CN111366070A - Multi-axis space coordinate system calibration method for combined type line laser measurement system - Google Patents
Multi-axis space coordinate system calibration method for combined type line laser measurement system Download PDFInfo
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Abstract
The invention belongs to the field of optical measurement, and relates to a method for calibrating a multi-axis space coordinate system of a composite line laser measurement system based on a plane target. The method for calibrating the multi-axis space coordinate system of the composite line laser measuring system based on the plane target is suitable for a four-axis measuring machine structure, and is used for primarily calibrating the line laser measuring system by utilizing the plane target for calibrating the position between a two-dimensional line laser sensor and a contact measuring head of the measuring machine, wherein the position is not available in an original image, the distance from a measuring point of the line laser sensor to a measuring plane of the contact measuring head is optimized, and the calibration result is a rotation and translation matrix from the line laser sensor to the contact measuring head.
Description
The technical field is as follows:
the invention belongs to the field of optical measurement, and relates to a multi-axis space coordinate system calibration method of a composite linear laser measurement system based on a planar target and a method for carrying out multi-axis space coordinate system calibration optimization by using a spherical target.
Background art:
the optical measurement is a new technology which combines the photoelectric technology and the mechanical measurement on the basis of using the computer technology so as to achieve the rapid and accurate measurement work. The method is widely applied to the precision machining fields of electronics, machinery, gear machining and the like at present, and has accurate measurement result and extremely small deviation. Compared with the traditional contact type measurement mode, the optical three-dimensional measurement has the advantages of non-contact, high precision and high speed, and is quite popular in the industries of industrial manufacturing, animation special effect making, game entertainment, medicine and the like. The laser line scanning measurement method is to reproduce the three-dimensional shape of an object by one or more laser ray (optical knife) images, namely, to extract the central position of the optical knife from the optical knife images and then to solve the central point of the optical knife point by utilizing the triangulation principle to obtain the three-dimensional data of the molded surface. The technology has the advantages of non-contact property, high sensitivity, good real-time property, strong anti-interference capability and the like.
The optical measuring system usually installs the optical sensor on three coordinate measuring machine, and the optical sensor can accurate non-contact measurement measured object profile, through the positional relationship of calibration optical sensor and three coordinate measuring machine, can convert optical sensor measurement data into three coordinate machine coordinate system data.
The calibration of the optical measurement system is an important step in the measurement system, and it needs to calibrate the conversion relationship from the optical measurement system to the contact measurement system, and the calibration precision directly determines the precision of the measurement result. The existing calibration method comprises a system calibration method of a point laser optical measuring head based on a standard ball, and a method for calibrating a measuring needle which equivalently uses a laser beam of the optical measuring head as a contact measuring head. However, for the calibration of a combined multi-axis measurement system composed of line laser two-dimensional sensors, the line laser sensor is a two-dimensional sensor on one hand, and the two-dimensional coordinate axis directions of the line laser sensor cannot be calibrated simultaneously by using a point laser calibration method, and on the other hand, the calibration by using spherical objects causes the difference of precision and the spherical fitting error because the line laser two-dimensional sensors are different in the laser incidence normal direction. Still other methods require knowledge of the raw captured image of the line laser sensor. While some line laser sensors cannot know the original image. Therefore, there is no effective calibration method for the calibration of the two-dimensional line laser sensor measurement system where the original image is not available.
The invention content is as follows:
aiming at the defects or the improvement requirements of the prior art, the invention provides a multi-axis space coordinate system calibration method of a composite linear laser measurement system based on a plane target and a method for carrying out multi-axis space coordinate system calibration optimization by utilizing a spherical target. The method is suitable for the structure of a four-axis measuring machine, and is used for calibrating the position between a two-dimensional line laser sensor and a contact measuring head of the measuring machine, wherein the two-dimensional line laser sensor and the contact measuring head of the measuring machine are unavailable for an original image. The method can simultaneously calibrate two directions of the two-dimensional line laser sensor and the translation relation between the line laser sensor and the contact measuring head, and can reduce the ball fitting error calibrated by adopting a spherical target.
The method utilizes two measuring heads, a line laser sensor and a contact measuring head to respectively measure the same standard plane, and the measured values of the two measuring heads theoretically simultaneously accord with the same plane equation. The initial value of the conversion relation between the two measuring heads can be solved. The method comprises the following steps of measuring standard balls with a plurality of angles by two measuring heads, optimizing the error of the whole system and obtaining the accurate conversion relation between the two measuring heads:
the method comprises the steps of firstly, directly collecting measuring points on a standard plane by using a contact type measuring head, and fitting a plane equation by using a least square method. Obtaining a plane equation:
Ax+By+Cz+D＝0
scanning the same plane by using the line laser sensor to obtain a series of line laser sensor acquisition points SnAnd the corresponding machine tool grating coordinate value is delta PnIn which the homogeneous coordinate system represents
And repeatedly scanning the other two planes to obtain corresponding data.
