Nonlinear control of spacecraft formation flying with disturbance rejection and collision avoidance

A nonlinear controller for disturbances rejection and collision avoidance is proposed for spacecraft formation flying. The formation flying is described by a nonlinear model with the J₂ perturbation and atmospheric drag. Based on the theory of the state-dependent Riccati equation (SDRE), a finite time nonlinear control law is developed for the nonlinear dynamics involved in formation flying. Then, a compensative internal mode (IM) control law is added to eliminate disturbances. These two control laws compose a finite time nonlinear tracking controller with disturbances rejection. Moreover, taking safety requirements into account, the repulsive control law is incorporated in the composite controller to perform collision avoidance manoeuvres. A numerical simulation is presented to demonstrate the effectiveness of the proposed method. Compared to the conventional control method, the proposed method provides better performance in the presence of the obstacles and external disturbances.