In this dissertation the solutions of the dynamics and real-time optimal control of magnetic attitude control and formation flying systems are presented. In magnetic attitude control, magnetic actuators for the time-optimal rest-to-rest maneuver with a pseudospectral algorithm are examined. The time-optimal magnetic control is bang-bang and the optimal slew time is about 232.7 seconds. The start time occurs when the maneuver is symmetric about the maximum field strength. For real-time computations, all the tested samples converge to optimal solutions or feasible solutions. We find the average computation time is about 0.45 seconds with the warm start and 19 seconds with the cold start, which is a great potential for real-time computations. Three-axis magnetic attitude stabilization is achieved by using a pseudospectral control law via the receding horizon control for satellites in eccentric low Earth orbits. The solutions from the pseudospectral control law are in excellent agreement with those obtained from the Riccati equation, but the computation speed improves by one order of magnitude. Numerical solutions show state responses quickly tend to the region where the attitude motion is in the steady state. Approximate models are often used for the study of relative motion of formation flying satellites. A modeling error index is introduced for evaluating and comparing the accuracy of various theories of the relative motion of satellites in order to determine the effect of modeling errors on the various theories. The numerical results show the sequence of the index from high to low should be Hill's equation, non- J2, small eccentricity, Gim-Alfriend state transition matrix index, with the unit sphere approach and the Yan-Alfriend nonlinear method having the lowest index and equivalent performance. A higher order state transition matrix is developed using unit sphere approach in the mean elements space. Based on the state transition matrix analytical control laws for formation flying maintenance and reconfiguration are proposed using low-thrust and impulsive scheme. The control laws are easily derived with high accuracy. Numerical solutions show the control law works well in real-time computations.

Future spacecraft missions are trending towards the use of distributed systems or fractionated spacecraft. Initiatives such as DARPA's System F6 are encouraging the satellite community to explore the realm of collaborative spacecraft teams in order to achieve lower cost, lower risk, and greater data value over the conventional monoliths in LEO today. Extensive research has been and is being conducted indicating the advantages of distributed spacecraft systems in terms of both capability and cost. Enabling collaborative behaviors among teams or formations of pico-satellites requires technology development in several subsystem areas including attitude determination and control subsystems, orbit determination and maintenance capabilities, as well as a means to maintain accurate knowledge of team members' position and attitude. All of these technology developments desire improvements (more specifically, decreases) in mass and power requirements in order to fit on pico-satellite platforms such as the CubeSat. In this thesis a solution for the last technology development area aforementioned is presented. Accurate knowledge of each spacecraft's state in a formation, beyond improving collision avoidance, provides a means to best schedule sensor data gathering, thereby increasing power budget efficiency. Our solution is composed of multiple software and hardware components. First, finely-tuned flight system software for the maintaining of state knowledge through equations of motion propagation is developed. Additional software, including an extended Kalman filter implementation, and commercially available hardware components provide a means for on-board determination of both orbit and attitude. Lastly, an inter-satellite communication message structure and protocol enable the updating of position and attitude, as required, among team members. This messaging structure additionally provides a means for payload sensor and telemetry data sharing. In order to satisfy the needs of many different missions, the software has the flexibility to vary the limits of accuracy on the knowledge of team member position, velocity, and attitude. Such flexibility provides power savings for simpler applications while still enabling missions with the need of finer accuracy knowledge of the distributed team's state. Simulation results are presented indicating the accuracy and efficiency of formation structure knowledge through incorporation of the described solution. More importantly, results indicate the collaborative module's ability to maintain formation knowledge within bounds prescribed by a user. Simulation has included hardware-in-the-loop setups utilizing an S-band transceiver. Two "satellites" (computers setup with S-band transceivers and running the software components of the collaborative module) are provided GPS inputs comparable to the outputs provided from commercial hardware; this partial hardware-in-the-loop setup demonstrates the overall capabilities of the collaborative module. Details on each component of the module are provided. Although the module is designed with the 3U CubeSat framework as the initial demonstration platform, it is easily extendable onto other small satellite platforms. By using this collaborative module as a base, future work can build upon it with attitude control, orbit or formation control, and additional capabilities with the end goal of achieving autonomous clusters of small spacecraft.

