Control analysis of an underactuated spacecraft 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 the actual case, the underactuated spacecraft with respect to the orbit frame is investigated in the presence of periodical oscillation disturbance. First, attitude dynamic model was 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. Second, Liouville theorem and Poincaré's recurrence theorem were used to confirm that the drift field is Weakly Positively Poisson Stable (WPPS). Furthermore, the sufficient and necessary condition of controllability was obtained on the basis of Lie Algebra Rank Condition (LARC). Finally, according to the case of two available thrusters, angular velocity stabilization and three-axis attitude stabilization control laws are designed, and proved by Lyapunov stability theory and LaSalle invariant theorem. The analysis and simulation results illustrate the feasibility of the proposed control law.