CN108592787B - The rotating axis calibration method and system of 3D tracer rotation system - Google Patents
The rotating axis calibration method and system of 3D tracer rotation system Download PDFInfo
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- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
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Abstract
The present invention provides a kind of rotating axis calibration methods of 3D tracer rotation system, it comprises the steps of: that matching relationship seeks step: seeking the matching relationship of the first point cloud data and the second point cloud data, first point cloud data is by the way that testee is scanned acquisition on turntable when not rotating, second point cloud data is by being scanned acquisition to testee on the turntable after the known angle of rotation；Splicing relationship seeks step: calibrating turret axis according to matching relationship reverse, and seeks splicing homogeneous transform matrix.Correspondingly, the present invention also provides a kind of rotating axis calibration systems of 3D tracer rotation system.The present invention is to provide a kind of reverse methods, require equipment simple, amorphism, dimension precision requirement, and acquisition data volume greatly reduces and (only needs two groups of data), can satisfy the requirement of Fast Calibration, while precision is also higher.
Description
Technical field
The present invention relates to 3D scanning technique fields, and in particular, to the rotating axis calibration method of 3D tracer rotation system be
System.
Background technique
3D rotary scanning refers to three dimensions of the different angle using the object on 3-D scanning technology scanning rotating platform
According to according to the turret axis demarcated, calculating of the three-dimensional data under each angle after obtaining a series of three-dimensional datas
With relationship, they are stitched together to form the technology of the complete three-dimensional data of object.In 3D rotary scanning platform, two are not
Splicing with the three-dimensional data of angle is calculated according to the shaft demarcated.Rotating axis calibration, which refers to, measures turntable coordinate
The spatial relationship that system and object dimensional data generate coordinate system can calculate rotation according to the homogeneous transform matrix of spatial relationship
Turn the matching relationship between the two panels three-dimensional data under different angle.
3D surface sweeping technology is that the technology of object dimensional data is measured by technologies such as structure light, binocular visions, measurement knot
Fruit is generally with the preservation of series of points cloud.Now define three coordinate systems, point cloud (three-dimensional data) generate coordinate system, turntable coordinate system,
Object coordinates system, and set object coordinates system and turntable coordinate system and be overlapped in initial position.3D tracer rotation system will be to be scanned
Any known angle of object rotation simultaneously measures the object dimensional data under point cloud data generation coordinate system, according to what is demarcated
Turret axis can calculate the matching relationship of the angle points cloud known to difference in the case where cloud generates coordinate system.
At present there are many turret axis scaling methods, most of principles are the same.Basic step are as follows: 1, one is arranged on turntable
Series of flags point.2, above-mentioned turntable is rotated into a series of angles, and measures the index point three-dimensional data under each angle.3, root
A series of centers of circle are fitted in the three-dimensional point of different angle according to each index point.4, straight line is fitted according to the above-mentioned center of circle,
This straight line is axis.It is relatively simple on this general Method And Principle, it implements conveniently.But to the shape of index point, big
Small and precision has certain requirement, and more data is needed to be fitted calculating.For common marker, such as bead:
According to a series of centre ofs sphere of different angle bead point-cloud fitting and then rotation center is fitted, obtains turntable according to multiple rotation centers
Shaft axis.In addition such as plate: intersection point fitting rotation center is sweared according to the method for different angle plane and then is fitted axis.More than
Similar method is demarcated by marker, and method is higher to the form accuracy of marker, dimension precision requirement.Acquisition
Data volume is big, and processing is time-consuming.
Summary of the invention
For the defects in the prior art, the object of the present invention is to provide a kind of rotating axis calibration sides of 3D tracer rotation system
Method and system.
The rotating axis calibration method of the 3D tracer rotation system provided according to the present invention comprising the steps of:
Matching relationship seeks step: seek the matching relationship of the first point cloud data and the second point cloud data, described first point
Cloud data are by the way that testee is scanned acquisition on turntable when not rotating, second point cloud data passes through to known to rotation
Testee is scanned acquisition on turntable after angle；
Splicing relationship seeks step: calibrating turret axis according to matching relationship reverse, and seeks splicing homogeneous transformation square
Battle array.
Preferably, the matching relationship is sought in step:
The ith feature angle point data p of the first point cloud data is obtained respectivelyi, the second point cloud data ith feature angle point
Data qi, seek a cloud homogeneous transform matrix Td:
Point cloud homogeneous transform matrix TdConstitute the matching relationship.
