On the stability and applications of distance-based flexible formations

Hector Garcia de Marina, Zhiyong Sun, Shaoshuai Mou

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

73 Downloads (Pure)

Abstract

This paper investigates the stability of distance-based flexible undirected formations in the plane. Without rigidity, there exists a set of connected shapes for given distance constraints, which is called the ambit. We show that a flexible formation can lose its flexibility, or equivalently may reduce the degrees of freedom of its ambit, if a small disturbance is introduced in the range sensor of the agents. The stability of the disturbed equilibrium can be characterized by analyzing the eigenvalues of the linearized augmented error system. Unlike infinitesimally rigid formations, the disturbed desired equilibrium can be turned unstable regardless of how small the disturbance is. We finally present two examples of how to exploit these disturbances as design parameters. The first example shows how to combine rigid and flexible formations such that some of the agents can move freely in the desired and locally stable ambit. The second example shows how to achieve a specific shape with fewer edges than the necessary for the standard controller in rigid formations.
Original languageEnglish
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherIEEE
Publication date18. Jan 2019
Pages1700-1705
Article number8619429
ISBN (Print)978-1-5386-1396-2
ISBN (Electronic)9781538613955
DOIs
Publication statusPublished - 18. Jan 2019
Event2018 IEEE Conference on Decision and Control - Florida, United States
Duration: 17. Dec 201819. Dec 2018

Conference

Conference2018 IEEE Conference on Decision and Control
CountryUnited States
CityFlorida
Period17/12/201819/12/2018
SeriesI E E E Conference on Decision and Control. Proceedings
ISSN0743-1546

Fingerprint

Rigidity
Controllers
Sensors

Cite this

Garcia de Marina, H., Sun, Z., & Mou, S. (2019). On the stability and applications of distance-based flexible formations. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 1700-1705). [8619429] IEEE. I E E E Conference on Decision and Control. Proceedings https://doi.org/10.1109/CDC.2018.8619429
Garcia de Marina, Hector ; Sun, Zhiyong ; Mou, Shaoshuai. / On the stability and applications of distance-based flexible formations. 2018 IEEE Conference on Decision and Control, CDC 2018. IEEE, 2019. pp. 1700-1705 (I E E E Conference on Decision and Control. Proceedings).
@inproceedings{b4ca47114a084985a9b4622478ae6ad1,
title = "On the stability and applications of distance-based flexible formations",
abstract = "This paper investigates the stability of distance-based flexible undirected formations in the plane. Without rigidity, there exists a set of connected shapes for given distance constraints, which is called the ambit. We show that a flexible formation can lose its flexibility, or equivalently may reduce the degrees of freedom of its ambit, if a small disturbance is introduced in the range sensor of the agents. The stability of the disturbed equilibrium can be characterized by analyzing the eigenvalues of the linearized augmented error system. Unlike infinitesimally rigid formations, the disturbed desired equilibrium can be turned unstable regardless of how small the disturbance is. We finally present two examples of how to exploit these disturbances as design parameters. The first example shows how to combine rigid and flexible formations such that some of the agents can move freely in the desired and locally stable ambit. The second example shows how to achieve a specific shape with fewer edges than the necessary for the standard controller in rigid formations.",
author = "{Garcia de Marina}, Hector and Zhiyong Sun and Shaoshuai Mou",
year = "2019",
month = "1",
day = "18",
doi = "10.1109/CDC.2018.8619429",
language = "English",
isbn = "978-1-5386-1396-2",
series = "I E E E Conference on Decision and Control. Proceedings",
publisher = "IEEE",
pages = "1700--1705",
booktitle = "2018 IEEE Conference on Decision and Control, CDC 2018",
address = "United States",

}

Garcia de Marina, H, Sun, Z & Mou, S 2019, On the stability and applications of distance-based flexible formations. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8619429, IEEE, I E E E Conference on Decision and Control. Proceedings, pp. 1700-1705, 2018 IEEE Conference on Decision and Control, Florida, United States, 17/12/2018. https://doi.org/10.1109/CDC.2018.8619429

On the stability and applications of distance-based flexible formations. / Garcia de Marina, Hector; Sun, Zhiyong; Mou, Shaoshuai.

2018 IEEE Conference on Decision and Control, CDC 2018. IEEE, 2019. p. 1700-1705 8619429 (I E E E Conference on Decision and Control. Proceedings).

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

TY - GEN

T1 - On the stability and applications of distance-based flexible formations

AU - Garcia de Marina, Hector

AU - Sun, Zhiyong

AU - Mou, Shaoshuai

PY - 2019/1/18

Y1 - 2019/1/18

N2 - This paper investigates the stability of distance-based flexible undirected formations in the plane. Without rigidity, there exists a set of connected shapes for given distance constraints, which is called the ambit. We show that a flexible formation can lose its flexibility, or equivalently may reduce the degrees of freedom of its ambit, if a small disturbance is introduced in the range sensor of the agents. The stability of the disturbed equilibrium can be characterized by analyzing the eigenvalues of the linearized augmented error system. Unlike infinitesimally rigid formations, the disturbed desired equilibrium can be turned unstable regardless of how small the disturbance is. We finally present two examples of how to exploit these disturbances as design parameters. The first example shows how to combine rigid and flexible formations such that some of the agents can move freely in the desired and locally stable ambit. The second example shows how to achieve a specific shape with fewer edges than the necessary for the standard controller in rigid formations.

AB - This paper investigates the stability of distance-based flexible undirected formations in the plane. Without rigidity, there exists a set of connected shapes for given distance constraints, which is called the ambit. We show that a flexible formation can lose its flexibility, or equivalently may reduce the degrees of freedom of its ambit, if a small disturbance is introduced in the range sensor of the agents. The stability of the disturbed equilibrium can be characterized by analyzing the eigenvalues of the linearized augmented error system. Unlike infinitesimally rigid formations, the disturbed desired equilibrium can be turned unstable regardless of how small the disturbance is. We finally present two examples of how to exploit these disturbances as design parameters. The first example shows how to combine rigid and flexible formations such that some of the agents can move freely in the desired and locally stable ambit. The second example shows how to achieve a specific shape with fewer edges than the necessary for the standard controller in rigid formations.

U2 - 10.1109/CDC.2018.8619429

DO - 10.1109/CDC.2018.8619429

M3 - Article in proceedings

SN - 978-1-5386-1396-2

T3 - I E E E Conference on Decision and Control. Proceedings

SP - 1700

EP - 1705

BT - 2018 IEEE Conference on Decision and Control, CDC 2018

PB - IEEE

ER -

Garcia de Marina H, Sun Z, Mou S. On the stability and applications of distance-based flexible formations. In 2018 IEEE Conference on Decision and Control, CDC 2018. IEEE. 2019. p. 1700-1705. 8619429. (I E E E Conference on Decision and Control. Proceedings). https://doi.org/10.1109/CDC.2018.8619429