Voronoi Coverage (Lloyd's Algorithm)

Problem Statement

Coverage control places agents to minimize sensing distance over an area. Voronoi partitioning with Lloyd descent yields distributed, geometrically interpretable coverage behavior.

Model and Formulation

Coverage objective:

$$ H(P)=\sum_{i=1}^{N}\int_{V_i}|q-p_i|^2\phi(q)dq $$

where V_i is the Voronoi cell of agent i. Lloyd update moves each agent to its cell centroid.

Practical Notes

• Convergence depends on bounded domain and update damping.
• Density \phi(q) can bias coverage toward high-priority regions.
• Voronoi recomputation cost grows with agent count.

Implementation and Execution

python -m uav_sim.simulations.swarm.voronoi_coverage

Evidence

References

• Cortes et al., Coverage Control for Mobile Sensing Networks (2004)
• Bullo et al., Distributed Control of Robotic Networks

Related Algorithms

• Consensus Formation
• Potential Swarm