CN114216395A - Space rotation axis solving method based on calibration plate - Google Patents

Space rotation axis solving method based on calibration plate Download PDF

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CN114216395A
CN114216395A CN202111528920.7A CN202111528920A CN114216395A CN 114216395 A CN114216395 A CN 114216395A CN 202111528920 A CN202111528920 A CN 202111528920A CN 114216395 A CN114216395 A CN 114216395A
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王秋
陈兆宽
汤楚楚
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Zhongzhi Shengshi Intelligent Technology Suzhou Co ltd
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    • G01—MEASURING; TESTING
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    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
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    • G01B11/26—Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes
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Abstract

The invention relates to the field of space rotating shaft solving methods, in particular to a space rotating shaft solving method based on a calibration plate. The method comprises the following steps: (1) fixing the calibration plate on a target object by using a jig; (2) the camera shoots the image of the calibration plate to calculate the position matrix H of the calibration plate relative to the camera1(ii) a (3) Rotating the target object; (4) the camera shoots the image of the calibration plate to calculate the position matrix H of the calibration plate relative to the camera2(ii) a (5) Calculating a rotation matrix; (6) the rotation axis V and the rotation angle Theta are calculated from the rotation matrix. The invention solves the air space by acquiring the image of the calibration plate by the calibration plate cameraThe extracted features are unified when the object rotating shaft and the object rotating angle are rotated, so that the features can be conveniently extracted by an algorithm, the extraction and calculation precision is improved, and the calculation speed is increased.

