CN111486802A - Rotating shaft calibration method based on self-adaptive distance weighting - Google Patents

Abstract

A rotary axis calibration method based on self-adaptive distance weighting uses a checkerboard calibration plate to calibrate the rotary axis of a turntable. Place the checkerboard calibration plate obliquely on the rotating platform and make the calibration plate in the camera field of view, rotate the rotating platform and collect the image of the calibration plate, and then establish the conversion relationship between the camera coordinate system Ov and the calibration plate coordinate system O _B , and use the conversion relationship, obtain the coordinates in the camera coordinate system of all the corner points of the checkerboard calibration board in at least 3 different rotation positions, and then calculate the center of the trajectory circle formed by the corner points of the checkerboard calibration board. According to the distance between the front and rear positions of the corner point, the weighting coefficient of the center of the trajectory circle of the corner point is determined, and the line with the smallest weighted sum of squares of the distance between the center of each trajectory circle and the rotation axis to be calibrated in the camera coordinates is taken as the rotation axis in the camera coordinate system. Through the invention, the calibration of the rotation axis can be realized quickly and accurately, and the error is reduced by 15.6% compared with the traditional calibration method.

Description

Rotation axis calibration method based on adaptive distance weighting

technical field

The invention relates to a rotary axis calibration method based on adaptive distance weighting, and belongs to the technical fields of optical measurement and mechanical engineering.

Background technique

When performing structured light 3D measurement, due to the camera's field of view, shooting angle and other problems, only a certain angle of point cloud can be measured in one measurement. At present, the commonly used point cloud stitching methods mainly include automatic stitching and instrument-dependent stitching. The automatic stitching of point clouds is mainly based on the Iterative Closest Point (ICP) method. This method has high accuracy, but it needs to have overlapping parts between the two point clouds, and the selection of the initial value has a great influence on the final stitching result. Instrument-dependent splicing methods mainly include the use of marker points and the use of rotating platforms. The mark point splicing method is mostly used for the measurement of large objects, and its accuracy is easily affected by the deformation of the mark points, so it is not suitable for the measurement of objects with large curvature and complex surfaces; The object is measured at multiple angles, and the conversion relationship between point clouds of different angles is obtained by means of the parameters of the rotation axis of the turntable, and finally the point cloud splicing is realized. This method has high speed and high accuracy, and is widely studied and used, but the accuracy of this method is greatly affected by the rotary axis of the turntable, so it is necessary to accurately calibrate the rotary axis.

Scholars at home and abroad have done a lot of research work on the method and optimization of rotary axis calibration. It mainly includes: a rotation axis calibration method based on a cylindrical calibration block, which measures more than three cylindrical point clouds with different angles, and uses its axis to calibrate the parameters of the rotation axis; a rotation axis calibration method based on a calibration ball, this method measures The calibration ball point cloud at different rotation positions, fit the center of the circle, and finally use the center to calibrate the parameters of the rotation axis; the rotation axis calibration method based on the cone calibration block, the method uses the coordinates of the cone vertex to calibrate the rotation axis; based on the L-type The rotation axis calibration method of the plane calibration object, the method solves the rotation axis equation by measuring the right angle plane before and after rotation and finding the intersection line. The above methods all use the standard calibration block to calibrate the rotation axis, which increases the measurement cost while improving the calibration accuracy, and introduces complex calculations such as cylindrical fitting and spherical fitting, which reduces the calibration efficiency. In addition, the calibration methods based on feature points include: calculating the parameters of the rotary axis of the turntable by attaching circular mark points on the plane calibration plate; installing a laser transmitter on the rotary table, and using the laser to manufacture feature points to calculate the parameters of the rotary axis; Additional datum points to determine the axis of rotation. These calibration methods are implemented with the help of feature points, which simplifies the amount of calculation to a certain extent, but does not consider the different contributions of different position feature points to the accuracy of fitting the rotating axis, so the calibration accuracy needs to be improved.

SUMMARY OF THE INVENTION

In view of the deficiencies of the prior art, the present invention provides a rotary axis calibration method based on adaptive distance weighting, so as to improve the calibration accuracy of the rotary axis.

