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Phd Thesis, University of the Armed Forces Germany, 2003 Multiphase Low-Thrust Trajectory Optimization Using Evolutionary Neurocontrol Multiphase Low-Thrust Trajectory Optimization Using Evolutionary Neurocontrol Proefschrift ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magnificus prof.ir. K.C.A.M. Luyben; voorzitter van het College voor Promoties, in het openbaar te verdedigen op dinsdag 7 juni 2016 om 12:30 uur door Andreas OHNDORF Diplom-Ingenieur Luft- und Raumfahrttechnik (univ.), Universit¨atder Bundeswehr M¨unchen, Duitsland geboren te Finsterwalde, Duitsland Dit proefschrift is goedgekeurd door de promotor: Prof.dr. E. K. A. Gill Samenstelling promotiecommissie: Rector Magnificus, voorzitter Prof.dr. E. K. A. Gill, Technische Universiteit Delft Onafhankelijke leden: Prof.ir. B. A. C. Ambrosius, Technische Universiteit Delft Prof.dr.ir. M. Mulder, Technische Universiteit Delft Prof. D. Scheeres, University of Colorado, U.S.A. Prof. B. Dachwald, Aachen University of Applied Sciences (FH), Germany Prof. M. Vasile, University of Strathclyde, U.K. Prof. M. Lavagna, Politecnico di Milano, Italy Abstract To fulfill the objectives of deep space missions, such as in situ measurements at an outer planet's moon or investigations at main belt asteroids, spacecraft must be provided with sufficient energy to get to these distant objects. This energy be expressed with the so-called ∆V -budget, which is the sum of required velocity changes along a spacecraft's trajectory. As today's and future deep space missions are infeasible using chemical propulsion alone, their trajectories involve one or more close flybys at mass-rich celestial bodies to gain additional orbit energy. These maneuvers are called gravity assists and depend on the relative positions of the assisting body and the respective target. Due to the orbital motion of both bodies, the required constellation may however repeat only every few decades. This constrains both trajectory and mission design and small launch windows can be the result. Any project delay hence threatens an on-time launch and thus potentially puts an entire mission at risk. Mitigation of that risk is possible through using low-thrust propulsion which can provide the required ∆V of a deep space mission without gravity assists. Con- trary to chemical propulsion, having thrust values up to kilo-Newtons at specific impulse (Isp) values of 300-400 s, low-thrust propulsion currently offers only ap- proximately one Newton at maximum. This thrust is achieved either through the ejection of carried-along particles, which are accelerated to very high velocities, or the reflection of sunlight photons. High exhaust gas velocities and very low propellant consumption make the respective Isp of low-thrust propulsion one mag- nitude higher than for chemical propulsion. The low-thrust propulsion concept of solar sailing even utilizes the solar radiation pressure for the generation of thrust, making it independent on any propellant. The different characteristics of low-thrust propulsion and chemical propulsion result in different trajectories. Therefore the methods for the optimization of tra- jectories of chemically propelled spacecraft are of limited use for the optimization of low-thrust trajectories. New methods were developed for this purpose, and one of them is Evolutionary Neurocontrol. This global optimization method combines the two biology-inspired mechanisms artificial neural networks and evolutionary algorithms. Called neurocontrollers, the artificial neural networks are used for spacecraft control. The optimization capability of evolutionary algorithms is used for the training of neurocontrollers. Contrary to other optimization methods, Evo- lutionary Neuroncontrol does not require an initial guess solution to work, which increases its usability for non-experts in optimal control and optimization. Evo- lutionary Neurocontrol was applied successfully in the past to various low-thrust transfer problems. Each of those problems, however, consisted of only one single heliocentric transfer from one celestial body to another. The problem of global optimization of multiphase low-thrust trajectories remained unsolved. This thesis describes how Evolutionary Neurocontrol can be extended to mul- tiphase low-thrust transfers. An existing implementation was revised and com- plemented with new capabilities, concepts, and functionalities. Examples of the new features are a generic multiphase simulation framework, the support of non- heliocentric transfers, and third-body perturbation. The resulting method has been validated on various complex low-thrust transfer problems, which included two-phase transfers, like Earth-Moon-transfers, or heliocentric rendezvous mis- sions with multiple targets or multiple propulsion