An underground pipe gallery detection method based on UAV point cloud scanning

Through drone point cloud scanning and SLAM algorithm, combined with GNSS technology, the problem of difficulty in accurately mapping large buried deep underground pipeline corridors is solved, and the real spatial location mapping of underground pipeline corridors is realized, providing reliable data support for urban management.

CN119986687BActive Publication Date: 2025-06-17QINGDAO INST OF SURVEYING & MAPPING SURVEY
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Patent Information

Application Number
CN202510457505.9
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-04-14
Publication Date
2025-06-17
Estimated Expiration
2045-04-14

AI Technical Summary

Technical Problem

Traditional measurement methods are difficult to accurately and efficiently obtain the real spatial location of underground pipeline corridors with large buried depths and harsh environments, affecting the operation and maintenance management, safety monitoring and disaster warning of pipeline corridors.

Method used

The drone is used to obtain continuous spatial point cloud data of the ground and underground pipeline corridors, and the point cloud under the relative coordinate system is solved through the SLAM algorithm, and the point cloud is converted to the absolute coordinate system using the GNSS control points collected in advance on the ground to draw a floor plan of the underground pipeline corridor.

Benefits of technology

It realizes accurate surveying and mapping of the real spatial location of underground pipeline corridors, provides reliable data support for urban planning and pipeline corridor maintenance, and improves detection efficiency and safety.

✦ Generated by Eureka AI based on patent content.

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Abstract

The present invention relates to the field of underground pipe gallery space detection, and specifically relates to an underground pipe gallery detection method based on UAV point cloud scanning, including Step 1: Deploying reflectors and collecting the three-dimensional coordinates of the reflectors in the absolute coordinate system; Step 2: Conducting three-dimensional laser scanning during the flight of the UAV to collect point clouds at the entrance of the underground pipe gallery. The lidar carried by the UAV collects spatial point cloud data, and the visual sensor records environmental image information; Step 3: Establishing a relative coordinate system with spatial feature association and performing point cloud SLAM solution; Step 4: Based on the SLAM algorithm, calculating the continuous spatial point clouds on the ground and underground, and extracting the three-dimensional coordinates in the scanned point clouds; Step 5: Applying the Rodrigues matrix transformation method to transform the point clouds in the relative coordinate system to the absolute coordinate system; Step 6: Obtaining the true spatial position information of the underground pipe gallery. Through continuous scanning by the UAV and combined with ground GNSS measurement, the true spatial position of the underground pipe gallery in the absolute coordinate system is obtained.
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Description

Technical Field

[0001] The present invention relates to the field of underground utility tunnel space detection, and particularly to a detection method for underground utility tunnels based on drone point cloud scanning. Background Art

[0002] As an important part of urban municipal infrastructure, underground utility tunnels undertake multiple functions such as water supply, drainage, communication, and power supply, and have a very important impact on the normal operation of the city and the quality of residents' lives. The accurate mapping of their spatial positions is of great significance for planning, maintenance management, and renovation. However, with the acceleration of the urbanization process and the in-depth development of underground space, the spatial layout of utility tunnels has become increasingly complex. Especially for underground utility tunnels with large burial depths, their environments are usually very harsh, with not only insufficient light and poor air quality, but also possible problems such as narrow structures and dense obstacles. For underground utility tunnels with large burial depths and harsh environments, traditional measurement methods often cannot accurately and efficiently obtain the spatial information of the utility tunnels, which not only affects the daily operation and maintenance management of the utility tunnels, but also may have an adverse impact on safety monitoring, hidden danger investigation, and disaster warning.

[0003] Therefore, how to break through the limitations of traditional technologies and explore an efficient, accurate, and low-risk detection method has become an urgent problem to be solved in the current field of underground utility tunnel management. Summary of the Invention

[0004] Aiming at the problems in the prior art that in the detection of underground utility tunnels, especially for the detection of underground utility tunnels with large burial depths and harsh environments, traditional measurement methods are difficult to comprehensively and accurately obtain the true spatial positions of underground utility tunnels, the purpose of the present invention is to provide a detection method for underground utility tunnels based on drone point cloud scanning, which uses a drone to obtain continuous spatial point cloud data of the ground and underground utility tunnels, solves the point cloud in the relative coordinate system through the SLAM algorithm, and uses the GNSS control points collected in advance on the ground to convert the point cloud into the absolute coordinate system, and finally draws drawings such as the plan view of the underground utility tunnel to obtain the true spatial position of the underground utility tunnel.

