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Asymptotic behaviour in the robot rendezvous problem

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Asymptotic behaviour in the robot rendezvous problem. / Paunonen, Lassi; Seifert, David.

julkaisussa: Automatica, Vuosikerta 79, 01.05.2017, s. 127-130.

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Paunonen, Lassi ; Seifert, David. / Asymptotic behaviour in the robot rendezvous problem. Julkaisussa: Automatica. 2017 ; Vuosikerta 79. Sivut 127-130.

Bibtex - Lataa

@article{428e11adca454555836bde1f3dfb1cb7,
title = "Asymptotic behaviour in the robot rendezvous problem",
abstract = "This paper presents a natural extension of the results obtained by Feintuch and Francis in (2012a,b) concerning the so-called robot rendezvous problem. In particular, we revisit a known necessary and sufficient condition for convergence of the solution in terms of Ces{\`a}ro convergence of the translates Skx0, k≥0, of the sequence x0 of initial positions under the right-shift operator S, thus shedding new light on questions left open in Feintuch and Francis (2012a,b). We then present a new proof showing that a certain stronger ergodic condition on x0 ensures that the corresponding solution converges to its limit at the optimal rate O(t−1/2) as t→∞. After considering a natural two-sided variant of the robot rendezvous problem already studied in Feintuch and Francis (2012a) and in particular proving a new quantified result in this case, we conclude by relating the robot rendezvous problem to a more realistic model of vehicle platoons.",
keywords = "Autonomous systems, Mobile robots, Rates of convergence, Stability",
author = "Lassi Paunonen and David Seifert",
year = "2017",
month = "5",
day = "1",
doi = "10.1016/j.automatica.2017.02.015",
language = "English",
volume = "79",
pages = "127--130",
journal = "Automatica",
issn = "0005-1098",
publisher = "Elsevier",

}

RIS (suitable for import to EndNote) - Lataa

TY - JOUR

T1 - Asymptotic behaviour in the robot rendezvous problem

AU - Paunonen, Lassi

AU - Seifert, David

PY - 2017/5/1

Y1 - 2017/5/1

N2 - This paper presents a natural extension of the results obtained by Feintuch and Francis in (2012a,b) concerning the so-called robot rendezvous problem. In particular, we revisit a known necessary and sufficient condition for convergence of the solution in terms of Cesàro convergence of the translates Skx0, k≥0, of the sequence x0 of initial positions under the right-shift operator S, thus shedding new light on questions left open in Feintuch and Francis (2012a,b). We then present a new proof showing that a certain stronger ergodic condition on x0 ensures that the corresponding solution converges to its limit at the optimal rate O(t−1/2) as t→∞. After considering a natural two-sided variant of the robot rendezvous problem already studied in Feintuch and Francis (2012a) and in particular proving a new quantified result in this case, we conclude by relating the robot rendezvous problem to a more realistic model of vehicle platoons.

AB - This paper presents a natural extension of the results obtained by Feintuch and Francis in (2012a,b) concerning the so-called robot rendezvous problem. In particular, we revisit a known necessary and sufficient condition for convergence of the solution in terms of Cesàro convergence of the translates Skx0, k≥0, of the sequence x0 of initial positions under the right-shift operator S, thus shedding new light on questions left open in Feintuch and Francis (2012a,b). We then present a new proof showing that a certain stronger ergodic condition on x0 ensures that the corresponding solution converges to its limit at the optimal rate O(t−1/2) as t→∞. After considering a natural two-sided variant of the robot rendezvous problem already studied in Feintuch and Francis (2012a) and in particular proving a new quantified result in this case, we conclude by relating the robot rendezvous problem to a more realistic model of vehicle platoons.

KW - Autonomous systems

KW - Mobile robots

KW - Rates of convergence

KW - Stability

U2 - 10.1016/j.automatica.2017.02.015

DO - 10.1016/j.automatica.2017.02.015

M3 - Article

VL - 79

SP - 127

EP - 130

JO - Automatica

JF - Automatica

SN - 0005-1098

ER -