  Fault tolerance is increasingly important for unmanned autonomous vehicles.
For example, in a multi robot system the agents need the ability to effectively
detect and tolerate internal failures in order to continue performing their
tasks without the need for immediate human intervention. The system must react
to unplanned events in order to optimize the task allocation between the
robots. In a broad sense, the resilience of a system can be defined as the
ability to maintain or recover a stable state when subject to disturbance and
it is related to the concept of robustness in industrial systems. In this
paper, we study the resilience in a synchronized multi-robot system stated as
follows:Consider a team of $n$ (ground or aerial) robots each moving along
predetermined periodic closed trajectories. Each of the agents needs to
communicate informationabout its operation to other agents, but the
communication links have a limited range. Hence, when two agents are within
communication range, a communication link is established, and information is
exchanged. Thus, two neighbors are synchronized if they visit the communication
link at the same time and a multi-robot system is called synchronized if each
pair of neighbors is synchronized. If a set of robots left the system, then
some trajectories has no robots. In these cases, when an alive robot detects no
neighboring robot then it pass to this neighboring trajectory to assume the
unattended task. In this framework, a fault-tolerance measure is introduced:
the resilience of the system is the largest number of robots that can fail
while executing the global task. Interesting combinatorial properties of the
resilience are showed that allow to know its value for some usual scenarios.
