DOCSLIB.ORG

Hybrid Optimal Control for Aircraft Trajectory Planning Literature Study

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Hybrid Optimal Control for Aircraft Trajectory Planning Literature Study G. Stolwijk A Hybrid Optimal Control Approach to Multi-Aircraft Formation Flying Master of Science Thesis II A Hybrid Optimal Control Approach to Multi-Aircraft Formation Flying Master of Science Thesis By G. Stolwijk in partial fulfilment of the requirements for the degree of Master of Science in Aerospace Engineering at the Delft University of Technology, to be defended publicly on Thursday November 30, 2017 at 2:00 PM. Supervisor: Dr. ir. S. Hartjes Thesis committee: Dr. ir. S. Hartjes, TU Delft Dr. ir. H.G. Visser TU Delft Dr. ir. E. van Kampen TU Delft This thesis is confidential and cannot be made public until November 30, 2017. An electronic version of this thesis is available at http://repository.tudelft.nl/. III IV Executive Summary With an expected rise in air traffic of 50% [1], new paradigms such as trajectory-based operations (TBO) are in development for air traffic control to enable more efficient aircraft trajectories. Because of this expected development, a great interest is currently shown in methods which can help determine the best trajectory for aircraft to fly given a certain optimization goal. The research field of aircraft trajectory optimization arose as a result, and in general studies in this field are based on optimal control theory using continuous variables. In this thesis, a Hybrid Optimal Control (HOC) framework which can be used in conjunction with existing optimal control software is presented. Hybrid optimal control theory aims to deal with systems that are both discrete time and continuous time from a mathematical perspective. The hybrid optimal control problem is “to find optimal hybrid – i.e., continuous and discrete – control trajectories such that an integral cost index – typically an integral of a function of the hybrid system state and control input – is minimized subject to the system dynamics, initial, terminal and further equality or inequality constraints” [2]. Much of the complexity of a hybrid optimal control problem depends on how much is known a priori about the switching structure between discrete states. A case study on multi-aircraft formation flying for civil aviation is chosen as an application to demonstrate the capabilities of the designed HOC method. In formation flight, trailing aircraft can experience a significant reduction in induced drag by ‘surfing’ the upwash of wing tip vortices generated by a leading aircraft. This in turn leads to a significant reduction in fuel burn for the trailing aircraft, making formation flight a more economical and environmentally friendly flying strategy. In previous research [3], the optimization of commercial flights for minimum fuel consumption was studied using multiple-phase trajectory optimization. However, only two-aircraft formations and three-aircraft formations with a fixed phase structure (the sequence in which aircraft join and leave the formation) are considered. By approaching this case as a hybrid optimal control problem, the phase structure can be left open as a discrete optimization parameter, enabling larger and more optimal formation trajectories. The existing software GPOPS [4], which is already capable of solving multiple-phase optimal control problems, is used as a basis for the developed HOC method. An efficient algorithm for the evaluation of the discrete solution space of the HOC problem, essentially all possible phase structures, is developed through implementation of a branch-and-bound method. In this approach, the discrete solution space is categorized in a tree structure where each tree level represents an additional discrete variable. The algorithm then only evaluates ‘branches’ which show promising characteristics, while ‘chopping’ the other branches. This way, a significant computation time reduction is achieved since a major part of the discrete solution space can be discarded. An initial guess adaptation method which translates trajectories to a correct initial guess for a given phase structure is also developed, as well as an implementation of multi-threaded computing. V The aircraft dynamics are evaluated as a reduced-order point mass model, with the formation flight phases using a single point, multiple mass model to accommodate the presence of multiple aircraft. The induced drag benefit for trailing aircraft is modelled in the aircraft dynamics by implementing a static reduction factor for each trailing aircraft in the relevant formation phases. All phases are connected appropriately using linkage constraints for the state vectors of the linked phases. The used aircraft model characteristics are based on the Boeing 747-400 aircraft. In several case studies, both a three-aircraft and a four-aircraft transatlantic formation flight scenario are evaluated using the developed HOC tool. The three-aircraft case yields a 4,74% overall reduction in fuel burn, while the four-aircraft case yields an 8.90% reduction. However, when using more pessimistic values for the induced drag reduction (50% less benefit), the fuel burn saving for the four-aircraft case is reduced to 3.48%. The fuel burn reduction also comes at the expense of flight time, since aircraft have to make a detour to join the formation. A three-aircraft case with existing scheduled flights to New York (JFK) is also evaluated, and yields an 11.47% fuel burn saving, a higher value because no significant detours have to be flown. In all experiments, a suboptimality is identified because the aircraft order in the formation is not part of the optimization. An alternative method for evaluating the fuel burn for the cruise formation phase, by using an analytical Bréguet range equation instead of a dynamic model is also tested. This method yields promising results; no significant deviation is observed in the fuel burn values compared to the point-mass dynamic model. However, the method turns out to be less computationally efficient for GPOPS. It is found that the developed tool is efficient and functional at evaluating the HOC problem of multi-aircraft formation flight trajectory optimization. Even for the four-aircraft experiments, computation time remains within practical limits at 5 hours. The convergence behavior of GPOPS is identified to be heavily influenced by the accuracy of the adapted initial guess. However, the robustness of the developed HOC tool leaves room for improvement. To conclude, it is found that the usefulness of a HOC approach is very high for the chosen application of trajectory optimization for multi-aircraft formation flying, since a promising fuel saving potential is identified. Given the number of flights that are performed every day, the impact of saving fuel