Description

Space rotation axis solving method based on calibration plate
Technical Field
The invention relates to the field of space rotating shaft solving methods, in particular to a space rotating shaft solving method based on a calibration plate.
Background
When the rotation parameters of the space object are solved, the rotating shaft and the rotating angle of the space object cannot be accurately calculated without the help of external auxiliary tools, if the rotating shaft and the rotating angle are calculated by only adopting the characteristics of the object, the grabbing characteristics are unstable, large characteristic changes occur when the target posture is changed, a unified algorithm cannot be adopted to meet the calculation requirements, and finally uncertainty and instability are brought to the calculation result.
Disclosure of Invention
In order to solve the technical problems described in the background art, the invention provides a calibration plate-based space rotating shaft solving method, and the method extracts features uniformly when solving the rotating shaft and the rotating angle of a space object by means of a calibration plate image acquisition mode by a calibration plate camera, so that the features are conveniently extracted by an algorithm, the extraction and calculation precision is improved, and the calculation speed is increased.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a method for solving a space rotation axis based on a calibration plate comprises the following steps:
(1) fixing the calibration plate on a target object by using a jig;
(2) the camera shoots the image of the calibration plate to calculate the position matrix H of the calibration plate relative to the camera1；
(3) Rotating the target object;
(4) the camera shoots the image of the calibration plate to calculate the position matrix H of the calibration plate relative to the camera2；
(5) Calculating a rotation matrix;
(6) the rotation axis V and the rotation angle Theta are calculated from the rotation matrix.
Specifically, the calibration plate is a dot matrix calibration plate or a chess board grid calibration plate.
Specifically, in the step (3), the target object and the calibration plate synchronously perform axial angle rotation motion.
In particular, the position matrix H1Is calculated in such a way that the coordinates of each point on the calibration plate in its reference coordinate system are W ═ x, y, z]TThe imaged image coordinate of the point is m ═ u, v]TConverting W, m into homogeneous coordinate form W' ═ x, y, z, l]T,m′＝[u,v,l]TThen the relationship between W 'and m' is：
sm′＝A[R t]WT；
In the formula, s is a scaling factor, R is a rotation matrix of the world coordinate system relative to the camera coordinate system, t is a translation vector of the world coordinate system relative to the camera coordinate system, a is a camera internal parameter matrix, and a is expressed as:
formula I,
Figure BDA0003410021510000021
Wherein (u)0,v0) As principal point coordinates of the image plane, ax，ayIs a scale factor of the image coordinate axis, axTransverse dimension of pixel, a ÷ lens focal length ÷ pixelxThe focal length of a lens divided by the vertical size of a pixel, r is the non-perpendicularity of u and v, the z of a three-dimensional coordinate of a point on a target is 0, the x coordinate axis direction of a reference coordinate system of the three-dimensional coordinate is horizontal to the right, the y coordinate axis direction is vertical to the downward, the z coordinate axis direction is vertical to the paper surface, and the r is usedi(i ═ l,2,3) represents each column of the matrix R, with equation one rewritten as:
the second formula,
Figure BDA0003410021510000022
Setting H ═ kA [ r ]1 r2 t]The H matrix is a 3-row and 3-column square matrix, wherein r1,r2Two columns are directional vectors of image coordinate axes x and y, k is a proportionality coefficient, and H is ═ H1 h2 h3]Then it follows:
formula III, [ hx h2 h3]＝kA[r1 r2 t]；
Formula three middle vector r1Perpendicular to r2T and r1,r2If the two are not coplanar, the H matrix is full rank, and the actual imaging coordinate point of the calibration plate is set as piLet the actual coordinate point piAnd calculating a coordinate point m'iIs defined as the following objective function:
Figure BDA0003410021510000023
n is the number of circles on the calibration plate;
to find H, let
Figure BDA0003410021510000024
After obtaining the H matrix, the r matrix is obtained1,r2Orthogonality: r is1 Tr2＝0，r1 Tr2＝r2 Tr2The equation can be found:
the formula IV,
Figure BDA0003410021510000025
Order to
Figure BDA0003410021510000031
After calculating matrix B, knowing that B is a main diagonal symmetric matrix, let:
b＝[B11 B12 B22 B13 B23 B33]T；
setting hi＝[h1i,h2i,h3i]TThe ith column vector of H, then
hi TBhj＝Vijb；
In the formula
Vij＝[h1ih1j,h1ih2j+h2ih1j,h2ih2j,h3ih1j+h1ih3j,h3ih2j+h2ih3j,h3ih3j]
Then the formula four is rewritten in the form of a homogeneous equation as:
the formula five,
Figure BDA0003410021510000032
The number of points on the calibration plate is more than 9, the physical coordinates of the calibration plate and the corresponding image coordinates of each point are substituted into a formula V, and the coordinates are obtained through the formula VObtaining b according to the formula V, obtaining a position matrix H of the camera through an equation after obtaining an A matrix1：
Figure BDA0003410021510000033
r3＝r1×r2
Figure BDA0003410021510000034
H1＝[r1 r2 r3 t]。
Specifically, in step (4), the position matrix H2Is calculated by the method and the position matrix H1The same is true.
Specifically, in step (5), the rotation matrix is calculated in the manner of H1,H2For a full rank invertible matrix, then:
Hrot＝H2 -1H1；
from HrotDecomposing a three-dimensional rotating part R:
Figure BDA0003410021510000035
specifically, the method of calculating the rotation axis V and the rotation angle Theta is to set four elements q ═ q (q)0，q1，q2，q3)；
Solving the corresponding rotation matrix R according to the definition of the shaft angleqComprises the following steps:
Figure BDA0003410021510000036
with rotation of R and RqThe matrix equality correspondence yields:
Figure BDA0003410021510000041
calculating any one of q0 to q4, and then according to the corresponding relationThe values of the remaining 3 components are determined, and the rotation axis V is [ q ]1 q2 q3]Rotation angle Theta ═ q0。
