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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

La robotique mobile autonome est un axe de recherche qui vise à donner à une machine la capacité de se mouvoir dans un environnement sans assistance ni intervention humaine. Cette thèse s’intéresse à la partie décisionnelle de la navigation robotique à savoir la planification de mouvement pour un robot mobile non-holonome, pour lequel, la prise en compte des contraintes cinématiques et non-holonomes est primordiale. Aussi, la nécessité de considérer la géométrie propre du robot et la bonne maîtrise de l’environnement dans lequel il évolue constituent des contraintes à assurer. En effet la planification de mouvement consiste à calculer un mouvement réalisable que doit accomplir le robot entre une position initiale et une position finale données. Selon la nature de l’environnement, notamment les obstacles qui s’y présentent, deux instances du problème se distinguent : la planification de chemin et la planification de trajectoire. L’objectif de cette thèse est de proposer de nouveaux algorithmes pour contribuer aux deux instances du problème de planification de mouvement. La méthodologie suivie repose sur des solutions génériques qui s’appliquent à une classe de systèmes robotiques plutôt qu’à une architecture particulière. Les approches proposées intègrent les B-splines Rationnelles non uniformes (NURBS) dans le processus de modélisation des solutions générées tout en s’appuyant sur la propriété de contrôle local, et utilisent les algorithmes génétiques pour une meilleure exploration de l’espace de recherche. / The mobile robotics is an area of research that aims to give a machine the ability to move in an environment without assistance or human intervention. This thesis focuses on the decisional part of robotic navigation, namely motion planning for a non-holonomic mobile robot, for which, the consideration of kinematic and non-holonomic constraints is paramount. Also, the need to consider the specific geometry of the robot and the good control of the environment in which it operates are constraints to insure. Indeed, motion planning is to calculate a feasible movement to be performed by the robot between an initial and a final given position. Depending on the nature of the environment, two instances of the problem stand out: the path planning and the trajectory planning. The objective of this thesis is to propose new algorithms to contribute to the two instances of motion planning problem. The followed methodology is based on generic solutions that are applicable to a class of robotic systems rather than a particular architecture. The proposed approaches include the Non-Uniform Rational B-Spline (NURBS) in the modeling process of the generated solutions while relying on the local control property. Also, they use genetic algorithms for better exploration of the search space.