[0005] To achieve the above purpose, the technical solution adopted by the present invention is: a detection method for underground utility tunnels based on drone point cloud scanning, including the following steps:

[0006] Step 1: Arrange ground reflectors, and use a GNSS receiver to collect the three-dimensional coordinates of the reflectors in the absolute coordinate system in the PTK mode;

[0007] Step 2: Install a lidar on the drone, connect the signal extension cable to the remote controller. When the drone is flying, perform three-dimensional lidar scanning synchronously to collect point cloud data at the entrance of the underground utility tunnel. The scanning range covers all the reflectors. Place the terminal of the signal extension cable into the utility tunnel, and control the drone to enter the underground utility tunnel through the entrance. The lidar carried by the drone collects spatial point cloud data, and the vision sensor records environmental image information;

[0008] Step 3: Extract feature points in the environment through the vision sensor, combine with the point cloud features of the lidar, establish a relative coordinate system with spatial feature association, and perform point cloud SLAM solution according to state update and observation update;

[0009] Step 4: Based on the SLAM algorithm, calculate the continuous spatial point cloud on the ground and underground. Utilize the difference in reflection intensity between the reflector and the surrounding environment in the point cloud to extract the three-dimensional coordinates of the reflector in the scanned point cloud under the relative coordinate system;

[0010] Step 5: Determine the conversion parameters and the conversion process, and apply the Rodrigues matrix conversion method to convert the point cloud under the relative coordinate system to the absolute coordinate system;

[0011] Step 6: Based on the converted point cloud, intercept a point cloud slice in the view. After adjusting the slice to the top view state, draw the plan view of the underground utility tunnel along the point cloud trajectory, and overlay the plan view with the topographic map to obtain the true spatial position information of the underground utility tunnel.

[0012] In the above underground utility tunnel detection method based on drone point cloud scanning, in Step 1, the ground reflector is a square reflector with a side length of 1 decimeter, and there are 4 such ground reflectors. The 4 ground reflectors are evenly distributed in a quadrilateral shape in space according to the size of the underground utility tunnel.

[0013] In the above underground utility tunnel detection method based on drone point cloud scanning, in Step 3, the establishment of the relative coordinate system with spatial feature association includes dynamically updating the relative position of the drone in space based on the Kalman filter algorithm and constructing a three-dimensional map of the environment.

[0014] In the above underground utility tunnel detection method based on drone point cloud scanning, in Step 3: The state update is expressed as: , where represents the current drone state, represents the drone state at the previous positioning moment, represents the control input of the current state, represents the noise;

[0015] The observation update is expressed as: , where represents the observation value, Represents the environmental map, Represents the observation noise.

[0016] For the above underground utility tunnel detection method based on UAV point cloud scanning, step 3 includes: By continuously iterating the state update equation and the observation update equation, the SLAM algorithm simultaneously optimizes the environmental map and the UAV position , dynamically updates the relative position of the UAV in space, and constructs a three-dimensional map of the environment.

[0017] For the above underground utility tunnel detection method based on UAV point cloud scanning, in step 5, the conversion parameters include three translation parameters , the scaling ratio parameter , three rotation parameters , and the conversion process includes translation, rotation, and scaling.

[0018] For the above underground utility tunnel detection method based on UAV point cloud scanning, step 5 includes:

[0019] Step 5-1: Establish a conversion process model: , where represents the rotation matrix, and determines the parameters of 4 ground reflectors that coexist in the absolute space coordinate system and the relative space coordinate system;

[0020] Step 5-2: Construct an anti-symmetric matrix S, , where represents the independent elements of the Rodrigues matrix;

[0021] Step 5-3: The rotation matrix R forms the Rodrigues matrix M from the anti-symmetric matrix S:

[0022] ,

[0023] ,

[0024] ;

[0025] Step 5-4: Subtract the equations of two adjacent ground reflectors to eliminate the translation parameters, and obtain the property equation according to the properties of the anti-symmetric matrix and the Rodrigues matrix: , where is the third-order identity matrix, represents the matrix transpose, represents the matrix inversion;

[0026] Step 5-5: Substitute the property equation into the equation obtained by subtracting two adjacent ground reflectors to obtain the subtraction equation:

[0027] ;

[0028] Step 5-6: Order , sorting out the subtraction equations to get the final equation:

[0029] ;

[0030] Step 5-7: Repeat steps 5-1 to 5-6 to calculate the final equation between the remaining two adjacent ground reflection pieces, combine the two final equations, solve the independent parameters of the transformation matrix, substitute the scale parameter and the rotation parameter into the transformation process model, and solve the translation parameter;

[0031] Step 5-8: Apply the transformation process model point by point to complete the transformation of all point cloud data in the relative coordinate system obtained by the drone to the absolute coordinate system.

