In recent times, as the National Aeronautics and Space Administration (NASA) focuses on establishing a sustained presence in cislunar space, there has been an increase in planned missions to the cislunar vicinity for lunar exploration. Due to this increase in planned missions, the use of cislunar structures available in the Circular Restricted Three-Body Problem (CRTBP) has become of greater interest. Traditionally, transfers that leverage CRTBP structures in the cislunar vicinity have been generated as point designs. As a consequence of the non-linearity of this model, transitioning these point designs to other epochs or mission scenarios is non-trivial. Hence, a trade space of transfer solutions, that leverage the underlying dynamics, is of interest for rapid mission design. In this study, numerical methods and dynamical systems theory are leveraged to extract available dynamical structures in the model, which are subsequently exploited for transfer design. A trade space of relatively low time of flight, two-maneuver transfers, from a 500 km altitude Low Earth Orbit (LEO) to the Earth-Moon L1 Lyapunov orbit family is generated and analyzed.

The number of objects occupying orbital regimes beyond Geosynchronous Earth Orbit and cislunar space are expected to grow in the coming years; Especially with the Moon reemerging as latest frontier in the race for space exploration and technological superiority. In order to support this growth, new methods of autonomously navigating in cislunar space are necessary to reduce demand and reliance on ground based tracking infrastructure. Periodic orbits about the first libration point offer favorable vantage points for scientific or military spacecraft missions involving the Earth or Moon. This thesis develops a new autonomous spacecraft navigation method for cislunar space and analyzes its performance applied to Lyapunov and halo orbits around $L_1$. This method uses existing lunar ranging retroreflectors (LRRR) installed on the Moon's surface in the 1960s and 1970s. A spacecraft can make laser ranging measurements to the LRRR to estimate its orbit states. A simulation platform was created to test this concept in the circular restricted three body problem and evaluate its performance. This navigation method was found to be successful for a subset of Lyapunov and halo orbits when cycling the five measurement targets. Simulation data showed that sub-kilometer position estimation and sub 2 centimeter per second velocity accuracies are achievable without receiving any state updates from external sources. / Master of Science / The number of objects occupying the space between the Earth and Moon (cislunar space) is expected to grow in the coming years as the Moon regains popularity in the latest race for space exploration and technological superiority. In order to support this growth, new methods of determining a spacecraft's position and velocity while in this region of space are necessary to reduce demand and dependence on Earth based methods, which have historically relied upon. Repeating orbits around the equilibrium point between the Earth and Moon provide valuable observation points for scientific and military spacecraft missions. This thesis develops a new spacecraft navigation method for cislunar space and analyzes how well it performs in two different types of orbits, Lyapunov and halo orbits. This method uses existing laser reflector panels that were installed on the Moon's surface in the 1960s and 70s. A spacecraft can use these panels to make range or distance measurements in order to estimate its position and velocity. Software was written to simulate the motion of a spacecraft as it is acted on by gravity from the Earth and Moon. Different scenarios were then simulated and used to test this concept and evaluate its performance. Lunar laser ranging was found to be successful for a some Lyapunov and halo orbits when switching between the five different reflector panels on the Moon. Data generated from the simulations show that position can be estimated with errors less than SI{1}{kilo meter}, and velocity error on the order of a few centimeters per second, all without receiving any additional information from Earth based systems.

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">With the increase in planned space missions in cislunar space, it is necessary to study the ability of observers to observe and track objects in this regime. This thesis focuses on creating a sensor tasking algorithm for constellations of optical observers to efficiently observe cislunar objects. The circular restricted three body problem is used for the dynamics of the objects while the bi-circular restricted four body problem is used to approximate the position of the sun.</p><p dir="ltr">A new way of discretizing the field of regard is proposed that respects the observers field of view on the unit sphere. A method for providing feedback to the observer in a delayed feedback environment is applied to mean state, single Gaussian, and particle representations of uncertainty. The method of determining a scaling coefficient for Sanson’s probability of detection is recorded. Sanson’s probability of detection is studied for determining the correct effective aperture dimensions of an optical observer. An approximation is presented for expediting calculations of Sanson’s probability of detection. An uncertainty propagation analysis shows there is an efficient number of particles to use for particle uncertainty far below the required number for a full Monte Carlo particle uncertainty representation. </p><p dir="ltr">Mean state, single Gaussian and particle methods of uncertainty characterization are compared in a cislunar simulation showing the benefits of the particles solution over other forms of uncertainty characterization. Particles are not only an effective uncertainty representation in a delayed feedback environment, they are computationally feasible for the sensor tasking problem. The performance of the particle algorithm for a constellation of observers is evaluated in a simulated small satellite breakup in a Lyapunov orbit and a simulated breakup of the proposed Lunar Gateway. The performance of observers in direct retrograde, low lunar, geosynchronous, and northern Halo orbits are evaluated in the breakup simulations. Results from these simulations show that observers in low lunar and Halo orbits can be valuable observation standpoints in breakups around the near-Moon region of cislunar space.</p>

<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 dir="ltr">This research considers orbit maintenance strategies for multi-body orbits in the context of the Earth-Moon Circular Restricted Three Body Problem (CR3BP). Dynamical requirements for successful long-term orbit maintenance strategies are highlighted.</p>

