Line laser array calibration method based on striped flat plate

Abstract

The invention discloses a line laser array calibration method based on a stripe flat plate. The method comprises the following steps: step 1, carrying out three-dimensional shape measurement on the surface of an end tooth rotor; step 2, linearly solving pose transformation between the measurement coordinate systems of the line laser sensor; and step 3, carrying out nonlinear optimization on pose transformation between the measurement coordinate systems of the line laser sensor, and realizing calibration of a pose relation between the measurement coordinate systems of the line laser sensor. A multi-line laser scanning measurement system is designed for an aero-engine end tooth structure, a multi-line laser measurement system calibration model based on a stripe calibration plate is provided for solving the problems that standard ball calibration is low in precision, high in cost and the like, and the measurement error does not exceed 2.4 micrometers after calibration.

Description

Technical Field

[0001] The invention belongs to the technical field of surface profile measurement, and in particular relates to a linear laser array calibration method based on a stripe plate. Background Art

[0002] The lack of high-performance aircraft engines has always been the biggest "heartache" that restricts the rapid development of my country's aviation industry. As aircraft engines develop towards a high thrust-to-weight ratio, arc end teeth are widely used in the connection of multi-stage rotors in the core of the engine due to their automatic centering and large load-bearing capabilities. During the assembly process of the multi-stage end-tooth rotor, the eccentricity error of each stage of the rotor will be transmitted and amplified through the end-tooth connection structure, resulting in excessive coaxiality after assembly. Coaxiality, as an important parameter for evaluating assembly quality, has a great impact on engine performance and life. Excessive coaxiality error after assembly of the multi-stage end-tooth rotor will cause engine vibration failure. Therefore, it is urgent to establish a multi-stage end-tooth rotor assembly coaxiality prediction and optimization model to provide guidance for assembly work, which is of great significance to improving assembly accuracy, reducing whole machine vibration, and ensuring smooth operation of the engine.

[0003] At present, the coaxiality control of end-tooth rotors in China is mostly achieved by measuring the high and low points of the end-tooth runout, and matching the high and low points of the runout to control the eccentricity error of the end-tooth rotor after assembly. However, this assembly method only controls the eccentricity error between two adjacent rotors, and does not truly control the overall coaxiality error of the multi-stage rotor after assembly, and may assemble a relatively bow-shaped rotor. It can be seen that there is currently a lack of effective control methods for the coaxiality of multi-stage end-tooth rotor assembly in China, and the problem of optimizing the coaxiality of multi-stage end-tooth rotor assembly needs to be solved urgently.

[0004] In order to simultaneously measure the end face runout and axial runout of the end gear of the aircraft engine, a multi-line laser scanning system is required to scan the end face and side of the end gear to measure the coaxiality. The traditional calibration method that relies on the standard ball has high marker processing cost and low calibration accuracy. A new multi-line laser sensor calibration method is urgently needed. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes a linear laser array calibration method based on a stripe plate.

[0006] The linear laser array calibration method based on a stripe plate of the present invention comprises the following steps:

[0007] Step 1, performing three-dimensional topography measurement on the end gear rotor surface;

[0008] Step 2: Linear solution of the pose transformation between the line laser sensor measurement coordinate systems;

[0009] Step 3: nonlinearly optimize the pose transformation between the line laser sensor measurement coordinate systems to achieve the calibration of the pose relationship between the line laser sensor measurement coordinate systems.

[0010] Furthermore, in step 1, the three-dimensional morphology measurement of the end tooth rotor surface is performed by a line laser sensor and an air floating turntable, and the line contour data of the outer cylindrical surface of the end tooth rotor and the tooth surface are measured respectively. The obtained data are spliced ​​and the end tooth rotor surface point cloud is reconstructed in three dimensions to realize the three-dimensional morphology measurement of the end tooth rotor surface.

[0011] Furthermore, the specific operation of step 2 is as follows: the line laser sensor projects laser light onto the calibration plate, collects a set of points with periodic intervals, and calculates the line segment distance l according to the point coordinate information collected by the line laser sensor. a , then the angle θ between the laser line and the stripe on the calibration plate can be calculated as:

[0012] Δd is the designed stripe spacing width. By introducing periodic stripes on the calibration plate, the line laser sensor can obtain angle information while obtaining the point coordinate information on the two-dimensional plate, thereby realizing the calibration of the three-dimensional target.