[0032] The beneficial effect of the underground pipe gallery detection method based on drone point cloud scanning of the present invention is as follows: the present invention uses a drone equipped with a laser radar to continuously scan the space from the ground to the underground pipe gallery, and combines ground GNSS measurement, and applies the Rodrigues matrix conversion method to obtain the real spatial position of the underground pipe gallery in the absolute coordinate system, providing reliable data support for urban planning and underground pipe gallery maintenance and transformation. The signal extension line is used to solve the communication problem between the drone and the ground remote control when flying in the underground pipe gallery; the drone continuously flies from the ground to the inside of the underground pipe gallery, and based on the SLAM algorithm, the point cloud data of the continuous space from the ground to the underground pipe gallery is calculated. By arranging 4 reflectors near the entrance of the ground pipe gallery, and using GNSS measurement to obtain its three-dimensional coordinates in the absolute coordinate system, the corresponding relative coordinates of the reflectors are extracted in the drone scanning point cloud, and the Rodrigues matrix conversion method is applied to match the relative point cloud to the absolute coordinate system, thereby obtaining the real spatial position information of the underground pipe gallery. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 A schematic diagram of on-site operations for the implementation of the present invention;

[0034] Figure 2 It is a flow chart of field operations implemented by the present invention. DETAILED DESCRIPTION

[0035] In order to enable those skilled in the art to better understand the technical solution of the present invention, the technical solution of the present invention is described below in conjunction with specific implementation methods and drawings.

[0036] Example 1

[0037] In recent years, with the development of drone technology, drones integrated with lidar have gradually become an important tool for spatial exploration. To solve the problems in the detection of underground utility tunnels, especially for those with large burial depths and harsh environments, where traditional surveying methods are difficult to comprehensively and accurately obtain the true spatial positions of underground utility tunnels, the present invention proposes a method for detecting underground utility tunnels by using a drone lidar to scan and collect continuous spatial point cloud data on the ground and underground, and combining it with the ground GNSS high-precision positioning technology.

[0038] A method for detecting underground utility tunnels based on drone point cloud scanning includes at least the following steps.

[0039] 1. Layout of ground reflectors and GNSS measurement. Four reflectors are laid out on the ground near the manhole covers of the underground utility tunnel, and the reflectors are evenly distributed in a quadrilateral shape in space. A GNSS receiver is used to collect the three-dimensional coordinates of the four reflectors in the absolute coordinate system by using operation methods such as the RTK mode.

[0040] 2. Drone flight operation and three-dimensional laser scanning. Prepare the drone on the ground before takeoff. Install a lidar on the drone body, connect the signal extension cable to the remote controller, start the drone, first remotely control the drone to fly on the ground and synchronously perform three-dimensional laser scanning so that the scanning range covers the four reflectors. Then remotely control the drone to fly into the underground utility tunnel through the manhole cover. At this time, place the signal extension cable into the tunnel, observe the internal situation of the tunnel through the high-definition camera on the drone body, and remotely control the drone to fly along the tunnel direction. After the flight task is completed, remotely control the drone to return to the ground and land and stop flying.

[0041] 3. Point cloud SLAM solution. During the flight of the drone, the lidar collects spatial point cloud data, and at the same time, the visual sensor on the body records the environmental image information. Feature points in the environment are extracted through the visual sensor, and at the same time, combined with the point cloud features of the lidar, spatial feature associations are established. Then, based on the Kalman filter algorithm, the relative position of the drone in space is dynamically updated, and a three-dimensional map of the environment is constructed.

[0042] 4. Extract the coordinates of the reflectors in the drone scan point cloud. After the continuous spatial point cloud on the ground and underground is calculated based on the SLAM algorithm, the three-dimensional coordinates of the four reflectors are manually extracted by using the difference in the reflection intensity between the reflectors and the surrounding environment in the point cloud. Since the obtained point cloud is in the relative coordinate system, the three-dimensional coordinates of the reflectors extracted are also the results in the relative coordinate system.

