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Air Traffic Management and Systems pp 205–247Cite as

Mathematical Models for Aircraft Trajectory Design: A Survey

Part of the Lecture Notes in Electrical Engineering book series (LNEE,volume 290)

Abstract

Air traffic management ensures the safety of flight by optimizing flows and maintaining separation between aircraft. After giving some definitions, some typical feature of aircraft trajectories are presented. Trajectories are objects belonging to spaces with infinite dimensions. The naive way to address such problem is to sample trajectories at some regular points and to create a big vector of positions (and or speeds). In order to manipulate such objects with algorithms, one must reduce the dimension of the search space by using more efficient representations. Some dimension reduction tricks are then presented for which advantages and drawbacks are presented. Then, front propagation approaches are introduced with a focus on Fast Marching Algorithms and Ordered upwind algorithms. An example of application of such algorithm to a real instance of air traffic control problem is also given. When aircraft dynamics have to be included in the model, optimal control approaches are really efficient. We present also some application to aircraft trajectory design. Finally, we introduce some path planning techniques via natural language processing and mathematical programming.

Keywords

  • Aircraft trajectory design
  • B-spline
  • Principal component analysis
  • Bézier
  • Homotopy
  • Optimal control
  • Air traffic management
  • Strategic planning
  • Pre-tactical planning
  • Tactical planning

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  • DOI: 10.1007/978-4-431-54475-3_12
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Notes

  1. 1.

    TMA: “Terminal Maneuvering Area”.

  2. 2.

    The convex hull or convex envelope of a set X of points in the Euclidean plane or Euclidean space is the smallest convex set that contains X.

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Authors and Affiliations

  1. Applied Mathematics Laboratory, French Civil Aviation University, Toulouse, France

    D. Delahaye & S. Puechmorel

  2. School of Aerospace Engineering Georgia Institute of Technology, Atlanta, GA, USA

    P. Tsiotras & E. Feron

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  1. D. Delahaye
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  2. S. Puechmorel
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  3. P. Tsiotras
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  4. E. Feron
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Correspondence to D. Delahaye .

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    Delahaye, D., Puechmorel, S., Tsiotras, P., Feron, E. (2014). Mathematical Models for Aircraft Trajectory Design: A Survey. In: Air Traffic Management and Systems. Lecture Notes in Electrical Engineering, vol 290. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54475-3_12

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