Continuous leaderless synchronization control of multiple spacecraft on $𝑺𝑶\mathbf{(}\mathrm{𝟑}\mathbf{)}$

This paper presents a solution to the leaderless consensus of multiple spacecraft on $SO(3)$ under a connected undirected graph. An algorithm is proposed to generate an undirected tree graph from a connected undirected communication topology. A distributed observer is designed to estimate the desired attitude and angular velocity for each spacecraft under the generated tree graph. An adaptive controller with a general connected undirected graph is developed to complete the synchronization task. Cases with zero and nonzero final angular velocities are considered. Theoretical proofs and numerical simulations are presented to demonstrate the effectiveness of the proposed controllers.