The present invention adopts following technical scheme:

A rotary axis calibration method based on adaptive distance weighting, the method comprises the following steps:

Step ₁ : Establish the camera coordinate system Ov, the calibration board coordinate system OB, and the conversion relationship between the camera coordinate system Ov and the calibration board coordinate system _OB ,

Step 2: Place the checkerboard calibration plate inclined on the rotating platform and make the calibration plate in the camera's field of view, rotate the rotating platform and collect the image of the calibration plate to obtain the calibration of the corner points of all the checkerboard calibration plates in at least 3 different rotation positions The coordinates under the board coordinate system, and then use the conversion relationship between the camera coordinate system and the calibration board coordinate system to obtain the coordinates under the camera coordinate system of all checkerboard corners at least 3 different rotation positions to calibrate the board corners,

(X_Qi,Y_Qi,Z_Qi)为第i个角点 对应的轨迹圆圆心坐标，i＝1,2….m表示角点序号，m为棋盘格标定板上的角点 总数量，再将点(a,b,c)作为旋转轴上的点，对随棋盘格标定板旋转的角点所形成 的轨迹圆圆心进行空间直线拟合并得到相机坐标下的旋转轴，最后，利用相机坐 标系和标定板坐标系间转换关系，对相机坐标下的旋转轴进行转换，完成旋转轴 标定，所述空间直线拟合采用以下方法：Step 3: Select the point (a, b, c) whose coordinates are the average of the coordinates of the center of the trajectory circle corresponding to each corner point,

(X _Qi , Y _Qi , Z _Qi ) are the coordinates of the center of the trajectory circle corresponding to the i-th corner point, i=1,2....m represents the number of the corner points, m is the total number of corner points on the checkerboard calibration board, and then Taking the point (a, b, c) as the point on the rotation axis, the center of the trajectory circle formed by the corner points of the checkerboard calibration board is fitted with a space line and the rotation axis in the camera coordinates is obtained. Finally, use the camera The conversion relationship between the coordinate system and the calibration plate coordinate system is to convert the rotation axis under the camera coordinates to complete the rotation axis calibration. The spatial straight line fitting adopts the following method:

其中，

d_i ²＝(X_Qi-a)²+(Y_Qi-b)²+(Z_Qi-c)²-[u(X_Qi-a)+v(Y_Qi-b)+w(Z_Qi-c)]²，d_i为第i个 角点轨迹圆圆心到待标定的旋转轴的距离，[u,v,w]为待标定的旋转轴的单位方向 向量，s.t.表示约束，min表示取最小值，α_i为第i个角点轨迹圆圆心对应的加权 系数，i为角点序号，j＝1,2….n表示标定板位置序号，n为标定板总位置数，l_ij为第i个角点在第j个旋转位置与第j+1个旋转位置之间的移动距离，p为大于1 的整数。Take the straight line L with the smallest weighted square sum of the distance from the center of each trajectory circle to the rotation axis to be calibrated in camera coordinates as the rotation axis in camera coordinates:

in,

d _i ² =(X _Qi -a) ² +(Y _Qi -b) ² +(Z _Qi -c) ² -[u(X _Qi -a)+v(Y _Qi -b)+w(Z _Qi - c)] ² , d _i is the distance from the i-th corner point trajectory circle center to the rotation axis to be calibrated, [u, v, w] is the unit direction vector of the rotation axis to be calibrated, st means constraint, min means take The minimum value, α _i is the weighting coefficient corresponding to the i-th corner point trajectory circle center, i is the corner point sequence number, j=1,2....n denotes the calibration plate position sequence number, n is the total number of calibration plate positions, l _ij is The moving distance of the i-th corner point between the j-th rotation position and the j+1-th rotation position, where p is an integer greater than 1.

