  In this paper we study a family of controllers that guarantees attitude
synchronization for a network of elements in the unit sphere domain, i.e.
$\mathcal{S}^2$. We propose distributed continuous controllers for elements
whose dynamics are controllable (i.e. control with torque as command), and
which can be implemented by each individual agent without the need of a common
global orientation frame among the network, i.e. it requires only local
information that can be measured by each individual agent from its own
orientation frame. The controllers are specified according to arbitrary
distance functions in $\mathcal{S}^2$, and we provide conditions on those
distance functions that guarantee that i) a synchronized network of agents is
locally asymptotically stable for an arbitrary network graph; ii) a
synchronized network can be achieved for almost all initial conditions in a
tree graph network. We also study the equilibria configurations that come with
specific types of network graphs. The proposed strategies can be used in
attitude synchronization of swarms of fully actuated rigid bodies, such as
satellites.
