Attitude Coordinated Control of Multiple Underactuated Axisymmetric Spacecraft

Attitude coordinated control of multiple underactuated spacecraft is studied in this paper. We adopt the parametrization proposed by Tsiotras et al. (1995) to describe attitude kinematics, which has been shown to be very convenient for control of underactuated axisymmetric spacecraft with two control torques. We first propose a partial attitude coordinated controller with angular velocity commands. The controller is based on the exchange of each spacecraft's information with local neighbors and a self-damping term. Under a necessary and general connectivity assumption and by use of a novel Lyapunov function, we show that the symmetry axes of all spacecraft are eventually aligned. Full attitude control of multiple underactuated spacecraft is also considered and a discontinuous distributed control algorithm is proposed. It is shown that the proposed algorithm succeeds in achieving stabilization given that control parameters are chosen properly. Discussions on the cases without self damping are also provided for both partial and full attitude controls. Simulations are given to validate the theoretical results and different steady-state behaviors are observed.