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 ℝ
³
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 ℝ
³
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.