Partial and full attitude synchronization of multiple underactuated spacecraft

We study leaderless attitude synchronization problem of multiple underactuated spacecraft in this paper. We adopt the special parameterizations of attitude 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. It is assumed that angular velocity commands are possible and this paper is confined to the kinematic level. We first propose a partial attitude synchronization controller that is based on the exchange of each spacecraft´s information with local neighbors. Under a necessary and general connectivity assumption and by use of an appropriate Lyapunov function, we show that the attitudes of spacecraft converge to a fixed or time-varying synchronization trajectory. Then, full attitude synchronization of multiple underactuated spacecraft is considered, where the discontinuous distributed algorithm is proposed. Simulations are given to validate the theoretical results and indicate several interesting observations.