[0013] Furthermore, in step 2, the stripe calibration plate is used to calibrate the two line laser sensors to measure the pose transformation between the coordinate systems. The two line laser sensors simultaneously project lasers onto the calibration plate, where the straight line l a With straight line l b are the light projected by line laser sensors A and B on the calibration board; angle θ a With angle θ b The straight lines l a With straight line l b The angle with the stripe direction on the calibration plate can be calculated using formula (2-7):

[0014]

[0015] Furthermore, in step 2, the coordinate system measured by the line laser sensor A is used as the world coordinate system, and the rotation transformation matrix R from the coordinate system measured by the line laser sensor B to the world coordinate system is assumed to be 0 And the displacement transformation matrix T 0 They are:

[0016]

[0017] T 0 =[T 1 T 2 T 3 ] T (2-9)

[0018] Straight line aWith straight line l b Both are located on the plane of the calibration plate, so the two straight lines are coplanar and satisfy the relationship:

[0019] (l a ′×R 0 l b ′)·(R 0 P b +Τ 0 -P a )=0 (2-10)

[0020] Among them, the vector l' a For the straight line l a The direction vector in the coordinate system measured by sensor A, vector l' b For the straight line l b The direction vector in the coordinate system measured by sensor B, P b For the straight line l b The coordinates of the previous point in the coordinate system of sensor B, P a For the straight line l a The coordinates of the previous point in the measurement coordinate system of sensor A;

[0021] The coordinates P of each point on it are measured by the line laser sensor 1 ={x i ,y i ,z i}(i=1,2,3...n), based on the least squares fitting principle of spatial straight line, we can get the straight line l a The spatial equation in the measurement coordinate system of the online laser sensor A is:

[0022]

[0023] In the formula

[0024]

[0025] Furthermore, in step 3, the data collected by the line laser sensor is two-dimensional contour point data, which only has x-coordinate and z-coordinate information, and the y-coordinate value of each point is 0, so there is b 1 =0 and y 1 =0; that is, straight line l a The direction vector is l' a =(a 1 ,0,1) T And pass point P a =(x 1 ,0,1) T .

[0026] Similarly, for the straight line l b The spatial equation in the measurement coordinate system of the online laser sensor B is obtained as follows:

[0027]

[0028] Then the straight line l b The direction vector is l' b =(a 2 ,0,1) T And pass point P b =(x 2 ,0,1) T According to the straight line l a With straight line l b The angle relationship between them can be obtained:

[0029] l a ′·R 0 l b ′=|l a ′|×|l b ′|cos(θ a +θ b ) (2-14)

[0030] The combined formulas (2-10) and (2-14) can establish the optimization objective function:

[0031]

[0032] By changing the position of the calibration plate multiple times, m groups of a can be fitted according to the measurement data of line laser sensors A and B. 1 、a 2 ,θ a and θ b The value of can be used to construct a nonlinear least squares optimization method based on the optimization objective function as shown in formula (2-16), and the pose transformation matrix between the two-line laser sensor measurement coordinate systems can be calculated.

[0033]

[0034] Furthermore, in step 6, the method for calculating the initial solution from the line laser measurement data is as follows:

[0035] First, expand and organize formula (2-14) to obtain:

[0036]

[0037] Multiple groups of a are fitted from the measurement data of line laser sensors A and B 1 、a 2 ,θ a and θ b The value of r can be calculated by using the multivariate linear regression method. 11 、r 13 、r 31 and r33 The value of

[0038] At the same time, by expanding and sorting formula (2-10), we can get:

[0039] K 1 x 1 +K 2 x 2 +K 3 a 1 +K 4 a 2 +K 5 x 1 a 2 +K 6 x 2 a 1 +K 7 a 1 a 2 +K 8 =0 (2-18)

[0040] Where K 1 -K 8 As shown in formula (2-19):

[0041]

[0042] Multiple groups of a fitted from the measurement data of line laser sensors A and B 1 、a 2 ,θ a and θ b The value of K can be obtained 1 -K 8 A set of special solutions [1,k 1 ,k 2 ,k 3 ,k 4 ,k 5 ,k 6 ,k 7 ] T ;

[0043] From K in formula (2-19) 4 , K 5 and K 8 We can get:

[0044] r 21 =k 4 r 23 (2-20)

[0045]

[0046] From the orthogonality of the rotation matrix, we can get:

[0047]

[0048] T can be determined based on the relative position of line laser sensors A and B. 2 The positive and negative nature of T 2 、r 21 With r 23 The value of .

