Surveying and mapping unmanned aerial vehicle route planning method based on intelligent algorithm

Through the improved depth-first search algorithm, the problem of path repetition and dead zone trapping in drone path planning is solved through the improved depth-first search algorithm, and the mapping efficiency and stability are improved to adapt to the navigation needs of complex environments.

CN119270896APending Publication Date: 2025-01-07XIHUA UNIV
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Patent Information

Application Number
CN202411381428.5
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-09-30
Publication Date
2025-01-07

AI Technical Summary

Technical Problem

Traditional UAV path planning methods cannot meet the high precision and comprehensive coverage requirements in complex surveying and mapping environments, and there are risks of high path repetition rates, easy to fall into dead zones, and inability to adapt to new environments.

Method used

The improved depth-first search intelligent algorithm is adopted, and by introducing the ‘bwlabel’ function and the ‘F_Orient_OK5’ function, the search direction is controlled, the dead zone and repeated paths are avoided, and the heading is updated in real time to adapt to environmental changes.

Benefits of technology

It significantly improves the task execution efficiency and search efficiency of drones in complex environments, reduces energy consumption and path planning complexity, enhances the universality and stability of the algorithm, and adapts to intelligent navigation in complex environments.

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Abstract

The invention relates to a surveying and mapping unmanned aerial vehicle route planning method based on an intelligent algorithm, and aims to improve the route planning efficiency and task execution capability of an unmanned aerial vehicle in a complex environment. The method comprises the following steps: firstly, constructing a task environment model, performing two-dimensional rasterization on an outdoor low-altitude environment in a mountainous area through a grid method, and taking bird flock density as one of main constraint conditions into the model; and then, an improved depth-first search (DFS) algorithm is used for flight path planning. According to the algorithm, a bwlabel function and a FOrientitOK5 function are introduced, the search direction is optimized, the unmanned aerial vehicle is prevented from falling into a search dead zone, repeated traversal is reduced, and therefore the search efficiency is remarkably improved. In addition, by simplifying the parameter adjustment process, the universality and stability of the algorithm are improved, and the method is suitable for unmanned aerial vehicle surveying and mapping tasks in various complex environments. Through the improvement, effective technical support is provided for intelligent navigation in a complex environment, and the task completion efficiency of the unmanned aerial vehicle is remarkably improved.
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Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle path planning, and in particular to a mapping unmanned aerial vehicle path planning method based on an improved depth-first search intelligent algorithm. Background Art

[0002] With the continuous development of drone technology, drones have been widely used in various fields, such as drone delivery of takeout, delivery of medical supplies, and geographic information collection. Especially in the field of geographic information collection and aerial surveying, compared with traditional surveying methods, drones can cover large areas in a short time and obtain high-resolution ground images. Among them, path planning is the key to ensure that drones can complete surveying tasks efficiently and accurately. For surveying drones, their mission objectives are relatively complex and delicate. Not only do they need to avoid obstacles, but they also need to ensure comprehensive and continuous data collection of designated areas in order to achieve high-quality mapping or three-dimensional model reconstruction. In the application scenarios of surveying drones, traditional drone path planning methods cannot meet the requirements of high precision and comprehensive coverage, and there are disadvantages such as high path repetition rate, easy to fall into dead zones, and the risk of being unable to adapt to new environments. Therefore, there is an urgent need for improvement in technology, that is, to develop an intelligent algorithm based on improved depth-first search to improve the efficiency and safety of drone path planning in complex surveying environments and adapt to the needs of efficient and accurate surveying tasks.

[0003] Prior art 1

[0004] Ke Shijie [1] Based on the analysis of existing intelligent algorithms, a UAV route planning method based on the improved Glowworm Swarm Optimization (GSO) is proposed to solve the mountain mapping problem and improve the UAV mapping accuracy. By using Chebyshev chaotic mapping and introducing the Levy flight strategy as a method to generate the initial population of fireflies, instead of randomly generating the initial population in the traditional firefly algorithm, the diversity of the population is guaranteed.

