  The present paper proposes a unified geometric framework for coordinated
motion on Lie groups. It first gives a general problem formulation and analyzes
ensuing conditions for coordinated motion. Then, it introduces a precise method
to design control laws in fully actuated and underactuated settings with simple
integrator dynamics. It thereby shows that coordination can be studied in a
systematic way once the Lie group geometry of the configuration space is well
characterized. This allows among others to retrieve control laws in the
literature for particular examples. A link with Brockett's double bracket flows
is also made. The concepts are illustrated on SO(3), SE(2) and SE(3).
