Distributed Cooperative Attitude Tracking for Multiple Flexible Spacecraft under a Directed Graph

This paper is concerned with the problem of cooperative attitude tracking and vibration reduction for multiple flexible spacecraft without modal variable measurement under a directed communication topology. Firstly, a distributed attitude synchronization control law for MRPs representation is proposed in the absence of external disturbances, where the modal information is obtained using a modal variable estimator. To deal with a more practical case that the spacecraft are affected by external disturbances, the control law is further modified by integrating a disturbance observer and a feedforward compensating scheme, in which the lumped disturbances including the external disturbances and errors of the estimated modal information are observed and compensated in finite time. Under this enhanced control scheme, the attitude tracking errors and vibration variables will converge to zero even in the presence of external disturbances, and the controller is continuous and chattering-free. Besides, compared with the existing results, the communication graph in this paper is assumed to be directed and contain a spanning tree with the virtual leader as the root node. A numerical example is illustrated to demonstrate the effectiveness of the proposed results.