Stability analysis on four agent tetrahedral formations

Myoung-Chul Park; Zhiyong Sun; Brian Anderson; Hyo-Sung Ahn

doi:10.1109/CDC.2014.7039452

Stability analysis on four agent tetrahedral formations

Myoung-Chul Park, Zhiyong Sun, Brian Anderson, Hyo-Sung Ahn

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

28 Citations (Scopus)

Abstract

We consider a four agent tetrahedral formation of mobile agents in 3-dimensional Euclidean space. Each agent is required to maintain prescribed inter-agent distances from its neighbors so that they collectively form a desired formation shape, a task which is now called distance-based formation control. Under a common gradient-based control law, there exists an incorrect equilibrium set in which the agents do not achieve the desired formation shape. By investigating the linearized dynamics of the system, we prove that all incorrect equilibria are unstable, which results in that desired formation shape is almost globally asymptotically stable. Numerical simulation results are also included.

Original language	English
Title of host publication	53rd IEEE Conference on Decision and Control,CDC 2014
Place of Publication	Piscataway, New Jersey, US
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	631-636
Number of pages	6
Edition	Peer Reviewed
ISBN (Electronic)	9781479977468
ISBN (Print)	9781479977451
DOIs	https://doi.org/10.1109/CDC.2014.7039452
Publication status	Published - 2014
Event	53rd IEEE Conference on Decision and Control - Los Angeles, USA, United States Duration: 1 Jan 2014 → …

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Number	February
Volume	2015-February
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	53rd IEEE Conference on Decision and Control
Country/Territory	United States
Period	1/01/14 → …
Other	December 15-17 2014

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10.1109/CDC.2014.7039452

Cite this

Park, M.-C., Sun, Z., Anderson, B., & Ahn, H.-S. (2014). Stability analysis on four agent tetrahedral formations. In 53rd IEEE Conference on Decision and Control,CDC 2014 (Peer Reviewed ed., pp. 631-636). Article 7039452 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2015-February, No. February). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2014.7039452

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title = "Stability analysis on four agent tetrahedral formations",

abstract = "We consider a four agent tetrahedral formation of mobile agents in 3-dimensional Euclidean space. Each agent is required to maintain prescribed inter-agent distances from its neighbors so that they collectively form a desired formation shape, a task which is now called distance-based formation control. Under a common gradient-based control law, there exists an incorrect equilibrium set in which the agents do not achieve the desired formation shape. By investigating the linearized dynamics of the system, we prove that all incorrect equilibria are unstable, which results in that desired formation shape is almost globally asymptotically stable. Numerical simulation results are also included.",

author = "Myoung-Chul Park and Zhiyong Sun and Brian Anderson and Hyo-Sung Ahn",

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language = "English",

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series = "Proceedings of the IEEE Conference on Decision and Control",

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Park, M-C, Sun, Z, Anderson, B & Ahn, H-S 2014, Stability analysis on four agent tetrahedral formations. in 53rd IEEE Conference on Decision and Control,CDC 2014. Peer Reviewed edn, 7039452, Proceedings of the IEEE Conference on Decision and Control, no. February, vol. 2015-February, Institute of Electrical and Electronics Engineers Inc., Piscataway, New Jersey, US, pp. 631-636, 53rd IEEE Conference on Decision and Control, United States, 1/01/14. https://doi.org/10.1109/CDC.2014.7039452

Stability analysis on four agent tetrahedral formations. / Park, Myoung-Chul; Sun, Zhiyong; Anderson, Brian et al.
53rd IEEE Conference on Decision and Control,CDC 2014. Peer Reviewed. ed. Piscataway, New Jersey, US: Institute of Electrical and Electronics Engineers Inc., 2014. p. 631-636 7039452 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2015-February, No. February).

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

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N2 - We consider a four agent tetrahedral formation of mobile agents in 3-dimensional Euclidean space. Each agent is required to maintain prescribed inter-agent distances from its neighbors so that they collectively form a desired formation shape, a task which is now called distance-based formation control. Under a common gradient-based control law, there exists an incorrect equilibrium set in which the agents do not achieve the desired formation shape. By investigating the linearized dynamics of the system, we prove that all incorrect equilibria are unstable, which results in that desired formation shape is almost globally asymptotically stable. Numerical simulation results are also included.

AB - We consider a four agent tetrahedral formation of mobile agents in 3-dimensional Euclidean space. Each agent is required to maintain prescribed inter-agent distances from its neighbors so that they collectively form a desired formation shape, a task which is now called distance-based formation control. Under a common gradient-based control law, there exists an incorrect equilibrium set in which the agents do not achieve the desired formation shape. By investigating the linearized dynamics of the system, we prove that all incorrect equilibria are unstable, which results in that desired formation shape is almost globally asymptotically stable. Numerical simulation results are also included.

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Park MC, Sun Z, Anderson B, Ahn HS. Stability analysis on four agent tetrahedral formations. In 53rd IEEE Conference on Decision and Control,CDC 2014. Peer Reviewed ed. Piscataway, New Jersey, US: Institute of Electrical and Electronics Engineers Inc. 2014. p. 631-636. 7039452. (Proceedings of the IEEE Conference on Decision and Control; February). doi: 10.1109/CDC.2014.7039452

Stability analysis on four agent tetrahedral formations

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