Estimating fuel-efficient air plane trajectories using machine learning

Airline industry has witnessed a tremendous growth in the recent past. Percentage of people choosing air travel as first choice to commute is continuously increasing. Highly demanding and congested air routes are resulting in inadvertent delays, additional fuel consumption and high emission of greenhouse gases. Trajectory planning involves creation identification of cost-effective flight plans for optimal utilization of fuel and time. This situation warrants the need of an intelligent system for dynamic planning of optimized flight trajectories with least human intervention required. In this paper, an algorithm for dynamic planning of optimized flight trajectories has been proposed. The proposed algorithm divides the airspace into four dimensional cubes and calculate a dynamic score for each cube to cumulatively represent estimated weather, aerodynamic drag and air traffic within that virtual cube. There are several constraints like simultaneous flight separation rules, weather conditions like air temperature, pressure, humidity, wind speed and direction that pose a real challenge for calculating optimal flight trajectories. To validate the proposed methodology, a case analysis was undertaken within Indian airspace. The flight routes were simulated for four different air routes within Indian airspace. The experiment results observed a seven percent reduction in drag values on the predicted path, hence indicates reduction in carbon footprint and better fuel economy

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

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 automation were proposed for integrated flight planning and re-routing 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 provided. 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, airspace and airport operations

Upravljanje putanjama vazduhoplova u kontroli letenja na pre-taktičkom i taktičkom nivou

Global air traffic demand is continuously increasing, and it is predicted to be tripled by 2050. The need for increasing air traffic capacity motivates a shift of ATM towards Trajectory Based Operations (TBOs). This implies the possibility to design efficient congestion-free aircraft trajectories more in advance (pre-tactical, strategic level) reducing controller’s workload on tactical level. As consequence, controllers will be able to manage more flights. Current flow management practices in air traffic management (ATM) system shows that under the present system settings there are only timid demand management actions taken prior to the day of operation such as: slot allocation and strategic flow rerouting. But the choice of air route for a particular flight is seen as a commercial decision to be taken by airlines, given air traffic control constraints. This thesis investigates the potential of robust trajectory planning (considered as an additional demand management action) at pre-tactical level as a mean to alleviate the en-route congestion in airspace. Robust trajectory planning (RTP) involves generation of congestion-free trajectories with minimum operating cost taking into account uncertainty of trajectory prediction and unforeseen event. Although planned cost could be higher than of conventional models, adding robustness to schedules might reduce cost of disruptions and hopefully lead to reductions in operating cost. The most of existing trajectory planning models consider finding of conflict-free trajectories without taking into account uncertainty of trajectory prediction. It is shown in the thesis that in the case of traffic disturbances, it is better to have a robust solution otherwise newly generated congestion problems would be hard and costly to solve. This thesis introduces a novel approach for route generation (3D trajectory) based on homotopic feature of continuous functions. It is shown that this approach is capable of generating a large number of route shapes with a reasonable number of decision variables. Those shapes are then coupled with time dimension in order to create trajectories (4D)...Globalna potražnja za vazdušnim saobraćajem u stalnom je porastu i prognozira se da će broj letova biti utrostručen do 2050 godine. Potreba za povećanjem kapaciteta sistema vazdušnog saobraćaja motivisala je promene u sistemu upravljanja saobraćajnim tokovima u kome će u budućnosti centralnu ulogu imati putanje vazduhoplova tzv. “trajectory-based” koncept. Takav sistem omogućiće planiranje putanja vazduhoplova koje ne stvaraju zagušenja u sistemu na pre-taktičkom nivou i time smanjiti radno opterećenje kontrolora na taktičkom nivou. Kao posledica, kontrolor će moći da upravlja više letova nego u današnjem sistemu. Današnja praksa upravljanja saobraćajnim tokovima pokazuje da se mali broj upravljačkih akcija primenjuje pre dana obavljanja letova npr.: alokacija slotova poletanja i strateško upravljanje saobraćajnim tokovima. Međutim izbor putanje kojom će se odviti let posmatra se kao komercijalna odluka aviokompanije (uz poštovanje postavljenih ograničenja od strane kontrole letenja) i stoga je ostavljen na izbor avio-kompaniji. Većina, do danas razvijenih, modela upravljanja putanjama vazduhoplova ima za cilj generisanje bez-konfliktnih putanja, ne uzimajući u obzir neizvesnost u poziciji vazduhoplova. U ovoj doktorskoj disertaciji ispitivano je planiranje robustnih putanja vazduhoplova (RTP) na pre-taktičkom nivou kao sredstvo ublažavanja zagušenja u vazdušnom prostoru . Robustno upravljanje putanjama vazduhoplova podrazumeva izbor putanja vazduhoplova sa minimalnim operativnim troškovima koje ne izazivaju zagušenja u vazdušnom prostoru u uslovima neizvesnosti buduđe pozicije vazduhoplova i nepredviđenih događaja. Iako predviđeni (planirani) operativni troškovi robustnih putanja mogu u startu biti veći od operativnih troškova bez-konfliktnih putanja, robusnost može uticati na smanjenje troškove poremećaja putanja jer ne zahteva dodatnu promenu putanja vazduhplova radi izbegavanja konfliktnih situacija na taktičkom nivou. To na kraju može dovesti i do smanjenja stvarnih operativnih troškova. U tezi je pokazano, da je u slučaju poremećaja saobraćaja bolje imati robustno rešenje (putanje), jer novo-nastali problem zagušenosti vazdušnog prostora je teško i skupo rešiti..