technolgies. If available, the results were compared with published reference solutions. Finally, Evolutionary Neurocontrol was successfully applied to the design of a trajectory for a so-called Interstellar Heliopause Probe mission. Including a close flyby at Jupiter and using two different propulsion technologies, the resulting transfer brought the spacecraft to a heliocentric distance of 200 AU in less than 25 years. Abstract Het doeleinde van missies in de verre ruimte, bijvoorbeeld in situ metingen bij een maan van een der buitenplaneten of onderzoekingen in de asteroidengordel, vereist een hoog v-budget. Dit is met chemische voortstuwing alleen niet te bereiken en daarom worden overdrachtsbanen gepland met een of meer passagen dicht aan een zwaar hemellichaam voorbij om extra baanenergie te verkrijgen. Zulke ma- noeuvres worden gravity assists genoemd, waarbij de energiewinst afhangt van de relatieve geometrie. Zowel het uiteindelijke doel als het ondersteunende lichaam onderweg bewegen zich, zodat de vereiste constellatie misschien niet vaker dan enkele malen per eeuw voorkomt. Dat beperkt de keuze van mogelijke trajecten, het tijdvenster van de lancering en de opzet van de gehele missie. Eventuele vertragingen bedreigen derhalve het complete project. Dit risico kan worden geband door een systeem met geringe stuwkracht te ge- bruiken ('low-thrust propulsion), dat de benodigde v voor een deep-space missie kan leveren zonder gravity assists. Zo'n 'low-thrust propulsion systeem biedt op het ogenblik maximaal n Newton, zulks in tegenstelling tot chemische voort- stuwingssystemen die, bij Isp waarden van 300 tot 400 seconden, kilo-Newtons kunnen bereiken. Een hoge snelheid van het uittredende gas en een zeer laag brandstofverbruik maken de Isp tienmaal groter. Het concept om de stralingsdruk van de zon te gebruiken middels zonnezeilen biedt een 'low-thrust voortstuwings- systeem dat van brandstof onafhankelijk is. De verschillende eigenschappen van systemen met geringe stuwkracht en van chemische voortstuwingssystemen leiden tot verschillende trajecten. Daarom zijn methoden ter optimalisatie van trajecten voor ruimtesondes met chemische voort- stuwing van weinig nut bij de optimalisatie van trajecten waarbij een 'low-thrust systeem wordt gebruikt. Daarvoor zijn nieuwe methoden ontwikkelt, waarvan n de zogenaamde 'evolutionary neurocontrol is. Deze globale optimalisatie methode kombineert twee mechanismen, die bekend zijn uit de biologie, n.l. kunstmatige neurale netwerken en evolutie algorithmen. Kunstmatige neurale netwerken wor- den voor het sturen van ruimtevaartuigen ingezet onder de naam neurocontrole. In tegenstelling tot andere optimalisatie methoden heeft 'evolutionary neurocon- trol geen vooronderstellingen nodig om te functioneren, wat de bruikbaarheid voor niet-experten verhoogt waar het optimale controle en optimalisatie betreft. 'Evolutionary neurocontrol werd al met succes toegepast op verschillende trans- ferproblemen met geringe stuwkracht. Elk van deze opgaven bestond echter uit slechts n enkele heliocentrische transfer van een hemellichaam naar een tweede. Een globale optimalisatie van trajecten in meerdere fasen en met geringe voort- stuwingskracht werd daarbij niet bereikt. Dit proefschrift beschijft op welke wijze de evolutionary neurocontrol methode werd uitgebreid om ook te kunnen worden gebruikt voor transferbanen met meer dan een 'low-thrust propulsion fase. Een bestaande aanwending werd herzien en met nieuwe functionaliteiten aangevuld. Voorbeelden van het laatste zijn een generisch kader voor simulaties met meerdere fasen, de mogelijkheid niet- heliocentrische overdrachtsbanen te berekenen en storingen van derde lichamen. De geldigheid van de nieuwe methode werd aangetoond voor verschillende trans- fer problemen, o.a. voor een met twee etappes zoals voor een aarde-maan over- drachtsbaan, of voor heliocentrische rendez-vous missies met meer dan een doel. De resultaten werden vergeleken met reeds gepubliceerde referentie oplossingen, indien die ter beschikking stonden. Tenslotte werd de evolutionary neurocontrol methode met succes gebruikt om een traject te ontwerpen voor een sonde in de interstellaire heliopauze. Het resultaat is een overdrachtsbaan met een gravity assist bij Jupiter, die de sonde in minder dan 25 jaar naar een heliocentrische afstand van 200 AE brengt, waarbij twee verschillende voortstuwingstechnieken worden gebruikt. Dedicated to my parents, Angelika and Dieter, to whom I owe so much. Acknowledgements I very much thank: • Prof. Dr.-Ing. B. Dachwald • Dr. rer. nat. W. Seboldt for their support and the many discussions, which raised and stimulated my in- terest in the presented field of research. Contents List of Figures viii List of Tables xi List of Acronyms xii List of Symbols
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