A concrete polishing operation planning method based on laser ranging and direction chain code tracking

Abstract

The application discloses a concrete polishing operation planning method based on laser ranging and direction chain code tracking, and comprises the following steps: acquiring laser ranging data L of each data collection point; subtracting a standard ranging value D from the ranging data L to establish a relative error distance matrix A1; if each component in the matrix A1 is less than o, the value is updated to zero, and if the component is greater than o, the original value is kept unchanged; reducing the order of the matrix A1 to obtain a reduced order relative error distance matrix A2; dividing the matrix A2 into a plurality of block relative error distance matrices A3; calculating the number of adjacent 0 components in each component in the matrix A3; calculating a path direction chain code of each starting point in all non-0 components in the reduced order relative error distance matrix A2; calculating the distance Jsum of each direction chain code; selecting a direction chain code Imin corresponding to the minimum direction chain code distance Jsum and a matrix A2 component corresponding to a polishing operation starting point, and designing a polishing operation path according to the direction chain code. The application can save energy consumption of a robot polishing operation and shorten the polishing operation time.

Description

Technical Field

[0001] This invention relates to the field of building engineering technology, specifically to a method for planning concrete grinding operations based on laser ranging and directional chain code tracking. Background Technology

[0002] Concrete structure flatness is a crucial quality control item in concrete pouring operations. Currently, flatness testing on construction sites typically uses a level, which requires repeated instrument repositioning and data recording at each measuring point—a time-consuming, labor-intensive, and cumbersome process with lengthy adjustments and complex data processing. Chinese Patent 202222205446.0 discloses an intelligent laser scanning device for distance measurement and flatness detection, optimizing the flatness testing process, improving efficiency, and providing flatness visualization. With the continuous advancement of informatization and intelligentization in the construction industry, robotic concrete structure grinding is becoming an inevitable trend. How robots can identify flatness quality issues and plan the optimal grinding path has become a challenge for researchers. Summary of the Invention

[0003] The purpose of this invention is to provide a concrete grinding operation planning method based on laser ranging and directional chain code tracking, which forms a command-controlled robot to move and grind, avoiding the grinding machine from staying in areas of the work surface that do not need to be ground, saving energy consumption of robot grinding operations, and shortening grinding operation time.

[0004] To achieve the above objectives, the present invention employs the following technical measures: a concrete grinding operation planning method based on laser ranging and direction chain code tracking, comprising the following steps:

[0005] S1. Perform laser scanning distance measurement on the concrete structure surface with length X and width Y, set data collection points every M along the length direction and every N along the width direction, and obtain the laser distance measurement data L of each data collection point;

[0006] S2. Define the standard distance measurement value D on the concrete structure surface. Subtract the standard distance measurement value D from the distance measurement data L to obtain the relative error distance DL at each location. Establish the relative error distance matrix A1. The relative error distance matrix is ​​as follows: 1-order matrix;

[0007] S3. Determine the flatness tolerance error value o. If each component in the relative error distance matrix A1 is less than o, update its value to zero. If it is greater than o, keep the original value unchanged.

[0008] S4. Based on the size R of the angle grinding disc of the concrete grinding equipment, reduce the relative error distance matrix A1 to the following order: From the order matrix, we obtain the reduced-order relative error distance matrix A2;

[0009] S5. Based on the reduced relative error distance matrix A2, determine the continuity of the area to be polished, and divide the reduced relative error distance matrix A2 into several block relative error distance matrices A3.

[0010] S6. Calculate the number of adjacent 0 components in each component of the block relative error distance matrix A3. If it is greater than zero, then take the concrete structure surface position corresponding to the adjacent 0 component as the candidate grinding operation starting point.

[0011] S7. Taking the starting component of each alternative grinding operation as the starting point, calculate the path direction chain code of the non-zero component in all reduced relative error distance matrices A2 for each starting point.

[0012] S8. Count the number J1 of components with values ​​of 1, 3, 5, and 7 and the number J2 of components with values ​​of 2, 4, 6, and 8 in each path direction chain code, and then... Calculate the chain code distance Jsum in each direction;

[0013] S9. Select the direction chain code Imin corresponding to the minimum direction chain code distance Jsum and the components (Xmin, Ymin) of the reduced-order relative error distance matrix A2 corresponding to the starting point of the grinding operation, and design the grinding operation path based on this direction chain code.

[0014] Optionally, the step S4 of reducing the relative error distance matrix A1 to the following order: From the order matrix, we obtain the reduced-order relative error distance matrix A2. The specific steps are as follows:

[0015] Q1: Obtain the relative error distance matrix A1 obtained in step S3;

[0016] Q2: Divide the relative error distance matrix A1 into blocks with side length R;

[0017] Q3: Calculate the mean value of each component in the relative error distance matrix A1 within each block;

[0018] Q4: Using the mean value calculated in step Q3 as a component, construct the reduced-order relative error distance matrix A2.

[0019] Optionally, the step S5, which involves dividing the reduced-order relative error distance matrix A2 into several block relative error distance matrices A3, specifically involves the following steps:

[0020] F1: Grid the reduced-order relative error distance matrix A2;

[0021] F2: Randomly select non-zero grids to establish the i-th grid set, count the number of non-zero grids that have not been added to the set at this time, and define the initial value of the set size i as 1;

[0022] F3: Add the non-zero grids that are adjacent to the grids in the i-th grid set to the grid set;

[0023] F4: Repeat step F3 until the i-th grid set has no adjacent non-zero grids. Count the number of non-zero grids that have not been added to the set. If it is 0, proceed to step F7. If it is not 0, proceed to step F5.

[0024] F5: Randomly select a grid from the non-zero grids that have not been added to the set, update the value of the set quantity i by adding one to the original value, establish the set of the i-th grid, and add the grid to the set of the i-th grid;

[0025] F6: Repeat step F4 until the number of non-zero grids not added to the set is 0;

[0026] F7: Divide the rectangular block regions using the non-zero grids within each set as boundaries, and assign values ​​to the relative error distance matrix A3 of each set block region according to the reduced-order relative error distance matrix A2 corresponding to the grid.

