Geometric Analysis of the Formation Problem for Autonomous Robots

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 ta...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2010-10, Vol.55 (10), p.2379-2384
Main Authors: Dörfler, Florian, Francis, Bruce
Format: Article
Language:English
Subjects:
Applied sciences
Autonomous
Computer science
control theory
systems
Control system analysis
Control system synthesis
Control theory. Systems
Convergence
Distributed control
Dynamic tests
Dynamics
Exact sciences and technology
Formation control
global stability analysis
hyperbolic invariant manifolds
Invariants
Lyapunov method
Mathematics
Mobile robots
Robot control
Robot kinematics
Robot sensing systems
Robotics
Robots
Sensor arrays
Sensor phenomena and characterization
Stability
Stability analysis
Surveillance
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Summary: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.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2010.2053735