Compared with the prior art, the present invention has the following beneficial effects:

α_i为第i个角点轨迹圆圆心对应的加权系数，i为角点序 号，j＝1,2….n表示标定板位置序号，n为标定板总位置数，l_ij为第i个角点在第 j个旋转位置与第j+1个旋转位置之间的距离，使得各角点轨迹圆心对应加权系 数实现自适应取值，从而保证对旋转轴拟合精度贡献越小的圆心，其加权系数越 小，而对旋转轴拟合精度贡献越大的圆心其加权系数越大，从而提高了旋转轴的 拟合精度。具体来说：When calibrating the rotation axis, the present invention proposes to design the weighting coefficient based on the moving distance between the front and rear positions of each corner point, considering that the center of the rotation track corresponding to different corner points has different effects on the fitting accuracy of the rotation axis, namely:

α _i is the weighting coefficient corresponding to the i-th corner point trajectory circle center, i is the corner point sequence number, j=1, 2....n denotes the calibration plate position sequence number, n is the total number of calibration plate positions, and l _ij is the i-th The distance between the j-th rotation position and the j+1-th rotation position of the corner point makes the weighting coefficient corresponding to the center of the trajectory of each corner point to achieve an adaptive value, so as to ensure that the center of the circle that contributes less to the fitting accuracy of the rotation axis, The smaller the weighting coefficient is, the larger the weighting coefficient is for the center of the circle that contributes more to the fitting accuracy of the rotating axis, thereby improving the fitting accuracy of the rotating axis. Specifically:

When calibrating the rotation axis, the present invention designs a weighting coefficient based on the distance between the front and rear positions of the corner point, taking into account the different contributions of the trajectory centers of the corner points at different positions to the rotation axis. The mean value of the moving distance l _i,j between the corner point and the previous position is used as the dividing line, so that the weighting coefficient corresponding to the corner point whose moving distance is less than the mean value is less than 1, and the weighting coefficient corresponding to the corner point greater than the mean value is greater than 1, In addition, the calculation of the p-th power can further expand the difference between the weight coefficients of different corner points, thereby reducing the contribution of the circle center with larger error to the fitting rotation axis, and increasing the contribution of the circle center with smaller error to the fitting rotation axis. This design method realizes the adaptive value of the weighting coefficient according to the moving distance of the front and rear positions of the corner points, so as to ensure that the trajectory center with the smaller error has a greater contribution to the rotation axis, avoiding the traditional method that defaults to the same contribution of the trajectory center of each corner point. The error can effectively improve the calibration accuracy of the rotary axis.

Description of drawings

Fig. 1 is a working flow chart of the present invention.

Figure 2 Schematic diagram of the position of the lower corner of the camera coordinate system.

Figure 3 Rotation axis fitting flow chart.

Figure 4 is a schematic diagram of the rotation axis calibration device, in which 1 vision bracket, 2 industrial cameras, 3 turntables, and 4 checkerboard calibration boards.

Figure 5 is a schematic diagram of the transformation relationship of the coordinate system, wherein the circle is the rotation trajectory of the corner point, the middle straight line is the fitted rotation axis, and the point near the straight line is the center of the corner point trajectory.

Fig. 6 Rotation axis fitting result graph.

Figure 7 Error evaluation results.

Detailed ways

A rotary axis calibration method based on adaptive distance weighting, comprising the following steps:

Step ₁ : Establish the camera coordinate system Ov, the calibration board coordinate system OB, and the conversion relationship between the camera coordinate system Ov and the calibration board coordinate system _OB ,

Step 2: Place the checkerboard calibration plate inclined on the rotating platform and make the calibration plate in the camera's field of view, rotate the rotating platform and collect the image of the calibration plate to obtain the calibration of the corner points of all the checkerboard calibration plates in at least 3 different rotation positions The coordinates under the board coordinate system, and then use the conversion relationship between the camera coordinate system and the calibration board coordinate system to obtain the coordinates under the camera coordinate system of all checkerboard corners at least 3 different rotation positions to calibrate the board corners,

(X_Qi,Y_Qi,Z_Qi)为第i个角点 对应的轨迹圆圆心坐标，i＝1,2….m表示角点序号，m为棋盘格标定板上的角点 总数量，再将点(a,b,c)作为旋转轴上的点，对随棋盘格标定板旋转的角点所形成 的轨迹圆圆心进行空间直线拟合并得到相机坐标下的旋转轴，最后，利用相机坐 标系和标定板坐标系间转换关系，对相机坐标下的旋转轴进行转换，完成旋转轴 标定，所述空间直线拟合采用以下方法：Step 3: Select the point (a, b, c) whose coordinates are the average of the coordinates of the center of the trajectory circle corresponding to each corner point,

