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

Coordinated motion design on Lie groups