This paper addresses the challenges in UAVs search and rescue missions by abstracting UAV swarms into a mobile sensing network. It transforms the exploration task into a coverage control problem, effectively addressing the coverage issues of UAVs in non-convex environments. The study explores the coverage problem within such scenarios and proposes a novel hybrid approach. By integrating the geodesic sensing model with Voronoi partitioning methods, this approach combines geodesic boundary sensing with Voronoi sensor centroid control, yielding superior coverage performance compared to individual methods. Leveraging both geodesic sensing for boundary exploration and Voronoi-based centroid control, the proposed approach significantly enhances coverage efficiency and adaptability in challenging environments. Extensive numerical simulations validate the method’s effectiveness in improving coverage, addressing non-convexity challenges, and meeting the stringent requirements of UAVs search-and-rescue missions. The research contributes to advancing UAVs capabilities in exploring and operating within complex non-convex environments, facilitating swift and comprehensive search-and-rescue missions. This work emphasizes the critical role of innovative strategies in enhancing the effectiveness and reliability of UAV operations, with implications for various applications in search-and-rescue, disaster response, and exploration tasks.