CN113503811A - Calibration method for bias matrix of iScan in five-axis cutting machine tool coordinate system - Google Patents

Calibration method for bias matrix of iScan in five-axis cutting machine tool coordinate system Download PDF

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CN113503811A
CN113503811A CN202110506470.5A CN202110506470A CN113503811A CN 113503811 A CN113503811 A CN 113503811A CN 202110506470 A CN202110506470 A CN 202110506470A CN 113503811 A CN113503811 A CN 113503811A
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刘锦潮
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Aipeiyi Intelligent Equipment Co ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/002—Measuring arrangements characterised by the use of optical techniques for measuring two or more coordinates
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/80—Analysis of captured images to determine intrinsic or extrinsic camera parameters, i.e. camera calibration
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10028—Range image; Depth image; 3D point clouds
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Abstract

The invention relates to the field of model calculation, and particularly discloses a method for calibrating an offset matrix of iScan in a five-axis cutting machine tool coordinate system, which comprises the following specific steps: acquiring original point cloud data by using iScan; step two, sorting and filtering the data; step three, roughly calculating a bias matrix and calibrating a sphere center coordinate; and step four, fitting calculation and accurate solution. The invention provides a calibration method for an offset matrix of iScan in a five-axis cutting machine tool coordinate system, which can reduce errors, further improve the precision of obtaining the end pose, improve the splicing precision of scanning data, improve the working accuracy of a scanner and compensate an optimized five-axis cutting machine kinematic model.

Description

Calibration method for bias matrix of iScan in five-axis cutting machine tool coordinate system
Technical Field
The invention relates to the field of model calculation, in particular to a method for calibrating an offset matrix of iScan in a five-axis cutting machine tool coordinate system.
Background
The iScan is a line scanning product of API company, the light source adopts two blue line lasers which mutually form 90-degree intersection, laser projection diffuse reflection and a single-camera imaging triangulation method are adopted, the projection of a scanning line on the surface of a measured object is measured, and point cloud data are formed through discretization. Each frame of image of the line scanner can only obtain one scanning line (dispersed into equidistant point clouds along the scanning line), if continuous scanning data of the surface of an object needs to be obtained, the line scanner needs to be moved to enable the laser line to continuously sweep the surface of the object, and the six-degree-of-freedom information, the position and the posture between the object and the scanner at the moment of shooting each frame of image are known, so that all the point clouds can be spliced under the same coordinate system.
The more comprehensive data of the five-axis cutting machine can be obtained by utilizing the iScan, the optimized kinematic model of the five-axis cutting machine can be compensated, and in order to further improve the accuracy of obtaining the terminal pose and improve the splicing accuracy of the scanning data, a method for calibrating the offset matrix of the iScan in the tool coordinate system of the five-axis cutting machine is provided.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for calibrating an offset matrix of iScan in a five-axis cutting machine tool coordinate system, which can effectively solve the problems in the prior art, and the invention provides the following technical scheme:
the method for calibrating the offset matrix of the iScan in the tool coordinate system of the five-axis cutting machine comprises the following specific steps:
acquiring original point cloud data by using iScan;
step two, sorting and filtering the data;
step three, roughly calculating a bias matrix and calibrating a sphere center coordinate;
and step four, fitting calculation and accurate solution.
Preferably, the iScan in step one is a typical laser line scanner, all the measurement data points are located in the plane swept by the line laser, and in order to ensure reliable coordinate transformation without considering the optimal use of local areas, the data for calibration must be widely distributed in the plane, covering the depth of field and each interval of the whole scanning line.
Preferably, the scanning data in the six-dimensional measurement system is obtained by processing the original point cloud data obtained by the iScan under a local coordinate system of the scanner:
Figure DEST_PATH_IMAGE001
wherein:
Figure 258433DEST_PATH_IMAGE002
-measuring point coordinate vectors in the scanner coordinate system;
Figure DEST_PATH_IMAGE003
-the transformation from the tool coordinate system, equivalent to the F3 coordinate system of I360, to the machine tool coordinate system, which is the pose of the end flange, i.e. the chosen T, for the robot, when measuring the point, is measured0Displaying the terminal pose under the base coordinate system;
Figure 516108DEST_PATH_IMAGE004
-coordinate values of measurement points in a machine coordinate system;
Figure DEST_PATH_IMAGE005
-a transformation matrix from the scanner coordinate system to the end tool coordinate system.
