A Safe and Efficient Global Path-Planning Method Considering Multiple Environmental Factors of the Moon Using a Distributed Computation Strategy

Abstract

Lunar-rover path planning is a key topic in lunar exploration research, with safety and computational efficiency critical for achieving long-distance planning. This paper proposes a distributed path-planning method that considers multiple lunar environmental factors, addressing the issues of inadequate safety considerations and low computational efficiency in current research. First, a set of safety evaluation rules is constructed by considering factors such as terrain slope, roughness, illumination, and rock abundance. Second, a distributed path-planning strategy based on a safety-map tile pyramid (DPPS-STP) is proposed, using a weighted A* algorithm with hash table-based open and closed lists (OC-WHT-A*) on a Spark cluster for efficient and safer path planning. Additionally, high-resolution digital orthophoto maps (DOM) are utilized for small crater detection, enabling more refined path planning built upon the overall mission-planning result. The method was validated in four lunar regions with distinct characteristics. The results show that DPPS-STP, which considers multiple environmental factors, effectively reduces the number of hazardous nodes and avoids crater obstacles. For long-distance tasks, it achieves an average speedup of up to 11.5 times compared to the single-machine OC-WHT-A*, significantly improving computational efficiency.

1. Introduction

The Moon is a primary target for human deep-space exploration and an ideal base and outpost for further extraterrestrial exploration [1]. NASA is actively advancing plans for humans to return to the Moon and is preparing to establish long-term infrastructure in orbit and on the lunar surface [2]. Russia has developed a lunar south-pole exploration plan, intending to establish a lunar base through five missions from “Luna-25” to “Luna-29” [3]. China’s lunar exploration program has successfully completed the three phases of orbiting, landing, and returning [4], with plans to achieve manned lunar landings by 2030 and to establish a comprehensive international lunar research station by 2040.

Currently, several nations have initiated various lunar and Mars rover exploration missions. The Soviet Lunokhod 2 rover landed in 1973, with a climbing capability of 30°, relying on ground remote control for exploration, with a total travel distance of 39 km. The U.S. Opportunity rover landed on Mars in 2004, also with a climbing capability of 30°, using remote operation and semi-autonomous control, covering a distance of 45.16 km [5]. China’s Yutu-2 rover landed on the Moon in 2019, with a climbing capability of 20°, employing remote operation and semi-autonomous control, covering a distance of 1.61 km [6]. Early rovers such as Lunokhod 2 relied on ground-based teleoperation, which was affected by signal delays and had a high level of operational complexity [7]. The Opportunity rover and the Yutu-2 rover possess a certain degree of semi-autonomous navigation capability but still depend on ground control, with limited navigation intelligence [5]. Future lunar exploration missions such as Artemis will involve larger-scale, longer-distance, and more complex environments, placing higher demands on the autonomous navigation capabilities and mobility of lunar rovers [8,9]. Rovers with extensive mobility and detection capabilities will be key to lunar exploration and the construction of lunar bases, providing necessary support for resource exploration and scientific experiments, and promoting the long-term exploration and development of the Moon [10].

Long-distance lunar exploration refers to the use of autonomous or semi-autonomous systems to conduct extensive scientific investigations and resource exploration on the lunar surface, typically over distances of tens to hundreds of kilometers [9,11]. It aims to study the Moon’s geology, resource distribution, and environmental characteristics, providing support for future lunar base construction and deep-space exploration [8]. The future lunar rover will face various risks and engineering challenges during thousand-kilometer exploration missions. First, the complex terrain on the lunar surface [12], such as steep slopes, rocks, and craters, may cause the rover to get stuck or overturn during its journey, presenting challenges to its obstacle-crossing capabilities. Second, the extreme environmental conditions on the Moon [13], including low temperatures, intense radiation, and long periods of darkness, will pose significant challenges to the rover’s batteries and electronic systems.

Lunar path planning can be divided into three levels: overall mission planning, periodic planning, and unit planning [14]. Overall mission planning uses remote sensing images to determine the general direction and path for the rover to reach target points, with planning path distances on the order of kilometers, primarily based on global path-planning algorithms using known environmental information. The global path-planning algorithms includes classic algorithms such as Dijkstra [15,16], Floyd [17], and A* [18], as well as intelligent algorithms like ant colony [19] and genetic algorithms [20]. Periodic planning breaks down the global path obtained from overall mission planning into several navigation points, serving as the start and end points for unit planning, typically spanning several tens of meters [14]. Unit planning provides the final path for the rover, with the distance of a unit typically less than 10 m [14], mainly based on sensor perception for local path planning to detect the surrounding environment and avoid obstacles, including methods based on artificial potential fields [21] and neural networks [22].The three-level path-planning method breaks down tasks hierarchically, implementing a coarse-to-fine path-planning approach that effectively addresses path-planning challenges of different scales and complexities.

Safe and efficient path planning is a prerequisite for the rover’s mobile detection. Currently, there has been significant research on overall mission planning for the Moon. Bai et al. [23] categorized lunar environmental constraints into static and dynamic constraints, proposing a global path-planning method for polar regions of the rover based on these constraints. The method considered factors such as slope, roughness, and illumination of the Moon. Yu et al. [24] introduced a large-scale path-planning algorithm based on digital elevation models (DEM), designing a terrain traversability analysis method and generating a Euclidean distance map to provide references for safe path planning. This algorithm improves the search mechanism of the A* algorithm, effectively enhancing the safety of the rover during autonomous exploration. Yu et al. [25] designed a comprehensive environmental cubic model for the lunar surface and a multi-constraint navigation point-search algorithm, breaking down lunar exploration tasks into different levels and establishing a cubic model to describe time-varying and non-time-varying environments, achieving path planning that comprehensively considers factors such as terrain accessibility, illumination conditions, and communication reachability. Hong et al. [26] proposed a distributed path-planning strategy that generates a pyramid from lunar DEM images and stores it in a distributed file system. Compared to the single-machine A* algorithm, the Spark-based distributed algorithm greatly enhances the efficiency of path planning, but only considers the slope of the lunar terrain during the planning process.

The preceding analysis demonstrates that substantial advancements have been achieved in the field of overall mission planning for lunar rovers; however, current research still faces several issues:

• (1). Insufficient comprehensive consideration of safety factors: The lunar surface has a complex topography with various terrains such as mountains and deep pits [12]. For large-scale, long-distance exploration tasks, the safety of path planning is crucial and should consider multiple factors such as terrain, illumination, craters, and rocks. Currently, most lunar path-planning research is based on DEM, but the resolution of global lunar DEM is relatively low, making it difficult to avoid all obstacles on the Moon, such as small craters. Few studies incorporate high-resolution DOM images for path planning. Additionally, rocks are a major feature of the lunar surface and pose potential dangers to landers and rovers; however, few studies have included rock abundance on the lunar surface as a consideration in path planning.

• (2). Insufficient computational efficiency in path planning: Current research on overall mission planning for the Moon often focuses on single-machine path planning within small areas. In the future, rovers with large-scale detection capabilities could expand their exploration radius from small local areas to tens or even hundreds of kilometers. As the exploration range increases, the complexity of path-planning calculations grows exponentially, making it difficult for single-machine computing power to handle large-scale path planning in the complex lunar environment.

