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

Tyler H Summers; Changbin Yu; Soura Dasgupta; Brian D. O Anderson

doi:10.1109/TAC.2011.2146890

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

Journal article

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

Tyler H Summers, Changbin Yu, Soura Dasgupta and Brian D. O Anderson

IEEE transactions on automatic control, Vol.56(12), pp.2778-2792

12/2011

DOI: 10.1109/TAC.2011.2146890

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Abstract

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.

graph rigidity

Shape control

graph persistence

Distributed control

formation shape control

Center manifold theory

Stability analysis

Eigenvalues and eigenfunctions

Closed loop systems

Information architecture

Details

Title: Subtitle: Control of Minimally Persistent Leader-Remote-Follower and Coleader Formations in the Plane
Creators: Tyler H Summers - Australian Nat. Univ., Canberra, ACT, Australia
Changbin Yu - Res. Sch. of Inf. Sci. & Eng., Australian Nat. Univ., Canberra, ACT, Australia
Soura Dasgupta - Dept. of Electr. & Comput. Eng., Univ. of Iowa, Iowa City, IA, USA
Brian D. O Anderson - Res. Sch. of Inf. Sci. & Eng., Australian Nat. Univ., Canberra, ACT, Australia
Resource Type: Journal article
Publication Details: IEEE transactions on automatic control, Vol.56(12), pp.2778-2792
DOI: 10.1109/TAC.2011.2146890
ISSN: 0018-9286
eISSN: 1558-2523
Publisher: IEEE
Language: English
Date published: 12/2011
Academic Unit: Electrical and Computer Engineering
Record Identifier: 9984083246802771

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