According to the above formula to obtain
Figure 507198DEST_PATH_IMAGE006
Wherein
Figure DEST_PATH_IMAGE007
For the coordinate values of the data points in the tool coordinate system, it can be known that in order to solve the coordinate transformation T, a typical set of data needs to be acquired, and the coordinate values of the typical set of data in the tool coordinate system are known
Figure 533929DEST_PATH_IMAGE007
And coordinate values in the scanner coordinate system
Figure 952272DEST_PATH_IMAGE002
If known, the matrix T can be solved for computation.
Preferably, the step two of sorting and filtering the data includes: searching arc data on each scanning line by using a sliding window, marking the positions of the initial point and the end point of a data segment with the fitting roundness error not exceeding 0.25mm and the fitting radius not larger than the maximum allowable spherical radius of 25mm by adopting an observation window with the width of 75 effective data, namely the length of about 15mm according to the point distance on the iScan scanning line, recording, fully selecting and fitting all points on the line which accord with the arc characteristics to calculate a 3D circle, and recording and storing the position and the radius of the circle center for later use.
Preferably, the rough calculation of the bias matrix and the calibration of the center of sphere coordinates in step three includes:
a) selecting the scanning line with the largest fitting radius from each group of scanning data, considering that the scanning line passes through the sphere center, the fitted circle center is approximate to the real sphere center position, and the circle/sphere center position si of each key scanning line meets the requirement
Figure 446312DEST_PATH_IMAGE008
Wherein, in the step (A),
Figure DEST_PATH_IMAGE009
c is the coordinate value of the standard ball in the machine coordinate system, which is an unknown quantity in the method;
b) in order to solve the sphere center coordinate, an estimated sphere center position is used as an initial value of iterative computation, and the method adopts the tool coordinate system origin points corresponding to the key scanning lines respectively to calculate the sphere center c in a fitting mode0As an initial value, c0Substituting the above formula to obtain an equation set, wherein the number of equations is the number of key scanning lines, and at least three key scanning line equations are required to be solved:
Figure DEST_PATH_IMAGE011
solve to obtain the initial value T of T0Application of T0Calculate the new sphere center coordinate c':
Figure DEST_PATH_IMAGE013
c) repeating the iterative calculation, setting a convergence condition as follows according to a residual error formula, and actually converging to 0.000001mm after 5 iterations:
Figure DEST_PATH_IMAGE015
d) and singular situation discussion: the above equation set theory can be solved, but actually, there is a risk of too large solving error, and the solving error actually occurs in the experimental data, in order to avoid this problem, we need to ensure that the calibration data is uniformly dispersed in the depth of field and width direction, for the calibration data close to the singular state, the method adopts a method of adding an auxiliary point pair, that is, adding the central point of the scanner handle to participate in fitting calculation, selecting the spherical center point of the first key scanning line, and making the x and y coordinate values of the first key scanning line under the scanner coordinate system be zero
Figure 365726DEST_PATH_IMAGE016
Fitting it to the target under the tool coordinate system
Figure 246964DEST_PATH_IMAGE018
Root front should be used when the tool coordinate system Z-axis points to the scanner handle
Figure DEST_PATH_IMAGE019
Adding the point pair into a solving equation to ensure that the Z axis of the scanner is vertical to the Z axis of the tool coordinate system in the solving process;
a coarse alignment matrix is obtained by following steps, and the coarse alignment is directly fitted to the center point of the common calibration sphere by using the circle center of the key scanning line without considering the optimization of the radius of the sphere.
