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Spacecraft Guidance Techniques for Maximizing Mission Success

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Utah State University DigitalCommons@USU All Graduate Theses and Dissertations Graduate Studies 5-2014 Spacecraft Guidance Techniques for Maximizing Mission Success Shane B. Robinson Utah State University Follow this and additional works at: https://digitalcommons.usu.edu/etd Part of the Mechanical Engineering Commons Recommended Citation Robinson, Shane B., "Spacecraft Guidance Techniques for Maximizing Mission Success" (2014). All Graduate Theses and Dissertations. 2175. https://digitalcommons.usu.edu/etd/2175 This Dissertation is brought to you for free and open access by the Graduate Studies at DigitalCommons@USU. It has been accepted for inclusion in All Graduate Theses and Dissertations by an authorized administrator of DigitalCommons@USU. For more information, please contact [email protected]. SPACECRAFT GUIDANCE TECHNIQUES FOR MAXIMIZING MISSION SUCCESS by Shane B. Robinson A dissertation submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in Mechanical Engineering Approved: Dr. David K. Geller Dr. Jacob H. Gunther Major Professor Committee Member Dr. Warren F. Phillips Dr. Charles M. Swenson Committee Member Committee Member Dr. Stephen A. Whitmore Dr. Mark R. McLellan Committee Member Vice President for Research and Dean of the School of Graduate Studies UTAH STATE UNIVERSITY Logan, Utah 2013 [This page intentionally left blank] iii Copyright c Shane B. Robinson 2013 All Rights Reserved [This page intentionally left blank] v Abstract Spacecraft Guidance Techniques for Maximizing Mission Success by Shane B. Robinson, Doctor of Philosophy Utah State University, 2013 Major Professor: Dr. David K. Geller Department: Mechanical and Aerospace Engineering Traditional spacecraft guidance techniques have the objective of deterministically min- imizing fuel consumption. These traditional approaches to guidance are developed indepen- dently of the navigation system, and without regard to stochastic effects. This work presents and demonstrates a new approach to guidance design. This new approach seeks to maxi- mize the probability of mission success by minimizing the variance of trajectory dispersions subject to a fuel consumption constraint. The fuel consumption constraint is imposed by formulating the dynamics in terms of a steering command, and placing a constraint on the final time. Stochastic quadratic synthesis is then used to solve for the nominal control along with the estimator and feedback gains. This new approach to guidance is demonstrated by solving a simple Zermelo boat problem. This example shows that a significant reduction in terminal dispersions is possible with small increases to fuel budgeted for the maneuver. (175 pages) [This page intentionally left blank] vii Public Abstract Spacecraft Guidance Techniques for Maximizing Mission Success by Shane B. Robinson, Doctor of Philosophy Utah State University, 2013 Major Professor: Dr. David K. Geller Department: Mechanical and Aerospace Engineering Traditional spacecraft guidance techniques have the objective of deterministically min- imizing fuel consumption. These traditional approaches to guidance are developed indepen- dently of the navigation system, and without regard to stochastic effects. This work presents and demonstrates a new approach to guidance design. This new approach seeks to maximize the probability of mission success subject to a total fuel consumption constraint. A novel mechanism for imposing the fuel consumption constraint on a stochastic system is presented. Once the fuel constraint is imposed techniques from stochastic linear system theory are used to find a solution to the problem. This new approach to guidance is demonstrated by solv- ing a simple Zermelo boat problem. This example shows a significant reduction in terminal dispersions is possible with small increases to fuel budgeted for the maneuver. [This page intentionally left blank] ix Acknowledgments I wish to offer heartfelt acknowledgment to all those who have helped and supported me as I have pursued my education. I have been truly blessed by the wonderful influence of many teachers, colleagues, kind friends, family, neighbors, and even strangers. Any attempt to list these good people would fall woefully short, and understate the magnitude of their true influence. Indeed, even the thought of attempting to create such a list seems overwhelming, and in some ways ungracious. Nevertheless, it is my desire to extend my sincerest gratitude to all those who have treated me so generously with their time time, talents, and kindness. It is my hope and aim that my life and efforts are a worthy reflection of all who have been so magnanimous. At the risk of thoughtless omissions, I wish to acknowledge a few