I. Introduction
Consider the following problem. An environment (such as a city, or a building) contains known static features of interest (such as intersections in the city, or rooms in the building). A group of robots is tasked with monitoring the features by visiting their locations. The environment is dynamic, and thus the properties of each feature change over time (i.e., the amount of traffic in each intersection, or the layout and number of people in each room). Features may change on different time scales. Thus, the robots must repeatedly visit the features to update their observations. The frequency of visits to each feature should be proportional to that feature's rate of change. The problem is to determine routes for the robots that allow them to guarantee the currency (or accuracy) of their most recent observations of each feature. That is, to determine routes that minimize the maximum change of a feature between visits (observations). We call this problem persistent monitoring.