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Analysis of robot navigation schemes using Rantzer's Dual Lyapunov Theorem
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0001-7309-8086
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0001-9940-5929
2008 (English)In: 2008 AMERICAN CONTROL CONFERENCE, 2008, 201-206 p.Conference paper, Published paper (Refereed)
Abstract [en]

When robots are driven by the negative gradient of a potential field that consists of the sum of an attractive and a repulsive term, convergence to the desired configuration cannot be guaranteed by traditional Lyapunov techniques. In this paper, sufficient conditions for convergence of such systems are provided instead with the use of Rantzer's Dual Lyaptinov Theorem. In particular, a condition that involves the trace of the Hessian matrix of the potential function is derived and then applied to the cases of navigation of a single robot and of multi-robot formation stabilization. The main result of the paper states that a sufficient condition for convergence to a desired configuration in both cases is that the attractive potential admits a sufficiently large gain. A lower bound on the attractive potential is computed. Computer simulations that support the new results are provided.

Place, publisher, year, edition, pages
2008. 201-206 p.
Series
PROCEEDINGS OF THE AMERICAN CONTROL CONFERENCE, ISSN 0743-1619
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-26526DOI: 10.1109/ACC.2008.4586491ISI: 000259261500036Scopus ID: 2-s2.0-52449129796OAI: oai:DiVA.org:kth-26526DiVA: diva2:385736
Conference
American Control Conference 2008 Seattle, WA, JUN 11-13, 2008
Note
Q 20110112Available from: 2011-01-12 Created: 2010-11-25 Last updated: 2012-02-01Bibliographically approved

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Dimarogonas, Dimos V.Johansson, Karl Henrik

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