To address the above issues, this paper proposes a safe and efficient distributed global path-planning method that considers multiple lunar environmental factors. This paper primarily focuses on the overall mission-planning level in path planning, and based on this, proposes a more refined periodic planning method. The major differences between our research and previous studies are that lunar environmental factors are more extensively considered from the perspective of safety, and distributed computing and an improved A* algorithm are adopted for greater efficiency. The main contributions of this paper are summarized as follows:

• (1). Different from existing studies, a new set of safety evaluation rules for the lunar environment has been established. The proposed method incorporating not only the lunar terrain slope, but also factors such as roughness, average illumination rate, rock abundance, and the distance and density of obstacle points around image pixels. The safety map generated based on these rules supports subsequent path-planning tasks, ensuring that the planning results can effectively avoid dangerous areas.

• (2). We propose a distributed path-planning strategy based on a safety-map tile pyramid. The method utilizes an optimized data structure and cost function within the A* algorithm to tackle the challenges of large-scale path-planning tasks, which are difficult to manage in a single-machine environment. Experimental results show that this method significantly improves the speed while ensuring path safety.

• (3). A periodic planning method that combines high-resolution DOM is introduced. By using CenterNet to detect small craters on the DOM and integrating the Bresenham algorithm to simplify the path, the method reduces the turning angles and distances of the path, effectively avoiding obstacles posed by small craters.

The organization of the paper is as follows: Section 2 introduces the specific methods of the paper, Section 3 discusses the experimental research regions and data sources, Section 4 presents the experimental results and analysis, Section 5 provides a discussion, and Section 6 concludes the paper.

2. Methods

The framework of the proposed method is shown in Figure 1. This method is composed of four parts. First, a safety map is generated based on DEM data, average lunar illumination data, and rock abundance data, and the safety map is stored in hadoop distributed file system (HDFS) in a tiled pyramid format. Second, a distributed path-planning strategy based on the safety-map tile pyramid (DPPS-STP) is employed to accelerate the overall lunar path planning. Additionally, the Bresenham algorithm is employed to simplify the path, determining the start and end coordinates for each planning period. Then, the CenterNet is used to detect small crater obstacles on high-resolution DOM, and these obstacles are overlaid onto the upsampled safety map. The map with overlaid obstacles is used for periodic planning to generate the final periodic planning nodes. Finally, a weighted A* algorithm with hash table-based open and closed lists (OC-WHT-A*) is introduced to enhance the speed and safety of executing path-planning tasks within each tile.

2.1. Generation and Distributed Storage of the Safety Map Considering Lunar Environmental Factors

To address the challenges posed by complex lunar terrain such as steep slopes and rocks encountered during long-distance exploration, this paper considers incorporating factors like lunar slope [6], roughness [27], and rock abundance [28] into the safety evaluation rules. To cope with extreme environmental conditions such as low temperatures and long periods of darkness, this paper considers incorporating solar illumination [29] factors into the safety evaluation rules.

The safety map is generated through a comprehensive analysis of DEM data, average illumination rate data, and rock abundance data. First, traversability analysis is conducted on these three datasets, taking into account the factors of lunar slope, roughness, average illumination rate, and rock abundance. Four corresponding traversability maps are generated for these factors. Then, an intersection operation is performed on these four traversability maps to obtain a traversability map with only two values, 0 and 1, where 0 represents an obstacle point that is non-traversable, and 1 represents a point that is traversable. Finally, convolution processing is applied to this traversability map to obtain the safety map. The specific descriptions and calculation formulas for the relevant factors are as follows:

• (1). Slope

The slope reflects the steepness of the lunar surface, and excessive slope can threaten the safety of the lunar rover’s movement. This paper uses the 8-neighborhood method to calculate the slope, and the calculation formula for the slope angle θ is as follows:

(1)$f_x={\displaystyle \frac{\left(H_7+2H_8+H_9-H_1-2H_2-H_3\right)}{8\times Cellsize}}$

(2)$f_y={\displaystyle \frac{\left(H_3+2H_6+H_9-H_1-2H_4-H_7\right)}{8\times Cellsize}}$

(3)$\mathsf{\theta }=\mathrm{arc}\tan \left(\sqrt{f_x^2+f_y^2}\right)\times {\displaystyle \frac{180}{\mathsf{\pi }}}$

Among them, the gradients of DEM in the horizontal and vertical directions are represented by $f_x$ and $f_y$, respectively. $H_i$ represents the elevation value of the i-th grid among the surrounding 9 grids, where the grids are numbered from left to right. $Cellsize$ represents the size of the image grid; the $Cellsize$ used for slope calculation in this paper is consistent with the resolution of the DEM image to ensure that the slope more accurately reflects the actual terrain. The slope traversability map $M^{slope}$ is generated under the following conditions: when the slope angle θ is greater than the threshold, it is considered non-traversable, with a value of 0; when it is less than the threshold, it is marked as 1, indicating that it is traversable.

• (2). Roughness

Roughness refers to the degree to which elevation points in the area deviate from the fitted plane, reflecting the undulation of the terrain. Excessive roughness can affect the safety and stability of the lunar rover’s movement. The calculation formula for roughness δ is as follows:

(4)$\mathsf{\delta }=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^9{\left(H_i-\overline{H}\right)}^2}{9}}}$

Among them, $\overline{H}$ represents the average value of all elevation values in the 9 grids. The roughness traversability map $M^{rough}$ is generated under the following conditions: when the roughness δ is greater than the threshold, it is marked as 0, indicating that it is non-traversable; otherwise, it is marked as 1.

• (3). Average Illumination Rate

Illumination is a necessary condition for the lunar rover to maintain warmth and sufficient solar energy [29]. The average illumination rate data were simulated over a long period with high temporal resolution using LOLA topography combined with a lunar ephemeris and the horizon method. The value at each pixel represents the average proportion of the solar disk area visible during this period. In actual lunar exploration missions, illumination conditions change in real time. Due to the long duration of distant exploration missions, the average illumination rate can reflect the real illumination conditions during the mission to some extent [30]. By restricting the average illumination rate, areas with poor illumination on the moon can be effectively avoided. If a certain area is in shadow for a long time and its average illumination rate is below the threshold, the illumination traversability map $M^{illumin}$ will mark this area as 0; otherwise, it will be marked as 1.

• (4). Rock Abundance

Rocks are one of the main features of the lunar surface and may pose potential dangers to landers and rovers [31]. Rock abundance is defined as the proportion of the cumulative fractional area (CFA) covered by rocks with a diameter greater than or equal to a specific value (usually 10 cm) within a certain area [32]. The calculation formula of the rock abundance model is shown in formula 5. Based on this model, the overall distribution of all rocks can be inferred from a definite number of rocks with sizes above a particular value. When the abundance is greater than the threshold, the rock abundance traversability map $M^{rock}$ will mark this area as 0, indicating non-traversable; when the abundance is less than the threshold, it will be marked as 1.

(5)$F_k\left(D\right)=k{e}^{-(0.5648+0.01285/k)D}$

where $k$ is the rock abundance and $F_k\left(D\right)$ refers to the areal fraction of rocks larger than $D$ in diameter. This rock abundance model describes the overall CFA of rocks versus their diameters.