And step three, establishing a mathematical model to enable all measuring points of the line laser sensor to accord with a plane equation measured by the corresponding contact measuring head.
Wherein i0,i1,j0,j1,k0,k1Is an element, x, from a line laser sensor coordinate system to a contact probe coordinate system rotation matrix0,y0,z0Elements in a translation matrix from the line laser sensor coordinate system to the contact probe coordinate system, and
the mathematical model can be written in matrix form as:
(KSn+ΔPn)TX＝0
in the formula:
and step four, solving the equation by a Newton iteration method. And selecting the target function as the distance between the measured point and the fitted plane as an error value, wherein the nonlinear optimization target function reaches the minimum.
Placing the calibrated standard ball on a turntable, wherein the radius of the standard ball is RsphereFirstly, a coordinate system of the rotary table is calibrated by a method of measuring a standard ball by a contact type measuring head. And then the contact measuring head and the line laser sensor simultaneously measure the standard balls at the same angle to obtain the profile data of the standard balls at the same angle theta. The turntable drives the standard ball to rotate, and the standard ball is repeatedly measured.
Standard ball data obtained by contact type measuring head measurement are spliced through the rotary table to obtain a standard ball center coordinate O of a rotary table coordinate systemcenter＝[xcenterycenterzcenter]T. The line laser sensor measurement data is substituted into the following equation:
[1111]·[RzKrot(KSn+ΔPn)-Ocenter]o[RzKrot(KSn+ΔPn)-Ocenter]-Rsphere 2＝0
in the formula: k, Sn,ΔPnThe step three is as described above;
the meaning represented by o is (A o B)i,j＝(A)i,j(B)i,j。
And step six, solving an equation by adopting a Levenberg-Marquardt iteration method. And selecting the target function as the distance from the line laser measuring point to the contact type measuring spherical surface, and optimizing the target function to minimize the distance sum.
Compared with the prior art, the invention can obtain the following beneficial effects:
1. the calibration method can calibrate only by knowing the measurement data of the two-dimensional line laser sensor without knowing the original image of the two-dimensional line laser sensor.
2. The method can simultaneously calibrate the rotation matrix and the translation matrix from the two-dimensional line laser sensor to the contact type measuring head coordinate system without respectively calibrating.
3. The method carries out initial parameter calibration based on the plane target, and avoids the problems of different precision caused by the fitting error of a small-angle standard sphere and the different incidence normal directions of the linear laser sensor.
4. The method finally utilizes the standard balls at different angles to calibrate, and can optimize to obtain the globally optimal calibration parameters of the system.
Description of the drawings:
FIG. 1 structure diagram of compound line laser measuring system
FIG. 2 is a schematic diagram of a line laser displacement sensor
FIG. 3 is a schematic diagram of the output values measured by the line laser displacement sensor
FIG. 4 is a simplified diagram of a calibration model of a line laser displacement sensor
The specific implementation mode is as follows:
the invention is described in further detail below with reference to the accompanying drawings:
a multi-axis space coordinate system calibration method of a composite linear laser measurement system based on a planar target and a method for carrying out multi-axis space coordinate system calibration optimization by utilizing a spherical target are disclosed. The hardware structure is similar to that shown in figure 1,
in the combined four-axis measuring system, a contact measuring head 1 and a line laser sensor 2 are connected by a rigid structure 3 and are simultaneously mounted on a coordinate machine shaft 4. The four-axis coordinate machine is attached with a rotary table 5.
The line laser sensor is a two-dimensional sensor, the measuring principle of the line laser sensor is a laser triangulation method, the method is different from a point source point-by-point scanning mode, the line laser sensor measures the shape of an object by adopting a line light source, and the measuring speed and the measuring efficiency are higher. Fig. 2 is a diagram of a measurement system of a line laser sensor, in which RO is an incident light source, and light is reflected by an object and imaged on a CCD through a lens. Point a is imaged at point a ' of the CCD, point B is imaged at point B ' of the CCD, and position O corresponds to the central position O ' of the CCD. As can be seen, the points with different heights correspond to different positions of the CCD.
For a line laser sensor capable of acquiring a CCD image, the conversion relationship from the sensor to a measuring machine is calibrated by shooting a calibration plate, usually by using the principle of a calibration camera. When the CCD image cannot be acquired, the method is not applicable any more, and only the output value of the sensor can be used as a calculation basis.