[0027] Optionally, the calculation of the starting point traversing all non-zero component path direction chain codes in the reduced-order relative error distance matrix A2 in step S6 is specifically performed as follows:

[0028] B1: Obtain the position (xq, yq) of the candidate starting point in the relative error distance matrix A3 of the block area as the initial value of the grinding path component. Take the vertical upward direction as the reference direction of the direction chain code, determine whether its adjacent components are non-zero, and count the number θ of non-zero components in the relative error distance matrix A3 of the block area.

[0029] B2: If there is a non-zero component in the starting component 0° of the grinding path, update the grinding path component to (xq, yq+1), that is, move the grinding position upward, add the value 1 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the relative error distance matrix A3 of the block area by one.

[0030] If there is a non-zero component in the 45° direction of the starting component of the grinding path, update the grinding path component to (xq+1, yq+1), that is, move the grinding position to the upper right, add the value 2 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the relative error distance matrix A3 of the block area by one.

[0031] If there is a non-zero component in the 90° direction of the starting component of the grinding path, update the grinding path component to (xq+1, yq-1), that is, move the grinding position to the right, add the value 3 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the block region relative error distance matrix A3 by one.

[0032] If there is a non-zero component in the 135° direction of the starting component of the grinding path, update the grinding path component to (xq-1, yq-1), that is, move the grinding position to the lower right, add the value 4 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the relative error distance matrix A3 of the block area by one.

[0033] If there is a non-zero component in the 180° direction of the starting component of the grinding path, update the grinding path component to (xq, yq-1), that is, move the grinding position downward, add the value 5 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the relative error distance matrix A3 of the block area by one.

[0034] If there is a non-zero component in the 225° direction of the starting component of the grinding path, update the grinding path component to (xq-1, yq-1), that is, move the grinding position to the lower left, add the value 6 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the block area relative error distance matrix A3 by one.

[0035] If there is a non-zero component in the 270° direction of the starting component of the grinding path, update the grinding path component to (xq-1, yq), that is, move the grinding position to the left, add the value 7 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the block region relative error distance matrix A3 by one.

[0036] If there is a non-zero component in the 315° direction of the starting component of the grinding path, update the grinding path component to (xq+1, yq-1), that is, move the grinding position to the upper left, add the value 8 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the relative error distance matrix A3 of the block area by one.

[0037] B3: Using the updated grinding path components, repeat the method described in step B2 to update the grinding path component values, add direction chain codes, and update the number θ of non-zero components in the block region and the relative error distance matrix A3 to obtain the non-zero component path direction chain code Ω, until the grinding path components have no adjacent non-zero components and the number θ of non-zero components in the block region's relative error distance matrix A3 is not 0. Then stop repeating the steps and return to step B1 to calculate the path direction chain code of the non-zero component of the next candidate starting point.

[0038] Optionally, the steps for designing the grinding operation path using directional chain codes in step S8 are as follows:

[0039] E1: Select the direction chain code and the starting component of the grinding operation corresponding to the minimum direction chain code distance Jsum;

[0040] E2: Determine the position of the concrete structure working surface (Xmin*R, Ymin*R) corresponding to the component (Xmin, Ymin) of the reduced order relative error distance matrix A2 corresponding to the starting point of the grinding operation, where: Xmin is the X-direction component of the starting point of the grinding operation in the reduced order relative error distance matrix A2, Ymin is the Y-direction component of the starting point of the grinding operation in the reduced order relative error distance matrix A2, and R is the size of the angle grinding disc of the grinding equipment;

[0041] E3: The grinding operation path is determined by controlling the direction chain code sequence. Taking the direction chain code (1, 2, 3, 4) as an example, the grinding operation path starts from (Xmin*R, Ymin*R), first moves upward by a distance R in the vertical direction, then moves upward by a distance R in the 45° direction, then moves to the left by a distance R in the horizontal direction, and finally moves by a distance R in the 135° direction.

[0042] Compared with the prior art, the beneficial effects of the technical solution provided by the present invention are as follows: Since the quality problem of concrete flatness is local and the separation on the structural wall is relatively discrete, compared with the current technology of scanning and grinding the entire wall surface, the present invention avoids the grinding machine staying in the area of ​​the work surface that does not need to be ground, saves energy consumption of robot grinding operation, and shortens grinding operation time. Attached Figure Description

[0043] Figure 1 This is an overall flowchart of the method described in this invention;

[0044] Figure 2 This is a flowchart illustrating the process of reducing the relative error distance matrix according to the present invention.

[0045] Figure 3 Flowchart for dividing the reduced-order relative error distance matrix into blocks;

[0046] Figure 4 This is a flowchart of the traversal path direction chain code for non-zero components as described in this invention;

[0047] Figure 5 This is a schematic diagram of the area to be polished in Example 4;

[0048] Figure 6 This is a schematic diagram of the path to be polished in Embodiment 4 of the method described in this invention. Detailed Implementation

[0049] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] A concrete grinding operation planning method based on laser ranging and direction chain code tracking, such as Figure 1 As shown, it includes the following steps:

[0051] S1. Perform laser scanning distance measurement on the concrete structure surface with length X and width Y. Set data collection points every M distance along the length direction and every N distance along the width direction. The values ​​of M and N are [0,X] and [0,Y], respectively, and X and Y are divisible by M and N, respectively. Obtain the laser distance measurement data L of each data collection point.

[0052] S2. Define the standard distance value D for the concrete structure surface. Subtract the standard distance value D from the distance data L to obtain the relative error distance DL at each location, and establish the relative error distance matrix A1. The relative error distance matrix is ​​as follows: 1-order matrix;

[0053] S3. Determine the flatness tolerance error value o. If each component in the relative error distance matrix A1 is less than o, update its value to zero. If it is greater than o, keep the original value unchanged.

[0054] S4. Based on the size R of the angle grinding disc of the concrete grinding equipment, reduce the relative error distance matrix A1 to the following order: From the order matrix, we obtain the reduced-order relative error distance matrix A2;

[0055] S5. Based on the reduced relative error distance matrix A2, determine the continuity of the area to be polished, and divide the reduced relative error distance matrix A2 into several block relative error distance matrices A3.

