<p>The 9:2 lunar synodic resonant near rectilinear halo orbit (NRHO) is the chosen orbit for the Gateway, a future lunar space station constructed by the National Aeronautics and Space Administration (NASA) as well as several commercial and international partners. Designing trajectories in this sensitive lunar region combined with the absence of a singular systematic methodology to approach mission design poses challenges as researchers attempt to design transfers to and from this nearly stable orbit. This investigation builds on previous research in Poincar\'e mapping strategies to design transfers from the 9:2 NRHO using higher-dimensional maps and maps with non-state variables. First, Poincar\'e maps are applied to planar transfers to demonstrate the utility of hyperplanes and establish that maps with only two or three dimensions are required in the planar problem. However, with the addition of two state variables, the spatial problem presents challenges in visualizing the full state. Higher-dimensional maps utilizing glyphs and color are employed for spatial transfer design involving the 9:2 NRHO. The visualization of all required dimensions on one plot accurately reveals low cost transfers into both a 3:2 planar resonant orbit and an L2 vertical orbit. Next, the application of higher-dimensional maps is extended beyond state variables. Visualizing time-of-flight on a map axis enables the selection of faster transfers. Additionally, glyphs and color depicting angular momentum rather than velocity lead to transfers with nearly tangential maneuvers. Theoretical minimum maneuvers occur at tangential intersections, so these transfers are low cost. Finally, a map displaying several initial and final orbit options, discerned through the inclusion of Jacobi constant on an axis, eliminates the need to recompute a map for each initial and final orbit pair. Thus, computation time is greatly reduced in addition to visualizing more of the design space in one plot. The higher-dimensional mapping strategies investigated are relevant for transfer design or other applications requiring the visualization of several dimensions simultaneously. Overall, this investigation outlines Poincar\'e mapping strategies for transfer scenarios of different design space dimensions and represents initial research into non-state variable mapping methods.</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>

<div>There is an increasing interest in future space missions devoted to the exploration of key moons in the Solar system. These many different missions may involve libration point orbits as well as trajectories that satisfy different endgames in the vicinities of the moons. To this end, an efficient design strategy to produce low-energy transfers between the vicinities of adjacent moons of a planetary system is introduced that leverages the dynamics in these multi-body systems. Such a design strategy is denoted as the moon-to-moon analytical transfer (MMAT) method. It consists of a general methodology for transfer design between the vicinities of the moons in any given system within the context of the circular restricted three-body problem, useful regardless of the orbital planes in which the moons reside. A simplified model enables analytical constraints to efficiently determine the feasibility of a transfer between two different moons moving in the vicinity of a common planet. Subsequently, the strategy builds moon-to-moon transfers based on invariant manifold and transit orbits exploiting some analytical techniques. The strategy is applicable for direct as well as indirect transfers that satisfy the analytical constraints. The transition of the transfers into higher-fidelity ephemeris models confirms the validity of the MMAT method as a fast tool to provide possible transfer options between two consecutive moons. </div><div> </div><div>The current work includes sample applications of transfers between different orbits and planetary systems. The method is efficient and identifies optimal solutions. However, for certain orbital geometries, the direct transfer cannot be constructed because the invariant manifolds do not intersect (due to their mutual inclination, distance, and/or orbital phase). To overcome this difficulty, specific strategies are proposed that introduce intermediate Keplerian arcs and additional impulsive maneuvers to bridge the gaps between trajectories that connect any two moons. The updated techniques are based on the same analytical methods as the original MMAT concept. Therefore, they preserve the optimality of the previous