[0043] 5. Apply the Rodrigues matrix transformation method to convert the point cloud in the relative coordinate system scanned by the UAV to the absolute coordinate system. According to the three-dimensional coordinates of the reflectors in the absolute coordinate system measured by the GNSS receiver on-site and the three-dimensional coordinates of the reflectors in the relative coordinate system extracted from the UAV point cloud, apply the Rodrigues matrix transformation method to convert the relative point cloud obtained by the UAV to the absolute coordinate system.

[0044] 6. Drawing of drawings such as floor plans. Based on the converted point cloud, intercept a point cloud slice with an appropriate thickness in the side view, and after adjusting the slice to the top view state, draw the floor plan of the underground utility tunnel along the point cloud trajectory. Use the same method to draw drawings such as sectional views, and overlay the floor plan with the topographic map to obtain the true spatial position information of the underground utility tunnel.

[0045] Embodiment 2

[0046] As Figure 1 - Figure 2 shown, a detection method for underground utility tunnels based on UAV point cloud scanning includes the following steps.

[0047] Step 1: Layout ground reflectors and use a GNSS receiver to collect the three-dimensional coordinates of the reflectors in the absolute coordinate system in the PTK mode.

[0048] Layout 4 square reflectors with a side length of 1 decimeter on the ground near the manhole covers on the ground of the underground utility tunnel, such as Figure 1 A, B, C, and D in. The 4 reflectors are evenly distributed in a quadrilateral in space and have an appropriate spacing. If the spacing is too far, the subsequent UAV flight scanning time will be long, affecting the effective operation flight time. If the spacing is too short, it will affect the subsequent coordinate conversion accuracy. Use a GNSS receiver to collect the three-dimensional coordinates of the 4 reflectors in the absolute coordinate system by operating methods such as the RTK mode: , , , .

[0049] Step 2: Prepare the UAV for takeoff on the ground. Install a lidar on the UAV body, connect the signal extension cable to the remote controller, start the UAV, first remotely control the UAV to fly on the ground, synchronously perform three-dimensional laser scanning, and collect point clouds around the ground perimeter of the manhole cover entrance of the underground utility tunnel so that the scanning range covers the 4 reflectors. Then remotely control the UAV to fly into the underground utility tunnel through the manhole cover. At this time, place the terminal of the signal extension cable into the tunnel, such as Figure 1 E in. Observe the internal situation of the tunnel through the high-definition camera on the UAV body, and remotely control the UAV to fly along the tunnel direction. After the flight task is completed, remotely control the UAV to return to the ground and land and stop flying. The lidar carried by the UAV collects spatial point cloud data, and the vision sensor records environmental image information.

[0050] Step 3: Point cloud SLAM solution. Extract feature points in the environment through the vision sensor, combine with the point cloud features of the lidar, establish a relative coordinate system for spatial feature association, and perform point cloud SLAM solution according to state update and observation update. Establishing a relative coordinate system for spatial feature association includes dynamically updating the relative position of the UAV in space based on the Kalman filter algorithm and constructing a three-dimensional map of the environment

[0051] During the flight of the UAV, the lidar collects spatial point cloud data, and at the same time, the vision sensor on the fuselage records environmental image information. Feature points in the environment are extracted through the vision sensor, and at the same time, combined with the point cloud features of the lidar, spatial feature association is established. In this process, the core of SLAM positioning lies in solving two problems: state update and observation update. The state update can be expressed as:

[0052] (1),

[0053] In Equation (1), is the current UAV state, is the UAV state at the previous positioning moment, is the control input of the current state, is the noise.

[0054] The observation update can be expressed as:

[0055] (2),

[0056] In Equation (2), is the observation value, is the environmental map, is the observation noise. By continuously iterating the above two equations, the SLAM algorithm can optimize the environmental map and the UAV position at the same time, so as to realize the dynamic update of the relative position of the UAV in space and construct a three-dimensional map of the environment.

[0057] Step 4: Extract the reflector coordinates in the scanned point cloud, solve the continuous spatial point cloud on the ground and underground based on the SLAM algorithm, and use the difference in the reflection intensity of the reflector and the surrounding environment in the point cloud to extract the three-dimensional coordinates of the reflector in the relative coordinate system.

[0058] Manually extract the three-dimensional coordinates of 4 reflectors: 、 、 、 , because the obtained point cloud is in the relative coordinate system, the three-dimensional coordinates of the extracted reflectors are also the results in the relative coordinate system.

