Controllability research of an underactuated spacecraft with thruster under disturbance

Based on the nonlinear controllability theory, this paper analyzes the attitude controllability for an underactuated spacecraft using two or one thrusters in sequence. In order to provide a preconditional guide on designing the control law for the underactuated attitude control system in actual case, the underactuated spacecraft with respect to the orbit frame is investigated in the presence of periodical oscillation disturbance. Firstly, attitude dynamic model is established for an underactuated spacecraft actuated by three thrusters, one or two of which has failed separately, and the special orthogonal group (SO(3)) is deployed to describe the attitude motions. Secondly, Liouville theorem and Poincaré's recurrence theorem is used to confirm that the underactuated system is Weakly Positively Poisson Stable (WPPS). Furthermore, the sufficient and necessary condition of controllability is obtained on the basis of Lie Algebra Rank Condition (LARC). Finally, for the case of two thrusters available, angular velocity stabilization control law and three-axis attitude stabilization control law are designed, and proved by Lyapunov stability theory and LaSalle invariant theorem. The analytical and simulation results show that the proposed control laws are effective.