[0005] Disadvantages of the prior art 1

[0006] This technology uses an improved traditional firefly algorithm to increase the diversity of the randomly generated initial population, which will make the initialization point distribution uneven or the search space larger, resulting in some areas being repeatedly visited by multiple fireflies, and cannot solve the problem of too high path repetition rate. The traditional firefly algorithm has problems such as slow calculation speed, high calculation complexity, long running time, and difficult parameter adjustment. Surveying and mapping drones need to ensure comprehensive and continuous data collection in the specified area, which will lead to high calculation complexity of the algorithm, and may cause oscillation, affect the convergence speed, and make the algorithm take a long time to find the optimal solution. In addition, due to unreasonable parameter settings, the algorithm performance may be reduced, increasing the risk of falling into the local optimal solution, thus falling into a dead zone. In actual surveying and mapping scenarios, the traditional firefly algorithm will have a great impact on the performance of the algorithm when it is trained in the face of huge parameters and data sets, so that the algorithm cannot fully achieve the purpose of surveying and mapping using drones in terms of universality.

[0007] Prior art 2

[0008] Zeng Qing [2][2] Combining the advantages and disadvantages of ant colony algorithm and particle swarm algorithm, a hybrid improved algorithm based on ant colony-particle swarm is proposed. The adaptive inertia weight is dynamically adjusted and the pheromone update rule is optimized by introducing the adaptive path guidance factor to reduce the algorithm iteration time. The safety and smoothness of the path are also used as indicators of pheromone update, which prompts the algorithm to jump out of the local extreme value and improves the accuracy of the algorithm in global search and local fine search.

[0009] Disadvantages of the second prior art

[0010] The results of the fusion algorithm of this technology may be affected by the randomness of parameter settings and the algorithm itself, resulting in unstable accuracy and difficulty in meeting strict surveying and mapping accuracy standards. This technology does not take into account the factors used in actual surveying and mapping UAVs, cannot adapt to the interference of risk factors in new environments, lacks the ability to plan paths in real time in the flight environment, and cannot achieve the function of dynamic obstacle avoidance.

[0011] Definitions of Abbreviations and Key Terms

[0012] Depth-First Search (DFS) is an algorithm for traversing or searching a tree or graph. The process is to start from a node, traverse along the depth of the tree or graph until the end node is reached, and then backtrack to find the result before returning. Its characteristics are low space complexity and the ability to find a path from the starting vertex to the target vertex more quickly. However, there are disadvantages such as the possibility of entering an infinite loop when there is a loop in the graph, and low search efficiency for graphs with forks.

[0013] Intelligent algorithm. In a broad sense, intelligent algorithm refers to a type of algorithm or theory commonly used in engineering practice. Intelligent algorithm solves combinatorial optimization problems such as autonomous trajectory planning of drones by simulating certain phenomena in nature or the self-organizing behavior of biological groups. It has the characteristics of easy implementation, inspiration, and parallel processing. In daily research, if an algorithm can achieve the corresponding environment to solve a class or a type of problem, it can also be called an intelligent algorithm.

[0014] References

[0015] [1] Ke Shijie. UAV route planning method based on improved firefly algorithm[J]. Jiangxi Surveying and Mapping, 2024, (01): 9-11+15.

[0016] [2] Zeng Qing. Research on UAV path planning based on swarm intelligence algorithm[D]. Chongqing University of Technology, 2022. Summary of the invention

[0017] In view of the defects of the prior art, the present invention provides a route planning method for a surveying and mapping UAV based on an intelligent algorithm. The depth-first search algorithm is improved, the path repetition rate is reduced to improve the efficiency of the UAV surveying and mapping, and the search direction is controlled to jump out of the dead zone, thus overcoming the problems existing in the prior art.

[0018] In order to achieve the above invention object, the technical solution adopted by the present invention is as follows:

[0019] A route planning method for a surveying and mapping UAV based on an intelligent algorithm comprises the following steps:

[0020] S1: Construct the task environment model, which includes the following sub-steps:

[0021] S11: Environmental modeling was performed in a low-altitude outdoor environment in a mountainous area. The map was divided using a grid method to create a two-dimensional grid map, where the drone could perform extended search in eight directions. Each grid in the grid map represented a small area of ​​the environment.

