Purdue University Purdue e-Pubs Open Access Dissertations Theses and Dissertations 12-2016 Interplanetary mission design with applications to guidance and optimal control of aero-assisted trajectories Peter J. Edelman Purdue University Follow this and additional works at: https://docs.lib.purdue.edu/open_access_dissertations Part of the Aerospace Engineering Commons Recommended Citation Edelman, Peter J., "Interplanetary mission design with applications to guidance and optimal control of aero-assisted trajectories" (2016). Open Access Dissertations. 982. https://docs.lib.purdue.edu/open_access_dissertations/982 This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional information. Graduate School Form 30 Updated 12/26/2015 PURDUE UNIVERSITY GRADUATE SCHOOL Thesis/Dissertation Acceptance This is to certify that the thesis/dissertation prepared By Peter J. Edelman Entitled INTERPLANETARY MISSION DESIGN WITH APPLICATIONS TO GUIDANCE AND OPTIMAL CONTROL OF AERO-ASSISTED TRAJECTORIES For the degree of Doctor of Philosophy Is approved by the final examining committee: James M. Longuski Chair Michael J. Grant William A. Crossley Kathleen C. Howell To the best of my knowledge and as understood by the student in the Thesis/Dissertation Agreement, Publication Delay, and Certification Disclaimer (Graduate School Form 32), this thesis/dissertation adheres to the provisions of Purdue University’s “Policy of Integrity in Research” and the use of copyright material. Approved by Major Professor(s): James M. Longuski Weinong Wayne Chen 12/6/2016 Approved by: Head of the Departmental Graduate Program Date i INTERPLANETARY MISSION DESIGN WITH APPLICATIONS TO GUIDANCE AND OPTIMAL CONTROL OF AERO-ASSISTED TRAJECTORIES A Dissertation Submitted to the Faculty of Purdue University by Peter J. Edelman In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy December 2016 Purdue University West Lafayette, Indiana ii A person who never made a mistake never tried anything new. –Albert Einstein Science is a way of thinking much more than it is a body of knowledge. –Carl Sagan Man strives to provide himself with food clothing and housing for the sake of the body. He must also provide himself with something to keep the mind healthy and happy. It is the mind that conditions even the body. The mind is the instrument, the flywheel, and the thickest comrade of man. Through it, one can ruin oneself or save oneself. Regulated and controlled, channeled properly it can liberate; wayward and let loose, it can entangle and bind fast. –Sri Sathya Sai Baba iii ACKNOWLEDGEMENTS You do not truly realize how much you do not know until you go for a master or doctoral degree. That being said, this was not easy and would not have made it without the helpful instruction and guidance of many people. First, I thank my friend and advisor, Professor James Longuski for cultivating the potential I did not know I possessed in the field of astrodynamics, his helpful guidance in times of frustration, and entertaining discussions about Star Trek, movies, and The Simpsons. I am grateful to Professor Howell, who helped me understand problems in a more visual manner and whose education in nonlinear systems theory was instrumental to the success of my research. I am grateful to Professor Crossley for introducing me to the usefulness and practicality of direct optimization methods. I am also grateful to Professor Grant for his robust guidance in my guidance research. Additionally, I would like to acknowledge Dave Skinner for repairing many issues that arose with software from past years. To my colleagues, past and present, you have made the research group feel like a second family, and I appreciate all the laughs and helpful suggestions to my research. Finally, I would like to thank my parents and grandmother for their unrelenting love and support. iv TABLE OF CONTENTS Page LIST OF TABLES ............................................................................................................ vii LIST OF FIGURES ......................................................................................................... viii ABSTRACT ...................................................................................................................... xii CHAPTER 1. INTRODUCTION .................................................................................... 1 CHAPTER 2. OPTIMAL CONTROL METHODS AND NUMERICAL SOLVERS ... 3 2.1 Indirect Optimization ......................................................................................... 4 2.1.1 Euler-Lagrange Theorem ................................................................................. 4 2.1.1.1 Adjoined versus Unadjoined Methods ....................................................... 9 2.2 Root-Solvers ..................................................................................................... 10 2.2.1 Newton’s Method .......................................................................................... 10 2.2.2 Broyden’s Method ......................................................................................... 13 2.3 Collocation ....................................................................................................... 13 2.3.1 Mesh Construction ......................................................................................... 14 2.3.2 Higher Odd Order Polynomial Collocation ................................................... 18 2.3.3 Collocation Applied to Solving Optimal Control Problems .......................... 19 2.3.4 Mesh Refinement ........................................................................................... 22 2.4 Shooting Methods ............................................................................................. 22 2.4.1 Single Shooting .............................................................................................. 24 2.4.2 Multiple Shooting .......................................................................................... 25 CHAPTER 3. AGA TRAJECTORY OPTIMIZATION ................................................ 28 3.1 Equations of Motion ......................................................................................... 29 3.2 Interplanetary AGA Tours with the Minimum (L/D)Max Solution .................. 32 3.2.1 STOUR-AGA ................................................................................................ 33 3.2.2 Interplanetary Trajectory Selection Using STOUR ....................................... 36 v 3.2.3 Approximate Calculation For AGA Boundary Conditions ........................... 38 3.2.4 Nondimensional Equations of Motion ........................................................... 44 3.2.5 Optimization of Atmospheric Flight .............................................................. 47 3.2.5.1 Two-Point Boundary Value Problem ....................................................... 47 3.2.5.2 V∞ Matching .............................................................................................. 50 3.2.5.3 Results ...................................................................................................... 51 3.3 Minimum AGA (L/D)Max Solution with Convective Heating-Rate Constraint 56 3.3.1 Optimal Control Problem with Heat Constraint ............................................ 59 3.3.2 Numerical Results .......................................................................................... 62 3.4 Minimum AGA Heat Load Solution ................................................................ 67 3.4.1 Optimal Control Problem Formulation .......................................................... 70 3.4.2 Results............................................................................................................ 73 CHAPTER 4. AGA GUIDANCE ALGORITHM ......................................................... 81 4.1 Radius Tracking ............................................................................................... 83 4.2 Vehicle Characteristics ..................................................................................... 84 4.3 Guidance Algorithm Phases ............................................................................. 86 4.3.1 Entry/Cruise Phase ......................................................................................... 87 4.3.1.1 Predictor-Corrector ................................................................................... 91 4.3.2 Exit Phase ...................................................................................................... 94 4.4 Modeled Dispersions and Assumptions ........................................................... 95 4.5 Monte Carlo Results and Analysis ................................................................... 98 CHAPTER 5. AEROCAPTURE TRAJECTORY OPTIMIZATION WITH ROTATING ATMOSPHERE ........................................................................................ 103 5.1 Aerocapture Vehicle and Model Assumptions ............................................... 104 5.2 The Rotating Atmosphere .............................................................................. 105 5.3 Optimal Control Formulation ......................................................................... 107 5.4 Simulation and Analysis ................................................................................. 110 5.5 Suboptimal Aerocapture Result .....................................................................