4D commercial trajectory optimization for fuel saving and environmemtal impact reduction

The main purpose of the thesis is to optimize commercial aircraft 4D trajectories to improve flight efficiency and reduce fuel consumption and environmental impact caused by airliners. The Trajectory Optimization Problem (TOP) technique can be used to accomplish this goal. The formulation of the aircraft TOP involves the mathematical model of the system (i.e., dynamics model, performance model, and emissions model of the aircraft), Performance Index (PI), and boundary and path constraints of the system. Typically, the TOP is solved by a wide range of numerical approaches. They can be classified into three basic classes of numerical methods: indirect methods, direct methods, and dynamic programming. In this thesis, several instances of problems were considered to optimize commercial aircraft trajectories. Firstly, the problem of optimal trajectory generation from predefined 4D waypoint networks was considered. A single source shortest path algorithm (Dijkstra’s algorithm) was applied to generate the optimal aircraft trajectories that minimize aircraft fuel burn and total trip time between the initial and final waypoint in the networks. Dijkstra’s Algorithm (DA) successfully found the path (trajectory) with the lowest cost (i.e., fuel consumption, and total trip time) from the predefined 4D waypoint networks. Next, the problem of generating minimum length optimal trajectory along a set of predefined 4D waypoints was considered. A cubic spline parameterization was used to solve the TOP. The state vector, its time derivative, and control vector are parameterized using Cubic Spline Interpolation (CSI). Consequently, the objective function and constraints are expressed as functions of the value of state and control at the temporal nodes, this representation transforms the TOP into a Nonlinear Programming (NLP) problem, which is then solved numerically using a well-established NLP solver. The proposed method generated a smooth 4D optimal trajectory with very accurate results. Following, the problem considers generating optimal trajectories between two 4D waypoints. Dynamic Programming (DP) a well-established numerical method was considered to solve this problem. The traditional DP bears some shortcomings that prevent its use in many practical real-time implementations. This thesis proposes a Modified Dynamic Programming (MDP) approach which reduces the computational effort and overcomes the drawbacks of the traditional DP. The proposed MDP approach was successfully implemented to generate optimal trajectories that minimize aircraft fuel consumption and emissions in several case studies, the obtained optimal trajectories are then compared with the corresponding reference commercial flight trajectory for the same route in order to quantify the potential benefit of reduction of aircraft fuel consumption and emissions. The numerical examples demonstrate that the MDP can successfully generate fuel and emissions optimal trajectory with little computational effort, which implies it can also be applied to online trajectory generation. Finally, the problem of predicting the fuel flow rate from actual flight data or manual data was considered. The Radial Basis Function (RBF) neural network was applied to predict the fuel flow rate in the climb, cruise, and descent phases of flight. In the RBF neural network, the true airspeed and flight altitude were taken as the input parameters and the fuel flow rate as the output parameter. The RBF neural network produced a highly accurate fuel flow rate model with a high value of coefficients of determination, together with the low relative approximation errors. Later on, the resulted fuel flow rate model was used to solve a 4D TOP by optimizing aircraft green cost between two 4D waypoints.O principal objetivo desta tese é otimizar as trajetórias em 4D de aeronaves comerciais, de forma a melhorar a eficiência de voo e reduzir o consumo de combustível e o impacto ambiental causado