Rigidity and Persistence of Three and Higher Dimensional Formations

Julien M. Hendrickx, Barıș Fidan, Changbin Yu, Brian D. O. Anderson, Vincent D. Blondel

Abstract

In this paper, we generalize the notion of persistence, which has been originally introduced for two-dimensional formations, to ℜd for d ≥ 3, seeking to provide a theoretical framework for real world applications, which often are in three-dimensional space as opposed to the plane. We verify that many of the properties of rigid and/or persistent formations established in ℜ2 are also valid for higher dimensions. Analysing the closed subgraphs and directed paths in persistent graphs, we derive some further properties of persistent formations. We also provide an easily checkable necessary condition for persistence.

References

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Paper Citation


in Harvard Style

M. Hendrickx J., Fidan B., Yu C., D. O. Anderson B. and D. Blondel V. (2005). Rigidity and Persistence of Three and Higher Dimensional Formations . In Proceedings of the 1st International Workshop on Multi-Agent Robotic Systems - Volume 1: MARS, (ICINCO 2005) ISBN 972-8865-34-1, pages 39-46. DOI: 10.5220/0001193600390046


in Bibtex Style

@conference{mars05,
author={Julien M. Hendrickx and Barıș Fidan and Changbin Yu and Brian D. O. Anderson and Vincent D. Blondel},
title={Rigidity and Persistence of Three and Higher Dimensional Formations},
booktitle={Proceedings of the 1st International Workshop on Multi-Agent Robotic Systems - Volume 1: MARS, (ICINCO 2005)},
year={2005},
pages={39-46},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001193600390046},
isbn={972-8865-34-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 1st International Workshop on Multi-Agent Robotic Systems - Volume 1: MARS, (ICINCO 2005)
TI - Rigidity and Persistence of Three and Higher Dimensional Formations
SN - 972-8865-34-1
AU - M. Hendrickx J.
AU - Fidan B.
AU - Yu C.
AU - D. O. Anderson B.
AU - D. Blondel V.
PY - 2005
SP - 39
EP - 46
DO - 10.5220/0001193600390046