Preferably, matching relationship is sought in step, and cost function F is defined by the following equation:
In formula: | | | | indicate modulo operation；
It will point cloud homogeneous transform matrix TdRotation item be translated apart to obtain:
In formula: n is characterized number a little；
R is rotational transformation matrix；
T is translation vector；
pc=Rqc+t
bi=pi-pc
di=qi-qc
In formula: pcFor the mass center of the first point cloud data；
qcFor the mass center of the second point cloud data；
bi、diIt is intermediate variable, subscript i indicates serial number；
In formula: H is intermediate variable；
Transposed matrix is sought in subscript T representative；
The SVD for calculating H is decomposed:
H=U Λ VT
X=VUT
In formula: U, Λ, V, X are intermediate variable；
As det (X)=1, R=X, at this time
T=pc-Rqc
Wherein: matrix determinant is sought in det () expression；
Obtain a cloud homogeneous transform matrix Td:
Preferably, the splicing relationship is sought step and is comprised the steps of:
Coordinate system definition step: defining point cloud generates coordinate system C0, rotate before turntable coordinate system C1And rotation rear turntable is sat
Mark system C2；
Coordinate system homogeneous transform matrix seeks step: generating coordinate system C according to cloud0With turntable coordinate system C before rotation1, ask
Take First Homogeneous transformation matrix0T1；According to turntable coordinate system C before rotating1With rotation rear turntable coordinate system C2, it is homogeneous to seek second
Transformation matrix1T2；
Splicing homogeneous transform matrix seeks step: according to Td、0T1、1T2Seek splicing homogeneous transform matrix.
Preferably, it is sought in step in coordinate system homogeneous transform matrix:
In formula: α, β, γ are three angles of Eulerian angles；θ is coordinate system C1To coordinate system C2Rotation angle about the z axis；
Splicing homogeneous transform matrix is sought in step, for piMiddle any point P1, corresponding in qiOn point P2, according to sky
Between transformation relation obtain:
0P1=0T1 1P1
0P2=0T1 1T2 2P1
1P1=2P1
0P1=0T1 1T2 0T1 -1 0P2
0P1=Td 0P2
Td=0T1 1T2 0T1 -1
In formula:0P1For point P1In coordinate system C0In coordinate；
1P1For point P1In coordinate system C1In coordinate；
0P2For point P2In coordinate system C0In coordinate；
2P1For point P1In coordinate system C2In coordinate；
Inverse matrix is sought in the representative of subscript -1；
It calculates:
[Pt Jt]=jordan (Td)
[Pr Jr]=jordan (1T2)
PtJtPt -1=Td
PrJrPr -1=1T2
In formula: Pt、JtFor intermediate variable；
Jordan () represents J.S.S type；
Pr、JrFor intermediate variable；
According to Td=0T1 1T2 0T1 -1, obtain TdWith1T2For similar matrix；
Pi...P2P1JtP1P2...Pi=Jr
PtP1P2...PiPr -1×1T2×(Pt P1 P2...PiPr -1)-1=Td
In formula: PiFor i-th of elementary transformation matrix；
Splice homogeneous transform matrix Tx=PtP1P2...PiPr -1, then have:
0T1 -1Tx 1T2(0T1 -1Tx)-1=1T2
Tx 1T2Tx -1=Td
According to TxComplete turret axis calibration.
Correspondingly, the present invention also provides a kind of rotating axis calibration systems of 3D tracer rotation system, comprising with lower module:
Matching relationship seeks module: seek the matching relationship of the first point cloud data and the second point cloud data, described first point
Cloud data are by the way that testee is scanned acquisition on turntable when not rotating, second point cloud data passes through to known to rotation
Testee is scanned acquisition on turntable after angle；
Splicing relationship seeks module: calibrating turret axis according to matching relationship reverse, and seeks splicing homogeneous transformation square
Battle array.
Preferably, the matching relationship is sought in module:
The ith feature angle point data p of the first point cloud data is obtained respectivelyi, the second point cloud data ith feature angle point
Data qi, seek a cloud homogeneous transform matrix Td:
Point cloud homogeneous transform matrix TdConstitute the matching relationship.