[0056] S6. Calculate the number of adjacent 0 components in each component of the block relative error distance matrix A3. If it is greater than zero, the concrete surface position corresponding to the adjacent 0 components of that component is taken as the candidate grinding start point. For example, if the three adjacent components (x1,y1)(x2,y2)(x3,y3) of a certain component are all 0, then the concrete surface (x1*R,y1*R)(x2*R,y2*R)(x3*R,y3*R) is taken as the candidate grinding start point, and the three components (x1,y1)(x2,y2)(x3,y3) in the reduced-order relative error distance matrix A2 are taken as the candidate grinding start components.

[0057] S7. Taking the starting component of each alternative grinding operation as the starting point, calculate the path direction chain code of the non-zero component in all reduced relative error distance matrices A2 for each starting point.

[0058] S8. Count the number J1 of components with values ​​of 1, 3, 5, and 7 and the number J2 of components with values ​​of 2, 4, 6, and 8 in each path direction chain code, and then... Calculate the chain code distance Jsum in each direction;

[0059] S9. Select the direction chain code Imin corresponding to the minimum direction chain code distance Jsum and the components (Xmin, Ymin) of the reduced order relative error distance matrix A2 corresponding to the starting point of the grinding operation. Xmin is the X-direction component of the starting point of the grinding operation in the reduced order relative error distance matrix A2, and Ymin is the Y-direction component of the starting point of the grinding operation in the reduced order relative error distance matrix A2. Design the grinding operation path based on this direction chain code.

[0060] like Figure 2 As shown, in step S4 of this invention, the relative error distance matrix A1 is reduced to its original order. From the order matrix, we obtain the reduced-order relative error distance matrix A2. The specific steps are as follows:

[0061] Q1: Obtain the relative error distance matrix A1 obtained in step S3;

[0062] Q2: Divide the relative error distance matrix A1 into blocks with side length R;

[0063] Q3: Calculate the mean of each component in the relative error distance matrix A1 within each block, in order to divide the blocks. For example, the mean value of each component in the relative error distance matrix A1 within this block is (a+b+c+d) / 4.

[0064] Q4: Using the mean value calculated in step Q3 as a component, construct the reduced-order relative error distance matrix A2.

[0065] like Figure 3 As shown, in step S5 of this invention, dividing the reduced-order relative error distance matrix A2 into several block relative error distance matrices A3 specifically involves the following steps:

[0066] F1: Grid the reduced-order relative error distance matrix A2;

[0067] F2: Randomly select non-zero grids to establish the i-th grid set, count the number of non-zero grids that have not been added to the set at this time, and define the initial value of the set size i as 1;

[0068] F3: Add the non-zero grids that are adjacent to the grids in the i-th grid set to the grid set;

[0069] F4: Repeat step F3 until the i-th grid set has no adjacent non-zero grids. Count the number of non-zero grids that have not been added to the set. If it is 0, proceed to step F7. If it is not 0, proceed to step F5.

[0070] F5: Randomly select a grid from the non-zero grids that have not been added to the set, update the value of the set quantity i by adding one to the original value, establish the set of the i-th grid, and add the grid to the set of the i-th grid;

[0071] F6: Repeat step F4 until the number of non-zero grids not added to the set is 0;

[0072] F7: Divide the rectangular block regions using the non-zero grids within each set as boundaries, and assign values ​​to the relative error distance matrix A3 of each set block region according to the reduced-order relative error distance matrix A2 corresponding to the grid.

[0073] like Figure 4 As shown, the specific steps for calculating the path direction chain codes of all non-zero components in the reduced-order relative error distance matrix A2, as described in step S6 of this invention, are as follows:

[0074] B1: Obtain the position (xq, yq) of the candidate starting point in the relative error distance matrix A3 of the block area as the initial value of the grinding path component. Take the vertical upward direction as the reference direction of the direction chain code, determine whether its adjacent components are non-zero, and count the number θ of non-zero components in the relative error distance matrix A3 of the block area.

[0075] B2: If there is a non-zero component in the starting component 0° of the grinding path, update the grinding path component to (xq, yq+1), that is, move the grinding position upward, add the value 1 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the relative error distance matrix A3 of the block area by one.

[0076] If there is a non-zero component in the 45° direction of the starting component of the grinding path, update the grinding path component to (xq+1, yq+1), that is, move the grinding position to the upper right, add the value 2 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the relative error distance matrix A3 of the block area by one.

[0077] If there is a non-zero component in the 90° direction of the starting component of the grinding path, update the grinding path component to (xq+1, yq-1), that is, move the grinding position to the right, add the value 3 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the block region relative error distance matrix A3 by one.

[0078] If there is a non-zero component in the 135° direction of the starting component of the grinding path, update the grinding path component to (xq-1, yq-1), that is, move the grinding position to the lower right, add the value 4 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the relative error distance matrix A3 of the block area by one.

[0079] If there is a non-zero component in the 180° direction of the starting component of the grinding path, update the grinding path component to (xq, yq-1), that is, move the grinding position downward, add the value 5 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the relative error distance matrix A3 of the block area by one.

[0080] If there is a non-zero component in the 225° direction of the starting component of the grinding path, update the grinding path component to (xq-1, yq-1), that is, move the grinding position to the lower left, add the value 6 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the block area relative error distance matrix A3 by one.

[0081] If there is a non-zero component in the 270° direction of the starting component of the grinding path, update the grinding path component to (xq-1, yq), that is, move the grinding position to the left, add the value 7 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the block region relative error distance matrix A3 by one.

[0082] If there is a non-zero component in the 315° direction of the starting component of the grinding path, update the grinding path component to (xq+1, yq-1), that is, move the grinding position to the upper left, add the value 8 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the relative error distance matrix A3 of the block area by one.

[0083] B3: Using the updated grinding path components, repeat the method described in step B2 to update the grinding path component values, add direction chain codes, and update the number θ of non-zero components in the block region and the relative error distance matrix A3 to obtain the non-zero component path direction chain code Ω, until the grinding path components have no adjacent non-zero components and the number θ of non-zero components in the block region's relative error distance matrix A3 is not 0. Then stop repeating the steps and return to step B1 to calculate the path direction chain code of the non-zero component of the next candidate starting point.

