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Anchor-Oriented Localized Voronoi Partitioning for GPS-denied Multi-Robot Coverage

Aiman Munir, Ehsan Latif, Ramviyas Parasuraman

TL;DR

The paper tackles GPS-denied multi-robot coverage by introducing an anchor-oriented coverage (AOC) framework that constructs dynamic, localized Voronoi partitions around a common anchor. A distributed boundary consensus enables each robot to define a local workspace in its own frame, enabling a Lloyd-like AOC controller to achieve partitioning equivalent to global Voronoi under the anchor consensus, with a regret bound $R(T) \leq \mathcal{O}(\sqrt{T(1+\sigma_{AP}^2)})$ due to anchor-position uncertainty. Theoretical results establish the equivalence to the global cost $H_{\mathcal{V}}$ and centroid convergence, while simulations and Robotarium experiments validate performance on par with GPS-based coverage and resilience to anchor noise. The approach scales to larger teams, works in GPS-denied environments, and is released as open-source for community use.

Abstract

Multi-robot coverage is crucial in numerous applications, including environmental monitoring, search and rescue operations, and precision agriculture. In modern applications, a multi-robot team must collaboratively explore unknown spatial fields in GPS-denied and extreme environments where global localization is unavailable. Coverage algorithms typically assume that the robot positions and the coverage environment are defined in a global reference frame. However, coordinating robot motion and ensuring coverage of the shared convex workspace without global localization is challenging. This paper proposes a novel anchor-oriented coverage (AOC) approach to generate dynamic localized Voronoi partitions based around a common anchor position. We further propose a consensus-based coordination algorithm that achieves agreement on the coverage workspace around the anchor in the robots' relative frames of reference. Through extensive simulations and real-world experiments, we demonstrate that the proposed anchor-oriented approach using localized Voronoi partitioning performs as well as the state-of-the-art coverage controller using GPS.

Anchor-Oriented Localized Voronoi Partitioning for GPS-denied Multi-Robot Coverage

TL;DR

The paper tackles GPS-denied multi-robot coverage by introducing an anchor-oriented coverage (AOC) framework that constructs dynamic, localized Voronoi partitions around a common anchor. A distributed boundary consensus enables each robot to define a local workspace in its own frame, enabling a Lloyd-like AOC controller to achieve partitioning equivalent to global Voronoi under the anchor consensus, with a regret bound due to anchor-position uncertainty. Theoretical results establish the equivalence to the global cost and centroid convergence, while simulations and Robotarium experiments validate performance on par with GPS-based coverage and resilience to anchor noise. The approach scales to larger teams, works in GPS-denied environments, and is released as open-source for community use.

Abstract

Multi-robot coverage is crucial in numerous applications, including environmental monitoring, search and rescue operations, and precision agriculture. In modern applications, a multi-robot team must collaboratively explore unknown spatial fields in GPS-denied and extreme environments where global localization is unavailable. Coverage algorithms typically assume that the robot positions and the coverage environment are defined in a global reference frame. However, coordinating robot motion and ensuring coverage of the shared convex workspace without global localization is challenging. This paper proposes a novel anchor-oriented coverage (AOC) approach to generate dynamic localized Voronoi partitions based around a common anchor position. We further propose a consensus-based coordination algorithm that achieves agreement on the coverage workspace around the anchor in the robots' relative frames of reference. Through extensive simulations and real-world experiments, we demonstrate that the proposed anchor-oriented approach using localized Voronoi partitioning performs as well as the state-of-the-art coverage controller using GPS.
Paper Structure (14 sections, 2 theorems, 25 equations, 9 figures, 1 algorithm)

This paper contains 14 sections, 2 theorems, 25 equations, 9 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Multi-Robot Coverage
  4. Anchor-oriented Coverage Approach
  5. Localized Voronoi Partitioning Problem
  6. Anchor Boundary Consensus
  7. Anchor-oriented Coverage (AOC) Controller
  8. Theoretical Analysis
  9. Regret Analysis
  10. Experiments and Results
  11. Scalability Analysis
  12. Impact of the AP Prediction Uncertainty
  13. Real-World Demonstration in Robotarium
  14. Conclusion

Key Result

Theorem 1

Applying anchor range consensus in eq:consensus, the anchor-oriented Voronoi partitioning in eq: anchor_oriented_voronoi with a local bounded region ${}^i \mathcal{Q} \subset \mathbb{R}^2$ will be equivalent to the global Voronoi partitioning in eq: Voronoi with a global bounded region $\mathcal{Q}$

Figures (9)

  • Figure 1: Overview of the proposed anchor-oriented multi-robot coverage, with consensus control on boundary size.
  • Figure 2: The distributed system architecture of multi-robot coverage for robot $i$ using anchor-oriented boundary consensus and partitioning to solve the GPS-denied coverage problem.
  • Figure 3: Coverage results in a $4\times4 m^2$ environment. The plots show the initial locations of robots and the final locations after running different coverage controllers. The right-most plots show the locational cost from Eq. \ref{['tarditionalLLoydCost']}, which shows the AOC with consensus closely tracks CVT's performance.
  • Figure 4: Coverage results in a $10\times10 m^2$ environment. The coverage results and the locational cost confirm the proposed approach's capability to solve the Localized Voronoi partitioning problem with equivalent performance to global Voronoi partitioning.
  • Figure 5: Coverage results when four robots have different initial orientations 0°,90°,45°, and 180°, respectively. The global FoR aligns with the first robot.
  • ...and 4 more figures

Theorems & Definitions (6)

  • Theorem 1
  • proof
  • proof
  • proof
  • Theorem 2
  • proof