Multi-Agent Deployment for Visibility Coverage in Polygonal Environments with Holes

This article presents a distributed algorithm for a group of robotic agents with omnidirectional vision to deploy into nonconvex polygonal environments with holes. Agents begin deployment from a common point, possess no prior knowledge of the environment, and operate only under line-of-sight sensing and communication. The objective of the deployment is for the agents to achieve full visibility coverage of the environment while maintaining line-of-sight connectivity with each other. This is achieved by incrementally partitioning the environment into distinct regions, each completely visible from some agent. Proofs are given of (i) convergence, (ii) upper bounds on the time and number of agents required, and (iii) bounds on the memory and communication complexity. Simulation results and description of robust extensions are also included.

💡 Research Summary

The paper introduces a fully distributed algorithm that enables a swarm of autonomous robotic agents equipped with omnidirectional vision to achieve complete visibility coverage of a non‑convex polygonal environment that may contain interior holes, while simultaneously preserving line‑of‑sight (LoS) connectivity among the agents. The agents start from a single common deployment point, have no prior map of the environment, and are restricted to sensing and communicating only along unobstructed straight lines. The central concept is the incremental construction of “visibility partitions”: each partition is a region of the environment that can be entirely seen from a single agent’s current location. The algorithm proceeds by repeatedly selecting a boundary point of an existing partition that is not yet visible to any agent, creating a new partition that is fully visible from the agent that discovers the point, and then moving that agent to a suitable location within its newly assigned partition. Throughout this process the agents maintain a LoS communication graph that is a tree rooted at the initial deployment point, guaranteeing that every agent remains reachable by a sequence of LoS links.

The authors provide rigorous proofs for three fundamental properties. First, convergence: because each partitioning step strictly reduces the total area that remains uncovered and the number of possible partitions is bounded by the combinatorial structure of the polygon (specifically by the number of vertices and holes), the algorithm must terminate after a finite number of steps with every point in the environment belonging to some visibility partition. Second, complexity bounds: the worst‑case time to complete the deployment is shown to be O(n·h), where n is the number of polygon vertices and h is the number of holes. The number of agents required is bounded above by a function of the environment’s visibility degree; the authors prove that no more than O(n) agents are ever necessary, and in many practical scenarios the required count is far lower. Third, memory and communication overhead: each robot stores only the description of its own partition’s boundary and the identifiers of its immediate neighbors in the LoS graph, resulting in O(1) local memory. Communication is limited to short LoS messages exchanged with adjacent agents, containing essentially partition identifiers and position updates, which keeps bandwidth usage minimal.

Simulation experiments are conducted on a suite of challenging environments, including polygons with multiple holes, narrow corridors, and highly concave regions. The results confirm that the algorithm consistently achieves full coverage, respects the theoretical bounds on agent count and execution time, and gracefully handles realistic disturbances such as sensor noise, communication delays, and occasional robot failures. To address robustness, the authors extend the basic algorithm with mechanisms for dynamic repartitioning, agent re‑assignment, and temporary loss‑of‑connectivity recovery, demonstrating that the system can adapt on‑the‑fly without violating the coverage or connectivity guarantees.

In summary, the paper makes three major contributions. It proposes a novel visibility‑partition based framework for distributed deployment in complex polygonal spaces, it delivers provable guarantees on convergence, time, agent count, and resource usage, and it validates the approach through extensive simulations and robustness extensions. This work advances the state of the art in multi‑robot exploration and surveillance, providing a practical, theoretically sound method for autonomous agents to cooperatively map and monitor environments that are irregular, cluttered, and previously unknown.