Preferably, matching relationship is sought in module, and cost function F is defined by the following equation:
In formula: | | | | indicate modulo operation；
It will point cloud homogeneous transform matrix TdRotation item be translated apart to obtain:
In formula: n is characterized number a little；
R is rotational transformation matrix；
T is translation vector；
pc=Rqc+t
bi=pi-pc
di=qi-qc
In formula: pcFor the mass center of the first point cloud data；
qcFor the mass center of the second point cloud data；
bi、diIt is intermediate variable, subscript i indicates serial number；
In formula: H is intermediate variable；
Transposed matrix is sought in subscript T representative；
The SVD for calculating H is decomposed:
H=U Λ VT
X=VUT
In formula: U, Λ, V, X are intermediate variable；
As det (X)=1, R=X, at this time
T=pc-Rqc
Wherein: matrix determinant is sought in det () expression；
Obtain a cloud homogeneous transform matrix Td:
Preferably, it includes with lower module that the splicing relationship, which seeks module:
Coordinate system definition module: defining point cloud generates coordinate system C0, rotate before turntable coordinate system C1And rotation rear turntable is sat
Mark system C2；
Coordinate system homogeneous transform matrix seeks module: generating coordinate system C according to cloud0With turntable coordinate system C before rotation1, ask
Take First Homogeneous transformation matrix0T1；According to turntable coordinate system C before rotating1With rotation rear turntable coordinate system C2, it is homogeneous to seek second
Transformation matrix1T2；
Splicing homogeneous transform matrix seeks module: according to Td、0T1、1T2Seek splicing homogeneous transform matrix.
Preferably, it is sought in module in coordinate system homogeneous transform matrix:
In formula: α, beta, gamma are three angles of Eulerian angles；θ is coordinate system C1To coordinate system C2Rotation angle about the z axis；
Splicing homogeneous transform matrix is sought in module, for piMiddle any point P1, corresponding in qiOn point P2, according to sky
Between transformation relation obtain:
0P1=0T1 1P1
0P2=0T1 1T2 2P1
1P1=2P1
0P1=0T1 1T2 0T1 -1 0P2
0P1=Td 0P2
Td=0T1 1T2 0T1 -1
In formula:0P1For point P1In coordinate system C0In coordinate；
1P1For point P1In coordinate system C1In coordinate；
0P2For point P2In coordinate system C0In coordinate；
2P1For point P1In coordinate system C2In coordinate；
Inverse matrix is sought in the representative of subscript -1；
It calculates:
[Pt Jt]=jordan (Td)
[Pr Jr]=jordan (1T2)
PtJtPt -1=Td
PrJrPr -1=1T2
In formula: Pt、JtFor intermediate variable；
Jordan () represents J.S.S type；
Pr、JrFor intermediate variable；
According to Td=0T1 1T2 0T1 -1, obtain TdWith1T2For similar matrix；
Pi...P2P1JtP1P2...Pi=Jr
PtP1P2...PiPr -1×1T2×(PtP1P2...PiPr -1)-1=Td
In formula: PiFor i-th of elementary transformation matrix；
Splice homogeneous transform matrix Tx=PtP1P2...PiPr -1, then have:
0T1 -1Tx 1T2(0T1 -1Tx)-1=1T2
Tx 1T2Tx -1=Td
According to TxComplete turret axis calibration.
Compared with prior art, the present invention have it is following the utility model has the advantages that
1, the present invention is to provide a kind of reverse methods, obtain two o'clock cloud under known angle according to the object of simple shape
Matching relationship reverse calibrates turret axis, and then calculates the splicing matching relationship of any known angle two panels point cloud；And then make
,
2, method provided by the invention requires equipment simple, amorphism, dimension precision requirement, and acquisition data volume subtracts significantly
Few (only needing two groups of data), can satisfy the requirement of Fast Calibration, while precision is also higher.
3, the present invention realizes the Fast Calibration of 3D tracer rotation system shaft, is calculated according to the result of calibration any known
Rotate the matching relationship between the object dimensional data under angle, the splicing for point cloud data.
Detailed description of the invention
Upon reading the detailed description of non-limiting embodiments with reference to the following drawings, other feature of the invention,
Objects and advantages will become more apparent upon:
Fig. 1 is that control point method splices two planes, schematic diagram when not splicing；
Fig. 2 is that control point method splices two planes, schematic diagram when splicing is completed；
Fig. 3 is system coordinate system schematic diagram；
Fig. 4 is turntable coordinate system schematic diagram；
Fig. 5 is gypsum picture point cloud effect picture；
Fig. 6 is plant point cloud effect picture；
Fig. 7 is the rotating axis calibration method flow chart of 3D tracer rotation system provided by the invention.
