付記する学位プログラム名: デザイン学大学院連携プログラム / 京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第21761号 / 工博第4578号 / 新制||工||1713(附属図書館) / 京都大学大学院工学研究科航空宇宙工学専攻 / (主査)教授 藤本 健治, 教授 泉田 啓, 教授 太田 快人 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM

<p>Increasingly, space flight missions are planned to traverse regions of space with complex dynamical environments influenced by multiple gravitational bodies. The nature of these systems produces motion and regions of sensitivity that are, at times, unintuitive,</p> <p>and the accumulation of trajectory dispersions from a variety of sources guarantees that spacecraft will deviate from their pre-planned trajectories in this complex environment, necessitating the use of a targeting process to generate a new feasible reference path. To ensure mission success and a robust path planning process, trajectory designers require insight into the interaction between the targeting process, the baseline trajectory, and the dynamical environment. In this investigation, the convergence behavior of these targeting processes is examined. This work summarizes a framework for characterizing and predicting the convergence behavior of perturbed targeting problems, consisting of a set of constraints, design variables, perturbation variables, and a reference solution within a dynamical system. First, this work identifies the typical features of a convergence basin and identifies a measure of worst-case performance. In the absence of an analytical method, efficient numerical discretization procedures are proposed based on the evaluation of partial derivatives at the reference solution to the perturbed targeting problem. A method is also proposed for approximating the tradespace of position and velocity perturbations that achieve reliable</p> <p>convergence toward the baseline solution. Additionally, evaluated scalar quantities are introduced to serve as predictors of the simulation-measured worst-case convergence behavior based on the local rate of growth in the constraints as well as the local relative change in the targeting-employed partial derivatives with respect to perturbations.</p> <p><br></p> <p>A variety of applications in different dynamical regions and force models are introduced to evaluate the improved discretization techniques and their correlation to the predictive metrics of convergence behavior. Segments of periodic orbits and transfer trajectories from past and planned missions are employed to evaluate the relative convergence performance across sets of candidate solutions. In the circular restricted three-body problem (CRTBP), perturbed targeting problems are formulated along a distant retrograde orbit and a near-rectilinear halo orbit (NRHO) in the Earth-Moon system. To investigate the persistence of results from the CRTBP in an ephemeris force model, a targeting problem applied to an NRHO is analyzed in both force models. Next, an L1 -to-L2 transit trajectory in the Sun-Earth system is studied to explore the effect of moving a maneuver downstream along</p> <p>a trajectory and altering the orientations of the gravitational bodies. Finally, a trans-lunar return trajectory is explored, and the convergence behavior is analyzed as the final maneuver time is varied.</p>

Trajectory planning is important in many applications involving unmanned aerial vehicles, underwater vehicles, spacecraft, and industrial manipulators. It is still a challenging task to rapidly find an optimal trajectory while taking into account dynamic and environmental constraints. In this dissertation, a unified, varying manifold based optimal trajectory planning method inspired by several predator-prey relationships is investigated to tackle this challenging problem. Biological species, such as hoverflies, ants, and bats, have developed many efficient hunting strategies. It is hypothesized that these types of predators only move along paths in a carefully selected manifold based on the prey’s motion in some of their hunting activities. Inspired by these studies, the predator-prey relationships are organized into a unified form and incorporated into the trajectory optimization formulation, which can reduce the computational cost in solving nonlinear constrained optimal trajectory planning problems. Specifically, three motion strategies are studied in this dissertation: motion camouflage, constant absolute target direction, and local pursuit. Necessary conditions based on the speed and obstacle avoidance constraints are derived. Strategies to tune initial guesses are proposed based on these necessary conditions to enhance the convergence rate and reduce the computational cost of the motion camouflage inspired strategy. The following simulations have been conducted to show the advantages of the proposed methods: a supersonic aircraft minimum-time-to-climb problem, a ground robot obstacle avoidance problem, and a micro air vehicle minimum time trajectory problem. The results show that the proposed methods can find the optimal solution with higher success rate and faster iv convergent speed as compared with some other popular methods. Among these three motion strategies, the method based on the local pursuit strategy has a relatively higher success rate when compared to the other two. In addition, the optimal trajectory planning method is embedded into a receding horizon framework with unknown parameters updated in each planning horizon using an Extended Kalman Filter

<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">A dramatic increase in the number of missions for inserting both large satellites as well as rideshare spacecraft into cislunar trajectories has been noted as of recently. While bal- listic lunar transfers (BLTs) have proven a reliable means for sending primary missions to their destination orbits, the inflexible jettison conditions imposed upon secondary payloads may significantly limit viable pathways. This investigation is centered about designing a framework to construct lunar transfers for secondary payloads from various commissioning maneuver (CM) states to select periodic orbits near the Moon. These continuous passage- ways are modelled in the Bi-Circular Restricted 4-Body Problem (BCR4BP), while necessary dynamical insights are recovered from the application of dynamical systems theory to both the BCR4BP and the Circular Restricted 3-Body Problem (CR3BP). To understand the impact of a Moon encounter on an outbound lunar transfer, families of BLTs are generated for primary payloads, where select members that have close flybys are isolated an examined. A modular, multi-phase framework is then developed, stemming from the lunar encounter. With this, transfers from a variety of sample CM states to Halo, Butterfly and Lyapunov orbits are presented. The versatility of the design framework is highlighted through a case study for a double-flyby transfer to a select Lyapunov orbit. The presented analysis provides an intuitive strategy for diversifying the otherwise limited pool of viable transfers that send secondary payloads to cislunar orbits.</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>

