<p>Autonomous guidance and control techniques for low-thrust spacecraft under multi-body dynamics via reinforcement learning</p>

<p>National security concerns regarding cislunar space have become more prominent due to</p> <p>the anticipated increase in cislunar activity. Predictability is one of these concerns. Cislunar</p> <p>motion is difficult to predict because it is chaotic. The chaotic nature of cislunar motion is</p> <p>pronounced near the L1 and L2 Lagrange points. For this reason, among others, it is likely</p> <p>that a red actor (an antagonist) would have its cislunar spacecraft perform a maneuver in</p> <p>one of the aforementioned vicinities to reach some cislunar point of interest. This realization</p> <p>unveils the need to ascertain some degree of predictability in the motion resulting from a</p> <p>maneuver performed in the L1 or L2 region. To investigate said motion, impulsive maneuvers</p> <p>are employed on the L1 and L2 Lagrange points and on L1 and L2 Lyapunov orbits in the</p> <p>model that is the circular restricted three-body problem. The behavior of the resultant</p> <p>trajectories is analyzed to understand how the magnitude and direction of a maneuver in</p> <p>said regions affect the behavior of the resultant trajectory. It is found that the direction</p> <p>of such maneuvers is particularly influential with respect to said behavior. Regarding both</p> <p>the L1 and L2 regions, certain maneuver directions yield certain behaviors in the resultant</p> <p>trajectory over a wide range of maneuver magnitudes. This understanding is informative to</p> <p>cislunar mission design.</p>

<p dir="ltr">The Global Navigation Satellite System (GNSS) is heavily relied on for the navigation of Earth satellites. For satellites in cislunar space and beyond, GNSS is not readily available. As a result, other sources such as NASA's Deep Space Network (DSN) must be relied on for navigation. However, DSN is overburdened and can only support a small number of satellites at a time. Furthermore, communication with external sources can become interrupted or deprived in these environments. Given NASA's current efforts towards cislunar space operations and the expected increase in cislunar satellite traffic, there will be a need for more autonomous navigation options in cislunar space and beyond.</p><p dir="ltr">In this thesis, a navigation system capable of accurate and computationally efficient orbit determination in these communication-deprived environments is proposed and investigated. The emphasis on computational efficiency is in support of cubesats which are constrained in size, cost, and mass; this makes navigation even more challenging when resources such as GNSS signals or ground station tracking become unavailable.</p><p dir="ltr">The proposed navigation system, which is called GRAVNAV in this thesis, involves a two-satellite formation orbiting a planet. The primary satellite hosts an Extended Kalman Filter (EKF) and is capable of measuring the relative position of the secondary satellite; accurate attitude estimates are also available to the primary satellite. The relative position measurements allow the EKF to estimate the absolute position and velocity of both satellites. In this thesis, the proposed navigation system is investigated in the two-body and three-body problems.</p><p dir="ltr">The two-body analysis illuminates the effect of the gravity model error on orbit determination performance. High-fidelity gravity models can be computationally expensive for cubesats; however, celestial bodies such as the Earth and Moon have non-uniform and highly-irregular gravity fields that require complex models to describe the motion of satellites orbiting in their gravity field. Initial results show that when a second-order zonal harmonic gravity model is used, the orbit determination accuracy is poor at low altitudes due to large gravity model errors while high-altitude orbits yield good accuracy due to small gravity model errors. To remedy the poor performance for low-altitude orbits, a Gravity Model Error Compensation (GMEC) technique is proposed and investigated. Along with a special tuning model developed specifically for GRAVNAV, this technique is demonstrated to work well for various geocentric and lunar orbits.</p><p><br></p><p dir="ltr">In addition to the gravity model error, other variables affecting the state estimation accuracy are also explored in the two-body analysis. These variables include the six Keplerian orbital elements, measurement accuracy, intersatellite range, and satellite formation shape. The GRAVNAV analysis shows that a smaller intersatellite range results in increased state estimation error. Despite the intersatellite range bounds, semimajor axis, measurement model, and measurement errors being identical for both orbits, the satellite formation shape also has a strong influence on orbit determination accuracy. Formations that place both satellites in different orbits significantly outperform those that place both satellites in the same orbit.</p><p dir="ltr">The three-body analysis primarily focuses on characterizing the unique behavior of GRAVNAV in Near Rectilinear Halo Orbits (NRHOs). Like the two-body analysis, the effect of the satellite formation shape is also characterized and shown to have a similar impact on the orbit determination performance. Unlike the two-body problem, however, different orbits possess different stability properties which are shown to significantly affect orbit determination performance. The more stable NRHOs yield better GRAVNAV performance and are also less sensitive to factors that negatively impact performance such as measurement error, process noise, and decreased intersatellite range.</p><p dir="ltr">Overall, the analyses in this thesis show that GRAVNAV yields accurate and computationally efficient orbit determination when GMEC is used. This, along with the independence of GRAVNAV from GNSS signals and ground-station tracking, shows that GRAVNAV has good potential for navigation in cislunar space and beyond.</p>