[0049] From K in formula (2-19) 1 And formula (2-21) can be obtained:

[0050]

[0051] From K in formula (2-19) 8 And formula (2-21) can be obtained:

[0052]

[0053] From the orthogonality of the rotation matrix, we can get:

[0054] (r 12 , r 22 , r 32 )=±(r 11 , r 21 , r 31 )×(r 13 , r 23 , r 33 ) (2-25)

[0055] The sign of formula (2-25) is determined by |R 0 |=1 to determine, so far we get the rotation transformation matrix R close to the global optimal solution 0 And the displacement transformation matrix T 0 The value of is taken as the initial solution for optimization and substituted into formula (2-16). The final solution can be obtained through nonlinear least squares optimization to realize the calibration of the pose relationship between the coordinate systems of the line laser sensor measurement.

[0056] Beneficial Effects

[0057] The present invention designs a multi-line laser scanning measurement system for the end gear structure of an aircraft engine, and proposes a calibration model of a multi-line laser measurement system based on a stripe calibration plate to address the problems of low precision and high cost of standard ball calibration. After calibration, the measurement error does not exceed 2.4 microns. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 This is a model diagram of the multi-line laser rotation scanning measurement system in the present invention.

[0059] Figure 2Schematic diagram of a fringe calibration plate used for calibrating a multi-line laser scanning system in the present invention.

[0060] Figure 3 It is a schematic diagram of the centerline laser measurement fringe calibration plate of the present invention.

[0061] Figure 4 And a schematic diagram of the point cloud result in the present invention.

[0062] Figure 5 It is a three-dimensional schematic diagram of the calibration method in the present invention. DETAILED DESCRIPTION

[0063] The following combination Figures 1 to 5 This embodiment will be described in detail.

[0064] The multi-line laser rotation scanning measurement model of the present invention is as follows Figure 1 As shown, it is mainly composed of a line laser sensor and an air-floating turntable.

[0065] When predicting and controlling the coaxiality of the end gear rotor, it is important to focus on the machining errors of the mating tooth surface and the outer cylindrical surface. Therefore, three line laser sensors are used to measure these areas respectively. Line laser sensor 1 measures the cross-sectional profile of the outer cylindrical surface of the end gear rotor, while line laser sensors 2 and 3 measure the cross-sectional profile of the mating tooth surface of the end gear rotor.

[0066] During actual measurement, the air-floating turntable provides a stable rotation center and drives the end-tooth rotor to rotate around the turntable axis. After the end-tooth rotor rotates 360°, the line laser sensors 1, 2, and 3 respectively measure the line profile data of the outer cylindrical surface of the end-tooth rotor and the tooth surface. The obtained data are spliced ​​to reconstruct the end-tooth rotor surface point cloud in three dimensions, realizing the three-dimensional morphology measurement of the end-tooth rotor surface.

[0067] The above data splicing includes two parts:

[0068] First, each line laser sensor has an independent measurement coordinate system, so it is necessary to unify the line laser measurement data into the same coordinate system; secondly, the measurement is a rotational scanning measurement, so it is necessary to rotate the measurement data of each line laser sensor around the axis of the turntable to the corresponding position. The splicing work is based on the known position relationship between each line laser sensor and the turntable. Therefore, when the line laser sensor measurement data is reconstructed in three dimensions, two calibration operations are required, specifically:

[0069] (1) Calibrate the pose transformation matrix between the measurement coordinate systems of each line laser sensor to achieve the splicing of multi-line laser sensor measurement data.

[0070] (2) Calibrate the spatial position of the turntable's rotation axis to achieve the splicing of the measured line profile data at different rotation angles of the end gear rotor.

[0071] The operation process is described in detail below.

[0072] Step 1: Linear solution of the pose transformation between coordinate systems measured by the line laser sensor

[0073] When the line laser sensor projects laser light onto the calibration plate, the laser produces specular reflection at the metal stripes, and the point coordinate information cannot be collected. However, diffuse reflection occurs at the ceramic stripes, and the point coordinate information can be collected. Therefore, the line laser sensor collects a set of points with periodic intervals, such as Figure 3 shown.

[0074] According to the point coordinate information collected by the line laser sensor, the Figure 3 a) Distance between midline segments l a , then the angle θ between the laser line and the stripe on the calibration plate can be calculated as:

[0075] Figure 2 Where Δd is the designed stripe spacing width. By introducing periodic stripes on the calibration plate, the line laser sensor can obtain angle information while obtaining point coordinate information on the two-dimensional plate, thereby achieving the calibration effect of a three-dimensional target.

