Formation flying is a new paradigm in space mission design, aimed at replacing large satellites with multiple small satellites. Some of the proposed benefits of formation flying satellites are: (i) Reduced mission costs and (ii) Multi mission capabilities, achieved through the reconfiguration of formations. This dissertation addresses the problems of initiatialization, maintenance and reconfiguration of satellite formations in Earth orbits. Achieving the objectives of maintenance and reconfiguration, with the least amount of fuel is the key to the success of the mission. Therefore, understanding and utilizing the dynamics of relative motion, is of significant importance. The simplest known model for the relative motion between two satellites is described using the Hill-Clohessy-Wiltshire(HCW) equations. The HCW equations offer periodic solutions that are of particular interest to formation flying. However, these solutions may not be realistic. In this dissertation, bounded relative orbit solutions are obtained, for models, more sophisticated than that given by the HCW equations. The effect of the nonlinear terms, eccentricity of the reference orbit, and the oblate Earth perturbation, are analyzed in this dissertation, as a perturbation to the HCW solutions. A methodology is presented to obtain initial conditions for formation establishment that leads to minimal maintenance effort. A controller is required to stabilize the desired relative orbit solutions in the presence of disturbances and against initial condition errors. The tradeoff between stability and fuel optimality has been analyzed for different controllers. An innovative controller which drives the dynamics of relative motion to control-free natural solutions by matching the periods of the two satellites has been developed under the assumption of spherical Earth. A disturbance accommodating controller which significantly brings down the fuel consumption has been designed and implemented on a full fledged oblate Earth simulation. A formation rotation concept is introduced and implemented to homogenize the fuel consumption among different satellites in a formation. To achieve the various mission objectives it is necessary for a formation to reconfigure itself periodically. An analytical impulsive control scheme has been developed for this purpose. This control scheme has the distinct advantage of not requiring extensive online optimization and the cost incurred compares well with the cost incurred by the optimal schemes.

An innovative dynamics and control algorithm is developed for a dual-nanosatellite formation flying mission. The principal function of this algorithm is to use regular GPS state measurements to determine the controlled satellite's tracking error from a set of reference trajectories in the local-vertical/local-horizontal reference frame. A linear state-feedback control law--designed using a linear quadratic regulator method--calculates the optimal thrusts necessary to correct this error and communicates the thrust directions to the attitude control system and the thrust durations to the propulsion system. The control system is developed to minimize the conflicting metrics of tracking error and ΔV requirements. To reconfigure the formation, an optimization algorithm is designed using the analytical solution to the state-space equation and the Hill-Clohessy-Wiltshire state transition matrix to solve for dual-thrust reconfiguration maneuvers. The resulting trajectories require low ΔV, use finite-time thrusts and are accurate in a fully nonlinear orbital environment. This algorithm will be used to control the CanX-4&5 formation flying demonstration mission. In addition, an iterative method which numerically generates quasi periodic trajectories for a satellite formation is presented. This novel technique utilizes a shooting approach to the Newton method to close the relative deputy trajectory over a specific number of orbits, then fits the actual perturbed motion of the deputy with a Fourier series to enforce periodicity. This process is applied to two well-known satellite formations: a projected circular orbit and a J2-invariant formation. Compared to conventional formations, these resulting quasi-periodic trajectories require a dramatically lower control effort to maintain and could therefore be used to extend ΔV-limited formation flying missions. Finally, an analytical study of the stability of the formation flying algorithm is conducted. To facilitate the proof, the control algorithm is converted into a discrete-time linear time-varying system. Stability of the system is determined via discrete Floquet theory. This analysis is applied to the CanX-4&5 control laws for tracking along-track orbits, projected circular orbits, and quasi J2-invariant formations.

