Attitude controllability study of an underactuated flexible spacecraft

In order to provide a preconditional guide on designing the controller of under-actuated attitude control systems, this article analyzes the attitude controllability of an underactuated flexible spacecraft. The object is a central rigid body fixed with a flexible beam, actuated by two available thrusters. Firstly, an attitude dynamic model of the underactuated flexible spacecraft is established with thrusters, and the special orthogonal group (SO (3)) is deployed to describe the attitude motions. Secondly, neglecting the elastic deformations of the beam, the attitude controllability of the corresponding rigid body is analyzed based on the nonlinear analysis methods, and the sufficient condition for state controllability is obtained on the use of Lie Algebra Rank Condition (LARC). Thirdly, the impact of the flexible beam reckoned in, the system is simplified to the form of the state equation when we select the appropriate state variables. Then, through the controllability matrix judgment theorem, the sufficient and necessary condition for vibration controllability is derived, and furthermore a controllability index is proposed, to measure the degree of controllability.