An unmanned aerial vehicle trajectory planning method for fan blade inspection task

Abstract

This invention discloses a UAV trajectory planning method for wind turbine blade inspection tasks. Applicable to wind turbine blade inspection, it provides efficient and feasible inspection paths. When the UAV deviates from the planned path due to external forces, the method also has the ability to quickly provide a new planned path. The approach involves designing a loss function and using backward dynamic programming to solve the trajectory based on the inspection environment and task requirements, followed by secondary planning optimization. Given prior information on the wind turbine's size and location, this invention plans an efficient and feasible inspection path. Combined with image information, it maintains good replanning capabilities even when the UAV deviates from its path, providing good samples for further inspection. Compared to manual control and simple point-based planning methods, it has higher applicability and robustness.

Description

Technical Field

[0001] This invention belongs to the field of unmanned aerial vehicle (UAV) inspection technology, specifically relating to a UAV trajectory planning method for wind turbine blade inspection tasks. Background Technology

[0002] In recent years, the use of drones for inspecting wind power infrastructure has received widespread attention. Drone inspection has enormous potential to increase the frequency and accuracy of inspections, helping maintenance personnel to identify problems early and shifting from "passive maintenance" to "proactive improvement." Timely detection of potential faults and prevention effectively improves equipment reliability and saves costs. In scenarios relying on autonomous drone inspections, the autonomous planning function of the drone inspection path is crucial. A well-designed planner that can plan safe, efficient, and intelligent inspection trajectories is of great significance for improving the safety, reliability, and effectiveness of drone inspections of wind turbine blades.

[0003] To achieve automated inspection of wind turbine blades using drones, a search revealed Chinese Patent Publication No. CN114740895A, which provides a drone-based method for planning inspection paths for wind turbine blades. This method involves manually controlling the turbine to the hub center and identifying the angles between each blade and the vertical direction, then setting a straight inspection path based on this data. Another Chinese Patent Publication No. CN115586789A discloses a vision-based method for confirming hovering points and conducting inspections using a drone. This method involves a drone carrying an aerial camera taking multiple photos along a circular route relatively far from the wind turbine. Existing technologies involve some manual operations, resulting in low automation levels, high skill requirements for personnel, and high inspection costs. Furthermore, the planners have low path planning intelligence, easily generating invalid and duplicate data, making data processing and classification difficult, thus impacting inspection efficiency.

[0004] In scenarios relying on drones for autonomous inspection, there are high requirements for the autonomous planning function of drone inspection paths. A well-designed planner that can plan safe, efficient and intelligent inspection trajectories is of great significance for improving the safety, reliability and effectiveness of drone inspection of wind turbine blades. Summary of the Invention

[0005] To address the aforementioned issues, this invention discloses a UAV trajectory planning method for wind turbine blade inspection tasks. This method is applicable to wind turbine blade inspection tasks and can provide efficient and feasible inspection paths. When the UAV deviates from the planned path due to external forces, the method also has the ability to quickly provide a new planned path, thereby improving the safety, feasibility, and reliability of UAV inspections.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] A method for UAV trajectory planning for wind turbine blade inspection tasks includes the following steps:

[0008] (1) Based on the shape of the wind turbine blades, a planning reference line and a trajectory planning space are selected based on the decoupled UAV motion mode;

[0009] (2) Sampling of path points is carried out according to the inspection task requirements and imaging equipment information;

[0010] (3) Construct a path planning loss function based on the dynamic characteristics of the UAV and the requirements of the inspection task, and calculate the cost value of each path;

[0011] (4) The optimal path is solved based on the backward dynamic programming method, and intermediate results are retained during the calculation process for replanning.

[0012] In step (1), the planning reference line and trajectory planning space are selected based on the shape of the wind turbine blades. The specific steps are as follows:

[0013] (1.1) The inspection path of the UAV can be considered as a general direction from one end of the blade to the other, with a certain radial offset around the reference line depending on the specific location of the inspection point. Therefore, the motion of the UAV is decoupled into longitudinal motion along the reference line and radial motion at a certain position in the longitudinal direction of the reference line that is radially offset from the reference line.

