Asymptotic behaviour in the robot rendezvous problem
Research output: Contribution to journal › Article › Scientific › peer-review
|Number of pages||4|
|Publication status||Published - 1 May 2017|
|Publication type||A1 Journal article-refereed|
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.