The CanX-4/-5 mission currently under development at the Space Flight Laboratory will demonstrate sub-metre formation control in four separate formations consisting of two nanosatellites. Formation maintenance is performed using a propulsion payload providing one axis of thrust, resulting in frequent slewing to meet thrust targets. Navigation is GPS dependent, with both satellites equipped with a receiver and antenna pair. Presented is a mission simulation developed for evaluating formation flying algorithm performance and the effects of frequent slewing on GPS coverage. CanX-4 and CanX-5 will be joined for commissioning prior to commencing formation flying via a mechanism, the Intersatellite Separation System. Details regarding the performance testing and troubleshooting of the system are described. Integration and testing of CanX-4/-5 flight hardware into a functional “FlatSat” is presented. Additionally, a description of satellite operations for two nanosatellites is given, with an emphasis on the relevance to the work performed for the CanX-4/-5 mission.

The CanX-4/-5 mission currently under development at the Space Flight Laboratory will demonstrate sub-metre formation control in four separate formations consisting of two nanosatellites. Formation maintenance is performed using a propulsion payload providing one axis of thrust, resulting in frequent slewing to meet thrust targets. Navigation is GPS dependent, with both satellites equipped with a receiver and antenna pair. Presented is a mission simulation developed for evaluating formation flying algorithm performance and the effects of frequent slewing on GPS coverage. CanX-4 and CanX-5 will be joined for commissioning prior to commencing formation flying via a mechanism, the Intersatellite Separation System. Details regarding the performance testing and troubleshooting of the system are described. Integration and testing of CanX-4/-5 flight hardware into a functional “FlatSat” is presented. Additionally, a description of satellite operations for two nanosatellites is given, with an emphasis on the relevance to the work performed for the CanX-4/-5 mission.

