Asymptotic behaviour in the robot rendezvous problem
Research output: Contribution to journal › Article › Scientific › peer-review
Details
| Original language | English |
|---|---|
| Pages (from-to) | 127-130 |
| Number of pages | 4 |
| Journal | Automatica |
| Volume | 79 |
| DOIs | |
| Publication status | Published - 1 May 2017 |
| Publication type | A1 Journal article-refereed |
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 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.
ASJC Scopus subject areas
Keywords
- Autonomous systems, Mobile robots, Rates of convergence, Stability