Distributed attitude synchronization control of multi-agent systems with directed topologies

In the present paper we consider the problem of attitude synchronization for a system of rigid body agents. We provide distributed kinematic control laws for two different synchronization problems. In the two problems the objective is the same, i.e., to synchronize the orientations of the agents, but what is assumed to be measurable by the agents differs. In problem 1 the agents measure their own orientations in a global reference frame, and obtain the orientations of their neighbors by means of communication. In problem 2 the agents only measure the relative orientations to their neighbors. By using the axis-angle representation of the orientation, we show that simple linear control laws solve both synchronization problems. Moreover we show that our proposed control laws work for directed and connected topologies on almost all SO(3) for problem 1 and on convex balls in SO(3) for problem 2.