[0076] Use the stripe calibration plate to calibrate the two line laser sensors to measure the pose transformation relationship between the coordinate systems. Figure 4 As shown in Figure 2, two line laser sensors simultaneously project laser light onto the calibration plate, where the straight line l a With straight line l b are the light rays projected by line laser sensors A and B on the calibration board; angle θ a With angle θ b The straight lines l a With straight line l b The angle with the stripe direction on the calibration plate can be calculated using formula (2-7).

[0077] If the coordinate system measured by line laser sensor A is used as the world coordinate system, and the rotation transformation matrix R from the coordinate system measured by line laser sensor B to the world coordinate system is assumed to be 0 And the displacement transformation matrix T 0 They are:

[0078]

[0079] T 0 =[T 1 T 2 T 3 ] T (2-9)

[0080] Since the straight line l a With straight line lb Both are located on the plane of the calibration plate, so the two straight lines are coplanar and satisfy the relationship:

[0081] (l a ′×R 0 l b ′)·(R 0 P b +Τ 0 -P a )=0 (2-10)

[0082] Among them, the vector l' a For the straight line l a The direction vector in the coordinate system measured by sensor A, vector l' b For the straight line l b The direction vector in the coordinate system measured by sensor B, P b For the straight line l b The coordinates of the previous point in the coordinate system of sensor B, P a For the straight line l a The coordinates of the previous point in the sensor A measurement coordinate system.

[0083] For the straight line l a , the coordinates of each point on it are measured by the line laser sensor 1 ={x i ,y i ,z i}(i=1,2,3...n), based on the principle of least squares fitting of spatial straight line, the spatial equation in the measurement coordinate system of the online laser sensor A can be obtained as follows:

[0084]

[0085] In the formula

[0086]

[0087] Step 2: Nonlinear optimization of the pose transformation between coordinate systems measured by the line laser sensor

[0088] Since the data collected by the line laser sensor is two-dimensional contour point data, only the x-coordinate and z-coordinate information are available, and the y-coordinate value of each point is 0, so there is b 1 =0 and y 1 = 0. That is, the straight line l a The direction vector is l' a =(a 1 ,0,1) T And pass point P a =(x 1 ,0,1) T .

[0089] Similarly, for the straight line l b The spatial equation in the measurement coordinate system of the online laser sensor B is obtained as follows:

[0090]

[0091] Then the straight line l b The direction vector is l' b =(a 2 ,0,1) T And pass point P b =(x 2 ,0,1) T According to the straight line l a With straight line l b The angle relationship between them can be obtained:

[0092] l a ′·R 0 l b ′=|l a ′|×|l b ′|cos(θ a +θ b ) (2-14)

[0093] The combined formulas (2-10) and (2-14) can establish the optimization objective function:

[0094]

[0095] By changing the position of the calibration plate multiple times, m groups of a can be fitted according to the measurement data of line laser sensors A and B. 1 、a 2 ,θ a and θ b The value of can be used to construct a nonlinear least squares optimization method based on the optimization objective function as shown in formula (2-16), and the pose transformation matrix between the two-line laser sensor measurement coordinate systems can be calculated.

[0096]

[0097] It should be noted that when performing nonlinear least squares optimization, the derivative form of the objective function cannot be directly written due to nonlinearity, so the initial solution provided should be as close to the global optimal solution as possible. The following is a method for calculating the initial solution from line laser measurement data.

[0098] First, expand and organize formula (2-14) to obtain:

[0099]

[0100] Multiple groups of a are fitted from the measurement data of line laser sensors A and B 1 、a2 ,θ a and θ b The value of r can be calculated by using the multivariate linear regression method. 11 、r 13 、r 31 and r 33 The value of .

[0101] At the same time, by expanding and sorting formula (2-10), we can get:

[0102] K 1 x 1 +K 2 x 2 +K 3 a 1 +K 4 a 2 +K 5 x 1 a 2 +K 6 x 2 a 1 +K 7 a 1 a 2 +K 8 =0 (2-18)

[0103] Where K 1 -K 8 As shown in formula (2-19):

[0104]

[0105] Similarly, multiple groups of a are fitted from the measurement data of line laser sensors A and B 1 、a 2 ,θ a and θ b The value of K can be obtained 1 -K 8 A set of special solutions [1,k 1 ,k 2 ,k 3 ,k 4 ,k 5 ,k 6 ,k 7 ] T .