In this thesis, the possibility of enabling space-mining for the upcoming decade is explored. Making use of recently-proven reusable rockets, we envision a fleet of spacecraft capable of reaching Near-Earth asteroids. To analyze this idea, the goal of this problem is to maximize the asteroid mass retrieved within a spacecraft max life span. Explicitly, the maximum lifetime of the spacecraft fleet is set at 30 years. A fuel supply-chain is proposed and designed so that each spacecraft is refueled before departing for each asteroid. To maximize access to the number of asteroids and retrievable mass for each mission, we propose launching each mission from an orbit with low escape velocity. The L2-Halo orbit at the libration point in the Earth-Moon system was selected due to its easy access from Low-Earth Orbit and for a cislunar synergy with NASA Gateway. Using data from NASA SmallBody and CNEOS databases, we investigated NEAs in the period between 2030 and 2060 could be captured in the ecliptic plane and returned to L2-Halo with two approaches, MARM-1 and MARM-2. Together, these databases provide all information for every asteroid's close approach known today. Returning the asteroid as a whole is explored in the MARM-1 method, while MARM-2 evaluates the possibility of reaching larger asteroids and returning a fragment of their masses, such that it optimizes the available cargo weight per time of flight of each mission. The following results are compared with previous work from the community. The results show a 96% reduction in the cost per kg, with an enormous increase in retrieved mass. With these results, this thesis shows that not solely energy or dynamic optimization will be responsible for proving space mining feasibility, but rather a combination of those and business best practices. Proving feasibility for space mining is a complex and immense problem. Although this thesis opens new possibilities for future work on the field and sparkes the interest of private endeavors, the final solution for this problem still requires additional exploration. / M.S. / In this thesis, the possibility of enabling space-mining for the upcoming decade is explored. Making use of recently-proven reusable rockets, we envision a fleet of spacecraft capable of reaching Near-Earth asteroids, NEAs. To analyze this idea, the goal of this problem is to maximize the asteroid mass retrieved within a spacecraft max life span. Explicitly, the maximum lifetime of the spacecraft fleet is set at 30 years. A fuel supply-chain is proposed and designed so that each spacecraft is refueled before departing for each asteroid. To maximize access to the number of asteroids and retrievable mass for each mission, we propose launching each mission from an orbit with low escape velocity. A location after the Moon, at the L2-Halo orbit, was selected due to its easy access from Low-Earth Orbit and for a synergy with the proposed new space station at the Moon orbit. Using data from NASA databases, we investigated the asteroids in the period between 2030 and 2060 that could be captured and returned with two approaches, MARM-1 and MARM-2. Together, these databases provide all information for every asteroid's close approach known today. Returning the asteroid as a whole is explored in the MARM-1 method, while MARM-2 evaluates the possibility of reaching larger asteroids and returning a fragment of their masses, such that it optimizes the available cargo weight per time of flight of each mission. The following results are compared with previous work from the community. The results show a 96% reduction in the cost per kg, with an enormous increase in retrieved mass. With these results, this thesis shows that not solely energy or dynamic optimization will be responsible for proving space mining feasibility, but rather a combination of those and business best practices. Proving feasibility for space mining is a complex and immense problem. Although this thesis opens new possibilities for future work on the field and sparkes the interest of private endeavors, the final solution for this problem still requires additional exploration.

<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"> 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>

<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>