An Extended Analytic Range Corrector Method for the Space Shuttle Entry Guidance Algorithm by Erin Elizabeth Evans B.S. Mechanical Engineering, California Institute of Technology (2015) Submitted to the Department of Aeronautics and Astronautics in partial fulfillment of the requirements for the degree of Master of Science in Aeronautical and Astronautical Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2018 Massachusetts Institute of Technology 2018. All rights reserved. Signature redacted Author ................. Department of Aeronautics and Astronautics redacted May 24, 2018 Certified by ........... Signature I. .... Professor Jonathan P. How, Ph.D. Professor, Department of Aeronautics and Astronautics Thesis Supervisor Certified by ............ Signature redacted...... Stephen Thrasher Guidance Engineer, C.S. Draper Laboratory Thesis Supervisor Accepted by .................... Signature redacted ...... MASSACHUSETTS INSTITUTE Professor Hamsa Balakrishnan OF TECHNOLOGY Associate Pr ofessor of Aeronautics and Astronautics JUN 28 2018 Chair, Graduate Program Committee LIBRARIES ARCHIVES 2 An Extended Analytic Range Corrector Method for the Space Shuttle Entry Guidance Algorithm by Erin Elizabeth Evans Submitted to the Department of Aeronautics and Astronautics on May 24, 2018, in partial fulfillment of the requirements for the degree of Master of Science in Aeronautical and Astronautical Engineering Abstract Space shuttle entry guidance with an extended analytic range corrector method is presented. The guidance method is a variation of Shuttle entry guidance in which the parameters that define the drag profile are modified using quadratic splines to make the drag profile smooth and easier to customize. In general, in order to account for off- nominal entry conditions and ensure the vehicle flies the correct range to the runway, the nominal reference drag profile is modified on-line utilizing analytic expressions for the derivative of range with respect to the relevant drag profile parameter. This new profile is then used to calculate a reference drag command in the subsequent guidance algorithm cycle. Typical implementations of Shuttle entry guidance modify the drag profile using only one variable to shift the profile by a constant value. This presents problems when the vehicle is highly constrained and can easily violate constraints such as heat load and heat rate constraints due to small drag profile variations. The methods by which the drag profile is updated are changed in order to provide multiple perturbation options. In providing multiple drag profile update parameters, a memoryless range error allocator is implemented with a vector of weights as a design variable. The allocator parameters are designed to take into account heat load while remaining within constraints using a high L/D vertical takeoff horizontal landing reusable launch vehicle simulation. The resulting algorithm seeks to leverage the high-TRL Shuttle entry guidance routine by making minimal modifications to the implementation, while increasing robustness to entry interface dispersions under tight heating constraints. A discussion of the design of the drag profile is included, in which the selection of profile update parameters is explored. Results from optimization of these parameters using a genetic algorithm are presented, as well as Monte Carlo results demonstrating that the allocator can reduce failure rates due to tight drag constraints from 42% to 0%, establishing the impact and success of this analytic range corrector method. Thesis Supervisor: Professor Jonathan P. How, Ph.D. 3 Title: Professor, Department of Aeronautics and Astronautics Thesis Supervisor: Stephen Thrasher Title: Guidance Engineer, C.S. Draper Laboratory 4 Acknowledgments There is an insanely large number of people without whom this thesis and my success in grad school would not be possible. First, I would like to thank Charles Stark Draper Laboratory, for giving me the opportunity to do research so closely aligned with my interests, and for providing the resources for me to pursue my Master's Degree at MIT. I would like to thank Stephen Thrasher, my mentor, for providing endless insight and being such a patient sounding board for many ideas, both good and very bad. Thanks also to my faculty advisor, Professor Jonathan How. It was truly a pleasure and an honor to be your student, and I value all the advice and insight you provided me these past two years. I also want to extend thanks to Ross, who is my teammate, my biggest cheerleader, my day one, and my infinite source of energy. From studying for my qualifying exams with me, listening to proofs half asleep on the floor, and bringing me dinner when I'm working too late, all the way to waiting outside my