pelos aviões. A técnica de otimização de trajetória pode ser utilizada para atingir este objetivo. A formulação do problema de otimização de trajetória de uma aeronave envolve o modelo matemático do sistema (isto é, modelo de dinâmica, modelo de desempenho, e modelo de emissões de aeronaves), a função objetiva e os limites e restrições do sistema. Normalmente, o problema de otimização de trajetória é solucionado por uma ampla variedade de abordagens numéricas, que podem ser classificadas em três classes básicas de métodos numéricos: métodos indiretos, métodos diretos e programação dinâmica. Nesta tese, foram consideradas várias instâncias de problemas para otimizar trajetórias de aeronaves comerciais. Em primeiro lugar, foi considerado um problema de geração de trajetória ótima em 4D a partir de redes de waypoints predefinidas. Para tal, foi aplicado um algoritmo de single source shortest path (neste caso, algoritmo de Dijkstra), de forma a gerar trajetórias ótimas que minimizem o consumo de combustível da aeronave e o seu tempo total de viagem. O algoritmo de Dijkstra encontrou com sucesso a trajetória com menor custo, isto é, a trajetória de menor consumo de combustível e menor tempo total de viagem, a partir da rede predefinida de waypoints. Em seguida, foi considerado o problema de gerar uma trajetória ótima em 4D de comprimento mínimo ao longo de um conjunto de waypoints predefinidos. Para tal, foi utilizada uma parametrização da spline cúbica. O vetor de estado, a sua derivada e o vetor de controlo são parametrizados utilizando a interpolação cúbica da spline. Consequentemente, a função objetivo e as restrições são expressas como funções do valor de estado e controlo nos nós temporais. Esta representação transforma o problema de otimização de trajetória em um problema de programação não-linear, que por sua vez, é resolvido numericamente por um solucionador já bem estabelecido de programação não-linear. O método proposto gerou uma trajetória ótima em 4D com resultados precisos. Posteriormente, considerou-se o problema de geração de trajetórias ótimas em 4D entre dois waypoints. Para solucionar este problema foi utilizado a programação dinâmica que é um método numérico já bem estabelecido. A programação dinâmica apresenta algumas deficiências que impedem o seu uso em muitas aplicações práticas de tempo-real. Por isso, esta tese propõe uma abordagem de programação dinâmica modificada que reduz o esforço computacional e supera as desvantagens do Programação Dinâmica tradicional. A abordagem programação dinâmica modificada proposta, foi implementada com sucesso em vários casos de estudo, em que foram geradas trajetórias ótimas que minimizam o consumo de combustível da aeronave e as suas emissões. Estas trajetórias são, posteriormente, comparadas com a trajetória de voo comercial de referência, para quantificar a potencial redução do consumo de combustível da aeronave e das suas emissões. Os exemplos numéricos demonstram que a programação dinâmica modificada pode gerar com sucesso e com pouco esforço computacional trajetórias ótimas para o combustível e as emissões, o que sugere que este método pode ser aplicado em situações online, isto é, geração de trajetórias online. Por fim, foi considerado o problema de previsão da taxa temporal de consumo de combustível (FF) a partir de dados de voo reais. A rede neural da função de base radial (RBF) foi aplicada para prever a essa mesma taxa temporal nas fases de voo: subida, cruzeiro e descida. Na aplicação da rede neural RBF, a velocidade real e a altitude de voo foram consideradas como parâmetros de entrada e a FF foi considerada como parâmetro de saída. A rede neural RBF foi capaz de produzir um modelo adequado para estimar corretamente essa taxa temporal, com um elevado valor de coeficientes de determinação, juntamente com baixos valores nos erros relativos de aproximação. Posteriormente, este modelo de FF foi utilizado para resolver o problema de otimização de trajetórias em 4D, em que o custo total entre dois waypoints foi otimizado

