Multi-robot monitoring in dynamic environments with guaranteed currency of observations

In this paper we consider the problem of monitoring a known set of stationary features (or locations of interest) in an environment. To observe a feature, a robot must visit its location. Each feature changes over time, and we assume that the currency, or accuracy of an observation decays linearly with time. Thus, robots must repeatedly visit the features to update their observations. Each feature has a known rate of change, and so the frequency of visits to a feature should be proportional to its rate. The goal is to route the robots so as to minimize the maximum change of a feature between observations. We focus on the asymptotic regime of a large number of features distributed according to a probability density function. In this regime we determine a lower bound on the maximum change of a feature between visits, and develop a robot control policy that, with probability one, performs within a factor of two of the optimal. We also provide a single robot lower bound which holds outside of the asymptotic regime, and present a heuristic algorithm motivated by our asymptotic analysis.