Group search of the plane with faulty robots.

A collection of k mobile robots, initially placed at the origin of the plane, are searching for a stationary target. Each robot r i has a unit visibility range and can move no faster than its maximal speed v i , for i = 1 , 2 ,... , k. The robots can communicate between themselves. We consider two communication models: wireless, in which a message sent by a robot can reach all other robots immediately, regardless of their positions, and face-to-face (F2F), in which robots can only exchange information when they are meeting. We assume that up to f robots, where f < k , may be unreliable. We consider two models of unreliability: (1) crash faults, in which we deal with an absence of some of the robots' capabilities (communication, perception, motion, etc.), and (2) byzantine faults, in which the robots may be malicious in that they may execute a wrong algorithm (e.g., transmitting wrong information). The goal is to minimize the group search time, which is equal to the time of arrival to the target of the last reliable robot. This is expressed as a function of d , the distance from the origin to the target. Our proposed algorithms for crash faults are asymptotically optimal in d in both communication models. For byzantine faults, our algorithm is asymptotically optimal for the wireless model. In the F2F model, we propose two algorithms: the first one has a competitive ratio of 2, while the second algorithm works for k ≥ 2 f + 2 and is optimal when the robots speeds are all equal. [ABSTRACT FROM AUTHOR]