Spacecraft trajectory optimization is a topic of crucial importance to space missions design. The less fuel required to accomplish the mission, the more payload that can be transported, and the higher the opportunity to lower the cost of the space mission. The objective is to find the optimal trajectory through space that will minimize the fuel used, and still achieve all mission constraints. Most space trajectories are designed using the simplified relative two-body problem as the base model. Using this patched conics approximation, however, constrains the solution space and fails to produce accurate initial guesses for trajectories in sensitive dynamics. This dissertation uses the Circular Restricted Three-Body Problem (CR3BP) as the base model for designing transfer trajectories in the Circular Restricted Four-Body Problem (CR4BP). The dynamical behavior of the CR3BP guides the search for useful low-energy trajectory arcs. Two distinct models of the CR4BP are considered in this research: the Concentric model, and the Bi-Circular model. Transfers are broken down into trajectory arcs in two separate CR3BPs and the stable and unstable manifold structures of both systems are utilized to produce low-energy transfer arcs that are later patched together to form the orbit-to-orbit transfer. The patched solution is then used as an initial guess in the CR4BP model. A vital contribution of this dissertation is the sequential process for initial guess generation for transfers in the CR4BP. The techniques discussed in this dissertation overcome many of the difficulties in the trajectory design process presented by the complicated dynamics of the CR4BP. Indirect optimization techniques are also used to derive the first order necessary conditions for optimality to assure the optimality of the transfers and determine whether additional impulses might further lower the total cost of the mission. / text

<p>An increasing interest in lunar exploration calls for low-cost techniques of reaching the Moon. Ballistic lunar transfers are long duration trajectories that leverage solar perturbations to reduce the multi-body energy of a spacecraft upon arrival into cislunar space. An investigation is conducted to explore methods of constructing ballistic lunar transfers. The techniques employ dynamical systems theory to leverage the underlying dynamical flow of the multi-body regime. Ballistic lunar transfers are governed by the gravitational influence of the Earth-Moon-Sun system; thus, multi-body gravity models are employed, i.e., the circular restricted three-body problem (CR3BP) and the bicircular restricted four-body problem (BCR4BP). The Sun-Earth CR3BP provides insight into the Sun’s effect on transfers near the Earth. The BCR4BP offers a coherent model for constructing end-to-end ballistic lunar transfers. Multiple techniques are employed to uncover ballistic transfers to conic and multi-body orbits in cislunar space. Initial conditions to deliver the spacecraft into various orbits emerge from Periapse Poincaré maps. From a chosen geometry, families of transfers from the Earth to conic orbits about the Moon are developed. Instantaneous equilibrium solutions in the BCR4BP provide an approximate for the theoretical minimum lunar orbit insertion costs, and are leveraged to create low-cost solutions. Trajectories to the <i>L</i>2 2:1 synodic resonant Lyapunov orbit, <i>L</i>2 2:1 synodic resonant Halo orbit, and the 3:1 synodic resonant Distant Retrograde Orbit (DRO) are investigated.</p>

<p>Secondary payloads have a rich and successful history of utilizing cheap rides to orbit to perform outstanding missions in Earth orbit, and more recently, in cislunar space and beyond. New launch vehicles, namely the Space Launch System (SLS), are increasing the science opportunity for rideshare class missions by providing regular service to the lunar vicinity. However, trajectory design in a multi-body regime brings a host of novel challenges, further exacerbated by constraints generated from the primary payload’s mission. Often, secondary payloads do not possess the fuel required to directly insert into lunar orbit and must instead perform a lunar flyby, traverse the Earth-Moon-Sun system, and later return to the lunar vicinity. This investigation develops a novel framework to construct low-cost, end-to-end lunar transfer trajectories for secondary payload missions. The proposed threephase approach provides unique insights into potential lunar transfer geometries. The phases consist of an arc from launch to initial perilune, an exterior transfer arc, and a lunar approach arc. The space of feasible transfers within each phase is determined through low-dimension grid searches and informed filtering techniques, while the problem of recombining the phases through differential corrections is kept tractable by reducing the dimensionality at each phase transition boundary. A sample mission demonstrates the trajectory design approach and example solutions are generated and discussed. Finally, alternate strategies are developed to both augment the analysis and for scenarios where the proposed three-phase technique does not deliver adequate solutions. The trajectory design methods described in this document are applicable to many upcoming secondary payload missions headed to lunar orbit, including spacecraft with only low-thrust, only high-thrust, or a combination of both. </p>