[0014] (1.2) Based on the decoupling of motion in (1.1), a reference line can be set along the longitudinal direction of the UAV's motion, i.e. from the starting point of the UAV at the blade root to the inspection endpoint at the blade tip. The relationship between the UAV and its surrounding environment can be evaluated within the framework constructed by the reference line.

[0015] (1.3) Define the planning space. Construct a Frenet frame based on the reference lines specified in (1.1) and the motion analysis in (1.2). Evaluate the relationship between the UAV and its surrounding environment, i.e., the planning space, within the frame constructed by the reference lines. The minimum safe distance r between the UAV and the blade during the inspection operation is determined. min and the maximum distance requirement r between the blade and the imaging equipment under the limitations of imaging quality. max The cylindrical planning space is set according to these maximum and minimum distances to ensure the feasibility of each point within the space.

[0016] In step (2), path point sampling is performed based on the inspection task requirements and imaging equipment information. The specific steps are as follows:

[0017] (2.1) Taking the reference line as the direction of advance, starting from the starting point, cut out normal planes of a certain size at certain intervals on the reference line, set them as the sampling point levels, and form a sampling point set;

[0018] (2.2) Uniform sampling is performed at each sampling point level, and path points of the same cross section are treated as one layer;

[0019] (2.3) For each sampling point on each layer, record its location information and layer information, and record its connectivity information with each point in the upper and lower adjacent layers; the information contained in each sampling point includes: location coordinates, connectivity information with each sampling point in the upper layer, and connectivity information with each sampling point in the lower layer.

[0020] In step (3), a path planning loss function is constructed based on the UAV's dynamic characteristics and inspection task requirements, and the cost value of each path is calculated. The specific steps are as follows:

[0021] (3.1) Feasibility factors: Multi-rotor UAVs must operate within their maneuverability limits, while minimizing entry into dangerous areas, especially at the root of wind turbine blades and the connection between the turbine hub and blades; positioning and control errors of the UAV must also be considered, and redundancy should be added in collision detection and spatial planning; feasibility constraints will be quantified by considering trajectory smoothness.

[0022] C smooth (f)=w1∫(f′(s)) 2 ds+w2∫(f″(s)) 2 ds+w3∫(f″′(s))2 d s

[0023] Where s is the offset distance of the UAV's radial motion, the first derivative f′(s) represents the velocity of the UAV's radial motion, the second derivative f″(s) represents the acceleration of the UAV's radial motion, the third derivative f″′(s) represents the jerk of the UAV's radial motion, this term mainly characterizes the stability of the UAV's radial maneuver, and w1, w2, w3 represent the weights of each value.

[0024] Interaction with obstacles:

[0025]

[0026] Where C obs (d) represents the obstacle interaction loss cost related to the obstacle distance d, where d is the current distance between the drone and the obstacle. n To account for the maximum distance threshold that takes obstacle factors into account, i.e., when the distance to an infeasible area exceeds this threshold, obstacle factors are not considered, and this loss cost is set to 0 to reduce computation; d c The minimum safe distance threshold from obstacles is defined as the threshold at which a danger is considered to occur when the distance to an inaccessible area is less than this threshold. A larger loss cost value C is assigned. collision To prevent the path from getting stuck in this situation; C nudge A function for calculating the loss cost when the distance to the obstacle is within the normal range;

[0027] The objective function considers the smoothness of the trajectory, the distance to obstacles including wind turbine blades, and the degree of deviation from the reference line, and combines these three factors with certain weights to construct an operational efficiency constraint loss function.

