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Geometric Analysis of the Formation Problem for Autonomous Robots.

Authors :
Dorfler, Florian
Francis, Bruce
Source :
IEEE Transactions on Automatic Control. Oct2010, Vol. 55 Issue 10, p2379-2384. 6p.
Publication Year :
2010

Abstract

In the formation control problem for autonomous robots, a distributed control law steers the robots to the desired target formation. A local stability result of the target formation can be derived by methods of linearization and center manifold theory or via a Lyapunov-based approach. Besides the target formation, the closed-loop dynamics of the robots feature various other undesired invariant sets such as nonrigid formations. This note addresses a global stability analysis of the closed-loop formation control dynamics. We pursue a differential geometric approach and derive purely algebraic conditions for local stability of invariant embedded submanifolds. These theoretical results are then applied to the well-known example of a cyclic triangular formation and result in instability of all invariant sets other than the target formation. [ABSTRACT FROM PUBLISHER]

Details

Language :
English
ISSN :
00189286
Volume :
55
Issue :
10
Database :
Academic Search Index
Journal :
IEEE Transactions on Automatic Control
Publication Type :
Periodical
Accession number :
54290296
Full Text :
https://doi.org/10.1109/TAC.2010.2053735