Joint 48th IEEE Conference on Decision and Control and
28th Chinese Control Conference
Shanghai, P.R. China, December 16-18, 2009
FrC10.3
Control of coleader formations in the plane
Tyler H. Summers† , Changbin Yu‡ , Brian D.O. Anderson‡ , and Soura Dasgupta§
†
University of Texas at Austin
‡
The Australian National University
Abstract—This paper addresses the 𝑛-agent formation shape
maintenance problem in the plane. We consider a class of
directed information architectures associated with so called
minimally persistent coleader formations. The formation shape
is specified by certain interagent distances. Only one agent is
responsible for maintaining each distance. We propose a control
law where each agent executes its control using only the relative
position measurements of agents it must maintain its distance
to. The resulting nonlinear closed-loop system has a manifold of
equilibria; thus the linearized system is nonhyperbolic. We apply
center manifold theory to show local exponential stability of the
desired formation shape that 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 coleader formations with generic
agent positions.
I. INTRODUCTION
Much attention has been given recently to control of autonomous vehicle formations and mobile sensor networks due
to many promising scientific and engineering applications. Applications include teams of UAVs performing military reconnaissance and surveillance missions in hostile environments,
satellite formations for high-resolution Earth and deep space
imaging, and submarine swarms for oceanic exploration and
mapping. For large formations, an overarching requirement
is decentralized implementation, where each agent operates
using only local information.
Precisely...