타원 궤도에서의 인공위성 군집비행을 위한 주기적 상대운동과 군집형상 변경에의 적용

학위논문 (박사)-- 서울대학교 대학원 : 기계항공공학부, 2012. 8. 김유단.Spacecraft formation flying has been widely investigated due to increasing interests in designing clusters around a planet and its applications including rendezvous and maneuver. Multiple spacecraft in formation have many advantages such as cooperative mission execution, reduced cost, flexible configuration, and robustness. Nonlinear relative motion and periodicity condition in elliptic orbits are required to achieve the precise and efficient formation flying and reconfiguration. This dissertation presents periodic relative motion, formation pattern analysis, and spacecraft maneuvers for the formation reconfiguration in elliptic reference orbits. The major achievement of this study is to present a general periodic condition which guarantees the bounded relative motion of spacecraft formation flying in elliptic orbits. The periodic condition of the circular orbit is easily obtained from the analytic solution of the Hill-Clohessy-Wiltshire equation. For the elliptic orbits, however, the periodic condition is restrictively described in near circular orbits and elliptic orbits at a specific initial position by the Tschauner-Hempel equation due to complex and coupled relative motion dynamics. In this dissertation, the general periodicity condition is derived using two analytic approaches: the first one based on the state transition matrix, and the second one based on the energy matching condition. Furthermore, the offset condition is investigated to make the leader spacecraft locate at the center of the formation geometry. As a result, the periodic relative motion is developed to remove the secular drift and the offset in the along-track direction. Numerical simulations verify that this periodic condition covers partial periodicity condition of previous studies. The periodic relative motion provides a substantial advantage in the sense that an additional correction is not required with respect to the initial position of the follower spacecraft. The second accomplishment is to design the formation geometry and to analyze the formation pattern in the elliptic reference orbit. From understanding the natural formation geometry, the spacecraft can remarkably reduce the fuel consumption. The formation design method for circular or nearly circular orbits has been describedhowever, the formation design and analysis in the elliptic orbits have not been extensively studied due to the nonlinearity and eccentricity. In this dissertation, two formation geometries in the elliptic orbit are designed by considering natural periodic relative motion: radial/along-track plane formation and along-track/cross-track plane formation. The formation patterns including the relative trajectory, velocity, and formation radius are analyzed with respect to the variation of eccentricity. The eccentricity of the reference orbit is a critical factor influencing on the variation of formation radius between two spacecraft in the relative motion. With the understanding of formation flying in elliptic orbits, the spacecraft maneuver problem for the formation reconfiguration is investigated considering two types of control input: continuous control input and impulsive control input. The formation configuration should be changeable according to the mission requirements and environments during the operation. The follower spacecraft changes the formation radius or the formation geometry with respect to the leader spacecraft, while minimizing the control effort. For the continuous control input, the optimal control problem in the relative motion is solved by the Gauss pseudospectral method, where the initial and final relative positions and velocities are specified. The optimal trajectories between the radial/along-track plane and the along-track/cross-track plane are provided using the minimum energy and minimum fuel cost functions. For the impulsive control input, the Lambert's problem is modified to construct the transfer problem in the relative motion, given two position vectors at the initial and final time and the flight time. In addition, the minimum velocity change for transferring orbits is designed through the grid search. The results of this research establish that the periodic relative motion is presented at an arbitrary true anomaly in the elliptic reference orbit, the formation geometries are designed and analyzed to reflect the eccentricity of the reference orbit, and the formation reconfiguration is described using two control input types. These results can provide the effective and efficient formation flying in elliptic reference orbits.Chapter 1 Introduction 1 1.1 Background and Motivation 1 1.2 Literature Survey 5 1.3 Contribution 13 1.4 Dissertation Outline . . . . . . . . . . . . . . . . . . . . . . . . 15 Chapter 2 Celestial Mechanics and Relative Motion Dynamics . . . . . . . . . . 18 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2 Reference Frame . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.1 Earth Centered Inertial Frame . . . . . . . . . . . . . . 19 2.2.2 Earth Centered Earth Fixed Frame . . . . . . . . . . . . 20 2.2.3 Local Vertical Local Horizontal Frame . . . . . . . . . . 21 2.3 Orbital Elements . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.4 Relative Motion Dynamics . . . . . . . . . . . . . . . . . . . . . 24 2.4.1 Hill-Clohessy-Wiltshire Equation . . . . . . . . . . . . . 27 2.4.2 Tschauner-Hempel Equation . . . . . . . . . . . . . . . 28 2.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . 30 Chapter 3 General Periodicity Condition . . . . . . . . . . . . . . . . . . . . . . 31 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 State Transition Matrix Approach . . . . . . . . . . . . . . . . 32 3.3 Energy Matching Condition Approach . . . . . . . . . . . . . . 42 3.4 Analytic Periodic Solution . . . . . . . . . . . . . . . . . . . . . 45 3.5 Numerical Simulation . . . . . . . . . . . . . . . . . . . . . . . 46 3.5.1 Radial/Along-Track Plane Formation . . . . . . . . . . 47 3.5.2 Along-Track/Cross-Track Plane Formation . . . . . . . 50 3.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . 53 Chapter 4 Formation Pattern Analysis and Design . . . . . . . . . . . . . . . . 54 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.2 Periodic Relative Motion . . . . . . . . . . . . . . . . . . . . . . 56 4.3 Radial/Along-Track Plane Formation . . . . . . . . . . . . . . . 58 4.4 Along-Track/Cross-Track Plane Formation . . . . . . . . . . . . 62 4.4.1 Along-Track/Cross-Track Plane Formation under D21 = D22 . . . . . . 62 4.4.2 Along-Track/Cross-Track Plane Formation under 4D21 =D22 . . . . . . 66 4.5 Numerical Simulation . . . . . . . . . . . . . . . . . . . . . . . 70 4.5.1 Radial/Along-Track Plane Formation . . . . . . . . . . 71 4.5.2 Along-Track/Cross-Track Plane Formation . . . . . . . 75 4.5.3 Angle Difference between Two Follower Spacecraft . . . 78 4.5.4 Pattern Analysis of the Spacecraft Formation . . . . . . 85 4.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . 88 Chapter 5 Maneuver for Formation Reconfiguration . . . . . . . . . . . . . . . . 89 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.2 Maneuver for Spacecraft Formation . . . . . . . . . . . . . . . . 91 5.3 Continuous Control Input . . . . . . . . . . . . . . . . . . . . . 94 5.3.1 Dynamic Model . . . . . . . . . . . . . . . . . . . . . . . 94 5.3.2 Problem Formulation . . . . . . . . . . . . . . . . . . . 95 5.3.3 Gauss Pseudospectral Method . . . . . . . . . . . . . . 96 5.4 Impulsive Control Input . . . . . . . . . . . . . . . . . . . . . . 97 5.4.1 Lambert's Problem . . . . . . . . . . . . . . . . . . . . . 97 5.4.2 Lambert's Problem for Follower Spacecraft . . . . . . . 100 5.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . 105 Chapter 6 Numerical Simulation: Formation Reconfiguration . . . . . . . . . . 106 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 6.2 Simulation Configuration . . . . . . . . . . . . . . . . . . . . . 107 6.3 Radial/Along-Track Plane Formation . . . . . . . . . . . . . . . 108 6.3.1 Continuous Control Input . . . . . . . . . . . . . . . . . 109 6.3.2 Impulsive Control Input . . . . . . . . . . . . . . . . . . 113 6.3.3 Global Minimum Velocity: Impulsive Control Input . . . 116 6.3.4 Analysis of Numerical Simulation Results . . . . . . . . 121 6.4 Along-Track/Cross-Track Plane Formation . . . . . . . . . . . . 126 6.4.1 Continuous Control Input . . . . . . . . . . . . . . . . . 127 6.4.2 Impulsive Control Input . . . . . . . . . . . . . . . . . . 131 6.4.3 Global Minimum Velocity: Impulsive Control Input . . . 134 6.4.4 Analysis of Numerical Simulation Results . . . . . . . . 139 6.5 Radial/Along-Track Plane to Along-Track/Cross-Track Plane Formation . . 144 6.5.1 Continuous Control Input . . . . . . . . . . . . . . . . . 144 6.5.2 Impulsive Control Input . . . . . . . . . . . . . . . . . . 149 6.5.3 Analysis of Numerical Simulation Results . . . . . . . . 152 6.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . 153 Chapter 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 7.2 Directions for Future Research . . . . . . . . . . . . . . . . . . 157 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 Abstract (Korean) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 Acknowledgements (Korean) . . . . . . . . . . . . . . . . . . . . . . . . 179Docto

