Multi-Covering a Point Set by $m$ Disks with Minimum Total Area

TL;DR

This paper addresses the problem of optimally placing $m$ disk-shaped sensors to cover a set of assets with robustness constraints, proposing a heuristic combined with integer programming for efficient solutions.

Contribution

It introduces a fast heuristic for sensor placement with robustness constraints and enhances it with an exact integer programming approach, including separation constraints.

Findings

The heuristic provides quick initial solutions.

The integer programming approach refines solutions for optimality.

Separation constraints improve sensor placement robustness.

Abstract

A common robotics sensing problem is to place sensors to robustly monitor a set of assets, where robustness is assured by requiring asset $p$ to be monitored by at least $\kappa(p)$ sensors. Given $n$ assets that must be observed by $m$ sensors, each with a disk-shaped sensing region, where should the sensors be placed to minimize the total area observed? We provide and analyze a fast heuristic for this problem. We then use the heuristic to initialize an exact Integer Programming solution. Subsequently, we enforce separation constraints between the sensors by modifying the integer program formulation and by changing the disk candidate set.