Relative attitude tracking of two satellites in the presence of third-body perturbation and considering actuator saturation

The Geometric method is one of the nonlinear methods for expressing the large-scale relative motion of satellites. In this paper, the equations of the Geometric method for perturbed orbits have been developed in the presence of third-body and J(2) gravitational perturbation. Then, these equations are employed for relative tracking and attitude control of two satellites to apply inter-satellite links. To validate the developed equations, the results obtained from these equations are compared to the main-body-centered-based relative motion (MCRM) model. Also, two control laws are designed to track and control the relative attitude of both satellites with consideration of external disturbances, the inertia uncertainty (due to fuel sloshing), and actuator saturation (due to bounded thrust). To establish inter-orbital links, it is necessary that the payload of satellites (the receiver and transmitter's antennas) are aligned in the same direction (named the reference trajectory). Due to the uncertainty in the attitude dynamics of systems and external disturbances, a robust controller must be applied to obtain control laws. The controller of the base satellite is designed so that the base satellite tracks the desired path (the reference trajectory) obtained from the relative motion equations. Furthermore, simultaneously and continuously, the target satellite control system tracks the base satellite antenna. For this reason, the external disturbances imposed on the base satellite affect the tracking control system of the target satellite. Also, a new definition of modified Rodrigues parameters (MRP) vector is proposed to design the tracking controllers that improve the control effort and convergence rate for the application of the inter-satellite links. Finally, two appropriate control laws for two satellites are designed through sliding mode control (SMC) theory subject to actuator saturation, inertia uncertainties, and external disturbances.