Coordinated motion design on Lie groups

Details Coordinated motion design on Lie groups Coordinated motion design on Lie groups

2008-07-28

arxiv.org/abs/0807.4416v1

Mathematics

Optimization and Control

Submitted

Scientific paper

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).

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