A drone inspection path planning method based on attention mechanism

Abstract

This invention provides a drone inspection path planning method based on an attention mechanism. The method comprises the following steps: S1: Selecting drone inspection path planning training samples to construct a training set; S2: Initializing the inspection task information and drone battery status in the samples; S3: Designing encoding and decoding modules using the attention mechanism to construct a drone inspection path planning model with an encoding module-feature fusion module-decoding module structure; S4: Inputting the inspection task information and drone battery status into the model to obtain the drone's current time step inspection node, and updating the inspection task information and drone battery status; S5: Repeating S4 until all nodes in the sample have been inspected and a complete path is obtained, calculating the loss function value and updating the model parameters accordingly; S6: Training ends, and the model is applied to drone inspection path planning. Advantages: Based on the attention mechanism, it optimizes the quality and efficiency of path planning, making drone inspection more reliable and efficient.

Description

Technical Field

[0001] This invention belongs to the field of path planning, specifically relating to a method for UAV inspection path planning based on an attention mechanism. Background Technology

[0002] With the expansion of power systems and the development of artificial intelligence, drone-based inspections are gradually replacing traditional manual inspections due to their ability to effectively reduce inspection risks. The key to drone inspection tasks lies in how to plan the path for the drone to traverse all inspection points at the lowest cost. However, existing drone path planning algorithms often rely on manually designed features and struggle to handle large-scale tasks, necessitating more advanced drone path planning algorithms to improve the efficiency and quality of drone inspections. Summary of the Invention

[0003] To address the current problems in UAV inspection path planning, the present invention aims to provide an attention-based UAV inspection path planning method to improve the efficiency and reliability of path planning.

[0004] To achieve the above objectives, the present invention adopts the following technical solution:

[0005] A method for unmanned aerial vehicle (UAV) inspection path planning based on an attention mechanism includes the following steps:

[0006] S1: Select training samples for UAV inspection path planning and construct a training set;

[0007] S2: Initialize the inspection task information and drone battery status in the sample;

[0008] S3: Design the encoding and decoding modules separately using the attention mechanism, and construct a UAV inspection path planning model with an encoding module-feature fusion module-decoding module structure;

[0009] S4: Input the inspection task information and the drone's battery status into the planning model, calculate the drone's current time step inspection node, and update the inspection task information and drone's battery status accordingly.

[0010] S5: Repeat S4 until all nodes of the sample have been inspected and a complete path has been obtained. Calculate the loss function value and update the model parameters accordingly.

[0011] S6: After training, the model will be applied to the path planning task in the UAV inspection scenario.

[0012] Furthermore, in S1, the training samples consist of a specified number of inspection nodes, including the starting node and other nodes. The node coordinates are randomly generated from a two-dimensional region of [0,100]×[0,100].

[0013] Furthermore, in S2, the inspection task information includes node information and edge information. The node information of the i-th node is represented as follows: ,in These are the static two-dimensional coordinates of the node. This represents the access information for this node; the edge information between the i-th node and the j-th node is represented as... In the calculation, the Euclidean distance between the two points is used.

[0014] Furthermore, in S2, during the initialization process, the access information of the starting node... The access information for the drone is set to 0, while the access information for the other nodes is set to 1; the drone's battery status is initialized to a preset value. .

[0015] Furthermore, in S3, the encoding module takes the inspection task information as input and encodes it according to the following steps:

[0016] First, a high-dimensional embedding of node and edge information is computed using an embedding layer: , ,in, For node information High-dimensional embedding, For edge information High-dimensional embedding, This is the weight parameter matrix for the embedded layer nodes. This is the edge weight parameter matrix of the embedding layer. For the bias parameter matrix of the embedded layer nodes, The matrix represents the edge bias parameters of the embedding layer, and BN() is the layer normalization operation.

[0017] After the embedding layer, the high-dimensional embedding vector of the node is obtained. With edge high-dimensional embedding vector , where m is the total number of nodes in the sample.

[0018] Secondly, and The inputs are fed into L consecutive encoding units, and the final task feature representation output by the encoding module is obtained from the last encoding unit. These coding units have the same structure but do not share parameters. For the l-th coding unit, its input is... and The encoding unit first processes the data using an attention mechanism to obtain a fused feature vector: ,in, for and The fused feature vector, (.) represents a non-linear activation operation, and EMHA() represents the multi-head attention operation for edge fusion. Let be the attention weight parameter matrix for the l-th coding unit. Let be the attention bias parameter matrix for the l-th coding unit. This is an element-wise multiplication operation.