[0022] S12: According to the actual outdoor low-altitude environment model in mountainous areas, additional constraints are added to the grid map. The density of bird flocks is the main factor affecting UAV mapping. The ratio of the number of grids occupied by bird flocks to the total number of grids is fitted as the density of bird flocks in the grid map, and it is included in the main constraints of UAV route planning.

[0023] S2: Plan the flight path of the drone, which is implemented through an improved depth-first search algorithm. The steps include:

[0024] S21: Select the current position of the UAV as the initial position node, and determine the coordinates of the target position node;

[0025] S22: Visit the current location node and mark it as visited to ensure that the node status is updated;

[0026] S23: Introduce the "bwlabel" function to constrain the drone's search direction and determine whether the location node has adjacent nodes;

[0027] S24: define the "F_Orient_OK5" function to determine the next valid passing position and perform deep exploration, recursively visit all unvisited adjacent position nodes from the current position node, and the "F_Orient_OK5" function reduces repeated traversal of the explored area by optimizing the search order;

[0028] S25: When all the adjacent position nodes of the current position node have been visited, backtrack to the previous position node, and use the "bwlabel" and "F_Orient_OK5" functions again to constrain the search direction and determine the effective passing position, continue to explore the unvisited position nodes, and repeat the above process until all position nodes have been visited;

[0029] S26: Based on the two-dimensional rasterized map obtained in step S1, an improved depth-first search algorithm is used to perform path planning, thereby obtaining a path planning result of the final surveying and mapping process.

[0030] Furthermore, the expression of the actual bird population density is:

[0031]

[0032] Among them, x is the grid contained in the grid map due to the bird flock factor, y is the total number of grids in the two-dimensional grid map, and ρ is the actual bird flock density.

[0033] Furthermore, the "bwlabel" function expression is:

[0034] L = bwlabel(BW,n)

[0035] Among them, n represents the connectivity parameter allowed to be specified. Common values ​​of n are 4 and 8. "4" represents simple connectivity that is only connected to the four neighbors above, below, left and right, while "8" includes eight neighbors and extends to the diagonal direction.

[0036] Furthermore, the implementation of the "F_Orient_OK5" function includes:

[0037] Define different movement priorities and dynamically adjust the search order based on actual obstacles and target locations;

[0038] Update the drone's heading in real time during the search process to avoid dead zones or repeated paths.

[0039] Furthermore, in step S26, the optimization of the path planning result further includes:

[0040] Smoothing the obtained preliminary path to reduce sharp turns and twists in the path;

[0041] The path is dynamically adjusted based on actual flight conditions to adapt to environmental changes and real-time data.

[0042] Furthermore, in step S21, determining the initial position node and the target position node includes:

[0043] Select the optimal initial position and target position according to the preset mission area and target coverage requirements;

[0044] Combined with GIS data, the initial and target positions are optimized to improve the efficiency and effectiveness of path planning.

[0045] Compared with the prior art, the advantages of the present invention are:

[0046] The execution efficiency and search efficiency of UAVs in complex environments have been significantly improved. These improvements not only improve the efficiency of UAVs in completing tasks, but also optimize their adaptability and responsiveness when facing complex real-world conditions, providing effective technical support for intelligent navigation in complex environments, which is specifically reflected in the following aspects:

[0047] Improved search efficiency: This paper introduces the "bwlabel" function and the "F_Orient_OK5" function to address the problem of the traditional depth-first search (DFS) algorithm being prone to dead loops and low search efficiency. These functions effectively control the search direction, prevent the drone from falling into a search dead zone, and reduce repeated searches of traversed areas, thereby improving search efficiency. This improvement not only saves energy consumption for drones, but also reduces unnecessary path planning, further improving task execution efficiency and operational performance.