Preferably, the fitting calculation in the fourth step includes:
a) for the data point of the circular arc part of each scanning line, converting the coordinate system of the scanner to the coordinate system of the tool by using a rough offset matrix, and then passing the coordinates of the center of the sphere through
Figure 836208DEST_PATH_IMAGE020
Converting to the tool coordinate system, starting from the sphere center to each sweep in the tool coordinate systemAnd multiplying the vector normalization of the points by the spherical radius value to obtain theoretical points on the spherical surface as target points for fitting calculation:
Figure 881524DEST_PATH_IMAGE022
wherein r is the radius of the calibration sphere, and the initial value is the average value of the radius of the circle fitted by the key scanning line
Figure DEST_PATH_IMAGE023
Substitution, T0Substituting a result matrix of the rough alignment;
b) and according to the formula, the data points s on all effective circular arcsiCalculating to obtain a set of fitting target values (t)0，t1，t2……tn) According to the system of equations
Figure 463684DEST_PATH_IMAGE024
Solve out new
Figure DEST_PATH_IMAGE025
。
c) Will be provided with
Figure RE-280437DEST_PATH_IMAGE020
Substitution formula
Figure RE-186076DEST_PATH_IMAGE021
Obtaining (m)0，m1，m2……mn) Re-fitting and calculating the standard sphere, updating the sphere radius and the sphere center coordinates, and repeating the step a) and the step b) to carry out iterative operation;
d) the mean square error of the fitting ball is used as a residual error of iterative calculation convergence, the RMS can be converged to about 0.000001mm about 100 times, and the corresponding coordinate variation of the center of the ball is less than 0.001 mm;
e) and finishing the iterative computation and outputting a matrix T.
Compared with the prior art, the invention provides a method for calibrating the offset matrix of the iScan in the tool coordinate system of the five-axis cutting machine, which has the following beneficial effects:
the calibration method can reduce errors, further improve the accuracy of acquiring the end pose, improve the splicing accuracy of scanning data, improve the working accuracy of the scanner and compensate the optimized five-axis cutting machine kinematic model.
Drawings
Fig. 1 is a flowchart of a calibration method of an offset matrix of iScan in a five-axis cutting machine tool coordinate system.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, a method for calibrating an offset matrix of iScan in a five-axis cutting machine tool coordinate system includes the following steps:
acquiring original point cloud data by using iScan;
step two, sorting and filtering the data;
step three, roughly calculating a bias matrix and calibrating a sphere center coordinate;
and step four, fitting calculation and accurate solution.
Further in the embodiment of the present invention, the iScan in the step one is a typical laser line scanner, all the measurement data points are located in the plane swept by the line laser, and in order to ensure reliable coordinate transformation without considering the condition of optimally using the local area, the data for calibration must be widely distributed in the plane, covering the depth of field and each section of the whole scanning line.
Further, in the embodiment of the present invention, the scanning data in the six-dimensional measurement system is obtained by processing the original point cloud data obtained by the iScan in the local coordinate system of the scanner:
Figure 140041DEST_PATH_IMAGE001
wherein:
Figure 165766DEST_PATH_IMAGE002
-measuring point coordinate vectors in the scanner coordinate system;
Figure 619750DEST_PATH_IMAGE003
-the transformation from the tool coordinate system, equivalent to the F3 coordinate system of I360, to the machine tool coordinate system, which is the pose of the end flange, i.e. the chosen T, for the robot, when measuring the point, is measured0Displaying the terminal pose under the base coordinate system;
Figure 818650DEST_PATH_IMAGE004
-coordinate values of measurement points in a machine coordinate system;
Figure 159632DEST_PATH_IMAGE005
-a transformation matrix from the scanner coordinate system to the end tool coordinate system.
According to the above formula to obtain
Figure 418575DEST_PATH_IMAGE006
Wherein
Figure 359855DEST_PATH_IMAGE007
For the coordinate values of the data points in the tool coordinate system, it can be known that in order to solve the coordinate transformation T, a typical set of data needs to be acquired, and the coordinate values of the typical set of data in the tool coordinate system are known
Figure 34550DEST_PATH_IMAGE007
And coordinate values in the scanner coordinate system
Figure 557936DEST_PATH_IMAGE002
Knowing, then the matrix T can be solvedAnd (4) calculating.