[0084] The specific steps for designing the grinding operation path using directional chain codes in step S8 of this invention are as follows:

[0085] E1: Select the direction chain code and the starting component of the grinding operation corresponding to the minimum direction chain code distance Jsum;

[0086] E2: Determine the position of the concrete structure working surface (Xmin*R, Ymin*R) corresponding to the component (Xmin, Ymin) of the reduced relative error distance matrix A2 corresponding to the starting point of the grinding operation. Xmin is the X-direction component of the starting point of the grinding operation in the reduced relative error distance matrix A2, Ymin is the Y-direction component of the starting point of the grinding operation in the reduced relative error distance matrix A2, and R is the size of the angle grinding disc of the grinding equipment.

[0087] E3: The grinding operation path is determined by controlling the direction chain code sequence. Taking the direction chain code (1, 2, 3, 4) as an example, the grinding operation path starts from (Xmin*R, Ymin*R), first moves upward by a distance R in the vertical direction, then moves upward by a distance R in the 45° direction, then moves to the left by a distance R in the horizontal direction, and finally moves by a distance R in the 135° direction.

[0088] Example 1

[0089] This embodiment aims to illustrate the step of reducing the order of the relative error distance matrix A1 of the present invention. For the description of the remaining steps, please refer to the other embodiments.

[0090] Step 1-1: Perform laser scanning distance measurement on the concrete structure surface with a length of 60cm and a width of 60cm. Set a data acquisition point every 10cm along the length direction and 10cm along the width direction, and obtain the laser distance measurement data L of each data acquisition point as shown below.

[0091] 53.13 51.43 51.72 50.42 51.93 50.35 50.24 52.54 52.06 51.42 51.70 51.50 54.82 52.89 53.92 54.07 53.64 54.18 54.51 52.08 51.77 52.00 53.36 54.60 51.94 53.91 50.18 54.81 51.58 50.27

[0092] Steps 1-2: Define the standard distance measurement value D of the concrete structure surface as 50cm. Subtract the standard distance measurement value from the distance measurement data L to obtain the relative error distance DL at each location, and establish the relative error distance matrix A1. The relative error distance matrix is ​​a 6*6 matrix. The relative error distance matrix A1 in Example 1 is shown below.

[0093] 3.13 1.43 1.72 0.42 1.93 0.35 0.24 2.54 2.06 1.42 1.70 1.50 4.82 2.89 3.92 4.07 3.64 4.18 4.51 2.08 1.77 2.00 3.36 4.60 1.94 3.91 0.18 4.81 1.58 0.27

[0094] Steps 1-3: Set the flatness tolerance error value o to 2. If each component in the relative error distance matrix A1 is less than 2, update its value to 0. If it is greater than 2, keep the original value unchanged. The updated relative error distance matrix A1 of Example 1 is shown below.

[0095] 3.13 0 0 0 0 0 0 2.54 2.06 0 0 0 4.82 2.89 3.92 4.07 3.64 4.18 4.51 2.08 0 2.00 3.36 4.60 0 3.91 0 4.81 0 0

[0096] Steps 1-4: Based on the concrete grinding angle grinder size R of 20cm, divide the relative error distance matrix A1 into multiple blocks of 20cm length and 20cm width. The blocks are shown below.

[0097]

[0098] Steps 1-5: Calculate the mean value of each component in the relative error distance matrix A1 within each block, and divide the blocks accordingly. For example, the mean value of each component in the relative error distance matrix A1 within this block is (4.88+3.13+0+0)=2.0025.

[0099] Steps 1-6: Using the mean calculated in Steps 1-5 as components, the order reduction is completed, and the order reduction relative error distance matrix A2 is constructed as shown below.

[0100] 2.5625 2.5125 1.955 2.625 1.7025 1.99

[0101] Example 2

[0102] This embodiment aims to illustrate the step in step S5 of the invention, which involves dividing the reduced relative error distance matrix A2 into several block relative error distance matrices A3. The specific steps are as follows:

[0103] Step 2-1: Perform laser scanning distance measurement on the concrete structure surface with a length of 100cm and a width of 100cm. Set a data acquisition point every 10cm along the length direction and every 10cm along the width direction, and obtain the laser distance measurement data L of each data acquisition point as shown below.

[0104]

[0105]

[0106] Step 2-2: Define the standard distance measurement value D of the concrete structure surface as 50cm. Subtract the standard distance measurement value D from the distance measurement data L to obtain the relative error distance DL at each position, and establish the relative error distance matrix A1. The relative error distance matrix is ​​a 10th order matrix. The relative error distance matrix A1 in Example 2 is shown below.

[0107] 0.19 1.86 0.69 0.41 1.58 0.90 1.90 1.03 0.01 1.21 0.94 0.71 1.54 1.43 1.55 0.88 0.77 1.85 1.40 0.37 0.28 1.06 1.77 1.11 1.38 0.56 1.98 0.99 0.76 1.03 0.62 0.57 0.14 1.96 1.13 1.03 1.62 1.44 0.21 1.29 0.21 0.91 0.82 0.30 0.87 0.63 0.46 0.06 0.40 0.45 0.64 0.58 1.40 1.13 0.85 1.47 1.09 0.93 0.47 0.02 1.14 1.04 1.95 1.25 1.80 1.87 0.88 1.97 1.37 0.33 1.83 1.16 0.35 1.59 1.31 1.57 0.84 0.93 1.92 1.26 0.77 1.21 1.46 1.61 1.14 1.03 0.37 1.84 1.95 1.52

[0108] Steps 2-3: Set the flatness tolerance error value o to 1. If each component in the relative error distance matrix A1 is less than 1, update its value to 0. If it is greater than 1, keep the original value unchanged. The updated relative error distance matrix A1 of Example 2 is shown below.