[0059] Step 5: Determine the conversion parameters and process, and apply the Rodrigues matrix conversion method to convert the point cloud in the relative coordinate system to the absolute coordinate system.

[0060] To convert the point cloud in the relative coordinate system collected by the drone to the absolute coordinate system, processes such as translation, rotation, and scaling are required, and it is necessary to determine , seven parameters.

[0061] Specifically, it includes:

[0062] Step 5-1: Establish a conversion process model. The transformation process can be represented by the following mathematical model:

[0063] (3),

[0064] In Equation (3), where represents the rotation matrix, which is composed of three rotation parameters and respectively represent the angles of rotation around the X, Y, and Z axes. Determine the parameters of the 4 ground reflectors that exist in both the absolute space coordinate system and the relative space coordinate system. There are 4 common points A, B, C, and D in the two coordinate systems. The 7 parameters are uniquely determined and can be directly solved. 9 elements in the rotation matrix R are determined by 3 angles, so only 3 are independent.

[0065] Step 5-2: Construct the skew-symmetric matrix S, (4), where represents the independent elements of the Rodrigues matrix.

[0066] Step 5-3: The rotation matrix R is composed of the skew-symmetric matrix S to form the Rodrigues matrix M:

[0067] (5),

[0068] In Equation (5),

[0069] (6),

[0070] (7).

[0071] During the calculation, first calculate the scale parameter, then solve the rotation matrix, and finally calculate the translation parameter. To calculate the scale parameter, take the coordinates of two common points in the two coordinate systems and calculate the ratio of the corresponding side lengths in reverse. After repeating the calculation for multiple pairs of common points, take the average value to improve the accuracy of the scale parameter. As can be seen from Equation (3), a set of 3 equations can be listed for each pair of common points. 12 equations can be listed on the 4 reflectors. Subtract the equation of reflector B from the equation of reflector A to eliminate the translation parameter, and then perform subsequent calculations based on the properties of the skew-symmetric matrix and the Rodrigues matrix.

[0072] Step 5-4: Subtract the equations of two adjacent ground reflectors to eliminate the translation parameters, and obtain the property equation according to the properties of the skew-symmetric matrix and the Rodrigues matrix: , where is a third-order identity matrix, represents matrix transpose, represents matrix inversion, which is the inverse matrix of the original matrix.

[0073] Step 5-5: Substitute the property equation into the equation obtained by subtracting two adjacent ground reflectors to get the subtraction equation:

[0074] .

[0075] Step 5-6: Let , and organize the subtraction equation to obtain the final equation:

[0076] .

[0077] Then subtract the equation listed on reflector D from the equation listed on reflector C to obtain a set of equations similar to Equation (11). Combine with Equation (11) to solve for the 3 independent parameters of the transformation matrix. Finally, substitute the scale parameter and the rotation parameter into Equation (3) to solve for the translation parameter. Apply the transformation formula (3) to all the point cloud data in the relative coordinate system obtained by the UAV point by point to complete the transformation of the point cloud data to the absolute coordinate system.

[0078] Specifically:

[0079] Step 5-7: Repeat Steps 5-1 to 5-6 to calculate the final equations between the remaining two adjacent ground reflectors, combine the two final equations, solve for the independent parameters of the transformation matrix, substitute the scale parameter and the rotation parameter into the transformation process model, and solve for the translation parameter.

[0080] Step 5-8: Apply the transformation process model to all the point cloud data in the relative coordinate system obtained by the UAV point by point to complete the transformation of the point cloud data to the absolute coordinate system.

[0081] Step 6: Draw drawings such as the plan view. Based on the transformed point cloud, intercept a point cloud slice in the view. After adjusting the slice to the top view state, trace the plan view of the underground pipe gallery along the point cloud trajectory. Overlay the plan view with the topographic map to obtain the true spatial position information of the underground pipe gallery.

[0082] Specifically, intercept a point cloud slice with an appropriate thickness in the side view. After adjusting the slice to the top view state, trace the plan view of the underground pipe gallery along the point cloud trajectory. Use the same method to trace drawings such as the cross-sectional view. Overlay the plan view with the topographic map to obtain the true spatial position information of the underground pipe gallery.

