This dissertation expands across three topics the geometric theory of phase space transit in the circular restricted three-body problem (CR3BP) and its generalizations. The first topic generalizes the low energy transport theory that relies on linearizing the Lagrange points in the CR3BP to time-periodic perturbations of the CR3BP, such as the bicircular problem (BCP) and the elliptic restricted three-body problem (ER3BP). The Lagrange points are no longer invariant under perturbation and are replaced by periodic orbits, which we call Lagrange periodic orbits. Calculating the monodromy matrix of the Lagrange periodic orbit and transforming into eigenbasis coordinates reveals that the transport geometry is a discrete analogue of the continuous transport geometry in the unperturbed problem. The second topic extends the theory of low energy phase space transit in periodically perturbed models using a nonlinear analysis of the geometry. This nonlinear analysis relies on calculating the monodromy tensors, which generalize monodromy matrices in order to encode higher order behavior, about the Lagrange periodic orbit. A nonlinear approximate map can be obtained which can be used to iterate initial conditions within the linear eigenbasis, providing a computationally efficient means of distinguishing transit and nontransit orbits that improves upon the predictions of the linear framework. The third topic demonstrates that the recently-discovered "arches of chaos" that stretch through the solar system, causing substantial phase space divergence for high energy particles, may be identified with the stable and unstable manifolds to the singularities of the CR3BP. We also study the arches in terms of particle orbital elements and demonstrate that the arches correspond to gravity assists in the two-body limit. / Doctor of Philosophy / Suppose that we have a spacecraft and we want to model its motion under gravity. Depending upon what trade-offs we are willing to make between accuracy and complexity, we have several options at our disposal. For example, the restricted three-body problem (R3BP) and its generalizations prove useful in many real-world situations and are rich in theoretical power despite seeming mathematically simple. The simplest restricted three-body problem is the circular restricted three-body problem (CR3BP). In the CR3BP, two masses (like a star and a planet or a planet and a moon) orbit their common center of gravity in circular orbits, while a much smaller body (like a spacecraft) moves freely, influenced by the gravitational fields that the two masses create. If we add in an extra force that acts on the spacecraft in a periodic, cycling way, the regular CR3BP becomes a periodically-perturbed CR3BP. Examples of periodically-perturbed CR3BP's include the bicircular problem (BCP), which adds in a third mass that appears to orbit the center of the system from a distance, and the elliptic restricted three-body problem (ER3BP), which allows the two masses to orbit more realistically as ellipses rather than circles. The purpose of this dissertation is to determine how to select trajectories that move spacecraft between places of interest in restricted three-body models. We generalize existing theories of CR3BP spacecraft motion to periodically-perturbed CR3BP's in the first two topics, and then we investigate some new areas of research in the unperturbed CR3BP in the third topic. We utilize numerical computations and mathematical methods to perform these analyses.

<p>Secondary payloads have a rich and successful history of utilizing cheap rides to orbit to perform outstanding missions in Earth orbit, and more recently, in cislunar space and beyond. New launch vehicles, namely the Space Launch System (SLS), are increasing the science opportunity for rideshare class missions by providing regular service to the lunar vicinity. However, trajectory design in a multi-body regime brings a host of novel challenges, further exacerbated by constraints generated from the primary payload’s mission. Often, secondary payloads do not possess the fuel required to directly insert into lunar orbit and must instead perform a lunar flyby, traverse the Earth-Moon-Sun system, and later return to the lunar vicinity. This investigation develops a novel framework to construct low-cost, end-to-end lunar transfer trajectories for secondary payload missions. The proposed threephase approach provides unique insights into potential lunar transfer geometries. The phases consist of an arc from launch to initial perilune, an exterior transfer arc, and a lunar approach arc. The space of feasible transfers within each phase is determined through low-dimension grid searches and informed filtering techniques, while the problem of recombining the phases through differential corrections is kept tractable by reducing the dimensionality at each phase transition boundary. A sample mission demonstrates the trajectory design approach and example solutions are generated and discussed. Finally, alternate strategies are developed to both augment the analysis and for scenarios where the proposed three-phase technique does not deliver adequate solutions. The trajectory design methods described in this document are applicable to many upcoming secondary payload missions headed to lunar orbit, including spacecraft with only low-thrust, only high-thrust, or a combination of both. </p>