methodology. The basic strategy and the significant additions are demonstrated through a number of applications for transfer scenarios of different types in the Galilean, Uranian, Saturnian and Martian systems. Results are compared with the traditional Lambert arcs. The propellant and time-performance for the transfers are also illustrated and discussed. As far as the exploration of Phobos and Deimos is concerned, a specific design framework that generates transfer trajectories between the Martian moons while leveraging resonant orbits is also introduced. Mars-Deimos resonant orbits that offer repeated flybys of Deimos and arrive at Mars-Phobos libration point orbits are investigated, and a nominal mission scenario with transfer trajectories connecting the two is presented. The MMAT method is used to select the appropriate resonant orbits, and the associated impulsive transfer costs are analyzed. The trajectory concepts are also validated in a higher-fidelity ephemeris model.</div><div> </div><div>Finally, an efficient and general design strategy for transfers between planetary moons that fulfill specific requirements is also included. In particular, the strategy leverages Finite-Time Lyapunov Exponent (FTLE) maps within the context of the MMAT scheme. Incorporating these two techniques enables direct transfers between moons that offer a wide variety of trajectory patterns and endgames designed in the circular restricted three-body problem, such as temporary captures, transits, takeoffs and landings. The technique is applicable to several mission scenarios. Additionally, an efficient strategy that aids in the design of tour missions that involve impulsive transfers between three moons located in their true orbital planes is also included. The result is a computationally efficient technique that allows three-moon tours designed within the context of the circular restricted three-body problem. The method is demonstrated for a Ganymede->Europa->Io tour.</div>

<p> </p> <p>In the coming decades, numerous missions plan to exploit multi-body orbits for operations. Given the complex nature of multi-body systems, trajectory designers must possess effective tools that leverage aspects of the dynamical environment to streamline the design process and enable these missions. In this investigation, a particular class of dynamical structures, quasi-periodic orbits, are examined. This work summarizes a computational framework to construct quasi-periodic orbits and a design framework to leverage quasi-periodic motion within the path planning process. First, quasi-periodic orbit computation in the Circular Restricted Three-Body Problem (CR3BP) and the Bicircular Restricted Four-Body Problem (BCR4BP) is summarized. The CR3BP and BCR4BP serve as preliminary models to capture fundamental motion that is leveraged for end-to-end designs. Additionally, the relationship between the Earth-Moon CR3BP and the BCR4BP is explored to provide insight into the effect of solar acceleration on multi-body structures in the lunar vicinity. Characterization of families of quasi-periodic orbits in the CR3BP and BCR4BP is also summarized. Families of quasi-periodic orbits prove to be particularly insightful in the BCR4BP, where periodic orbits only exist as isolated solutions. Computation of three-dimensional quasi-periodic tori is also summarized to demonstrate the extensibility of the computational framework to higher-dimensional quasi-periodic orbits. Lastly, a design framework to incorporate quasi-periodic orbits into the trajectory design process is demonstrated through a series of applications. First, several applications were examined for transfer design in the vicinity of the Moon. The first application leverages a single quasi-periodic trajectory arc as an initial guess to transfer between two periodic orbits. Next, several quasi-periodic arcs are leveraged to construct transfer between a planar periodic orbit and a spatial periodic orbit. Lastly, transfers between two quasi-periodic orbits are demonstrated by leveraging heteroclinic connections between orbits at the same energy. These transfer applications are all constructed in the CR3BP and validated in a higher-fidelity ephemeris model to ensure the geometry persists. Applications to ballistic lunar transfers are also constructed by leveraging quasi-periodic motion in the BCR4BP. Stable manifold trajectories of four-body quasi-periodic orbits supply an initial guess to generate families of ballistic lunar transfers to a single quasi-periodic orbit. Poincare mapping techniques are used to isolate transfer solutions that possess a low time of flight or an outbound lunar flyby. Additionally, impulsive maneuvers are introduced to expand the solution space. This strategy is extended to additional orbits in a single family to demonstrate "corridors" of transfers exist to reach a type of destination motion. To ensure these transfers exist in a higher fidelity model, several solutions are transitioned to a Sun-Earth-Moon ephemeris model using a differential corrections process to show that the geometries persist.</p>

