ORBIT TRANSFER OPTIMIZATION OF SPACECRAFT WITH IMPULSIVE THRUSTS USING GENETIC ALGORITHM A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES OF MIDDLE EAST TECHNICAL UNIVERSITY BY AHMET YILMAZ IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN MECHANICAL ENGINEERING SEPTEMBER 2012 Approval of the thesis: ORBIT TRANSFER OPTIMIZATION OF A SPACECRAFT WITH IMPULSIVE THRUST USING GENETIC ALGORITHM Submitted by AHMET YILMAZ in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Department, Middle East Technical University by, Prof. Dr. Canan Özgen Dean, Graduate School of Natural and Applied Sciences Prof. Dr. Süha Oral Head of Department, Mechanical Engineering Prof. Dr. M. Kemal Özgören Supervisor, Mechanical Engineering Dept., METU Examining Committee Members Prof. Dr. S. Kemal İder Mechanical Engineering Dept., METU Prof. Dr.M. Kemal Özgören Mechanical Engineering Dept., METU Prof. Dr. Ozan Tekinalp Aerospace Engineering Dept., METU Asst. Prof. Dr. Yiğit Yazıcıoğlu Mechanical Engineering Dept., METU Başar SEÇKİN, M.Sc. Roketsan Missile Industries Inc. Date: I hereby declare that all information in this document has been obtained and presented in accordance with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I have fully cited and referenced all material and results that are not original to this work. Name, Last name: Ahmet Yılmaz Signature : iii ABSTRACT ORBIT TRANSFER OPTIMIZATION OF A SPACECRAFT WITH IMPULSIVE THRUST USING GENETIC ALGORITHM Yılmaz, Ahmet M.S., Department of Mechanical Engineering Supervisor: Prof. Dr. M.Kemal Özgören September 2012, 127 pages This thesis addresses the orbit transfer optimization problem of a spacecraft. The optimal orbit transfer is the process of altering the orbit of a spacecraft with minimum propellant consumption. The spacecrafts are needed to realize orbit transfer to reach, change or keep its orbit. The spacecraft may be a satellite or the last stage of a launch vehicle that is operated at the exo-atmospheric region. In this study, a genetic algorithm based orbit transfer method has been developed. The applicability of genetic algorithm based orbit transfer method has been verified using orbit transfers which are optimal at specific cases. The solution to orbit transfer problem is also searched using steepest descent algorithm. While genetic algorithm can reach the optimal solution, steepest descent algorithm can reach optimal solution when a good initial prediction is provided. The effects of the initial orbital values on the orbit transfer solutions are also studied. Keywords: Orbit transfer, optimal orbit transfer, minimum propellant consumption, impulsive maneuvers, genetic algorithms. iv ÖZ GENETİK ALOGRİTMA KULLANILARAK BİR UZAY ARACININ DARBESEL İTKİYLE YÖRÜNGE TRANSFER OPTİMİZASYONU Yılmaz, Ahmet Yüksek Lisans, Makina Mühendisliği Bölümü Tez Yöneticisi: Prof. Dr. M.Kemal Özgören Eylül 2012, 127 sayfa Bu tez çalışması bir uzay aracının yörünge transfer eniyileme problemini içermektedir. Eniyilenmiş yörünge transferi asgari yakıt tüketimi ile uzay aracının yörüngesinin değiştirilmesidir. Uzay araçları yörüngeye erişmek, değiştirmek ve korumak amaçlı yörünge transferi gerçekleştirirler. Uzay aracı uydu ya da atmosfer dışı bölgede kullanılan uydu fırlatma aracı son kademesidir. Bu çalışmada bir genetik algoritma tabanlı yörünge transfer metodu geliştirilmiştir. Genetik algoritma tabanlı yörünge transfer yönteminin uygulanabilirliğinin belirli koşullarda eniyilenmiş yörünge transferleri kullanılarak doğrulanmıştır. Yörünge transfer problemine çözüm ayrıca ‘steepest descent’ algoritması ile de aranmıştır. Genetik algoritma eniyilenmiş sonuca ulaşabilirken, ‘steepest descent’ algoritması yanlızca iyi bir ilk tahmin sağlandığında eniyilenmiş sonuca ulaşabilmektedir. İlk yörünge değerlerinin yörünge transfer problem çözümüne etkileri de bu çalışmada incelenmiştir. Anahtar Kelimeler: Yörünge transferi, eniyilenmiş yörünge transferi, asgari yakıt tüketimi, darbeli manevra, genetik algoritma. v ACKNOWLEDGMENTS I would like to express sincere gratitude and thanks to my thesis supervisor Prof. Dr. M. Kemal Özgören for his invaluable guidance and encouragement throughout this study. I would also like to express my sincere appreciation to my colleagues in ROKETSAN who contributed to this thesis with valuable suggestions and comments. I would like to especially thank to İlke Akbulut, Başar Seçkin, Osman Yücel and Ezgi Civek. I can never thank enough my love İlkay Keneş, who has supported me with such remarkable patience and sensitivity. Without her love and patience, I could not handle these difficult months with that much ease. Very special thanks go to my family who has always supported me throughout