On-orbit satellite servicing is critical to maximizing space utilization and sustainability and is of growing interest for commercial, civil, and defense applications. Reliance on astronauts or anchored robotic arms for the servicing of next-generation large, complex space structures operating beyond Low Earth Orbit is impractical. Substantial literature has investigated the mission design and analysis of robotic servicing missions that utilize a single servicing satellite to approach and service a single target satellite. This motivates the present research to investigate a fleet of servicing satellites performing several operations for a large, central space structure. This research leverages a distributed control approach, implemented using the Horizon Simulation Framework (HSF), to develop a tool capable of integrated mission modeling and task scheduling for a servicing satellite fleet. HSF is a modeling and simulation framework for verification of system level requirements with an emphasis on state representations, modularity, and event scheduling. HSF consists of two major modules: the main scheduling algorithm and the system model. The distributed control architecture allocates processing and decision making for this multi-agent cooperative control problem across multiple subsystem models and the main HSF scheduling algorithm itself. Models were implemented with a special emphasis on the dynamics, control, trajectory constraints, and trajectory optimization for the servicing satellite fleet. The integrated mission modeling and scheduling tool was applied to a sample scenario in which a fleet of 3 servicing assets is tasked with performing 12 servicing activities for a large satellite in Geostationary Orbit. The tool was able to successfully determine a schedule in which all 12 servicing activities were completed in under 32 hours, subject to the fuel and trajectory constraints of the servicing assets.

<p dir="ltr">As traffic in cislunar space grows and missions become increasingly complex, effective understanding of relative motion between spacecraft is paramount. Additional tools are necessary to more accurately determine favorable relative behaviors in a multi-body gravitational environment. In this investigation, relative states are characterized as linear combinations of principal stretching and restoring directions to introduce techniques for relative trajectory design in the circular restricted three-body problem. These dynamically-informed directions form sets of orthonormal vector bases employed to describe and design spacecraft motion relative to a reference trajectory. Properties unique to 3x3 subsets of the state transition matrix are exploited to derive methodologies for two relative motion applications. First, the formulation is presented from a spacecraft loitering perspective, providing a framework to methodically determine ballistic relative trajectory options for visiting spacecraft. Secondly, modifications are introduced for flexible maneuver planning in a collision avoidance scenario. The two methodologies are assessed for a variety of test cases along four different periodic orbits in the Earth-Moon system.</p>

Approved for public release, distribution is unlimited / This thesis explores using a direct pseudospectral method for the solution of optimal control problems with mixed dynamics. An easy to use MATLAB optimization package known as DIDO is used to obtain the solutions. The modeling of both low thrust interplanetary trajectories as well as aerocapture trajectories is detailed and the solutions for low thrust minimum time and minimum fuel trajectories are explored with particular emphasis on verification of the optimality of the obtained solution. Optimal aerocpature trajectories are solved for rotating atmospheres over a range of arrival Vinfinities. Solutions are obtained using various performance indexes including minimum fuel, minimum heat load, and minimum total aerocapture mass. Finally, the problem formulation and solutions for the mixed dynamic problem of low thrust trajectories with a terminal aerocapture maneuver is addressed yielding new trajectories maximizing the total scientific mass at arrival. / Lieutenant, United States Navy

In this work, sensor tasking refers to assigning the times and pointing directions for a sensor to collect observations of cataloged objects, in order to maintain the accuracy of the orbit estimates. Sensor tasking must consider the dynamics of the objects and uncertainty in their positions, the coordinate frame in which the sensor tasking is defined, the timing requirements for observations, the sensor capabilities, the local visibility, and constraints on the information processing and communication. This research focuses on finding efficient ways to solve the sensor tasking optimization problem. First, different coordinate frames are investigated, and it is shown that the observer fixed Local Meridian Equatorial (ground-based) and Satellite Meridian Equatorial (space-based) coordinate frames provide consistent sets of pointing directions and accurate representations of orbit uncertainty for use by the optimizers in solving the sensor tasking problem. Next, two classical optimizers (greedy and Weapon-Target Assignment) which rely on convexity are compared with two Machine Learning optimizers (Ant Colony Optimization and Distributed Q-learning) which attempt to learn about the solution space in order to approximate a global optimal solution. It is shown that the learning optimizers are able to generate better solutions, while the classical optimizers are more efficient to run and require less tuning to implement. Finally, the realistic scenario where the optimization algorithm receives no feedback before it must make the next decision is introduced. The Predicted Measurement Probability (PMP) is developed, and employed in a two sensor optimization framework. The PMP is shown to provide effective feedback to the optimization algorithm regarding the observations of each sensor.<br>

