Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 55, Issue 5, Pages 1047-1058Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2010.2042003
Keywords
Cooperative systems; distributed control; motion planning; Lie groups; geometric control
Funding
- Belgian Network Dynamical Systems, Control, and Optimization (DYSCO)
- Belgian State, Science Policy Office
- FNRS
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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. Applying the proposed general methodology to particular examples allows to retrieve control laws that have been proposed in the literature on intuitive grounds. 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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