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Distributed Area Coverage Control with Imprecise Robot Localization

Sotiris Papatheodorou, Yiannis Stergiopoulos, Anthony Tzes

TL;DR

The proposed control law is distributed, demands the positioning information about its GV-Delaunay neighbors and has an inherent collision avoidance property.

Abstract

This article examines the problem of area coverage for a network of mobile robots with imprecise agent localization. Each robot has uniform radial sensing ability, governed by first order kinodynamics. The convex-space is partitioned based on the Guaranteed Voronoi (GV) principle and each robot's area of responsibility corresponds to its GV-cell, bounded by hyperbolic arcs. The proposed control law is distributed, demands the positioning information about its GV-Delaunay neighbors and has an inherent collision avoidance property.

Distributed Area Coverage Control with Imprecise Robot Localization

TL;DR

The proposed control law is distributed, demands the positioning information about its GV-Delaunay neighbors and has an inherent collision avoidance property.

Abstract

This article examines the problem of area coverage for a network of mobile robots with imprecise agent localization. Each robot has uniform radial sensing ability, governed by first order kinodynamics. The convex-space is partitioned based on the Guaranteed Voronoi (GV) principle and each robot's area of responsibility corresponds to its GV-cell, bounded by hyperbolic arcs. The proposed control law is distributed, demands the positioning information about its GV-Delaunay neighbors and has an inherent collision avoidance property.

Paper Structure

This paper contains 12 sections, 1 theorem, 23 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Main assumptions - Preliminaries
  4. Voronoi Diagram
  5. Guaranteed Voronoi Diagram
  6. Guaranteed Voronoi diagram of disks
  7. Spatially Distributed Coordination Algorithm
  8. Coverage control law development
  9. Simulation Studies
  10. Case Study I
  11. Case Study II
  12. Conclusions

Key Result

Theorem 1

Considering a mobile sensor network consisting of nodes with uniform range--limited radial performance as in (sensing), governed by the individual robot's kinodynamics described in (kinematics), and the GV--partitioning of $\Omega$ defined in (guaranteed_voronoi_cell), the coordination scheme where $n_i$ is the outward unit normal on $\partial V_i^{gs}$ and $\alpha_i$ a positive constant, maximiz

Figures (10)

  • Figure 1: Voronoi diagram (left) for 6 dimensionless nodes, with its equivalent Guaranteed Voronoi diagram (right) in the case of disks (centered on those points).
  • Figure 2: Dependence of the GV cells on $\left\|x_i-x_j\right\|$.
  • Figure 3: Dependence of the GV cells on $r_i^u + r_j^u$.
  • Figure 4: The decomposition of $\partial V_i^{gs}$ into disjoint sets (solid red, green and blue).
  • Figure 5: The domains of integration of the control law (\ref{['control_law']}).
  • ...and 5 more figures

Theorems & Definitions (8)

  • Remark 1
  • Remark 2
  • Remark 3
  • Theorem 1
  • proof
  • Remark 4
  • Remark 5
  • Conjecture 1