Quaternion-Based Backstepping Control of Relative Attitude in a Spacecraft Formation

In this paper we present a solution to the problem of controlling relative attitude in a leader-follower spacecraft formation, with focus on the rotation path for the follower spacecraft. Mathematical models of relative attitude kinematics and dynamics are presented, and a nonlinear control law designed by use of integrator backstepping is used to control the relative attitude in the formation. The resulting control law is proved to result in asymptotically stable equilibrium points in the closed loop system, and by a convenient choice of backstepping variables, it is ensured that a proper rotation path is used. Simulation results for a leader-follower spacecraft formation are presented to illustrate the performance of the presented control law