Based on the above four factors, four corresponding traversability maps are obtained. By performing an intersection operation on the maps $M^{slope}$, $M^{rough}$, $M^{illumin}$, and $M^{rock}$, the final traversability map $M^{traverse}$ is obtained. That is, only the pixels that meet the traversability conditions of all four factors are marked as traversable points in the map $M^{traverse}$. The calculation formula is as follows:

(6)$M^{traverse}=M^{slope}\cap M^{rough}\cap M^{illumin}\cap M^{rock}$

Since the pixel values on the traversability map $M^{traverse}$ only reflect whether the current grid is an obstacle point and do not comprehensively reflect the density of obstacle points in the surrounding area, the traditional A* algorithm typically uses path length as an evaluation metric during path planning and does not consider the distance between the planned path and obstacle points. This can result in paths that are too close to obstacles, increasing the risk during the rover’s movement. Therefore, the traversability map has limitations in complex lunar environments, making it difficult to fully consider the distribution density of obstacles and their safe distance from the path.

Thus, this paper defines a 7 × 7 convolution kernel K based on the generated traversability map $M^{traverse}$ to calculate the safety of pixel points, with points closer to the center of the convolution kernel receiving higher weights. The following operation is performed on each pixel point of the traversability map. If the pixel point is an obstacle point (value of 0), the operation is skipped. The final result is a safety map $M^{safety}$ with a value range of 0 to 1, where a higher value indicates greater safety and fewer surrounding obstacle points, while a lower value indicates lower safety and more surrounding obstacle points. When the value is 0, it indicates that the point is an obstacle and is non-traversable. The pixel values on the safety map $M^{safety}$ after convolution can effectively reflect the density of obstacle points in the grid and its surrounding area. The calculation formula for $M^{safety}$ is as follows:

(7)$M^{\mathrm{safety}}\left(i,j\right)={\displaystyle \frac{{\sum }_{u=-3}^3{\sum }_{v=-3}^3{M}^{traverse}\left(i+u,j+v\right)\cdot K\left(u,v\right)}{S_K}}$

(8)$S_K={\sum }_{u=-3}^3\sum _{v=-3}^{3}K\left(u,v\right)$

In this context, the pixel points on the map $M^{traverse}$ are represented as $M^{traverse}\left(i,j\right)$, the elements in the convolution kernel $K$ are represented as $K\left(u,v\right)$, and the convolution result of the kernel $K$ at point $\left(i,j\right)$ is represented as $M^{\mathrm{safety}}\left(i,j\right)$. The sum of the weights of the convolution $K$ is indicated $S_K$.

Finally, the safety map $M^{safety}$ is upsampled to create a pyramid with a 2:1 ratio, consisting of 5 layers. Using the properties of the pyramid model, layer-by-layer computation from coarse to fine can be achieved. The computation results of the upper-layer tiles are used to reduce the search space of path nodes in the lower layer, thereby improving the algorithm’s efficiency. Every level within the pyramid structure is then partitioned into uniformly sized rectangular sections, forming a safety-map tile pyramid. Each tile in every layer has a corresponding tile row number and column number for the rapid identification of tile positions within the pyramid. This paper uses HDFS to store the tile pyramid, as HDFS offers high data throughput and built-in redundancy, making it highly suitable for managing large-scale remote sensing datasets. Figure 2 shows the segmentation and storage process for a three-layer safety-map tile pyramid in HDFS.

2.2. Overall Mission Path Planning Based on a Distributed Path-Planning Strategy

This paper proposes a distributed path-planning strategy based on a safety-map tile pyramid (DPPS-STP), and implements it using the distributed computing engine Spark. The strategy utilizes the properties of the pyramid model, performing parallel computation to calculating the starting and ending point sets for each tile from coarse to fine. It begins with coarse-grained path planning at the top layer of tiles, and then, based on the results of this layer, calculates the starting and ending points on the next layer of tiles. Subsequently, path planning is performed for the next layer of tiles, employing a divide-and-conquer approach to the sub-path-planning tasks on each tile. This process is iterated as described above, until the paths for the bottom layer of tiles are computed, ultimately yielding the overall path-planning results.

In a master–worker cluster, Spark decomposes the path-planning task into multiple sub-tasks, which are subsequently allocated to worker nodes for execution. Each worker node retrieves the requisite tile data from HDFS, performs the designated sub-task as instructed by the master node, and ultimately stores the resultant path-planning data back into HDFS.

The fundamental procedure for executing DPPS-STP using Apache Spark is outlined as follows: First, the top-level pyramid tile data are loaded from HDFS. Then, a resilient distributed dataset (RDD) is created for these tiles in memory. Next, the start and end coordinates of the top-level tiles are input, and the relevant tiles are filtered based on the specified coordinate set. Distributed path planning is performed on the filtered tiles to generate the path RDD for that layer. For tiles not located at the bottom layer, the generated path RDD is used to compute the start and end points required for path planning in the next layer, i.e., the path results from the current layer are mapped to the next layer, finding the path points located at the boundary of the next layer tiles. These path points are then used as the start and end point sets for each tile in the next layer. This iterative path-planning process continues until all tiles in the bottom layer are processed, at which point the path results are written back to HDFS. The path iteration process of a pyramid with three levels is shown in Figure 3.

Due to the use of the eight-direction A* path-planning algorithm, the calculated paths contain many turning points, making them less smooth. Therefore, the overall mission planned path can be simplified based on the Bresenham algorithm [33], removing redundant nodes, reducing turning angles, and minimizing path length, ultimately resulting in a set of simplified path nodes that are obstacle-free between each pair, preparing for periodic planning. The Bresenham algorithm, which is a classic line-drawing algorithm in computer graphics that determines the next pixel position to draw by incrementally checking the intersection points of the line with the grid boundaries based on integer operations, can efficiently compute the pixel coordinates along the straight line between two given points.

The core process of optimizing the path based on the Bresenham algorithm is as follows: Starting from the initial point, traverse each node in the path sequentially. Use the Bresenham algorithm to check if the line connecting the current starting point and the traversed node is close to obstacle points, i.e., to determine if there are any hazardous nodes along the line. If there are none, continue traversing; if there are, add the previous node of the current traversed node to the key point list and set that node as the starting point for the next round of traversal. Repeat this process until reaching the endpoint, ultimately generating the simplified path. Since only path points on the line between two nodes that do not contain hazardous nodes are added to the key point list, the simplified path maintains the same level of safety as the original path.

2.3. Refined Periodic Planning Based on CenterNet Small Crater Detection

Due to the relatively low resolution of the global lunar DEM, the overall task path planned based on it cannot avoid some small craters. Therefore, high-resolution DOM images are needed for more precise path planning to enhance the safety of the path.

This paper first determines the latitude and longitude range for periodic path planning based on the simplified overall planned path nodes, taking every two nodes as one cycle. Then, high-resolution DOM images corresponding to the latitude and longitude are found, and the CenterNet network is used to detect small craters. Finally, the detected crater obstacles are overlaid onto a safety map to support periodic path planning.

CenterNet is an object detection model that utilizes keypoint detection to approach the task of object detection by identifying the center of an object and directly regressing its attributes, thereby eliminating the need for non-maximum suppression. This approach significantly enhances both the speed and accuracy of detection processes [34]. The model integrates features from various levels to produce more representative and robust hierarchical features, which improves the estimation of crater centers, particularly for smaller craters. The minimum size of a crater that can be detected using this methodology is 500 m. In comparison to the Robbins crater database, this method achieves a recall rate of 73.66% and a precision rate of 78.27% for crater detection. The algorithm is publicly available at https://github.com/ShuoweiZhang/crater_detection (accessed on 4 March 2025) [35].

