<p dir="ltr">Object tracking in cislunar space has become an area of interest within many communities where cislunar space domain awareness (SDA) is critical to operations. Due to the influence of both the Earth and Moon on objects in this domain, the classical two body problem does not accurately describe the dynamics of the state. Legacy tracking capabilities fall short in providing accurate state estimates due to the large volume of space and the highly non-linear dynamics involved. In order to advance SDA in cislunar space, tracking capabilities must be updated for this domain. </p><p dir="ltr">Both the Extended Kalman Filter (EKF) and Gaussian Mixture Extended Kalman Filter (GM-EKF) are used for orbit determination in this thesis along side the Circular Restricted Three Body Problem (CR3BP) to model the non-linear dynamics. The filters are utilized to determine the best estimate of the state as well as its covariance. The two filter's performances are compared to highlight areas in which the assumptions surrounding the EKF are violated resulting in failed tracking, as well as to highlight the power of the GM-EKF for non-linear systems using splitting and merging techniques. </p><p dir="ltr">This thesis presents single and multiple object tracking of objects in a multitude of cislunar orbits using a Moon ground-based sensor. Multiple object tracking is accomplished using a novel Lyapunov-based scheduler in order to reduce the total system uncertainty. The environment is modeled to include exclusion zones which preclude measurements. These zones consist of conjunction from the Earth and Sun, brightness constraints, and camera field of regard (FOR). When measurements are unavailable the uncertainty in the state estimation rises significantly.</p><p dir="ltr">An investigation of varied sensor placements and Sun-Earth-Moon geometries provides results to inform locations and trends which are able to confidently track both single and multiple objects in cislunar orbits. </p>

<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>

To leave Earth’s gravity well and ascend into Cislunar space takes ingenuity, and the engineering feats of many. Now to propel humanity further into space, rockets will need assistance to provide the large requirements of mass to be used for space structures. Tsiolkovsky’s Rocket Equation greatly limits the advantages of rockets and leaves an opening for Space Elevators to assist in a dual space access approach. By moving a large amount of mass routinely, efficiently, environmentally friendly and with daily launches towards space. Along with the apex anchor situated at 100,000 km for emergency assistance across all Cislunar space, and to act as both storage facilities and a construction zone. Space Elevators are the railway to space and can supplement rockets by transforming how mass is transported to Cislunar space and beyond. / Att lämna jordens gravitationsbrunn och stiga upp i Cislunar-rymden kräver uppfinningsrikedom och mångas ingenjörsprestationer. För att nu driva mänskligheten längre ut i rymden kommer raketer att behöva hjälp för att tillhandahålla de stora kraven på massa som ska användas för rymdstrukturer. Tsiolkovskys raketekvation begränsar i hög grad fördelarna med raketer och lämnar en öppning för rymdhissar för att hjälpa till med en dubbel rymdtillgång. Rymdhissar kan att flytta en stor mängd massa rutinmässigt, effektivt, miljövänligt och med dagliga uppskjutningar mot rymden. Apex-ankaret som ligger på 100 000 km kan fungera för nödhjälp över hela Cislunar-utrymmet och som både lagringsutrymmen och en konstruktionszon. Rymdhissar är järnvägen till rymden och kan komplettera raketer genom transformation hur massa transporteras till Cislunar rymden och bortom.

<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>

<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>

<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>