my life. Their endless love, support and sacrifices have enabled this study’s completion. The work presented in this thesis could not have been accomplished without the support from many individuals. Finally, my thanks go to all those who are not specifically mentioned here. Ankara, 5 August 2012 Ahmet Yılmaz vi TABLE OF CONTENTS ABSTRACT ...................................................................................................... iv ÖZ .................................................................................................................. v ACKNOWLEDGMENTS ...................................................................................... vi TABLE OF CONTENTS ......................................................................................vii LIST OF TABLES ............................................................................................. xi LIST OF FIGURES ........................................................................................... xv LIST OF SYMBOLS ......................................................................................... xvii LIST OF ABBREVIATIONS ............................................................................. xviii CHAPTERS ....................................................................................................... 1 CHAPTER 1 INTRODUCTION ............................................................................................ 1 1.1 INTRODUCTION .............................................................................................1 1.2 MOTIVATION .................................................................................................4 1.3 LITERATURE SURVEY ......................................................................................6 1.4 SCOPE ......................................................................................................... 11 1.5 THESIS OUTLINE .......................................................................................... 12 CHAPTER 2 MATHEMATICAL MODEL .............................................................................. 13 2.1 ORBITAL ELEMENTS ..................................................................................... 13 2.2 ORBITAL MOTION ........................................................................................ 19 2.2.1 Kepler’s Laws ............................................................................................ 19 2.2.1.1 Kepler’s First Law ............................................................................... 19 2.2.1.2 Kepler’s Second Law .......................................................................... 20 2.2.1.3 Kepler’s Third Law ............................................................................. 22 2.2.2 Newton’s Law of Gravitational Attraction ..................................................... 23 vii 2.2.3 Two Body Problem .................................................................................... 24 2.2.4 Rocket Equation ........................................................................................ 26 2.2.5 Orbit Transfer Force Models ....................................................................... 29 2.2.5.1 Continuous Force Model ..................................................................... 29 2.2.5.2 Impulsive Force Model ........................................................................ 31 CHAPTER 3 ORBIT TRANSFER OPTIMIZATION PROBLEM ................................................ 37 3.1 OPTIMAL ORBIT TRANSFERS ......................................................................... 37 3.1.1 Hohmann Orbit Transfer (Coplanar Orbit Transfer) ....................................... 37 3.1.2 Only Inclination Change (OIC) Orbit Transfer .............................................. 41 3.2 ORBIT TRANSFER OPTIMIZATION PROBLEM .................................................. 44 3.3 OPTIMIZATION METHODS ............................................................................ 51 3.3.1 Genetic Algorithm ..................................................................................... 52 3.3.2 Steepest Descent Optimization Method ....................................................... 56 3.4 COMPARISON OF OPTIMIZATION METHODS FOR ORBIT TRANSFER OPTIMIZATION ....................................................................................................... 57 3.4.1 Problem-1 Coplanar Circular-Circular Orbit Transfer ..................................... 57 3.4.1.1 Application Of Genetic Algorithm Method To Problem-1 ......................... 59 3.4.1.2 Application Of Steepest Descent Algorithm To Problem-1 ...................... 60 3.4.2 Problem-2