[0028] C total (f(s)=w1C smooth (f)+w2C obs (f)+w3C guidance (f)

[0029] Where C total C represents the total loss cost. smooth C represents the cost of smoothing loss. obs C represents the cost of interacting with obstacles. guidance The cost value represents the amount of loss due to deviation from the reference line, where w1, w2, and w3 represent the weights of each cost value, satisfying the following:

[0030] And 0 < w i ≤1; i = 1, 2, 3

[0031] (3.2) Consider optimizing the inspection path as much as possible while meeting the task requirements, shortening the length of the inspection trajectory as much as possible, and selecting the most regular and continuous inspection trajectory so that the UAV can follow the trajectory well with the least possible maneuver cost.

[0032] (3.3) When the sampling points at both ends of the path to be connected to the loss function are located on both sides of the obstacle, it is determined whether a collision has occurred by calculating whether the connecting line intersects with the surface of the obstacle. If the connecting line between the two inspection points intersects with the surface of the obstacle, it can be determined that a collision has occurred, and it is necessary to resample in the candidate track area and reconnect the inspection points.

[0033] (3.4) The entire inspection trajectory will consist of n segments of flight trajectory connecting n+1 inspection points. The overall loss function will be the sum of the loss functions constructed from the n segments of flight trajectory.

[0034] In step (4), the optimal path is solved based on the backward dynamic programming method. The specific steps are as follows:

[0035] (4.1) Each level can be viewed as a multi-stage optimization problem. A dynamic programming framework is constructed to solve the optimization problem of the multi-stage decision-making process, transforming the multi-stage decision-making problem into a series of single-stage optimization problems. Thus, finding the optimal path is transformed into finding the optimal strategy. Given the value of the state variable x(k) at stage k, if the decision variable of this stage is determined, the state variable x(k+1) of stage k+1 is also completely determined. That is, the value of x(k+1) changes with the values ​​of x(k) and the decision u(k) at stage k. This relationship can be seen as a correspondence between (x(k), u(k)) and x(k+1), i.e.:

[0036] x(k+1)=Tk(x(k),u(k))

[0037] Where Tk represents the state transition function from stage k to stage k+1. Specifically, in this path planning problem, x(k+1) is the optimal cost value for a node in layer k+1 to reach the destination, x(k) is the optimal cost value for the predecessor node of this node in layer k on the optimal path to reach the destination, and u(k) is the optimal strategy in this stage, i.e., the path loss cost value for connecting these two nodes. Thus, the state transition equation for this problem is:

[0038] x(k+1)=x(k)+u(k)

[0039] (4.2) Using backward dynamic programming, starting from the endpoint, obtain the optimal path from each path node to the endpoint. According to Bellman's optimization principle, for the initial state x1∈X1, the strategy... The necessary and sufficient condition for an optimal strategy is that for any k, 1 < k < n, we have:

[0040]

[0041] like If it is the optimal policy, then for any k, 1 < k < n, its sub-policies are... *For x1 and Determined For the k-th to n-th subsequent subprocesses starting from this point, this is also the optimal strategy. Based on this inference, the fundamental equation of dynamic programming can be obtained:

[0042]

[0043] Where f n+1 (x n+1 The condition ) = 0 is the boundary condition of the decision-making process. In solving the optimal path problem, the loss cost value of the starting state in the recursion is set to 0, so that the recursive equation has a starting point for recursion. It is the optimal state. That is, for each stage traversed by the optimal path, the path from the starting point of each stage to the end point of the entire process must be the optimal path among all possible paths from the starting point of that stage to the end point of the entire process;

[0044] (4.3) Record the intermediate calculation results of the backward dynamic programming, that is, the optimal path from each intermediate point to the destination is retained. After the UAV is deviated from the original path by external force, find the intermediate point with the closest distance according to the position coordinates and quickly obtain the optimal path from the intermediate point to the current destination.

[0045] (4.4) After traversing all nodes, each node obtains the next node in the optimal path from itself to the destination. At this point, the optimal path for the UAV to reach the destination from any point can be obtained in constant time complexity.