[0106] From K in formula (2-19) 4 , K 5 and K 8 We can get:

[0107] r 21 =k 4 r 23 (2-20)

[0108]

[0109] From the orthogonality of the rotation matrix, we can get:

[0110]

[0111] T can be determined based on the relative position of line laser sensors A and B. 2 The positive and negative nature of T 2 、r 21 With r 23 The value of .

[0112] From K in formula (2-19) 1 And formula (2-21) can be obtained:

[0113]

[0114] From K in formula (2-19) 8 And formula (2-21) can be obtained:

[0115]

[0116] From the orthogonality of the rotation matrix, we can get:

[0117] (r 12 , r 22 , r 32 )=±(r 11 , r 21 , r 31 )×(r 13 , r 23 , r 33 ) (2-25)

[0118] The sign of formula (2-25) still depends on |R 0 |=1 to determine, so far a set of rotation transformation matrices R close to the global optimal solution has been calculated 0 And the displacement transformation matrix T 0 The value of is taken as the initial solution for optimization and substituted into formula (2-16). The final solution can be obtained through nonlinear least squares optimization to realize the calibration of the pose relationship between the coordinate systems of the line laser sensor measurement.

[0119] Example

[0120] The experimental device for calibrating the position and posture relationship between coordinate systems using a line laser sensor is mainly composed of a line laser sensor, a stripe calibration plate, a calibration plate adapter, etc.

[0121] The calibration plate of the present invention is as follows Figure 2The calibration plate is made of ceramic material, which has high flatness and small thermal expansion rate. High-precision metal reflective stripes are processed on its surface through photolithography.

[0122] The stripe calibration plate is made of zirconium oxide material through ultra-precision processing, and its surface flatness error is less than 1.0μm. The surface is processed with reflective metal stripes with an interval of 3mm using a photolithography process. Taking the calibration of the position relationship between the coordinate systems of the line laser sensor 1 and sensor 2 as an example, when calibrating, first adjust the position of the stripe calibration plate so that it is within the range of the two line laser sensors at the same time, and then collect the measurement results of the two line laser sensors at the same time through the host computer software. Finally, fit the linear equation based on the measurement data and calculate the angle between the two line laser sensor lights.

[0123] The above contents of the present invention are only preferred embodiments of the present invention and are not intended to limit the implementation scheme of the present invention. A person skilled in the art can easily make corresponding changes or modifications based on the main concept and spirit of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope required by the claims.

Claims

1. A line laser array calibration method based on a stripe plate, characterized in that: The steps include: Step 1, performing three-dimensional topography measurement on the end gear rotor surface; Step 2: Linear solution of the pose transformation between the line laser sensor measurement coordinate systems; Step 3: nonlinearly optimize the pose transformation between the line laser sensor measurement coordinate systems to achieve the calibration of the pose relationship between the line laser sensor measurement coordinate systems.

2. The line laser array calibration method based on a stripe plate according to claim 1, characterized in that: In step 1, the three-dimensional morphology measurement of the end tooth rotor surface is performed by using a line laser sensor and an air floating turntable, and the line contour data of the outer cylindrical surface of the end tooth rotor and the tooth surface are measured respectively. The obtained data are spliced ​​and the end tooth rotor surface point cloud is reconstructed in three dimensions to realize the three-dimensional morphology measurement of the end tooth rotor surface.

3. The line laser array calibration method based on a stripe plate according to claim 1, characterized in that: The specific operation of step 2 is as follows: the line laser sensor projects laser light onto the calibration plate and collects a set of points with periodic intervals. Based on the point coordinate information collected by the line laser sensor, the line segment distance l can be calculated. a , then the angle θ between the laser line and the stripe on the calibration plate can be calculated as: Δd is the designed stripe spacing width. By introducing periodic stripes on the calibration plate, the line laser sensor can obtain angle information while obtaining the point coordinate information on the two-dimensional plate, thereby realizing the calibration of the three-dimensional target.