Further in the embodiment of the present invention, the sorting and filtering the data in the second step includes: searching arc data on each scanning line by using a sliding window, marking the positions of the initial point and the end point of a data segment with the fitting roundness error not exceeding 0.25mm and the fitting radius not larger than the maximum allowable spherical radius of 25mm by adopting an observation window with the width of 75 effective data, namely the length of about 15mm according to the point distance on the iScan scanning line, recording, fully selecting and fitting all points on the line which accord with the arc characteristics to calculate a 3D circle, and recording and storing the position and the radius of the circle center for later use.
Further in the embodiment of the present invention, the step three of roughly calculating the offset matrix and calibrating the center coordinates includes:
a) selecting the scanning line with the largest fitting radius from each group of scanning data, considering that the scanning line passes through the sphere center, the fitted circle center is approximate to the real sphere center position, and the circle/sphere center position si of each key scanning line meets the requirement
Figure 174731DEST_PATH_IMAGE008
Wherein, in the step (A),
Figure 150777DEST_PATH_IMAGE009
c is the coordinate value of the standard ball in the machine coordinate system, which is an unknown quantity in the method;
b) in order to solve the sphere center coordinate, an estimated sphere center position is used as an initial value of iterative computation, and the method adopts the tool coordinate system origin points corresponding to the key scanning lines respectively to calculate the sphere center c in a fitting mode0As an initial value, c0Substituting the above formula to obtain an equation set, wherein the number of equations is the number of key scanning lines, and at least three key scanning line equations are required to be solved:
Figure 629163DEST_PATH_IMAGE011
solve to obtain the initial value T of T0Application of T0Calculate the new sphere center coordinate c':
Figure 272634DEST_PATH_IMAGE013
c) repeating the iterative calculation, setting a convergence condition as follows according to a residual error formula, and actually converging to 0.000001mm after 5 iterations:
Figure 797680DEST_PATH_IMAGE015
d) and singular situation discussion: the above equation set theory can be solved, but actually, there is a risk of too large solving error, and the solving error actually occurs in the experimental data, in order to avoid this problem, we need to ensure that the calibration data is uniformly dispersed in the depth of field and width direction, for the calibration data close to the singular state, the method adopts a method of adding an auxiliary point pair, that is, adding the central point of the scanner handle to participate in fitting calculation, selecting the spherical center point of the first key scanning line, and making the x and y coordinate values of the first key scanning line under the scanner coordinate system be zero
Figure 526602DEST_PATH_IMAGE016
Fitting it to the target under the tool coordinate system
Figure 543100DEST_PATH_IMAGE028
Root front should be used when the tool coordinate system Z-axis points to the scanner handle
Figure 228028DEST_PATH_IMAGE019
Adding the point pair into a solving equation to ensure that the Z axis of the scanner is vertical to the Z axis of the tool coordinate system in the solving process;
a coarse alignment matrix is obtained by following steps, and the coarse alignment is directly fitted to the center point of the common calibration sphere by using the circle center of the key scanning line without considering the optimization of the radius of the sphere.
Further in the embodiment of the present invention, the fitting calculation in step four includes:
a) for the data point of the circular arc part of each scanning line, converting the coordinate system of the scanner to the coordinate system of the tool by using a rough offset matrix, and then passing the coordinates of the center of the sphere through
Figure 734095DEST_PATH_IMAGE020
Converting into a tool coordinate system, normalizing the vector starting from the sphere center to each scanning point in the tool coordinate system, and multiplying the normalized vector by the sphere radius value to obtain a theoretical point on the spherical surface as a target point for fitting calculation:
Figure 887996DEST_PATH_IMAGE022
wherein r is the radius of the calibration sphere, and the initial value is the average value of the radius of the circle fitted by the key scanning line
Figure 770502DEST_PATH_IMAGE023
Substitution, T0Substituting a result matrix of the rough alignment;
b) and according to the formula, the data points s on all effective circular arcsiCalculating to obtain a set of fitting target values (t)0，t1，t2……tn) According to the system of equations
Figure 309936DEST_PATH_IMAGE024
Solve out new
Figure 252484DEST_PATH_IMAGE025
。
c) Will be provided with
Figure 628102DEST_PATH_IMAGE025
Substitution formula
Figure 48719DEST_PATH_IMAGE027
Obtaining (m)0，m1，m2……mn) After the standard sphere is fit and calculated again and the sphere radius and the sphere center coordinates are updatedRepeating the step a) and the step b) to carry out iterative operation;
d) the mean square error of the fitting ball is used as a residual error of iterative calculation convergence, the RMS can be converged to about 0.000001mm about 100 times, and the corresponding coordinate variation of the center of the ball is less than 0.001 mm;
e) and finishing the iterative computation and outputting a matrix T.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (6)

  1. The method for calibrating the offset matrix of the iScan in the tool coordinate system of the five-axis cutting machine is characterized by comprising the following steps: the method comprises the following specific steps:
    acquiring original point cloud data by using iScan;
    step two, sorting and filtering the data;
    step three, roughly calculating a bias matrix and calibrating a sphere center coordinate;
    and step four, fitting calculation and accurate solution.