Spacecraft formation flying (SFF) offers robust observations of multi-scale ionospheric space weather. A number of hardware-in-the-loop (HIL) SFF simulation testbeds based on Global-Navigation-Satellite-Systems (GNSS) have been developed to support GNSS-based SFF mission design, however, none of these testbeds has been directly applied to ionospheric space weather studies. The Virginia Tech Formation Flying Testbed (VTFFTB), a GNSS-based HIL simulation testbed, has been developed in this work to simulate closed-loop real-time low Earth orbit (LEO) SFF scenarios. The final VTFFTB infrastructure consists of three GNSS hardware signal simulators, three multi-constellation multi-band GNSS receivers, three navigation and control systems, an STK visualization system, and an ionospheric remote sensing system. A fleet of LEO satellites, each carrying a spaceborne GNSS receiver for navigation and ionospheric measurements, is simulated in scenarios with ionospheric impacts on the GPS and Galileo constellations. Space-based total electron density (TEC) and GNSS scintillation index S4 are measured by the LEO GNSS receivers in simulated scenarios. Four stages of work were accomplished to (i) build the VTFFTB with a global ionospheric modeling capability, and (ii) apply the VTFFTB to incubate future ionospheric measurement techniques. In stage 1, a differential-TEC method was developed to use space-based TEC measurements from a pair of LEO satellites to determine localized electron density (Ne). In stage 2, the GPS-based VTFFTB was extended to a multi-constellation version by adding the Galileo. Compared to using the GPS constellation only, using both GPS and Galileo constellations can improve ionospheric measurement quality (accuracy, precision, and availability) and relative navigation performance. Sensitivity studies found that Ne retrieval characteristics are correlated with LEO formation orbit, the particular GNSS receivers and constellation being used, as well as GNSS carrier-to-noise density C/N0. In stage 3, the VTFFTB for dual-satellite scenarios was further extended into a 3-satellite version, and then implemented to develop a polar orbit scenario with more fuel-efficient natural motion. In stage 4, a global 4-dimensioanl ionospheric model (TIE-CGM) was incorporated into the VTFFTB to significantly improve the modelling fidelity of multi-scale ionospheric space weather. Equatorial and polar space weather structures (e.g. plasma bubbles, tongues-of-ionization) were successfully simulated in 4-dimensional ionospheric scenarios on the enhanced VTFFTB. The dissertation has demonstrated the VTFFTB is a versatile GNSS-based SFF mission incubator to study ionospheric space weather impacts and develop next-generation multi-scale ionospheric observation missions. / Doctor of Philosophy / Spacecraft formation flying (SFF) is a space mission architecture with a group of spacecraft flying together and working as a team. SFF provides new opportunities for robust, flexible and low-cost observations of various phenomena in the ionized layer of Earth's atmosphere (called the ionosphere). Several hardware SFF simulation platforms based on Global Navigation Satellite Systems (GNSS) have been established to develop GNSS-based SFF missions, however, none of these platforms has ever directly used on-board GNSS receivers to study the impact of space weather on ionospheric density structures. The Virginia Tech Formation Flying Testbed (VTFFTB), a hardware simulation infrastructure using multiple GNSS signals, has been built in this work to emulate realistic SFF scenarios in low altitude orbits. The overall VTFFTB facility comprises three GNSS hardware signal emulators, three GNSS signal receivers, three navigation and control components, a software visualization component, and an ionospheric measurement component. Both Global-Positioning-System (GPS) and Galileo (the European version GNSS) are implemented in the VTFFTB. The objectives of this work are to (i) develop the VTFFTB with a high-fidelity ionospheric modeling capability, and (ii) apply the VTFFTB to incubate future ionospheric measurement techniques with GNSS receivers in space. A fleet of two or three spacecraft, each having a GNSS receiver to navigate and sense the ionosphere is emulated in several space environments. The electron concentration of the ionosphere and the GNSS signal fluctuation are measured by the GNSS receivers from space in simulated scenarios. These measurements are advantageous to study the location, size and structure of irregular ionospheric phenomena nearby the trajectory of spacecraft fleet. The culmination of this study is incorporation of an external global ionospheric model with temporal variations into the VTFFTB infrastructure to model a variety of realistic ionospheric structures and space weather impacts. Equatorial and polar space weather phenomenon were successfully simulated on the VTFFTB to verify a newly developed space-borne electron density measurement technique in the 3-dimensional ionosphere. Overall, it was successfully demonstrated that the VTFFTB is a versatile GNSS-based SFF mission incubator to study multiple kinds of ionospheric space weather impacts and develop next-generation space missions for ionospheric measurements.

The Coulomb propulsion system has no exhaust plume impingement problem with neighboring spacecraft and does not contaminate their sensors because it requires essentially no propellant. It is suitable to close formation control on the order of dozens of meters. The Coulomb forces are internal forces of the formation and they influence all charged spacecraft at the same time. Highly nonlinear and strongly coupled equations of motion of Coulomb formation makes creating a Coulomb control method a challenging task. Instead of positioning all spacecraft, this study investigates having a sensor craft be sequentially controlled using dedicated drone craft. At least three drone craft are required to control a general sensor craft position in the inertial space. However, the singularity of a drone plane occurs when a sensor craft moves across the drone plane. A bang-bang control method with a singularity check can avoid this problem but may lose formation control as the relative distances grow bounded. A bang-coast-bang control method utilizing a reference trajectory profile and drone rest control is introduced to increase the control effectiveness. The spacecraft are assumed to be floating freely in inertial space, an approximation of environments found while underway to other solar system bodies. Numerical simulation results show the feasibility of sensor craft control using Coulomb forces. / Master of Science