[0046] The beneficial effects of this invention are:

[0047] To address the issues of low automation and reliance on manual experience in current UAV-based remote control inspections or simple point-marking straight-line inspections, this invention proposes a novel UAV trajectory planning method for wind turbine blade inspection. This method provides efficient and feasible inspection paths and can quickly generate new paths when the UAV deviates from the planned path due to external forces. The approach involves designing a loss function and using backward dynamic programming to solve the trajectory based on the inspection environment and task requirements, followed by secondary planning optimization. This invention plans efficient and feasible inspection paths based on prior information about the wind turbine's size and location. The image information captured at the inspection points effectively reflects the surface information of the wind turbine blades and demonstrates good replanning capability when the UAV deviates from its trajectory, providing good samples for further inspection. Compared to manual control and simple point-marking planning methods, this method has higher applicability and robustness, and significant engineering value. Attached Figure Description

[0048] Figure 1 A flowchart of a UAV trajectory planning method for wind turbine blade inspection tasks;

[0049] Figure 2 A schematic diagram illustrating the relationship between the drone reference lines, the planned space, and the actual environment;

[0050] Figure 3 This is a schematic diagram of the path point sampling process. Detailed Implementation

[0051] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the present invention.

[0052] like Figure 1 The diagram shown is a schematic representation of the method flow of the present invention.

[0053] The present invention provides a UAV trajectory planning method for wind turbine blade inspection tasks, which can improve the safety, reliability, and effectiveness of UAV inspection of wind turbine blades, and includes the following steps:

[0054] (1) Based on the shape of the wind turbine blades, a planning reference line and a trajectory planning space are selected based on the decoupled UAV motion mode;

[0055] (2) Sampling of path points is carried out according to the inspection task requirements and imaging equipment information;

[0056] (3) Construct a path planning loss function based on the dynamic characteristics of the UAV and the requirements of the inspection task, and calculate the cost value of each path;

[0057] (4) The optimal path is solved based on the backward dynamic programming method, and intermediate results are retained during the calculation process for replanning.

[0058] In step (1), the planning reference line and trajectory planning space are selected according to the shape of the wind turbine blades. The specific steps are as follows:

[0059] (1.1) The inspection path of the UAV can be considered as a general direction from one end of the blade to the other, with a certain radial offset around the reference line depending on the specific location of the inspection point. Therefore, the motion of the UAV is decoupled into longitudinal motion along the reference line and radial motion at a certain position in the longitudinal direction of the reference line that is radially offset from the reference line.

[0060] (1.2) Based on the decoupling of motion in (1.1), a reference line is set along the longitudinal direction of the UAV's motion, i.e., from the starting point of the UAV at the blade root to the inspection endpoint at the blade tip. The reference line information specifically includes the position coordinates of the starting point and the endpoint, including latitude and longitude coordinates and altitude information, such as the reference line starting point (31.4926175N,120.7609971E,15.7H) and the reference line endpoint (31.4926179N,120.7609980E,16.3H). The relationship between the UAV and its surrounding environment is evaluated within the framework constructed by the reference line.

[0061] (1.3) Define the planning space. Construct a Frenet frame based on the reference lines specified in (1.1) and the motion analysis in (1.2). Evaluate the relationship between the UAV and its surrounding environment, i.e., the planning space, within the frame constructed by the reference lines. The minimum safe distance r between the UAV and the blade during the inspection operation is determined. min And the maximum distance r between the blade and the imaging equipment under imaging quality limitations maxThe cylindrical planning space, set according to these maximum and minimum distances, ensures the feasibility of each point within the space. Based on the size information of the UAV and wind turbine used in this embodiment, the minimum safe distance r is determined. min The distance is set to 2 meters. Based on the imaging equipment used in this embodiment, which produces 12-megapixel images with a resolution of 4000*3000, and the inspection task requirement of detecting damage at the millimeter-wide level, it can be deduced that the length and width of the wind turbine surface area captured by the drone in each imaging session cannot exceed 4 meters * 3 meters. Therefore, the maximum distance estimate r is calculated based on the camera's field of view information. max It can be set to 5 meters, and the planning space and reference line diagram are as follows: Figure 2 .