This paper uses the 7 m resolution Chang’e 2 global lunar DOM and the 100 m resolution Lunar Reconnaissance Orbiter (LRO) global lunar DOM images, unifying both to a common resolution of 7 m for fusion processing. Crater detection is performed on the fused DOM images, and the detected crater obstacles are overlaid onto the upsampled 7 m resolution safety map to prepare for periodic path planning.

2.4. Path Planning Using an A* Algorithm with Improved Data Structure and Cost Function (OC-WHT-A* Algorithm)

Hong et al. proposed an improved A* algorithm with a random-access data structure for open and closed lists (OC-RA-A* Algorithm) [18], which uses a min-heap and a two-dimensional array to implement the open list, reducing the time complexity of checking whether adjacent nodes are in the open list from O(n) to O(1). However, this method requires a large amount of memory to be allocated in advance for the two-dimensional array when dealing with large-sized images. Moreover, the nodes actually accessed by the A* algorithm are usually concentrated around the path from the starting point to the endpoint, meaning that even if a very large two-dimensional array is allocated, only a small portion of the space is actually used, leading to a significant waste of memory resources.

This paper makes two improvements based on the OC-RA-A* algorithm. First, it improves the data structure of the open and closed lists. Second, it incorporates the safety of path points into the cost estimation calculation of the A* algorithm.

Firstly, by improving the data structure, the algorithm’s space complexity is significantly reduced while maintaining the average time complexity of node lookup in the open list. As shown in Figure 4, in the improved A* algorithm with hash table-based open and closed lists (OC-HT-A* Algorithm), the data structure of the open list uses a min-heap and a hash table, while the closed list uses a hash table. Compared to OC-RA-A*, the average time complexity for determining whether the adjacent nodes of the current node are in the open list in OC-HT-A* remains O(1), but the space complexity is reduced from O(m²) to O(n), where m is the size of the image and n is the number of nodes accessed during the pathfinding process. The improved data structure of the A* algorithm effectively reduces space complexity while ensuring search efficiency. It should be noted that the data structures of the OC-HT-A* Algorithm and the OC-WHT-A* Algorithm are identical, differing only in the design of their cost functions.

Second, in response to the issue of traditional A* algorithm paths being too close to obstacles, this paper incorporates the safety of path points into the cost-estimation calculation based on the aforementioned improvements. When the safety of path point $N$ is lower, the estimated cost of that point increases. This modification allows the A* algorithm to prioritize nodes with higher safety when searching for paths, thereby avoiding areas with many obstacles and improving the overall safety of the path. The calculation formula for the OC-WHT-A* is as follows.

(9)$F\left(N\right)=G\left(N\right)+\left(1.5-w\times M^{\mathrm{safety}}\left(N\right)\right)\times H\left(N\right)$

$F\left(N\right)$ denotes the total cost, $G\left(N\right)$ represents the actual cost from the starting point to the current point $N$, and $H\left(N\right)$ represents the estimated cost from the current point $N$ to the endpoint. $w$ is a static weight that reflects the safety of the current point $N$. When the safety of the path point is high, the coefficient in front of $H\left(N\right)$ is smaller, resulting in a lower total cost $F\left(N\right)$ for the path point. Additionally, different values of $w$ lead to different path-selection tendencies in the algorithm: a larger $w$ slows down the algorithm and favors finding paths with higher safety; a smaller $w$ speeds up the algorithm and prioritizes quickly finding a path from start to end. Experimental validation shows that with a weight of $w=0.4$, the OC-WHT-A* algorithm achieves a balance between computation speed and path safety. Therefore, this paper uses the OC-WHT-A* algorithm with a weight value of 0.4 in all experiments.

The heuristic function formulas for the other A* algorithms in this experiment are as follows:

(10)$F\left(N\right)=G\left(N\right)+H\left(N\right)$

(11)$G\left(N\right)=G\left(N^{\mathrm{‘}}\right)+\sqrt{{\left(N_x-N_x^{\mathrm{‘}}\right)}^2+{\left(N_y-N_y^{\mathrm{‘}}\right)}^2}$

(12)$H\left(N\right)=\left|N_x^{\mathrm{end}}-N_x\right|+\left|N_y^{\mathrm{end}}-N_y\right|+\left(\sqrt{2}-2\right)\cdot \min \left(\left|N_x^{\mathrm{end}}-N_x\right|,\left|N_y^{\mathrm{end}}-N_y\right|\right)$

$G\left(N^{\mathrm{‘}}\right)$ represents the actual distance from the starting point to $N^{\mathrm{‘}}$, $G\left(N\right)$ represents the actual distance from the starting point through $N^{\mathrm{‘}}$ to point $N$, and $H\left(N\right)$ represents the estimated distance from point $N$ to the endpoint. $N^{end}$ indicates the position of the endpoint, while $x$ and $y$ represent the horizontal and vertical positions of the nodes, respectively.

3. Research Regions and Data

3.1. Research Regions

This paper selects four regions as research regions: the Oceanus Procellarum region, the landing region of Chang’e 4 (CE-4), the lunar south-pole region, and the proposed landing region of the Endurance mission, as shown in Figure 5. The Oceanus Procellarum region is located between 0° and 45°N and 72°W–21°W, covering a region of approximately 2,359,296 km². This region is primarily characterized by lunar maria, with a flat terrain that records the late volcanic activity of the Moon, making it a key region for studying the thermal evolution of the Moon. It is significant for understanding the origin and geological evolution history of the basalt in the lunar maria [36]. The CE-4 landing zone is located between 33°S and 55°S and 161°E–166°W, covering a region of approximately 921,600 km². This region is mainly composed of highlands and has many impact craters, preserving early information about the Moon. It is important for studying the early history and evolution of the Moon, as well as its deep structure and composition. The south-pole region is located between 85°S and 90°S and 180°W–180°E, covering a region of approximately 65,536 km². The terrain and landforms in the south-pole region are complex, with areas of permanent shadow, making it significant for studying the sources and distribution of lunar water ice and volatile components, the deep material and internal structure of the Moon, and the morphological structure of the Moon [3]. The proposed landing region of the Endurance mission is located between 56.69°S–57.76°S and 161.86°W–161.46°W, covering a region of approximately 30 km². This paper selects the Endurance landing region to validate the effectiveness of the DPPS-STP algorithm on high-resolution, meter-scale data. The proposed Endurance mission aims to land in the South Pole–Aitken (SPA) basin, travel nearly 2000 km, and collect 12 distinct sets of samples from the far side of the Moon [11]. The mission will coordinate with Artemis astronauts near the lunar south pole. These samples will help address long-standing scientific questions regarding the early solar system’s dynamics, the properties of the lunar mantle, and the thermochemical evolution of rocky worlds [37]. The four research regions have unique topographical and geomorphological features, providing ideal cases for validating the effectiveness of the methods. Detailed information about the research regions is provided in Table 1.