A thermal is a column of warm rising air triggered by differential heating on the ground. In recent studies UAVs were programmed to exploit this free atmospheric energy from thermals to improve their range and endurance. Researchers had successfully flown UAVs autonomously with thermal soaring method. Most research involved some form of flight simulation. Improvements to the aircraft and thermal models for simulation purpose would enable researchers to better design their UAVs and explore any potential flaws in their designs. An aircraft simulation with a thermal environment was created in Horizon Simulation Framework, a modeling and verification framework that was developed by Cal Poly Space Technologies and Applied Research laboratory. The objective of this study is to enhance the fidelity of existing modeling and simulation methods on autonomous thermal soaring, and to advance and demonstrate the capabilities of Horizon Simulation Framework through such implementation. The geometry of a small remote controlled glider was used in this simulation. Aerodynamic prediction programs DATCOM+ and AVL were used to obtained stability and control derivatives for this glider. The induced roll effect caused by the asymmetric vertical velocity distribution of a thermal was included in the aerodynamic roll moment calculation. The autonomous guidance algorithm for the glider included a turn logic which would determine the correct turn direction for the glider when a thermal is detected. The thermal model developed in this thesis included the capabilities to vary the time dependent location, height, radius, and vertical velocity characteristics of naturally occurring thermals.

Several methods are presented for the design of satellite formations for science missions in high-eccentricity reference orbits with quantifiable performance criteria specified throughout only a portion the orbit, called the Region of Interest (RoI). A modified form of the traditional average along-track drift minimization condition is introduced to account for the fact that performance criteria are only specified within the RoI, and a robust formation design algorithm (FDA) is defined to improve performance in the presence of formation initialization errors. Initial differential mean orbital elements are taken as the design variables and the Gim-Alfriend state transition matrix (G-A STM) is used for relative motion propagation. Using mean elements and the G-A STM allows for explicit inclusion of J2 perturbation effects in the design process. The methods are applied to the complete formation design problem of the NASA Magnetospheric Multiscale (MMS) mission and results are verified using the NASA General Mission Analysis Tool (GMAT). Since satellite formations in high-eccentricity orbits will spend long times at high altitude, third-body perturbations are an important design consideration as well. A detailed analytical analysis of third-body perturbation effects on satellite formations is also performed and averaged dynamics are derived for the particular case of the lunar perturbation. Numerical results of the lunar perturbation analysis are obtained for the example application of the MMS mission and verified in GMAT.

Made available in DSpace on 2014-06-11T19:25:30Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-12Bitstream added on 2014-06-13T20:33:10Z : No. of bitstreams: 1 peixoto_ln_me_guara.pdf: 13781791 bytes, checksum: 7047ea962d175dfc7039c195697ef84d (MD5) / Com o lançamento do primeiro satélite artificial da Terra, Sputnik I, surgiu a necessidade do desenvolvimento de satélites mais eficientes e mais econômicos. Um dos mecanismos utilizados para economizar combustível numa transferência completa de um veículo espacial em órbita da Terra para uma órbita em torno da Lua, é o fenômeno de captura gravitacional temporária. Nesse trabalho é feita a análise numérica de diversas trajetórias em torno da Lua, considerando-se as dinâmicas de três e quatro corpos, com o objetivo de estudar o fenômeno da captura gravitacional temporária, através do monitoramento do sinal da energia relativa de dois corpos partícula-Lua e das componentes radiais das forças gravitacionais da Terra, da Lua e do Sol. Através desses estudos também foram obtidos diversos mapas de escape e colisão, considerando-se os movimentos prógrado e retrógrado. / With the launch of the first artificial satellite of the Earth, Sputnik I, arose the necessity of the development of the satellites more efficient and more economic. One of the mechanisms used to save fuel in a complete transference of one spacecraft in orbit of the Earth to an orbit around the Moon, is the phenomena of the temporary gravitational capture. In this paper is made the numerical analysis of the several trajectories around the Moon, considering the dynamics of the three and four-bodies, with the objective of studying the phenomena of temporary gravitational capture, through monitoring the sign of the relative two-body energy particle-Moon and the radial component of the force of attraction, gravitational of the Earth, of the Moon and of the Sun. Though of these studies also were obtained several maps of the escape and collision, considering the prograde and retrograde movements.

Space debris has become an increasingly hazardous obstacle to continued spaceflight operations. In an effort to mitigate this problem an investigation of the feasibility of a microsatellite active debris removal system was conducted. Through proposing a novel concept of operation, utilizing a grapple-and-tug system architecture, and by analyzing each resultant mission phase in the frame of a representative example, it was found that microsatellite scale systems are capable of fulfilling the active debris removal mission. Analysis of rendezvous, docking, control and deorbit mission requirements determined that the design of a grapple-and-tug system will be driven by sizing of the propellant required to deorbit the target vehicle. Further sensitivity analysis determined that target altitude and mass are critical factors in determining the capabilities of a microsatellite mission. Preliminary sizing demonstrated that hardware considerations for both satellite core and mission related activities do not impede microsatellite feasibility. Further investigation of microsatellite debris removal missions including detailed design analysis and engineering is suggested.