[0062] In step (2), path point sampling is performed according to the inspection task requirements and imaging equipment information. The specific steps are as follows:

[0063] (2.1) Taking the reference line as the direction of travel, starting from the starting point, intercept normal planes of a certain size at certain intervals along the reference line, and set them as the sampling point levels, forming a sampling point set L{L1, L2, ..., L... N In this embodiment, the spacing is set to 0.5 meters based on the requirements of the inspection task. For a 1.5MW wind turbine with a blade length of about 35 meters, 70 sampling points can be sampled.

[0064] (2.2) Uniform sampling is performed at each sampling point level to obtain the sampling point set P{p} of the current layer. 11 p 12 , ..., p mn}, and treat path points on the same cross section as one layer;

[0065] (2.3) For each sampling point on each layer, record its location information and layer information, and record its connectivity information with each point in the upper and lower adjacent layers; the information contained in each sampling point includes: location coordinates, connectivity information with each sampling point in the upper layer, and connectivity information with each sampling point in the lower layer. For example, in this embodiment, the information of a certain sampling point includes the layer number (17 layers), the sequence in the current layer ([6, 3]), location coordinates (31.4926175N, 120.7609971E, 15.7H), sampling point layer, and uniform sampling. Figure 3 .

[0066] In step (3), a path planning loss function is constructed based on the UAV's dynamic characteristics and inspection task requirements, and the cost value of each path is calculated. The specific steps are as follows:

[0067] (3.1) Feasibility factors: Multi-rotor UAVs must operate within their maneuverability limits, while minimizing entry into dangerous areas, especially at the root of wind turbine blades and the connection between the turbine hub and blades; positioning and control errors of the UAV must also be considered, and redundancy should be added in collision detection and spatial planning; feasibility constraints will be quantified by considering trajectory smoothness.

[0068] C smooth (f)=w1∫(f′(s)) 2 ds+w2∫(f″(s)) 2 ds+w2∫(f″′(s)) 2 ds

[0069] Where s is the offset distance of the UAV's radial motion, the first derivative f′(s) represents the velocity of the UAV's radial motion, the second derivative f″(s) represents the acceleration of the UAV's radial motion, the third derivative f″′(s) represents the jerk of the UAV's radial motion, this term mainly characterizes the stability of the UAV's radial maneuver, and w1, w2, w3 represent the weights of each value.

[0070] Interaction with obstacles:

[0071]

[0072] Where C obs (d) represents the obstacle interaction loss cost related to the obstacle distance d, where d is the current distance between the drone and the obstacle. n To account for the maximum distance threshold that takes obstacle factors into account, i.e., when the distance to an infeasible area exceeds this threshold, obstacle factors are not considered, and this loss cost is set to 0 to reduce computation; d c The minimum safe distance threshold from obstacles is defined as the threshold at which a danger is considered to occur when the distance to an inaccessible area is less than this threshold. A larger loss cost value C is assigned. collision To prevent the path from getting stuck in this situation; C nudge To calculate the loss cost function when the distance to the obstacle is within the normal range, we examine the square of the distance and constrain the range of cost values ​​using weighting coefficients.

[0073] and the degree of deviation from the reference line:

[0074] C guidancs (f)=∫(f(s)-g(s)) 2 ds

[0075] The objective function will consider the smoothness of the trajectory, the distance relationship with obstacles including wind turbine blades, and the degree of deviation from the reference line. The three factors will be combined with certain weights to construct an operational efficiency constraint loss function:

[0076] Ctotal (f(s))=w1C smooth (f)+w2C obs (f)+w3C guidance (f);

[0077] Where C total C represents the total loss cost. smooth C represents the cost of smoothing loss. obs C represents the cost of interacting with obstacles. guidance The cost value represents the amount of loss due to deviation from the reference line, where w1, w2, and w3 represent the weights of each cost value, satisfying the following:

[0078] And 0 < w i ≤1; i = 1, 2, 3

[0079] (3.2) Consider optimizing the inspection path as much as possible while meeting the task requirements, shortening the length of the inspection trajectory as much as possible, and selecting the most regular and continuous inspection trajectory so that the UAV can follow the trajectory well with minimal maneuvering cost:

