Persistent Monitoring of Dynamically Changing Environments Using an Unmanned Vehicle
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We consider the problem of planning a closed walk 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 ≥ n allowed visits to them, find an optimal closed walk W^*(k) so that every target is visited at least once and the maximum revisit time over all the targets, R( W(k)), is minimized. We prove the following: If k ≥ n^2-n, R( W^*(k)) (or simply, R^*(k)) takes only two values: R^*(n) when k is an integral multiple of n, and R^*(n+1) otherwise. This result suggests significant computational savings - one only needs to determine W^*(n) and W^*(n+1) to construct an optimal solution W^*(k). We provide MILP formulations for computing W^*(n) and W^*(n+1). Furthermore, for any given k, we prove that R^*(k) ≥ R^*(k+n).
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