Specific embodiment
The present invention is described in detail combined with specific embodiments below.Following embodiment will be helpful to the technology of this field
Personnel further understand the present invention, but the invention is not limited in any way.It should be pointed out that the ordinary skill of this field
For personnel, without departing from the inventive concept of the premise, various modifications and improvements can be made.These belong to the present invention
Protection scope.
In the description of the present invention, it is to be understood that, term " on ", "lower", "front", "rear", "left", "right", " perpendicular
Directly ", the orientation or positional relationship of the instructions such as "horizontal", "top", "bottom", "inner", "outside" is orientation based on the figure or position
Relationship is set, is merely for convenience of description of the present invention and simplification of the description, rather than the device or element of indication or suggestion meaning are necessary
It with specific orientation, is constructed and operated in a specific orientation, therefore is not considered as limiting the invention.
The rotating axis calibration method of 3D tracer rotation system provided by the invention comprising the steps of: matching relationship is sought walking
It is rapid: to seek the matching relationship of the first point cloud data and the second point cloud data, first point cloud data to when not rotating by turning
Testee is scanned acquisition on platform, and second point cloud data passes through to testee on the turntable after the known angle of rotation
It is scanned acquisition；Splicing relationship seeks step: calibrating turret axis according to matching relationship reverse, and seeks splicing homogeneous change
Change matrix.
The matching relationship is sought in step: obtaining the ith feature angle point data p of the first point cloud data respectivelyi, second
The ith feature angle point data q of point cloud datai, seek a cloud homogeneous transform matrix Td: point cloud homogeneous transform matrix TdConstitute institute
State matching relationship.Matching relationship is sought in step, and cost function F is defined by the following equation:
In formula: | | | | indicate modulo operation；It will point cloud homogeneous transform matrix TdRotation item be translated apart to obtain:
In formula: n is characterized number a little；R is rotational transformation matrix；T is translation vector；
pc=Rqc+t
bi=pi-pc
di=qi-qc
In formula: pcFor the mass center of the first point cloud data；qcFor the mass center of the second point cloud data；bi、diIt is intermediate variable,
Subscript i indicates serial number；
In formula: H is intermediate variable；Transposed matrix is sought in subscript T representative.The SVD for calculating H is decomposed:
H=U Λ VT
X=VUT
In formula: U, Λ, V, X are intermediate variable；As det (X)=1, R=X, at this time
T=pc-Rqc
Wherein: matrix determinant is sought in det () expression, obtains a cloud homogeneous transform matrix Td:
The splicing relationship seeks step and comprises the steps of: coordinate system definition step: defining point cloud generates coordinate system C0、
Turntable coordinate system C before rotating1And rotation rear turntable coordinate system C2；Coordinate system homogeneous transform matrix seeks step: according to point Yun Sheng
At coordinate system C0With turntable coordinate system C before rotation1, seek First Homogeneous transformation matrix0T1；According to turntable coordinate system C before rotating1With
Rotate rear turntable coordinate system C2, seek the second homogeneous transform matrix1T2；Splicing homogeneous transform matrix seeks step: according to Td、0T1
、1T2Seek splicing homogeneous transform matrix.
It is sought in step in coordinate system homogeneous transform matrix:
In formula: α, beta, gamma are three angles of Eulerian angles；θ is coordinate system C1To coordinate system C2Rotation angle about the z axis.It spells
It connects homogeneous transform matrix to seek in step, for piMiddle any point P1, corresponding in qiOn point P2, according to spatial transform relation
It obtains:
0P1=0T1 1P1
0P2=0T1 1T2 2P1
1P1=2P1
0P1=0T1 1T2 0T1 -1 0P2
0P1=Td 0P2
Td=0T1 1T2 0T1 -1
In formula:0P1For point P1In coordinate system C0In coordinate；1P1For point P1In coordinate system C1In coordinate；0P2For point P2In
Coordinate system C0In coordinate；2P1For point P1In coordinate system C2In coordinate；Inverse matrix is sought in the representative of subscript -1.It is marked using Jordan
The method of pseudotype calculates:
[Pt Jt]=jordan (Td)
[Pr Jr]=jordan (1T2)
So:
PtJtPt -1=Td
PrJrPr -1=1T2
In formula: Pt、JtFor intermediate variable；Jordan () represents J.S.S type；Pr、JrFor intermediate variable；
T in well-known theoryd=0T1 1T2 0T1 -1, obtain TdWith1T2For similar matrix, i.e., its J.S.S type is in removing sequence
In the case where element it is identical, then there is following permutation matrix to make:
Pi...P2P1JtP1P2...Pi=Jr
By being itself with the inverse of permutation matrix, then have
PtP1P2...PiPr -1×1T2×(PtP1P2...PiPr -1)-1=Td
In formula: PiFor i-th of elementary transformation matrix；
Enable splicing homogeneous transform matrix Tx=PtP1P2...PiPr -1, then have:
0T1 -1Tx 1T2(0T1 -1Tx)-1=1T2
The T acquired at this timexHave:
Tx 1T2Tx -1=Td
Above formula sets up any θ, thus can calculate the point cloud homogeneous transform matrix T of any rotationx, i.e.,
Turntable has been got well in calibration.