Traffic synchronization with controlled time of arrival for cost-efficient trajectories in high-density terminal airspace

The growth in air traffic has led to a continuously growing environmental sensitivity in aviation, encouraging the research into methods for achieving a greener air transportation. In this context, continuous descent operations (CDOs) allow aircraft to follow an optimum flight path that delivers major environmental and economic benefits, giving as a result engine-idle descents from the cruise altitude to right before landing that reduce fuel consumption, pollutant emissions and noise nuisance. However, this type of operations suffers from a well-known drawback: the loss of predictability from the air traffic control (ATC) point of view in terms of overfly times at the different waypoints of the route. In consequence, ATC requires large separation buffers, thus reducing the capacity of the airport. Previous works investigating this issue showed that the ability to meet a controlled time of arrival (CTA) at a metering fix could enable CDOs while simultaneously maintaining airport throughput. In this context, more research is needed focusing on how modern arrival managers (AMANs)—and extended arrival managers (E-AMANs)—could provide support to select the appropriate CTA. ATC would be in charge to provide the CTA to the pilot, who would then use four-dimensional (4D) flight management system (FMS) trajectory management capabilities to satisfy it. A key transformation to achieve a more efficient aircraft scheduling is the use of new air traffic management (ATM) paradigms, such as the trajectory based operations (TBO) concept. This concept aims at completely removing open-loop vectoring and strategic constraints on the trajectories by efficiently implementing a 4D trajectory negotiation process to synchronize airborne and ground equipment with the aim of maximizing both flight efficiency and throughput. The main objective of this PhD thesis is to develop methods to efficiently schedule arrival aircraft in terminal airspace, together with concepts of operations compliant with the TBO concept. The simulated arrival trajectories generated for all the experiments conducted in this PhD thesis, to the maximum possible extent, are considered to be energy-neutral CDOs, seeking to reduce the overall environmental impact of aircraft operations in the ATM system. Ultimately, the objective of this PhD is to achieve a more efficient arrival management of traffic, in which higher levels of predictability and similar levels of capacity are achieved, while the safety of the operations is kept. The designed experiments consider a TBO environment, involving a high synchronization between all the involved actors of the ATM system. Higher levels of automation and information sharing are expected, together with a modernization of both current ATC ground-support tools and aircraft FMSs to comply with the new TBO paradigm.L’increment de tràfic aeri ha portat a una major sensibilitat mediambiental en l’aviació, motivant la recerca en mètodes per aconseguir un transport aeri més ecològic. En aquest context, les operacions de descens continu (CDOs) permeten a les aeronaus seguir una trajectòria que aporta grans beneficis econòmics i ambientals, donant com a resultat descensos amb els motors al ralentí des de l’altitud de creuer fins just abans d’aterrar. Aquestes trajectòries redueixen el consum de combustible, les emissions contaminants i el soroll generat per les aeronaus. No obstant això, aquest tipus d’operacions té un gran desavantatge: la pèrdua de predictibilitat des del punt de vista del controlador aeri (ATC) en termes de temps de pas als diferents punts de la ruta. Com a conseqüència, l’ATC necessita assignar una major separació entre les aeronaus, la qual cosa comporta una reducció en la capacitat de l’aeroport. Estudis previs investigant aquest problema han demostrat que la capacitat de complir amb un temps controlat d’arribada (CTA) a un punt de la ruta (utilitzat per seqüenciar les aeronaus) podria habilitar les CDOs tot mantenint la capacitat de l’aeroport. En aquest context, es necessita investigar més en com els gestors d’arribades (AMANs) i els gestors d’arribades ampliats (E-AMANs) podrien donar suport en la selecció de la CTA més adequada. L’ATC seria l’encarregat d’enviar la CTA al pilot, el qual, per tal de complir amb la CTA, faria servir la capacitat de gestió de trajectòries d’un sistema de gestió de vol (FMS) de quatre dimensions (4D). Una transformació clau per aconseguir una gestió més eficient del tràfic d’arribada és l’ús de nous paradigmes de gestió del tràfic aeri (ATM), com per exemple el concepte d’operacions basades en trajectòries (TBO). Aquest concepte té com a objectiu eliminar completament de les trajectòries la vectorització en “bucle obert” i les restriccions estratègiques. Per aconseguir-ho, es proposa implementar de manera eficient una negociació de la trajectòria 4D, amb l’objectiu de sincronitzar l’equipament de terra amb el de l’aeronau, maximitzant d’aquesta manera l’eficiència dels vols i la capacitat del sistema. El principal objectiu d’aquest doctorat és desenvolupar mètodes per gestionar aeronaus de manera eficient en espai aeri terminal, juntament amb conceptes d’operacions que compleixin amb el concepte de TBO. Les trajectòries d’arribada simulades per tots els experiments definits en aquesta tesi doctoral, en la mesura que s’ha pogut, són CDOs d’energia neutral. D’aquesta manera, la idea és reduir el màxim possible l’impacte mediambiental de les operacions aèries al sistema ATM. En definitiva, l’objectiu d’aquest doctorat és aconseguir una gestió del tràfic d’arribada més eficient, obtenint una major predictibilitat i capacitat, i assegurant que la seguretat de les operacions es manté. Els experiments dissenyats consideren una situació on el concepte de TBO és present, el que comporta una sincronització elevada entre tots els actors implicats en el sistema ATM. Així mateix, s’esperen nivells majors d’automatització i de compartició d’informació, juntament amb una modernització de les eines de suport en terra a l’ATC