Higher order sliding mode control of formation flying satellites with J₂ perturbation

It is very important to design the relative orbital controller which is robust to the J₂ perturbation and other bounded disturbances for the formation flying satellites. The relative motion with J₂ perturbation and other bounded disturbances is firstly modeled accurately, and the description is not only applicable to the circular reference orbit, but also to the elliptical reference orbit. Then, a higher order sliding mode controller is presented for the relative motion, which is based on the free variable transformation, Lyapunov transformation and the analysis of the boundedness of some J₂ perturbation terms, and the convergences of the position error and velocity error for the formation are derived. Simulation results demonstrate the effectiveness of the method.