<p dir="ltr">The recent and upcoming increase in spaceflight missions to the lunar vicinity necessitates methodologies to enable operations beyond the Earth. In particular, there is a pressing need for a Space Domain Awareness (SDA) and Space Situational Awareness (SSA) architecture that encompasses the realm of space beyond the sub-geosynchronous region to sustain humanity's long-term presence in that region. Naturally, the large distances in the cislunar domain restrict access rapid and economical access from the Earth. In addition, due to the long ranges and inconsistent visibility, the volume contained within the orbit of the Moon is inadequately observed from Earth-based instruments. As such, space-based assets to supplement ground-based infrastructure are required. The need for space-based assets to support a sustained presence is further complicated by the challenging dynamics that manifest in cislunar space. Multi-body dynamical models are necessary to sufficiently model and predict the motion of any objects that operate in the space between the Earth and the Moon. The current work seeks to address these challenges in dynamical modeling and cislunar accessibility via the exploration of resonant orbits. These types of orbits, that are commensurate with the lunar sidereal period, are constructed in the Earth-Moon Circular Restricted Three-Body Problem (CR3BP) and validated in the Higher-Fidelity Ephemeris Model (HFEM). The expansive geometries and energy options supplied by the orbits are favorable for achieving recurring access between the Earth and the lunar vicinity. Sample orbits in prograde resonance are explored to accommodate circumlunar access from underlying cislunar orbit structures via Poincaré mapping techniques. Orbits in retrograde resonance, due to their operational stability, are employed in the design of space-based observer constellations that naturally maintain their relative configuration over successive revolutions. </p><p dir="ltr"> Sidereal resonant orbits that are additionally commensurate with the lunar synodic period are identified. Such orbits, along with possessing geometries inherent to sidereal resonant behavior, exhibit periodic alignments with respect to the Sun in the Earth-Moon rotating frame. This characteristic renders the orbits suitable for hosting space-based sensors that, in addition to naturally avoiding eclipses, maintain visual custody of targets in the cislunar domain. For orbits that are not eclipse-favorable, a penumbra-avoidance path constraint is implemented to compute baseline trajectories that avoid Earth and Moon eclipse events. Constellations of observers in both sidereal and sidereal-synodic resonant orbits are designed for cislunar SSA applications. Sample trajectories are assessed for the visibility of various targets in the cislunar volume, and connectivity relative to zones of interest in Earth-Moon plane. The sample constellations and observer trajectories demonstrate the utility of resonant orbits for various applications to sustain operations in cislunar space. </p>

Integrating unmanned aerial vehicles (UAVs) as aerial user equipments (UEs) into cellular networks is now considered as a promising solution to provide extensive wireless connectivity for supporting UAV-centric commercial or civilian applications. However, the co-existence of UAVs with conventional terrestrial UEs is one of the primary challenges for this solution. Flying at higher altitudes with maneuverability advantage, UAVs are able to establish line-of-sight (LoS) connectivity with more base stations (BSs) than terrestrial UEs. Although LoS connectivity reduces the communication delay of UAVs, they also simultaneously increase the interference that UAVs cause to terrestrial UEs. In scenarios involving multiple UAVs, LoS connectivity can even lead to interference issues among themselves. In addition, LoS connectivity leads to extensive overlapping coverage areas of multiple BSs for UAVs, forcing them to perform frequent handovers during the flight if the received signal strength (RSS)-based handover policy