DMCA
Mathematical Models for Aircraft Trajectory Design: A Survey
BibTeX
@MISC{Delahaye_mathematicalmodels,
author = {D. Delahaye and S. Puechmorel and P. Tsiotras and E. Feron and D. Delahaye and S. Puechmorel and P. Tsiotras and E. Feron},
title = {Mathematical Models for Aircraft Trajectory Design: A Survey},
year = {}
}
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Abstract
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 belong-ing 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 dimen-sion 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. Fi-nally, we introduce some path planning techniques via natural language processing and mathematical programming.
Keyphrases
mathematical model aircraft trajectory design big vector real instance path planning technique regular point search space dimen-sion reduction trick typical feature trajectory design natural language processing aircraft trajectory naive way abstract air traffic management fast marching algorithm mathematical programming infinite dimension optimal control approach efficient representation air traffic control problem aircraft dynamic front propagation approach