[0048] Improve the versatility and stability of the algorithm: This invention adopts an improved DFS algorithm, which significantly reduces the number of parameters required to be adjusted by the algorithm and simplifies the parameter adjustment process compared to traditional intelligent algorithms. This design makes the algorithm more versatile and stable in a wider range of application scenarios, and can better meet the mapping needs of drones in complex environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is a flow chart of a method for unmanned aerial vehicle path planning based on an intelligent algorithm according to an embodiment of the present invention;

[0050] Figure 2A flowchart of the detailed steps of improving the depth-first search algorithm in an embodiment of the present invention;

[0051] Figure 3 This is a result diagram of establishing a two-dimensional grid map using the grid method in an embodiment of the present invention;

[0052] Figure 4 This is a working principle diagram of the "bwlabel" function in an embodiment of the present invention;

[0053] Figure 5 The working principle diagram of the direction search function "F_Orient_OK5" is defined in the embodiment of the present invention;

[0054] Figure 6 A two-dimensional grid environment modeling map for an embodiment of the present invention;

[0055] Figure 7 This is a diagram of the simulation results of the initial DFS algorithm of an embodiment of the present invention;

[0056] Figure 8 This is a simulation result diagram of the improved DFS algorithm without adding constraints in the embodiment of the present invention;

[0057] Fig. 9 This is a simulation result diagram of the improved DFS algorithm after adding airspace situation in an embodiment of the present invention. DETAILED DESCRIPTION

[0058] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and examples.

[0059] like Figure 1 As shown, the present invention provides a surveying and mapping UAV route planning method based on an intelligent algorithm, the steps are as follows:

[0060] S1, build the mission environment model and set the constraints of the UAV path planning based on the actual environment model;

[0061] S2, taking the location of the drone as the starting point and the target moving location as the end point, plans the flight path.

[0062] The specific sub-steps of step S1 include:

[0063] S11, for the application scenario, the environment modeling is performed outdoors at 120m in the mountainous area, and the map is divided by the grid method to establish a two-dimensional grid map ( Figure 3 ), the drone has a total of eight directions in which it can extend and expand its search.

[0064] S12, according to the actual mountain outdoor low-altitude environment model, additional constraints are added to the grid map, the density of bird flocks is taken as the main factor affecting UAV mapping, the ratio of the number of grids occupied by bird flocks to the total number of grids is fitted as the density of bird flocks in the grid map, and it is included in the main constraints of UAV route planning. Its expression is:

[0065]

[0066] Among them, x is the grid contained in the grid map due to the bird flock factor, y is the total number of grids in the two-dimensional grid map, and ρ is the actual bird flock density.

[0067] like Figure 2 As shown, in step S2, planning the flight path of the drone is achieved by improving the depth-first search algorithm, and the specific sub-steps include:

[0068] S21, select the current position of the UAV as the initial position node: start from an unvisited position node, and determine the coordinates of the initial position node and the target position node.

[0069] S22, visit position node: visit the current position node and mark it as visited.

[0070] S23, such as Figure 4 As shown in the figure, the "bwlabel" function is introduced to constrain the drone's search direction and determine whether the location node has adjacent nodes. Among them, "bwlabel" is a function commonly used in image processing in MATLAB, mainly used to process binary images. This function mainly marks and identifies the connected areas, and performs labeling and assignment processing on each connected domain in the binary image. Its expression is:

[0071] L = bwlabel(BW,n)

[0072] Among them, n represents the connectivity parameter allowed to be specified. Common values ​​of n are 4 and 8. "4" represents simple connectivity that is only connected to the four neighbors above, below, left and right, while "8" includes eight neighbors and extends to the diagonal direction.

[0073] By setting the connectivity parameter to "4", the search direction of the drone can be effectively constrained, changing its search direction to the four basic directions of up, down, left, and right.

[0074] S24, after determining that there are adjacent nodes, define a "F_Orient_OK5" function to determine the next valid passing position, and perform deep exploration, starting from the current position node, recursively visit all its unvisited adjacent position nodes.

[0075] like Figure 5As shown in the figure, the "F_Orient_OK5" function is designed to optimize the navigation decisions of mobile entities in grid-shaped maps. Its core function is to analyze the potential movement paths around the current location of the entity, and then determine the next valid and passable location. When it is impossible to move around, the function can give an error signal in time to prevent the mobile entity from getting into trouble.

[0076] Specifically, "F_Orient_OK5" optimizes path selection through a unique and innovative search order. The traditional search mode checks the surrounding moving directions in the order of "1→2→3→4". However, "F_Orient_OK5" breaks the convention and searches in the order of "1→3→2→4". This small but critical adjustment enables the function to quickly change the search direction when encountering obstacles or dead zones, thereby avoiding long wandering on invalid paths and significantly reducing repeated traversal of explored areas.

