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Aircraft Trajectory Planning without Conflict : Biharmonic Functions and Harmonic Navigation Function

Résumé : We consider a planning of aircraft trajectories in free-route sectors, i.e. sectors where aircraft do not have to follow air routes anymore. The planning is done several days, or even weeks before take-off. Our goal does not entail control of the aircraft in real time to avoid conflicts, but an organization of the traffic so the only conflicts the controllers have to manage come from perturbations of the system (like meteorological hazard). Such a planning tool could also be used as a simulation tool, to determine for example take-off planning. This thesis focuses on the potential fields method to plan conflict-free trajectories for a large number of aircraft. The study of harmonic potential fields, as well as biharmonic fields highlights the limits of these methods: their computation time explodes with the increase of the number of flights. This conclusion brought us to study another type of potential fields: the navigation functions, already used for conflict-avoidance. We propose in the last part of this thesis a new navigation function, based on previous work on harmonic functions and navigation functions. This harmonic navigation function is able to plan a large number of aircraft trajectories with a very small computation time. It also guarantees some good properties for the planned trajectories, like constant speed. Some leads are also given on how to improve the harmonic navigation function, especially how to optimize the trajectories it produces.
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https://hal-enac.archives-ouvertes.fr/tel-01084037
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Submitted on : Tuesday, November 18, 2014 - 1:47:35 PM
Last modification on : Wednesday, July 24, 2019 - 11:48:01 PM
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  • HAL Id : tel-01084037, version 1

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Laureline Guys. Aircraft Trajectory Planning without Conflict : Biharmonic Functions and Harmonic Navigation Function. Optimisation et contrôle [math.OC]. Université Toulouse 3 Paul Sabatier, 2014. Français. ⟨tel-01084037⟩

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