[0019] For the fused feature vector, the coding unit further processes it based on the feedforward operation to obtain the output feature vector of the l-th coding unit: ,in, Let be the output feature vector of the l-th coding unit, and FF() be the feedforward operation. Let be the feedforward weight parameter matrix of the l-th coding unit. Let be the feedforward bias parameter matrix of the l-th coding unit.

[0020] After the encoder encodes the input through L consecutive coding units, the final output task feature representation is obtained. .

[0021] Furthermore, the edge fusion multi-head attention operation includes the following steps:

[0022] For the input and First, the fusion compatibility value of the h-th attention head is calculated based on the multi-head attention mechanism: ,in, The compatibility value is calculated for the h-th attention head between node i and node j. for The number of vector dimensions, The edge fusion query value weight parameter matrix for node i. Let J be the edge fusion key-value weight parameter matrix for node j. This is a matrix transpose operation. For the input of node i, This is the input for node j.

[0023] Then, calculate the attention score: ,in, The attention score is calculated for the h-th attention head between node i and node j. For the attention score weight parameter matrix, For the attention scoring bias parameter matrix, This is a non-linear activation operation.

[0024] The final output is calculated as follows: ,in, Multi-head attention operation for edge fusion targeting input and The output result, where H is the number of attention heads in the multi-head attention mechanism. The edge fusion key-value weight parameter matrix for nodes. This is the attention bias parameter matrix for the coding unit.

[0025] Furthermore, in S3, the feature fusion module represents the UAV's battery status with mission characteristics. The dynamic feature values ​​are calculated as follows, using the input: , ,in, This represents the dynamic task features at time step t. Let be a 1×m dimensional vector corresponding to m nodes, where the value corresponding to the inspected nodes is 1 and the value corresponding to the uninspected nodes is 0; These are the dynamic feature values ​​output by the feature fusion module at time step t. `Concat(.)` performs a horizontal concatenation operation, and `max{.}` performs the maximum value operation. For the feature fusion weight parameter matrix, For the feature fusion bias parameter matrix, This represents the drone's battery status at time step t.

[0026] Furthermore, in S3, the decoding module uses dynamic feature values. With task feature representation As input, the current time step inspection node is determined as follows:

[0027] First, calculate the feature representation of the masking task: ,in, The masked task feature representation at time step t. This is the mask weight parameter matrix. This is the mask bias parameter matrix.

[0028] Then obtain the dynamic context embedding: ,in, This represents the dynamic context embedding at time step t, where mean{.} is the average value operation. This represents the task characteristics of the starting node. This represents the dynamic task features at time step t-1.

[0029] Then, the compatibility value is calculated based on the attention mechanism: ,in, Let C be the compatibility value of the i-th node, and C be a manually set constant. For the context query value weight parameter matrix, Here is the context key-value weight parameter matrix, and tanh(.) is the hyperbolic tangent function. Let i represent the task characteristics of node i.

[0030] For nodes that have already been visited, set their compatibility values. Set as .

[0031] Subsequently, based on the softmax operation, the probability value of the decoder selecting the i-th node as the node to be visited at the current time step is calculated: ,in, This represents the probability value that the model will select node i as the inspection node at the current time step t. Let be the compatibility value of the j-th node.

[0032] Furthermore, in S4, based on the probability values ​​of all uninspected nodes... The sampling method is used to select the nodes that the drone should inspect at the current time step t, and then the inspection action is performed. Afterwards, the drone's battery status was updated to... The access information f in the inspection task information is also updated accordingly, that is, the access information f corresponding to node i. The value was updated from 1 to 0.

[0033] Furthermore, in S5, after all inspection nodes have been visited, the complete path planning trajectory corresponding to sample s is obtained. ,in This indicates the final inspection action.

[0034] Furthermore, in S5, the method for updating model parameters is as follows:

[0035] First, calculate the trajectory reward: ,in, This indicates that the drone has completed its inspection. Energy consumption This represents the energy consumption required to return from the last inspection node to the starting node. For the model in parameters The trajectory reward obtained below.