[0077] S25, backtracking: After all adjacent position nodes of the current position node have been visited, backtrack to the previous position node, and use the "bwlabel" and "F_Orient_OK5" functions again to constrain the search direction and determine the effective passing position, and continue to explore the unvisited position nodes.

[0078] S26, repeat: repeat the above process until all location nodes are visited.

[0079] S27, by using the two-dimensional rasterized map obtained in step S1, such as Figure 6 As shown, the above-mentioned improved DFS algorithm is used for path planning, thereby obtaining the path planning result of the final surveying and mapping process.

[0080] The application effect of the solution of this embodiment is explained below with a simulation experiment case.

[0081] Figure 7-9 The comparison charts of the running results of the initial depth-first search algorithm and the improved depth-first search algorithm are shown respectively.

[0082] Subsequently, in order to fit the actual working scenario of drone mapping, we considered the possible airspace situation, added bird density as the main influencing factor, and carried out route planning again. Fig. 9 The diagram shows the results of the improved depth-first search algorithm after adding airspace situation. In the map, obstacles are set as black grids, traversed grids are represented by number 1, repeated grids are represented by number 2, and grids with bird flock density as airspace situation are represented by number 3. Figure 7-9 The comparison between them verifies that the solution of this embodiment can improve the planning efficiency of the UAV path.

[0083] The embodiment of the present invention introduces three parameter indicators, namely the number of drone turns, step length and path repetition rate, to verify the feasibility and effectiveness of the solution.

[0084] During the UAV mapping process, the number of turns will directly affect energy consumption, and the limited endurance has become a bottleneck for rotary-wing UAVs in various applications. By optimizing route planning and reducing unnecessary turns, UAVs can complete mapping tasks more directly and quickly, thereby improving the overall execution efficiency of the task. The formula for calculating the number of turns is as follows:

[0085] M=M i +1

[0086] In the formula, M is the number of turns, and its value is accumulated from 0 until the end of the operation. The value obtained by assignment is the number of turns of the drone.

[0087] In order to clearly compare the difference between the algorithms before and after the improvement, the length of the path is also an important comparison condition, so the drone step length calculation is introduced. The step length formula is as follows:

[0088]

[0089] In the formula, P n is the coordinates of the path point on the grid map {x n ,y n}; ‖P n+1 -P n ‖ is P n+1 With its previous path point P n The Euclidean distance between them; N is the total number of path points.

[0090] Reducing the repetition rate of drone paths is crucial to improving mission efficiency, reducing energy consumption and costs. Through reasonable route planning, the mission completion rate can be effectively improved and the drone's endurance can be extended, while reducing the impact of the environment on data quality.

[0091] Define Q as the path repetition rate:

[0092]

[0093] Among them, c is the number of repeated grids, d is the total number of running grids, and Q is the path repetition rate. During the simulation experiment, the grids that are repeatedly traversed are marked as 2, and the grids that are only traversed once are marked as 1. The values ​​of c and d are obtained by accumulation, and the path repetition rate is further calculated.

[0094] Specifically, in order to ensure the accuracy of the scheme, 5 simulation experiments were carried out for each of the three schemes, and the average value of the experimental results for each scheme was calculated.

[0095] Table 1 shows the performance comparison results of the initial DFS, improved DFS, and improved DFS with airspace situation added. As can be seen from the table, the average execution time, average running step length, average path repetition rate, and average number of turns of the improved DFS algorithm are lower than those of the initial DFS algorithm. These data show that the improved DFS algorithm can complete route planning in a shorter time, significantly reduce the path repetition rate and number of turns, and effectively improve the efficiency and accuracy of path planning.

[0096] The data show that after adding the bird flock, the path repetition rate and the average path repetition rate of the improved DFS algorithm dropped to 18.3%. With the introduction of the bird flock as an obstacle and the reduction of the drone mapping area, the average running time, average step length and average number of turns decreased to a certain extent, which is consistent with the actual results.