[0080] S(t i )≤S(t i+1 ), i = 0, 1, 2, ..., n-1

[0081]

[0082] S′(ti)≤V upper

[0083] -Dec max ≤S″(t i )≤Acc max

[0084] -J max ≤S″′(t i )≤J max

[0085] (3.3) When the sampling points at both ends of the path to be connected to the loss function are located on both sides of the obstacle, the collision with the obstacle is determined by calculating whether the connecting line intersects with the surface of the obstacle. If the connecting line between the two inspection points intersects with the surface of the obstacle, it can be determined that a collision has occurred, and it is necessary to resample in the candidate track area and reconnect the inspection points.

[0086] (3.4) The entire inspection trajectory will consist of n segments of flight trajectory connecting n+1 inspection points. The overall loss function will be the sum of the loss functions constructed from the n segments of flight trajectory.

[0087]

[0088] In step (4), the optimal path is solved based on the backward dynamic programming method. The specific steps are as follows:

[0089] (4.1) Each level can be viewed as a multi-stage optimization problem. A dynamic programming framework is constructed to solve the optimization problem of the multi-stage decision-making process, transforming the multi-stage decision-making problem into a series of single-stage optimization problems. Thus, finding the optimal path is transformed into finding the optimal strategy. Given the value of the state variable x(k) at stage k, if the decision variable of this stage is determined, the state variable x(k+1) of stage k+1 is also completely determined. That is, the value of x(k+1) changes with the values ​​of x(k) and the decision u(k) at stage k. This relationship can be seen as a correspondence between (x(k), u(k)) and x(k+1), i.e.:

[0090] x(k+1)=Tk(x(k),u(k))

[0091] Where Tk represents the state transition function from stage k to stage k+1. Specifically, in this path planning problem, x(k+1) is the optimal cost value for a node in layer k+1 to reach the destination, x(k) is the optimal cost value for the predecessor node of this node in layer k on the optimal path to reach the destination, and u(k) is the optimal strategy in this stage, i.e., the path loss cost value for connecting these two nodes. Thus, the state transition equation for this problem is:

[0092] x(k+1)=x(k)+u(k)

[0093] In this embodiment, only the loss function constructed in step (3) connecting these two nodes is used as the decision variable for this stage, that is:

[0094] x(k+1)=x(k)+C total (k+1, k)

[0095] (4.2) Using backward dynamic programming, starting from the endpoint, obtain the optimal path from each path node to the endpoint. According to Bellman's optimization principle, for the initial state x1∈X1, the strategy... The necessary and sufficient condition for an optimal strategy is that for any k, 1 < k < n, we have:

[0096]

[0097] like If it is the optimal policy, then for any k, 1 < k < n, its sub-policies are... *For x1 and Determined For the k-th to n-th subsequent subprocesses starting from this point, this is also the optimal strategy. Based on this inference, the fundamental equation of dynamic programming can be obtained:

[0098]

[0099] Where f n+1 (x n+1 The condition ) = 0 is the boundary condition of the decision-making process. In solving the optimal path problem, the loss cost value of the starting state in the recursion is set to 0, so that the recursive equation has a starting point for recursion. It is the optimal state. That is, for each stage traversed by the optimal path, the path from the starting point of each stage to the end point of the entire process must be the optimal path among all possible paths from the starting point of that stage to the end point of the entire process.

[0100] (4.3) Record the intermediate calculation results of the backward dynamic programming, that is, the optimal path from each intermediate point to the destination is retained. After the UAV deviates from the original path due to external force, find the intermediate point with the closest distance matching according to the position coordinates, and quickly obtain the optimal path from the intermediate point to the current destination. If the deviation distance between the UAV and the original path point is too large, use the UAV's current position coordinates (x, y, h) in the sampling point set in step (2) to match the nearest sampling point coordinates (x1, y1, h1) with the position distance. Through the level number L1 and the sequence [r1, c1] of the sampling point in the level, the optimal path to the destination is found from the intermediate calculation results retained when using dp operation starting from the point.

