In this paper, both the proportional derivative feedback control and variable-structure sliding mode control approaches based on dual numbers are presented to design space flyaround and in-orbit inspection missions. Dual-number-based spacecraft kinematics and dynamics models are formulated. The integrated translational and rotational motions can be described in one compact expression, and the mutual coupling effect can be considered. A space flyaround and in-orbit inspection mission model based on dual numbers is derived. Both proportional derivative feedback control and variable-structure sliding mode control laws are designed using dual numbers. Simulation results indicate that both the proposed control system can provide high-precision control for relative position and attitude. Of the two systems, the variable-structure sliding mode control system performs the best.