3.2. Data

The experiment used five types of data: lunar DEM data, Digital Terrain Model (DTM) data, average illumination rate data, rock abundance data, and DOM data. The resolution of the DEM data is 20 m, sourced from the Chang’e 2 mission, covering the entire Moon. The resolution of the DTM data is 2 m, sourced from the LRO, and it covers only some local regions of the Moon. This study utilizes local DTM data from the South Pole–Aitken region. The lunar average illumination rate data have resolutions of 1900 m and 120 m, covering the entire Moon and the region from 85°S to 90°S, respectively, with the 1900 m resolution data coming from Tongji University. The rock abundance data have a resolution of 128 m and cover the range from 85°N to 80°S. This paper resampled the lunar average illumination rate data and rock abundance data to match the resolution of the Chang’e 2 DEM. The DOM data have resolutions of 7 m and 100 m, covering the entire Moon, sourced from Chang’e 2 and LRO, respectively. The 7 m resolution DOM data have higher detail, but their textures in low-latitude areas are not clear enough, making it difficult to effectively identify craters. In contrast, the 100 m DOM data, although lower in resolution, provide a more balanced effect across different latitudes, allowing for better identification of craters. Therefore, this paper integrates the advantages of the two types of DOM data and performs fusion processing, resulting in a fused resolution of 7 m. This study also utilizes DOM data with a resolution of 0.59 m, sourced from the LRO, covering the same areas as the aforementioned 2 m DTM data. Detailed information about the data used in the experiment is provided in Table 2.

4. Results

4.1. Experimental Design and Evaluation Metrics

The experiment was conducted on a distributed cluster consisting of three Linux virtual machines built on a computer with an Intel i9-11900K processor, each equipped with 16 GB of memory, a 6-core processor, and 100 GB of storage space. All single-machine experiments in this study were conducted on one of the virtual machines from the above configuration. Additionally, before the experiment, the image data were generated into a tile pyramid and stored in HDFS.

Referencing the design of dynamic parameter constraints for the Endurance-R lunar rover from the Endurance mission [37], the maximum slope threshold was set to 20° [6,43], and the roughness threshold was set to Cellsize/5 [27]. To ensure the rover’s traverse performance [28], and based on recommendations for similar tasks, the rock abundance threshold was limited to 7% [44]. To enable the rover to effectively avoid areas with insufficient illumination during its traverse, based on manual experimental testing, the average-illumination-rate threshold for the Oceanus Procellarum region and the CE-4 landing region was set to 44%, while the average-illumination-rate threshold for the polar region was set to 7% [30].

This paper evaluates the efficiency of path-planning algorithms using the concept of time cost, defined as the overall duration of the path-planning process, encompassing the startup time for the cluster and the time spent on parallel processing in the distributed algorithm. The calculation is outlined as follows:

(13)$T=T_{start}+T_{compute}$

Furthermore, path distance, the count of hazardous nodes along the path, and the cumulative angle of turns along the path are applied to assess the quality of the generated path. Path distance signifies the actual distance covered along the path from the start to the endpoint. Hazardous nodes are identified as path points with obstacle points within a radius of 40 m. The cumulative turning angle of the path is determined by computing the angles between the direction vectors of every three successive points along the path and summing these values incrementally.

4.2. Comparison of Different A* Algorithm Path Planning in a Single-Machine Environment

In order to assess the efficacy of the enhanced A* algorithm for path planning across varying distances on tiles, the experiment employed single-machine computation to simulate path-planning tasks associated with different A* algorithms on a safety map. A safety map of size 4000 × 4000 was cropped from the Oceanus Procellarum region, and a comparison of different distance path planning was conducted using OC-WHT-A*, OC-HT-A*, OC-RA-A*, and the traditional A algorithm, as shown in Table 3.

In short-distance scenarios, the traditional A* algorithm took the longest time, at 81.348 s; OC-RA-A* and OC-HT-A* took almost the same amount of time, differing by less than 0.1 s. It can be seen that OC-HT-A* reduced the algorithm’s space complexity without increasing its time complexity. The OC-WHT-A* algorithm was the fastest, improving by 6.93% compared to OC-HT-A*. The time cost of the traditional A* algorithm was approximately 10.96 times that of OC-HT-A* and about 11.78 times that of OC-WHT-A*. Since OC-RA-A* and OC-HT-A* only made improvements in data structure while keeping the cost-function design the same as the traditional A* algorithm, the paths planned by the three algorithms were also the same, with the same number of hazardous nodes, which was 70. However, OC-WHT-A* improved the cost function $H\left(N\right)$ by introducing a weight to avoid areas with dense obstacles, resulting in a significant reduction in the number of hazardous nodes in the planned path, which was 0.

In medium-distance scenarios, the time taken by the traditional A* algorithm significantly increased to 1418.512 s. OC-RA-A* and OC-HT-A* took approximately the same amount of time. The OC-WHT-A* algorithm was the fastest, showing a clear speed advantage over OC-HT-A*, improving by 48.74%. The time cost of the traditional A* algorithm was about 113.50 times that of OC-WHT-A*. It can be seen that as the distance increases, the path search space expands, and the planning time of the traditional A* algorithm grows exponentially. Meanwhile, OC-WHT-A* introduced the weight w, optimizing the path search space, making it more efficient for large-scale path planning. Additionally, the path planned by OC-WHT-A* still ensured safety, with the number of hazardous nodes on its path being 0, significantly better than the path results obtained by the other three algorithms.

In long-distance scenarios, the traditional algorithm took 10,145.400 s. OC-RA-A* and OC-HT-A* took approximately the same amount of time, with OC-HT-A* being slightly faster at 77.760 s. The OC-WHT-A* algorithm remained the fastest, taking only 36.160 s, which was an improvement of 53.49% over OC-HT-A*. Furthermore, the path planned by the OC-WHT-A* algorithm still ensured safety, with the number of hazardous nodes on its path being 0. It can be seen that the traditional A* algorithm is difficult to apply to long-distance path planning. In contrast, the OC-WHT-A* algorithm maintained the fastest planning speed across short, medium, and long distances, with its performance advantage continuously expanding as the distance increased. While ensuring speed, the OC-WHT-A* algorithm also guaranteed the safety of the path results, effectively avoiding obstacles in short, medium, and long-distance scenarios. The comparison of path results from different algorithms is shown in Figure 6.

The path-selection tendency of the A* algorithm is closely tied to the design of its heuristic function h(n). In this paper, traditional A*, OC-RA-A*, and OC-HT-A* differ in data structures but all use diagonal distance as h(n), equal to the actual cost, resulting in length-optimal paths. In contrast, OC-WHT-A* incorporates weighting, making its heuristic cost exceed the actual cost. This prioritizes movement toward the target, improving computational efficiency while causing a slight but insignificant increase in path length. Additionally, OC-WHT-A* avoids high-obstacle-density areas, favoring safer paths, whereas the other three algorithms optimize only for path length, often leading to routes that closely follow obstacles, increasing traverse risks.

4.3. Comparison of Path-Planning Results for the DPPS-STP Distributed Algorithm

To verify the efficiency of the DPPS-STP distributed algorithm, this paper conducted path-planning experiments in three regions: the Oceanus Procellarum, the landing zone of Chang’e 4, and the lunar south pole. The experiments compared the single-machine OC-WHT-A* algorithm, the DPPS-STP using OC-HT-A* algorithm, and the DPPS-STP using OC-WHT-A* algorithm. The results are summarized in Table 4 and Table 5.