As shown in FIG. 3, the line laser sensor is a two-dimensional system, and the line length direction is X in the coordinate system of the measuring headLAxial direction and light source emitting direction of YLAxial direction, origin O of the coordinate systemLAnd (0,0) is positioned at the midpoint of the length of the laser line in the standard working plane, namely the optical center of the line laser on the standard plane. As shown in the third figure, the measured point A is recorded in the sensorHas an output value of (x)A L,yA L) Then y isA LIs the distance, x, from point A to the standard working planeA LIs a projection point of the point A on the reference plane and is away from the origin O of the coordinate systemLA distance of (0, 0).
In order to obtain the pose relationship between a line laser sensor and a measuring machine, the patent provides a calibration method based on a standard plane target, two measuring heads are used for measuring the same standard plane respectively, and a transformation matrix between coordinate systems of the two measuring heads can be obtained by fitting an equation of the plane. The calibration model comprises the following specific steps:
the method comprises the steps of firstly, directly collecting measuring points on a standard plane by using a contact type measuring head, and fitting a plane equation by using a least square method.
Ax+By+Cz+D＝0
Scanning the same plane by using the line laser sensor to obtain a series of line laser sensor acquisition points SnAnd the corresponding machine tool grating coordinate value is delta PnIn which the homogeneous coordinate system represents
And repeatedly scanning the other two planes to obtain corresponding data.
Step three, simplifying the mathematical model of the line laser measurement system, as shown in FIG. 4, OMXYZ is a machine tool coordinate system, the directions of three coordinate axes are the same as the grating direction of the machine tool, and the origin O isMWhen the grating is at the zero position, the contact type measuring needle is at the position of the ruby sphere center. At the zero position, the optical center on the standard working plane of the line laser sensor is OMCoordinate in-XYZ as P0(x0,y0,z0)。
When the laser measures a standard plane, a point opposite to the optical center is set as N0Then P at this time0N0The direction of (b) is the laser emission direction, and the direction vector thereof is (i)0,j0,k0) The long direction vector of the laser line is (i)1,j1,k1). Let an arbitrary point on the light be M0，M0Distance N0Is a distance w0At a distance of l from the standard working plane0Then M at this time0At OMCoordinates in-XYZ of (x)0,y0,z0)+l0·(i0,j0,k0)+w0·(i1,j1,k1)。
Driving a laser to slide and scan on a standard plane by a machine tool for measurement, wherein delta x, delta y and delta z are respectively the increment of the reading of grating rulers of each axis of the machine tool, and then, an initial measurement point M is obtained0Changes into any measuring point M1,M2,…,MnFrom a distance N of0Is changed to w1,w2,…,wnThe distance from the standard working plane varies by l1,l2,…,ln。
At this time, M1,M2,…,MnThe coordinates are changed to:
the coordinates of the points conform to the plane equation Ax + By + Cz + D of the plane, which can be obtained By the contact type measuring head point-taking fitting, wherein (C ≠ 0).
Handle MnThe coordinate axis of (a) is substituted into the plane equation Ax + By + Cz + D is 0, and the equation set is formed By the following equation:
written in matrix form as follows:
(KSn+ΔPn)TX＝0
in the formula:
where R can be converted to a matrix of 3 degrees of freedom, t has 3 unknowns and the remaining parameters are known.
R is a rotation matrix, which can represent the rotation around the coordinate axis with only one vector according to the rodgers transformation. The length of the vector represents the rotation angle and the vector itself represents the rotation axis. Let the vector of the Reed-Solomon transform be r ═ rx,ry,rz]Then, then
The system of equations has 6 unknown parameters. Solving for [ r ] by Newton iteration methodx,ry,rz]And t.
And step four, solving the equation by a Newton iteration method. Because of the existence of system errors, the actual measured points can not be completely distributed on the standard plane, the distance from the measured points to the fitted plane is selected as an objective function as an error value,
the nonlinear optimization objective function is minimized. The process of newton's iteration is to minimize the error value,
thereby obtaining the unknown parameters at the moment as the calibration parameters of the line laser sensor.
I.e. to minimize the following objective function:
in the formula:
further simplification is as follows:
fi 2(x)＝(a(x0+Δxi+lii0+wii1)+b(y0+Δyi+lij0+wij1)+c(z0+Δzi+lik0+wik1)+d)2
in the above formula fi(x) Is a non-linear function and there is a continuous partial derivative of f (x). The basic idea of solving nonlinear least squares is to solve the nonlinear least squares problem by solving a series of linear least squares problems.
