Guidance of a Small Spacecraft for Soft Landing on an Asteroid using Fuzzy Control A thesis submitted to the Graduate School of the University of Cincinnati in partial fulfillment of the requirements for the degree of Master of Science in the Department of Aerospace Engineering of the College of Engineering by Jacob Hartmann B.S. University of Cincinnati May 12th, 2015 Committee Chairs: Grant Schaffner, Ph.D. Elad Kivelevitch, Ph.D. Abstract The problem of landing a small spacecraft on the surface of an asteroid is analyzed in this thesis. The main effort of the thesis is focused around developing a fuzzy logic system to act as the controller. The fuzzy logic system is paired with a genetic algorithm to optimize the controller’s membership functions. This optimized controller is then compared with two established controllers: an Optimal Control approach, and a Multiple Sliding-Surfaces Guidance algorithm. The genetic-fuzzy approach presented is applicable to designing controllers for various spacecraft and asteroid profiles. ii iii Acknowledgements The author would like to thank Dr. Elad Kivelevitch at the University of Cincinnati for his support throughout this research. Parts of this research was presented as part of Dr. Kelly Cohen’s AEEM6096 Fuzzy Control Systems and Dr. Bingjing Su’s MECH6004 Monte Carlo Methods courses at the University of Cincinnati. iv Table of Contents ABSTRACT .............................................................................................................................................................. II ACKNOWLEDGEMENTS ......................................................................................................................................... IV TABLE OF CONTENTS .............................................................................................................................................. V LIST OF FIGURES ................................................................................................................................................... VII LIST OF TABLES ................................................................................................................................................... VIII 1. INTRODUCTION ............................................................................................................................................ 1 1.1 MOTIVATION ....................................................................................................................................................... 1 1.2 PROBLEM STATEMENT ........................................................................................................................................... 2 1.3 ASSUMPTIONS ..................................................................................................................................................... 3 1.4 GOALS ............................................................................................................................................................... 3 1.5 THESIS OUTLINE ................................................................................................................................................... 4 2. LITERATURE REVIEW ..................................................................................................................................... 5 2.1 MISSIONS TO ASTEROIDS ....................................................................................................................................... 5 2.1.1 NEAR Shoemaker ................................................................................................................................... 5 2.1.2 Hayabusa ............................................................................................................................................... 7 2.1.3 Rosetta and Philae ................................................................................................................................. 9 2.1.4 Reflections ............................................................................................................................................ 10 2.2 BENCHMARK ALGORITHMS ................................................................................................................................... 11 2.2.1 Optimal Control Approach ................................................................................................................... 11 2.2.2 Multiple Sliding Surfaces Guidance ...................................................................................................... 12 2.3 ELECTRIC PROPULSION ........................................................................................................................................ 14 2.3.1 Electrothermal ..................................................................................................................................... 14 2.3.2 Electrostatic ......................................................................................................................................... 14 2.3.3 Electromagnetic ................................................................................................................................... 14 2.3.4 Comparisons ........................................................................................................................................ 15 2.4 FUZZY LOGIC SYSTEMS ........................................................................................................................................ 15 2.4.1 Fuzzy Inference Systems ....................................................................................................................... 16 2.4.2 Genetic-Fuzzy Systems ......................................................................................................................... 17 2.5 DISCUSSION ...................................................................................................................................................... 18 3. SIMULATION MODELS ................................................................................................................................ 20 3.1 SIMULATION ENVIRONMENT AND OVERVIEW ........................................................................................................... 20 3.2 ASTEROID MODELING ......................................................................................................................................... 22 3.2.1 Physical Parameters ............................................................................................................................. 22 3.2.2 Gravitational Field ............................................................................................................................... 23 3.2.3 Orbital Parameters .............................................................................................................................. 24 3.3 LANDER MODEL ................................................................................................................................................. 25 3.3.1 Reference Frames – Cartesian vs Spherical .......................................................................................... 25 3.3.2 Kinematics and Dynamics .................................................................................................................... 26 3.3.3 Thruster Arrays .................................................................................................................................... 26 v 4. FUZZY SYSTEM ............................................................................................................................................ 28 4.1 DEVELOPED FUZZY SYSTEM .................................................................................................................................. 28 4.1.1 Membership Functions ......................................................................................................................... 29 4.1.2 Rule Bases ............................................................................................................................................ 31 4.2 GENETIC – FUZZY APPROACH ................................................................................................................................ 32 4.2.1 Parameters .......................................................................................................................................... 33 4.2.2 Other GA Parameters ........................................................................................................................... 35 4.2.3 FLS Optimization Approach .................................................................................................................. 35 4.2.4 Fitness Scoring ..................................................................................................................................... 36 4.2.5 Resulting FIS’s ...................................................................................................................................... 38 5. RESULTS ...................................................................................................................................................... 44 5.1 SPHERICAL CASES ............................................................................................................................................... 44 5.1.1 Parameters .........................................................................................................................................