Logarithmic Sliding-Mode Control for Attitude and Orbit Synchronous Tracking of Spacecraft

In this paper, the integrated modeling and the high-precision motion control problem for space flying-around mission are investigated. Firstly, based on the dual quaternion, the kinematic and dynamic model of the space relative attitude and orbital motion is formulated, and the solution mechanism for the anticipated attitude is proffered such that the kinematic and dynamic of the flying-around mission can be described in a unified mathematical framework. Then, the logarithmic slidingmodel (LnSM) manifold and its corresponding control are devised by introducing the error dual quaternion and its derivatives. The stability of the controlled closed-loop system is proved. A set of numerical simulations are executed, and the outcomes manifest that the controlled active spacecraft can promptly track the desired flying-around command in the presence of model uncertainties and external disturbances.