is employed. The trajectories and BS associations of UAVs, along with their radio resource allocation are essential design parameters aimed at enabling their seamless integration into cellular networks, with a particular focus on managing interference levels they generate and reducing the redundant handovers they performe. Hence, this thesis designs two joint trajectory and handover management approaches for single-UAV and multi-UAVs scenarios, respectively, aiming to minimize the weighted sum of three key performance indicators (KPIs): transmission delay, up-link interference, and handover numbers. The approaches are based on deep reinforcement learning (DRL) frameworks with dueling double deep Q-network (D3QN) and Q-learning with a MIXer network (QMIX) algorithms being selected as the training agents, respectively. The choice of these DRL algorithms is motivated by their capability in designing sequential decision-making policies consisting of trajectory design and handover management. Results show that the proposed approaches effectively address the aforementioned challenges while ensuring the low transmission delay of cellular-connected UAVs. These results are in contrast to the performance of benchmark scheme, which directs UAVs to follow the shortest path and perform handovers based on RSS. Specifically, when considering the single-UAV scenario, the D3QN-based approach reduces the up-link interference by 18% and the handover numbers by 90% with a 59% increase in transmission delay as compared to the benchmark. The equivalent delay increase is 15 microseconds, which is considered negligible. For the multi-UAVs scenario, the QMIX-based approach jointly optimizes three performance metrics as compared to the benchmark scheme, resulting in a 70% decrease in interference, a 91% decrease in handover numbers, and a 47% reduction in transmission delay. It is noteworthy that an increase of UAVs operating within the same network leads to performance degradation due to UAVs competing for communication resources and mutual interference. When transitioning from the single-UAV scenario to the multi-UAVs scenario, the performance of the benchmark scheme experiences a significant decline, with an increase of 199% in interference, 89% in handover numbers, and 652% in transmission delay. In contrast, the proposed QMIX algorithm effectively coordinates multiple UAVs, mitigating performance degradation and achieving performance similar to the D3QN algorithm applying in the single-UAV scenario: an interference increase of 9%, a handover numbers increase of 9% and a delay increase of 152%. The delay increase is attributed to the reduced communication resources available to each individual UAVs, given the constant communication resources of the network. / Att integrera obemannade flygfordon (UAV) som flyganvändarutrustning (UE) i cellulära nätverk anses nu vara en lovande lösning för att tillhandahålla omfattande trådlös anslutning för att stödja UAV-centrerade kommersiella eller civila tillämpningar. Men samexistensen av UAV med konventionella markbundna UE är en av de främsta utmaningarna för denna lösning. Flygande på högre höjder med manövrerbarhetsfördelar kan UAV:er etablera siktlinje (LoS)-anslutning med fler basstationer (BS) än markbundna UE. Även om LoS-anslutning minskar kommunikationsfördröjningen för UAV:er, ökar de samtidigt störningen som UAV:er orsakar för markbundna UE. I scenarier som involverar flera UAV:er kan LoS-anslutning till och med leda till störningsproblem sinsemellan. Dessutom leder LoS-anslutning till omfattande överlappande täckningsområden för flera BS:er för UAV, vilket tvingar dem att utföra frekventa överlämningar under flygningen om den mottagna signalstyrkan (RSS)-baserad överlämningspolicy används. UAV:s banor och BS-associationer, tillsammans med deras radioresursallokering, är väsentliga designparametrar som syftar till att möjliggöra deras sömlösa integrering i cellulära nätverk, med särskilt fokus på att hantera störningsnivåer de genererar och minska de redundanta handovers de utför. Därför designar denna avhandling två gemensamma bana och handover-hanteringsmetoder för en-UAV-respektive multi-UAV-scenarier, som syftar till att minimera den viktade summan av tre nyckelprestandaindikatorer (KPI:er): överföringsfördröjning, upplänksinterferens och överlämningsnummer . Tillvägagångssätten är baserade på ramverk för djup förstärkning inlärning (DRL) med duellerande dubbla djupa Q-nätverk (D3QN) och Q-lärande med ett MIXer-nätverk (QMIX) algoritmer som väljs som träningsagenter. Valet av dessa DRL-algoritmer