In this paper, we provide a survey on available numerical approaches for solving low-thrust trajectory optimization problems. First, a general mathematical framework based on hybrid optimal control will be presented. This formulation and their elements, namely objective function, continuous and discrete state and controls, and discrete and continuous dynamics, will serve as a basis for discussion throughout the whole manuscript. Thereafter, solution approaches for classical continuous optimal control problems will be briefly introduced and their application to low-thrust trajectory optimization will be discussed. A special emphasis will be placed on the extension of the classical techniques to solve hybrid optimal control problems. Finally, an extensive review of traditional and state-of-the art methodologies and tools will be presented. They will be categorized regarding their solution approach, the objective function, the state variables, the dynamical model, and their application to planetocentric or interplanetary transfers.

In this paper, an approach to aircraft trajectory optimization is presented in which integer and continuous variables are considered. Integer variables model decision-making processes, and continuous variables describe the state of the aircraft, which evolves according to differential-algebraic equations. The problem is formulated as a multiphase mixed-integer optimal control problem. It is transcribed into a mixed-integer nonlinear programming problem by applying a fifth degree Gauss&-Lobatto direct collocation method and is then solved using a nonlinear- programming-based branch-and-bound algorithm. The approach is applied to the following en route flight planning problem: Given an aircraft point mass model, a wind forecast, an airspace structure, and the relevant flying information regions with their associated overflying costs, find the control inputs that steer the aircraft from the initial fix to the final fix, following a route of waypoints while minimizing the fuel consumption and overflying costs during the flight. The decision-making process arises in determining the optimal sequence of waypoints. The optimal times at which the waypoints are to be overflown are also to be determined. Numerical results are presented and discussed, showing the effectiveness of the approach.Publicad

The strong growth rate of the aviation industry in recent years has created significant challenges in terms of environmental impact. Air traffic contributes to climate change through the emission of carbon dioxide (CO₂) and other non-CO₂ effects, and the associated climate impact is expected to soar further. The mitigation of CO₂ contributions to the net climate impact can be achieved using novel propulsion, jet fuels, and continuous improvements of aircraft efficiency, whose solutions lack in immediacy. On the other hand, the climate impact associated with non-CO₂ emissions, being responsible for two-thirds of aviation radiative forcing, varies highly with geographic location, altitude, and time of the emission. Consequently, these effects can be reduced by planning proper climate-aware trajectories. To investigate these possibilities, this paper presents a survey on operational strategies proposed in the literature to mitigate aviation’s climate impact. These approaches are classified based on their methodology, climate metrics, reliability, and applicability. Drawing upon this analysis, future lines of research on this topic are delineated.

This work is partially supported by the Spanish Government through the Ministerio de Ciencia e Innovación, the Comunidad de Madrid, and the project i-Math Ingenio Mathematica. This work has been carried out within the framework of the Atlantida project, partially funded by the Spanish Centro para el Desarrollo Tecnológico e Industrial, in which the Universidad Rey Juan Carlos is collaborating with GVM Aerospace and Defence.Publicad

Climate impact models of the non-${\mathrm{CO}}_2$ emissions of aviation are still subject to significant uncertainties. Condensation trails, or contrails, are one of these non-${\mathrm{CO}}_2$ effects. In order to validate the contrail simulation models, a dataset of observations covering the entire lifetime of the contrails will be required, as well as the characteristics of the aircraft which produced them. This study carries on the work on contrail observation from geostationary satellite by proposing a new way to track contrails and identify the flight that produced it using geostationary satellite infrared images, weather data as well as air traffic data. It solves the tracking and the identification problem as one, each process leveraging information from the other to achieve a better overall result. This study is a new step towards a consistent contrail dataset that could be used to validate contrail models.