Attitude Trajectory Planning for Spacecraft Actuated by Two Single Gimbal Control Moment Gyroscopes

In this article, we study the rest-to-rest attitude trajectory planning problem of a spacecraft actuated by two single gimbal control moment gyroscopes (SGCMGs) with control and pointing constraints, which relates to solving a challenging nonlinear optimal control problem. We first alleviate the nonlinearity in CMG-driven attitude dynamics through a mechanism combining variable redefinition and constraints relaxation. By designing an appropriate objective function, we prove that the relaxation is lossless, i.e., the solution of the relaxed problem is also optimal to the original one. This result enables us to enhance the computational performance of the nonlinear optimization problem. Thanks to the completely decoupled control input structure in the redefined dynamics, the trajectory initialization to start the optimization solver can be easily generated. Specifically, one only needs to compute the geodesic from the initial attitude to the desired one and then to recover the input by control allocation. It is worth noting that this treatment avoids the so-called singularity problem of the combined SGCMG-spacecraft dynamics. The theoretical results are validated by numerical examples.