Asymptotic behaviour in the robot rendezvous problem. (May 2017)

• Record Type: Journal Article
• Authors: Paunonen, Lassi; Seifert, David
• Is Part Of: Automatica. Volume 79(2017)
• Page Start: 127
• Page End: 130
• Publication Date: 2017-05
• Subjects: Autonomous systems -- Mobile robots -- Stability -- Rates of convergence; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2017.02.015
• Languages: English
• ISSNs: 0005-1098

Abstract

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 Cesàro convergence of the translates S k x 0, k ≥ 0, of the sequence x 0 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 x 0 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.