Au cours des dernières décennies, l’étude de la dynamique autour des points de Lagrange des systèmes Terre-Lune (EMLi) et Terre-Soleil (SELi) a ouvert de nouvelles possibilités pour les orbites et les transferts spatiaux. Souvent modélisés comme des Problèmes à Trois Corps (CR3BP) distincts, ces deux systèmes ont également été combinés pour produire des trajectoiresà faible coût dans le système Terre-Lune-Soleil étendu. Cette approximation (PACR3BP) a permis de mettre en évidence un réseau à faible énergie de trajectoires (LEN) qui relie la Terre, la Lune, EML1,2 et SEL1,2. Cependant, pour chaque trajectoire calculée, le PACR3BP nécessite une connexion arbitraire entre les CR3BPs, ce qui complique son utilisation systématique. Cette thèse vise à mettre en place une modélisation à quatre corps non autonome pour l’étude du LEN basé sur un système Hamiltonien périodique cohérent, le Problème Quasi-Bicirculaire (QBCP). Tout d’abord, la Méthode de Paramétrisation est appliquée afin d’obtenir une représentation semi-analytique des variétés invariantes autour de chaque point de Lagrange. Une recherche systématique de connexions EML1,2-SEL1,2 peut alors être effectuée dans l’espace des paramètres : les conditions initiales sur la variété centrale-instable de EML1,2 sont propagées et les trajectoires résultantes sont projetées sur la variété centrale de SEL1,2 . Un transfert est détecté lorsque la distance de projection est proche de zéro. Les familles de transfert obtenues sont corrigées dans un modèle newtonien haute-fidélité du système solaire. La structure globale des connections est largement préservée et valide l’utilisation du QBCP comme modèle de base du LEN. / In recent decades, the dynamics about the libration points of the Sun-Earth (SELi) and Earth-Moon (EMLi ) systems have been increasingly studied and used, both in terms of transfer trajectory computation and nominal orbit design. Often seen as two distinct Circular Restricted Three Body Problems (CR3BP), both systems have also been combined to produce efficient transfers in the Sun-Earth-Moon system. This patched CR3BP approximation (PACR3BP) allowed to uncover a low-energy network (LEN) of trajectories that interconnect the Earth, the Moon, EML1,2 and SEL1,2 . However, for every computed trajectory, the PACR3BP requires an arbitrary connection between the CR3BPs, which limits its use in a systematic tool. This thesis introduces a single non-autonomous four-body framework for the study of the LEN based on a coherent periodically-forced Hamiltonian system, the Quasi-Bicircular Problem (QBCP). First, the Parameterization Method is applied in order to obtain high-order, periodic, semi-analytical parameterizations of the invariant manifolds about each libration point. A systematic search for EML1,2 -SEL1,2 connections can then be performed in the parameterization space: initial conditions on the center-unstable manifold at EML1,2 are propagated and projected on the center manifold at SEL1,2. A transfer is found each time that the distance of projection is close to zero. These trajectories are refined as solutions of a Boundary Value Problem, which uncover families of natural transfers, later transitioned into a higher-fidelity model. The global structure of the connecting orbits is largely preserved, which validates the QBCP as a relevant model for the LEN.

<p dir="ltr"> With NASA's Artemis program and international collaborations focused on building a sustainable infrastructure for human exploration of the Moon, there is a growing demand for lunar exploration and complex spaceflight operations in cislunar space. However, designing efficient transfer trajectories between the Earth and the Moon remains complex and challenging. This investigation focuses on developing a dynamically informed framework for constructing low-energy transfers in the Earth-Moon-Sun Bicircular Restricted Four-body Problem (BCR4BP). Techniques within dynamical systems theory and numerical methods are exploited to construct transfers to various cislunar orbits. The analysis aims to contribute to a deeper understanding of the dynamical structures governing spacecraft motion. It addresses the characteristics of dynamical structures that facilitate the construction of propellant-efficient pathways between the Earth and the Moon, exploring periodic structures and energy properties from the Circular Restricted Three-body Problem (CR3BP) and BCR4BP. The investigation also focuses on constructing families of low-energy transfers by incorporating electric propulsion, i.e., low thrust, in an effort to reduce the time of flight and offer alternative transfer geometries. Additionally, the investigation introduces a process to transition solutions to the higher fidelity ephemeris force model to accurately model spacecraft motion through the Earth-Moon-Sun system. This research provides insights into constructing families of ballistic lunar transfers (BLTs) and cislunar low-energy flight paths (CLEFs), offering a foundation for future mission design and exploration of the Earth-Moon system.</p>