Necessary and Sufficient Graphical Conditions for Affine Formation Control

被引：193

作者：

Lin, Zhiyun ^{[1
,2
]}

Wang, Lili ^{[3
]}

Chen, Zhiyong ^{[4
]}

Fu, Minyue ^{[4
,5
]}

Han, Zhimin ^{[1
]}

机构：

[1] Zhejiang Univ, Coll Elect Engn, State Key Lab Ind Control Technol, Hangzhou 310027, Zhejiang, Peoples R China

[2] Univ Newcastle, Sch Elect Engn & Comp Sci, Callaghan, NSW 2308, Australia

[3] Yale Univ, Dept Elect Engn, New Haven, CT 06520 USA

[4] Univ Newcastle, Sch Elect Engn & Comp Sci, Callaghan, NSW 2308, Australia

[5] Zhejiang Univ, Dept Control Sci & Engn, State Key Lab Ind Control Technol, Hangzhou 310027, Zhejiang, Peoples R China

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2016年 / 61卷 / 10期

基金：

中国国家自然科学基金;

关键词：

Distributed control; formation control; graph theory; multi-agent systems; MOBILE AUTONOMOUS AGENTS; MULTIAGENT SYSTEMS; CONTAINMENT CONTROL; COMPLEX LAPLACIAN; LOCAL-CONTROL; NETWORKS; SYNCHRONIZATION; TOPOLOGIES; DYNAMICS; RIGIDITY;

D O I：

10.1109/TAC.2015.2504265

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper introduces a new multi-agent control problem, called an affine formation control problem, with the objective of asymptotically reaching a configuration that preserves collinearity and ratios of distances with respect to a target configuration. Suppose each agent updates its own state using a weighted sum of its neighbor's relative states with possibly negative weights. Then the affine control problemcan be solved for either undirected or directed interaction graphs. It is shown in this paper that an affine formation is stabilizable over an undirected graph if and only if the undirected graph is universally rigid, while an affine formation is stabilizable over a directed graph in the d-dimensional space if and only if the directed graph is (d + 1)-rooted. Rigorous analysis is provided, mainly relying on Laplacian associated with the interaction graph, which contain both positive and negative weights.

引用

页码：2877 / 2891

页数：15

共 30 条

[1] On bar frameworks, stress matrices and semidefinite programming [J].

Alfakih, A. Y. .

MATHEMATICAL PROGRAMMING, 2011, 129 (01) :113-128

[2] Consensus Problems on Networks With Antagonistic Interactions [J].

Altafini, Claudio .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2013, 58 (04) :935-946

[3]

Anderson BDO, 2008, IEEE CONTR SYST MAG, V28, P48, DOI 10.1109/MCS.2008.929280

[4]

[Anonymous], 2010, AM J MATH

[5] RIGIDITY OF GRAPHS [J].

ASIMOW, L ;

ROTH, B .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1978, 245 (NOV) :279-289

[6] STABILIZATION BY A DIAGONAL MATRIX [J].

BALLANTINE, CS .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 25 (04) :728-+

[7] Distributed Containment Control for Multiple Autonomous Vehicles With Double-Integrator Dynamics: Algorithms and Experiments [J].

Cao, Yongcan ;

Stuart, Daniel ;

Ren, Wei ;

Meng, Ziyang .

IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, 2011, 19 (04) :929-938

[8] Generic global rigidity [J].

Connelly, R .

DISCRETE & COMPUTATIONAL GEOMETRY, 2005, 33 (04) :549-563

[9] Mutual Synchronization of Multiple Robot Manipulators with Unknown Dynamics [J].

Cui, Rongxin ;

Yan, Weisheng .

JOURNAL OF INTELLIGENT & ROBOTIC SYSTEMS, 2012, 68 (02) :105-119

[10] A Barycentric Coordinate Based Distributed Localization Algorithm for Sensor Networks [J].

Diao, Yingfei ;

Lin, Zhiyun ;

Fu, Minyue .

IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2014, 62 (18) :4760-4771

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