| 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 DeltaV 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 DeltaV, 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.;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 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 DeltaV-limited formation flying missions. |