The invention has the beneficial effects that: the invention provides a calibration plate-based space rotating shaft solving method, which extracts unified features when solving a space object rotating shaft and a rotating angle by means of acquiring calibration plate images by a calibration plate camera, thereby facilitating the feature extraction of an algorithm, improving the extraction and calculation precision and improving the calculation speed.
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The invention is further illustrated with reference to the following figures and examples.
FIG. 1 is a flow chart of the present invention;
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings.
FIG. 1 is a flow chart of the present invention.
As shown in the attached figure 1 of the drawings,
1. the calibration plate is fixed on a target object by using a special jig, and is a dot matrix calibration plate or a chess board grid calibration plate.
2. The camera shoots the image of the calibration plate to calculate the position matrix H of the calibration plate relative to the camera1Here the camera and lens parameters a have been calibrated by the camera. The concrete H1 solving steps are as follows:
the coordinate of each point on the calibration plate under the reference coordinate system is W ═ x, y, z]TThe imaged image coordinate of the point is m ═ u, v]T(coordinates in the image coordinate system), W, m is converted into homogeneous coordinate form W' ═ x, y, z, l]T,m′＝[u,v,l]TThen, W 'and m' are related as follows:
formula one, sm' ═ a [ R t]WT
Wherein s is a scaling factor, R is a rotation matrix of the world coordinate system relative to the camera coordinate system, t is a translation vector of the world coordinate system relative to the camera coordinate system, A is a camera internal parameter matrix, and A is expressed as follows:
Figure BDA0003410021510000051
wherein (u)0,v0) As principal point coordinates of the image plane, ax，ayIs a scale factor of the image coordinate axis, axTransverse dimension of pixel, a ÷ lens focal length ÷ pixelxLens focal length ÷ vertical dimension of the pixel, r is the non-perpendicularity of u and v. Generally we establish the world coordinate system on the surface of a two-dimensional planar target, so that the z of the three-dimensional coordinates of a point on the target is 0. The direction of the x coordinate axis of the reference coordinate system is horizontally towards the right, the direction of the y coordinate axis is vertically towards the lower part, and the direction of the z coordinate axis can be determined to be perpendicular to the paper surface and inwards according to the right-hand rule. By ri(i ═ l,2,3) represents each column of the matrix R, and equation one can be rewritten as the following equation two:
the second formula,
Figure BDA0003410021510000052
Setting H ═ kA [ r ]1 r2 t]The H matrix is a 3-row and 3-column square matrix, wherein r1,r2Two columns are directional vectors of image coordinate axes x and y, k is a proportionality coefficient, and H is ═ H1 h2 h3]Then:
formula III, [ hx h2 h3]＝kA[r1 r2 t]
Formula three middle vector r1Perpendicular to r2T and r1,r2Not coplanar, the H matrix is full rank. Setting the actual imaging coordinate point of the calibration plate as piTo obtain an ideal H matrix, one must let the actual coordinate point piAnd calculating a coordinate point m'iIs defined as the following objective function:
Figure BDA0003410021510000053
(n is the number of dots on the calibration plate)
To find H, let
Figure BDA0003410021510000054
After obtaining the H matrix, the r matrix is obtained1,r2Orthogonality: r is1 Tr2＝0，r1 Tr2＝r2 Tr2The following equation four can be obtained:
the formula IV,
Figure BDA0003410021510000055
Order to
Figure BDA0003410021510000056
After calculating the matrix B, B is known as a main diagonal symmetric matrix. Then order:
b＝[B11 B12 B22 B13 B23 B33]T
setting hi＝[h1i,h2i,h3i]TThe ith column vector of H, then
hi TBhj＝Vijb
In the formula
Vij＝[h1ih1j,h1ih2j+h2ih1j,h2ih2j,h3ih1j+h1ih3j,h3ih2j+h2ih3j,h3ih3j]
Then equation four can be rewritten in the form of a homogeneous equation to equation five:
the formula five,
Figure BDA0003410021510000061
The number of points on the calibration plate is larger than 9, the physical coordinates and the corresponding image coordinates of the calibration plate of each point are substituted into the formula, b can be solved by the formula, A is the internal reference matrix of the camera which is solved when the camera is calibrated, and the external reference of the camera can be obtained by the following equation after the matrix A is obtained:
Figure BDA0003410021510000062
Figure BDA0003410021510000063
namely, it is
H1＝[r1 r2 r3 t]。
3. Rotating target object
The calibration plate is tightly fixed on the target to do axial angle rotation movement, and no relative position and posture deviation exists.
4. The camera shoots the image of the calibration plate to calculate the position matrix H of the calibration plate relative to the camera2. Specific H2Solving step and H1In the same way, H is obtained2。
5. And calculating a rotation matrix, wherein the specific rotation matrix is calculated as follows:
due to H1,H2For a full rank invertible matrix, then:
Hrot＝H2 -1H1
from HrotDecomposing a three-dimensional rotating part R:
Figure BDA0003410021510000071
6. calculating the rotation axis V and the rotation angle Theta from the rotation matrix:
setting four elements q ═ q (q)0，q1，q2，q3)
The corresponding rotation matrix R can be solved according to the definition of the shaft angleqComprises the following steps:
Figure BDA0003410021510000072
with rotation of R and RqMatrix equal correspondenceThe following are known:
Figure BDA0003410021510000073
if any of q0 through q4 is calculated, the remaining 3 components can be found from the above relationship, assuming we first found q0, then:
Figure BDA0003410021510000074
rotation axis V ═ q1 q2 q3]，Theta＝q0
In light of the foregoing description of the preferred embodiment of the present invention, many modifications and variations will be apparent to those skilled in the art without departing from the spirit and scope of the invention. The technical scope of the present invention is not limited to the content of the specification, and must be determined according to the scope of the claims.

