  We study a fundamental cooperative message-delivery problem on the plane.
Assume $n$ robots which can move in any direction, are placed arbitrarily on
the plane. Robots each have their own maximum speed and can communicate with
each other face-to-face (i.e., when they are at the same location at the same
time). There are also two designated points on the plane, $S$ (the source) and
$D$ (the destination). The robots are required to transmit the message from the
source to the destination as quickly as possible by face-to-face message
passing. We consider both the offline setting where all information (the
locations and maximum speeds of the robots) are known in advance and the online
setting where each robot knows only its own position and speed along with the
positions of $S$ and $D$.
  In the offline case, we discover an important connection between the problem
for two-robot systems and the well-known Apollonius circle which we employ to
design an optimal algorithm. We also propose a $\sqrt 2$ approximation
algorithm for systems with any number of robots. In the online setting, we
provide an algorithm with competitive ratio $\frac 17 \left( 5+ 4 \sqrt{2}
\right)$ for two-robot systems and show that the same algorithm has a
competitive ratio less than $2$ for systems with any number of robots. We also
show these results are tight for the given algorithm. Finally, we give two
lower bounds (employing different arguments) on the competitive ratio of any
online algorithm, one of $1.0391$ and the other of $1.0405$.