[0036] Then, calculate the loss function value: ,in, Indicates the model in parameters The loss function value for sample s is as follows: Represents the loss function value with respect to parameters The gradient; For the model in parameters The probability of generating trajectory A for sample s is given below. This is the logarithmic gradient of the probability value; The expectation operator indicates that the model is in response to the parameters. The expected value of the generated trajectory A for sample s; For the baseline model in parameters The trajectory reward obtained is obtained by using the same UAV inspection path planning model structure as described above, but the nodes are selected in a greedy manner based on the probability value generated by the decoding module.

[0037] Finally, based on the loss function value, the parameters of the UAV inspection path planning model are updated using gradient descent.

[0038] Compared with the prior art, the beneficial effects achieved by the present invention are:

[0039] This invention employs an attention mechanism to design the encoding module, and integrates node information and edge information within it, thereby obtaining richer task feature representations;

[0040] This invention designs a feature fusion module that integrates the dynamic power status of the drone with the task feature representation, thereby enhancing the model's dynamic perception of the drone's power level.

[0041] This invention uses dynamic context embedding to improve the decoding module, overcoming the shortcomings of the original static embedding information, enhancing the model's dynamic perception capability, and thus improving the model's path planning quality for UAV inspection. Attached Figure Description

[0042] Figure 1 A schematic diagram of the unmanned aerial vehicle (UAV) inspection path planning model.

[0043] Figure 2 Example diagram of drone inspection path planning. Detailed Implementation

[0044] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to embodiments. It should be understood that the embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0045] S1: Select training samples for UAV inspection path planning and construct a training set. The training samples consist of a specified number of inspection nodes, including the starting node and other nodes. Node coordinates are randomly generated within a two-dimensional region of [0,100]×[0,100].

[0046] In this example, the training set constructed includes three node sizes, and the number of samples for each size is shown in Table 1.

[0047] Table 1 Three Node Sizes

[0048] Node size 10 20 50 Sample size 1280000 1280000 640000

[0049] S2: Initialize the inspection task information and UAV battery status in the sample. The inspection task information includes node information and edge information. The node information of the i-th node is represented as follows: ,in These are the static two-dimensional coordinates of the node. This represents the access information for this node; the edge information between the i-th node and the j-th node is represented as... In the calculation, the Euclidean distance between the two points is used.

[0050] During the initialization process, the access information of the starting node The access information for the drone is set to 0, while the access information for the other nodes is set to 1; the drone's battery status is initialized to a preset value. .

[0051] S3: Utilize attention mechanisms to design separate encoding and decoding modules, constructing a UAV inspection path planning model with an encoding module-feature fusion module-decoding module structure, such as... Figure 1 As shown;

[0052] The encoding module takes inspection task information as input and encodes it according to the following steps:

[0053] First, a high-dimensional embedding of node and edge information is computed using an embedding layer: , ,in, For node information High-dimensional embedding, For edge information High-dimensional embedding, This is the weight parameter matrix for the embedded layer nodes. This is the edge weight parameter matrix of the embedding layer. For the bias parameter matrix of the embedded layer nodes, The matrix represents the edge bias parameters of the embedding layer, and BN() is the layer normalization operation.

[0054] After the embedding layer, the high-dimensional embedding vector of the node is obtained. With edge high-dimensional embedding vector , where m is the total number of nodes in the sample.

[0055] Secondly, and The inputs are fed into L consecutive encoding units, where L is 3 in this example. The final task feature representation output by the encoding module is obtained from the last encoding unit. These coding units have the same structure but do not share parameters. For the l-th coding unit, its input is... and The encoding unit first processes the data using an attention mechanism to obtain a fused feature vector: ,in, for and The fused feature vector, (.) represents a non-linear activation operation, and EMHA() represents the multi-head attention operation for edge fusion. Let be the attention weight parameter matrix for the l-th coding unit. Let be the attention bias parameter matrix for the l-th coding unit. This is an element-wise multiplication operation.

[0056] The edge fusion multi-head attention operation includes the following steps:

[0057] For the input and First, the fusion compatibility value of the h-th attention head is calculated based on the multi-head attention mechanism: ,in, The compatibility value is calculated for the h-th attention head between node i and node j. for The number of vector dimensions, The edge fusion query value weight parameter matrix for node i. Let J be the edge fusion key-value weight parameter matrix for node j. This is a matrix transpose operation. For the input of node i, This is the input for node j.