<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>

<p dir="ltr">Design under uncertainty (DUU) for spacecraft is crucial in ensuring mission success, especially given the criticality of their failure. To obtain a more realistic understanding of space systems, it is beneficial to holistically couple the modeling of the spacecraft and its trajectory as a multidisciplinary analysis (MDA). In this work, a MDA model is developed for an Earth-Mars mission by employing the general mission analysis tool (GMAT) to model the mission trajectory and rocket propulsion analysis (RPA) to design the engines. By utilizing this direct MDA model, the deterministic optimization (DO) of the system is performed first and yields a design that completed the mission in 307 days while requiring 475 kg of fuel. The direct MDA model is also integrated into a Monte Carlo simulation (MCS) to investigate the uncertainty quantification (UQ) of the spacecraft and trajectory system. When considering the combined uncertainty in the launch date for a 20-day window and the specific impulses, the time of flight ranges from 275 to 330 days and the total fuel consumption ranges from 475 to 950 kg. The spacecraft velocity exhibits deviations ranging from 2 to 4 km/s at any given instance in the Earth inertial frame. The amount of fuel consumed during the TCM ranges from 1 to 250 kg, while during the MOI, the amount of fuel consumed ranges from 350 to 810 kg. The usage of the direct MDA model for optimization and uncertainty quantification of the system can be computationally prohibitive for DUU. To address this challenge, the effectiveness of utilizing surrogate-based approaches for performing UQ is demonstrated, resulting in significantly lower computational costs. Gaussian processes (GP) models trained on data from the MDA model were implemented into the UQ framework and their results were compared to those of the direct MDA method. When considering the combined uncertainty from both sources, the surrogate-based method had a mean error of 1.67% and required only 29% of the computational time. When compared to the direct MDA, the time of flight range matched well. While the TCM and MOI fuel consumption ranges were smaller by 5 kg. These GP models were integrated into the DUU framework to perform reliability-based design optimization (RBDO) feasibly for the spacecraft and trajectory system. For the combined uncertainty, the DO design yielded a poor reliability of 54%, underscoring the necessity for performing RBDO. The DUU framework obtained a design with a significantly improved reliability of 99%, which required an additional 39.19 kg of fuel and also resulted in a reduced time of flight by 0.55 days.</p>

<p dir="ltr">With increasing interest in cislunar operations and exploration of deep space destinations like Mars, a foundational understanding of cislunar dynamics and their potential for facilitating departure from the vicinity of Earth is essential. This investigation addresses this need by analyzing system departure characteristics from a variety of periodic orbit families with unstable members in the Earth-Moon Circular-Restricted 3-Body Problem (CR3BP).</p><p dir="ltr">Specifically, a cislunar-to-Mars transfer methodology is developed, leveraging multi-body dynamical systems theory, especially invariant manifolds of periodic orbits, to design lower energy deep space transfers in comparison to traditional methods. The proposed approach generates families of end-to-end transfers that vary in total maneuver delta-v cost and time-of flight, originating from different unstable cislunar orbits. The tradespaces of these transfer families are then analyzed and compared across various departure orbits to identify departure characteristics across orbit families and energy levels (Jacobi constants). The analysis reveals certain unstable Earth-Moon CR3BP orbit families with more favorable departure characteristics.</p><p dir="ltr">Additionally, this investigation compares the computed deep space transfer costs with those of traditional interplanetary transfers and others from existing literature. Although this transfer design strategy is specifically applied to Mars transfers in this investigation, the methodology is broadly applicable to other deep space destinations. Furthermore, the general findings on cislunar departure characteristics have implications for mission designs to destinations beyond the Earth-Moon region.</p>

<div><div>Designing trajectories in dynamically complex environments is challenging and can easily become intractable via solely manual design efforts. Thus, the problem is recast to blend traditional astrodynamics approaches with machine learning to develop a rapid and flexible trajectory design framework. This framework incorporates knowledge of the spacecraft performance specifications via the computation of Accessible Regions (ARs) that accommodate specific spacecraft acceleration levels for varied mission scenarios in a complex multi-body dynamical regime. Specifically, pathfinding agents, via Heuristically Accelerated Reinforcement Learning (HARL) and Dijkstra's algorithms, engage in a multi-dimensional combinatorial search to sequence advantageous natural states emerging from the ARs to construct initial guesses for end-to-end transfers. These alternative techniques incorporate various design considerations, for example, prioritizing computational time versus the pursuit of globally optimal solutions to meet multi-objective mission goals. The initial guesses constructed by pathfinding agents then leverage traditional numerical corrections processes to deliver continuous transport of a spacecraft from departure to destination. Solutions computed in the medium-fidelity Circular Restricted Three Body (CR3BP) model are then transitioned to a higher-fidelity ephemeris regime where the impact of time-dependent gravitational influences from multiple bodies is also explored.</div><div><br></div><div>A broad trade-space arises in this investigation in large part due to the rich and diverse dynamical flows available in the CR3BP. These dynamical pathways included in the search space via: (i) a pre-discretized database of known periodic orbit families; (ii) flow-models of these families of orbits/arcs `trained' via the supervised learning algorithms Artificial Neural Networks (ANNs) and Support Vector Machines (SVMs); and, finally (iii) a free-form search that permits selection of both chaotic and ordered motion. All three approaches deliver variety in the constructed transfer paths. The first two options offer increased control over the nature of the transfer geometry while the free-form approach eliminates the need for a priori knowledge about available flows in the dynamical environment. The design framework enables varied transfer scenarios including orbit-orbit transport, s/c recovery during contingency events, and rendezvous with a pre-positioned object at an arrival orbit. Realistic mission considerations such as altitude constraints with respect to a primary are also incorporated.</div></div>