The Global Navigation Satellite System (GNSS) is significantly advantageous to absolute and relative navigation for spacecraft formation flying. Ionospheric remote sensing, such as Total Electron Content (TEC) measurements or ionospheric irregularity studies are important potential Low Earth Orbit (LEO) applications. A GNSS-based Hardware-in-the-loop (HIL) simulation testbed for LEO spacecraft formation flying has been developed and evaluated. The testbed infrastructure is composed of GNSS simulators, multi-constellation GNSS receiver(s), the Navigation & Control system and the Systems Tool Kit (STK) visualization system. A reference scenario of two LEO spacecraft is simulated with the initial in-track separation of 1000-m and targeted leader-follower configuration of 100-m along-track offset. Therefore, the feasibility and performance of the testbed have been demonstrated by benchmarking the simulation results with past work. For ionospheric remote sensing, multi-constellation multi-frequency GNSS receivers are used to develop the GNSS TEC measurement and model evaluation system. GPS, GLONASS, Galileo and Beidou constellations are considered in this work. Multi-constellation GNSS TEC measurements and the GNSS-based HIL simulation testbed were integrated and applied to design a LEO satellite formation flying mission for ionospheric remote sensing. A scenario of observing sporadic E is illustrated and adopted to demonstrate how to apply GNSS-based spacecraft formation flying to study the ionospheric irregularities using the HIL simulation testbed. The entire infrastructure of GNSS-based spacecraft formation flying simulation and ionospheric remote sensing developed at Virginia Tech is capable of supporting future ionospheric remote sensing mission design and validation. / Master of Science / Global Navigation Satellite Systems (GNSS), such as the Global Positioning System (GPS), are not only used to navigate vehicles such as automobiles and spacecraft, but they are also used as a tool to remotely study the Earth’s ionosphere. A GNSS-based hardware simulation testbed for a group of spacecraft flying in low altitude orbit with the capability to remotely sense the ionosphere has been developed and evaluated. The hardware testbed developed is composed of GNSS signal emulators, GNSS signal receiver(s), the spacecraft navigation & control system and a mission visualization system. A reference scenario of two spacecraft in low altitude orbit with an initial horizontal distance of 1000-m and a final separation of 100-m is successfully simulated. Therefore, the feasibility and performance of the hardware testbed have been demonstrated by comparing the simulation results with past work. To study the Earth’s ionosphere, advanced GNSS receivers along with newly developed software are used to measure the ionospheric electron concentration. This software can be integrated with the hardware testbed and utilized to design spacecraft missions to study the ionosphere from the space. A scenario for observing a unique ionospheric structure is implemented to demonstrate application of the hardware testbed to more general ionospheric studies. Combining the software for ionospheric measurement and the hardware testbed for two spacecraft flying in formation can support future mission design and validation.

A spacecraft formation possesses several benefits over a single-satellite mission. However, launching a fleet of satellites is a high-cost, high-risk venture. One way to mitigate much of this risk is to demonstrate hardware and algorithm performance in groundbased testbeds. It is typically difficult to experimentally replicate satellite dynamics in an Earth-bound laboratory because of the influences of gravity and friction. An air bearing provides a very low-torque environment for experimentation, thereby recapturing the freedom of the space environment as effectively as possible. Depending upon con- figuration, air-bearing systems provide some combination of translational and rotational freedom; the three degrees of rotational freedom provided by a spherical air bearing are ideal for investigation of spacecraft attitude dynamics and control problems. An interest in experimental demonstration of formation flying led directly to the development of the Distributed Spacecraft Attitude Control System Simulator (DSACSS). The DSACSS is a unique facility, as it uses two air-bearing platforms working in concert. Thus DSACSS provides a pair of "spacecraft" three degrees of attitude freedom each. Through use of the DSACSS we are able to replicate the relative attitude dynamics between nodes of a formation such as might be required for co-observation of a terrestrial target. Many dissertations present a new mathematical technique or prove a new theory. This dissertation presents the design and development of a new experimental system. Although the DSACSS is not yet fully operational, a great deal of work has gone into its development thus far. This work has ranged from configuration design to nonlinear analysis to structural and electrical manufacturing. In this dissertation we focus on the development of the attitude determination subsystem. This work includes development of the equations of motion and analysis of the sensor suite dynamics. We develop nonlinear filtering techniques for data fusion and attitude estimation, and extend this problem to include estimation of the mass properties of the system. We include recommendations for system modifications and improvements. / Ph. D.

