  The global attitude synchronization problem is studied for networked rigid
bodies under directed topologies. To avoid the asynchronous pitfall where only
vector parts converge to some identical value but scalar parts do not,
multiplicative quaternion errors are leveraged to develop attitude
synchronization protocols for rigid bodies with the absolute measurements. It
is shown that global synchronization of networked rigid bodies can be achieved
if and only if the directed topology is quasi-strongly connected.
Simultaneously, a novel double-energy-function analysis method, equipped with
an ordering permutation technique about scalar parts and a coordinate
transformation mechanism, is constructed for the quaternion behavior analysis
of networked rigid bodies. In particular, global synchronization is achieved
with our analysis method regardless of the highly nonlinear and strongly
coupling problems resulting from multiplicative quaternion errors, which
seriously hinder the traditional analysis of global synchronization for
networked rigid bodies. Simulations for networked spacecraft are presented to
show the global synchronization performances under different directed
topologies.
