Leaderless attitude synchronization control of multiple flexible spacecraft on SO(3)

Abstract

This paper presents adaptive controllers for leaderless attitude synchronization of multiple flexible spacecraft on $SO\left(3\right)$ under communication topologies containing spanning tree(s). To provide a reference attitude for each spacecraft, distributed observers in 9-dimensional Euclidean space are proposed based on a smooth mapping from Euclidean space ${ℝ}^{3\times 3}$ to Lie group $SO\left(3\right)$. Both the scenarios with arbitrary and almost zero final angular velocities are considered. Subsequently, adaptive continuous controllers on $SO\left(3\right)$ are presented to achieve the leaderless attitude synchronization subject to external disturbance, while guaranteeing boundedness of flexible vibration. Rigorous proofs are presented to show the convergence of the proposed control methods. The effectiveness of the proposed strategies is further demonstrated by numerical simulations.