Persistent Monitoring of Dynamically Changing Environments Using an Unmanned Vehicle
This work addresses efficient monitoring in robotics and surveillance, but it is incremental as it builds on existing persistent monitoring frameworks with specific theoretical bounds.
The paper tackles the problem of planning optimal closed walks for a UAV to persistently monitor stationary targets with dynamic properties, minimizing the maximum revisit time. It proves that for k ≥ n^2 - n, the optimal revisit time takes only two values, leading to significant computational savings by requiring only two MILP formulations.
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 $\mathcal R^*(k) \geq \mathcal R^*(k+n)$.