An Eikonal Approach for Globally Optimal Free Flight Trajectories

Ralf Borndörfer; Arturas Jocas; Martin Weiser

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arXiv · 2603.11830

An Eikonal Approach for Globally Optimal Free Flight Trajectories

Ralf Borndörfer·Arturas Jocas·Martin Weiser

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Abstract

We present an eikonal-based approach that is capable of finding a continuous globally optimal trajectory for an aircraft in a stationary wind field. This minimizes emissions and fuel consumption. If the destination is close to a cut locus of the associated Hamilton-Jacobi-Bellman equation, small numerical discretization errors can lead to selecting a merely locally optimal trajectory and missing the globally optimal one. Based on finite element error estimates, we construct a trust region around the cut loci in order to guarantee uniqueness of trajectories for destinations sufficiently far from cut loci.

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Ralf Borndörfer, Arturas Jocas, Martin Weiser. 2026-03-12. An Eikonal Approach for Globally Optimal Free Flight Trajectories. https://arxiv.org/abs/2603.11830

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