Saturated Backstepping Control of Underactuated Spacecraft Hovering for Formation Flights

Based on the inherent coupling of system states, backstepping controllers are designed for underactuated spacecraft hovering without either the radial or in-track thrust and in the presence of input saturation and unmatched disturbances. Feasible hovering positions for either saturated underactuated case are derived. A Lyapunov-based approach is used to prove the asymptotical convergence of state errors and system robustness against unmatched disturbances. The validity of theoretical analysis is verified by simulations in a J2 -perturbed environment.