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.

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.

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.

<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>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>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>

<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>

This thesis describes the design, implementation and analysis for a preliminary study for DLR's MASCOT lander's next mission to Small Solar System Bodies (SSSB). MASCOT (Mobile Asteroid Surface Scout) is a nano-lander that flew aboard Hayabusa2 (JAXA) to an asteroid, Ryugu. It is a passive nano-spacecraft that can only be deployed ballistically from a hovering spacecraft. Current research focusses on optimizing similar close-approach missions for deploying landers or small cubesats into periodic orbits but does not provide solutions with semi-autonomous small landers deployed from farther distances. This study aims to overcome this short-coming by proposing novel yet simple Guidance, Navigation and Control (GNC) and Propulsion systems for MASCOT. Due to its independent functioning and customisable anatomy, MASCOT can be adapted for several mission scenarios. In this thesis, a particular case-study is modelled for the HERA (ESA) mission. The first phase of the study involves the design of a landing trajectory to the moon of the Didymos binary asteroid system. For a preliminary analysis, the system - Didymain (primary body), Didymoon (secondary body) and MASCOT (third body) - are modelled as a Planar Circular Restricted Three Body Problem (PCR3BP). The numerical integration methodology used for the trajectory is the variable-step Dormand–Prince (Runge Kutta) ODE-4,5 (Ordinary Differential Equation) solver. The model is built in MATLAB-Simulink (2019a) and refined iteratively by conducting a Monte Carlo analysis using the Sensitivity Analysis Tool. Two models - a thruster-controlled system and an alternative hybrid propulsion system of solar sails and thrusters - are simulated and proven to be feasible. The results show that the stable manifold near Lagrange 2 points proposed by Tardivel et. al. for ballistic landings can still be exploited for distant deployments if a single impulse retro-burn is done at an altitude of 65 m to 210 m above ground with error margins of 50 m in position, 5 cm/s in velocity and 0.1 rad in attitude. The next phase is the conceptual design of a MASCOT-variant with GNC abilities. Based on the constraints and requirements of the flown spacecraft, novel GNC and Propulsion systems are chosen. To identify the overriding factors in using commercial-off-the-shelf (COTS) for MASCOT, a market survey is conducted and the manufacturers of short-listed products are consulted. The final phase of the study is to analyse the proposed equipment in terms of parameter scope and capability-oriented trade-offs. Two traceability matrices, one for devised solutions and system and another for solutions versus capabilities, are constructed. The final proposed system is coherent with the given mass, volume and power constraints. A distant deployment of MASCOT-like landers for in-situ observation is suggested as an advantageous and risk-reducing addition to large spacecraft missions to unknown micro-gravity target bodies. Lastly, the implications of this study and the unique advantages of an enhanced MASCOT lander are explored for currently planned SSSB missions ranging from multiple rendezvous, fly-by or sample-return missions. Concluding, this study lays the foundation for future work on advanced GNC concepts for unconventional spacecraft topology for the highly integrated small landers. / <p>This thesis is submitted as per the requirements for the Spacemaster (Round 13) dual master's degree under the Erasmus Mundus Joint Master's Degree Programme. </p> / MASCOT team, DLR