The CalPoly Spacecraft Attitude Dynamics Simulator mimics the rotational dynamics of a spacecraft in orbit and acts as a testbed for spacecraft attitude control system development and demonstration. Prior to this thesis, the simulator platform and several subsystems had been designed and manufactured, but the total simulator system was not yet capable of closed-loop attitude control. Previous attempts to make the system controllable were primarily mired by data transport performance. Rather than exporting data to an external command computer, the strategy implemented in this thesis relies on a compact computer onboard the simulator platform to handle both attitude control processing and data acquisition responsibilities. Software drivers were created to interface the computer’s data acquisition boards with Matlab, and a Simulink library was developed to handle hardware interface functions and simplify the composition of attitude control schemes. To improve the usability of the system, a variety of actuator control, hardware testing, and data visualization utilities were also created. A closedloop attitude control strategy was adapted to facilitate future sensor installations, and was tested in numerical simulation. The control model was then updated to interface with the simulator hardware, and for the first time in the project history, attitude control was performed onboard the CalPoly spacecraft attitude dynamics simulator. The demonstration served to validate the numerical model and to verify the functionality of the entire simulator system.

Due to mass and volume constraints on planetary missions, the development of control techniques that do not require fuel are of big interest. For those planets that have a dense enough atmosphere, aerodynamic drag can play an important role. The use of atmospheric differential drag for formation keeping was first proposed by Carolina L. Leonard in 1986, and has been proven to work in Earth atmosphere by many missions. Moreover, atmospheric drag has been used in the Mars atmosphere as aerobraking technique to decelerate landing vehicles, and to circularize the orbit of the spacecraft. Still, no literature was available related to formation flying on Mars. To analyze the use of differential drag on the Mars atmosphere, the researcher accessed the two high resolution models available: NASA’s Mars-GRAM and ESA’s Mars Climate Database. These models allowed the simulation of conditions that a spacecraft would experience while in orbit around the planet. To explore the feasibility, the researcher first conducted a study where Mars atmosphere density was compared to Earth atmosphere, determining its applicability. Then, a simulation using MATLAB® was conducted, using a Keplerian two-body problem including the effects of Mars zonal harmonics (i.e. J2) and drag perturbations. Two 6U CubeSat were used in the simulation with deployable drag plates of different sizes, giving the possibility of having five differential drag scenarios as means of formation control. The conclusions showed that, although with some limitations, the use of differential drag as means of autonomous formation flying and proximity operations control is feasible using proven techniques previously validated in Low Earth Orbit. Lyapunov control was selected as the control strategy, where three different methods were evaluated and compared.

The paper describes the background and concepts behind a master’s thesis platform known as COMET (Constrained Optimization of Multiple-dimensions for Efficient Trajectories) created for mission designers to determine and evaluate suitable interplanetary trajectories. This includes an examination of the improvements to the global optimization algorithm, Differential Evolution, through a cascading search space pruning method and decomposition of optimization parameters. Results are compared to those produced by the European Space Agency’s Advanced Concept Team’s Multiple Gravity Assist Program. It was found that while discrepancies in the calculation of ΔV’s for flyby maneuvers exist between the two programs, COMET showed a noticeable improvement in its ability to avoid premature convergence and find highly isolated solutions.

As satellites become smaller, cheaper, and quicker to manufacture, constellation systems will be an increasingly attractive means of meeting mission objectives. Optimizing satellite constellation geometries is therefore a topic of considerable interest. As constellation systems become more achievable, providing coverage to specific regions of the Earth will become more common place. Small countries or companies that are currently unable to afford large and expensive constellation systems will now, or in the near future, be able to afford their own constellation systems to meet their individual requirements for small coverage regions. The focus of this thesis was to optimize constellation geometries for small coverage regions with the constellation design limited between 1-6 satellites in a Walker-delta configuration, at an altitude of 200-1500km, and to provide remote sensing coverage with a minimum ground elevation angle of 60 degrees. Few Pareto-frontiers have been developed and analyzed to show the tradeoffs among various performance metrics, especially for this type of constellation system. The performance metrics focus on geometric coverage and include revisit time, daily visibility time, constellation altitude, ground elevation angle, and the number of satellites. The objective space containing these performance metrics were characterized for 5 different regions at latitudes of 0, 22.5, 45, 67.5, and 90 degrees. In addition, the effect of minimum ground elevation angle was studied on the achievable performance of this type of constellation system. Finally, the traditional Walker-delta pattern constraint was relaxed to allow for asymmetrical designs. These designs were compared to see how the Walker-delta pattern performs compared to a more relaxed design space. The goal of this thesis was to provide both a framework as well as obtain and analyze Pareto-frontiers for constellation performance relating to small regional coverage LEO constellation systems. This work provided an in-depth analysis of the trends in both the design and objective space of the obtained Pareto-frontiers. A variation on the εNSGA-II algorithm was utilized along with a MATLAB/STK interface to produce these Pareto-frontiers. The εNSGA-II algorithm is an evolutionary algorithm that was developed by Kalyanmoy Deb to solve complex multi-objective optimization problems. The algorithm used in this study proved to be very efficient at obtaining various Pareto-frontiers. This study was also successful in characterizing the design and solution space surrounding small LEO remote sensing constellation systems providing small regional coverage.