In terms of time taken, it can be seen that the distributed algorithm significantly reduced the time required for path planning. From the results of Table 3, it is evident that under the same conditions in a single-machine environment, the OC-WHT-A* algorithm has a faster path-planning speed, with the time taken reduced by about 50% compared to the OC-HT-A* algorithm. The DPPS-STP using OC-HT-A* algorithm showed significantly lower time taken across all three regions compared to the single-machine OC-WHT-A* algorithm, with a maximum reduction of 90.15%, indicating the efficiency advantage of the DPPS-STP distributed algorithm in path planning. Additionally, in all three regions, the DPPS-STP using OC-WHT-A* algorithm took less time than the one using OC-HT-A*, with an average time-cost reduction of about 28.5%. This is because the DPPS-STP using OC-WHT-A* algorithm became faster due to the inclusion of the weight w in the path-planning calculations for individual tiles.

Regarding path length, the DPPS-STP using OC-HT-A* algorithm produced the shortest path lengths in all three regions, while the path lengths obtained from the single-machine OC-WHT-A* algorithm and the DPPS-STP using OC-WHT-A* algorithm were similar. Compared to the DPPS-STP using OC-HT-A* algorithm, the DPPS-STP using OC-WHT-A* algorithm resulted in a path length that was 30.749 km longer in the Oceanus Procellarum region, 23.96 km longer in the CE-4 landing zone, and 23.463 km longer in the south-pole region. The maximum increase in path length across the three regions was less than 8%.

In terms of the number of hazardous nodes, although the DPPS-STP using OC-HT-A* algorithm planned shorter paths than the one using OC-WHT-A*, the number of hazardous nodes along its path significantly increased. The path planned by the DPPS-STP using OC-HT-A* algorithm in the Oceanus Procellarum region resulted in 604 hazardous nodes, while the paths in the Chang’e 4 landing zone and the south-pole region each had over 1000 hazardous nodes. In contrast, the DPPS-STP using OC-WHT-A* algorithm resulted in 0 hazardous nodes in both the Oceanus Procellarum and Chang’e 4 landing zone, and only 40 hazardous nodes in the south-pole region, indicating that the paths effectively avoided areas around obstacles, ensuring the safety of the path results. The time comparison of different algorithms is shown in Figure 7, and the path comparison results are shown in Figure 8.

Compared to the single-machine OC-WHT-A* algorithm, the DPPS-STP algorithm using OC-WHT-A* achieves an average speedup of 11.50 across the three regions. It is important to note that the OC-WHT-A* algorithm in this paper constructs a min-heap to quickly find the node with the smallest cost Fn. The time complexity of heap sort is O(nlog n), so the algorithm’s runtime grows logarithmically with the increase in the number of nodes in the heap, rather than linearly increasing. Due to the adoption of the tile pyramid approach, the distributed algorithm not only distributes path-planning tasks across three machines but also constrains the search space of each sub-path-planning task to the size of the top-level tile, significantly reducing the number of nodes in the min-heap. This shortens the heap sort time during the algorithm’s search process and mitigates the negative impact of logarithmic growth. Therefore, the speedup of the distributed algorithm in this paper surpasses linear acceleration.

4.4. Comparison of Path-Planning Results in the High-Resolution Data Region

To verify the effectiveness of the DPPS-STP algorithm on high-resolution data, this paper focuses on the proposed landing site of the Endurance mission. A high-resolution safety map of 1500 × 5000 pixels with a resolution of 2 m was generated for this region, and path-planning experiments were conducted based on this map. Due to the significant resolution differences between the DTM data, rock abundance data, and average-illumination-rate data, this experiment only used the DTM data to generate the safety map and conducted comparative experiments. The experiments compared the single-machine OC-WHT-A* algorithm, the DPPS-STP using OC-HT-A* algorithm, and the DPPS-STP using OC-WHT-A* algorithm. The experimental results are shown in Table 6.

In terms of time, the path-planning time for the single-machine OC-WHT-A* algorithm was 149.577 s. All DPPS-STP algorithms took less time than the single-machine algorithm. Among them, the DPPS-STP algorithm using OC-WHT-A* achieved the shortest time of 23.489 s, resulting in a speedup factor of 6.36 compared to the single-machine environment. This indicates that the DPPS-STP algorithm demonstrates good efficiency on high-resolution data as well. It is important to note that although the image size used in this experiment is similar to that in the experiments of Section 4.2, the complexity of the environment in this region is higher. This requires a larger search space for the path node, which results in a longer planning time for the OC-WHT-A* algorithm in a single-machine environment.

In terms of path length, the DPPS-STP using OC-HT-A* algorithm generated the shortest path, measuring 8.763 km. The path lengths generated by the OC-WHT-A* algorithm in both the single-machine and distributed environments were similar, with lengths of 9.044 km and 9.034 km, respectively. It can be seen that the OC-WHT-A* algorithm generates a slightly longer path than the OC-HT-A* algorithm, but the increase is not significant, only about 3.2%.

In terms of the number of hazardous nodes, the OC-WHT-A* algorithm in the single-machine environment had the fewest, with only 67 hazardous nodes. The DPPS-STP using OC-WHT-A* algorithm followed, with 79 hazardous nodes along the planned path. The path generated by the DPPS-STP using OC-HT-A* algorithm had a much higher number of hazardous nodes, with 522, far exceeding the results of using OC-WHT-A*. The experimental results are shown in Figure 9. As can be seen from Figure 9, the OC-HT-A* algorithm, which prioritizes optimal path length, neglects considerations of path safety. As a result, the planned path closely follows the edges of obstacles in many places. In contrast, the OC-WHT-A* algorithm introduces a weight factor w, achieving a better balance between path length and safety. Consequently, the path planned by OC-WHT-A* contains fewer hazardous nodes.

It is important to note that due to the upper-level path influencing the lower-level results in the DPPS-STP algorithm, the path generated by the distributed OC-WHT-A* algorithm is slightly different from that of the single-machine algorithm, but the path length and safety are nearly identical.

4.5. Comparison of Path Optimization Results Based on the Bresenham Algorithm

This paper optimizes the path results obtained from overall task planning based on the Bresenham algorithm. Table 7 shows a comparison of the long path optimization before and after for three selected regions. It can be seen that the total distance of the three paths has decreased after optimization, with the average path length shortened by 3.019%. This indicates that the Bresenham algorithm successfully reduced the path length and improved the efficiency of path planning. At the same time, the total turning angle of the optimized paths has significantly decreased, with an average reduction of 96.642%. The paths are smoother, with fewer turns and less turning amplitude, enhancing the feasibility and safety of the paths. The comparison of path optimization results is shown in Figure 10.

4.6. Comparison of Path-Planning Results Before and After Adding Small Crater Obstacles

Figure 11 presents a comparison of the path-planning outcomes before and after the inclusion of meteorite crater obstacles. Red circles highlight the detected crater obstacles. It is evident that a majority of small meteorite craters were accurately identified, with an accuracy of 78.27%. Currently, the undetected craters are neglected during the path-planning process. This will be addressed in our future research. However, compared with existing research, our method outperforms those that do not take craters into account and can provide a safer path in the global planning stage. The blue path represents the original path, which is the path-planning result without the inclusion of crater obstacles, while the green path represents the outcome of periodic path planning after integrating crater obstacles. It is evident that the original path still traverses significant obstacle areas in the high-resolution DOM. However, by using CenterNet to detect small meteorite craters and adding these obstacles to the safety map, the path can avoid obstacles that cannot be identified solely with DEM, thereby enhancing the safety of path planning.