(X _Qi , Y _Qi , Z _Qi ) are the coordinates of the center of the trajectory circle corresponding to the i-th corner point, i=1,2....m represents the number of the corner points, m is the total number of corner points on the checkerboard calibration board, and then Taking the point (a, b, c) as the point on the rotation axis, the center of the trajectory circle formed by the corner points of the checkerboard calibration board is fitted with a space line and the rotation axis in the camera coordinates is obtained. Finally, use the camera The conversion relationship between the coordinate system and the calibration plate coordinate system is to convert the rotation axis under the camera coordinates to complete the rotation axis calibration. The spatial straight line fitting adopts the following method:

其中，

d_i ²＝(X_Qi-a)²+(Y_Qi-b)²+(Z_Qi-c)²-[u(X_Qi-a)+v(Y_Qi-b)+w(Z_Qi-c)]²，d_i为第i个 角点轨迹圆圆心到待标定的旋转轴的距离，[u,v,w]为待标定的旋转轴的单位方向 向量，s.t.表示约束，min表示取最小值，α_i为第i个角点轨迹圆圆心对应的加权 系数，i为角点序号，j＝1,2….n表示标定板位置序号，n为标定板总位置数，l_ij为第i个角点在第j个旋转位置与第j+1个旋转位置之间的移动距离，p为大于1 的整数，本实施例可将p取值为7。在本实施例中，Take the straight line L with the smallest weighted square sum of the distance from the center of each trajectory circle to the rotation axis to be calibrated in camera coordinates as the rotation axis in camera coordinates:

in,

d _i ² =(X _Qi -a) ² +(Y _Qi -b) ² +(Z _Qi -c) ² -[u(X _Qi -a)+v(Y _Qi -b)+w(Z _Qi - c)] ² , d _i is the distance from the i-th corner point trajectory circle center to the rotation axis to be calibrated, [u, v, w] is the unit direction vector of the rotation axis to be calibrated, st means constraint, min means take The minimum value, α _i is the weighting coefficient corresponding to the i-th corner point trajectory circle center, i is the corner point sequence number, j=1,2....n denotes the calibration plate position sequence number, n is the total number of calibration plate positions, l _ij is The moving distance of the i-th corner point between the j-th rotational position and the j+1-th rotational position, p is an integer greater than 1, and p may be set to be 7 in this embodiment. In this embodiment,

The origin of the camera coordinate system is set at the optical center of the camera, the z-axis passes through the optical center and is perpendicular to the camera imaging plane, and the direction toward the photographed object is positive, and the x-axis passes through the optical center and is perpendicular to the z-axis, located in the imaging plane. The horizontal direction, facing the object horizontally to the right is the positive direction, the y-axis passes through the optical center and is perpendicular to the x and z axes, and facing the object upwards is the positive direction; the origin of the calibration board coordinate system is set at the lower right corner of the calibration board. , its z-axis passes through the corner point and is perpendicular to the plane of the calibration board, and the direction toward the camera is the positive direction; the x-axis passes through the corner point and is perpendicular to the z-axis, located in the horizontal direction of the calibration board plane, and the left direction is the positive direction when facing the calibration board , the y-axis is perpendicular to the x and z-axes through this corner point, and the upward direction is the positive direction when facing the calibration plate; the conversion relationship between the camera coordinate system Ov and the calibration plate coordinate system O _B is [X _V Y _V Z _V ] ^T = R[X _B Y _B Z _B ] ^T +t, X _B , _{Y B} , Z _B are the coordinates of any corner point on the calibration board under the calibration board coordinate system OB, and the coordinate value Z _B under the calibration board coordinate system OB is the default is 0, X _V , Y _V , Z _V are the coordinate values of the corresponding points in the camera coordinate system Ov of any corner point on the calibration board, and the coordinate values of the corresponding points (X _V , Y _V , Z _V ) are determined by the camera Obtained by shooting, using the coordinates of any corner point (X _B , Y _B , Z _B ) under the calibration board coordinate system O _B and the corresponding point (X _V , Y _V , Z _V ) of any corner point under the camera coordinate system Ov Coordinates, calculate the external parameter matrix R and t.

The rotating platform includes a vision support 2 and a rotating platform 3, a camera 1 is provided on the vision support 2, a checkerboard calibration plate 4 is placed on the rotating platform 3, and the checkerboard calibration plate 4 is located in the camera field of view.

