  This article presents a unified synchronization framework with application to
precision formation flying spacecraft. Central to the proposed innovation, in
applying synchronization to both translational and rotational dynamics in the
Lagrangian form, is the use of the distributed stability and performance
analysis tool, called contraction analysis that yields exact nonlinear
stability proofs. The proposed decentralized tracking control law synchronizes
the attitude of an arbitrary number of spacecraft into a common time-varying
trajectory with global exponential convergence. Moreover, a decentralized
translational tracking control law based on phase synchronization is presented,
thus enabling coupled translational and rotational maneuvers. While the
translational dynamics can be adequately controlled by linear control laws, the
proposed method permits highly nonlinear systems with nonlinearly coupled
inertia matrices such as the attitude dynamics of spacecraft whose large and
rapid slew maneuvers justify the nonlinear control approach. The proposed
method integrates both the trajectory tracking and synchronization problems in
a single control framework.
