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We formulate the problem of robots ferrying messages betweenstatically-placed source and sink pairs that they can communicate withwirelessly. We first analyze the capacity region for this problem under bothideal (arbitrarily high velocity, long scheduling periods) and realisticconditions. We indicate how robots could be scheduled optimally to satisfy anyarrival rate in the capacity region, given prior knowledge about arrival rates.We find that if the number of robots allocated grows proportionally with thenumber of source-sink pairs, then the capacity of the network scales as$\Theta(1)$, similar to what was shown previously by Grossglauser and Tse foruncontrolled mobility; however, in contrast to that prior result, we also findthat with controlled mobility this constant capacity scaling can be obtainedwhile ensuring finite delay. We then consider the setting where the arrivalrates are unknown and present a coarse-grained backpressure message ferryingalgorithm (CBMF) for it. In CBMF, the robots are matched to sources and sinksonce every epoch to maximize a queue-differential-based weight. The matchingcontrols both motion and transmission for each robot: if a robot is matched toa source, it moves towards that source and collects data from it; and if it ismatched to a sink, it moves towards that sink and transmits data to it. We showthrough analysis and simulations the conditions under which CBMF can stabilizethe network. We show that the maximum achievable stable throughput with thispolicy tends to the ideal capacity as the schedule duration and robot velocityincrease.

Robotic Message Ferrying for Wireless Networks using Coarse-Grained Backpressure Control