PID+ backstepping control of relative spacecraft attitude

In this paper we present a PID+ backstepping controlIer, as a solution to the problem of coordinated attitude control in spacecraft formations. The control scheme is based on quaternions and modified Rodrigues parameters as attitude representation of the relative attitude error. Utilizing the invertibility of the modified Rodrigues parameter kinematic differential equation, a globally exponentially stable control law for the relative attitude error dynamics is obtained through the use of integrator augmentation and backstepping. Finally, simulation results are presented to show controller performance.