Control of Minimally Persistent Leader-Remote-Follower and Coleader Formations in the Plane

This paper solves an n -agent formation shape control problem in the plane. The objective is to design decentralized control laws so that the agents cooperatively restore a prescribed formation shape in the presence of small perturbations from the prescribed shape. We consider two classes of directe...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2011-12, Vol.56 (12), p.2778-2792
Main Authors: Summers, Tyler H., Changbin Yu, Dasgupta, Soura, Anderson, Brian D. O.
Format: Article
Language:English
Subjects:
Applied sciences
Center manifold theory
Closed loop systems
Computer science
control theory
systems
Control system analysis
Control system synthesis
Control theory. Systems
Decentralized control
Design engineering
Distributed control
Eigenvalues and eigenfunctions
Exact sciences and technology
formation shape control
Formations
Gain
graph persistence
graph rigidity
Information architecture
Manifolds
Planes
Position measurement
Robotics
Shape control
Simulation
Stability analysis
Studies
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Summary:This paper solves an n -agent formation shape control problem in the plane. The objective is to design decentralized control laws so that the agents cooperatively restore a prescribed formation shape in the presence of small perturbations from the prescribed shape. We consider two classes of directed, cyclic information architectures associated with so-called minimally persistent formations: leader-remote-follower and coleader. In our framework the formation shape is maintained by controlling certain interagent distances. Only one agent is responsible for maintaining each distance. We propose a decentralized control law where each agent executes its control using only the relative position measurements of agents to which it must maintain its distance. The resulting nonlinear closed-loop system has a manifold of equilibria, which implies that the linearized system is nonhyperbolic. We apply center manifold theory to show local exponential stability of the desired formation shape. The result circumvents the non-compactness of the equilibrium manifold. Choosing stabilizing gains is possible if a certain submatrix of the rigidity matrix has all leading principal minors nonzero, and we show that this condition holds for all minimally persistent leader-remote-follower and coleader formations with generic agent positions. Simulations are provided.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2011.2146890