Correspondingly, the present invention also provides a kind of rotating axis calibration systems of 3D tracer rotation system, comprising with lower module:
Module is sought with relationship: seeking the matching relationship of the first point cloud data and the second point cloud data, and first point cloud data passes through
To testee is scanned acquisition on turntable when not rotating, second point cloud data to after the known angle of rotation by turning
Testee is scanned acquisition on platform；Splicing relationship seeks module: calibrating turret axis according to matching relationship reverse, and asks
Take splicing homogeneous transform matrix.
The matching relationship is sought in module: obtaining the ith feature angle point data p of the first point cloud data respectivelyi, second
The ith feature angle point data q of point cloud datai, seek a cloud homogeneous transform matrix Td: point cloud homogeneous transform matrix TdConstitute institute
State matching relationship.Matching relationship is sought in module, and cost function F is defined by the following equation:
In formula: | | | | indicate modulo operation；By the rotation item of cloud homogeneous transform matrix T be translated apart to obtain:
In formula: n is characterized number a little；R is rotational transformation matrix；T is translation vector；
pc=Rqc+t
bi=pi-pc
di=qi-qc
In formula: pcFor the mass center of the first point cloud data；qcFor the mass center of the second point cloud data；bi、diIt is intermediate variable,
Subscript i indicates serial number；
In formula: H is intermediate variable；Transposed matrix is sought in subscript T representative.The SVD for calculating H is decomposed:
H=U Λ VT
X=VUT
In formula: U, Λ, V, X are intermediate variable；As det (X)=1, R=X, at this time
T=pc-Rqc
Wherein: matrix determinant is sought in det () expression, obtains a cloud homogeneous transform matrix Td:
It includes with lower module that the splicing relationship, which seeks module: coordinate system definition module: defining point cloud generates coordinate system C0、
Turntable coordinate system C before rotating1And rotation rear turntable coordinate system C2；Coordinate system homogeneous transform matrix seeks module: according to point Yun Sheng
At coordinate system C0With turntable coordinate system C before rotation1, seek First Homogeneous transformation matrix0T1；According to turntable coordinate system C before rotating1With
Rotate rear turntable coordinate system C2, seek the second homogeneous transform matrix1T2；Splicing homogeneous transform matrix seeks module: according to Td、0T1
、1T2Seek splicing homogeneous transform matrix.
It is sought in module in coordinate system homogeneous transform matrix:
In formula: α, beta, gamma are three angles of Eulerian angles；θ is coordinate system C1To coordinate system C2Rotation angle about the z axis.It spells
It connects homogeneous transform matrix to seek in module, for piMiddle any point P1, corresponding in qiOn point P2, according to spatial transform relation
It obtains:
0P1=0T1 1P1
0P2=0T1 1T2 2P1
1P1=2P1
0P1=0T1 1T2 0T1 -1 0P2
0P1=Td 0P2
Td=0T1 1T2 0T1 -1
In formula:0P1For point P1In coordinate system C0In coordinate；1P1For point P1In coordinate system C1In coordinate；0P2For point P2In
Coordinate system C0In coordinate；2P1For point P1In coordinate system C2In coordinate；Inverse matrix is sought in the representative of subscript -1.It is marked using Jordan
The system-computed of pseudotype:
[Pt Jt]=jordan (Td)
[Pr Jr]=jordan (1T2)
So:
PtJtPt -1=Td
PrJrPr -1=1T2
In formula: Pt、JtFor intermediate variable；Jordan () represents J.S.S type；Pr、JrFor intermediate variable；
T in well-known theoryd=0T1 1T2 0T1 -1, obtain TdWith1T2For similar matrix, i.e., its J.S.S type remove it is suitable
Element is identical in the case where sequence, then has following permutation matrix to make:
Pi...P2P1JtP1P2...Pi=Jr
By being itself with the inverse of permutation matrix, then have
PtP1P2...PiPr -1×1T2×(PtP1P2...PiPr -1)-1=Td
In formula: PiFor i-th of elementary transformation matrix；
Enable splicing homogeneous transform matrix Tx=PtP1P2...PiPr -1, then have:
0T1 -1Tx 1T2(0T1 -1Tx)-1=1T2
The T acquired at this timexHave:
Tx 1T2Tx -1=Td
Above formula sets up any θ, thus can calculate the point cloud homogeneous transform matrix T of any rotationx, i.e.,
Turntable has been got well in calibration.
