<p>This paper addresses the coverage control problem for multi-agent system while ensuring persistent connectivity among unmanned aerial vehicles (UAVs). A Voronoi-based partitioning method is employed to optimize area coverage, and algebraic connectivity—a spectral measure derived from the graph Laplacian—is utilized to quantify network connectivity. The system is deemed connected when algebraic connectivity remains positive. To enforce connectivity guarantees, control barrier functions (CBFs) are integrated to constrain the algebraic connectivity above a predefined threshold <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\lambda_{2} &gt; \varepsilon\)</EquationSource> </InlineEquation>. Notably, since algebraic connectivity is inherently a global metric and incompatible with distributed architectures, a novel distributed estimation strategy is proposed to approximate this metric locally, eliminating reliance on centralized computation. The proposed approach not only resolves the challenge of implementing global connectivity metrics in distributed frameworks but also circumvents the inflexibility inherent in local methods that rigidly preserve initial connectivity structures. The proposed algorithm introduces minimal modifications to the baseline Voronoi coverage controller, ensuring that connectivity constraints are satisfied while preserving the maximum operational flexibility for the primary coverage task. The simulation results show that the proposed algorithm not only has a good coverage effect, but also can always maintain the algebraic connectivity greater than the expected threshold, ensuring the connectivity of the UAVs.</p>

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Maintaining connectivity in coverage control: a distributed algebraic connectivity estimation approach using control barrier functions

  • Junwu Li,
  • Chenggang Wang,
  • Bochen Li,
  • Qiang Wei,
  • Lei Song,
  • Dan Huang

摘要

This paper addresses the coverage control problem for multi-agent system while ensuring persistent connectivity among unmanned aerial vehicles (UAVs). A Voronoi-based partitioning method is employed to optimize area coverage, and algebraic connectivity—a spectral measure derived from the graph Laplacian—is utilized to quantify network connectivity. The system is deemed connected when algebraic connectivity remains positive. To enforce connectivity guarantees, control barrier functions (CBFs) are integrated to constrain the algebraic connectivity above a predefined threshold \(\lambda_{2} > \varepsilon\) . Notably, since algebraic connectivity is inherently a global metric and incompatible with distributed architectures, a novel distributed estimation strategy is proposed to approximate this metric locally, eliminating reliance on centralized computation. The proposed approach not only resolves the challenge of implementing global connectivity metrics in distributed frameworks but also circumvents the inflexibility inherent in local methods that rigidly preserve initial connectivity structures. The proposed algorithm introduces minimal modifications to the baseline Voronoi coverage controller, ensuring that connectivity constraints are satisfied while preserving the maximum operational flexibility for the primary coverage task. The simulation results show that the proposed algorithm not only has a good coverage effect, but also can always maintain the algebraic connectivity greater than the expected threshold, ensuring the connectivity of the UAVs.