[0109] 0.00 1.86 0.00 0.00 1.58 0.00 1.90 0.00 0.00 1.21 0.00 0.00 1.54 1.43 1.55 0.00 0.00 1.85 1.40 0.00 0.00 1.06 1.77 1.11 1.38 0.00 1.98 0.00 0.00 1.03 0.00 0.00 0.00 1.96 1.13 1.03 1.62 1.44 0.00 1.29 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.40 1.13 0.00 1.47 1.09 0.00 0.00 0.00 1.14 1.04 1.95 1.25 1.80 1.87 0.00 1.97 1.37 0.00 1.83 1.16 0.00 1.59 1.31 1.57 0.00 0.00 1.92 1.26 0.00 1.21 1.46 1.61 1.14 1.03 0.00 1.84 1.95 1.52

[0110] Steps 2-4: Based on the concrete grinding angle grinder size R being 10cm, the relative error distance matrix A1 is divided into multiple blocks, each 10cm long and 10cm wide. The blocks are shown below:

[0111]

[0112]

[0113] Steps 2-5: Calculate the mean value of each component in the relative error distance matrix A1 within each block, as shown below.

[0114] 0.00 1.86 0.00 0.00 1.58 0.00 1.90 0.00 0.00 1.21 0.00 0.00 1.54 1.43 1.55 0.00 0.00 1.85 1.40 0.00 0.00 1.06 1.77 1.11 1.38 0.00 1.98 0.00 0.00 1.03 0.00 0.00 0.00 1.96 1.13 1.03 1.62 1.44 0.00 1.29 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.40 1.13 0.00 1.47 1.09 0.00 0.00 0.00 1.14 1.04 1.95 1.25 1.80 1.87 0.00 1.97 1.37 0.00 1.83 1.16 0.00 1.59 1.31 1.57 0.00 0.00 1.92 1.26 0.00 1.21 1.46 1.61 1.14 1.03 0.00 1.84 1.95 1.52

[0115] Step 2-6: Using the mean value calculated in Step 2-5 as a component, complete the order reduction and construct the order reduction relative error distance matrix A2 as shown below.

[0116] 0.00 1.86 0.00 0.00 1.58 0.00 1.90 0.00 0.00 1.21 0.00 0.00 1.54 1.43 1.55 0.00 0.00 1.85 1.40 0.00 0.00 1.06 1.77 1.11 1.38 0.00 1.98 0.00 0.00 1.03 0.00 0.00 0.00 1.96 1.13 1.03 1.62 1.44 0.00 1.29 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.40 1.13 0.00 1.47 1.09 0.00 0.00 0.00 1.14 1.04 1.95 1.25 1.80 1.87 0.00 1.97 1.37 0.00 1.83 1.16 0.00 1.59 1.31 1.57 0.00 0.00 1.92 1.26 0.00 1.21 1.46 1.61 1.14 1.03 0.00 1.84 1.95 1.52

[0117] Steps 2-7: Grid the reduced relative error distance matrix A2, with each component as a grid as shown below.

[0118] 0.00 1.86 0.00 0.00 1.58 0.00 1.90 0.00 0.00 1.21 0.00 0.00 1.54 1.43 1.55 0.00 0.00 1.85 1.40 0.00 0.00 1.06 1.77 1.11 1.38 0.00 1.98 0.00 0.00 1.03 0.00 0.00 0.00 1.96 1.13 1.03 1.62 1.44 0.00 1.29 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.40 1.13 0.00 1.47 1.09 0.00 0.00 0.00 1.14 1.04 1.95 1.25 1.80 1.87 0.00 1.97 1.37 0.00 1.83 1.16 0.00 1.59 1.31 1.57 0.00 0.00 1.92 1.26 0.00 1.21 1.46 1.61 1.14 1.03 0.00 1.84 1.95 1.52

[0119] Steps 2-8: Randomly select non-zero grids to establish the i-th grid set. In this embodiment, the non-zero grid (2, 2) is selected. The grid value is 1.86, and there are 5 zero grids around it. Count the number of non-zero grids that have not been added to the set. At this time, 51 non-zero grids have not been added to the set. Define the initial value of i as 1.

[0120] Step 2-9: Add the non-zero grids that are adjacent to the grids in the i-th grid set to the grid set.

[0121] Step 2-10: Repeat Step 2-9 until the i-th grid set has no adjacent non-zero grids. Count the number of non-zero grids not added to the set. If the count is 0, proceed to Step 2-13; otherwise, proceed to Step 2-11. In this embodiment, when the first grid set has no adjacent non-zero grids, there are still 27 non-zero grids not added to the set.

[0122] Step 2-11: Randomly select a grid from the non-zero grids that have not been added to the set, update the value of the set quantity i by adding one to the original value, establish the set of the i-th grid, and add the grid to the set of the i-th grid. In this embodiment, the (8, 1) grid is selected, and the value of this grid is 1;

[0123] Step 2-12: Repeat steps 2-9 and 2-10 until the number of non-zero grids not added to the set is 0.

[0124] Step 2-13: Divide the set into rectangular blocks using the non-zero grids within each set as boundaries. Assign values ​​to the relative error distance matrix A3 of each set's block region based on the reduced-order relative error distance matrix A2 corresponding to the grid. The relative error distance matrix of the block region for set 1 in this embodiment is shown below:

[0125] 1.86 0.00 0.00 1.58 0.00 1.90 0.00 0.00 1.21 0.00 1.54 1.43 1.55 0.00 0.00 1.85 1.40 0.00 1.06 1.77 1.11 1.38 0.00 1.98 0.00 0.00 1.03 0.00 0.00 1.96 1.13 1.03 1.62 1.44 0.00 1.29

[0126] This embodiment sets a relative error distance matrix for two block regions:

[0127] 1.14 1.04 1.95 1.25 1.80 1.87 0.00 1.97 1.37 0.00 1.83 1.16 0.00 1.59 1.31 1.57 0.00 0.00 1.92 1.26 0.00 1.21 1.46 1.61 1.14 1.03 0.00 1.84 1.95 1.52

[0128] Example 3

[0129] This embodiment aims to illustrate the steps for calculating the non-zero component path direction chain code in the relative error distance matrix A3 of all block regions from the starting point. The specific steps are as follows:

[0130] Step 3-1: Obtain the relative error distance matrix A3 of the segmented region. In this embodiment, the relative error distance matrix A3 of the segmented region is shown below.