just by optimizing their trajectories using formation flying can be very high on a global scale, both environmentally and economically. VI Table of Contents Executive Summary .................................................................................................................................... V List of Figures .............................................................................................................................................. IX List of Tables ............................................................................................................................................... XI List of Abbreviations .............................................................................................................................. XIII Nomenclature ........................................................................................................................................... XV 1 Introduction .......................................................................................................................................... 1 1.1 Hybrid Optimal Control ............................................................................................................................ 1 1.2 Formation Flying in Civil Aviation ......................................................................................................... 2 1.3 Optimization software .............................................................................................................................. 3 1.4 Research Proposal ..................................................................................................................................... 4 1.5 Thesis Structure .......................................................................................................................................... 5 2 Optimization using hybrid optimal control ............................................................................... 7 2.1 Conventional optimal control and numerical methods review .................................................. 7 2.2 Hybrid Optimal Control Theory .......................................................................................................... 13 2.3 Overview of recent aviation research involving hybrid optimal control ............................... 16 2.4 Analysis of currently common HOC problem-solving techniques ......................................... 18 3 Formation flight and its application for civil aviation ........................................................... 27 3.1 Aerodynamic concept ............................................................................................................................ 27 3.2 Positioning between aircraft in formation ....................................................................................... 28 4 Optimization problem description
Load more

Recommended publications
  • Aviation Week & Space Technology
    STARTS AFTER PAGE 34 Using AI To Boost How Emirates Is Extending ATM Efficiency Maintenance Intervals ™ $14.95 JANUARY 13-26, 2020 2020 THE YEAR OF SUSTAINABILITY RICH MEDIA EXCLUSIVE Digital Edition Copyright Notice The content contained in this digital edition (“Digital Material”), as well as its selection and arrangement, is owned by Informa. and its affiliated companies, licensors, and suppliers, and is protected by their respective copyright, trademark and other proprietary rights. Upon payment of the subscription price, if applicable, you are hereby authorized to view, download, copy, and print Digital Material solely for your own personal, non-commercial use, provided that by doing any of the foregoing, you acknowledge that (i) you do not and will not acquire any ownership rights of any kind in the Digital Material or any portion thereof, (ii) you must preserve all copyright and other proprietary notices included in any downloaded Digital Material, and (iii) you must comply in all respects with the use restrictions set forth below and in the Informa Privacy Policy and the Informa Terms of Use (the “Use Restrictions”), each of which is hereby incorporated by reference. Any use not in accordance with, and any failure to comply fully with, the Use Restrictions is expressly prohibited by law, and may result in severe civil and criminal penalties. Violators will be prosecuted to the maximum possible extent. You may not modify, publish, license, transmit (including by way of email, facsimile or other electronic means), transfer, sell, reproduce (including by copying or posting on any network computer), create derivative works from, display, store, or in any way exploit, broadcast, disseminate or distribute, in any format or media of any kind, any of the Digital Material, in whole or in part, without the express prior written consent of Informa.
    [Show full text]
  • Optimisation of Aircraft Position in the Formation Flight for the Drag Reduction
    Journal of KONES Powertrain and Transport, Vol. 25, No. 3 2018 ISSN: 1231-4005 e-ISSN: 2354-0133 DOI: 10.5604/01.3001.0012.4312 OPTIMISATION OF AIRCRAFT POSITION IN THE FORMATION FLIGHT FOR THE DRAG REDUCTION Adam Antczak, Krzysztof Sibilski Warsaw University of Technology Faculty of Power and Aeronautical Engineering Nowowiejska Street 24, 00-665 Warsaw, Poland e-mail: [email protected], [email protected] Abstract This article presents optimisation of necessary flight thrust in a V-shaped flight formation of small-unmanned plane “Sikorka”. At the beginning is showed analyse of birds behaviour. Their formation flying was the cause of attention in order to minimalize fuel consumption. Afterwards there are overlooked scientific articles about the formation flying subject contain pure physic analyses, and articles about researches which was made in order to explain economic beneficial for airlines. Thus, the article presents mathematical model, which was optimised for three different starting position of a longitudinal axis. After optimisation there are presented results of the wingman position in regard of the leader. Influence of the calculation results on the formation flying was analysed, allowing for some conclusions about the future of the UAV’s flights. The given process is aimed to achieve the best (optimal) solution from the point of view of the specific criterion. The following most important terms can be distinguished within the optimization process: decisive variables – parameters determining the basic project assumptions. The basic design variables and design constrains are described. Keywords: UAV, formation flying, optimisation, dynamic of flight, aerodynamic 1. Introduction In order to engage a client airlines around the world have always been forced not only to offer the highest quality of their services but first of all the most profit able price of a ticket.