[0101] (4.4) After traversing all nodes, each node obtains the next node in the optimal path from itself to the destination. At this point, the optimal path for the UAV to reach the destination from any point can be obtained in constant time complexity.

[0102] It should be noted that the above content merely illustrates the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principle of the present invention, and all such improvements and modifications fall within the scope of protection of the claims of the present invention.

Claims

1. A method for UAV trajectory planning for wind turbine blade inspection tasks, characterized in that, Includes the following steps: (1) Based on the shape of the wind turbine blades, select the planning reference line and delineate the trajectory planning space according to the decoupled UAV motion mode; (2) Sampling of path points is carried out according to the requirements of the inspection task and the information of the imaging equipment; (3) Construct a path planning loss function based on the dynamic characteristics of the UAV and the requirements of the inspection task, and calculate the cost value of each path; The specific steps are as follows: (3.1) Feasibility factors: Multi-rotor UAVs must operate within their maneuverability limits. Care must be taken to minimize entry into the dangerous area at the root of the wind turbine blades, where the turbine hub connects to the blades. Simultaneously, the positioning and control errors of the UAV must be considered, and redundancy should be added during collision detection and spatial planning. Feasibility constraint quantification will consider trajectory smoothness. ； Where s is the offset distance of the UAV's radial motion, and the first derivative term The second derivative represents the radial velocity of the UAV. The third derivative of the acceleration representing the radial motion of the UAV. This represents the jerk of the drone's radial motion, which characterizes the stability of the drone's radial maneuvers. Indicates the weight of each value; Interaction with obstacles: ； in Distance to the obstacle Related obstacle interaction loss costs, The current distance between the drone and the obstacle. To account for the maximum distance threshold that takes into account obstacles, i.e., when the distance to an infeasible area exceeds this threshold, the obstacle factor is not considered, and this loss cost is set to 0 to reduce computation. A minimum safe distance threshold from obstacles is set, meaning a danger is considered to have occurred when the distance to an inaccessible area is less than this threshold, and a larger loss cost value is assigned. To prevent the path from getting stuck in this situation; A function for calculating the loss cost when the distance to the obstacle is within the normal range; The objective function considers the smoothness of the trajectory, the distance to obstacles including wind turbine blades, and the degree of deviation from the reference line, and combines these three factors with certain weights to construct an operational efficiency constraint loss function. ； in This represents the total loss cost. This represents the cost of smoothing loss. This represents the cost of interacting with obstacles. This indicates the cost value lost due to deviation from the reference line. The weights of each cost value are represented, satisfying: ； (3.2) Consider optimizing the inspection path as much as possible while meeting the task requirements, shortening the length of the inspection trajectory as much as possible, and selecting the most regular and continuous inspection trajectory so that the UAV can follow the trajectory well with the least possible maneuver cost. (3.3) When the sampling points at both ends of the path to be connected to the loss function are located on both sides of the obstacle, it is determined whether a collision has occurred with the obstacle by calculating whether the connecting line intersects with the surface of the obstacle. If the connecting line between the two inspection points intersects with the surface of the obstacle, it is determined that a collision has occurred, and it is necessary to resample in the candidate track area and reconnect the inspection points. (3.4) The entire inspection trajectory will consist of n segments of flight trajectory connecting n+1 inspection points, and the overall loss function will be the sum of the loss functions constructed from the n segments of flight trajectory; (4) Solve for the optimal path based on the backward dynamic programming method, and retain intermediate results for replanning during the calculation process. The specific steps are as follows: (4.1) Treat each level as a multi-stage optimization problem, construct a dynamic programming framework to solve the optimization problem of the multi-stage decision-making process, and transform the multi-stage decision-making problem into a series of single-stage optimization problems. In this way, finding the optimal path is transformed into finding the optimal strategy, given k stage state variables. After the value is determined, if the decision variable for this stage is determined, the state variable for stage k+1... Therefore, it is completely certain that... The value varies and the decision in stage k The value changes as the relationship changes. and A definite correspondence, namely: ； in Let represent the state transition function from stage k to stage k+1; specifically, in this path planning problem... Let $\frac{k+1}{k+1}$ be the optimal cost value for a node to reach the destination. This represents the optimal cost value for the predecessor node of this node at level k on the optimal path to reach the destination. The optimal strategy for this stage is the path loss cost that connects the two nodes. Therefore, the state transition equation for this problem is: ； (4.2) Using backward dynamic programming, starting from the endpoint, obtain the optimal path from each path node to the endpoint; according to Bellman's optimization principle, for the initial state... ,Strategy The necessary and sufficient condition for a strategy to be optimal is that for any k, ,have: ； like If it is the optimal strategy, then for any k, Its sub-strategy *For those by and Determined For the kth to nth subsequent subprocesses starting from the optimal point, this is also the optimal strategy. Based on this inference, the fundamental equation of dynamic programming is obtained: ； in These are boundary conditions for the decision-making process. In solving this optimal path problem, the loss cost of the starting state in the recursion is set to 0, ensuring that the recursive equation has a starting point. It is the optimal state, that is, for each stage traversed by the optimal path, the path from the start point of each stage to the end point of the whole process must be the optimal path among all possible paths from the start point of that stage to the end point of the whole process. (4.3) Record the intermediate calculation results of the backward dynamic programming, that is, the optimal path from each intermediate point to the destination is retained. After the UAV is deviated from the original path by external force, find the intermediate point with the closest distance according to the position coordinates and quickly obtain the optimal path from the intermediate point to the current destination. (4.4) After traversing all nodes, each node obtains the next node in the optimal path from itself to the destination. At this time, the optimal path from any point to the destination of the UAV is obtained in a constant time complexity.