[0131] 1.7 2.4 1.7 1.9 3.5 1.6

[0132] Step 3-2: Calculate the number of adjacent 0 components in the relative error distance matrix A3 of the segmented region. The number of adjacent 0 components is 2. (1,2) and (1,3) in the relative error distance matrix A3 of the segmented region are used as the starting components of the candidate grinding operation.

[0133] Step 3-3: Using (1,2) as the initial value of the grinding path component, and taking the vertical upward direction as the reference direction of the direction chain code, determine whether its adjacent components are non-zero. The number of non-zero components θ of the relative error distance matrix A3 of the block area is 7.

[0134] Steps 3-4: There is a non-zero component in the 270° direction of the starting component of the grinding path. Update the grinding path component to (1, 1) and add the value 7 to the non-zero component path direction chain code. At this time, the direction chain code is 7, and the number of non-zero components θ of the reduced relative error distance matrix A2 is 6.

[0135] Steps 3-5: There is a non-zero component in the 180° direction of the starting component of the grinding path. Update the grinding path component to (1, 2) and add the value 5 to the non-zero component path direction chain code. At this time, the direction chain code is 75, and the number of non-zero components θ of the reduced order relative error distance matrix A2 is 5.

[0136] Steps 3-6: There are non-zero components in the 180° direction of the starting component of the grinding path. Update the grinding path component to (1, 3) and add the value 5 to the non-zero component path direction chain code. At this time, the direction chain code is 755, and the number of non-zero components θ of the reduced relative error distance matrix A2 is 4.

[0137] Steps 3-7: There is a non-zero component in the 90° direction of the starting component of the grinding path. Update the grinding path component to (2, 3) and add the value 3 to the non-zero component path direction chain code. At this time, the direction chain code is 7553, and the number of non-zero components θ of the reduced relative error distance matrix A2 is 3.

[0138] Step 3-8: There is a non-zero component in the 0° direction of the starting component of the grinding path. Update the grinding path component to (2, 2) and add the value 1 to the non-zero component path direction chain code. At this time, the direction chain code is 75531, and the number of non-zero components θ of the reduced order relative error distance matrix A2 is 2.

[0139] Steps 3-9: There is a non-zero component in the 90° direction of the starting component of the grinding path. Update the grinding path component to (2, 3) and add the value 3 to the non-zero component path direction chain code. At this time, the direction chain code is 755313, and the number of non-zero components θ of the reduced relative error distance matrix A2 is 1.

[0140] Step 3-10: There is a non-zero component in the 180° direction of the starting component of the grinding path. Update the grinding path component to (3, 3) and add the value 5 to the non-zero component path direction chain code. At this time, the direction chain code is 7553135, and the number of non-zero components θ of the reduced order relative error distance matrix A2 is 0.

[0141] Step 3-11: Obtain the starting point (1,2) and traverse all non-zero components of the path direction chain code 7553135 in the reduced relative error distance matrix A2.

[0142] Example 4

[0143] This embodiment describes the overall process of the present invention. For details on directional chain code calculation, matrix order reduction, and grinding region segmentation, please refer to Embodiments 1-3. This embodiment will not elaborate further.

[0144] Step 4-1: Perform laser scanning distance measurement on the concrete structure surface with a length of 100mm and a width of 100mm. Set a data acquisition point every 10mm along the length direction and every 10mm along the width direction to obtain the laser distance measurement data L of each control point.

[0145] 51.07 50.72 51.28 50.82 50.04 50.87 51.20 50.64 50.34 50.30 51.07 50.41 50.43 50.75 50.15 50.85 50.94 50.22 50.83 50.39 50.32 50.39 50.51 50.30 50.30 50.39 51.30 51.23 50.49 50.13 50.77 50.51 50.11 51.08 50.16 50.91 51.03 50.88 50.28 51.20 50.45 50.15 50.22 50.52 50.53 50.17 51.13 50.17 51.28 50.58 51.21 50.93 51.03 51.05 50.87 50.48 50.26 50.14 50.60 51.10 50.05 50.20 50.46 50.66 50.62 50.42 50.80 50.43 50.88 50.71 51.19 50.09 51.09 50.11 51.21 50.86 50.79 50.66 51.09 51.05 50.19 50.92 51.20 50.06 50.25 51.06 50.58 50.08 50.43 51.26

[0146] Step 4-2: Define the standard distance measurement value D of the concrete structure surface as 50mm. Subtract the standard distance measurement value from the distance measurement data L to obtain the relative error distance DL at each location, and establish the relative error distance matrix A1. The relative error distance matrix is ​​a 10th order matrix.

[0147] 1.07 0.72 1.28 0.82 0.04 0.87 1.20 0.64 0.34 0.30 1.07 0.41 0.43 0.75 0.15 0.85 0.94 0.22 0.83 0.39 0.32 0.39 0.51 0.30 0.30 0.39 1.30 1.23 0.49 0.13 0.77 0.51 0.11 1.08 0.16 0.91 1.03 0.88 0.28 1.20 0.45 0.15 0.22 0.52 0.53 0.17 1.13 0.17 1.28 0.58 1.21 0.93 1.03 1.05 0.87 0.48 0.26 0.14 0.60 1.10 0.05 0.20 0.46 0.66 0.62 0.42 0.80 0.43 0.88 0.71 1.19 0.09 1.09 0.11 1.21 0.86 0.79 0.66 1.09 1.05 0.19 0.92 1.20 0.06 0.25 1.06 0.58 0.08 0.43 1.26

[0148] Step 4-3: Set the flatness tolerance error value o to 1. If each component in the relative error distance matrix A1 is less than o, update its value to zero. If it is greater than o, keep the original value unchanged. The updated relative error distance matrix A1 is shown below.

