A robust adaptive control law for satellite formation flying

This paper considers the relative control problem of earth-orbiting formations based on the leader-follower scheme. The full nonlinear dynamics describing the relative motion between the leader and the follower are derived. The non-perturbed form of the full dynamics is utilized to formulate the optimal reference trajectory generation problem which is transformed into a nonlinear programming problem for numerical solution by Gauss pseudospectral method. A robust adaptive controller is designed based on the Lyapunov method. Despite the presence of unknown disturbance, unknown reference orbit parameters, unknown control of the leader, and unknown mass of the follower, this controller can guarantee the global uniform ultimate boundedness of the closed-loop system using only relative measurements. The ultimate bound of the tracking error can be made arbitrarily small by proper choice of controller parameters. Simulation results are presented to illustrate the efficiency of the main results in this paper.