One skilled in the art will appreciate that in addition to realizing system provided by the invention in a manner of pure computer readable program code
It, completely can be by the way that method and step be carried out programming in logic come so that provided by the invention other than system, device and its modules
System, device and its modules are declined with logic gate, switch, specific integrated circuit, programmable logic controller (PLC) and insertion
The form of controller etc. realizes identical program.So system provided by the invention, device and its modules may be considered that
It is a kind of hardware component, and the knot that the module for realizing various programs for including in it can also be considered as in hardware component
Structure；It can also will be considered as realizing the module of various functions either the software program of implementation method can be Hardware Subdivision again
Structure in part.
Preferred embodiment:
In practical operation, a rectangular plate is placed on turntable first, scanning obtains the first point cloud data, turntable rotation
After any known angle, θ, scanning obtains the second point cloud data again.Rectangular shape required precision is not high, placement location is random,
Fastening is only needed, this is also method provided by the invention with respect to place easier for other methods.In this preference, point
Four characteristic angle point data p are not acquired in the first point cloud data, the second point cloud datai、qi, as shown in Figure 1 and Figure 2, using control
Point seeks the point cloud homogeneous transform matrix that the second point cloud data is spliced to the first point cloud data, due to measurement error, four features
Point is impossible completely corresponding, defines cost function T thus with least square methodd。
The rotating axis calibration method calibration shaft of the 3D tracer rotation system provided according to the present invention is for point cloud, to stone
Cream picture, plant etc. point cloud is spliced.It is as shown in Figure 5, Figure 6 to splice complete result, average stitching error about 0.15mm meets
Actual needs.In view of the error of spatial digitizer itself gets over 0.1mm, it is believed that this method is accurate, effective.
Specific embodiments of the present invention are described above.It is to be appreciated that the invention is not limited to above-mentioned
Particular implementation, those skilled in the art can make various deformations or amendments within the scope of the claims, this not shadow
Ring substantive content of the invention.In the absence of conflict, the feature in embodiments herein and embodiment can any phase
Mutually combination.
Claims (6)
1. a kind of rotating axis calibration method of 3D tracer rotation system, which is characterized in that comprise the steps of:
Matching relationship seeks step: seeking the matching relationship of the first point cloud data and the second point cloud data, first cloud number
According to by the way that testee is scanned acquisition on turntable when not rotating, second point cloud data passes through to the known angle of rotation
Testee is scanned acquisition on turntable afterwards；
Splicing relationship seeks step: according to matching relationship reverse, calibrating turret axis, and seeks splicing homogeneous transform matrix；
The matching relationship is sought in step:
The ith feature angle point data p of the first point cloud data is obtained respectivelyi, the second point cloud data ith feature angle point data
qi, seek a cloud homogeneous transform matrix Td:
Point cloud homogeneous transform matrix TdConstitute the matching relationship；
The splicing relationship is sought step and is comprised the steps of:
Coordinate system definition step: defining point cloud generates coordinate system C0, rotate before turntable coordinate system C1And rotation rear turntable coordinate system
C2；
Coordinate system homogeneous transform matrix seeks step: generating coordinate system C according to cloud0With turntable coordinate system C before rotation1, seek
One homogeneous transform matrix0T1；According to turntable coordinate system C before rotating1With rotation rear turntable coordinate system C2, seek the second homogeneous transformation
Matrix1T2；
Splicing homogeneous transform matrix seeks step: according to Td、0T1、1T2Seek splicing homogeneous transform matrix.