motiveras av deras förmåga att utforma sekventiella beslutsfattande policyer som består av banadesign och handover-hantering. Resultaten visar att de föreslagna tillvägagångssätten effektivt tar itu med ovannämnda utmaningar samtidigt som de säkerställer den låga överföringsfördröjningen för mobilanslutna UAV:er. Dessa resultat står i kontrast till prestanda för benchmark-schemat, som styr UAV:er att följa den kortaste vägen och utföra överlämningar baserat på RSS. Närmare bestämt, när man överväger singel-UAV-scenariot, minskar det D3QN tillvägagångssättet upplänksinterferensen med 18% och överlämningssiffrorna med 90% med en 59% ökning av överföringsfördröjningen jämfört med riktmärket. Den ekvivalenta fördröjningsökningen är 15 mikrosekunder, vilket anses vara försumbart. För scenariot med flera UAV:er optimerar det QMIX-baserade tillvägagångssättet tillsammans tre prestandamått jämfört med benchmark-schemat, vilket resulterar i en 70% minskning av störningar, en 91% minskning av överlämningssiffror och en 47% minskning av överföringsfördröjningen. Det är anmärkningsvärt att en ökning av UAV:er som arbetar inom samma nätverk leder till prestandaförsämring på grund av UAV:er som konkurrerar om kommunikationsresurser och ömsesidig störning. Vid övergången från scenariot med en UAV till scenariot med flera UAV, upplever prestanda för benchmark-schemat en betydande nedgång, med en ökning på 199% av störningar, 89% i överlämnandetal och 652% i överföringsfördröjning. Däremot koordinerar den föreslagna QMIX-algoritmen effektivt flera UAV, vilket minskar prestandaförsämring och uppnår prestanda liknande D3QN-algoritmen som tillämpas i single-UAV-scenariot: en störningsökning på 9%, en ökning av antalet överlämningar med 9% och en fördröjningsökning på 152%. Ökningen av fördröjningen tillskrivs de minskade kommunikationsresurserna tillgängliga för varje enskild UAV, givet nätverkets konstanta kommunikationsresurser.

Preliminary interplanetary trajectory designs frequently use simplified two-body orbital mechanics and linked conics methodology to model the complex trajectories in multi-body systems. Incorporating gravity assists provides highly efficient interplanetary trajectories, enabling otherwise infeasible spacecraft missions. Future missions may employ powered gravity assists, using a propulsive maneuver during the flyby, improving the overall trajectory performance. This dissertation provides a complete description and analysis of a new interplanetary trajectory design tool known as TRACT (TRAjectory Configuration Tool). TRACT is capable of modeling complex interplanetary trajectories, including multiple ballistic and/or powered gravity assists, deep space maneuvers, parking orbits, and other common maneuvers. TRACT utilizes an adaptable architecture of modular boundary value problem (BVP) algorithms for all trajectory segments. A bi-level optimization scheme is employed to reduce the number of optimization variables, simplifying the user provided trajectory information. The standardized optimization parameter set allows for easy use of TRACT with a variety of optimization algorithms and mission constraints. The dissertation also details new research in powered gravity assists. A review of literature on optimal powered gravity assists is presented, where many optimal solutions found are infeasible for realistic spacecraft missions. The need was identified for a mission feasible optimal powered gravity assist algorithm using only a single impulsive maneuver. The solution space was analyzed and a complete characterization was developed for solution types of the optimal single-impulse powered gravity assist. Using newfound solution space characteristics, an efficient and reliable optimal single-impulse powered gravity assist BVP algorithm was formulated. The mission constraints were strictly enforced, such as maintaining the closest approach above a minimum radius and below a maximum radius. An extension of the optimal powered gravity assist research is the development of a gravity assist BVP algorithm that utilizes an asymptote ΔV correction maneuver to produce ballistic gravity assist trajectory solutions. The efficient algorithm is tested with real interplanetary mission trajectory parameters and successfully converges upon ballistic gravity assists with improved performance compared to traditional methods. A hybrid approach is also presented, using the asymptote maneuver algorithm together with traditional gravity assist constraints to reach ballistic trajectory solutions more reliably, while improving computational performance.

