Relative Motion Integrated Coupled Control for Spacecraft Formation Using Gauss Pseudospectral Method

This paper addresses the problem of how to control spacecraft formation with coupled translational and rotational dynamics with optimized fuel usage using a single body fixed thruster and reaction wheels. The orientation of the thrust vector is constrained by the attitude and angular velocity. In particular, the star camera cannot point at the sun during formation maneuvering. The formation coupled control, which is a difficult problem with nonlinear and nonconvex attitude dynamics, is posed as a nonlinear optimal control problem and solved via direct transcription using the Gauss pseudospectral method. Examples demonstrate application of the proposed approach with simulated trajectory optimization of a dual-spacecraft formation initialization and a three-spacecraft reconfiguration problem.