[0149] 1.07 0.00 1.28 0.00 0.00 0.00 1.20 0.00 0.00 0.00 1.07 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.30 1.23 0.00 0.00 0.00 0.00 0.00 1.08 0.00 0.00 1.03 0.00 0.00 1.20 0.00 0.00 0.00 0.00 0.00 0.00 1.13 0.00 1.28 0.00 1.21 0.00 1.03 1.05 0.00 0.00 0.00 0.00 0.00 1.10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.19 0.00 1.09 0.00 1.21 0.00 0.00 0.00 1.09 1.05 0.00 0.00 1.20 0.00 0.00 1.06 0.00 0.00 0.00 1.26

[0150] Step 4-4: Based on the size R of the angle grinding disc for concrete grinding operations being 20mm, the relative error distance matrix A1 is reduced to a 5th order matrix to obtain the reduced relative error distance matrix A2.

[0151] 0.27 0.00 0.00 0.63 0.00 0.00 0.27 0.00 0.54 0.62 0.30 0.52 0.00 0.00 0.28 0.30 0.57 0.57 0.00 0.85

[0152] Steps 4-5: Based on the reduced relative error distance matrix A2, determine the continuity of the area to be polished, and divide the reduced relative error distance matrix A2 into several block relative error distance matrices A3. In this embodiment, the first block relative error distance matrix A3-1 and the second block relative error distance matrix A3-2 are shown below:

[0153] 0.27 0.00 0.00 0.00 0.27 0.00 0.30 0.52 0.00 0.30 0.57 0.57

[0154] 0.63 0.00 0.54 0.62 0.00 0.28 0.00 0.85

[0155] Steps 4-6: Calculate the number of adjacent zero components in each component of the relative error distance matrix A3. If an adjacent zero component is greater than 0, the concrete surface position corresponding to the adjacent zero component is used as the candidate starting point for grinding. Taking the second relative error distance matrix A3-2 as an example, the concrete surface positions corresponding to the components (1,2), (2,2), (1,4), and (1,5) in the matrix are used as candidate starting points for grinding. Figure 5 As shown.

[0156] Steps 4-7: Using the starting component of each candidate grinding operation as the starting point, calculate the path direction chain code of the non-zero components in the relative error distance matrix A3 of all blocks for each starting point. Starting from (1,2), the path direction chain code of the non-zero components in the relative error distance matrix A3 of all blocks is 755355; starting from (2,2), the path direction chain code of the non-zero components in the relative error distance matrix A3 of all blocks is 855355; starting from (1,4), the path direction chain code of the non-zero components in the relative error distance matrix A3 of all blocks is 411711; starting from (1,5), the path direction chain code of the non-zero components in the relative error distance matrix A3 of all blocks is 311711.

[0157] Steps 4-8: Count the number J1 of components with values ​​of 1, 3, 5, and 7 and the number J2 of components with values ​​of 2, 4, 6, and 8 in each path direction chain code, and then... Calculate the chain code distance Jsum in each direction. The chain code distances in each direction for paths 1-4 are 6, , and , respectively. 6.

[0158] Steps 4-9: Select the direction chain code Imin corresponding to the minimum direction chain code distance Jsum and the starting component (Xmin, Ymin) of the grinding operation, and design the grinding operation path based on this direction chain code. In this embodiment, the minimum direction chain code distance Jsum in the first block relative error distance matrix A3-1 is... The corresponding direction chain code is 775457533, and the starting point of the grinding operation corresponds to component (1, 3) of the reduced-order relative error distance matrix A2. The minimum direction chain code distance Jsum of the second block relative error distance matrix A3-2 is 6, and the corresponding direction chain code is 755355. The starting point of the grinding operation corresponds to component (1, 5) of the reduced-order relative error distance matrix A2.

[0159] Steps 4-10: Determine the position of the concrete structure working surface corresponding to the component (Xmin, Ymin) of the reduced order relative error distance matrix A2 corresponding to the starting point of the grinding operation [(Xmin-0.5)*R, (Ymin-0.5)*R]. In this embodiment, there are two starting points [10mm, 50mm] and [10mm, 90mm].

[0160] Steps 4-11: Determine the grinding operation path according to the direction chain code sequence. For example... Figure 6 As shown.

[0161] Starting from [10mm, 50mm], the corneal disc moves as follows:

[0162] (1) Move 20mm to the left.

[0163] (2) Move to the left by 20mm.

[0164] (3) Move down 20mm.

[0165] (4) Move along the 135° direction

[0166] (5) Move down 20mm.

[0167] (6) Move 20mm to the left.

[0168] (7) Move down 20mm.

[0169] (8) Move 20mm to the right.

[0170] (9) Move 20mm to the right.

[0171] Starting from [10mm, 90mm], the corneal disc moves as follows:

[0172] (1) Move 20mm to the left.

[0173] (2) Move down 20mm.

[0174] (3) Move down 20mm.

[0175] (4) Move 20mm to the right.

[0176] (5) Move down 20mm.

[0177] (6) Move down 20mm.

[0178] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any transformations or substitutions that can be understood by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of the present invention.

Claims

1. A method for planning concrete grinding operations based on laser ranging and directional chain code tracking, characterized in that, Includes the following steps: S1. Perform laser scanning distance measurement on the concrete structure surface with length X and width Y, set data collection points every M along the length direction and every N along the width direction, and obtain the laser distance measurement data L of each data collection point; S2. Define the standard distance measurement value D on the concrete structure surface. Subtract the standard distance measurement value D from the distance measurement data L to obtain the relative error distance DL at each location. Establish the relative error distance matrix A1. The relative error distance matrix is ​​as follows: 1-order matrix; S3. Determine the flatness tolerance error value o. If each component in the relative error distance matrix A1 is less than o, update its value to zero. If it is greater than o, keep the original value unchanged. S4. Based on the size R of the angle grinding disc of the concrete grinding equipment, reduce the relative error distance matrix A1 to the following order: From the order matrix, we obtain the reduced-order relative error distance matrix A2; S5. Based on the reduced relative error distance matrix A2, determine the continuity of the area to be polished, and divide the reduced relative error distance matrix A2 into several block relative error distance matrices A3. S6. Calculate the number of adjacent 0 components in each component of the block relative error distance matrix A3. If it is greater than zero, then take the concrete structure surface position corresponding to the adjacent 0 component as the candidate grinding operation starting point. S7. Taking the starting component of each alternative grinding operation as the starting point, calculate the path direction chain code of the non-zero component in all reduced relative error distance matrices A2 for each starting point. S8. Count the number J1 of components with values ​​of 1, 3, 5, and 7, and the number J2 of components with values ​​of 2, 4, 6, and 8 in each path direction chain code, and calculate Jsum = J1 + J2. Calculate the chain code distance Jsum in each direction; S9. Select the direction chain code Imin corresponding to the minimum direction chain code distance Jsum and the components (Xmin, Ymin) of the reduced-order relative error distance matrix A2 corresponding to the starting point of the grinding operation, and design the grinding operation path based on this direction chain code.

