First Order Hadamard Variation of the Harmonic Navigation Function on a Sphere World

Isabelle Santos (1) , Stéphane Puechmorel (1) , Guillaume Dufour (2)

1 ENAC - Ecole Nationale de l'Aviation Civile
2 ONERA - The French Aerospace Lab [Toulouse]

Planning conflict-free trajectories is a long-standing problem in Air Traffic Management. 1 Navigation functions designed specifically to produce flyable trajectories have been previously 2 considered, but lack the robustness to uncertain weather conditions needed for use in an operational 3 context. These uncertainties can be taken into account be modifying the boundary of the domain 4 on which the navigation function is computed. In the following work, we present a method for 5 efficiently taking into account boundary variations, using the Hadamard variation. 6

Mots clés: Navigation Function; Hadamard Formula; Trajectory Planning; Air Traffic Control

Domaines: Analyse numérique [math.NA]; Modélisation et simulation

Isabelle Santos, Stéphane Puechmorel, Guillaume Dufour. First Order Hadamard Variation of the Harmonic Navigation Function on a Sphere World. Mathematical and computational applications, 2018, 23, 3, ⟨10.3390/mca23030048⟩. ⟨hal-01855142⟩