i dels FMSs de les aeronaus, tot amb l’objectiu de complir amb el nou paradigma de TBO.El incremento de tráfico aéreo ha llevado a una mayor sensibilidad medioambiental en la aviación, motivando la investigación de métodos para conseguir un transporte aéreo más ecológico. En este contexto, las operaciones de descenso continuo (CDOs) permiten a las aeronaves seguir una trayectoria que aporta grandes beneficios económicos y ambientales, dando como resultado descensos con los motores al ralentí desde la altitud de crucero hasta justo antes de aterrizar. Estas trayectorias reducen el consumo de combustible, las emisiones contaminantes y el ruido generado por las aeronaves. No obstante, este tipo de operaciones tiene una gran desventaja: la pérdida de predictibilidad desde el punto de vista del controlador aéreo (ATC) en términos de tiempos de paso en los diferentes puntos de la ruta. Como consecuencia, el ATC necesita asignar una mayor separación entre las aeronaves, lo cual comporta una reducción en la capacidad del aeropuerto. Estudios previos investigando este problema han demostrado que la capacidad de cumplir con un tiempo controlado de llegada (CTA) en un punto de la ruta (utilizado para secuenciar las aeronaves) podría habilitar las CDOs manteniendo al mismo tiempo la capacidad del aeropuerto. En este contexto, es necesario investigar más en cómo los gestores de llegadas (AMANs)—y los gestores de llegadas extendidos (E-AMANs)—podrían dar soporte en la selección de la CTA más adecuada. El ATC sería el encargado de enviar la CTA al piloto, el cual, para cumplir con la CTA, usaría la capacidad de gestión de trayectorias de un sistema de gestión de vuelo (FMS) de cuatro dimensiones (4D). Una transformación clave para conseguir una gestión más eficiente del tráfico de llegada es el uso de nuevos paradigmas de gestión del tráfico aéreo (ATM), como por ejemplo el concepto de operaciones basadas en trayectorias (TBO). Este concepto tiene como objetivo eliminar completamente de las trayectorias la vectorización en “bucle abierto” y las restricciones estratégicas. Para conseguirlo, se propone implementar de manera eficiente una negociación de la trayectoria 4D, con el objetivo de sincronizar el equipamiento de tierra con el de la aeronave, maximizando de esta manera la eficiencia de los vuelos y la capacidad del sistema. El principal objetivo de este doctorado es desarrollar métodos para gestionar aeronaves de manera eficiente en espacio aéreo terminal, junto con conceptos de operaciones que cumplan con el concepto de TBO. Las trayectorias de llegada simuladas para todos los experimentos definidos en esta tesis doctoral, en la medida de lo posible, son CDOs de energía neutra. De esta manera, la idea es reducir lo máximo posible el impacto medioambiental de las operaciones aéreas en el sistema ATM. En definitiva, el objetivo de este doctorado es conseguir una gestión del tráfico de llegada más eficiente, obteniendo una mayor predictibilidad y capacidad, y asegurando que la seguridad de las operaciones se mantiene. Los experimentos diseñados consideran una situación xxi donde el concepto de TBO está presente, lo que comporta una sincronización elevada entre todos los actores implicados en el sistema ATM. Asimismo, se esperan mayores niveles de automatización y de compartición de información, junto con una modernización de las herramientas de soporte en tierra al ATC y de los FMSs de las aeronaves, todo con el objetivo de cumplir con el nuevo paradigma de TBO. Primero de todo, se define un marco para la optimización de trayectorias utilizado para generar las trayectorias simuladas para los experimentos definidos en esta tesis doctoral. A continuación, se evalúan los beneficios de volar CDOs de energía neutra comparándolas con trayectorias reales obtenidas de datos de vuelo históricos. Se comparan dos fuentes de datos, concluyendo cuál es la más adecuada para estudios de eficiencia en espacio aéreo terminal. Las CDOs de energía neutra son el tipo preferido de trayectorias desde un punto de vista medioambiental pero, dependiendo de la cantidad de tráfico, podría ser imposible para el ATC asignar una CTA que pueda ser cumplida por las aeronaves mientras vuelan la ruta de llegada publicada. En esta tesis doctoral, se comparan dos estrategias con el objetivo de cumplir con la CTA asignada: volar CDOs de energía neutra por rutas más largas/cortas o volar descensos con el motor accionado por la ruta publicada. Para ambas estrategias, se analiza la sensibilidad del consumo de combustible a diferentes parámetros, como la altitud inicial de crucero o la velocidad del viento. Finalmente, en esta tesis doctoral se analizan dos estrategias para gestionar de manera eficiente el tráfico de llegada en espacio aéreo terminal. Primero, se utiliza una estrategia provisional a medio camino entre la negociación completa de trayectorias 4D y la vectorización en “bucle abierto”: se propone una metodología para gestionar de manera eficaz tráfico de llegada donde las aeronaves vuelan CDOs de energía neutra en un procedimiento de navegación de área (RNAV) conocido como trombón. A continuación, se propone una nueva metodología para generar rutas de llegada dinámicas que se adaptan automáticamente a la demanda actual de tráfico. De igual manera, se aplican CDOs de energía neutra a todo el tráfico de llegada. Hay diferentes factores a considerar que podrían limitar los beneficios de las soluciones propuestas. La cantidad y distribución del tráfico de llegada tiene un gran efecto sobre los resultados obtenidos, limitando en algunos casos una gestión eficiente de las aeronaves de llegada. Además, algunas de las soluciones propuestas comportan elevadas cargas computacionales que podrían limitar su aplicación operacional, motivando mayor investigación en el futuro con el fin de optimizar los modelos y metodologías utilizados. Finalmente, permitir a algunos aviones volar descensos con el motor accionado podría facilitar la gestión de las aeronaves de llegada en los experimentos que se centran en el procedimiento de trombón y en la generación de rutas de llegada dinámicas.Postprint (published version

