Persistent Monitoring of Dynamically Changing Environments Using an Unmanned Vehicle
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abstract
We consider the problem of planning a closed walk $mathcal W$ for a UAV to persistently monitor a finite number of stationary targets with equal priorities and dynamically changing properties. A UAV must physically visit the targets in order to monitor them and collect information therein. The frequency of monitoring any given target is specified by a target revisit time, $i.e.$, the maximum allowable time between any two successive visits to the target. The problem considered in this paper is the following: Given $n$ targets and $k geq n$ allowed visits to them, find an optimal closed walk $mathcal W^*(k)$ so that every target is visited at least once and the maximum revisit time over all the targets, $mathcal R(mathcal W(k))$, is minimized. We prove the following: If $k geq n^2-n$, $mathcal R(mathcal W^*(k))$ (or simply, $mathcal R^*(k)$) takes only two values: $mathcal R^*(n)$ when $k$ is an integral multiple of $n$, and $mathcal R^*(n+1)$ otherwise. This result suggests significant computational savings - one only needs to determine $mathcal W^*(n)$ and $mathcal W^*(n+1)$ to construct an optimal solution $mathcal W^*(k)$. We provide MILP formulations for computing $mathcal W^*(n)$ and $mathcal W^*(n+1)$. Furthermore, for {it any} given $k$, we prove that $mathcal R^*(k) geq mathcal R^*(k+n)$.