[0058] Then, calculate the attention score: ,in, The attention score is calculated for the h-th attention head between node i and node j. For the attention score weight parameter matrix, For the attention scoring bias parameter matrix, This is a non-linear activation operation.

[0059] The final output is calculated as follows: ,in, Multi-head attention operation for edge fusion targeting input and The output result shows that H is the number of attention heads in the multi-head attention mechanism, which is 8 in this example. The edge fusion key-value weight parameter matrix for nodes. This is the attention bias parameter matrix for the coding unit.

[0060] For the fused feature vector, the coding unit further processes it based on the feedforward operation to obtain the output feature vector of the l-th coding unit: ,in, Let be the output feature vector of the l-th coding unit, and FF() be the feedforward operation. Let be the feedforward weight parameter matrix of the l-th coding unit. Let be the feedforward bias parameter matrix of the l-th coding unit.

[0061] After the encoder encodes the input through L consecutive coding units, the final output task feature representation is obtained. .

[0062] The feature fusion module represents the UAV's battery status and mission characteristics. The dynamic feature values ​​are calculated as follows, using the input: , ,in, This represents the dynamic task features at time step t. Let be a 1×m dimensional vector corresponding to m nodes, where the value corresponding to the inspected nodes is 1 and the value corresponding to the uninspected nodes is 0; These are the dynamic feature values ​​output by the feature fusion module at time step t. `Concat(.)` performs a horizontal concatenation operation, and `max{.}` performs the maximum value operation. For the feature fusion weight parameter matrix, For the feature fusion bias parameter matrix, This represents the drone's battery status at time step t.

[0063] The decoding module uses dynamic feature values With task feature representation As input, the current time step inspection node is determined as follows:

[0064] First, calculate the feature representation of the masking task: ,in, The masked task feature representation at time step t. This is the mask weight parameter matrix. This is the mask bias parameter matrix.

[0065] Then obtain the dynamic context embedding: ,in, This represents the dynamic context embedding at time step t, where mean{.} is the average value operation. This represents the task characteristics of the starting node. This represents the dynamic task features at time step t-1.

[0066] Then, the compatibility value is calculated based on the attention mechanism: ,in, Let be the compatibility value of the i-th node. C This is a constant set by the user; in this example, it is set to 10. For the context query value weight parameter matrix, Here is the context key-value weight parameter matrix, and tanh(.) is the hyperbolic tangent function. Let i represent the task characteristics of node i.

[0067] For nodes that have already been visited, set their compatibility values. Set as .

[0068] Subsequently, based on the softmax operation, the probability value of the decoder selecting the i-th node as the node to be visited at the current time step is calculated: ,in, This represents the probability value that the model will select node i as the inspection node at the current time step t. Let be the compatibility value of the j-th node.

[0069] S4: Input the inspection task information and the drone's battery status into the model, calculate the drone's current time step inspection node, and update the inspection task information and drone's battery status accordingly.

[0070] Among them, the probability values ​​of all uninspected nodes. The sampling method is used to select the nodes that the drone should inspect at the current time step t, and then the inspection action is performed. Afterwards, the drone's battery status was updated to... The access information f in the inspection task information is also updated accordingly, that is, the access information f corresponding to node i. The value was updated from 1 to 0.

[0071] S5: Repeat S4 until all nodes of the sample have been inspected and a complete path has been obtained. Calculate the loss function value and update the model parameters accordingly.

[0072] After all inspection nodes have been visited, the complete path planning trajectory corresponding to sample s is obtained. ,in This indicates the final inspection action.

[0073] S6: After training, apply the model to the path planning task in the drone inspection scenario;

[0074] The method for updating model parameters is as follows:

[0075] First, calculate the trajectory reward: ,in, This indicates that the drone has completed its inspection. Energy consumption This represents the energy consumption required to return from the last inspection node to the starting node. For the model in parameters The trajectory reward obtained below.

