# Aircraft Trajectory Planning under Wind Uncertainties

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1 ENAC - Ecole Nationale de l-Aviation Civile

Abstract : Wind optimal trajectory planning is a critical issue for airlines in order to save fuel for all their flights. This planning is difficult due to the uncertainties linked to wind data. Based on the current weather situation, weather forecast institutes compute wind maps prediction with a given level of confidence. Usually, 30-50 wind maps prediction can be produced. Based on those predictions, airlines have to compute trajectory planning for their aircraft in an efficient way. Such planning has to propose robust solutions which take into account wind variability for which average and standard deviation have to be taken into account. It is then better to plan trajectories in areas where wind has low standard deviation even if some other plannings induce less fuel consumption but with a higher degree of uncertainty. In this paper, we propose an efficient wind optimal algorithm based on two phases. The first phase considers the wind map predictions and computes for each of them the associated wind optimal trajectory also called geodesic. Such geodesics are computed with a classical Bellman algorithm on a grid covering an elliptical shape projected on the sphere. This last point enable the algorithm to address long range flights which are the most sensitive to wind direction. At the end of this first phase, we get a set of wind optimal trajectories. The second phase of the algorithm extract the most robust geodesic trajectories by the mean of a new trajectory clustering algorithm. This clustering algorithm is based on a new mathematical distance involving continuous deformation approach. In order to measure this mathematical distance between two trajectories, a continuous deformation between them is first built. This continuous deformation is called homotopy. For any homotopy, one can measure the associated energy used to shift from the first trajectory to the second one. The homotopy with the minimum energy is then computed, for which the associated energy measure the mathematical distance between trajectories. Based on this new distance, an EM clustering algorithm has been used in order to identify the larger clusters which correspond to the most robust wind optimal trajectories. This new approach avoids the main drawback of the classical approach which uses the mean of the trajectories issued from the first phase. This algorithm has been successfully applied to north Atlantic flights.

Autor: ** Karim Legrand - Stéphane Puechmorel - Daniel Delahaye - Yao Zhu - **

Fuente: https://hal.archives-ouvertes.fr/