Control of leader-follower spacecraft formation using coupling between attitude and translation

In this paper we present a navigation and guidance algorithm for leader-follower satellite formation flying, based on mathematical models of relative translation and rotation between two spacecraft, where the follower is assumed to be equipped with only one main thruster, and hence under actuated with regard to position control. An integrator backstepping controller and a passivity-based sliding surface controller are derived for control of relative rotation and translation, respectively, and both closed-loop models are shown to be asymptotically stable according to standard Lyapunov theorems. The models are then coupled through an algorithm. The idea of the algorithm is as follows: Let the follower spacecraft change its attitude relative to the leader spacecraft. Then the relative position is regulated to a reference point in space. At the end, the spacecraft is regulated back to pointing at the leader spacecraft. Simulations have been performed using Matlab to visualize the results. The results from the simulation shows that both the attitude error and position error converges towards zero.