5. Discussion

Currently, lunar exploration missions are primarily conducted in the mid-latitude regions of the Moon. In recent years, the lunar south pole has gradually attracted more attention due to its complex terrain and numerous impact craters, which may contain water ice. NASA’s Artemis program, Russia’s Luna-25, and China’s Chang’e 7 mission all plan to conduct exploration in the lunar south pole. However, the permanently shadowed regions at the lunar south pole can hinder the normal charging of rovers, and the low-temperature environment caused by insufficient illumination poses a serious threat to their equipment. Therefore, illumination is crucial for the rover’s exploration tasks in the south pole.

To investigate the impact of illumination factors on path-planning results in the south-pole region, this paper created a safety map of the south-pole region without illumination restrictions and used a distributed OC-WHT-A* algorithm to conduct path-planning experiments on two images of the south-pole region. On the safety map without illumination rate restrictions, the average illumination rate of the planned path was 24.47%. On the safety map with an illumination rate restriction of 7%, the average illumination rate of the planned path was 26.82%, indicating an increase of 9.6% in the average illumination rate. The path-planning results are shown in Figure 12, where the blue areas represent regions with an average illumination rate below 7%. It can be seen that the path planned without illumination restrictions clearly traverses low-illumination-rate areas. By introducing average-illumination-rate restrictions, the rover can effectively avoid low illumination areas during path planning, ensuring a continuous energy supply.

Roughness reflects the topographical fluctuations within the window area, and excessive roughness can affect the safety and stability of the lunar rover’s movement. To explore the impact of roughness factors on path-planning results, this paper created a safety map of the CE-4 landing zone without roughness factor restrictions and used the distributed OC-WHT-A* algorithm to conduct path-planning experiments on two images of the CE-4 landing zone, as shown in Figure 13. In the absence of roughness factor restrictions, the planned path length was 407.02 km, with an average slope of 5.91°. When roughness factor restrictions were added, the planned path length increased to 412.84 km, with an average slope of 5.18°. Although the path planned with roughness factor restrictions was slightly longer, the increase in path length was not significant, only rising by 1.42%. However, the average slope of the path planned with roughness factor restrictions significantly decreased by 12.35%, indicating that the inclusion of roughness factor restrictions effectively allowed the lunar rover to avoid areas with excessive topographical fluctuations during the path-planning process. Additionally, it can be seen from the figure that the planned path without roughness factor restrictions tends to traverse more craters, increasing the danger of the lunar rover’s movement. In contrast, the path planned with roughness factor restrictions successfully avoids complex topographical areas, resulting in a generally smoother path. It should be noted that the area between 41°S and 46°S and 172°E–180°E, although a crater, has some parts of its edge where the terrain is not steep, with both slope and roughness factors below the threshold, which is why both paths traverse this crater.

Rocks are one of the primary features of the lunar surface and pose potential hazards to landers and rovers. To ensure the traversal performance of the lunar rover and in reference to similar missions, this study sets the threshold for rock abundance at 7%. To investigate the impact of rock abundance on path-planning results, a safety map of the Oceanus Procellarum region without rock abundance constraints was created. The distributed OC-WHT-A* algorithm was then applied to conduct path-planning experiments on both the unconstrained and rock abundance-constrained images of the region. The results were visualized on the corresponding rock abundance images, as shown in Figure 14. The red path represents the path-planning result on the safety map without rock abundance constraints, while the white path represents the result on the safety map incorporating rock abundance constraints. It is evident that the red path traverses multiple areas with rock abundance exceeding 7%, whereas the white path effectively avoids high rock abundance areas, ensuring the safety of the lunar rover’s traversal.

It is important to note that the safety evaluation rules established in this paper are designed for the global lunar environment, and certain environmental factors may have a limited impact on lunar path-planning results in specific regions. For instance, in the Oceanus Procellarum region, the difference in average illumination rates across pixels is minimal due to its lower latitude. The illumination threshold, which was determined through extensive experimentation, mainly serves to avoid small craters and has minimal impact on the overall path results. Furthermore, in the CE-4 landing zone, there are virtually no regions where rock abundance exceeds the 7% threshold, meaning that the consideration of rock abundance does not significantly influence the path-planning outcomes in this region. However, by integrating these factors, the safety and reliability of the path results are better ensured, while providing the flexibility to address the task requirements of different lunar regions.

6. Conclusions

This paper presents a distributed path-planning strategy that integrates environmental factors of the Moon to achieve safe and efficient path planning over large lunar regions. Based on the Spark distributed computing engine, the method establishes safety evaluation rules for the lunar environment and employs a distributed strategy using an improved data structure and cost-function A* algorithm, significantly enhancing path-planning safety and efficiency. The method was validated in four lunar regions, a number of conclusions can be drawn as follows:

• (1). Compared to considering a single factor, this paper integrates slope, roughness, rock abundance, solar illumination, and the presence of small craters, which can significantly enhance the safety of lunar-rover path planning.

• (2). By using DPPS-STP strategy the issue of single-machine computation being limited by machine memory has been successfully addressed. For long-distance missions conducted in the south polar region, the distributed strategy improved speed by 13.47 times compared to single-machine computation.

• (3). The proposed OC-WHT-A* algorithm uses a hash table as the data structure for the open and closed lists, significantly reducing the time and space complexity of the algorithm. It incorporates the safety of path points into the A* algorithm’s evaluation function, effectively avoiding obstacle points.

A limitation of this paper is that average illumination rate is used due to lack of real-time illumination data. This issue will be addressed in our future research.

Author Contributions

Conceptualization, R.Z. and Z.H.; methodology, R.Z., Y.L. and Z.H.; software, Y.L.; validation, H.P., Y.Z., Y.H. and J.T.; formal analysis, R.Z.; investigation, R.Z.; resources, Z.H.; data curation, Y.L.; writing—original draft preparation, R.Z. and Y.L.; writing—review and editing, R.Z., Y.L., Z.H. and H.P.; visualization, R.Z.; supervision, Z.H. and H.P.; project administration, Z.H.; funding acquisition, Z.H. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The data that support the findings of this study are available in China National Space Administration at http://moon.bao.ac.cn (accessed on 4 March 2025); in United States Geological Survey at https://pgda.gsfc.nasa.gov/products/69 (accessed on 4 March 2025) and https://astrogeology.usgs.gov/search/map/moon_lro_lroc_wac_global_morphology_mosaic_100m (accessed on 4 March 2025).

Acknowledgments

We thank China National Space Administration for providing the Chang’e-2 CCD stereo camera DEM-20m and DOM-7m data that made this article possible. This dataset is processed and produced by “Ground Research and Application System (GRAS)of China’s Lunar and Planetary Exploration Program, provided by China National Space Administration (http://moon.bao.ac.cn (accessed on 4 March 2025))”.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:

DPPS-STP	Distributed path-planning strategy based on a safety-map tile pyramid;
DOM	Digital Orthophoto Map;
DEM	Digital Elevation Model;
DTM	Digital Terrain Model;
HDFS	Hadoop distributed file system;
CFA	cumulative fractional area;
RDD	Resilient distributed dataset;
LRO	Lunar Reconnaissance Orbiter;
OC-RA-A*	A* algorithm with a random-access data structure for open and closed lists, using a min-heap and a two-dimensional array to implement the open list.
OC-HT-A*	A* algorithm with hash table-based open and closed lists, using a min-heap and a hash table to implement the open list.
OC-WHT-A*	Weighted A* algorithm with hash table-based open and closed lists, using a min-heap and a hash table to implement the open list.

