Optimizing a Solar Sailing Polar Mission to the Sun Development and Application of a New Ant Colony Optimizer Giacomo Acciarini Optimizing a Solar Sailing Polar Mission to the Sun Development and Application of a New Ant Colony Optimizer by Giacomo Acciarini to obtain the degree of Master of Science at the Delft University of Technology, to be defended publicly on Friday November 1, 2019 at 1:30 PM. Student number: 4754883 Project duration: January 4, 2019 – November 1, 2019 Thesis committee: Prof. Dr. P. Visser, TU Delft, chair Dr. ir. E. Mooij, TU Delft, supervisor Dr. F. Oliviero, TU Delft Dr. D. Izzo, European Space Agency This thesis is confidential and cannot be made public until December 31, 2020. An electronic version of this thesis is available at http://repository.tudelft.nl/. Cover image credit: https://www.theguardian.com/science/2015/jun/11/ spacewatch-lightsail-deploys-solar-sail, date of access: August 2019. ii Preface After months of hard work, I am proud to present to you my thesis to obtain the Master of Science degree at the faculty of Aerospace Engineering, at the Delft University of Technology. It has been an amazing experience that allowed me to come in contact with many researchers from all over the world who share my same love and interest in space exploration. I have always felt privileged and honored to be able to study such a marvelous and challenging subject. First of all, I would thus like to thank my parents, Andrea and Manuela, and my sister, Chiara, without your help and support I would have never been able to reach this point. Your confidence in me has never wavered and I will always be grateful for that. My gratitude is also directed to my daily supervisor, Erwin, without you, this would have never been possible. Thank you for your support and precious suggestions. Moreover, I would like to thank Dario Izzo, from the European Space Agency’s Advanced Concepts Team, for his guidance in the development of the optimization software. His innovative and creative ideas, as well as his commitment and long term experience in the field, have been a source of inspiration for me. Also, thank you for offering me the SOCIS summer job: it has been a crucial element for better understanding and diving into the software development world. Finally, special thanks go to all my friends from Perugia (with special mention to Riccio, Mao, Nikki and Greg), and to my girlfriend, Ursula. Crossing entire Europe by car for coming to my thesis presentation is the umpteenth demonstration of our deep and strong bond. Giacomo Acciarini Delft, November 1, 2019 iii iv Abstract The Sun is the main contributor to birth and thriving of life on Earth. Yet, a little is known about many physical phenomena that happen on it and that influence the behavior and well being of all the planets in the Solar System. Moreover, as we rely more in technology, our dependency on the Sun increases, and we need to be prepared to limit the damages of disruptive events in advance. Sunspots and other features of the Sun are strongly related to these phenomena, and their study and observation might increase the predictability of these events. However, to monitor and properly investigate these phenomena we need a mission that can offer us a unique and advantaged point of view of the Sun. The aforesaid scientific aspects can only be addressed with a very inclined solar mission, which is near enough to the Sun. Furthermore, since the current technology does not make possible to reach polar orbits in the proximity of the Sun, a solar-sail is pivotal to reach this objective. In particular, the optimal orbit for achieving the objectives would be a circular orbit with 90∘inclination with respect to the heliographic equator. These aspects are the cornerstone of our research and have led to the formulation of the following research question: Can the time and cost of a solar-sail mission to the Sun be optimized by using a global optimization technique? In literature, there have already been some studies for optimizing a solar sailing polar mission towards the Sun. However, this has never been done using an ant colony optimizer and considering multiple objectives (i.e., cost and duration). In this research, we would like to implement a new global ant colony single and multi-objective optimizer with the aim to reduce the duration and cost of such a mission. Although ant colony optimization has re- cently demonstrated to be very powerful in solving trajectory optimization problems in space missions, this algorithm is not available in an open-source fashion and it has never been applied to such a mission. The main purpose of this research is thus to generate new op- timal trajectories for a solar sailing polar mission around the Sun by implementing