Compact workspace decomposition based on a bottom-up approach

In this paper, we present an algorithm that addresses the challenge of dividing a workspace among multiple UAVs. The workspace can be any convex or non-convex polygon and may contain holes of various shapes that represent no-fly zones. The UAVs can be heterogeneous, with different levels of autonomy, speed, and range. The goal of the workspace division is to obtain areas whose sizes are best matched to the capabilities of the UAVs while maximizing compactness. The algorithm decomposes the polygon representing the workspace into a triangular grid, followed by an iterative process of accumulating adjacent triangles while maximizing the compactness of the resulting regions. The performance of the algorithm and the quality of the partitions generated by the algorithm are compared to existing methods. Results show that this approach outperforms others in several metrics, achieving a 5% to 10% improvement in compactness, while maintaining reasonable performance, with a time overhead of up to approximately two seconds when splitting a polygon into ten parts.