Robust H∞ control for spacecraft formation flying with coupled translational and rotation Dynamics

In this paper, the problem on robust H-infinity control for 6-DOF spacecraft formation flying in the presence of parameter uncertainties and external disturbances is addressed. Firstly, the model of coupled translation and rotation motion of spacecraft formation is established. Subsequently, a robust H-infinity controller is proposed, which is constructed by the solution to the Hamilton-Jacobi-Inequality (HJI). It is proved that the 6-DOF coupled system is asymptotically stable and robust in respect to parameter uncertainties, and the H-infinity norm between external disturbances and regulated output is ensured to be no more than a prescribed attenuation level. Since it is hard to solve the HJI analytically, a modified theta - D method is proposed, which is an effective approach to find an approximate solution to the HJI. It is illustrated that the modified theta - D method is feasible and convenient to implement onboard in the practical situation. Finally, numerical simulations are performed to demonstrate the effectiveness of the robust H-infinity controller based on the modified theta - D method.