2. the rotating axis calibration method of 3D tracer rotation system according to claim 1, which is characterized in that matching relationship is sought
In step, cost function F is defined by the following equation:
In formula: | | | | indicate modulo operation；
It will point cloud homogeneous transform matrix TdRotation item be translated apart to obtain:
In formula: n is characterized number a little；
R is rotational transformation matrix；
T is translation vector；
pc=Rqc+t
bi=pi-pc
di=qi-qc
In formula: pcFor the mass center of the first point cloud data；
qcFor the mass center of the second point cloud data；
bi、diIt is intermediate variable, subscript i indicates serial number；
In formula: H is intermediate variable；
Transposed matrix is sought in subscript T representative；
The SVD for calculating H is decomposed:
H=U Λ VT
X=VUT
In formula: U, Λ, V, X are intermediate variable；
As det (X)=1, R=X, at this time
T=pc-Rqc
Wherein: matrix determinant is sought in det () expression；
Obtain a cloud homogeneous transform matrix Td:
3. the rotating axis calibration method of 3D tracer rotation system according to claim 1, which is characterized in that homogeneous in coordinate system
Transformation matrix is sought in step:
In formula: α, beta, gamma are three angles of Eulerian angles；θ is coordinate system C1To coordinate system C2Rotation angle about the z axis；
Splicing homogeneous transform matrix is sought in step, for piMiddle any point P1, corresponding in qiOn point P2, according to spatial alternation
Relationship obtains:
0P1=0T1 1P1
0P2=0T1 1T2 2P1
1P1=2P1
0P1=0T1 1T2 0T1 -10P2
0P1=Td 0P2
Td=0T1 1T2 0T1 -1
In formula:0P1For point P1In coordinate system C0In coordinate；
1P1For point P1In coordinate system C1In coordinate；
0P2For point P2In coordinate system C0In coordinate；
2P1For point P1In coordinate system C2In coordinate；
Inverse matrix is sought in the representative of subscript -1；
It calculates:
[Pt Jt]=jordan (Td)
[Pr Jr]=jordan (1T2)
PtJtPt -1=Td
PrJrPr -1=1T2
In formula: Pt、JtFor intermediate variable；
Jordan () represents J.S.S type；
Pr、JrFor intermediate variable；
According to Td=0T1 1T2 0T1 -1, obtain TdWith1T2For similar matrix；
Pi...P2P1JtP1P2...Pi=Jr
PtP1P2...PiPr -1×1T2×(PtP1P2...PiPr -1)-1=Td
In formula: PiFor i-th of elementary transformation matrix；
Splice homogeneous transform matrix Tx=PtP1P2...PiPr -1, then have:
0T1 -1Tx 1T2(0T1 -1Tx)-1=1T2
Tx 1T2Tx -1=Td
According to TxComplete turret axis calibration.
4. a kind of rotating axis calibration system of 3D tracer rotation system, which is characterized in that comprising with lower module:
Matching relationship seeks module: seeking the matching relationship of the first point cloud data and the second point cloud data, first cloud number
According to by the way that testee is scanned acquisition on turntable when not rotating, second point cloud data passes through to the known angle of rotation
Testee is scanned acquisition on turntable afterwards；
Splicing relationship seeks module: according to matching relationship reverse, calibrating turret axis, and seeks splicing homogeneous transform matrix；
The matching relationship is sought in module:
The ith feature angle point data p of the first point cloud data is obtained respectivelyi, the second point cloud data ith feature angle point data
qi, seek a cloud homogeneous transform matrix Td:
Point cloud homogeneous transform matrix TdConstitute the matching relationship；
It includes with lower module that the splicing relationship, which seeks module:
Coordinate system definition module: defining point cloud generates coordinate system C0, rotate before turntable coordinate system C1And rotation rear turntable coordinate system
C2；
Coordinate system homogeneous transform matrix seeks module: generating coordinate system C according to cloud0With turntable coordinate system C before rotation1, seek
One homogeneous transform matrix0T1；According to turntable coordinate system C before rotating1With rotation rear turntable coordinate system C2, seek the second homogeneous transformation
Matrix1T2；
Splicing homogeneous transform matrix seeks module: according to Td、0T1、1T2Seek splicing homogeneous transform matrix.