[0097] Table 1

[0098]

[0099] The method according to the present invention described above can be implemented in hardware, firmware, or as software or computer code that can be stored in a recording medium (such as a CD ROM, RAM, floppy disk, hard disk or magneto-optical disk), or as computer code that is originally stored in a remote recording medium or a non-temporary machine-readable medium downloaded through a network and will be stored in a local recording medium, so that the method described herein can be stored in such software processing on a recording medium using a general-purpose computer, a dedicated processor or programmable or dedicated hardware (such as an ASIC or FPGA). It can be understood that a computer, a processor, a microprocessor controller or programmable hardware includes a storage component (e.g., RAM, ROM, flash memory, etc.) that can store or receive software or computer code, and when the software or computer code is accessed and executed by a computer, a processor or hardware, the mapping drone route planning method described herein is implemented. In addition, when a general-purpose computer accesses the code for implementing the processing shown herein, the execution of the code converts the general-purpose computer into a dedicated computer for executing the processing shown herein.

[0100] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the implementation methods of the present invention, and should be understood that the protection scope of the present invention is not limited to such special statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A route planning method for surveying and mapping UAV based on intelligent algorithm, characterized in that: The following steps are involved: S1: Construct the task environment model, which includes the following sub-steps: S11: Environmental modeling was performed in a low-altitude outdoor environment in a mountainous area. The map was divided using a grid method to create a two-dimensional grid map, where the drone could perform extended search in eight directions. Each grid in the grid map represented a small area of ​​the environment. S12: According to the actual outdoor low-altitude environment model in mountainous areas, additional constraints are added to the grid map. The density of bird flocks is the main factor affecting UAV mapping. The ratio of the number of grids occupied by bird flocks to the total number of grids is fitted as the density of bird flocks in the grid map, and it is included in the main constraints of UAV route planning. S2: Plan the flight path of the drone, which is implemented through an improved depth-first search algorithm. The steps include: S21: Select the current position of the UAV as the initial position node, and determine the coordinates of the target position node; S22: Visit the current location node and mark it as visited to ensure that the node status is updated; S23: Introduce the "bwlabel" function to constrain the drone's search direction and determine whether the location node has adjacent nodes; S24: Define the "F_Orient_OK5" function to determine the next valid passing position and perform deep exploration, recursively visiting all unvisited adjacent position nodes from the current position node, The "F_Orient_OK5" function reduces repeated traversal of the explored area by optimizing the search order; S25: When all the adjacent position nodes of the current position node have been visited, backtrack to the previous position node, and use the "bwlabel" and "F_Orient_OK5" functions again to constrain the search direction and determine the effective passing position, continue to explore the unvisited position nodes, and repeat the above process until all position nodes have been visited; S26: Based on the two-dimensional rasterized map obtained in step S1, an improved depth-first search algorithm is used to perform path planning, thereby obtaining a path planning result of the final surveying and mapping process.

2. The method for mapping UAV route planning according to claim 1, characterized in that: The expression of the actual bird flock density is: Among them, x is the grid contained in the grid map due to the bird flock factor, y is the total number of grids in the two-dimensional grid map, and ρ is the actual bird flock density.

3. The method for mapping UAV route planning according to claim 1, characterized in that: The "bwlabel" function expression is: L = bwlabel(BW,n) Among them, n represents the connectivity parameter allowed to be specified. Common values ​​of n are 4 and 8. "4" represents simple connectivity that is only connected to the four neighbors above, below, left and right, while "8" includes eight neighbors and extends to the diagonal direction.

4. The method for mapping UAV route planning according to claim 1, characterized in that: Said The implementation of the "F_Orient_OK5" function includes: Define different movement priorities and dynamically adjust the search order based on actual obstacles and target locations; Update the drone's heading in real time during the search process to avoid dead zones or repeated paths.

5. The method for mapping UAV route planning according to claim 1, characterized in that: In step S26, the optimization of the path planning result further includes: Smoothing the obtained preliminary path to reduce sharp turns and twists in the path; The path is dynamically adjusted based on actual flight conditions to adapt to environmental changes and real-time data.

6. The method for mapping UAV route planning according to claim 1, characterized in that: In step S21, the determination of the initial position node and the target position node includes: Select the optimal initial position and target position according to the preset mission area and target coverage requirements; Combined with GIS data, the initial and target positions are optimized to improve the efficiency and effectiveness of path planning.

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