Based on the nonlinear controllability theory, this paper analyzes the attitude controllability for an underactuatedspacecraft using two or one thrusters in sequence. In order to provide a preconditional guide on designing the controllaw for the underactuated attitude control system in actual case, the underactuated spacecraft with respect to the orbitframe is investigated in the presence of periodical oscillation disturbance. Firstly, attitude dynamic model isestablished for an underactuated spacecraft actuated by three thrusters, one or two of which has failed separately, andthe special orthogonal group (SO(3)) is deployed to describe the attitude motions. Secondly, Liouville theorem andPoincaré'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 LieAlgebra Rank Condition (LARC). Finally, for the case of two thrusters available, angular velocity stabilizationcontrol law and three-axis attitude stabilization control law are designed, and proved by Lyapunov stability theoryand LaSalle invariant theorem. The analytical and simulation results show that the proposed control laws areeffective.
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