Rotate the platform every 4°~10° and collect the image of the calibration plate, specifically, rotate the platform every 5° and collect the image of the calibration plate.

The moving distance l _ij of the i-th corner point between the j-th rotation position and the j+1-th rotation position is: l _i,j =||P _i,j+1 -P _i,j ||, where P _i,j is the i-th corner point on the j-th position calibration board, i=1,2....m represents the corner point number, m is the total number of corner points, and the corner point number is formed from right to left and bottom to top s-shaped increment, j=1,2….n represents the position number of the calibration board, n is the total number of positions of the calibration board, and |||| represents the norm.

The point (a,b,c) is taken as a point on the axis of rotation for the following reasons: Let (x ₀ , y ₀ , z ₀ ) be a point on the line L:

_{x 0} =a+δx

y ₀ =b+ _δy

z ₀ =a+δ _z

中得：Substitute x ₀ , y ₀ , z ₀ into the formula

Win:

in:

f(u,v,w)=(1-u ² )B ₁₁ +(1-v ² )B ₂₂ +(1-w ² )B ₃₃ -2uvB ₁₂ -2uwB ₁₃ -2vwB ₂₃

Therefore, for any (u,v,w), we have:

When δ _x =δ _y =δ _z =0

可取最小值，即直线L通过点(a,b,c)。at this time,

Take the minimum value, that is, the straight line L passes through the point (a, b, c).

The design idea of the weighting coefficient is: take the average value of the relative moving distances l _i,j between all the corner points on the jth position calibration board and the previous position as the dividing line, so that the moving distance is less than the average value of the corresponding corner points. The weighting coefficient is less than 1, and the weighting coefficient corresponding to the corner points greater than the average value is greater than 1, so that the weighting coefficient corresponding to the center of the trajectory of each corner point realizes an adaptive value. The purpose of taking p to the 7th power is to further expand the difference between the weight coefficients of different corner points, thereby reducing the contribution of the circle center with larger error to the fitting of the rotation axis, and increasing the contribution of the circle center with smaller error to the fitting of the rotation axis.

The design can give the corresponding weight to the center of the corner trajectory according to the moving distance of the corner, that is, the error of the center of the circle.

其中|| ||表示求范数，则，The above di can be calculated by the following formula:

Where || || represents the norm, then,

d _i ² =(X _Qi -a) ² +(Y _Qi -b) ² +(Z _Qi -c) ² -[u(X _Qi -a)+v(Y _Qi -b)+w(Z _Qi - c)] ² .

Below in conjunction with specific examples and the specific implementation method of the present invention will be described.

As shown in FIG. 3 , the experimental device of the present invention includes 1 vision stand, 2 industrial cameras, and 3 turntables. There are mounting holes on the vision bracket, and the camera is fixed to the vision bracket through bolts.

_The camera coordinate system Ov and the calibration board coordinate system OB are established, wherein the camera coordinate system Ov is fixed, and the calibration board coordinate system _OB changes with the rotation of the turntable. Then the determination of the rotation axis of the turntable can be transformed into the representation of the rotation axis in the camera coordinate system.

The coordinates of the corner points in the calibration plate coordinate system are known, and according to the conversion relationship, the coordinates of the corner points in the camera coordinate system can be obtained.

Convert all corner coordinates to the camera coordinate system, and the subsequent processes are carried out in the camera coordinate system. Let the plane equation of the corner locus circle be:

Ax+By+Cz+D=0

和向量

进行叉乘可获得该平面空间法向量，即Among them, A, B, and C respectively represent the parameters of the normal vector of the plane, which can be obtained by using the coordinates of the three positions of any corner point. Take three positions q ₁ (x ₁ , y ₁ , z ₁ ), q ₂ (x ₂ , y ₂ , z ₂ ), q ₃ (x ₃ , y ₃ , z ₃ ) of the same corner point, pair the vector

and vector

The plane space normal vector can be obtained by performing the cross product, that is,

