This paper presents a natural extension of the results obtained by Feintuch and Francis in [5, 6] 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`aro convergence of the translates S kx0, k ≥ 0, of the sequence x0 of initial positions under the right-shift operator S, thus shedding new light on questions left open in [5, 6]. We then present a new proof showing that a certain ...