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A Generalized Voronoi Graph based Coverage Control Approach for Non-Convex Environment

Zuyi Guo, Ronghao Zheng, Meiqin Liu, Senlin Zhang

TL;DR

This paper proposes a coverage control method based on the Generalized Voronoi Graph (GVG), which has two phases: Load-Balancing Algorithm phase and Collaborative Coverage phase, which considers the quality differences among sub-regions.

Abstract

To address the challenge of efficient coverage by multi-robot systems in non-convex regions with multiple obstacles, this paper proposes a coverage control method based on the Generalized Voronoi Graph (GVG), which has two phases: Load-Balancing Algorithm phase and Collaborative Coverage phase. In Load-Balancing Algorithm phase, the non-convex region is partitioned into multiple sub-regions based on GVG. Besides, a weighted load-balancing algorithm is developed, which considers the quality differences among sub-regions. By iteratively optimizing the robot allocation ratio, the number of robots in each sub-region is matched with the sub-region quality to achieve load balance. In Collaborative Coverage phase, each robot is controlled by a new controller to effectively coverage the region. The convergence of the method is proved and its performance is evaluated through simulations.

A Generalized Voronoi Graph based Coverage Control Approach for Non-Convex Environment

TL;DR

This paper proposes a coverage control method based on the Generalized Voronoi Graph (GVG), which has two phases: Load-Balancing Algorithm phase and Collaborative Coverage phase, which considers the quality differences among sub-regions.

Abstract

To address the challenge of efficient coverage by multi-robot systems in non-convex regions with multiple obstacles, this paper proposes a coverage control method based on the Generalized Voronoi Graph (GVG), which has two phases: Load-Balancing Algorithm phase and Collaborative Coverage phase. In Load-Balancing Algorithm phase, the non-convex region is partitioned into multiple sub-regions based on GVG. Besides, a weighted load-balancing algorithm is developed, which considers the quality differences among sub-regions. By iteratively optimizing the robot allocation ratio, the number of robots in each sub-region is matched with the sub-region quality to achieve load balance. In Collaborative Coverage phase, each robot is controlled by a new controller to effectively coverage the region. The convergence of the method is proved and its performance is evaluated through simulations.
Paper Structure (8 sections, 4 theorems, 21 equations, 7 figures, 2 algorithms)

This paper contains 8 sections, 4 theorems, 21 equations, 7 figures, 2 algorithms.

Table of Contents

  1. INTRODUCTION
  2. PROBLEM STATEMENT
  3. GVG
  4. PROBLEM FORMULATION
  5. LOAD-BALANCING ALGORITHM
  6. COLLABORATIVE COVERAGE
  7. EXPERIMENTAL VALIDATION
  8. CONCLUSIONS

Key Result

Theorem 1

In the execution of Algorithms alg:1 and alg:2, Eq. e3 is satisfied as $t \rightarrow \infty$.

Figures (7)

  • Figure 1: Overview of the proposed method, which includes Load-Balancing Algorithm phase (top) and Collaborative Coverage phase (bottom). Load-Balancing Algorithm determines the final number of robots in each region. In Collaborative Coverage phase, each robot are controlled to efficiently cover its region based on the designed controller.
  • Figure 2: $V_{ij}$ and $V_{ji}$ are two GVG nodes defined by $E_{ij}$. The circle is the node circle. The blue line represents the connection between the node and the intersection point of the circle and an obstacle, and it also serves as the boundary of the region.
  • Figure 3: The non-convex area $D$ with four black holes. The red line represents the GVG curve, and each GVG cell is denoted by a distinct color.
  • Figure 4: The final configuration of robots in each region.
  • Figure 5: A comparison between the actual number of robots and the ideal number of robots in each region.
  • ...and 2 more figures

Theorems & Definitions (6)

  • Definition 1
  • Theorem 1
  • Definition 2
  • Theorem 2
  • Lemma 1
  • Theorem 3