Sensor Placement for Globally Optimal Coverage of 3D-Embedded Surfaces

TL;DR

This paper studies the problem of optimally placing sensors on 3D surfaces for various applications, demonstrating computational intractability and proposing approximation algorithms with practical evaluations.

Contribution

It introduces a unified framework for sensor placement on 3D surfaces, analyzes its computational complexity, and develops approximation schemes for near-optimal solutions.

Findings

All formulations are computationally intractable.

Proposed approximation schemes achieve near-optimal coverage.

Methods are validated on realistic scenarios.

Abstract

We carry out a structural and algorithmic study of a mobile sensor coverage optimization problem targeting 2D surfaces embedded in a 3D workspace. The investigated settings model multiple important applications including camera network deployment for surveillance, geological monitoring/survey of 3D terrains, and UVC-based surface disinfection for the prevention of the spread of disease agents (e.g., SARS-CoV-2). Under a unified general "sensor coverage" problem, three concrete formulations are examined, focusing on optimizing visibility, single-best coverage quality, and cumulative quality, respectively. After demonstrating the computational intractability of all these formulations, we describe approximation schemes and mathematical programming models for near-optimally solving them. The effectiveness of our methods is thoroughly evaluated under realistic and practical scenarios.