Placing the calibrated standard ball on a turntable, wherein the radius of the standard ball is RsphereFirstly, a coordinate system of the rotary table is calibrated by a method of measuring a standard ball by a contact type measuring head. The conversion relation from the turntable coordinate system to the contact type measuring head coordinate system is as follows:
And then the contact measuring head and the line laser sensor simultaneously measure the standard balls at the same angle to obtain the profile data of the standard balls at the same angle theta. The turntable drives the standard ball to rotate, and the standard ball is repeatedly measured.
Standard ball data obtained by contact type measuring head measurement are spliced through the rotary table to obtain a standard ball center coordinate O of a rotary table coordinate systemcenter＝[xcenterycenterzcenter]T. The line laser sensor measurement data is substituted into the following equation:
[1111]·[RzKrot(KSn+ΔPn)-Ocenter]o[RzKrot(KSn+ΔPn)-Ocenter]-Rsphere 2＝0
in the formula: k, Sn,ΔPnThe step three is as described above;
the meaning represented by o is (A o B)i,j＝(A)i,j(B)i,j。
And step six, solving an equation by adopting a Levenberg-Marquardt iteration method. And selecting the target function as the distance from the line laser measuring point to the contact type measuring spherical surface, and optimizing the target function to minimize the distance sum.
I.e. the objective function is:
in the formula:
can be replaced by:
fn 2(x)＝([1111]·[RzKrot(KSn+ΔPn)-Ocenter]ο[RzKrot(KSn+ΔPn)-Ocenter]-Rsphere 2)2
and finally obtaining the globally optimal calibration parameters of the line laser measurement system.
Claims (7)
1. A multi-axis space coordinate system calibration method of a composite line laser measurement system based on a plane target is characterized by comprising the following steps: the method is suitable for a four-axis measuring machine structure, and for calibration between a two-dimensional line laser sensor and a contact measuring head of the measuring machine, which are unavailable in an original image, a plane target is utilized to perform initial calibration on a line laser measuring system, the calibration method is to optimize the distance from a measuring point of the line laser sensor to a measuring plane of the contact measuring head, and the calibration result is a rotation and translation matrix from the line laser sensor to the contact measuring head.
2. The method of claim 1, comprising the steps of:
the method comprises the following steps that firstly, a contact type measuring head is used for directly collecting measuring points on a standard plane, and a least square method is used for fitting a plane equation;
scanning the same plane by using the line laser sensor to obtain a series of line laser sensor acquisition pointsSnAnd the corresponding machine tool grating coordinate value is delta Pn；
Step three, establishing a mathematical model to enable all measuring points of the line laser sensor to accord with a plane equation measured by a corresponding contact type measuring head;
solving an equation by a Newton iteration method; and selecting the target function as the distance between the measured point and the fitted plane as an error value, wherein the nonlinear optimization target function reaches the minimum.
3. The method of claim 1, wherein the method comprises the steps of: the line laser sensor is a two-dimensional sensor, and the CCD original acquisition image of the line laser sensor cannot be acquired.
4. The method of claim 1, wherein the method comprises the steps of: the line laser measuring system can obtain the directions of two coordinate axes of the line laser sensor in a contact measuring head coordinate system at the same time through calibration to form a rotation and translation matrix.
5. The method of claim 1, wherein the method comprises the steps of: firstly, calibrating the relationship between a line laser sensor and a contact measuring head of a measuring machine through a plane target, taking the calibration result as a relatively initial value, and then optimizing system calibration parameters by utilizing the ball target at different angles of a rotary table.
6. The method of claim 5, comprising the steps of:
firstly, calibrating a coordinate system of a rotary table by a method for measuring a standard ball by a contact type measuring head. Then the contact measuring head and the line laser sensor measure the standard ball at multiple angles simultaneously, and the data measured by the line laser sensor are brought into the following formula:
and step two, solving an equation by adopting a Levenberg-Marquardt iterative method, selecting a target function as the distance from the line laser measuring point to the contact type measuring spherical surface, and optimizing the target function to minimize the distance sum.
7. The method of claim 5, wherein the method comprises: in the optimized measurement process, measurement data of a plurality of angles of the rotary table are needed.
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| CN111928776A (en) * | 2020-07-31 | 2020-11-13 | 中国航空工业集团公司济南特种结构研究所 | Multi-sensor-based non-contact online measurement system and method for numerical control machine tool |
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| CN115507769B (en) * | 2022-05-24 | 2023-09-22 | 北京工业大学 | Gear rapid measurement method integrating vision and optical principles |
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