  2. 2. The method for calibrating the offset matrix of the iScan in the five-axis cutting machine tool coordinate system according to claim 1, wherein the method comprises the following steps: in the first step, the iScan is a typical laser line scanner, all measurement data points are located in a plane swept by the line laser, and in order to ensure reliable coordinate transformation without considering the condition of optimally using a local area, data for calibration must be widely distributed in the plane to cover the depth of field and each interval of the whole scanning line.
  3. 3. The method for calibrating the offset matrix of the iScan in the five-axis cutting machine tool coordinate system according to claim 1, wherein the method comprises the following steps: processing the scanning data in the six-dimensional measurement system according to the original point cloud data acquired by the iScan under a local coordinate system of the scanner:
    Figure 36421DEST_PATH_IMAGE001
    wherein:
    Figure 218004DEST_PATH_IMAGE002
    -measuring point coordinate vectors in the scanner coordinate system;
    Figure 345360DEST_PATH_IMAGE003
    -the transformation from the tool coordinate system, equivalent to the F3 coordinate system of I360, to the machine tool coordinate system, which is the pose of the end flange, i.e. the chosen T, for the robot, when measuring the point, is measured0Displaying the terminal pose under the base coordinate system;
    Figure 423344DEST_PATH_IMAGE004
    -coordinate values of measurement points in a machine coordinate system;
    Figure 927138DEST_PATH_IMAGE005
    -a transformation matrix from the scanner coordinate system to the end tool coordinate system;
    according to the above formula to obtain
    Figure 415757DEST_PATH_IMAGE006
    Wherein
    Figure 776331DEST_PATH_IMAGE007
    For the coordinate values of the data points in the tool coordinate system, it can be known that in order to solve the coordinate transformation T, a typical set of data needs to be acquired, and the coordinate values of the typical set of data in the tool coordinate system are known
    Figure 101133DEST_PATH_IMAGE007
    And coordinate values in the scanner coordinate system
    Figure 657885DEST_PATH_IMAGE002
    If known, the matrix T can be solved for computation.
  4. 4. The method for calibrating the offset matrix of the iScan in the five-axis cutting machine tool coordinate system according to claim 1, wherein the method comprises the following steps: the step two of sorting and filtering the data comprises the following steps: searching arc data on each scanning line by using a sliding window, marking the positions of the initial point and the end point of a data segment with the fitting roundness error not exceeding 0.25mm and the fitting radius not larger than the maximum allowable spherical radius of 25mm by adopting an observation window with the width of 75 effective data, namely the length of about 15mm according to the point distance on the iScan scanning line, recording, fully selecting and fitting all points on the line which accord with the arc characteristics to calculate a 3D circle, and recording and storing the position and the radius of the circle center for later use.