4DT generator and guidance system

This thesis describes a 4D Trajectories Generator and Guidance system. 4D trajectory is a concept that will improve the capacity, efficiency and safety of airspace. First a 4D trajectories synthetizer design is proposed. A flight plan composed by a set of waypoints, aircraft dynamics model and a set of limits and constraints are assembled into an optimal control problem. Optimal solution is found by making use of an optimal control solver which uses pseudo spectral parametrization together with a generic nonlinear programming solver. A 4D Trajectories generator is implemented as a stand-alone application and combined with a graphic user interface to give rise to 4D Trajectories Research Software (4DT RS) capable to generate, compare and test optimal trajectories. A basic Tracking & Guidance system with proportional navigation concept is developed. The system is implemented as a complementary module for the 4D trajectories research software. Simulation tests have been carried out to demonstrate the functionalities and capabilities of the 4DT RS software and guidance system. Tests cases are based on fuel and time optimization on a high-traffic commercial route. A standard departure procedure is optimized in order to reduce the noise perceived by village’s population situated near airport. The tracking & guidance module is tested with a commercial flight simulator for demonstrating the performance of the optimal trajectories generated by the 4DT RS software

Time and Energy Managed Operations (TEMO): Cessna Citation II Flight Trials

From 9-26 October 2015 the Netherlands Aerospace Centre (NLR) in cooperation with Delft University of Technology (DUT) has executed Clean Sky flight trials with the Cessna Citation II research aircraft. The trials consisted of several descents and approaches at the Eelde airport near Groningen, demonstrating the TEMO (Time and Energy Managed Operations) concept developed in the Clean Sky Joint Technology Initiative research programme as part of the Systems for Green Operations (SGO) Integrated Technology Demonstrator. A TEMO descent aims to achieve an energy-managed idle-thrust continuous descent operation (CDO) while satisfying ATC time constraints, to maintain runway throughput. An optimal descent plan is calculated with an advanced on-board real-time aircraft trajectory optimisation algorithm considering forecasted weather and aircraft performance. The optimised descent plan was executed using the speed-on-elevator mode of an experimental Fly-By-Wire (FBW) system connected to the pitch servo motor of the Cessna Citation II aircraft. Several TEMO conceptual variants have been flown. It has been demonstrated that the TEMO concept enables arrival with timing errors below 10 seconds. The project was realised with the support of CONCORDE partners Universitat Politècnica de Catalunya (UPC) and PildoLabs from Barcelona, and the Royal Netherlands Meteorological Institute (KNMI).Peer ReviewedPostprint (published version

Multi-objective and multi-phase 4d trajectory optimization for climate mitigation-oriented flight planning

Aviation contribution to global warming and anthropogenic climate change is increasing every year. To reverse this trend, it is crucial to identify greener alternatives to current aviation technologies and paradigms. Research in aircraft operations can provide a swift response to new environmental requirements, being easier to exploit on current fleets. This paper presents the development of a multi-objective and multi-phase 4D trajectory optimization tool to be integrated within a Flight Management System of a commercial aircraft capable of performing 4D trajectory tracking in a Free Route Airspace context. The optimization algorithm is based on a Chebyshev pseudospectral method, adapted to perform a multi-objective optimization with the two objectives being the Direct Operating Cost and the climate cost of a climb-cruise-descent trajectory. The climate cost function applies the Global Warming Potential metric to derive a comprehensive cost index that includes the climate forcing produced by CO2 and non-CO2 emissions, and by the formation of aircraft-induced clouds. The output of the optimization tool is a set of Pareto-optimal 4D trajectories among which the aircraft operator can choose the best solution that satisfies both its economic and environmental goals