    [Show full text]
  • Global Challenges
    6–10 JANUARY 2020 | ORLANDO, FL DRIVING AEROSPACE SOLUTIONS FOR GLOBAL CHALLENGES What’s going on in Page 25 aiaa.org/scitech #aiaaSciTech From the forefront of innovation to the frontlines of the mission. No matter the mission, Lockheed Martin uses a proven approach: engineer with purpose, innovate with passion and define the future. We take time to understand our customer’s challenges and provide solutions that help them keep the world secure. Their mission defines our purpose. Learn more at lockheedmartin.com. © 2019 Lockheed Martin Corporation FG19-23960_002 AIAA sponsorship.indd 1 12/10/19 3:20 PM Live: n/a Trim: H: 8.5in W: 11in Job Number: FG18-23208_002 Bleed: .25 all around Designer: Kevin Gray Publication: AIAA Sponsorship Gutter: None Communicator: Ryan Alford Visual: Male and female in front of screens. Resolution: 300 DPI Due Date: 12/10/19 Country: USA Density: 300 Color Space: CMYK NETWORK NAME: SciTech ON-SITE Wi-Fi From the forefront of innovation › PASSWORD: 2020scitech to the frontlines of the mission. CONTENTS Technical Program Committee .................................................................4 Welcome ........................................................................................................5 Sponsors and Supporters ..........................................................................7 Forum Overview ...........................................................................................8 Pre-Forum Activities .................................................................................
    [Show full text]
  • Extracurricular Projects Enhance Student Learning Page 18 Four New Faculty Join AE Page 4
    Newsletter of the Department of Aerospace Engineering University of Illinois at Urbana-Champaign Vol. 16 • 2014 Extracurricular Projects Enhance Student Learning PAGE 18 Four New Faculty Join AE PAGE 4 AE to Gain Composites Manufacturing, Nanosatellite Labs PAGE 15 AE Begins Online MS Degree Program PAGE 16 Inside Welcome to the 2014 Edition Faculty News of the Alumni Newsletter of Four New Faculty Join AE at Illinois ..............................4 AE at Illinois Hilton Made Fellow of ASC ....................................7 Chew: Searching the Small for the Strong and the Tough .............8 At the start of a new academic year, I am delighted Campus Recognizes Geubelle for Guiding Undergraduate Research .....9 to report that four new faculty members will join AE Selig Selected for AIAA 2014 Aerodynamics Award .................10 during the 2014-15 academic year and reinforce our Dutton, Jeffers, Gain Teacher, Staff of the Year Awards ..............10 strength in research and teaching in computational Bodony Named Blue Waters Associate Professor; AIAA Associate Fellow . 11 fluid dynamics (CFD) and applied aerodynamics. Dr. Chung Named Center for Advanced Study Fellow; Recognized for Deborah Levin (PhD Caltech, 1979) is a recognized Research ..............................................11 White Achieves International Recognition world leader in the area of computational multi-phys- for Research; Earns Local Honors for Graduate Student Mentoring ...12 ics modeling of reacting and plasma flows, such as Conway Retires; Continues Research, Teaching ....................13 those encountered in hypersonic and reentry vehicles Elliott Wins 2014 Pierce Award ................................13 under extremely high Mach numbers. Dr. Vincent Le Freund Organizes/Chairs Symposium ............................13 Chenadec brings his unique expertise in computa- Lambros Wins Frocht Award ..................................14 tional combustion, and Dr.
