) Avoidance maneuvering in the vicinity of the top of descent. J Aerosp Eng 17(4):176–181 · doi:10.1061/(ASCE)0893-1321(2004)17:4(176)
[18] Mao Z-H, Feron E, Bilimoria K (2001) Stability and performance of intersecting aircraft flows under decentralized conflict avoidance rules. IEEE Trans Intell Transp Syst 2(2):101–109 · doi:10.1109/6979.928721
[19] Mao ZH, Dugail D, Feron E, Bilimoria K (2005) Stability of intersecting aircraft flows using heading-change maneuvers for conflict avoidance. IEEE Trans Intell Transp Syst 6(4):357–369 · doi:10.1109/TITS.2005.858789
[20] Pallottino L, Feron E, Bicchi A (2002) Conflict resolution problems for air traffic management systems solved with mixed integer programming. IEEE Trans Intell Transp Syst 3(1):3–11 · doi:10.1109/6979.994791
[21] Pannequin JJ, Bayen AM, Mitchell IM, Chung H, Sastry S (2007) Multiple aircraft deconflicted path planning with weather avoidance constraints. In: AIAA guidance, navigation and control conference, Hilton Head (South Carolina, USA)
[22] Prandini M, Hu J (2008) Application of reachability analysis for stochastic hybrid systems to aircraft conflict prediction. IEEE Trans Autom Control · Zbl 1367.93422
[23] Richards AG, How JP (2002) Aircraft trajectory planning with collision avoidance using mixed integer linear programming. In: American control conference, Anchorage (Alaska, USA)
[24] Radio Technical Committee on Aeronautics RTCA (1983) Minimum performance specifications for tcas airborne equipment. Document No RTCA/DO185, Washington DC, USA
[25] Tewari A (2007) Atmospheric and space flight dynamics: modeling and simulation with MATLAB and simulink. Birkhäuser, Basel · Zbl 1119.70001
[26] Treleaven K, Mao ZH (2008) Conflict resolution and traffic complexity of multiple intersecting flows of aircraft. IEEE Trans Intell Transp Syst 9(4):633–643 · doi:10.1109/TITS.2008.2006771
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