In this dissertation the linearized dynamics and stability of a two-craft Coulomb tether formation are investigated. With a Coulomb tether the relative distance between two satellites is controlled using electrostatic Coulomb forces. A charge feedback law is introduced to stabilize the relative distance between the satellites to a constant value. Compared to previous Coulomb thrusting research, this is the first feedback control law that stabilizes a particular formation shape. The two craft are connected by an electrostatic virtual tether that essentially acts as a long, slender near-rigid body. Inter-spacecraft Coulomb forces cannot influence the inertial angular momentum of this formation. However, the differential gravitational attraction can be exploited to stabilize the attitude of this Coulomb tether formation about an orbit nadir direction. Stabilizing the separation distance will also stabilize the in-plane rotation angle, while the out-of-plane rotational motion remains unaffected. The other two relative equilibriums of the charged 2-craft problem are along the orbit-normal and the along-track direction. Unlike the charged 2-craft formation scenario aligned along the orbit radial direction, a feedback control law using inter-spacecraft electrostatic Coulomb forces and the differential gravitational accelerations is not sufficient to stabilize the Coulomb tether length and the formation attitude. Therefore, hybrid feedback control laws are presented which combine conventional thrusters and Coulomb forces. The Coulomb force feedback requires measurements of separation distance error and error rate, while the thruster feedback is in terms of Euler angles and their rates. This hybrid feedback control is designed to asymptotically stabilize the satellite formation shape and attitude while avoiding plume impingement issues. The relative distance between the two satellites can be increased or decreased using electrostatic Coulomb forces. The linear dynamics and stability analysis of such reconfiguration are studied for all the three equilibrium. The Coulomb tether expansion and contraction rates affect the stability of the structure and limits on these rates are discussed using the linearized time-varying dynamical models. These limits allow the reference length time histories to be designed while ensuring linear stability of the virtual structure. Throughout this dissertation the Coulomb tether is modeled as a massless, elastic component and, a point charge model is used to describe the charged craft. / Ph. D.

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This thesis presents a method for managing periods of communication loss between multiple spacecraft in formation flying (MSFF), and analyzes the effects of this method on the stability of the formation keeping control algorithm. The controller of interest in this work in an adaptive nonlinear controller, where synchronization is also incorporated to force the position tracking errors to converge to zero at the same rate. The communication loss compensation technique proposed in this thesis is to use the previously communicated data in lieu of the lost data, which is an effective and computationally-efficient technique that is advantageous for small satellites. The performance parameter of interest in this research is the maximum rate of communication loss that an MSFF system can withstand before going unstable, and this is analyzed theoretically and through simulations. Finally, experiments involving multiple robots in formation with communication loss are conducted, and the results are presented.

This thesis presents a method for managing periods of communication loss between multiple spacecraft in formation flying (MSFF), and analyzes the effects of this method on the stability of the formation keeping control algorithm. The controller of interest in this work in an adaptive nonlinear controller, where synchronization is also incorporated to force the position tracking errors to converge to zero at the same rate. The communication loss compensation technique proposed in this thesis is to use the previously communicated data in lieu of the lost data, which is an effective and computationally-efficient technique that is advantageous for small satellites. The performance parameter of interest in this research is the maximum rate of communication loss that an MSFF system can withstand before going unstable, and this is analyzed theoretically and through simulations. Finally, experiments involving multiple robots in formation with communication loss are conducted, and the results are presented.

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 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