4. The line laser array calibration method based on a stripe plate according to claim 3, characterized in that: In step 2, the stripe calibration plate is used to calibrate the two line laser sensors to measure the pose transformation between coordinate systems. The two line laser sensors simultaneously project lasers onto the calibration plate, where the straight line l a With straight line l b are the light projected by line laser sensors A and B on the calibration board; angle θ a With angle θ b The straight lines l a With straight line l b The angle with the stripe direction on the calibration plate can be calculated using formula (2-7):

5. The line laser array calibration method based on a stripe plate according to claim 4, characterized in that: In step 2, the coordinate system measured by the line laser sensor A is used as the world coordinate system, and it is assumed that the rotation transformation matrix R0 and the displacement transformation matrix T0 from the coordinate system measured by the line laser sensor B to the world coordinate system are: <h2 style=";text-align:left;direction:ltr">T0=[T1 T2 T3]<h2 style=";text-align:left;direction:ltr"> T <h2 style=";text-align:left;direction:ltr"> (2-9) Straight line a With straight line l b Both are located on the plane of the calibration plate, so the two straight lines are coplanar and satisfy the relationship: (l a ′×R0l b ′)·(R0P b +Τ0-P a )=0 (2-10) Among them, the vector l' a For the straight line l a The direction vector in the coordinate system measured by sensor A, vector l' b For the straight line l b The direction vector in the coordinate system measured by sensor B, P b For the straight line l b The coordinates of the previous point in the coordinate system of sensor B, P a For the straight line l a The coordinates of the previous point in the measurement coordinate system of sensor A; The coordinates of each point on it are measured by the line laser sensor P1 = {x i ,y i ,z i }(i=1,2,3...n), based on the least squares fitting principle of spatial straight line, we can get the straight line l a The spatial equation in the measurement coordinate system of the online laser sensor A is: In the formula 6. The line laser array calibration method based on a stripe plate according to claim 1, characterized in that: In step 3, the data collected by the line laser sensor is two-dimensional contour point data, which only has x-coordinate and z-coordinate information, and the y-coordinate value of each point is 0, so b1=0 and y1=0; that is, the straight line l a The direction vector is l' a =(a1,0,1) T And pass point P a =(x1,0,1) T ; Similarly, for the straight line l b The spatial equation in the measurement coordinate system of the online laser sensor B is obtained as follows: Then the straight line l b The direction vector is l' b =(a2,0,1) T And pass point P b =(x2,0,1) T According to the straight line l a With straight line l b The angle relationship between them can be obtained: l a ′·R0l b ′=|l a ′|×|l b ′|cos(θ a +θ b ) (2-14) The combined formulas (2-10) and (2-14) can establish the optimization objective function: By changing the position of the calibration plate multiple times, m groups of a1, a2, θ can be fitted according to the measurement data of line laser sensors A and B. a and θ b The value of can be used to construct a nonlinear least squares optimization as shown in formula (2-16) based on the optimization objective function, and the pose transformation matrix between the two-line laser sensor measurement coordinate systems can be calculated:

7. The line laser array calibration method based on a stripe plate according to claim 1, characterized in that: In step 6, the method for calculating the initial solution from the line laser measurement data is as follows: First, expand and organize formula (2-14) to obtain: Multiple groups of a1, a2, θ are fitted from the measurement data of line laser sensors A and B. a and θ b The value of r can be calculated by using the multivariate linear regression method. 11 、r 13 、r 31 and r 33 The value of At the same time, by expanding and sorting formula (2-10), we can get: K1x1+K2x2+K3a1+K4a2+K5x1a2+K6x2a1+K7a1a2+K8=0 (2-18) Where K1-K8 is as shown in formula (2-19): Multiple groups of a1, a2, θ fitted from the measurement data of line laser sensors A and B a and θ b The value of can be used to obtain a set of special solutions of K1-K8 [1,k1,k2,k3,k4,k5,k6,k7] T ; From K4, K5 and K8 in formula (2-19), we can get: r 21 ＝k4r 23 (2-20) From the orthogonality of the rotation matrix, we can get: The positive and negative of T2 can be determined according to the relative position of line laser sensors A and B, and then T2 and r can be calculated. 21 With r 23 The value of From K1 in formula (2-19) and formula (2-21), we can get: From K8 in formula (2-19) and formula (2-21), we can get: From the orthogonality of the rotation matrix, we can get: (r 12 , r 22 , r 32 )＝±(r 11 , r 21 , r 31 )×(r 13 , r 23 , r 33 ) (2-25) The sign of formula (2-25) is determined by |R0|=1. At this point, the values ​​of the rotation transformation matrix R0 and the displacement transformation matrix T0 close to the global optimal solution are obtained. They are substituted into formula (2-16) as the initial solution for optimization. The final solution can be obtained through nonlinear least squares optimization, thereby realizing the calibration of the pose relationship between the linear laser sensor measurement coordinate systems.

Images