Where N=[A, B, C], × represents the cross product. At this time, the value of D can be calculated by substituting the coordinates of any corner point into the plane equation. It is known that the distance from different positions of the same corner point on the trajectory circle to the center of the circle is equal to the radius, and the center of the circle and the corner point are on the same plane, this relationship satisfies the equation:

||P _i,j -Q _i ||=r ²

AX _Qi +BY _Qi +CZ _Qi +D=0

Where |||| represents the norm, point P _i,j (X _P , Y _P , Z _P ) is the i-th corner point on the j-th position calibration board, Q _i (X _Qi , Y _Qi , Z _Qi ) ) is the center of the trajectory circle corresponding to the i-th corner point, i=1, 2....m represents the number of the corner points, m is the total number of corner points, j=1, 2....n represents the position number of the calibration plate, and n is the calibration plate The total number of positions of the board, and r is the radius of the track circle. By taking the coordinates of three or more positions of any corner point and substituting them into the calculation, the center coordinates of the rotation track circle corresponding to the corner point can be obtained. Substitute different corner points into the calculation, and finally obtain the center of the rotation trajectory circle corresponding to all the corner points.

Before starting the measurement, adjust the vision stand to be at a suitable position and angle to ensure that the camera has a suitable field of view; place the calibration plate in a suitable position on the 3 turntable, and collect the corresponding calibration image every 5° of the turntable;

The internal and external parameters of the camera are calibrated, and the corner coordinates are converted from the calibration plate coordinate system to the camera coordinate system using the calibration results. The schematic diagram of the conversion relationship is shown in Figure 4;

Calculate the circle center of the rotation trajectory of the corner point, and use all the circle centers to fit the equation of the straight line where the rotation axis is located. The result is shown in Figure 5.

Using the above error evaluation method to calculate the error, the comparison results of the ordinary least squares method and the weighted least squares method are shown in Figure 6.

The implementation results of specific examples prove that the method proposed in the present invention effectively reduces the calibration error of the rotary axis, and the total error is reduced by 2.52 mm, about 15.6%. Therefore, the reduction of the present invention can significantly improve the calibration accuracy of the rotary axis. The present invention can evaluate the error through the following models, namely: establishing an error evaluation model to evaluate the calibration accuracy of the rotating shaft. It is known that the rotated arbitrary corner point P _i,j (j>1) has a relative rotation of the angle θ relative to the initial position corner point P _{i, 1} , and the corresponding conversion can be obtained by combining the parameters of the fitting rotation axis and the value of the angle θ Matrix H, through which the rotated corners can be restored to their original positions. Considering that there is an error between the fitted rotation axis and the actual rotation axis, after restoring the rotated corner points P _i,j to the initial position, the two do not completely coincide, but there is a certain offset, and it is easy to know the offset distance. The size of can indicate the size of the calibration error of the rotation axis. Calculate the offset distance of the i-th corner point of all position calibration boards after restoring to the initial position, and take the mean value M _i of the offset distances corresponding to all positions of the corner point. M _i can be expressed as follows:

_Mi can be used to represent the error corresponding to each corner point, and further calculate the sum S of _Mi corresponding to all corner points:

This evaluation method can ensure that the smaller the S value, the smaller the calibration error of the rotating axis. Then S can effectively evaluate the calibration error of the rotary axis.

Claims (5)

1. a rotation axis calibration method based on adaptive distance weighting, is characterized in that, comprises the steps: Step ₁ : Establish the camera coordinate system Ov, the calibration board coordinate system OB, and the conversion relationship between the camera coordinate system Ov and the calibration board coordinate system _OB , Step 2: Place the checkerboard calibration plate inclined on the rotating platform and make the calibration plate in the field of view of the camera, rotate the rotating platform and collect the image of the calibration plate, and obtain the calibration of all the corner points of the checkerboard calibration plate in at least 3 different rotation positions The coordinates under the board coordinate system, and then use the conversion relationship between the camera coordinate system and the calibration board coordinate system to obtain the coordinates under the camera coordinate system of all checkerboard corners at least 3 different rotation positions to calibrate the board corners, Step 3: Select the point (a, b, c) whose coordinates are the average of the coordinates of the center of the trajectory circle corresponding to each corner point,

