Forgive and forget: Self-stabilizing swarms in spite of Byzantine robots

In this article, we consider the case in which a swarm of robots collaborates in a mission, where a few of the robots behave maliciously. These malicious Byzantine robots may be temporally or constantly controlled by an adversary. The scope is synchronized full information robot operations, where a robot that does not follow the program/policy of the swarm is immediately identified and can be remembered as Byzantine. As robots may be suspected of being Byzantine due to benign temporal malfunctions, it is imperative to forgive and forget, otherwise, a robot cannot assume collaborative actions with any other robot in the swarm. Still, remembering for a while may facilitate a policy of surrounding, isolating and freezing the movement of the misbehaving robots, by several robots, allowing the rest to perform the swarm task with no intervention. We demonstrate the need to periodically forgive and forget to realize swarm several tasks including patrolling/cleaning in the presence of possible Byzantine robots. The policy for achieving the task consists of blocking the movement of the Byzantine robot(s) by some of the robots, while the rest patrol/clean the plane.