A Common Framework for Attitude Synchronization of Unit Vectors in Networks with Switching Topology

In this paper, we study attitude synchronization for elements in the unit sphere of R3 and for elements in the 3D rotation group, for a network with switching topology. The agents angular velocities are assumed to be the control inputs, and a switching control law for each agent is devised that guarantees synchronization, provided that all elements are initially contained in a given region, unknown to the network. The control law is decentralized and it does not require a common orientation frame among all agents. We refer to synchronization of unit vectors in R3 as incomplete synchronization, and of 3D rotation matrices as complete synchronization. Our main contribution lies on showing that these two problems can be analyzed under a common framework, where all elements' dynamics are transformed into unit vectors dynamics on a sphere of appropriate dimension.