qualifying exam room door for me and packing up your life to start our next adventure in Seattle, you've been there for me with patience and enthusiastic encouragement every single day. I couldn't have done it without you. To Nikita, Bjorn, Brandon, Noam, Brett, Chris, Kris, and all the members of the ACL, you made being part of the lab a fun and rewarding experience. Thanks for the Nerf fights and late nights, the long talks and coffee breaks. To my roommates, Alison, Justin, Kelly, and Scott, you made living in Boston a very exciting two years. To my family, for supporting me and giving me every possible opportunity. I would never have had the opportunity to attend MIT without you. And finally, to Ali, Brian, Pat, and my Lord Hobo family, thank you for being fantastic humans and fantastic friends. You were there when I needed you, and I'm so lucky I had you at my side through grad school. 5 6 Contents 1 Introduction 21 1.1 B ackground . ........ ........ ......... ...... 23 1.1.1 Shuttle Entry Guidance . ...... ...... ...... .. 23 1.1.2 Literature Review .... ...... ...... ..... .... 29 1.2 M otivation . ..... ...... .... ..... ..... ..... .. 30 1.3 Thesis Objective . ....... ...... ...... ...... ... 32 1.4 Thesis Overview .... ..... ..... ..... ..... ..... 33 2 Simulation Environment 35 2.1 U nits .. ..... ...... .... ..... ..... ..... .... 35 2.2 Reference Coordinate Frames .... ....... ...... ..... 36 2.2.1 North, East, Down ... ..... .... ..... ..... .. 36 2.2.2 Earth Centered, Earth Fixed .... ........ ....... 36 2.2.3 Earth Centered, Inertial ...... ........ ....... 37 2.2.4 Body Centered, Body Fixed .... ........ ....... 37 2.3 Coordinate Transformations ..... ........ ......... 38 2.3.1 North, East, Down Frame to Earth Centered, Earth Fixed Frame 38 2.3.2 Earth Centered, Earth Fixed Frame to Earth Centered, Inertial ..38 Fram e ... .... ... .... ... .... ... .... 2.3.3 Earth Centered, Inertial Frame to Body Centered, Body Fixed Fram e ... .... ... .... ... .... ... .... ... 39 2.4 Environment Models . ..... ..... ..... ..... ..... 39 2.4.1 Earth Gravity Model ..... ..... .... ..... .... 39 7 2.4.2 Earth Atmosphere ... ...... .. .... .... .. 40 2.5 Vehicle M odel .... ....... ..... .... ........ 40 2.6 Simulation State Propagation ....... ... ........ 41 2.6.1 Bank Angle and Angle of Attack . ............ 41 2.6.2 Equations of Motion ........ ............ 41 2.7 Aerodynamic Heating .... ........ ............ 41 2.8 Simulation Initialization .... ...... ........ ... 43 2.8.1 Initial Conditions ....... ... .... ........ 43 2.8.2 Terminal Conditions .... .... ...... ...... 43 2.8.3 Monte Carlo Parameters ...... ............ 44 3 Shuttle Orbiter Guidance Algorithm 45 3.1 Reference Drag Profile ........... .... ........ 45 3.2 Reference Drag Profile Parameters .... ...... ...... 48 3.3 Equations of Motion ........... ........ .... 48 3.4 Range Prediction ............. ............ 49 3.5 Reference Trajectory Range Update .... ... ........ 52 3.6 Other Reference Trajectory Parameters . ........ ... 54 3.7 Angle of Attack and Bank Angle Commands ... ........ 55 3.8 Lateral Logic ... ............. ............ 57 4 Problem Description 59 5 Allocator Overview 63 5.1 Quadratic Splines .... 64 5.2 Updated Range Equations 66 5.3 Parameter 1: Di .... 67 5.4 Parameter 2: kq...... 68 5.5 Parameter 3: V .. .. .. 70 5.6 Memoryless Design . 71 5.7 Parameter Limits ... 73 8 5.8 Weight Selection .. ....... ........ ........ ... .7 74 6 Allocator Optimization Design 75 6.1 Genetic Algorithm Overview . ... .. .. .. ... .. .. ... 77 6.1.1 Crossover ... .... ..... .. .. .. .. .. 78 6.1.2 M utation ... ...... ... .. .. .. .. .. .. 79 6.2 Nominal Trajectory Parametrization . .. .. .. .. .. .. 79 6.3 Nominal Optimization Fitness Function . .... ... ... ... 82 7 Results 87 7.1 Monte Carlo Results under Turbulent Flow Transition Constraints . 87 7.2 Heat Load Example ..... ...... ...... .. .. ... .. 89 7.3 Reference Trajectory Optimization .. ...... ... ... ... 92 7.3.1 Standard Constraints .. ...... ..... .. .. ... .. 92 7.3.2 Turbulent Flow Transition Constraints . .. ... ... .. 94 8 Conclusion 97 8.1 Results Summary .. .. ..... .... ..... .... ... 97 8.2 Future Work. .... .. .... ..... ..... .... .. 98 9 10 List of Figures 1-1 NASA's X-38 vehicle ................. 23 1-2 Sierra Nevada's Dream Chaser vehicle ... ..... 24 1-3 Typical spaceplane constraints in drag-velocity space 26 1-4 Example angle of attack reference profile ...... 27 1-5 Azimuth error deadband ............... 29 2-1 NED and ECEF coordinate frames ......... 36 2-2 HL-20 with BCBF axes ................ 37 2-3 Euler angle definition ................. 39 2-4 HL-20 ...... .......................... 40 2-5 Trim angle of attack vs. Mach number ...... 42 2-6 Trim