Attitude synchronization control for multi-agent systems on unit quaternions

This paper discusses an attitude synchronization problem for multi-agent systems in 3-D spaces and proposes a synchronization control law based on the quaternion representation of 3D rotations. The proposed control strategy takes advantage of the geometry of the unit quaternion space and synchronizes agents to have representative quaternions that map to the same physical 3D rotation. Each agent's attitude state is represented by a unit quaternion, and the attitude synchronization law ensures the states remain in the unit quaternion space. We show that this control law is stable for the desired equilibrium using a Lyapunov approach, and provide a simulation of nine agents interacting in an undirected graph to justify our results. We also provide a detailed analysis of the two-agent system to provide intuition behind the control law's operation.