Optimal Planning for Multi-Robot Simultaneous Area and Line Coverage Using Hierarchical Cyclic Merging Regulation

--The double coverage problem focuses on determining efficient, collision-free routes for multiple robots to simultaneously cover linear features (e.g., surface cracks or road routes) and survey areas (e.g., parking lots or local regions) in known environments. In these problems, each robot carries two functional roles: service (linear feature footprint coverage) and exploration (complete area coverage). Service has a smaller operational footprint but incurs higher costs (e.g., time) compared to exploration. T o reduce the complexity for optimal planning solutions, we analyze the manifold attachment process during graph traversal from a Morse theory perspective. We show that solutions satisfying minimum path length and collision-free constraints must belong to a Morse-bounded collection. T o identify this collection, we introduce the HCMR algorithm. In HCMR, cyclic merging search regulates traversal behavior, while edge sequence back propagation converts these regulations into graph edge traversal sequences. Incorporating balanced partitioning, the optimal sequence is selected to generate routes for each robot. We prove the optimality of the HCMR algorithm under a fixed sweep direction. The multi-robot simulation results demonstrate that the HCMR algorithm significantly improves planned path length by at least 10.0%, reduces task time by at least 16.9% in average, and ensures conflict-free operation compared to other state-of-the-art planning methods. Area coverage and line coverage have emerged as key challenges in a wide range of robotic applications. Area coverage focuses on surveying open spaces to ensure full visibility and detect various objects of interest [4], supporting tasks in environmental monitoring [13], infrastructure inspection [18], agricultural surveying [14], and search-and-rescue operations [8]. A practical example of combined area and line coverage requirements is a bridge deck inspection [11], as illustrated in Figure 1.