Footnotes

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Figures and Tables

Figure 1. The overall framework of the proposed method.

Figure 2. The cutting and storage process of the safety-map tile pyramid.

Figure 3. The iterative process of DPPS-STP.

Figure 4. The data structure design of the A* algorithm with hash table-based open and closed lists, and the weighted A* algorithm with hash table-based open and closed lists.

Figure 5. Research regions and corresponding locations.

Figure 6. Path comparison of different A* algorithms in single-machine environment: (a) short-distance path-planning results. (b) Medium-distance path-planning results. (c) Long-distance path-planning results.

Figure 7. Time cost comparison of path planning for single-machine and distributed A* algorithms across three regions.

Figure 8. Comparison of single-machine and distributed path planning in three regions. (a) Path result in the Oceanus Procellarum region. (b) Path result in the CE-4 landing region. (c) Path result in the south-pole region. (d) Local size enlargement of (a). (e) Local size enlargement of (b). (f) Local size enlargement of (c).

Figure 9. Comparison of single-machine and distributed path-planning algorithms in Endurance landing region. (a) Local size enlargement of (c). (b) Local size enlargement of (c). (c) Path result in the Endurance mission landing region.

Figure 10. (a) Long-distance path optimization comparison in the south-pole region based on the Bresenham algorithm. (b) Local size enlargement of (a).

Figure 11. Comparison of path-planning results with and without crater obstacles.

Figure 12. Comparison of path-planning results in the south-pole region with and without average-illumination-rate constraints.

Figure 13. Comparison of path-planning results in the CE-4 landing region with and without roughness factor constraints.

Figure 14. Comparison of path-planning results in the Oceanus Procellarum region with and without rock abundance factor constraint.

Table 1

Information of the four research regions.

Research Regions	Latitude and Longitude Range	Area (km2)	Image Size (Pixels × Pixels)	Features
Oceanus Procellarum Region	0°–45°N 72°W–21°W	2,359,296	76,800 × 76,800	Primarily Lunar Maria, Wide Terrain, Flat
CE-4 Landing Region	33°S–55°S 161°E–166°W	921,600	48,000 × 48,000	Primarily Highlands, Many Impact Craters, Rugged Terrain
South Pole Region	85°S–90°S 180°W–180°E	65,536	12,800 × 12,800	Complex Terrain, Many Impact Craters, Presence of Permanent Shadows
Endurance Landing Region	56.69°S–57.76°S, 161.86°W–161.46°W	30	1500 × 5000	Complex Terrain, Many Impact Craters, Unique Geological Composition

Table 2

Data details and sources.

Data	Data Source	Coverage Range	Resolution	Download Link
DEM	Chang’e 2 [38]	Global Lunar	20 m	https://moon.bao.ac.cn/ (accessed on 4 March 2025)
DTM	LRO	Local Area	2 m	https://wms.lroc.asu.edu/lroc/ (accessed on 4 March 2025)
Average Lunar Illumination Rate	LRO [39]	Global Lunar	1900 m	Provided by Tongji University
	LRO [40]	85°S–90°S	120 m	https://pgda.gsfc.nasa.gov/products/69 (accessed on 4 March 2025)
Rock Abundance	LRO [41]	85°N–80°S	128 m	https://ode.rsl.wustl.edu/moon/datasets (accessed on 4 March 2025)
DOM	Chang’e 2 [3]	Global Lunar	7 m	https://moon.bao.ac.cn/ (accessed on 4 March 2025)
	LRO [42]	Global Lunar	100 m	https://astrogeology.usgs.gov/search/map/moon_lro_lroc_wac_global_morphology_mosaic_100m (accessed on 4 March 2025)
	LRO	Local Area	0.59 m	https://wms.lroc.asu.edu/lroc/ (accessed on 4 March 2025)

Table 3

Time cost and number of hazardous nodes comparison for path planning using different A* algorithms in a single-machine environment.

Algorithm	Short Distance		Medium Distance		Long Distance
	Time Cost (s)	Hazardous Nodes	Time Cost (s)	Hazardous Nodes	Time Cost (s)	Hazardous Nodes
Traditional A*	81.348	70	1418.512	241	10,145.400	276
OC-RA-A*	7.520	70	24.259	241	79.477	276
OC-HT-A*	7.424	70	24.383	241	77.760	276
OC-WHT-A*	6.909	0	12.497	0	36.160	0

Table 4

Time cost of long-distance path planning in single-machine and distributed environments across three research regions.

Algorithm	Oceanus Procellarum Region			CE-4 Landing Region			South Pole Region
	Start-Up Time (s)	Running Time (s)	Sum Time (s)	Start-up Time (s)	Running Time (s)	Sum Time (s)	Start-Up Time (s)	Running Time (s)	Sum Time (s)
Single-Machine (using OC-WHT-A*)	0	1228.540	1228.540	0	689.687	689.687	0	3176.751	3176.751
DPPS-STP (using OC-HT-A*)	1.492	148.140	149.632	1.568	113.678	115.246	1.541	311.589	313.130
DPPS-STP (using OC-WHT-A*)	1.536	90.618	92.154	1.563	87.828	89.391	1.560	234.278	235.838

Table 5

Time cost, path length, and number of hazardous nodes in long-distance path planning for sin-gle-machine and distributed environments across three research regions.

Algorithm	Oceanus Procellarum Region			CE-4 Landing Region			South Pole Region
	Time Cost (s)	Path Length (km)	Hazardous Nodes	Time Cost (s)	Path Length (km)	Hazardous Nodes	Time Cost (s)	Path Length (km)	Hazardous Nodes
Single-Machine (using OC-WHT-A*)	1228.54	1478.796	0	689.687	1041.952	0	3176.751	299.450	0
DPPS-STP (using OC-HT-A*)	149.632	1454.115	604	115.246	1018.438	1110	313.130	292.237	1459
DPPS-STP (using OC-WHT-A*)	92.154	1484.864	0	89.391	1042.398	0	235.838	315.700	40

Table 6

Time cost, path length, and number of hazardous nodes in path planning for single-machine and distributed environments across the Endurance landing region.

Algorithm	Endurance Mission Landing Region
	Time Cost (s)	Path Length (km)	Hazardous Nodes
Single-Machine (using OC-WHT-A*)	149.577	9.044	67
DPPS-STP (using OC-HT-A*)	32.062	8.763	522
DPPS-STP (using OC-WHT-A*)	23.489	9.034	79

Table 7

Path length and turning-angle comparison before and after path simplification based on the Bresenham algorithm.

Simplification	Oceanus Procellarum Region		CE-4 Landing Region		South Pole Region
	Path Length (km)	Turning Angle (°)	Path Length (km)	Turning Angle (°)	Path Length (km)	Turning Angle (°)
Before	1484.864	21,195.000	521.199	40,815.000	315.700	43,425.000
After	1461.532	622.637	506.127	1280.224	301.218	1736.238

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