[0076] Then, calculate the loss function value: ,in, Indicates the model in parameters The loss function value for sample s is as follows: Represents the loss function value with respect to parameters The gradient; For the model in parameters The probability of generating trajectory A for sample s is given below. This is the logarithmic gradient of the probability value; The expectation operator indicates that the model is in response to the parameters. The expected value of the generated trajectory A for sample s; For the baseline model in parameters The trajectory reward obtained is obtained by using the same UAV inspection path planning model structure as described above, but the nodes are selected in a greedy manner based on the probability value generated by the decoding module.

[0077] Finally, based on the loss function value, the parameters of the UAV inspection path planning model are updated using gradient descent.

[0078] In this example, the UAV inspection path planning model was trained for 100 rounds. After training, it was tested using a public dataset at different node scales. The results of the path planning task are shown in Table 2.

[0079] Table 2 Results of Path Planning Task

[0080]

[0081] The trained UAV inspection path planning model is tested using a single test sample, such as... Figure 2 As shown, the UAV inspection path planning method based on the attention mechanism proposed in this invention can effectively solve the UAV path planning problem and help improve the reliability and efficiency of UAV inspection.

Claims

1. A method for unmanned aerial vehicle (UAV) inspection path planning based on an attention mechanism, characterized in that, Includes the following steps: S1: Select training samples for UAV inspection path planning and construct a training set; S2: Initialize the inspection task information and drone battery status in the sample; S3: An encoding and decoding module are designed separately using an attention mechanism, constructing a UAV inspection path planning model with an encoding module-feature fusion module-decoding module structure; the feature fusion module represents the UAV's battery status and task features. The dynamic feature values ​​are calculated as follows, using the input: , ,in, This represents the dynamic task features at time step t. Let be a 1×m dimensional vector corresponding to m nodes, where the value corresponding to the inspected nodes is 1 and the value corresponding to the uninspected nodes is 0; These are the dynamic feature values ​​output by the feature fusion module at time step t. `Concat(.)` performs a horizontal concatenation operation, and `max{.}` performs the maximum value operation. For the feature fusion weight parameter matrix, For the feature fusion bias parameter matrix, The drone's battery status at time step t; S4: Input the inspection task information and the drone's battery status into the planning model, calculate the drone's current time step inspection node, and update the inspection task information and drone's battery status accordingly. S5: Repeat S4 until all nodes of the sample have been inspected and a complete path has been obtained. Calculate the loss function value and update the model parameters accordingly. S6: After training, the model will be applied to the path planning task in the UAV inspection scenario.

2. The UAV inspection path planning method based on attention mechanism according to claim 1, characterized in that, In S1, the training samples consist of a specified number of inspection nodes, including the starting node and other nodes, and the node coordinates are randomly generated from a two-dimensional region of [0,100]×[0,100].

3. The UAV inspection path planning method based on attention mechanism according to claim 1, characterized in that, In S2, the inspection task information includes node information and edge information, where the node information of the i-th node is represented as follows: , where x i These are the static two-dimensional coordinates of the node. f i This represents the access information for this node; the edge information between the i-th node and the j-th node is represented as... e ij In the calculation, the Euclidean distance between the two points is used; In S2, during the initialization process, the access information of the starting node... f 0 is set to 0, and the access information of the other nodes is set to 1; The drone's battery status was initialized to a preset value. q 0.

4. The UAV inspection path planning method based on attention mechanism according to claim 1, characterized in that, In S3, the encoding module takes the inspection task information as input and encodes it according to the following steps: First, a high-dimensional embedding of node and edge information is computed using an embedding layer: , , where n i 0 For node information n i High-dimensional embedding, e for edge information ij High-dimensional embedding, This is the weight parameter matrix for the embedded layer nodes. This is the edge weight parameter matrix of the embedding layer. b n For the bias parameter matrix of the embedded layer nodes, b e The edge bias parameter matrix of the embedding layer. BN () represents the layer normalization operation; After the embedding layer, the high-dimensional embedding vector of the node is obtained. With edge high-dimensional embedding vector , where m is the total number of nodes in the sample; Secondly, n 0 and The inputs are fed into L consecutive encoding units, and the final task feature representation output by the encoding module is obtained from the last encoding unit. n L These coding units have the same structure but do not share parameters. For the l-th coding unit, its input is... and The encoding unit first processes the data using an attention mechanism to obtain a fused feature vector: ,in, for and The fused feature vector, (.) represents a non-linear activation operation. EMHA () represents the multi-head attention operation for edge fusion. Let be the attention weight parameter matrix for the l-th coding unit. Let be the attention bias parameter matrix for the l-th coding unit. This is an element-wise multiplication operation; For the fused feature vector, the coding unit further processes it based on the feedforward operation to obtain the output feature vector of the l-th coding unit: ,in, Let l be the output feature vector of the l-th coding unit. FF () represents a feedforward operation. Let be the feedforward weight parameter matrix of the l-th coding unit. Let L be the feedforward bias parameter matrix of the l-th coding unit; After the encoder encodes the input through L consecutive coding units, the final output task feature representation is obtained. n L .