2. The concrete grinding operation planning method based on laser ranging and direction chain code tracking according to claim 1, characterized in that, Step S4 describes reducing the relative error distance matrix A1 to its order. From the order matrix, we obtain the reduced-order relative error distance matrix A2. The specific steps are as follows: Q1: Obtain the relative error distance matrix A1 obtained in step S3; Q2: Divide the relative error distance matrix A1 into blocks with side length R; Q3: Calculate the mean value of each component in the relative error distance matrix A1 within each block; Q4: Using the mean value calculated in step Q3 as a component, construct the reduced-order relative error distance matrix A2.

3. The concrete grinding operation planning method based on laser ranging and direction chain code tracking according to claim 1, characterized in that, Step S5, which involves dividing the reduced-order relative error distance matrix A2 into several block relative error distance matrices A3, specifically involves the following steps: F1: Grid the reduced-order relative error distance matrix A2; F2: Randomly select non-zero grids to establish the i-th grid set, count the number of non-zero grids that have not been added to the set at this time, and define the initial value of the set size i as 1; F3: Add the non-zero grids that are adjacent to the grids in the i-th grid set to the grid set; F4: Repeat step F3 until the i-th grid set has no adjacent non-zero grids. Count the number of non-zero grids that have not been added to the set. If it is 0, proceed to step F7. If it is not 0, proceed to step F5. F5: Randomly select a grid from the non-zero grids that have not been added to the set, update the value of the set quantity i by adding one to the original value, establish the set of the i-th grid, and add the grid to the set of the i-th grid; F6: Repeat step F4 until the number of non-zero grids not added to the set is 0; F7: Divide the rectangular block regions using the non-zero grids within each set as boundaries, and assign values ​​to the relative error distance matrix A3 of each set block region according to the reduced-order relative error distance matrix A2 corresponding to the grid.

4. The concrete grinding operation planning method based on laser ranging and direction chain code tracking according to claim 1, characterized in that, The specific steps for calculating the path direction chain code of all non-zero components in the reduced relative error distance matrix A2, as described in step S7, are as follows: B1: Obtain the position (xq, yq) of the candidate starting point in the relative error distance matrix A3 of the block area as the initial value of the grinding path component. Take the vertical upward direction as the reference direction of the direction chain code, determine whether its adjacent components are non-zero, and count the number θ of non-zero components in the relative error distance matrix A3 of the block area. B2: If there is a non-zero component in the starting component 0° of the grinding path, update the grinding path component to (xq, yq+1), that is, move the grinding position upward, add the value 1 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the relative error distance matrix A3 of the block area by one. If there is a non-zero component in the 45° direction of the starting component of the grinding path, update the grinding path component to (xq+1, yq+1), that is, move the grinding position to the upper right, add the value 2 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the block region relative error distance matrix A3 by one. If there is a non-zero component in the 90° direction of the starting component of the grinding path, update the grinding path component to (xq+1, yq-1), that is, move the grinding position to the right, add the value 3 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the block region relative error distance matrix A3 by one. If there is a non-zero component in the 135° direction of the starting component of the grinding path, update the grinding path component to (xq-1, yq-1), that is, move the grinding position to the lower right, add the value 4 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the relative error distance matrix A3 of the block area by one. If there is a non-zero component in the 180° direction of the starting component of the grinding path, update the grinding path component to (xq, yq-1), that is, move the grinding position downwards, add the value 5 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the relative error distance matrix A3 of the block area by one. If there is a non-zero component in the 225° direction of the starting component of the grinding path, update the grinding path component to (xq-1, yq-1), that is, move the grinding position to the lower left, add the value 6 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the relative error distance matrix A3 of the block area by one. If there is a non-zero component in the 270° direction of the starting component of the grinding path, update the grinding path component to (xq-1, yq), that is, move the grinding position to the left, add the value 7 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the relative error distance matrix A3 of the block area by one. If there is a non-zero component in the 315° direction of the starting component of the grinding path, update the grinding path component to (xq+1, yq-1), that is, move the grinding position to the upper left, add the value 8 to the non-zero component path direction chain code, and decrease the number θ of the non-zero components in the relative error distance matrix A3 of the block area by one. B3: Using the updated grinding path components, repeat the method described in step B2 to update the grinding path component values, add direction chain codes, and update the number θ of non-zero components in the block region and the relative error distance matrix A3 to obtain the non-zero component path direction chain code Ω, until the grinding path components have no adjacent non-zero components and the number θ of non-zero components in the block region's relative error distance matrix A3 is not 0. Then stop repeating the steps and return to step B1 to calculate the path direction chain code of the non-zero component of the next candidate starting point.

5. The concrete grinding operation planning method based on laser ranging and direction chain code tracking according to claim 1, characterized in that, The specific steps for designing the grinding operation path using directional chain codes as described in step S9 are as follows: E1: Select the direction chain code and the starting component of the grinding operation corresponding to the minimum direction chain code distance Jsum; E2: Determine the location of the concrete structure working surface (Xmin) corresponding to the component (Xmin, Ymin) of the reduced-order relative error distance matrix A2 corresponding to the starting point of the grinding operation. R, Ymin R), where: Xmin is the X-direction component of the grinding operation starting point in the reduced order relative error distance matrix A2, Ymin is the Y-direction component of the grinding operation starting point in the reduced order relative error distance matrix A2, and R is the size of the grinding disc of the grinding equipment; E3: Determine the grinding operation path according to the direction chain code sequence.

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