Output feedback control of relative translation in a leader-follower spacecraft formation

We present a solution to the problem of tracking relative translation in a leader-follower spacecraft formation using feedback from relative position only. Three controller configurations are presented which enables the follower spacecraft to track a desired reference trajectory relative to the leader. The controller design is performed for different levels of knowledge about the leader spacecraft and its orbit. The first controller assumes perfect knowledge of the leader and its orbital parameters, and renders the equilibrium points of the closed-loop system uniformly globally asymptotically stable (UGAS). The second controller uses the framework of the first to render the closed-loop system uniformly globally practically asymptotically stable (UGPAS), with knowledge of bounds on some orbital parameters, only. That is, the state errors in the closed-loop system are proved to converge from any initial conditions to a ball in close vicinity of the origin in a stable way, and this ball can be diminished arbitrarily by increasing the gains in the control law. The third controller, based on the design of the second, utilizes adaptation to estimate the bounds that were previously assumed to be known. The resulting closed-loop system is proved to be uniformly semiglobally practically asymptotically stable (USPAS). The last two controllers assume boundedness only of orbital perturbations and the leader control force. Simulation results of a leader-follower spacecraft formation using the proposed controllers are presented.