Introduction to Chang'e-3 and Analysis of Estimated Mission Trajectory

달 착륙선과 탐사 로버로 구성된 창어 3호는 2013년 12월 1일 시창 위성 발사 센터에서 장정 3B 발사체를 이용하여 발사되었다. 약 5일의 직접 전이궤적을 지나 달 궤도에 진입한 창어 3호는 달의 공전궤도에서 약 8일간 머무르다가 달 표면에 성공적으로 착륙하였다. 창어 3호의 성공적인 착륙은 한국의 달 탐사선 개발이 예정된 상황에서 향후 필요한 서브시스템의 기술 등을 분석하고, 발사에서 달 착륙까지의 궤적 및 운영 시퀀스 등을 도출하는데 많은 도움이 된다. 따라서 해외 언론에서 공지된 발사 현황을 바탕으로 창어 3호의 형상 및 전반적인 임무내용을 분석하고 시뮬레이션을 수행하였다. 그 결과 경계조건을 이용하여 제어변수를 추정 및 수렴값을 도출하여 착륙선의 전반적인 궤적을 생성하였다. 또한 이를 기반으로 교신 현황 및 식 현상을 분석하여 교신 및 전력충전이 양호함을 확인하였으며, 속도증분()을 이용하여 비추력에 따른 착륙선의 여유 질량을 도출하였다.