  In multi-robot systems where a central decision maker is specifying the
movement of each individual robot, a communication failure can severely impair
the performance of the system. This paper develops a motion strategy that
allows robots to safely handle critical communication failures for such
multi-robot architectures. For each robot, the proposed algorithm computes a
time horizon over which collisions with other robots are guaranteed not to
occur. These safe time horizons are included in the commands being transmitted
to the individual robots. In the event of a communication failure, the robots
execute the last received velocity commands for the corresponding safe time
horizons leading to a provably safe open-loop motion strategy. The resulting
algorithm is computationally effective and is agnostic to the task that the
robots are performing. The efficacy of the strategy is verified in simulation
as well as on a team of differential-drive mobile robots.
