Equitable Persistent Coverage of Non-Convex Environments with Graph-Based Planning

TL;DR

The paper addresses persistent coverage by a team of robots in non-convex environments, introducing a two-stage solution: offline equitable partitioning via geodesic-distance power diagrams to balance workload according to point importance, followed by online per-partition graph-based planning to generate sweep-like paths. The partitioning is extended with connectivity-aware and capability-aware enhancements, and planning inside each partition is reduced to efficient graph path optimization using a modified Bellman-Ford approach, enabling fast online computation. The authors demonstrate convergence guarantees, perform extensive simulations across challenging environments, and validate the approach with real-world experiments using TurtleBot robots, showing robust performance and improved coverage balance compared to Voronoi-based partitions. The work advances scalable, equitable, non-convex persistent-coverage methods with provable convergence and practical applicability in robotics.

Abstract

In this paper we tackle the problem of persistently covering a complex non-convex environment with a team of robots. We consider scenarios where the coverage quality of the environment deteriorates with time, requiring to constantly revisit every point. As a first step, our solution finds a partition of the environment where the amount of work for each robot, weighted by the importance of each point, is equal. This is achieved using a power diagram and finding an equitable partition through a provably correct distributed control law on the power weights. Compared to other existing partitioning methods, our solution considers a continuous environment formulation with non-convex obstacles. In the second step, each robot computes a graph that gathers sweep-like paths and covers its entire partition. At each planning time, the coverage error at the graph vertices is assigned as weights of the corresponding edges. Then, our solution is capable of efficiently finding the optimal open coverage path through the graph with respect to the coverage error per distance traversed. Simulation and experimental results are presented to support our proposal.

Figures (19)

• Figure 1: Schematic of the overlap of the coverage areas for two consecutive sweeps in the $x$ direction and the optimal separation between them.
• Figure 2: Example of graph construction.
• Figure 3: Normalized work function $\lambda(\mathbf{q})$ over the Open Rooms environment. White areas represent obstacles.
• Figure 4: Example of partitioning in the four different environments under control law \ref{['Eq:ControlLaw1']} (top row) and under control law \ref{['Eq:ControlLaw2']} (bottom row). The resulting partitions are shown in different colors. The initial locations of the generators are represented with white circumferences and the final location with white crosses. Blue lines in the bottom row represent the path of the generators until the equitable partitions are achieved. In the cases where a generator ended outside its own partition, it has been plotted with the color of its partition instead of white to show the correspondences.
• Figure 5: Evolution of the workload, weight and gradient of the cost function with respect to the weight for the Spiral environment under control law \ref{['Eq:ControlLaw1']}. Different colors represent the variables for the different robots.

Theorems & Definitions (5)

• Theorem 3.1
• Remark 3.2
• Theorem 4.1
• Remark 4.2
• Proposition 5.1