  We formulate the problem of robots ferrying messages between
statically-placed source and sink pairs that they can communicate with
wirelessly. We first analyze the capacity region for this problem under both
ideal (arbitrarily high velocity, long scheduling periods) and realistic
conditions. We indicate how robots could be scheduled optimally to satisfy any
arrival rate in the capacity region, given prior knowledge about arrival rates.
We find that if the number of robots allocated grows proportionally with the
number of source-sink pairs, then the capacity of the network scales as
$\Theta(1)$, similar to what was shown previously by Grossglauser and Tse for
uncontrolled mobility; however, in contrast to that prior result, we also find
that with controlled mobility this constant capacity scaling can be obtained
while ensuring finite delay. We then consider the setting where the arrival
rates are unknown and present a coarse-grained backpressure message ferrying
algorithm (CBMF) for it. In CBMF, the robots are matched to sources and sinks
once every epoch to maximize a queue-differential-based weight. The matching
controls both motion and transmission for each robot: if a robot is matched to
a source, it moves towards that source and collects data from it; and if it is
matched to a sink, it moves towards that sink and transmits data to it. We show
through analysis and simulations the conditions under which CBMF can stabilize
the network. We show that the maximum achievable stable throughput with this
policy tends to the ideal capacity as the schedule duration and robot velocity
increase.