<p dir="ltr">At the cusp of scientific discovery and innovation, mankind's next greatest challenge lies in developing capabilities to enable human presence in deep space. This entails setting up space infrastructure, travel pathways, managing spacecraft traffic, and building up deep space operation logistics. Spacecrafts that are a part of the infrastructure must be able to perform myriad of operations and transfers such as rendezvous and docking, station-keeping, loitering, collision avoidance etc. In support of this endeavour, an investigation is done to analyze and recreate the solution space for fuel-optimal trajectories and control histories required for onboard trajectory design of inexpensive spacecraft transfers and operations. This study investigates close range rendezvous (CRR), nearby orbital transfer, collision avoidance, and long range transfer maneuvers for spacecrafts whose highly complex and nonlinear behavior is modelled using the circular restricted three-body problem (CR3BP) dynamics and to which a finite-burn maneuver is augmented to model low-propulsion maneuvers. In order to study the nonlinear solution space for such maneuvers, this investigation contributes new formulations of nonlinear programming (NLP) optimal control problems solved to minimize fuel consumption, and validated by traditional methods already in use. This investigation proposes a Feature Learning based Optimal Control Method (L-OCM) to learn the solution space and recreate results in real-time. The NLP problem is solved off-line for a range of initial conditions. The set of solutions is used to generate datasets with initial conditions as inputs and the identified features of the optimal control solution as outputs. These features are inherent to reconstructing the optimal control histories of the solution and are selected keeping onboard computational capabilities in mind. Deep Neural Networks (DNNs) are trained to map the complex, nonlinear relationship between the inputs and outputs, and then implemented to find on-line solutions to any initial condition. The L-OCM method provides fuel-optimal, real-time solutions that can be implemented by a spacecraft performing operations in cislunar space.</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>A dynamical understanding of orbits in the Earth-Moon neighborhood that can sustain long-term activities and trajectories that link locations of interest forms a critical foundation for the creation of infrastructure to support a lasting presence in this region of space. In response, this investigation aims to identify and exploit fundamental dynamical motion in the vicinity of a candidate ‘hub’ orbit, the L2 southern 9:2 lunar synodic resonant near rectilinear halo orbit (NRHO), while incorporating realistic mission constraints. The strategies developed in this investigation are, however, not restricted to this particular orbit but are, in fact, applicable to a wide variety of stable and nearly-stable cislunar orbits. Since stable and nearly-stable orbits that may lack useful manifold structures are of interest for long-term activities in cislunar space due to low orbit maintenance costs, strategies to alternatively initiate transfer design into and out of these orbits are necessary. Additionally, it is crucial to understand the complex behaviors in the neighborhood of any candidate hub orbit. In this investigation, a bifurcation analysis is used to identify periodic orbit families in close proximity to the hub orbit that may possess members with favorable stability properties, i.e., unstable orbits. Stability properties are quantified using a metric defined as the stability index. Broucke stability diagrams, a tool in which the eigenvalues of the monodromy matrix are recast into two simple parameters, are used to identify bifurcations along orbit families. Continuation algorithms, in combination with a differential corrections scheme, are used to compute new families of periodic orbits originating at bifurcations. These families possess unstable members with associated invariant manifolds that are indeed useful for trajectory design. Members of the families nearby the L2 NRHOs are demonstrated to persist in a higher-fidelity ephemeris model. </p><p><br></p> <p>Transfers based on the identified nearby dynamical structures and their associated manifolds are designed. To formulate initial guesses for transfer trajectories, a Poincaré mapping technique is used. Various sample trajectory designs are produced in this investigation to demonstrate the wide applicability of the design methodology. Initially, designs are based in the circular restricted three-body problem, however, geometries are demonstrated to persist in a higher-fidelity ephemeris model, as well. A strategy to avoid Earth and Moon eclipse conditions along many-revolution quasi-periodic ephemeris orbits and transfer trajectories is proposed in response to upcoming mission needs. Lunar synodic resonance, in combination with careful epoch selection, produces a simple eclipse-avoidance technique. Additionally, an integral-type eclipse avoidance path constraint is derived and incorporated into a differential corrections scheme as well. Finally, transfer trajectories in the circular restricted three-body problem and higher-fidelity ephemeris model are optimized and the geometry is shown to persist.</p>

An integral part of NASA's vision for the coming years is a sustained infrastructure in cislunar space. The current baseline trajectory for this facility is a Near Rectilinear Halo Orbit (NRHO), a periodic orbit in the Circular Restricted Three-Body Problem. One of the goals of the facility is to serve as a proving ground for human spaceflight operations in deep space. Thus, this investigation focuses on transfers between the baseline NRHO and a family of periodic orbits that originate from a period-doubling bifurcation along the halo family. This new family of orbits has been termed the ``butterfly" family. This investigation also provides an overview of the evolution for a large subset of the butterfly family. Transfers to multiple subsets of the family are found by leveraging different design strategies and techniques from dynamical systems theory. The different design strategies are discussed in detail, and the transfers to each of these regions are compared in terms of propellant costs and times of flight.