Remorquer des satellites peut être utiles pour de nombreuses raisons : les désorbiter ou ré-orbiter, nécessaire dans le cas des satellites en fin de vie, ou pour finaliser les lancements par exemple. Dans ce cas, cette manœuvre augmenterait la capacité des étages supérieurs de lanceurs. Plusieurs moyens peuvent être envisagés pour modifier l’orbite d’un satellite cible grâce à un autre satellite. Parmi eux, les concepts sans contact sont intéressants, car ils fournissent un moyen d’éviter le besoin d’interfaces normalisées. Ils permettent ausside ne pas réaliser d’amarrages non coopératifs, qui représentent une grande difficulté. Enfin, ils contribuent à réduire le risque de créer de nouveaux débris par collision. Dans cette thèse, nous proposons d’utiliser les forces magnétiques pour remorquer le satellite cible. En effet, de nombreux satellites, en particulier en orbite terrestre basse, sont équipés de magnéto-coupleur, utilisés pour le contrôle d’attitude. Un satellite chasseur équipé d’un dipôle magnétique puissant pourrait donc générer des forces sur la cible. Cependant, la création d’une force entre deux dipôles magnétiques génère automatiquement des couples sur les deux dipôles. Par conséquent, la viabilité d’un remorqueur magnétique spatial n’est a priori pas assurée, étant donné qu’appliquer en permanence des couples sur les deux satellites ne serait pas acceptable. / Satellite tugging can be undertaken for various reasons: de-orbiting or reorbiting,necessary in the case of satellites at the end-of-life, or for instance to finalise launches,in which case this manoeuvre would increase the capacity of launchers’ upper stages. Severalmeans can be considered to modify the orbit of a target satellite by tugging it with anothersatellite. Contact-less concepts are interesting, as they provide a way to avoid standardisedinterfaces and hazardous docking phases. They also help to prevent the creation of new debrisby reducing the risk of collision. In this thesis, we suggest using magnetic forces to tug the target. Indeed many satellites, especially in Low Earth Orbit, are equipped with Magnetic Torque Bars used for attitudecontrol. A chaser satellite equipped with a powerful magnetic dipole could hence generateforces on the target. However, creating a force between two magnetic dipoles automaticallycreates torque on both of them. Therefore, the feasibility of magnetic tugging is a priori notassured, considering that applying constant torques on both satellites would not be acceptable.

Coulomb forces acting between close flying charged spacecraft provide near zero propellant relative motion control, albeit with added nonlinear coupling and limited controllability. This novel concept has numerous potential applications, but also many technical challenges. In this dissertation, two- and three-craft Coulomb formations near GEO are investigated, using a rotating Hill frame dynamical model, that includes Debye shielding and differential gravity. Aspects of dynamical systems theory and optimization are applied, for insights regarding stability, and how inherent nonlinear complexities may be beneficially exploited to maintain and maneuver these electrostatic formations. Periodic relative orbits of two spacecraft, enabled by open-loop charge functions, are derived for the first time. These represent a desired extension to more substantially studied, constant charge, static Coulomb formations. An integral of motion is derived for the Hill frame model, and then applied in eliminating otherwise plausible periodic solutions. Stability of orbit families are evaluated using Floquet theory, and asymptotic stability is shown unattainable analytically. Weak stability boundary dynamics arise upon adding Coulomb forces to the relative motion problem, and therefore invariant manifolds are considered, in part, to more efficiently realize formation shape changes. A methodology to formulate and solve two-craft static Coulomb formation reconfigurations, as parameter optimization problems with minimum inertial thrust, is demonstrated. Manifolds are sought to achieve discontinuous transfers, which are then differentially corrected using charge variations and impulsive thrusting. Two nonlinear programming algorithms, gradient and stochastic, are employed as solvers and their performances are compared. Necessary and sufficient existence criteria are derived for three-craft collinear Coulomb formations, and a stability analysis is performed for the resulting discrete equilibrium cases. Each specified configuration is enabled by non-unique charge values, and so a method to compute minimum power solutions is outlined. Certain equilibrium cases are proven maintainable using only charge control, and feedback stabilized simulations demonstrate this. Practical scenarios for extending the optimal reconfiguration method are also discussed. Lastly, particular Hill frame model trajectories are integrated in an inertial frame with primary perturbations and interpolated Debye length variations. This validates qualitative stability properties, reveals particular periodic solutions to exhibit nonlinear boundedness, and illustrates higher-fidelity solution accuracies. / text