As electronics become smaller and more capable, it has become possible to conduct meaningful and sophisticated satellite missions in a small form factor. However, the capability of small satellites and the range of possible applications are limited by the capabilities of several technologies, including attitude determination and control systems. This dissertation evaluates the use of image-based visual attitude propagation as a compliment or alternative to other attitude determination technologies that are suitable for miniature satellites. The concept lies in using miniature cameras to track image features across frames and extracting the underlying rotation. The problem of visual attitude propagation as a small satellite attitude determination system is addressed from several aspects: related work, algorithm design, hardware and performance evaluation, possible applications, and on-orbit experimentation. These areas of consideration reflect the organization of this dissertation. A “stellar gyroscope” is developed, which is a visual star-based attitude propagator that uses relative motion of stars in an imager’s field of view to infer the attitude changes. The device generates spacecraft relative attitude estimates in three degrees of freedom. Algorithms to perform the star detection, correspondence, and attitude propagation are presented. The Random Sample Consensus (RANSAC) approach is applied to the correspondence problem to successfully pair stars across frames while mitigating false-positive and false-negative star detections. This approach provides tolerance to the noise levels expected in using miniature optics and no baffling, and the noise caused by radiation dose on orbit. The hardware design and algorithms are validated using test images of the night sky. The application of the stellar gyroscope as part of a CubeSat attitude determination and control system is described. The stellar gyroscope is used to augment a MEMS gyroscope attitude propagation algorithm to minimize drift in the absence of an absolute attitude sensor. The stellar gyroscope is a technology demonstration experiment on KySat-2, a 1-Unit CubeSat being developed in Kentucky that is in line to launch with the NASA ELaNa CubeSat Launch Initiative. It has also been adopted by industry as a sensor for CubeSat Attitude Determination and Control Systems (ADCS).

A Variable Speed Control Moment Gyro (VSCMG) is a recently introduced actuator for spacecraft attitude control. As its name implies, a VSCMG is essentially a single-gimbal control moment gyro (CMG) with a flywheel allowed to have variable spin speed. Thanks to its extra degrees of freedom, a VSCMGs cluster can be used to achieve additional objectives, such as power tracking and/or singularity avoidance, as well as attitude control. In this thesis, control laws for an integrated power/attitude control system (IPACS) for a satellite using VSCMGs are introduced. The power tracking objective is achieved by storing or releasing the kinetic energy in the wheels. The proposed control algorithms perform both the attitude and power tracking goals simultaneously. This thesis also provides a singularity analysis and avoidance method using CMGs/VSCMGs. This issue is studied for both the cases of attitude tracking with and without a power tracking requirement. A null motion method to avoid singularities is presented, and a criterion is developed to determine the momentum region over which this method will successfully avoid singularities. The spacecraft angular velocity and attitude control problem using a single VSCMG is also addressed. A body-fixed axis is chosen to be perpendicular to the gimbal axis, and it is controlled to aim at an arbitrarily given inertial direction, while the spacecraft angular velocity is stabilized. Finally, an adaptive control algorithm for the spacecraft attitude tracking in case when the actuator parameters, for instance the spin axis directions, are uncertain is developed. The equations of motion in this case are fully nonlinear and represent a Multi-Input-Multi-Output (MIMO) system. The smooth projection algorithm is applied to keep the parameter estimates inside a singularity-free region. The design procedure can also be easily applied to general MIMO dynamical systems.

<div>As the number of Resident Space Objects around Earth continues to increase, the need for an optimal sensor tasking strategy, specifically with Ground-Based Optical sensors, continues to be of great importance. This thesis focuses on the single and multi-sensor tasking problem with realistic optical sensor modeling for the observation of objects in the Geosynchronous Earth Orbit regime. In this work, sensor tasking refers to assigning the specific?c observation times and viewing directions of a single or multi sensor framework to either survey for or track new or existing objects. For this work specifically, the sensor tasking problem will seek to maximize the total number of Geosynchronous Earth Orbiting objects to be observed from a catalog of existing objects with a single and multi optical sensor tasking framework. This research focuses on the physical assumptions and limitations on an optical sensor, and how these assumptions affect the single and multi sensor tasking scenario. First, the concept of the probability of detection of a resident space object is calculated based on the viewing geometry of the resident space object. Then, this probability of detection is compared to the system that avoids the computational process by implementing a classical heuristic minimum elevation constraint to an electro-optical charged coupled optical sensor. It is shown that in the single and multi-sensor tasking scenario if the probability of detection is not considered in the sensor tasking framework, then a rigid elevation constraint of around 25^o-35^o is recommended for tasking Geosynchronous objects. Secondly, the topic of complete geo-coverage within a single night is explored. A sensor network proposed by Ackermann et al. (2018) is studied with and without the probability of detection considerations, and with and without uncertainties in the resident space objects' states. (then what you have). For the multi-sensor system, it is shown that with the assumed covariance model for this work, the framework developed by Ackermann et al. (2018) does not meet the design requirements for the cataloged Geosynchronous objects from March 19th, 2019. Finally, the concept of a variable repositioning time for the slewing of the ground-based sensors is introduced and compared to a constant repositioning time model. A model for the variable repositioning time is derived from data retrieved from the Purdue Optical Ground Station. This model is applied to a single sensor scenario. Optimizers are developed using the two repositioning time functions derived in this work. It is shown that the constant repositioning models that are greater than the maximum repositioning time produce results close to the variable repositioning solution. When the optimizers are tested, it is shown that there is a small increase in performance only when the maximum repositioning time is significant.</div>

Shape and attitude of near-Earth objects directly affect the orbit propagation via drag and solar radiation pressure. Obtaining information beyond the object states (position and velocity) is integral to identifying an object. It also enables tracing origin and can improve the orbit accuracy. For objects that have a significant distance to the observer, only non-resolved imaging is available, which does not show any details of the object. So-called non-resolved light curve measurements, i.e. photometric measurements over time can be used to determined the shape of space objects using a two step inversion scheme. It follows the procedure to first determine the Extended Gaussian Image and then going through the shape reconstruction process to retrieve the closed shape even while measurement noise is present. Furthermore, it is also possible to generate high confidence candidates when follow-up observations are provided through a multi-hypotheses process.

<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>