An innovative dynamics and control algorithm is developed for a dual-nanosatellite formation flying mission. The principal function of this algorithm is to use regular GPS state measurements to determine the controlled satellite's tracking error from a set of reference trajectories in the local-vertical/local-horizontal reference frame. A linear state-feedback control law--designed using a linear quadratic regulator method--calculates the optimal thrusts necessary to correct this error and communicates the thrust directions to the attitude control system and the thrust durations to the propulsion system. The control system is developed to minimize the conflicting metrics of tracking error and ΔV requirements. To reconfigure the formation, an optimization algorithm is designed using the analytical solution to the state-space equation and the Hill-Clohessy-Wiltshire state transition matrix to solve for dual-thrust reconfiguration maneuvers. The resulting trajectories require low ΔV, use finite-time thrusts and are accurate in a fully nonlinear orbital environment. This algorithm will be used to control the CanX-4&5 formation flying demonstration mission. In addition, an iterative method which numerically generates quasi periodic trajectories for a satellite formation is presented. This novel technique utilizes a shooting approach to the Newton method to close the relative deputy trajectory over a specific number of orbits, then fits the actual perturbed motion of the deputy with a Fourier series to enforce periodicity. This process is applied to two well-known satellite formations: a projected circular orbit and a J2-invariant formation. Compared to conventional formations, these resulting quasi-periodic trajectories require a dramatically lower control effort to maintain and could therefore be used to extend ΔV-limited formation flying missions. Finally, an analytical study of the stability of the formation flying algorithm is conducted. To facilitate the proof, the control algorithm is converted into a discrete-time linear time-varying system. Stability of the system is determined via discrete Floquet theory. This analysis is applied to the CanX-4&5 control laws for tracking along-track orbits, projected circular orbits, and quasi J2-invariant formations.

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.

CanX-4/-5 is a formation flying technology demonstration mission that shall demonstrate sub-meter formation tracking control. The key to this precision control is carrier phase differential GPS state estimation, which enables centimeter-level relative state estimation. In this thesis, the formation flying controller design is reviewed in detail, and an innovative closed-loop formation reconfiguration strategy is presented. In addition, the designs of both coarse- and fine-mode relative state estimators are presented. Formation flying simulations demonstrate the efficacy of the proposed control and coarse estimation. Furthermore, hardware tests are performed to test the computational efficiency of the control algorithms and to validate the fine-mode relative navigation filter.

CanX-4/-5 is a formation flying technology demonstration mission that shall demonstrate sub-meter formation tracking control. The key to this precision control is carrier phase differential GPS state estimation, which enables centimeter-level relative state estimation. In this thesis, the formation flying controller design is reviewed in detail, and an innovative closed-loop formation reconfiguration strategy is presented. In addition, the designs of both coarse- and fine-mode relative state estimators are presented. Formation flying simulations demonstrate the efficacy of the proposed control and coarse estimation. Furthermore, hardware tests are performed to test the computational efficiency of the control algorithms and to validate the fine-mode relative navigation filter.

No description available.

A novel continuous low-thrust fuel-efficient model predictive control strategy for multi-satellite formations flying in low earth orbit is presented. State prediction relies on a full nonlinear relative motion model, based on quasi-nonsingular relative orbital elements, including earth oblateness effects and, through state augmentation, differential drag. The optimal control problem is specically designed to incorporate latest theoretical results concerning maneuver optimality in the state-space, yielding to a sensible total delta-V reduction, while assuring feasibility and stability though imposition of a Lyapunov constraint. The controller is particularly suitable for networked architectures since it exploits the predictive strategy and the dynamics knowledge to provide robustness against feedback losses and delays. The Networked MPC is validated through real missions simulation scenarios using a high-fidelity orbital propagator which accounts for high-order geopotential, solar radiation pressure, atmospheric drag and third-body effects.

Small satellites are growing in popularity because they offer an effective option that enables missions otherwise too schedule or cost limited. However, many possible missions require improved platform capabilities without sacrificing the cost effective nature of small satellites before they become viable. Described is the development and validation of high performance attitude determination and control for nanosatellite missions. Considered are astronomy missions, requiring very fine pointing stability, and formation flying missions requiring rapid manoeuvring while maintaining antenna coverage towards secondary pointing targets. It will be shown that power and volume limited nanosatellites are capable of this level of attitude performance by leveraging the techniques normally reserved for larger spacecraft. Discussed are attitude state estimation techniques and control laws developed for the BRITE stellar photometry constellation and CanX-4 and CanX-5 formation flying mission, along with the challenges associated with implementing and validating these designs for real space missions.

Small satellites are growing in popularity because they offer an effective option that enables missions otherwise too schedule or cost limited. However, many possible missions require improved platform capabilities without sacrificing the cost effective nature of small satellites before they become viable. Described is the development and validation of high performance attitude determination and control for nanosatellite missions. Considered are astronomy missions, requiring very fine pointing stability, and formation flying missions requiring rapid manoeuvring while maintaining antenna coverage towards secondary pointing targets. It will be shown that power and volume limited nanosatellites are capable of this level of attitude performance by leveraging the techniques normally reserved for larger spacecraft. Discussed are attitude state estimation techniques and control laws developed for the BRITE stellar photometry constellation and CanX-4 and CanX-5 formation flying mission, along with the challenges associated with implementing and validating these designs for real space missions.