ISTANBUL TECHNICAL UNIVERSITY FACULTY OF AERONAUTICS AND ASTRONAUTICS DEVELOPMENT OF A RENDEZVOUS AND DOCKING SIMULATION GRADUATION PROJECT Utkan GÜDER Department of Astronautical Engineering Thesis Advisor: Dr. Öğr. Üyesi Cuma YARIM MARCH, 2021 ISTANBUL TECHNICAL UNIVERSITY FACULTY OF AERONAUTICS AND ASTRONAUTICS DEVELOPMENT OF A RENDEZVOUS AND DOCKING SIMULATION GRADUATION PROJECT Utkan GÜDER (110140129) Department of Astronautical Engineering Thesis Advisor: Dr. Öğr. Üyesi Cuma YARIM MARCH, 2021 ii Utkan Güder, student of ITU Faculty of Aeronautics and Astronautics student ID 110140129, successfully defended the graduation entitled “DEVELOPMENT OF A RENDEZVOUS AND DOCKING SIMULATION”, which he prepared after fulfilling the requirements specified in the associated legislations, before the jury whose signatures are below. Thesis Advisor : Dr. Öğr. Üyesi Cuma YARIM .............................. İstanbul Technical University Jury Members : Date of Submission : 10.06.2021 Date of Defense : iii FOREWORD Even though my main interests have shifted towards software programming and computer graphics over the years of being an astronautical student, I have always been interested in orbital mechanics since I have began studying. Hence the topic of my thesis that I hope someone will find it useful or inspiring, although I have worked full-time while writing it. March 2021 Utkan Güder iv TABLE OF CONTENTS Page FOREWORD ............................................................................................................. iv TABLE OF CONTENTS ........................................................................................... v LIST OF ABBREVIATIONS .................................................................................. vi LIST OF TABLES ................................................................................................... vii LIST OF FIGURES ................................................................................................ viii SUMMARY ............................................................................................................... ix 1. INTRODUCTION .................................................................................................. 1 1.1 Purpose of Thesis ............................................................................................... 1 1.2 Literature Review ............................................................................................... 1 2. MANEUVERING IN SPACE ............................................................................... 5 2.1 Rendezvous Phase .............................................................................................. 5 2.1.1 Orbital Insertions ......................................................................................... 5 2.1.2 Rendezvous Calculations ............................................................................ 9 2.2 Docking Phase .................................................................................................. 13 3. SIMULATION ..................................................................................................... 16 3.1 Development .................................................................................................... 16 3.1.1 Tools .......................................................................................................... 16 3.1.2 Calculations ............................................................................................... 17 3.2 Graphical Interface ........................................................................................... 21 3.3 Example Scenario ............................................................................................. 24 4. CONCLUSION ..................................................................................................... 26 v LIST OF ABBREVIATIONS R&D : Rendezvous and Docking ISS : International Space Station EOR : Earth Orbit Rendezvous LOR : Lunar Orbit Rendezvous ECI : Earth-Centered Inertial vi LIST OF TABLES Page Table 2.1 : ΔVs for the Hohmann transfer to ISS ....................................................... 7 Table 2.2 : Final phase angles for different altititudes .............................................. 10 vii LIST OF FIGURES Page Figure 2.1 : Hohmann Transfer ................................................................................... 6 Figure 2.2 : Bi-elliptic Transfer .................................................................................. 7 Figure 2.3 : Bi-elliptic Transfer for an ISS Rendezvous Mission ............................... 8 Figure 2.4 : Final Phase Angle and Lead Angle ....................................................... 