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Geometric Analysis of the Formation Problem for Autonomous Robots


F. Dörfler

University of Toronto

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.


Type of Publication:

(12)Diploma/Master Thesis

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% Autogenerated BibTeX entry
@PhdThesis { Xxx:2008:IFA_4927
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