Spacecraft attitude control using two control torques

The problem of attitude stabilizing control for underactuated spacecraft is addressed in this paper. Previously in the literature, a quaternion-based kinematic control law with a singularity has been presented to stabilize the attitude of an axially symmetric spacecraft using two independent control inputs for the case of zero spin rate. This method, however, may require a significant amount of control effort, especially for initial conditions close to the singular manifold. To reduce the control effort, a novel control law is proposed for the kinematic system of an axially symmetric underactuated spacecraft. The control inputs are small and bounded even if the initial conditions are close to the singular manifold. Then, a control law for the complete spacecraft system (both kinematics and dynamics) is designed. The control law is subsequently extended to solve the problem of attitude stabilizing control for an underactuated nonsymmetric spacecraft. The stability of the closed-loop system is guaranteed through a Lyapunov-based approach together with a corollary of Barbalat's Lemma. The performance of the control laws derived here is demonstrated by numerical simulations.