Formation design and nonlinear control of spacecraft formation flying

The fundamental control challenges associated with Spacecraft Formation Flying (SFF) can be classified into two categories: (i) trajectory design and (ii) trajectory tracking. In this research, we address these challenges for several different operating environments.; The first part of this research focuses on providing a trajectory generation and an adaptive control design methodology to facilitate SFF missions near the Sun-Earth L2 Lagrange point. Specifically, we create a spacecraft formation by placing a leader spacecraft on a desired Halo orbit and a follower spacecraft on a desired quasi-periodic orbit surrounding the Halo orbit. We develop the nonlinear dynamics of the leader spacecraft and the follower spacecraft relative to the leader spacecraft, wherein the leader spacecraft is assumed to be on a desired Halo orbit trajectory. Finally, we design formation maintenance controllers such that the leader and follower spacecraft track desired trajectories. In particular, we design a set of adaptive position tracking controllers for the leader and follower spacecraft in the presence of unknown spacecraft mass. The proposed control laws are simulated for the case of the leader and follower spacecraft pair and are shown to yield asymptotic convergence of the position tracking errors.; The second part of this research focuses on providing nonlinear trajectory tracking control designs for SFF missions near Earth. First, we address output feedback tracking control problems for the coupled translation and attitude motion of a leader and a follower spacecraft. It is assumed that the translation and angular velocity measurements of the two spacecraft are not available for feedback. Second, we address a periodic trajectory tracking problem arising in spacecraft formation flying. In particular, the nonlinear position dynamics of a follower spacecraft relative to a leader spacecraft are utilized to develop a learning controller which learns a periodic, unknown model reference control. Using a Lyapunov-based approach, a full state feedback control law, a parameter update algorithm, and a model reference control estimate are designed that facilitate the tracking of given periodic reference trajectories in the presence of unknown leader and follower spacecraft masses. Furthermore, using a discrete Lyapunov-type stability analysis, model reference control error is shown to converge to zero. Illustrative simulations are included to demonstrate the efficacy of the proposed controllers.; The third part of this research explores the feasibility of using the effects of J2 perturbations as a mechanism to deploy pico-satellites (e.g., cubesats) to create a spacecraft constellation. Specifically, using two deployer spacecraft, both moving on polar Earth orbits, we insert one hundred cubesats into sparsely populated 60 degree inclination orbits around the Earth using a change in orbital inclination only. We also outline a proof-of-concept single stage propulsion system that provides necessary propulsive input for the velocity change needed for the orbital inclination change of cubesats. A series of illustrative simulations are given to demonstrate that sufficient and effective coverage of the Earth is achieved using the designed cubesat constellation. (Abstract shortened by UMI.)...