Integrated Geometric Optimal Control of Spacecraft Attitude and Orbit Based on SE(3)

A model predictive convex programming (MPCP) on
$SE(3)$
parametrized by trigonometric series control is proposed in this paper, to solve the optimal control problem of spacecraft attitude orbit integration. Firstly, the geometric modeling of the spacecraft with six degrees of freedom for the attitude orbit integration is performed by the differential manifold
$SE(3)$
, which can effectively avoid the problems of ambiguity, receding winding, and singularity that occurs in the conventional methods for rigid body attitude description. Then, based on differential geometric theories, such as the variational principle, the left-invariant principle of Lie group, and the topology of Lie algebraic space, MPCP is applied to
$SE(3)$
. It can solve a class of optimization problems with process constraints and control input constraints during spacecraft flight. Furthermore, a control framework of trigonometric series is constructed, which is seamlessly integrated into MPCP to achieve smoother trajectory optimization control. Finally, the practicality and effectiveness of the proposed method are verified by numerical simulation.