Mouaad Boughellaba, Soulaimane Berkane, Abdelhamid Tayebi
This paper addresses the distributed attitude synchronization problem for a network of rigid-body systems on the special orthogonal group SO(3). Each agent measures, in its body frame, its own angular velocity and a set of vectors whose corresponding directions in the inertial frame are unknown. Under an undirected, connected, and acyclic interaction graph topology, we develop four distributed synchronization schemes relying solely on local vector measurements, without the need for attitude estimation and attitude exchange between agents. Specifically, two leaderless schemes are proposed at the kinematic and dynamic levels to achieve synchronization to a common unknown orientation. In addition, two leader-follower schemes are proposed to align all agents with a prescribed constant orientation defined by reference vector measurements available only to a designated leader. All control laws are formulated directly on SO(3), preserving the geometric structure of the attitude dynamics. A rigorous stability analysis is provided showing that the closed-loop systems achieve almost global asymptotic stability, which is the strongest stability property one can achieve on SO(3) with smooth controllers. %Compared with existing vector-measurement-based approaches that provide only local stability or convergence results, the proposed methods significantly strengthen the theoretical guarantees while maintaining a fully distributed architecture. Numerical simulations are provided to illustrate the effectiveness and performance of the proposed distributed control schemes.