An Eikonal Approach for Globally Optimal Free Flight Trajectories

TL;DR

This paper introduces an eikonal-based method to compute globally optimal aircraft trajectories in stationary wind fields, addressing challenges near cut loci to ensure true optimality and reduce emissions.

Contribution

It develops a novel approach combining eikonal equations with finite element error estimates to guarantee globally optimal trajectories despite numerical discretization issues.

Findings

Successfully finds globally optimal trajectories in stationary wind fields.

Guarantees trajectory uniqueness away from cut loci.

Reduces emissions and fuel consumption through optimal routing.

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.