Shape control of charged spacecraft cluster with two or three nodes

In 2002, King, Parker, Deshmukh and Chong presented a technical report introducing the idea of using electrostatic forces in spacecraft formation flying. This was the birth of the Coulomb formation flying concept. Since then, many areas related to Coulomb formation flying have been studied, such as the equilibrium solutions for a static multiple-craft Coulomb formation, the equilibrium solutions for a spinning two- and three-craft Coulomb formation, Coulomb virtual tether control, and hybrid formation flying control, et al. This dissertation investigates two aspects related to the shape control of a Coulomb cluster: two-craft collision avoidance using only Coulomb forces; two- and three-craft Coulomb virtual structure control.;A Lyapunov-based nonlinear feedback control and an open-loop patched-conic-section trajectory programming algorithm are developed to achieve the instant collision avoidance of two spacecraft. The Lyapunov-based control requires only separation distance and rate as feedback, the control achieves collision avoidance and retains the relative kinetic energy level. The trajectory programming algorithm searches a three-phase patched-conic-section trajectory to avoid a potential collision. This approach achieves collision avoidance, retains the direction and magnitude of the relative velocity. There is an extra degree of freedom which can be utilized to find an optimal trajectory corresponding to a specific cost function.;On the side of Coulomb virtual structure control, at first a Lyapunov-based partial state feedback control is developed to control the separation distance of a spinning two-craft formation to the desired distance. The boundaries of the separation distance error due to the lack of the full position vector measurements are found analytically. The study of the one-dimensional constraint three-craft Coulomb virtual structure control develops two approaches to solve the charge implementation issue. Then a switched Lyapunov-based control strategy is developed to stabilize the shape of a three-craft formation to the desired triangular configuration. The stability of the switched control is ensured using multiple Lyapunov function analysis tool. In the end a nonlinear control strategy is presented to stabilize the three-craft formation to a desired collinear configuration. The collinear configuration control does not require high-frequency switching of the control charges.