10 Figure 2.5 : Possible Phase Angles for a Bi-elliptic Transfer to ISS ........................ 12 Figure 2.6 : Wait Times for Angle Differences to ISS ............................................. 13 Figure 2.7 : ISS Relocation Corridor for a Russian Vehicle ..................................... 14 Figure 3.1 : Matrix Multiplications for the Initial State Vectors .............................. 18 Figure 3.2 : Obtaining Position or Velocity Vectors ................................................. 19 Figure 3.3 : Applying the Calculated Maneuver ....................................................... 20 Figure 3.4 : Rendezvous Planning ............................................................................ 21 Figure 3.5 : Start and Custom Paramter Menu .......................................................... 22 Figure 3.6 : Focus Panel ............................................................................................ 22 Figure 3.7 : Time and Transfer Panels ...................................................................... 23 Figure 3.8 : Spacecraft Calculating for the Next Rendezvous .................................. 25 Figure 3.8 : The Spacecraft in Docking Mode, Parked Near the ISS ....................... 25 viii DEVELOPMENT OF A RENDEZVOUS AND DOCKING SIMULATION SUMMARY This thesis covers the development and usage of an orbital simulation in the Unity Engine where a rendezvous and docking (R&D) operation takes place to the International Space Station (ISS) from a circular orbit around the Earth. It discusses the usage and short history of R&D, its methods and how it is implemented to this specific software in which some constraints and assumptions on certain conditions are made. The main use of the program is to visualize a Hohmann transfer to the ISS’s orbit from a user defined circular orbit. It enables the user to plan an engine burn, with a start and end shown on the orbit, where the delta-V required for orbit matching and the time of the maneuver is calculated. This is done by finding the wait time between the two vehicles, for them to enter the correct phase, and is further optimized by taking the burn time into account and finding the closest approach via a simple iteration from its maneuver start position. However, the software does not find the most efficient maneuver, either in fuel consuption or duration, but rather shows how a transfer could be done from the given state of both the spacecraft and the ISS. The spacecraft in discussion is visualized as a Soyuz vehicle, which is one of the most frequent visitors to the ISS. This thesis could be divided into two parts where the first part touches on R&D and what aspects of it are applied to this project while the second part refers to the software, in which the development and use of the program is discussed. This includes information about the Unity Engine, a game engine that is used in a variety of fields and provides some useful tools to create the environment. The code is written in C#, an object oriented programming language, that Unity supports. This part also contains a guide on how to use the software and an example R&D mission. ix ÖZET Bu tez, Dünya etrafında dairesel bir yörüngeden, Uluslararası Uzay İstasyonuna bir randevu ve kenetlenme görevinin Unity motorunda geliştirilmesi ve kullanımı hakkındadır. Bu tip görevlerin tarihçesinden başlayarak, nasıl uygulandıklarını ve programa nasıl entegre edildiğine de değinir. Özetle program, kullanıcının tanımladığı dairesel bir yörüngeden uzay istasyonuna tek bir Hohmann transferi ile nasıl gidilebileceğini hesaplar ve gösterir. Bununla birlikte, daha yüksek bir yörüngeye bir manevra hesaplaması da mümkün. Görevin ilk aşaması gereken delta- v ve motorun çalıştırılması gereken anları gösterirken, ikinci aşamada kenetlenme için aracın istasyona doğru navigasyonunu kullanıcıya bırakır. Görseller için, Uluslararası Uzay İstasyonunu en sık ziyaret eden araçlardan biri olan Soyuz aracı tercih edildi. Tez iki genel olarak iki kısımdan oluşur. İlki yörünge hareketlerinden ve bir randevu görevi için yapılabilecek manevralardan bahseder. Bunlar tek ya da çift Hohmann transferlerinin farklı yörüngelerden uygulanmasını ve manevralar arası farkları ele alır. Ikinci bölüm ise programın geliştirilmesi ve yazılımın kullanılışının anlatıldığı kısımdır. Bu, çeşitli alanlarda kullanılan ve ortamı oluşturmak için bazı yararlı araçlar sağlayan bir oyun motoru olan Unity Engine hakkında bilgileri içerir. Kod, Unity'nin desteklediği nesne yönelimli bir programlama dili olan C# ile yazılmıştır. Ayrıca örnek bir görevin nasıl uygulanabileceği de mevcuttur. x 1. INTRODUCTION 1.1 Purpose of Thesis The main objective of this thesis is to create a readable visualization of a rendezvous and docking operation. This simulation does not cover rendezvous