5. The UAV inspection path planning method based on attention mechanism according to claim 4, characterized in that, The edge fusion multi-head attention operation includes the following steps: For the input and First, the fusion compatibility value of the h-th attention head is calculated based on the multi-head attention mechanism: ,in, The compatibility value is calculated for the h-th attention head between node i and node j. for The number of vector dimensions, The edge fusion query value weight parameter matrix for node i. Let J be the edge fusion key-value weight parameter matrix for node j. This is a matrix transpose operation. For the input of node i, For the input of node j; Then, calculate the attention score: ,in, The attention score is calculated for the h-th attention head between node i and node j. For the attention score weight parameter matrix, For the attention scoring bias parameter matrix, This is a non-linear activation operation; The final output is calculated as follows: ,in, Multi-head attention operation for edge fusion targeting input and The output result, where H is the number of attention heads in the multi-head attention mechanism. The edge fusion key-value weight parameter matrix for nodes. This is the attention bias parameter matrix for the coding unit.

6. The UAV inspection path planning method based on attention mechanism according to claim 1, characterized in that, In S3, the decoding module uses dynamic feature values. With task feature representation As input, the current time step inspection node is determined as follows: First, calculate the feature representation of the masking task: ,in, The masked task feature representation at time step t. This is the mask weight parameter matrix. This is the mask bias parameter matrix; Then obtain the dynamic context embedding: ,in, This represents the dynamic context embedding at time step t, where mean{.} is the average value operation. This represents the task characteristics of the starting node. This represents the dynamic task features at time step t-1. Then, the compatibility value is calculated based on the attention mechanism: ,in, Let C be the compatibility value of the i-th node, and C be a manually set constant. For the context query value weight parameter matrix, Here is the context key-value weight parameter matrix, and tanh(.) is the hyperbolic tangent function. Let i be the task feature representation; For nodes that have already been visited, set their compatibility values. Set as ; Subsequently, based on the softmax operation, the decoder calculates the probability value of selecting the i-th node as the node visited at the current time step: ,in, This represents the probability value that the model will select node i as the inspection node at the current time step t. Let be the compatibility value of the j-th node.

7. The UAV inspection path planning method based on attention mechanism according to claim 1, characterized in that, In S4, based on the probability values ​​of all uninspected nodes... The sampling method is used to select the nodes that the drone should inspect at the current time step t, and then the inspection action is performed. Afterwards, the drone's battery status was updated to... The access information f in the inspection task information is also updated accordingly, that is, the f corresponding to node i. i The value was updated from 1 to 0.

8. The UAV inspection path planning method based on attention mechanism according to claim 1, characterized in that, In S5, after all inspection nodes have been visited, the complete path planning trajectory corresponding to sample s is obtained. .

9. The UAV inspection path planning method based on attention mechanism according to claim 1, characterized in that, In S5, the method for updating model parameters is as follows: First, calculate the trajectory reward: ,in, This indicates that the drone has completed its inspection. energy consumption This represents the energy consumption required to return from the last inspection node to the starting node. For the model in parameters The trajectory reward obtained below; Then, calculate the loss function value: ,in, This represents the loss function value of the model for sample s under parameters θ. This represents the gradient of the loss function value with respect to the parameter θ; Let θ be the probability value of the model generating trajectory A for sample s. This is the logarithmic gradient of the probability value; The expectation operator indicates that the model is in response to the parameters. The expected value of the generated trajectory A for sample s; For the baseline model in parameters The trajectory reward obtained is obtained by using the same UAV inspection path planning model structure as described above, but the nodes are selected in a greedy manner based on the probability values ​​generated by the decoding module. Finally, based on the loss function value, the parameters of the UAV inspection path planning model are updated using gradient descent.

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