<div>The orbits of interest for potential missions are stable or nearly stable to maintain long term presence for conducting scientific studies and to reduce the possibility of rapid departure. Near Rectilinear Halo Orbits (NRHOs) offer such stable or nearly stable orbits that are defined as part of the L1 and L2 halo orbit families in the circular restricted three-body problem. Within the Earth-Moon regime, the L1 and L2 NRHOs are proposed as long horizon trajectories for cislunar exploration missions, including NASA's upcoming Gateway mission. These stable or nearly stable orbits do not possess well-distinguished unstable and stable manifold structures. As a consequence, existing tools for stationkeeping and transfer trajectory design that exploit such underlying manifold structures are not reliable for orbits that are linearly stable. The current investigation focuses on leveraging stretching direction as an alternative for visualizing the flow of perturbations in the neighborhood of a reference trajectory. The information supplemented by the stretching directions are utilized to investigate the impact of maneuvers for two contrasting applications; the stationkeeping problem, where the goal is to maintain a spacecraft near a reference trajectory for a long period of time, and the transfer trajectory design application, where rapid departure and/or insertion is of concern.</div><div><br></div><div>Particularly, for the stationkeeping problem, a spacecraft incurs continuous deviations due to unmodeled forces and orbit determination errors in the complex multi-body dynamical regime. The flow dynamics in the region, using stretching directions, are utilized to identify appropriate maneuver and target locations to support a long lasting presence for the spacecraft near the desired path. The investigation reflects the impact of various factors on maneuver cost and boundedness. For orbits that are particularly sensitive to epoch time and possess distinct characteristics in the higher-fidelity ephemeris model compared to their CR3BP counterpart, an additional feedback control is applied for appropriate phasing. The effect of constraining maneuvers in a particular direction is also investigated for the 9:2 synodic resonant southern L2 NRHO, the current baseline for the Gateway mission. The stationkeeping strategy is applied to a range of L1 and L2 NRHOs, and validated in the higher-fidelity ephemeris model.</div><div><br></div><div>For missions with potential human presence, a rapid transfer between orbits of interest is a priority. The magnitude of the state variations along the maximum stretching direction is expected to grow rapidly and, therefore, offers information to depart from the orbit. Similarly, the maximum stretching in reverse time, enables arrival with a minimal maneuver magnitude. The impact of maneuvers in such sensitive directions is investigated. Further, enabling transfer design options to connect between two stable orbits. The transfer design strategy developed in this investigation is not restricted to a particular orbit but applicable to a broad range of stable and nearly stable orbits in the cislunar space, including the Distant Retrograde Orbit (DROs) and the Low Lunar Orbits (LLO) that are considered for potential missions. Examples for transfers linking a southern and a northern NRHO, a southern NRHO to a planar DRO, and a southern NRHO to a planar LLO are demonstrated.</div>

<div>As destinations of missions in both human and robotic spaceflight become more exotic, a foundational understanding the dynamical structures in the gravitational environments enable more informed mission trajectory designs. One particular type of structure, quasi-periodic orbits, are examined in this investigation. Specifically, efficient computation of quasi-periodic orbits and leveraging quasi-periodic orbits as trajectory design alternatives in the Earth-Moon and Sun-Earth systems. First, periodic orbits and their associated center manifold are discussed to provide the background for the existence of quasi-periodic motion on n-dimensional invariant tori, where n corresponds to the number of fundamental frequencies that define the motion. Single and multiple shooting differential corrections strategies are summarized to compute families 2-dimensional tori in the Circular Restricted Three-Body Problem (CR3BP) using a stroboscopic mapping technique, originally developed by Howell and Olikara. Three types of quasi-periodic orbit families are presented: constant energy, constant frequency ratio, and constant mapping time families. Stability of quasi-periodic orbits is summarized and characterized with a single stability index quantity. For unstable quasi-periodic orbits, hyperbolic manifolds are computed from the differential of a discretized invariant curve. The use of quasi-periodic orbits is also demonstrated for destination orbits and transfer trajectories. Quasi-DROs are examined in the CR3BP and the Sun-Earth-Moon ephemeris model to achieve constant line of sight with Earth and avoid lunar eclipsing by exploiting orbital resonance. Arcs from quasi-periodic orbits are leveraged to provide an initial guess for transfer trajectory design between a planar Lyapunov orbit and an unstable halo orbit in the Earth-Moon system. Additionally, quasi-periodic trajectory arcs are exploited for transfer trajectory initial guesses between nearly stable periodic orbits in the Earth-Moon system. Lastly, stable hyperbolic manifolds from a Sun-Earth L₁ quasi-vertical orbit are employed to design maneuver-free transfer from the LEO vicinity to a quasi-vertical orbit.</div>