(X _Qi , Y _Qi , Z _Qi ) are the coordinates of the center of the trajectory circle corresponding to the i-th corner point, i=1,2....m represents the number of the corner points, m is the total number of corner points on the checkerboard calibration board, and then Taking the point (a, b, c) as the point on the rotation axis, the center of the trajectory circle formed by the corner points of the checkerboard calibration board is fitted with a space line and the rotation axis in the camera coordinates is obtained. Finally, use the camera The conversion relationship between the coordinate system and the calibration plate coordinate system is to convert the rotation axis under the camera coordinates to complete the rotation axis calibration. The spatial straight line fitting adopts the following method: Take the straight line L with the smallest weighted square sum of the distance from the center of each trajectory circle to the rotation axis to be calibrated in camera coordinates as the rotation axis in camera coordinates:

in,

d _i ² =(X _Qi -a) ² +(Y _Qi -b) ² +(Z _Qi -c) ² -[u(X _Qi -a)+v(Y _Qi -b)+w(Z _Qi - c)] ² , d _i is the distance from the i-th corner point trajectory circle center to the rotation axis to be calibrated, [u, v, w] is the unit direction vector of the rotation axis to be calibrated, st means constraint, min means take The minimum value, α _i is the weighting coefficient corresponding to the i-th corner point trajectory circle center, i is the corner point sequence number, j=1,2....n denotes the calibration plate position sequence number, n is the total number of calibration plate positions, l _ij is The moving distance of the i-th corner point between the j-th rotation position and the j+1-th rotation position, where p is an integer greater than 1. 2. The rotation axis calibration method based on adaptive distance weighting according to claim 1, wherein the origin of the camera coordinate system is set at the optical center of the camera, and its z-axis passes through the optical center and is perpendicular to the camera imaging plane , the direction toward the object is positive, the x-axis passes through the optical center and is perpendicular to the z-axis, is located in the horizontal direction of the imaging plane, faces the object horizontally to the right, and the y-axis passes through the optical center and is perpendicular to the x and z axes, facing the The upward direction of the object is the positive direction; the origin of the coordinate system of the calibration plate is set at the corner point of the lower right corner of the calibration plate, the z-axis passes through the corner point and is perpendicular to the plane of the calibration plate, the direction toward the camera is the positive direction, and the x-axis passes through the The corner point is perpendicular to the z-axis, and is located in the horizontal direction of the calibration plate plane. When facing the calibration plate, the left direction is the positive direction. The y-axis is perpendicular to the x and z axes when passing through the corner point. The conversion relationship between the coordinate system Ov and the calibration plate coordinate system O _B is [X _V Y _V Z _V ] ^T = R[X _B Y _B Z _B ] ^T +t, X _B , Y _B , Z _B are any corners of the calibration plate The coordinates of the point under the calibration board coordinate system OB, the coordinate value Z _B under the calibration board coordinate system OB is 0 by default, and X _V , _{Y V} , and Z _V are corresponding to the camera coordinate system Ov of any corner point on the calibration board. The coordinate value of the point and the coordinate value of the corresponding point (X _V , Y _V , Z _V ) are captured by the camera, and the coordinates of any corner point (X _B , Y _B , Z _B ) under the calibration board coordinate system _OB are used. and the coordinates of the corresponding point (X _V , Y _V , Z _V ) of any corner point in the camera coordinate system Ov, and the external parameter matrices R and t are obtained by calculation. 3. The rotary axis calibration method based on self-adaptive distance weighting according to claim 1, wherein the rotary platform comprises a vision support (2) and a rotating platform (3), and the vision support (2) is provided with a camera (1), a checkerboard calibration plate (4) is placed on the rotating platform (3), and the checkerboard calibration plate (4) is located in the field of view of the camera. 4 . The method for calibrating a rotation axis based on adaptive distance weighting according to claim 1 , wherein the platform is rotated every 4° to 10° and an image of the calibration plate is collected. 5 . 5. The rotary axis calibration method based on self-adaptive distance weighting according to claim 1, is characterized in that, the moving distance l _ij of the i th corner point between the j th rotational position and the j+1 th rotational position is: l _i,j =||P _i,j+1 -P _i,j ||, where P _i,j is the i-th corner point on the j-th position calibration board, i=1,2.... m represents the number of the corner points, m is the total number of corner points, the number of the corner points increases in an s-shape from right to left from bottom to top, j=1,2....n represents the position number of the calibration board, n is the total number of positions of the calibration board, |||| means to find the norm.

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