Multi-objective optimisation of aircraft flight trajectories in the ATM and avionics context

Abstract

The continuous increase of air transport demand worldwide and the push for a more economically viable and environmentally sustainable aviation are driving significant evolutions of aircraft, airspace and airport systems design and operations. Although extensive research has been performed on the optimisation of aircraft trajectories and very efficient algorithms were widely adopted for the optimisation of vertical flight profiles, it is only in the last few years that higher levels of integration were proposed for automated flight planning and rerouting functionalities of innovative Communication Navigation and Surveillance/Air Traffic Management (CNS/ATM) and Avionics (CNS+A) systems. In this context, the implementation of additional environmental targets and of multiple operational constraints introduces the need to efficiently deal with multiple objectives as part of the trajectory optimisation algorithm. This article provides a comprehensive review of Multi-Objective Trajectory Optimisation (MOTO) techniques for transport aircraft flight operations, with a special focus on the recent advances introduced in the CNS+A research context. In the first section, a brief introduction is given, together with an overview of the main international research initiatives where this topic has been studied, and the problem statement is given. The second section introduces the mathematical formulation and the third section reviews the numerical solution techniques, including discretisation and optimisation methods for the specific problem formulated. The fourth section summarises the strategies to articulate the preferences and to select optimal trajectories when multiple conflicting objectives are introduced. The fifth section introduces a number of models defining the optimality criteria and constraints typically adopted in MOTO studies, including fuel consumption, air pollutant and noise emissions, operational costs, condensation trails, current airspace and airport operations. A brief overview of atmospheric and weather modelling is also included. Key equations describing the optimality criteria are presented, with a focus on the latest advancements in the respective application areas. In the sixth section, a number of MOTO implementations in the CNS+A systems context are mentioned with relevant simulation case studies addressing different operational tasks. The final section draws some conclusions and outlines guidelines for future research on MOTO and associated CNS+A system implementations.

Trajectory Optimization of Extended Formation Flights for Commercial Aviation

“…Many direct and indirect techniques are available for resolving a multi-phase trajectory optimization problem [23]. As noted in [23], pseudospectral methods are considered some of the most computationally effective families among the global collocation techniques available for the direct resolution of nonlinear trajectory optimization problems. In this study, the so-called Radau pseudospectral method [24] has been selected for resolving the MOC problem.…”

Multiaircraft Optimal 4D Trajectory Planning Using Logical Constraints

“…where WM i and FM i denote if at discretization instant i, the aircraft is in waypoint mode or free flight mode, respectively. Once again, following the technique described above, if we define new variables κ 1 i , κ 2 i ∈ ½0, 1 satisfying condition…”

“…In the ATM context, logical constraints describe, for instance, policies to apply in conflict detection and resolution and operational constraints to be fulfilled during flight. The main operational constraints to be fulfilled during flight are separation constraints, keep-out constraints to avoid no-fly zones, and passage constraints through or by waypoints [1].…”

Trajectory optimisation for avionics-based GNSS integrity augmentation system

“…As pointed out earlier, the following conditions cause navigation data outages or severe performance degradations: antenna obscuration, bad satellite geometries and low Carrier-toNoise ratios (C/N 0 ), Doppler shifts, interference and multipath [8][9][10]. The last two problems could be mitigated by existing technology solutions (i.e., by suitable selection of VHF/UHF data links, filtering the radio frequency signals reaching the GNSS antenna, identifying suitable locations for the GNSS antenna, etc.).…”

“…"Determine the states ( ) , the controls ( ) , the parameters , the initial time and the final time , that optimise the performance index [10]:…”