Guidance and Control for Multiple Spacecraft Formation

DOCTORAL T H E SIS Department of Computer Science, Electrical and Space Engineering Division of Space Sumeet Gajanan Satpute ISSN 1402-1544 Guidance and Control for Multiple ISBN 978-91-7790-723-7 (print) ISBN 978-91-7790-724-4 (pdf) Spacecraft Formation Luleå University of Technology 2021 Guidance and Control for Multiple Spacecraft Formation Guidance and Control Sumeet Gajanan Satpute Onboard Space Systems 133065-LTU_Satpute.indd Alla sidor 2021-01-07 10:03 Guidance and Control for Multiple Spacecraft Formation Sumeet Gajanan Satpute Division of Space Technology Dept. of Computer Science, Electrical and Space Engineering Lule˚aUniversity of Technology Kiruna, Sweden Supervisors: Prof. George Nikolakopoulos Dr. Per Bodin ii To my loving wife and my family. iii iv Abstract Multiple spacecraft formation forms a distributed space system where multiple spacecraft cooperatively exhibit the functionality of a single monolithic spacecraft or work in a cooperative way towards the completion of a common goal. This possibility of distributing the workload between different spacecraft provides the ability to work in parallel, enable economic and simple solutions in terms of spacecraft design, while is redundant towards partial or complete failure of a spacecraft. Some of the challenges, associated to the guidance and control aspects of the spacecraft formation, are to maintain a safe separation distance between each spacecraft in the formation to avoid any collision, the distribution of workload between the spacecraft group, and designing fuel efficient trajectories for each spacecraft. This thesis focuses on studying these challenges through two respective mission scenarios, a) the co-location of geostationary satellites, and b) the cooperative visual coverage of an asteroid. The first part of the thesis covers the development of guidance and control strategies to co-locate multiple geostationary satellites safely with a single operational slot. This part of the research is motivated by the growing demand to access the limited Earth resource of geostationary region; the growing use of low-thrust electric propulsion systems for geostationary satellite platforms; and the use of the same propulsion system for station keeping and momentum management of the reaction wheels to maintain a nadir pointing attitude for the satellites. Thus, to address the concurrent maneuver planning problem, a convex-optimization-based algorithm is proposed that incorporates a dual-rate prediction model to address the time scaling difference between the coupled slow orbital and fast attitude dynamics. The use of a combined prediction model in the optimization problem facilitates to include state constraints accounting for the desired orbital and momentum unloading requirements. This algorithm is then extended to the co-location problem, where a leader-follower architecture is adopted to define relative orbital elements of the satellites. The separation distance between the satellites is maintained by defining convex bounds on the relative orbital elements of the follower satellites. The algorithm is then implemented in receding horizon control form to introduce autonomy and to maintain tighter state constraints. The second part covers the trajectory planning for a spacecraft group for the visual coverage mission of an asteroid. In asteroid missions, it is of a specific interest to determine the surface and material properties of the target asteroid by obtaining high- resolution measurements from multiple sites over the asteroid surface. This task can be accomplished using a group of spacecraft, equipped with optical sensors that are moving in proximity to the asteroid. During this mission, an important problem to solve is to de- v termine a fuel optimal observing sequence and the associated trajectories for a given set of target sites for each spacecraft. However, the completion of the observation task, for a specific site, is limited to the observation time window, usually referred as the period for which a site is illuminated by the Sun. Two trajectory planning algorithms are proposed, which are tested for a single spacecraft case to compare their performance in terms of finding an optimal solution. The travelling salesman based planning algorithm provided near-optimal results in terms of fuel consumption. This algorithm is then extended to the multiple spacecraft case to determine the near-optimal unique observing tour for each spacecraft. The efficacy of the proposed algorithms are evaluated, in terms of fuel consumption and constraints enforcement using several numerical simulations that take into account dominant perturbations in the respective environment. vi Contents Chapter 1 { Thesis Introduction 1 1.1 Introduction to Formation Flying . .1 1.2 Motivation and Background . .3 1.3 Thesis Outline and Contributions . .8 Part I: Co-location of Geostationary Satellites 13 Chapter 2 { Geostationary Satellite Dynamic Model 15 2.1 Definition of Coordinate Frames . 