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

Formation control in multi-agent systems represents a groundbreaking intersection of various research fields with lots of emerging applications in various technologies. The realm of space exploration also can benefit significantly from formation control, facilitating a wide range of functions from astronomical observations, and climate monitoring to enhancing telecommunications, and on-orbit servicing and assembly. In this thesis, we present a novel 3D formation control scheme for directed graphs in a leader-follower configuration, achieving (almost) global convergence to the desired shape. Specifically, we introduce three controlled variables representing bispherical coordinates that uniquely describe the formation in 3D. Acyclic triangulated directed graphs (a class of minimally acyclic persistent graphs) are used to model the inter-agent sensing topology, while the agents’ dynamics are governed by the single-integrator model and 2nd order nonlinear version representing spacecraft formation flight. The analysis demonstrates that the proposed decentralized robust formation controller using prescribed performance control ensures (almost) global asymptotic stability while avoiding potential shape ambiguities in the final formation. Furthermore, the control laws are implementable in arbitrarily oriented local coordinate frames of follower agents using only low-cost onboard vision sensors, making them suitable for practical applications. Formation maneuvering and collision avoidance among agents are also addressed which play crucial roles in the safety of space operations. Finally, we validate our formation control approach by simulation studies. / Formationskontroll i system med flera agenter representerar en banbrytande skärningspunkt av olika forskningsområden med massor av nya tillämpningar inom olika teknologier. Rymdutforskningens rike kan också dra stor nytta av formationskontroll, underlättar ett brett utbud av funktioner från astronomiska observationer och klimat övervakning för att förbättra telekommunikation och service och montering i omloppsbana. I denna avhandling presenterar vi ett nytt 3D-formationskontrollschema för riktade grafer i en ledare-följare-konfiguration, vilket uppnår (nästan) global konvergens till önskad form. Specifikt introducerar vi tre kontrollerade variabler som representerar bisfäriska koordinater som unikt beskriver formationen i 3D. Acykliska triangulerade riktade grafer (en klass av minimalt acykliska beständiga grafer) används för att modellera avkänningstopologin mellan agenter, medan agenternas dynamik styrs av singelintegratormodellen och 2:a ordningen olinjär version som representerar rymdfarkostbildningsflygning. Analysen visar att den föreslagna decentraliserade robusta formationskontrollanten använder föreskriven prestanda kontroll säkerställer (nästan) global asymptotisk stabilitet samtidigt som potentiell form undviks oklarheter i den slutliga formationen. Dessutom är kontrolllagarna implementerbara i godtyckligt orienterade lokala koordinatramar för efterföljare som endast använder lågkostnad ombord visionsensorer, vilket gör dem lämpliga för praktiska tillämpningar. Formationsmanövrering och undvikande av kollisioner mellan agenter tas också upp som spelar avgörande roller i säkerheten vid rymdoperationer. Slutligen validerar vi vår strategi för formningskontroll genom simuleringsstudier

In this dissertation, we discuss the Distributed Spacecraft Attitude Control System Simulator (DSACSS) testbed developed at Virginia Polytechnic Institute and State University for the purpose of investigating various control techniques for single and multiple spacecraft. DSACSS is comprised of two independent hardware-in-the-loop simulators and one software spacecraft simulator. The two hardware-in-the-loop spacecraft simulators have similar subsystems as flight-ready spacecraft (e.g. command and data handling; communications; attitude determination and control; power; payload; and guidance and navigation). The DSACSS framework is a flexible testbed for investigating a variety of spacecraft control techniques, especially control scenarios involving coupled attitude and orbital motion. The attitude hardware simulators along with numerical simulations assist in the development and evaluation of Lyapunov based asymptotically stable, nonlinear attitude controllers with three reaction wheels as the control device. The angular rate controller successfully tracks a time varying attitude trajectory. The Modified Rodrigues Parmater (MRP) attitude controller results in successfully tracking the angular rates and MRP attitude vector for a time-varying attitude trajectory. The attitude controllers successfully track the reference attitude in real-time with hardware similar to flight-ready spacecraft. Numerical simulations and the attitude hardware simulators assist in the development and evaluation of a robust, asymptotically stable, nonlinear attitude controller with three reaction wheels as the actuator for attitude control. The MRPs are chosen to represent the attitude in the development of the controller. The robust spacecraft attitude controller successfully tracks a time-varying reference attitude trajectory while bounding system uncertainties. The results of a Global Positioning System (GPS) hardware-in-the-loop simulation of two spacecraft flying in formation are presented. The simulations involve a chief spacecraft in a low Earth orbit (LEO), while a deputy spacecraft maintains an orbit position relative to the chief spacecraft. In order to maintain the formation an orbit correction maneuver (OCM) for the deputy spacecraft is required. The control of the OCM is accomplished using a classical orbital element (COE) feedback controller and simulating continual impulsive thrusting for the deputy spacecraft. The COE controller requires the relative position of the six orbital elements. The deputy communicates with the chief spacecraft to obtain the current orbit position of the chief spacecraft, which is determined by a numerical orbit propagator. The position of the deputy spacecraft is determined from a GPS receiver that is connected to a GPS hardware-in-the-loop simulator. The GPS simulator creates a radio frequency (RF) signal based on a simulated trajectory, which results in the GPS receiver calculating the navigation solution for the simulated trajectory. From the relative positions of the spacecraft the COE controller calculates the OCM for the deputy spacecraft. The formation flying simulation successfully demonstrates the closed-loop hardware-in-the-loop GPS simulator. This dissertation focuses on the development of the DSACSS facility including the development and implementation of a closed-loop GPS simulator and evaluation of nonlinear feedback attitude and orbit control laws using real-time hardware-in-the-loop simulators. / Ph. D.