A new analysis tool for attitude synchronization of multiple spacecraft with communication delays

In this paper, we investigate the attitude synchronization problem of multiple spacecraft with communication time delays, and the spacecraft agents are assumed to form a cyclic undirected graph. We use Euler parameters to represent the attitude deviation between spacecraft agents. We propose a new PD-type attitude synchronization control algorithm. With the help of Lyapunov stability analysis and Schwarz inequality, we show that the proposed control approach ensures stability of the closed-loop networked system so long as the dissipation gain satisfies some delay-dependent inequality. To show the convergence of the attitude synchronization errors, we develop a new tool called Tree Expanding approach. With this synthesis tool, we show that attitude synchronization is indeed achieved without requiring any assumption of the spacecraft orientations. Simulation results are provided to show the performance of the proposed synchronization algorithm.