Morse theory and formation control

Brian D.O. Anderson

doi:10.1109/MED.2011.5983133

Morse theory and formation control

Brian D.O. Anderson^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

20 Citations (Scopus)

Abstract

Formation shape control for a collection of point agents is concerned with devising decentralized control laws which will ensure that the formation will move so that certain inter-agent distances assume prescribed values. A number of algorithms based on steepest descent of an error function have been suggested for various problems, and all display the existence of incorrect equilibria, though often the equilibria are saddle points or unstable. This paper introduces Morse theory as a tool for analyzing the number of such equilibria. A key conclusion is that for two-dimensional rigid formations of point agents, there will always be incorrect equilibria associated with any steepest descent law.

Original language	English
Title of host publication	2011 19th Mediterranean Conference on Control and Automation, MED 2011
Pages	656-661
Number of pages	6
DOIs	https://doi.org/10.1109/MED.2011.5983133
Publication status	Published - 2011
Event	2011 19th Mediterranean Conference on Control and Automation, MED 2011 - Corfu, Greece Duration: 20 Jun 2011 → 23 Jun 2011

Publication series

Name	2011 19th Mediterranean Conference on Control and Automation, MED 2011

Conference

Conference	2011 19th Mediterranean Conference on Control and Automation, MED 2011
Country/Territory	Greece
City	Corfu
Period	20/06/11 → 23/06/11

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10.1109/MED.2011.5983133

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title = "Morse theory and formation control",

abstract = "Formation shape control for a collection of point agents is concerned with devising decentralized control laws which will ensure that the formation will move so that certain inter-agent distances assume prescribed values. A number of algorithms based on steepest descent of an error function have been suggested for various problems, and all display the existence of incorrect equilibria, though often the equilibria are saddle points or unstable. This paper introduces Morse theory as a tool for analyzing the number of such equilibria. A key conclusion is that for two-dimensional rigid formations of point agents, there will always be incorrect equilibria associated with any steepest descent law.",

keywords = "Formation control, Morse Theory, autonomous formations, shape control",

author = "Anderson, {Brian D.O.}",

year = "2011",

doi = "10.1109/MED.2011.5983133",

language = "English",

isbn = "9781457701252",

series = "2011 19th Mediterranean Conference on Control and Automation, MED 2011",

pages = "656--661",

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note = "2011 19th Mediterranean Conference on Control and Automation, MED 2011 ; Conference date: 20-06-2011 Through 23-06-2011",

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T1 - Morse theory and formation control

AU - Anderson, Brian D.O.

PY - 2011

Y1 - 2011

N2 - Formation shape control for a collection of point agents is concerned with devising decentralized control laws which will ensure that the formation will move so that certain inter-agent distances assume prescribed values. A number of algorithms based on steepest descent of an error function have been suggested for various problems, and all display the existence of incorrect equilibria, though often the equilibria are saddle points or unstable. This paper introduces Morse theory as a tool for analyzing the number of such equilibria. A key conclusion is that for two-dimensional rigid formations of point agents, there will always be incorrect equilibria associated with any steepest descent law.

AB - Formation shape control for a collection of point agents is concerned with devising decentralized control laws which will ensure that the formation will move so that certain inter-agent distances assume prescribed values. A number of algorithms based on steepest descent of an error function have been suggested for various problems, and all display the existence of incorrect equilibria, though often the equilibria are saddle points or unstable. This paper introduces Morse theory as a tool for analyzing the number of such equilibria. A key conclusion is that for two-dimensional rigid formations of point agents, there will always be incorrect equilibria associated with any steepest descent law.

KW - Formation control

KW - Morse Theory

KW - autonomous formations

KW - shape control

UR - http://www.scopus.com/inward/record.url?scp=80052349643&partnerID=8YFLogxK

U2 - 10.1109/MED.2011.5983133

DO - 10.1109/MED.2011.5983133

M3 - Conference contribution

SN - 9781457701252

T3 - 2011 19th Mediterranean Conference on Control and Automation, MED 2011

SP - 656

EP - 661

BT - 2011 19th Mediterranean Conference on Control and Automation, MED 2011

T2 - 2011 19th Mediterranean Conference on Control and Automation, MED 2011

Y2 - 20 June 2011 through 23 June 2011

ER -

Morse theory and formation control

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