On events in multi-robot patrol in adversarial environments

The problem of multi-robot patrol in adversarial environments has been gaining considerable interest during the recent years. In this problem, a team of mobile robots is required to repeatedly visit some target area in order to detect penetrations that are controlled by an adversary. Little has been written so far on the nature of the event of penetration, and it is commonly assumed that the goal of the robots is to detect the penetration at any time during its occurrence. In this paper we offer a new definition of an event, with correlation to a utility function such that the detection of the event by the robots in different stages of its occurrence grants the robots a different reward. The goal of the robots is, then, to maximize their utility from detecting the event. We provide three different models of events, for which we describe algorithms for calculating the expected utility from detecting the event and discuss the how the model influences the optimality of the patrol algorithm. In the first and basic model, we assume that there exists a reward function such that detecting an event at different times grants the robots with an associated reward. In the second model, the event might evolve during its occurrence, and this progression correlates to both different rewards and to growing probability of detection. Finally, we consider a general model, in which the event can be detected from distance, where the probability of detection depends both on the distance from the robot and on the current state of the event. Last, we discuss how the new event models presented in this paper set grounds for handling the problem of patrol in heterogeneous environments, where parts of the perimeter could be more sensitive to occurrence of events.