Relative Motion Decoupled Control for Spacecraft Formation with Coupled Translational and Rotational Dynamics

The formation relative motion control by using one body fixed thruster and reaction wheels is a challenging problem due to the coupled translational and rotational dynamics. As the thruster vector depends on the current attitude and its angular velocity, and some of the attitude constraints also couple the position and attitude of the spacecraft, it makes the formation control problem high dimensional. This paper develops two decoupling conditions, including thrust vector maneuverability condition and included angle condition between the thruster and the star camera boresight, and then presents two methods to calculate the target attitude quaternion. Both of the two methods need first design the optimal trajectory of the thrust vector, and then use geometric and nonlinear programming methods to calculate the attitude trajectory. The validity of the proposed approach is demonstrated in a typical application of a dual-spacecraft formation initialization.