[0083] The above embodiments are only for illustrating the inventive concept and features of the present invention, and are intended to enable those of ordinary skill in the art to understand the content of the present invention and implement it accordingly, and should not be used to limit the protection scope of the present invention. Any equivalent changes or modifications made according to the essence of the content of the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for detecting underground pipe corridors based on drone point cloud scanning, characterized in that: The following steps are involved: Step 1: Lay out ground reflectors and use a GNSS receiver in PTK mode to collect the three-dimensional coordinates of the reflectors in an absolute coordinate system; Step 2: Install a laser radar on the drone, connect the signal extension line to the remote control, and perform 3D laser scanning while the drone is flying to collect point cloud data at the entrance of the underground corridor. The scanning range covers all reflectors, and the terminal of the signal extension line is placed in the corridor. The drone is controlled to enter the underground corridor through the entrance. The laser radar carried by the drone collects spatial point cloud data, and the visual sensor records environmental image information. Step 3: Extract feature points in the environment through visual sensors, combine them with the point cloud features of the lidar, establish a relative coordinate system associated with spatial features, and perform point cloud SLAM solution based on state updates and observation updates; Step 4: Calculate the continuous spatial point cloud above and below the ground based on the SLAM algorithm, and use the difference in reflection intensity between the reflector and the surrounding environment in the point cloud to extract the three-dimensional coordinates of the reflector in the scanned point cloud in the relative coordinate system; Step 5: Determine the transformation parameters and transformation process, and apply the Rodrigues matrix transformation method to transform the point cloud in the relative coordinate system into the absolute coordinate system; Step 6: Based on the converted point cloud, capture the point cloud slices in the view, adjust the slices to the top view state, draw the floor plan of the underground pipeline corridor along the point cloud trajectory, overlay the floor plan with the topographic map, and obtain the real spatial location information of the underground pipeline corridor.

2. The underground pipe gallery detection method based on drone point cloud scanning according to claim 1 is characterized in that: In step 1, the ground reflector is a square reflector with a side length of 1 decimeter. There are 4 ground reflectors, and the 4 ground reflectors are evenly distributed in a quadrilateral in space according to the size of the underground pipe gallery.

3. The underground pipe gallery detection method based on drone point cloud scanning according to claim 1 is characterized in that: In step 3, the establishment of a relative coordinate system for associating spatial features includes dynamically updating the relative position of the drone in space based on a Kalman filter algorithm to construct a three-dimensional map of the environment.

4. The underground pipe gallery detection method based on drone point cloud scanning according to claim 3 is characterized in that: In step 3: the status update is expressed as: ,in Indicates the current drone status. Indicates the drone status at the last positioning moment. The control input representing the current state, Indicates noise; The observation update is expressed as: ,in represents the observed value, Represents an environment map, represents the observation noise.

5. The underground pipe gallery detection method based on drone point cloud scanning according to claim 4 is characterized in that: The step 3 includes: by continuously iterating the state update equation and the observation update equation, the SLAM algorithm simultaneously optimizes the environment map With drone location , dynamically updates the relative position of the drone in space and builds a three-dimensional map of the environment.

6. The underground pipe gallery detection method based on drone point cloud scanning according to claim 2 is characterized in that: In step 5, the conversion parameters include three translation parameters , scaling parameters , three rotation parameters , the conversion process includes translation, rotation, and scaling.

7. The underground pipe gallery detection method based on drone point cloud scanning according to claim 6 is characterized in that: The step 5 comprises: Step 5-1: Build a transformation process model: ,in Represents the rotation matrix, which determines the parameters of the four ground reflection pieces that exist in both the absolute space coordinate system and the relative space coordinate system; Step 5-2: Construct the antisymmetric matrix S, ,in represents the independent elements of the Rodriguez matrix; Step 5-3: The rotation matrix R is constructed from the antisymmetric matrix S to form the Rodriguez matrix M: , , ; Step 5-4: Subtract the equations of two adjacent ground reflectors, eliminate the translation parameter, and obtain the property equation based on the properties of the antisymmetric matrix and the Rodriguez matrix: ,in is the third-order identity matrix, represents the matrix transpose, represents matrix inversion; Step 5-5: Substitute the property equation into the equation for subtracting two adjacent ground reflection pieces to obtain the subtraction equation: ; Step 5-6: Order , sorting out the subtraction equations to get the final equation: ; Step 5-7: Repeat steps 5-1 to 5-6 to calculate the final equation between the remaining two adjacent ground reflection pieces, combine the two final equations, solve the independent parameters of the transformation matrix, substitute the scale parameter and the rotation parameter into the transformation process model, and solve the translation parameter; Step 5-8: Apply the transformation process model point by point to convert all point cloud data in the relative coordinate system obtained by the drone to the absolute coordinate system.

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