Tracking and relative attitude control of satellite in the presence of position dynamics and third-body perturbation with SMC

The geometric method is one of the nonlinear methods of large-scale relative motion that is used for all the eccentricity and relative distances. In this paper, the relative motion equations for perturbed orbits are developed in the presence of third body. The purpose of this paper is to design a control law to track and control the relative attitude of one satellite in the presence of position dynamics and uncertainty of the moment of inertia. For the orientation of satellite, it is first necessary through the theory of relative motion, to obtain some relative parameters such as position and relative velocity, and so on. The geometric method is used to obtain relative parameters. After obtaining relative parameters, we must track and control the dynamic equations for the target trajectory. Due to the uncertainty in the dynamics of the system, a robust controller must be used to obtain control law. Sliding mode control theory is used to obtain control law. The uncertainty in the satellite inertia is considered due to fuel sloshing during this maneuver. Finally, an appropriate control law is designed that is resistant to uncertainties and has good accuracy.