Robust aircraft trajectory optimization under meteorological uncertainty

Mención Internacional en el título de doctorThe Air Traffic Management (ATM) system in the busiest airspaces in the world is currently being overhauled to deal with multiple capacity, socioeconomic, and environmental challenges. One major pillar of this process is the shift towards a concept of operations centered on aircraft trajectories (called Trajectory-Based Operations or TBO in Europe) instead of rigid airspace structures. However, its successful implementation (and, thus, the realization of the associated improvements in ATM performance) rests on appropriate understanding and management of uncertainty. Due to its complex socio-technical structure, the design and operations of the ATM system are heavily impacted by uncertainty, proceeding from multiple sources and propagating through the interconnections between its subsystems. One major source of ATM uncertainty is weather. Due to its nonlinear and chaotic nature, a number of meteorological phenomena of interest cannot be forecasted with complete accuracy at arbitrary lead times, which leads to uncertainty or disruption in individual air and ground operations that propagates to all ATM processes. Therefore, in order to achieve the goals of SESAR and similar programs, it is necessary to deal with meteorological uncertainty at multiple scales, from the trajectory prediction and planning processes to flow and traffic management operations. This thesis addresses the problem of single-aircraft flight planning considering two important sources of meteorological uncertainty: wind prediction error and convective activity. As the actual wind field deviates from its forecast, the actual trajectory will diverge in time from the planned trajectory, generating uncertainty in arrival times, sector entry and exit times, and fuel burn. Convective activity also impacts trajectory predictability, as it leads pilots to deviate from their planned route, creating challenging situations for controllers. In this work, we aim to develop algorithms and methods for aircraft trajectory optimization that are able to integrate information about the uncertainty in these meteorological phenomena into the flight planning process at both pre-tactical (before departure) and tactical horizons (while the aircraft is airborne), in order to generate more efficient and predictable trajectories. To that end, we frame flight planning as an optimal control problem, modeling the motion of the aircraft with a point-mass model and the BADA performance model. Optimal control methods represent a flexible and general approach that has a long history of success in the aerospace field. As a numerical scheme, we use direct methods, which can deal with nonlinear systems of moderate and high-dimensional state spaces in a computationally manageable way. Nevertheless, while this framework is well-developed in the context of deterministic problems, the techniques for the solution of practical optimal control problems under uncertainty are not as mature, and the methods proposed in the literature are not applicable to the flight planning problem as it is now understood. The first contribution of this thesis addresses this challenge by introducing a framework for the solution of general nonlinear optimal control problems under parametric uncertainty. It is based on an ensemble trajectory scheme, where the trajectories of the system under multiple scenarios are considered simultaneously within the same dynamical system and the uncertain optimal control problem is turned into a large conventional optimal control problem that can be then solved by standard, well-studied direct methods in optimal control. We then employ this approach to solve the robust flight plan optimization problem at the planning horizon. In order to model uncertainty in the wind and estimating the probability of convective conditions, we employ Ensemble Prediction System (EPS) forecasts, which are composed by multiple predictions instead of a single deterministic one. The resulting method can be used to optimize flight plans for maximum expected efficiency according to the cost structure of the airline; additionally, predictability and exposure to convection can be incorporated as additional objectives. The inherent tradeoffs between these objectives can be assessed with this methodology. The second part of this thesis presents a solution for the rerouting of aircraft in uncertain convective weather scenarios at the tactical horizon. The uncertain motion of convective weather cells is represented with a stochastic model that has been developed from the output of a deterministic satellite-based nowcast product, Rapidly Developing Thunderstorms (RDT). A numerical optimal control framework, based on the pointmass model with the addition of turn dynamics, is employed for optimizing efficiency and predictability of the proposed trajectories in the presence of uncertainty about the future evolution of the storm. Finally, the optimization process is initialized by a randomized heuristic procedure that generates multiple starting points. The combined framework is able to explore and as exploit the space of solution trajectories in order to provide the pilot or the air traffic controller with a set of different suggested avoidance trajectories, as well as information about their expected cost and risk. The proposed methods are tested on example scenarios based on real data, showing how different user priorities lead to different flight plans and what tradeoffs are then present. These examples demonstrate that the solutions described in this thesis are adequate for the problems that have been formulated. In this way, the flight planning process can be enhanced to increase the efficiency and predictability of individual aircraft trajectories, which would lead to higher predictability levels of the ATM system and thus improvements in multiple performance indicators.El sistema de gestión del tráfico aéreo (Air Traffic Management, ATM) en los espacios aéreos más congestionados del mundo está siendo reformado para lidiar con múltiples desafíos socioeconómicos, medioambientales y de capacidad. Un pilar de este proceso es el gradual reemplazo de las estructuras rígidas de navegación, basadas en aerovías y waypoints, hacia las operaciones basadas en trayectorias. No obstante, la implementación exitosa de este concepto y la realización de las ganancias esperadas en rendimiento ATM requiere entender y gestionar apropiadamente la incertidumbre. Debido a su compleja estructura socio-técnica, el diseño y operaciones del sistema ATM se encuentran marcadamente influidos por la incertidumbre, que procede de múltiples fuentes y se propaga por las interacciones entre subsistemas y operadores humanos. Uno de los principales focos de incertidumbre en ATM es la meteorología. Debido a su naturaleza no-linear y caótica, muchos fenómenos de interés no pueden ser pronosticados con completa precisión en cualquier horizonte temporal, lo que crea disrupción en las operaciones en aire y tierra que se propaga a otros procesos de ATM. Por lo tanto, para lograr