The precise control of spacecraft with flexible appendages is extremely difficult. The complexity of this task is magnified many times when several flexible spacecraft must be controlled precisely and collaboratively, as in formation flying. Formation flying requires a group of spacecraft to fly in a desired trajectory while maintaining both relative positions and velocities with respect to each other. This work enhances two current state-of-the-art formation flying algorithms, specifically leader-follower and virtual-structure architectures. First, a flexible satellite model is integrated into each of these architectures. Second, input shaping is used to generate the satellites desired trajectories, thereby enhancing the performance of the system. This dissertation addresses key issues regarding the application of command generation techniques to flexible satellites controlled with formation flying control architectures. The temporal tracking and the trajectory tracking of each architecture are examined as well as the vibration characteristics of the formation satellites. Design procedures for applying trajectory shaping for the leader-follower and virtual-structure architecture are developed. Experiments performed on a flexible satellite testbed verify key simulated results.

The problem of reference trajectory reconfiguration and long-term uncontrolled recovery of a formation of spacecraft is considered in an eccentric orbit under the influence of the J2 perturbation. Reference trajectories considered are the Projected Circular Orbit, Along-Track Orbit, and their eccentric modifications. Reconfiguration is accomplished using two, finite-pulse thrusts, modeled as impulses. The state transition matrix (STM) is calculated by four methods: (i) analytically from the Hill-Clohessy-Wiltshire equations, (ii) numerical integration using a fourth-order Runge-Kutta method, (iii) from the fundamental matrix of the linearized equations of motion, and (iv) computing the STM for the relative mean orbital elements, the geometric method. Only the geometric method takes into account J2, and it is shown to perform the transfers most accurately of all the methods. The methods are also applied to the reconfiguration maneuvers of the University of Toronto's CanX 4/5 formation flying mission.

The problem of reference trajectory reconfiguration and long-term uncontrolled recovery of a formation of spacecraft is considered in an eccentric orbit under the influence of the J2 perturbation. Reference trajectories considered are the Projected Circular Orbit, Along-Track Orbit, and their eccentric modifications. Reconfiguration is accomplished using two, finite-pulse thrusts, modeled as impulses. The state transition matrix (STM) is calculated by four methods: (i) analytically from the Hill-Clohessy-Wiltshire equations, (ii) numerical integration using a fourth-order Runge-Kutta method, (iii) from the fundamental matrix of the linearized equations of motion, and (iv) computing the STM for the relative mean orbital elements, the geometric method. Only the geometric method takes into account J2, and it is shown to perform the transfers most accurately of all the methods. The methods are also applied to the reconfiguration maneuvers of the University of Toronto's CanX 4/5 formation flying mission.

Autonomous proximity operations are the future of Deep space robotic exploration for searchof life, mining for resources and to establish outposts. Part of that future depends on howwell the spacecraft is capable to navigate around the complex environment of the smallcelestial body. The shift from huge monolithic spacecraft to a lightweight distributed Spacesystems has opened up a new opportunity for early characterization and global mappingmissions around these bodies. This project aims to contribute to help solve a part of thedream, wherein multiple spacecrafts operate cooperatively in proximity of small celestialbodies. To that extent, a 6 DoF controlled software-in-loop simulation is performed withsimulated optical sensors and IMU on board the spacecraft for verification of the controlledcooperative operation of two spacecrafts in a Leader-Follower configuration.

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Clusters of low-performance spacecraft flying in formation may provide enhanced performance over single high-performance spacecraft. This is especially true for remote sensing missions where interferometry or stereographic imaging may provide higher resolution data. The configurations of such formations vary during an orbit due to orbital dynamics, and over longer time scales due to perturbations. Selection of a configuration should be based on overall performance of the formation. In this thesis, performance measures are developed and evaluated based on integration over one orbit. The measures involve the angular separation of spacecraft, the distance between spacecraft, and an area-based measure of the separation of the spacecraft. Numerical techniques are employed to evaluate the performance measures to determine optimal scenarios for two formations. Simplifying assumptions are made to allow a closed-form analytic solution and the results are compared to those obtained numerically. Finally, the sensitivity of the measures to linearized propagation techniques is investigated. / Master of Science

For the upcoming formation flying technology demonstration mission NetSat a relative orbit propagator as well as a relative orbit controller were developed. The formation will consist of four equal nano-satellites with an electric propulsion system for orbit correction manoeuvres. This demands the use of continuous low-thrust models for relative orbit control, which is a novel field. A software framework was developed which allows orbit simulations of the whole fleet in a fully non-linear environment. The final on-board relative propagator is based on the Gim-Alfriend STM and incorporates eccentricity and the non-spherical shape of the Earth. The controller uses control Lyapunov function-based design and model predictive control, depending on the task. The guidance and control system is able to safely govern the relative motion for one-, two and three-dimensional formation configurations with inter-satellite distances as low as 50m. Based on these results, a complete mission plan is proposed.

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.

Several methods are presented for the design of satellite formations for science missions in high-eccentricity reference orbits with quantifiable performance criteria specified throughout only a portion the orbit, called the Region of Interest (RoI). A modified form of the traditional average along-track drift minimization condition is introduced to account for the fact that performance criteria are only specified within the RoI, and a robust formation design algorithm (FDA) is defined to improve performance in the presence of formation initialization errors. Initial differential mean orbital elements are taken as the design variables and the Gim-Alfriend state transition matrix (G-A STM) is used for relative motion propagation. Using mean elements and the G-A STM allows for explicit inclusion of J2 perturbation effects in the design process. The methods are applied to the complete formation design problem of the NASA Magnetospheric Multiscale (MMS) mission and results are verified using the NASA General Mission Analysis Tool (GMAT). Since satellite formations in high-eccentricity orbits will spend long times at high altitude, third-body perturbations are an important design consideration as well. A detailed analytical analysis of third-body perturbation effects on satellite formations is also performed and averaged dynamics are derived for the particular case of the lunar perturbation. Numerical results of the lunar perturbation analysis are obtained for the example application of the MMS mission and verified in GMAT.