2. The UAV trajectory planning method for wind turbine blade inspection tasks according to claim 1, characterized in that, In step (1), the planning reference line and trajectory planning space are selected according to the shape of the wind turbine blades. The specific steps are as follows: (1.1) The inspection path of the UAV is considered to be a radial movement along the direction from one end of the blade to the other, with a certain radial offset around the reference line according to the specific position of the inspection point. Therefore, the movement of the UAV is decoupled into longitudinal movement along the reference line and radial movement that is radially offset from the reference line at a certain position in the longitudinal direction of the reference line. (1.2) Based on the decoupling of motion in (1.1), a reference line is set along the longitudinal direction of the UAV's motion, i.e. from the starting point of the UAV at the leaf root to the inspection endpoint at the leaf tip. The relationship between the UAV and its surrounding environment is evaluated within the framework constructed by the reference line. (1.3) Define the planning space. Based on the reference lines specified in (1.1) and the motion analysis in (1.2), construct a Frenet frame. Evaluate the relationship between the UAV and its surrounding environment, i.e., the planning space, within the frame constructed by the reference lines. Based on the minimum safe distance between the UAV and the blades during the inspection operation... And the estimation of the maximum distance to the blade under the imaging quality limitations of the imaging equipment. The cylindrical planning space is set according to these maximum and minimum distances to ensure the feasibility of each point within the space.

3. The UAV trajectory planning method for wind turbine blade inspection tasks according to claim 1, characterized in that, In step (2), path point sampling is performed according to the inspection task requirements and imaging equipment information. The specific steps are as follows: (2.1) Taking the reference line as the direction of travel, starting from the starting point, intercept normal planes of a certain size on the reference line at certain intervals, and set them as the sampling point layers to form a sampling point layer set. ; (2.2) Uniform sampling is performed at each sampling point level, and path points of the same cross section are treated as one layer; (2.3) For each sampling point on each layer Record its location and hierarchy information, and record its connectivity information with each point in the upper and lower adjacent layers; finally, the information contained in each sampling point includes: location coordinates, connectivity information with each sampling point in the upper layer, and connectivity information with each sampling point in the lower layer.

Images