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A Radius of Robust Feasibility Approach to Directional Sensors in Uncertain Terrain

Vanshika Datta, C. Nahak

TL;DR

This work tackles the degradation of directional sensing under sensor-location uncertainty by introducing the radius of robust feasibility (RRF) for directional sensor networks and embedding it within a Voronoi-based distributed greedy framework. It derives an exact RRF formula for DSNs, linearizes the uncertainty in sensor-coefficient terms, and uses Voronoi vertices as robust orientation targets to maximize coverage while preserving feasibility. The proposed methodology combines robust optimization with geometric partitioning and local collaboration, yielding improved resilience and near-optimal coverage in uncertain environments, as demonstrated by simulations across varied parameters. The approach offers practical impact for real-world deployments in forests, disaster zones, and other terrains where precise placement is infeasible, while providing a foundation for extensions to heterogeneous sensors and terrain-aware optimization.

Abstract

A sensor has the ability to probe its surroundings. However, uncertainties in its exact location can significantly compromise its sensing performance. The radius of robust feasibility defines the maximum range within which robust feasibility is ensured. This work introduces a novel approach integrating it with the directional sensor networks to enhance coverage using a distributed greedy algorithm. In particular, we provide an exact formula for the radius of robust feasibility of sensors in a directional sensor network. The proposed model strategically orients the sensors in regions with high coverage potential, accounting for robustness in the face of uncertainty. We analyze the algorithm's adaptability in dynamic environments, demonstrating its ability to enhance efficiency and robustness. Experimental results validate its efficacy in maximizing coverage and optimizing sensor orientations, highlighting its practical advantages for real-world scenarios.

A Radius of Robust Feasibility Approach to Directional Sensors in Uncertain Terrain

TL;DR

This work tackles the degradation of directional sensing under sensor-location uncertainty by introducing the radius of robust feasibility (RRF) for directional sensor networks and embedding it within a Voronoi-based distributed greedy framework. It derives an exact RRF formula for DSNs, linearizes the uncertainty in sensor-coefficient terms, and uses Voronoi vertices as robust orientation targets to maximize coverage while preserving feasibility. The proposed methodology combines robust optimization with geometric partitioning and local collaboration, yielding improved resilience and near-optimal coverage in uncertain environments, as demonstrated by simulations across varied parameters. The approach offers practical impact for real-world deployments in forests, disaster zones, and other terrains where precise placement is infeasible, while providing a foundation for extensions to heterogeneous sensors and terrain-aware optimization.

Abstract

A sensor has the ability to probe its surroundings. However, uncertainties in its exact location can significantly compromise its sensing performance. The radius of robust feasibility defines the maximum range within which robust feasibility is ensured. This work introduces a novel approach integrating it with the directional sensor networks to enhance coverage using a distributed greedy algorithm. In particular, we provide an exact formula for the radius of robust feasibility of sensors in a directional sensor network. The proposed model strategically orients the sensors in regions with high coverage potential, accounting for robustness in the face of uncertainty. We analyze the algorithm's adaptability in dynamic environments, demonstrating its ability to enhance efficiency and robustness. Experimental results validate its efficacy in maximizing coverage and optimizing sensor orientations, highlighting its practical advantages for real-world scenarios.
Paper Structure (24 sections, 7 theorems, 45 equations, 8 figures, 5 tables, 1 algorithm)

This paper contains 24 sections, 7 theorems, 45 equations, 8 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Construction of Voronoi Regions
  4. Radius of Robust Feasibility
  5. Sensing Model in Directional Sensor Networks
  6. Problem Description
  7. Radius of Robust Feasibility for Directional Sensor Networks
  8. Proposed Model
  9. Sensing Model and Problem Definition
  10. Optimization Formulation
  11. Geometric Considerations and Assumptions
  12. Stopping Condition and Practical Considerations
  13. Proposed Methodology
  14. Greedy Sensor Placement Algorithm
  15. Localized Orientation Optimization
  16. ...and 9 more sections

Key Result

Lemma 2.1

(Schur complement[ben2001lectures, Lemma 4.2.1]) $W:= $ be a symmetric matrix with a positive definite matrix $A$ of order $k$ and block $C$ of order $l$. Then, $W$ is positive semi-definite if and only if $C-BA^{-1}B^T$ is positive semi-definite. ∎

Figures (8)

  • Figure 1: Voronoi diagram for a set of sensors $s_1,s_2,s_3,s_4,s_5,s_6,s_i$
  • Figure 2: Sensing model for directional sensors
  • Figure 3: Illustration of sensor coverage analysis
  • Figure 4: Possible cases for area coverage
  • Figure 5: Illustration of the four possible cases of sensor coverage within a Voronoi cell
  • ...and 3 more figures

Theorems & Definitions (14)

  • Lemma 2.1
  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Lemma 2.2: schirotzek2007nonsmooth, Lemma 1.3.13
  • Lemma 2.3
  • Lemma 2.4
  • Theorem 2.1
  • Definition 3.1
  • ...and 4 more