los objetivos de SESAR e iniciativas análogas, es imprescindible tener en cuenta la incertidumbre en múltiples escalas espaciotemporales, desde la predicción de trayectorias hasta la planificación de flujos y tráfico. Esta tesis aborda el problema de la planificación de vuelo de aeronaves individuales considerando dos fuentes importantes de incertidumbre meteorológica: el error en la predicción del viento y la actividad convectiva. Conforme la realización del viento se desvía de su previsión, la trayectoria real se desviará temporalmente de la planificada, lo que implica incertidumbre en tiempos de llegada a sectores y aeropuertos y en consumo de combustible. La actividad convectiva también tiene un impacto en la predictibilidad de las trayectorias, puesto que obliga a los pilotos a desviarse de sus planes de vuelo para evitarla, cambiado así la situación de tráfico. En este trabajo, buscamos desarrollar métodos y algoritmos para la optimización de trayectorias que puedan integrar información sobre la incertidumbre en estos fenómenos meteorológicos en el proceso de diseño de planes de vuelo en horizontes de planificación (antes del despegue) y tácticos (durante el vuelo), con el objetivo de generar trayectorias más eficientes y predecibles. Con este fin, formulamos la planificación de vuelo como un problema de control óptimo, modelando la dinámica del avión con un modelo de masa puntual y el modelo de rendimiento BADA. El control óptimo es un marco flexible y general con un largo historial de éxito en el campo de la ingeniería aeroespacial. Como método numérico, empleamos métodos directos, que son capaces de manejar sistemas dinámicos de alta dimensión con costes computacionales moderados. No obstante, si bien esta metodología es madura en contextos deterministas, la solución de problemas prácticas de control óptimo bajo incertidumbre en la literatura no está tan desarrollada, y los métodos propuestos en la literatura no son aplicables al problema de interés. La primera contribución de esta tesis hace frente a este reto mediante la introducción de un marco numérico para la resolución de problemas generales de control óptimo no-lineal bajo incertidumbre paramétrica. El núcleo de este método es un esquema de conjunto de trayectorias, en el que las trayectorias del sistema dinámico bajo múltiples escenarios son consideradas de forma simultánea, y el problema de control óptimo bajo incertidumbre es así transformado en un problema convencional que puede ser tratado mediante métodos existentes en control óptimo. A continuación, empleamos este método para resolver el problema de la planificación de vuelo robusta. La incertidumbre en el viento y la probabilidad de ocurrencia de condiciones convectivas son modeladas mediante el uso de previsiones de conjunto o ensemble, compuestas por múltiples predicciones en lugar de una única previsión determinista. Este método puede ser empleado para maximizar la eficiencia esperada de los planes de vuelo de acuerdo a la estructura de costes de la aerolínea; además, la predictibilidad de la trayectoria y la exposición a la convección pueden ser incorporadas como objetivos adicionales. El trade-off entre estos objetivos puede ser evaluado mediante la metodología propuesta. La segunda parte de la tesis presenta una solución para reconducir aviones en escenarios tormentosos en un horizonte táctico. La evolución de las células convectivas es representada con un modelo estocástico basado en las proyecciones de Rapidly Developing Thunderstorms (RDT), un sistema determinista basado en imágenes de satélite. Este modelo es empleado por un método de control óptimo numérico, basado en un modelo de masa puntual en el que se modela la dinámica de viraje, con el objetivo de maximizar la eficiencia y predictibilidad de la trayectoria en presencia de incertidumbre sobre la evolución futura de las tormentas. Finalmente, el proceso de optimizatión es inicializado por un método heurístico aleatorizado que genera múltiples puntos de inicio para las iteraciones del optimizador. Esta combinación permite explorar y explotar el espacio de trayectorias solución para proporcionar al piloto o al controlador un conjunto de trayectorias propuestas, así como información útil sobre su coste y el riesgo asociado. Los métodos propuestos son probados en escenarios de ejemplo basados en datos reales, ilustrando las diferentes opciones disponibles de acuerdo a las prioridades del planificador y demostrando que las soluciones descritas en esta tesis son adecuadas para los problemas que se han formulado. De este modo, es posible enriquecer el proceso de planificación de vuelo para incrementar la eficiencia y predictibilidad de las trayectorias individuales, lo que contribuiría a mejoras en el rendimiento del sistema ATM.These works have been financially supported by Universidad Carlos III de Madrid through a PIF scholarship; by Eurocontrol, through the HALA! Research Network grant 10-220210-C2; by the Spanish Ministry of Economy and Competitiveness (MINECO)'s R&D program, through the OptMet project (TRA2014-58413-C2-2-R); and by the European Commission's SESAR Horizon 2020 program, through the TBO-Met project (grant number 699294).Programa de Doctorado en Mecánica de Fluidos por la Universidad Carlos III de Madrid; la Universidad de Jaén; la Universidad de Zaragoza; la Universidad Nacional de Educación a Distancia; la Universidad Politécnica de Madrid y la Universidad Rovira iPresidente: Damián Rivas Rivas.- Secretario: Xavier Prats Menéndez.- Vocal: Benavar Sridha

En-Route Optimal Flight Planning Constrained to Pass Through Waypoints using MINLP

Abstract: In this paper we study the en-route strategic flight planning of a commercial aircraft constrained to pass through a set of waypoints whose sequence is not predefined. This problem has been solved as an hybrid optimal control problem in which, given the dynamic model of the aircraft, the initial and final states, the path constraints constituting the envelope of flight, and a set of waypoints in the European air space, one has to find the control inputs, the switching times, the optimal sequence of waypoints and the corresponding trajectory of the aircraft that minimize the direct operating cost during the flight. The complete layout of waypoints in the European airspace is reduced and waypoints are gathered into a small number of clusters. The aircraft is constrained to pass through one waypoint inside every cluster of waypoints. The presence of multi point constraints makes the optimal control problem particularly difficult to solve. The hybrid optimal control problem is converted into a mixed integer non linear programming problem first making the unknown switching times part of the state, then introducing binary variable to enforce the constraint of passing through one waypoint inside every cluster, and finally applying a direct collocation method. The resulting mixed integer non linear programming problem has been solved using a branch and bound algorithm. The cases studied and the numerical results show the effectiveness, efficiency and applicability of this method for enroute strategic flight plans definition