15 2.2 Thrust Configurations . 16 2.3 Equations of Motion . 21 2.4 Linearized Satellite Model . 25 2.5 Simulation Environment . 26 Chapter 3 { Concurrent Station Keeping and Momentum Manage- ment of Single Satellite 31 3.1 Maneuver Planning Problem . 31 3.2 Ground-in-loop Implementation . 35 3.3 Simulation Results . 36 3.4 Summary . 45 Chapter 4 { Concurrent Co-location Maneuver Planning for Mul- tiple Satellites 47 4.1 Co-location Problem . 47 4.2 Ground-in-loop Operation Architecture . 54 4.3 Simulation Results . 56 4.4 Summary . 64 Part II: Cooperative Visual Coverage of an Asteroid 67 Chapter 5 { Spacecraft Dynamics and Multi-site Visual Coverage Problem Formulation 69 5.1 Introduction . 69 5.2 Spacecraft Dynamics . 70 5.3 Multi-site Visual Coverage Problem Formulation . 73 vii Chapter 6 { Single Spacecraft Trajectory Planning Algorithms 77 6.1 Trajectory Optimization Problem . 77 6.2 Coverage Algorithms . 80 6.3 Simulation Results . 86 6.4 Summary . 96 Chapter 7 { Cooperative Visual Coverage Algorithm 99 7.1 Problem Formulation . 99 7.2 Multiple Spacecraft Traveling Salesman Problem . 102 7.3 Simulation Results . 106 7.4 Summary . 111 Chapter 8 { Conclusions and Future Directions 113 References 115 viii Acknowledgments First of all, I would like to express my profound gratitude to Prof. George Niko- lakopoulos for his valuable time with constructive feedback and thoughtful counsel. His constant support has led towards the completion of my research work. Dr. Per Bodin from OHB Sweden, my co-supervisor, has been a close collaborator on the research projects we worked on together, especially regarding the first part of this thesis. His industrial insights and perspective has been of great help. I would also like to thank Prof. M. Reza Emami, former supervisor, for the initial drive and contribution in this work. To late Dr. A.P.J. Abdul Kalam, a teacher, scientist, former President of India, I owe my deepest gratitude who ignited the scientific attitude and curiosity towards my research oriented mindset. I extend my gratitude to the funding provisions by the Rymd förInnovation och Tillväxt(RIT), Graduate School of Space Technology, LTU, Swedish National Space Agency (SNSA) and OHB Sweden. Thanks to the colleagues at Space division and Robotics and AI group for the close col- laboration at LTU. I take this opportunity to thank my colleagues and friends, Cristóbal, Leonard, Kanika, Tobias, Moses and Niklas for all the discussions and much needed support in the time of crisis. In addition, I thank all my friends and acquaintances, Dhananjay, George, Sissy, Sandra, Rita, to name a few, for making my time wonderful and memorable in Kiruna (where the time freezes as well, corner of the world, best place to live during pandemic!). All the after-work Thursdays at The Bishops Arms will be remembered! And finally, I thank my family for everything. I thank my best friend and wife Rucha for all her unflinching support and companionship on our journey together. I must ac- knowledge my family members, Sailee, Himanshu, especially my parents Dr. Gajanan and Pratibha Satpute for their endless love and efforts. They have loved and supported me constantly, regardless of my faults and flaws. Their contribution to my life and career remains incomparable. Kiruna, December 2020 Sumeet G. Satpute ix x Chapter 1 Thesis Introduction \You cannot change your future, but you can change your habits, and surely your habits will change your future." Dr. A.P.J. Abdul Kalam 1.1 Introduction to Formation Flying Multiple spacecraft formation is the concept of distributing the functionality of a single monolithic spacecraft into cost-effective, small, cooperative spacecraft or sharing the same spatial location with multiple space elements. During the early days of space program, formation flying was focused towards the rendezvous and docking of two spacecraft. Later, the focus shifted towards the distributed payloads on multiple spacecraft for interferometric measurements in order to enhance the angular resolutions of the stel- lar observations. However, the trend was still to design large complex spacecraft with multiple payloads to satisfy multiple desired tasks. The cost and development cycle of such large spacecraft in addition to their launch in space costed a huge amount of money and time. Also, the risk of failure of even a single component, which could lead to the failure of the entire mission, may lead to immense losses. Thus, since past decade, the space industry is exploring innovative concepts involving distributed space

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