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Radius of Robust Feasibility for Ground Coverage in Aerial Sensor Networks

Vanshika Datta, C. Nahak

TL;DR

This work addresses robust ground coverage in aerial directional sensor networks subject to spatial placement uncertainty. It integrates the Radius of Robust Feasibility (RRF) into a Voronoi-based orientation framework, projecting 3D sensing footprints onto the ground as annular sectors and optimizing orientations under bounded location perturbations. The authors derive an exact RRF expression, embed robust constraints into nominal and robust optimization models, and propose a distributed greedy orientation algorithm that adapts to uncertainty while balancing coverage and robustness. Experimental results show that RRF-driven robustified orientations preserve coverage under worst-case displacements and outperform baselines in perturbed deployments, offering a practical, non-probabilistic approach to resilient aerial sensing. The methodology has implications for UAV surveillance, disaster response, and environmental monitoring where reliable coverage under uncertainty is critical.

Abstract

Sensors are vital for environmental monitoring, yet their effectiveness diminishes under spatial uncertainty. We propose a robust optimization framework for maximizing the coverage of aerial directional sensors under spatial uncertainty. Each sensor projects a truncated sector on the ground, parameterized by its altitude, field of view, and orientation. To address sensor displacement uncertainty, we introduce the radius of robust feasibility (RRF) as a measure of tolerance against positional perturbations. We formulate an exact expression for the RRF of aerial sensor networks and embed it into the coverage maximization model as a robustness constraint. Our approach guarantees that the optimized configuration remains feasible under bounded uncertainty. A distributed greedy algorithm based on Voronoi partitioning is used for orientation adjustment, ensuring scalable and adaptive deployment toward high-impact regions. Experimental results validate the effectiveness of our model in preserving robust coverage across complex terrain and varying uncertainty conditions.

Radius of Robust Feasibility for Ground Coverage in Aerial Sensor Networks

TL;DR

This work addresses robust ground coverage in aerial directional sensor networks subject to spatial placement uncertainty. It integrates the Radius of Robust Feasibility (RRF) into a Voronoi-based orientation framework, projecting 3D sensing footprints onto the ground as annular sectors and optimizing orientations under bounded location perturbations. The authors derive an exact RRF expression, embed robust constraints into nominal and robust optimization models, and propose a distributed greedy orientation algorithm that adapts to uncertainty while balancing coverage and robustness. Experimental results show that RRF-driven robustified orientations preserve coverage under worst-case displacements and outperform baselines in perturbed deployments, offering a practical, non-probabilistic approach to resilient aerial sensing. The methodology has implications for UAV surveillance, disaster response, and environmental monitoring where reliable coverage under uncertainty is critical.

Abstract

Sensors are vital for environmental monitoring, yet their effectiveness diminishes under spatial uncertainty. We propose a robust optimization framework for maximizing the coverage of aerial directional sensors under spatial uncertainty. Each sensor projects a truncated sector on the ground, parameterized by its altitude, field of view, and orientation. To address sensor displacement uncertainty, we introduce the radius of robust feasibility (RRF) as a measure of tolerance against positional perturbations. We formulate an exact expression for the RRF of aerial sensor networks and embed it into the coverage maximization model as a robustness constraint. Our approach guarantees that the optimized configuration remains feasible under bounded uncertainty. A distributed greedy algorithm based on Voronoi partitioning is used for orientation adjustment, ensuring scalable and adaptive deployment toward high-impact regions. Experimental results validate the effectiveness of our model in preserving robust coverage across complex terrain and varying uncertainty conditions.
Paper Structure (24 sections, 7 theorems, 32 equations, 7 figures, 1 table, 1 algorithm)

This paper contains 24 sections, 7 theorems, 32 equations, 7 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Modeling the notion of RRF to handle data uncertainty
  4. Maximizing coverage in sensor networks
  5. Handling data uncertainty in optimization frameworks
  6. Modeling framework and problem setup
  7. Preliminaries and notation
  8. Sensor geometry and sensing model
  9. Optimization models under uncertainty
  10. Nominal and uncertainty model
  11. Robust counterpart under location uncertainty
  12. Formulation of robustified optimization model
  13. Problem overview and solution flow
  14. Orientation adjustment strategy for coverage enhancement
  15. Classification of Voronoi-projection intersection cases
  16. ...and 9 more sections

Key Result

Lemma 3.1

(Schur complement chuong2017exact, Lemma 2.1) Let $W= $ be symmetric with $A \succ 0$. Then $W \succeq 0$ if and only if $C - BA^{-1}B^T \succeq 0$. ∎

Figures (7)

  • Figure 1: Voronoi diagram for a set of generators
  • Figure 2: Sensing model in 3D and its ground projection
  • Figure 3: Flowchart for RRF-based robust sensor orientation framework
  • Figure 4: Voronoi diagrams showing coverage under best-case (nominal) sensor deployment.
  • Figure 5: Voronoi diagrams showing coverage under worst-case (perturbed) sensor deployment.
  • ...and 2 more figures

Theorems & Definitions (12)

  • Lemma 3.1
  • Definition 3.1
  • Definition 3.2
  • Definition 3.3
  • Lemma 3.2: See chuong2017exact, Lemma 2.2
  • Lemma 3.3
  • Lemma 3.4
  • Theorem 3.5
  • Definition 3.4
  • Lemma 3.1: Coverage Under Uncertainty
  • ...and 2 more