Global Attitude Synchronization for Heterogeneous Multiagent Systems on $\text{SO}(3)$

In this paper, we address the problem of attitude synchronization for a group of rigid body systems evolving on$SO(3)$. The interaction among these systems is modeled through an undirected, connected, and acyclic graph topology. First, we present an almost global continuous distributed attitude synchronization scheme with rigorously proven stability guarantees. Thereafter, we propose two global distributed hybrid attitude synchronization schemes on$SO(3)$. The first scheme is a hybrid control law that leverages angular velocities and relative orientations to achieve global alignment to a common orientation. The second scheme eliminates the dependence on angular velocities by introducing dynamic auxiliary variables, while ensuring global asymptotic attitude synchronization. This velocity-free control scheme relies exclusively on attitude information. The proposed schemes are applicable to heterogeneous multi-agent systems, where agents may have distinct inertia matrices. Simulation results are provided to illustrate the effectiveness of the proposed distributed attitude synchronization schemes.