a novel ant colony optimizer. First of all, to achieve this, a simulation model to represent the solar-sail orbits around the Earth and the Sun is set up. In this simulator, the solar radiation pressure force, the atmo- spheric forces and other environmental aspects are included. Also, a guidance model for the sail is set up, so that the attitude of the sail can be controlled during its journey to the Sun. This entire framework is then formulated as both a single and multi-objective problem. Each of these problems is optimized with the novel ant colony optimizer developed in this research. The results are then also compared and traded-off with other state-of-art global optimizers. In particular, for single-objective, six different optimizers have been benchmarked with our ant colony technique: artificial bee colony (ABC), standard differential evolution (DE), a stan- dard evolution variant (DE1220), self-adaptive differential evolution (SADE), particle swarm optimization (PSO) and simple genetic algorithm (SGA). Whereas for the multi-objective case, three different optimizers have been tested against the multi-objective ant colony extension: multi-objective evolutionary algorithm with decomposition (MOEA/D), nondominated sorting genetic algorithm (NSGA-II) and nondominated sorting particle swarm optimization (NSPSO). The found results are very promising: for the single-objective problem, the ant colony opti- mizer has managed to find the best overall solution. On the other hand, for the multi-objective case, NSGA-II seems to provide the best solutions, although the multi-objective ant colony optimizer displays a set of solutions that is competitive with those of NSGA-II, especially for lower function evaluations, and that outperforms both NSPSO and MOEA/D. Once the mission was optimized, the best found mission profile was studied. It was found that the best overall solution happens for the multi-objective case: indeed, in this case, we managed to halve the mass of the single-objective mission, while still keeping a similar time v vi of flight. Interestingly, we also discovered that a flyby to the Moon is crucial when the time of flight has to be strongly reduced. We hence recommend considering such a gravity assist in future studies. List of Acronyms ABC Artifical Bee Colony ACO Ant Colony Optimization ACOmi single-objective mixed integer Ant Colony Optimizer ASA Adaptive Simulated Annealing CD Crowding Distance CEC2006 Congress on Evolutionary Computation 2006 CME Corona Mass Ejections CPU Central Processing Unit CSTRS selft-adaptive constraints handling meta-algorithm DE Differential Evolution DE1220 Differential Evolution variant DLR german aerospace center DTLZ Deb, Thiele, Laumanns and Zitzler EA Evolutionary Algorithm EACO Extended Ant Colony Optimization EP External Population ESA European Space Agency GA Genetic Algorithm GEO GEOcentric GR Golomb Ruler GTO Geostationary Transfer Orbit GTOP Global Trajectory Optimization Problems H Heliocentric IHS Improved Harmony Search IMF Interplanetary Magnetic Field JAXA Japanese Aerospace Exploration Agency JD Julian Day LEO Low Earth Orbit M2P2 Mini magnetospheric Plasma propulsion MaxMin Maximum Minimum diversity strategy MC Monte Carlo MEE Modified Equinoctial Elements MHACO Multi-objective Hypervolume-based Ant Colony Optimizer MIDACO Mixed Integer Distributed Ant Colony Optimization MINLP Mixed Integer Non Linear Programming MOEA/D Multi-Objective Evolutionary Algorithm based on Decomposition MOP Multi-Objective Problems MPSO Modified Particle Swarm Optimization MRP Modified Rodrigues Parameters NASA National Aeronautics and Space Administration NC Niche Count NEP Nuclear Electric Propulsion NSGA Nondominated Sorting Genetic Algoritm NSPSO Nondominated Sorting Particle Swarm Optimizer OKEANOS Outsized Kite-craft for Exploration and AstroNautics in the Outer Solar system PaGMO Parallel Global Multi-objective Optimizer vii viii PyGMO Python parallel Global Multi-objective Optimizer PF Pareto Front pop population PSO Particle Swarm Optimization REP Radioisotope Electric Propulsion SA Simulated Annealing SADE Self-Adaptive Differential Evolution SGA Simple Genetic Algorithm SO Single-Objective SBX Simulated Binary crossover SEP Solar Electric Propulsion SMRP Shadow Modified Rodrigues Parameters SPICE Spacecraft Planet Instrument C-matrix Events tof time of flight Tudat TU Delft astrodynamics toolbox USM Unified State Model V&V Verification and Validation WFG Walking Fish Group ZDT Zitzler Deb and Thiele List of Symbols 퐴 sail area [m] 푎 semi-major axis [m] â Euler axis [-] 푎 characteristic acceleration [m/s ] 푎 solar gravitational acceleration [m/s ] a perturbing acceleration vector [m/s ] 퐵 non-Lambertian coefficient [-] 퐶 mission cost [$] 퐶 reflectivity [-] C