without whom this work would have been impossible. Firstly, I wish to thank both my immediate and extended family for many years of patience, unconditional love, and gentle encouragement. Secondly, I would like to thank the many teachers who have always insisted that I extend my knowledge and develop the few talents I have. Finally, I dearly appreciate those who cared enough to privately offer me corrective feedback. I owe an immeasurable debt of gratitude to my major advisor, Dr. David Geller. The majority of my technical skills are directly attributable to Dr. Geller’s excellent teaching and mentorship. However, my deepest indebtedness to Dr. Geller is centered on his basic goodness. I will be forever changed by his example of kindness, patience, and generosity. I realize that this may seem like a trite overly sentimental statement of gratitude, but it is the true feeling of my heart. Lastly, I wish acknowledge my dear wife and companion. Our companionship is the very best part of my life. Shane B. Robinson [This page intentionally left blank] xi Contents Page Abstract ::::::::::::::::::::::::::::::::::::::::::::::::::::::: v Public Abstract ::::::::::::::::::::::::::::::::::::::::::::::::: vii Acknowledgments :::::::::::::::::::::::::::::::::::::::::::::::: ix List of Tables ::::::::::::::::::::::::::::::::::::::::::::::::::: xiii List of Figures :::::::::::::::::::::::::::::::::::::::::::::::::: xv 1 Anatomy of Guidance Navigation and Control Systems on Spacecraft and Rockets :::::::::::::::::::::::::::::::::::::::::::::::::::::::: 1 1.1 Introduction.....................................1 1.2 Overview......................................2 1.3 GNC Subsystems..................................4 2 Modern Spacecraft Navigation ::::::::::::::::::::::::::::::::::: 7 2.1 Linear Batch Estimation..............................8 2.2 Linear Sequential Estimation........................... 10 2.3 Kalman Filter.................................... 12 2.4 The Linearized Kalman Filter........................... 15 3 Modern Spacecraft Guidance :::::::::::::::::::::::::::::::::::: 17 3.1 Historical Roots................................... 17 3.2 Deterministic Guidance Schemes......................... 24 3.2.1 Fly-the-Wire and Explicit Guidance................... 25 3.2.2 Delta Guidance............................... 26 3.2.3 The Powered Flight Maneuver Equation and Cross-Product Steering. 27 3.2.4 Powered Descent Guidance........................ 30 3.2.5 The Bilinear Linear Tangent Law and Powered Explicit Guidance... 31 3.2.6 The Inverse Optimal Control Problem.................. 36 3.3 Stochastic Guidance Schemes........................... 37 3.3.1 Relationship between Time-of-Flight and the Probability of Mission Failure.............................. 37 3.3.2 Quadratic Synthesis and the Certainty and Equivalence Principle... 38 3.3.3 Trajectory Desensitization......................... 39 3.3.4 Mission Success Maximization....................... 40 3.4 Summary...................................... 41 4 Neighboring Optimal Control ::::::::::::::::::::::::::::::::::: 43 xii 5 Classical Quadratic Synthesis :::::::::::::::::::::::::::::::::::: 55 5.1 Linear Perturbation Model............................. 55 5.2 Expansion of the Performance Index....................... 60 5.3 An Explicit Expression for the Stochastic Cost................. 62 5.4 Solution to the Classical Quadratic Synthesis Problem............. 64 5.5 A Simple Example................................. 70 6 Stochastic Quadratic Synthesis :::::::::::::::::::::::::::::::::: 79 6.1 Summary of the Equations............................. 84 6.1.1 Neighboring Optimal Control....................... 84 6.1.2 Classical Quadratic Synthesis....................... 85 6.1.3 Stochastic Quadratic Synthesis...................... 86 6.2 A Simple Example................................. 87 6.2.1 Solution via Classical Quadratic Synthesis............... 87 6.2.2 Solution via Stochastic Quadratic Synthesis............... 91 6.2.3 Results................................... 92 7 Fuel-Limited Mission Success Guidance ::::::::::::::::::::::::::: 101 7.1 Limiting Fuel Use.................................. 101 7.2 Proposed Fuel-Limited Mission Success Guidance Scheme........... 103 7.3 The Zermelo Boat Problem and its Classical Solutions............. 104 7.3.1 Arbitrary Flow Field........................... 105 7.3.2 Linearly Varying Flow Field........................ 109 7.3.3 Constant Flow Field............................ 114 7.4 Statistical GN&C Analysis............................. 116 7.5 Summary...................................... 129 8 Conclusion ::::::::::::::::::::::::::::::::::::::::::::::::::: 131 References :::::::::::::::::::::::::::::::::::::::::::::::::::::: 133 Appendix ::::::::::::::::::::::::::::::::::::::::::::::::::::::
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