    [Show full text]
  • Singapore Aerospace
    SINGAPORE AEROSPACE 2017 MROs - OEMs - Engineering - R&D - Aviation - Satellites SINGAPORE AEROSPACE 2017 SINGAPORE AEROSPACE Dear Reader, This is the first time Global Business Reports has developed an has been coupled with the presence of a growing base of both local aerospace report on Singapore. We are pleased to have worked and multinational aerospace suppliers such as RLC Engineering with the team to showcase Singapore’s strength as an air hub and and Singapore Aerospace Manufacturing (SAM). the various industry players across the value chain within our aerospace sector. As you read through the pages of this report, we Many companies have cited Singapore’s strong manufacturing hope that it not only gives you a better understanding of the sector base, skilled manpower and focus on science and engineering but also an idea of how Singapore can be your trusted location as reasons for setting up manufacturing activities here. The from which to write your Asia growth story. burgeoning aerospace R&D landscape in Singapore, that taps into our existing strengths in science and technology research In the span of time since Changi Airport first opened in 1981, capabilities, further allows companies to leverage industry- Singapore has achieved a strong reputation as a Global Aviation aligned research institutes and universities as well as a growing Hub. With over 500 accolades, Changi Airport is widely pool of research talent to enhance their manufacturing and MRO recognised as one of the world’s best international airports. activities through innovation. Singapore Airlines has likewise become a widely known brand. Building on our strengths as an air hub, Singapore has developed With the increasing adoption of disruptive technologies such a leading aerospace industry that includes manufacturing, as robotics and automation, additive manufacturing, digital engineering, research and development (R&D), maintenance, manufacturing and the emergence of new business segments such repair and overhaul (MRO), and other aerospace-related services.
    [Show full text]
  • Multiple-Phase Trajectory Optimization for Formation Flight in Civil Aviation Master of Science Thesis M.E.G
    Multiple-Phase Trajectory Optimization for Formation Flight in Civil Aviation Master of Science Thesis M.E.G. van Hellenberg Hubar Technische Universiteit Delft Cover photo: Copyright AIRBUS S.A.S. 2014 – photo by S.Ramadier (http://aviationweek.com/blog/photo-airbus-a350-formation-flight) Multiple-Phase Trajectory Optimization for Formation Flight in Civil Aviation Master of Science Thesis by M.E.G. van Hellenberg Hubar in partial fulfillment of the requirements for the degree of Master of Science in Aerospace Engineering at the Delft University of Technology, to be defended publicly on Tuesday July 19, 2016 at 2:00 PM. Supervisor (Primary): Dr. ir. H.G. Visser Supervisor (Secondary): Dr. ir. S. Hartjes Thesis committee: Dr. ir. H.G. Visser TU Delft Dr. ir. S. Hartjes TU Delft Dr. ir. E. van Kampen TU Delft This thesis is confidential and cannot be made public until July 19, 2016. An electronic version of this thesis is available at http://repository.tudelft.nl/. Summary In this research the focus is on developing a tool that can optimize multiple-phase trajectories for com- mercial formation flights for minimum fuel consumption. In the past years, research has been conducted into formation flight and trajectory optimization, but not as a combined entity. Researchers have in- vestigated the aerodynamics behind formation flight and conducted flight tests to validate their results. The results show that a significant reduction in induced drag of 10-50% can be obtained for the trailing aircraft in a formation. Others, investigated the optimal routing for commercial aircraft and what the savings of formation flight could be when applied to certain flights.
    [Show full text]
  • Optimisation of Aircraft Position in the Formation Flight for the Drag Reduction
    Journal of KONES Powertrain and Transport, Vol. 25, No. 3 2018 ISSN: 1231-4005 e-ISSN: 2354-0133 DOI: 10.5604/01.3001.0012.4312 OPTIMISATION OF AIRCRAFT POSITION IN THE FORMATION FLIGHT FOR THE DRAG REDUCTION Adam Antczak, Krzysztof Sibilski Warsaw University of Technology Faculty of Power and Aeronautical Engineering Nowowiejska Street 24, 00-665 Warsaw, Poland e-mail: [email protected], [email protected] Abstract This article presents optimisation of necessary flight thrust in a V-shaped flight formation of small-unmanned plane “Sikorka”. At the beginning is showed analyse of birds behaviour. Their formation flying was the cause of attention in order to minimalize fuel consumption. Afterwards there are overlooked scientific articles about the formation flying subject contain pure physic analyses, and articles about researches which was made in order to explain economic beneficial for airlines. Thus, the article presents mathematical model, which was optimised for three different starting position of a longitudinal axis. After optimisation there are presented results of the wingman position in regard of the leader. Influence of the calculation results on the formation flying was analysed, allowing for some conclusions about the future of the UAV’s flights. The given process is aimed to achieve the best (optimal) solution from the point of view of the specific criterion. The following most important terms can be distinguished within the optimization process: decisive variables – parameters determining the basic project assumptions. The basic design variables and design constrains are described. Keywords: UAV, formation flying, optimisation, dynamic of flight, aerodynamic 1. Introduction In order to engage a client airlines around the world have always been forced not only to offer the highest quality of their services but first of all the most profit able price of a ticket.
    [Show full text]