  We present a non-technical overview of the results obtained by the authors
(2015) concerning the so-called robot rendezvous problem studied by Feintuch
and Francis (2012). In particular, we present a necessary and sufficient
condition for convergence of the solution in terms of Ces\`aro convergence of
the translates $S^k x_0$, $k\ge0$, of the sequence $x_0$ of initial positions
under the right-shift operator $S$, thus shedding new light on questions left
open in by Feintuch and Francis. We also formulate a stronger ergodic condition
on $x_0$ which ensures that the corresponding solution converges to its limit
at the rate $O(t^{-1/2})$ as $t\to\infty$. We conclude with a brief discussion
of a natural two-sided variant of the robot rendezvous problem and by relating
the robot rendezvous problem to a more realistic model of vehicle platoons, for
which the authors' earlier general results lead to analogous statements.