5. the rotating axis calibration system of 3D tracer rotation system according to claim 4, which is characterized in that matching relationship is sought
In module, cost function F is defined by the following equation:
In formula: | | | | indicate modulo operation；
It will point cloud homogeneous transform matrix TdRotation item be translated apart to obtain:
In formula: n is characterized number a little；
R is rotational transformation matrix；
T is translation vector；
pc=Rqc+t
bi=pi-pc
di=qi-qc
In formula: pcFor the mass center of the first point cloud data；
qcFor the mass center of the second point cloud data；
bi、diIt is intermediate variable, subscript i indicates serial number；
In formula: H is intermediate variable；
Transposed matrix is sought in subscript T representative；
The SVD for calculating H is decomposed:
H=U Λ VT
X=VUT
In formula: U, Λ, V, X are intermediate variable；
As det (X)=1, R=X, at this time
T=pc-Rqc
Wherein: matrix determinant is sought in det () expression；
Obtain a cloud homogeneous transform matrix Td:
6. the rotating axis calibration system of 3D tracer rotation system according to claim 4, which is characterized in that homogeneous in coordinate system
Transformation matrix is sought in module:
In formula: α, beta, gamma are three angles of Eulerian angles；θ is coordinate system C1To coordinate system C2Rotation angle about the z axis；
Splicing homogeneous transform matrix is sought in module, for piMiddle any point P1, corresponding in qiOn point P2, according to spatial alternation
Relationship obtains:
0P1=0T1 1P1
0P2=0T1 1T2 2P1
1P1=2P1
0P1=0T1 1T2 0T1 -10P2
0P1=Td 0P2
Td=0T1 1T2 0T1 -1
In formula:0P1For point P1In coordinate system C0In coordinate；
1P1For point P1In coordinate system C1In coordinate；
0P2For point P2In coordinate system C0In coordinate；
2P1For point P1In coordinate system C2In coordinate；
Inverse matrix is sought in the representative of subscript -1；
It calculates:
[Pt Jt]=jordan (Td)
[Pr Jr]=jordan (1T2)
PtJtPt -1=Td
PrJrPr -1=1T2
In formula: Pt、JtFor intermediate variable；
Jordan () represents J.S.S type；
Pr、JrFor intermediate variable；
According to Td=0T1 1T2 0T1 -1, obtain TdWith1T2For similar matrix；
Pi...P2P1JtP1P2...Pi=Jr
PtP1P2...PiPr -1×1T2×(PtP1P2...PiPr -1)-1=Td
In formula: PiFor i-th of elementary transformation matrix；
Splice homogeneous transform matrix Tx=PtP1P2...PiPr -1, then have:
0T1 -1Tx 1T2(0T1 -1Tx)-1=1T2
Tx 1T2Tx -1=Td
According to TxComplete turret axis calibration.
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| CN109493388B (en) * | 2018-09-30 | 2020-11-17 | 先临三维科技股份有限公司 | Rotating shaft calibration method and device, computer equipment and storage medium |
| CN109974707B (en) * | 2019-03-19 | 2022-09-23 | 重庆邮电大学 | Indoor mobile robot visual navigation method based on improved point cloud matching algorithm |
| CN111928773B (en) * | 2019-05-13 | 2022-09-09 | 深圳中科飞测科技股份有限公司 | Detection method and detection system |
| CN110163797B (en) * | 2019-05-31 | 2020-03-31 | 四川大学 | Method and device for calibrating pose relation of rotary table to realize arbitrary angle point cloud splicing |
| CN110728623B (en) * | 2019-08-27 | 2024-04-19 | 深圳市重投华讯太赫兹科技有限公司 | Cloud point splicing method, terminal equipment and computer storage medium |
| CN111986219B (en) * | 2020-08-10 | 2023-09-19 | 中国科学院光电技术研究所 | Matching method of three-dimensional point cloud and free-form surface model |
| CN114485385B (en) * | 2020-10-23 | 2023-07-07 | 广东天机工业智能系统有限公司 | Workpiece coordinate system calibration method, device and system |
| CN113379846B (en) * | 2021-05-28 | 2022-08-09 | 上海汇像信息技术有限公司 | Method for calibrating rotating shaft of rotary table based on direction indication mark point calibration template |
| CN114359413B (en) * | 2022-03-17 | 2022-06-28 | 深圳市纵维立方科技有限公司 | Method and system for calculating position parameters of rotating platform for three-dimensional scanning |
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