Global trajectory design for position and attitude control of an underactuated satellite

Underactuated control offers fault-tolerance for satellite systems, which not only enables the position and attitude control of a satellite with fewer thrusters, but also can reduce the number of thrusters equipped on the satellite even when considering the need for backups. Due to having fewer thrusters, the coupling effect between the translational motion and rotational motion of the satellite cannot be avoided, and the coupled motion must be considered in control procedures. This paper presents a global trajectory design procedure required for the position and attitude control of an underactuated satellite. The satellite has four thrusters with constant thrust magnitudes on one plane of the satellite body. Then, an analytical solution for coupled motion between the rotation and translation of the satellite is obtained using three-step maneuvers of attitude control. The trajectory design based on the analytical solution is shown for the control of translational and rotational motion in three dimensions. Finally, a numerical simulation is performed to verify the effectiveness of the proposed design procedure.