  5. 5. The method for calibrating the offset matrix of the iScan in the five-axis cutting machine tool coordinate system according to claim 1, wherein the method comprises the following steps: the rough calculation of the offset matrix and the calibration of the sphere center coordinates in the third step comprise:
    a) selecting the scanning line with the largest fitting radius from each group of scanning data, considering that the scanning line passes through the sphere center, the fitted circle center is approximate to the real sphere center position, and the circle/sphere center position si of each key scanning line meets the requirement
    Figure 548481DEST_PATH_IMAGE008
    Wherein, in the step (A),
    Figure 283219DEST_PATH_IMAGE009
    c is the coordinate value of the standard ball in the machine coordinate system, which is an unknown quantity in the method;
    b) in order to solve the sphere center coordinate, an estimated sphere center position is used as an initial value of iterative computation, and the method adopts the tool coordinate system origin points corresponding to the key scanning lines respectively to calculate the sphere center c in a fitting mode0As an initial value, c0Substituting the above formula to obtain an equation set, wherein the number of equations is the number of key scanning lines, and at least three key scanning line equations are required to be solved:
    Figure 79005DEST_PATH_IMAGE010
    solve to obtain the initial value T of T0Application of T0Calculate the new sphere center coordinate c':
    Figure 252498DEST_PATH_IMAGE011
    c) repeating the iterative calculation, setting a convergence condition as follows according to a residual error formula, and actually converging to 0.000001mm after 5 iterations:
    Figure 200862DEST_PATH_IMAGE012
    d) and singular situation discussion: the above equation set theory can be solved, but actually, there is a risk of too large solving error, and it actually happens in the experimental data, and in order to avoid this problem, we need to ensure that the calibration data is uniformly spread in both depth of field and width direction, and for the near singular stateThe method adopts a method of adding an auxiliary point pair, namely adding the central point of a scanner handle to participate in fitting calculation, selecting the spherical center point of a first key scanning line, and enabling the lower x and y coordinate values of the first key scanning line under the coordinate system of the scanner to be zero
    Figure 168818DEST_PATH_IMAGE013
    Fitting it to the target under the tool coordinate system
    Figure 454830DEST_PATH_IMAGE014
    Root front should be used when the tool coordinate system Z-axis points to the scanner handle
    Figure 166435DEST_PATH_IMAGE015
    Adding the point pair into a solving equation to ensure that the Z axis of the scanner is vertical to the Z axis of the tool coordinate system in the solving process;
    a coarse alignment matrix is obtained by following steps, and the coarse alignment is directly fitted to the center point of the common calibration sphere by using the circle center of the key scanning line without considering the optimization of the radius of the sphere.
  6. 6. The method for calibrating the offset matrix of the iScan in the five-axis cutting machine tool coordinate system according to claim 1, wherein the method comprises the following steps: the fitting calculation accurate solution in the fourth step comprises the following steps:
    a) for the data point of the circular arc part of each scanning line, converting the coordinate system of the scanner to the coordinate system of the tool by using a rough offset matrix, and then passing the coordinates of the center of the sphere through
    Figure 969305DEST_PATH_IMAGE016
    Converting into a tool coordinate system, normalizing the vector starting from the sphere center to each scanning point in the tool coordinate system, and multiplying the normalized vector by the sphere radius value to obtain a theoretical point on the spherical surface as a target point for fitting calculation:
    Figure DEST_PATH_IMAGE017
    wherein r is the radius of the calibration sphere, and the initial value is the average value of the radius of the circle fitted by the key scanning line
    Figure 295113DEST_PATH_IMAGE018
    Substitution, T0Substituting a result matrix of the rough alignment;
    b) and according to the formula, the data points s on all effective circular arcsiCalculating to obtain a set of fitting target values (t)0，t1，t2……tn) According to the system of equations
    Figure 816225DEST_PATH_IMAGE019
    Solve out new
    Figure 65940DEST_PATH_IMAGE020
    ；
    c) Will be provided with
    Figure 238165DEST_PATH_IMAGE020
    Substitution formula
    Figure DEST_PATH_IMAGE021
    Obtaining (m)0，m1，m2……mn) Re-fitting and calculating the standard sphere, updating the sphere radius and the sphere center coordinates, and repeating the step a) and the step b) to carry out iterative operation;
    d) the mean square error of the fitting ball is used as a residual error of iterative calculation convergence, the RMS can be converged to about 0.000001mm about 100 times, and the corresponding coordinate variation of the center of the ball is less than 0.001 mm;
    e) and finishing the iterative computation and outputting a matrix T.
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