This thesis evaluates decommissioning strategies for the International Space Station ISS. A permanent solution is attempted by employing energy efficient invariant manifolds that arise in the circular restricted three body problem CRTBP to transport the ISS from its low Earth orbit LEO to a lunar orbit. Although the invariant manifolds provide efficient transport, getting the the ISS onto the manifolds proves quite expensive, and the trajectories take too long to complete. Therefore a more practical, although temporary, solution consisting of an optimal re-boost maneuver with the European Space Agency's automated transfer vehicle ATV is proposed. The optimal re-boost trajectory is found using control parameterization and the sequential quadratic programming SQP algorithm. The model used for optimization takes into account the affects of atmospheric drag and gravity perturbations. The optimal re-boost maneuver produces a satellite lifetime of approximately ninety-five years using a two ATV strategy.

The general station-keeping problem is a focal topic when considering any spacecraft mission application. Recent missions are increasingly requiring complex trajectories to satisfy mission requirements, necessitating the need for accurate station-keeping controllers. An ideal controller reliably corrects for spacecraft state error, minimizes the required propellant, and is computationally efficient. To that end, this investigation assesses the effectiveness of several controller formulations in the circular restricted three-body model. Particularly, a spacecraft is positioned in a L₁ southern halo orbit within the Sun-Earth Moon Barycenter system. To prevent the spacecraft from departing the vicinity of this reference halo orbit, the Floquet mode station-keeping approach is introduced and evaluated. While this control strategy generally succeeds in the station-keeping objective, a breakdown in performance is observed proportional to increases in state error. Therefore, a new hybrid controller is developed which leverages Floquet mode and reinforcement learning. The hybrid controller is observed to efficiently determine corrective maneuvers that consistently recover the reference orbit for all evaluated scenarios. A comparative analysis of the performance metrics of both control strategies is conducted, highlighting differences in the rates of success and the expected propellant costs. The performance comparison demonstrates a relative improvement in the ability of the hybrid controller to meet the mission objectives, and suggests the applicability of reinforcement learning to the station-keeping problem.

With the growth of human interest in the Lunar region, methods of enabling Lunar access including surface and Low Lunar Orbit (LLO) from periodic orbit in the Lunar region is becoming more important. The current investigation explores the Lunar access capabilities of these periodic orbits. Impact trajectories originating from the 9:2 Lunar Synodic Resonant (LSR) Near Rectilinear Halo Orbit (NRHO) are determined through explicit propagation and mapping of initial conditions formed by applying small maneuvers at locations across the orbit. These trajectories yielding desirable Lunar impact final conditions are then used to converge impacting transfers from the NRHO to Shackleton crater near the Lunar south pole. The stability of periodic orbits in the Lunar region is analyzed through application of a stability index and time constant. The Lunar access capabilities of the Lunar region periodic orbits found to be sufficiently unstable are then analyzed through impact and periapse maps. Using the impact data, candidate periodic orbits are incorporated in the the NRHO to Shackleton crater mission design to control mission geometry. Finally, the periapse map data is used to determine periodic orbits with desirable apse conditions that are then used to design NRHO to LLO transfer trajectories.

<div> <div> <div> <p>Resonant orbits in a multi-body environment have been investigated in the past to aid the understanding of perceived chaotic behavior in the solar system. The invariant manifolds associated with resonant orbits have also been recently incorporated into the design of trajectories requiring reduced maneuver costs. Poincaré sections are now also extensively utilized in the search for novel, maneuver-free trajectories in various systems. This investigation employs dynamical systems techniques in the computation and characterization of resonant orbits in the higher-fidelity Circular Restricted Three-Body model. Differential corrections and numerical methods are widely leveraged in this analysis in the determination of orbits corresponding to different resonance ratios. The versatility of resonant orbits in the design of low cost trajectories to support exploration for several planet-moon systems is demonstrated. The efficacy of the resonant orbits is illustrated via transfer trajectory design in the Earth-Moon, Saturn-Titan, and the Mars-Deimos systems. Lastly, Poincaré sections associated with different resonance ratios are incorporated into the search for natural, maneuver-free trajectories in the Saturn-Titan system. To that end, homoclinic and heteroclinic trajectories are constructed. Additionally, chains of periodic orbits that mimic the geometries for two different resonant ratios are examined, i.e., periodic orbits that cycle between different resonances are determined. The tools and techniques demonstrated in this investigation are useful for the design of trajectories in several different systems within the CR3BP. </p> </div> </div> </div>

<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.

<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>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>Many future satellite applications in cislunar space require repeating, periodic transfers that shift away from some operational orbit and eventually return. Resonant orbits are investigated in the Earth-Moon Circular Restricted Three Body Problem (CR3BP) as a mechanism to enable these transfers. Numerous resonant orbit families possess a ratio of orbital period to lunar period that is sufficiently close to an integer ratio and can be exploited to uncover period-commensurate transfers due to their predictable periods. Resonant orbits also collectively explore large swaths of space, making it possible to select specific orbits that reach a region of interest. A framework for defining period-commensurate transfers is introduced that leverages the homoclinic connections associated with an unstable operating orbit to permit ballistic transfers that shuttle the spacecraft to a certain region. Resonant orbits are incorporated by locating homoclinic connections that possess resonant structures, and the applicability of these transfers is extended by optionally linking them to resonant orbits. In doing so, transfers are  available for in-orbit refueling/maintenance as well as surveillance/communications applications  that depart and return to the same phase in the operating orbit.</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>