For close proximity flying on the order of 10-100 meters, Coulomb thrusting presents a promising alternative to other methods of propulsion. This clean and fuel-efficient propulsion method is being investigated for use in formation flying and virtual structures. In the latter application, the individual spacecraft assume fixed positions relative to each other through the use of Coulomb forces. In the work presented here, an analytical and numerical analysis is performed on such virtual structures. In the analytical portion, the constant, open-loop charges necessary to maintain a Hill-frame-static formation are determined for the cases of linear two- and three-spacecraft formations and for the case of equilateral triangular formations with spacecraft of equal mass. In addition, analysis is provided for the N-craft case so that the inter-craft charge products can be determined for any static formation. In the numerical portion, a genetic algorithm is employed to support the analytical results by determining formation geometries and charging schemes such that the formation craft remain static in the Hill frame in the absence of perturbation. The results of the numerical analysis include examples of static two-craft through nine-craft formations, including several formations that display a broader range of configurations than considered in previous works. Issues encountered during the numerical analysis are discussed, as well as the course of action taken to overcome these issues. Finally, a method is presented by which the genetic algorithm could be extended to take advantage of cluster computing. / Master of Science

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.

The contribution of this thesis is on the temporal adjustment of the consensus weights, as applied to spacecraft formation control. Such an objective is attained by dynamically enforcing attitude synchronization via coupling terms included in each spacecraft controller. It is assumed that each spacecraft has identical dynamics but with unknown inertia parameters and external disturbances. By augmenting a standard adaptive controller that accounts for the unknown parameters, made feasible via an assumption on parameterization, with adaptation of the consensus weights, one opts to improve spacecraft synchronization. The coupling terms, responsible for enforcing synchronization amongst spacecraft, are weighted dynamically in proportion to the disagreement between the states of the spacecraft. The time adjustment of edge-dependent gains as well as the special cases of node-dependent and agent-independent constant gains are derived using Lyapunov redesign methods. The proposed adaptive control architectures which allow for adaptation of both parameter uncertainties and consensus penalty terms are demonstrated via extensive numerical studies of spacecraft networks with limited connectivity. By considering the sum of deviation-from-the-mean and rotational kinetic energy as appropriate metrics for synchronization and controller performance, the numerical studies also provide insights on the choice of optimal consensus gains.

The decentralized consensus control of a formation of rigid-body spacecraft is studied in the framework of geometric mechanics while accounting for a constant communication time delay between spacecraft. The relative position and attitude (relative pose) are represented on the Lie group SE(3) and the communication topology is modeled as a digraph. The consensus problem is converted into a local stabilization problem of the error dynamics associated with the Lie algebra se(3) in the form of linear time-invariant delay differential equations with a single discrete delay in the case of a circular orbit, whereas it is in the form of linear time-periodic delay differential equations in the case of an elliptic orbit, in which the stability may be assessed using infinite-dimensional Floquet theory. The proposed technique is applied to the consensus control of four spacecraft in the vicinity of a Molniya orbit.

No description available.

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.

<div> <div> <div> <p>A control methodology to design and establish spacecraft formations is presented. The intuitive design of complex spacecraft formation geometry is achieved by utilizing two different sets of relative orbital elements derived from a linearization of the dynamics. These sets provide strong insights into the shape, size, and orientation of the relative trajectory and facilitate the design of relative orbits in addition to relative positions. An artificial potential function (APF) composed of an attractive potential for goal seeking and a repulsive potential for obstacle avoidance is constructed. The derivation of a control law from this APF results in a computationally efficient algorithm able to fully control the relative position and velocity of the spacecraft and therefore to establish spacecraft formations. The autonomous selection of some of the design parameters of the model based on fuel minimization considerations is described. An assessment of the formation establishment accuracy is conducted for different orbital perturbation as well as various degrees of thrust errors and state uncertainties. Then, the performance of the control algorithm is demonstrated with the numerical simulation of four different scenarios. The first scenario is the design and establishment of a 10-spacecraft triangular lattice, followed by the establishment of a 37-spacecraft formation composed of two hexagonal lattices on two different relative planes. The control method is used to illustrate proximity operations with the visual inspection of an on-orbit structure in the third scenario. Finally, a formation composed of four spacecraft arranged in a tetrahedron is presented.<br></p> </div> </div> </div>

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