## 1 Introduction
utilized Voronoi diagrams to construct initial route networks, which were subsequently optimized through the A* algorithm for obstacle avoidance, demonstrating significant reductions in total route length and improvements in airspace coverage; however, this method is based on 2D maps [29]. Similarly, in energy-efficient path planning for unmanned surface vehicles (USVs), the integration of Voronoi diagrams and [PERSON]'s algorithm effectively minimized navigation energy consumption [30]. Furthermore, Voronoi diagrams have been innovatively applied to enhance optimization algorithm initialization. [PERSON] et al. developed a multi-frequency vibrational genetic algorithm (mVGA) that incorporates Voronoi diagrams to improve population diversity, substantially reducing computational time for 3D path planning [31]. In complex dynamic environments, Voronoi diagrams have been synergistically combined with reinforcement learning techniques, such as Q-learning for multi-UAV obstacle avoidance path optimization [32], and enhanced through morphological dilation (MVDRM algorithm) to improve real-time obstacle avoidance capabilities for mobile robots [33]. These applications collectively highlight Voronoi diagrams' versatility and computational efficiency across autonomous systems. The A* algorithm serves as a core algorithm in the field of UAV route planning and is widely adopted due to its unique advantages in balancing global optimality and efficient search capabilities. By employing a heuristic search mechanism, it significantly reduces computational complexity while ensuring path quality, making it an essential tool for path planning in complex environments. However, when confronted with dynamic environments and challenging terrain, the standalone A* algorithm still exhibits limitations in real-time performance and local adaptability. As shown in Table 1, A* is often applied in combination with other methods to preserve its inherent advantages in path optimality while leveraging complementary strengths from other approaches, thereby substantially enhancing the overall system stability and scenario adaptability [34; 35; 36]. Building upon the algorithmic analysis, we propose a hybrid approach that synergistically combines Voronoi diagrams' environmental abstraction capability with A*'s optimal search properties for UAV 3D path planning in complex mountainous terrain. First, by combining the key feature points of the Voronoi diagram with the vertex heuristic function, an initial flight path network is quickly generated. For paths that cannot be directly generated, A* is used to close gaps, and path points are optimized to ensure the generation of efficient, flyable paths. Secondly, building upon the hierarchical flight concept of UAVs [37], an adaptive layering strategy is designed based on drone flight performances and Digital Elevation Model (DEM) data, transforming 3D planning into a layer-switching method between adjacent planes and significantly reducing computational complexity. Furthermore, a flight path point optimization mechanism is introduced to avoid terrain obstacles while enhancing both path efficiency and safety. The simulation of real mountain scenarios with multiple sets of test cases shows that, compared to traditional methods such as A*, PSO, and RRT, this method has significant advantages in terms of planning success rates, path lengths, and computation times. The remainder of this study is organized as follows: Section 2 reviews the foundational methodologies relevant to the proposed algorithm, encompassing DEM-based adaptive layering strategies, regional Voronoi vertex search diagrams, A* searches, and their hybrid integration for trajectory planning. Section 3 elaborates on the framework and operational workflow of the proposed algorithm, which enables rapid trajectory planning through a combination of multiple algorithms. Section 4 presents simulation experiments that validate the efficacy and computational efficiency of the fusion algorithm in mountainous terrain.