Claims (7)

1. A space rotation axis solving method based on a calibration plate is characterized by comprising the following steps:
(1) fixing the calibration plate on a target object by using a jig;
(2) the camera shoots the image of the calibration plate to calculate the position matrix H of the calibration plate relative to the camera1；
(3) Rotating the target object;
(4) the camera shoots the image of the calibration plate to calculate the position matrix H of the calibration plate relative to the camera2；
(5) Calculating a rotation matrix;
(6) the rotation axis V and the rotation angle Theta are calculated from the rotation matrix.
2. The calibration-board-based spatial rotation axis solving method according to claim 1, wherein the calibration board is a lattice-shaped calibration board or a chess board lattice calibration board.
3. The calibration plate-based spatial rotation axis solving method according to claim 1 or 1, wherein in the step (3), the target object and the calibration plate perform axial angular rotation motion synchronously.
4. The calibration plate-based spatial rotation axis solving method according to claim 1, wherein the position matrix H1Is calculated in such a way that the coordinates of each point on the calibration plate in its reference coordinate system are W ═ x, y, z]TThe imaged image coordinate of the point is m ═ u, v]TConverting W, m into homogeneous coordinate form W' ═ x, y, z, l]T,m′＝[u,v,l]TThen the relationship between W 'and m' is:
sm′＝A[R t]WT；
in the formula, s is a scaling factor, R is a rotation matrix of the world coordinate system relative to the camera coordinate system, t is a translation vector of the world coordinate system relative to the camera coordinate system, a is a camera internal parameter matrix, and a is expressed as:
formula I,
Figure FDA0003410021500000011
Wherein (u)0,v0) As principal point coordinates of the image plane, ax，ayIs a scale factor of the image coordinate axis, axTransverse dimension of pixel, a ÷ lens focal length ÷ pixelxThe focal length of a lens divided by the vertical size of a pixel, r is the non-perpendicularity of u and v, the z of a three-dimensional coordinate of a point on a target is 0, the x coordinate axis direction of a reference coordinate system of the three-dimensional coordinate is horizontal to the right, the y coordinate axis direction is vertical to the downward, the z coordinate axis direction is vertical to the paper surface, and the r is usedi(i ═ l,2,3) represents each column of the matrix R, with equation one rewritten as:
the second formula,
Figure FDA0003410021500000021
Setting H ═ kA [ r ]1 r2 t]The H matrix is a 3-row and 3-column square matrix, wherein r1,r2Two columns are directional vectors of image coordinate axes x and y, k is a proportionality coefficient, and H is ═ H1 h2 h3]Then it follows:
formula III, [ hx h2 h3]＝kA[r1 r2 t]；
Formula three middle vector r1Perpendicular to r2T and r1,r2If the two are not coplanar, the H matrix is full rank, and the actual imaging coordinate point of the calibration plate is set as piLet the actual coordinate point piAnd calculating a coordinate point m'iIs defined as the following objective function:
Figure FDA0003410021500000022
n is the number of circles on the calibration plate;
to find H, let
Figure FDA0003410021500000023
After obtaining the H matrix, the r matrix is obtained1,r2Orthogonality: r is1 Tr2＝0，r1 Tr2＝r2 Tr2The equation can be found:
the formula IV,
Figure FDA0003410021500000024
Order to
Figure FDA0003410021500000025
After calculating matrix B, knowing that B is a main diagonal symmetric matrix, let:
b＝[B11 B12 B22 B13 B23 B33]T；
setting hi＝[h1i,h2i,h3i]TThe ith column vector of H, then
hi TBhj＝Vijb；
In the formula
Vij＝[h1ih1j,h1ih2j+h2ih1j,h2ih2j,h3ih1j+h1ih3j,h3ih2j+h2ih3j,h3ih3j]
Then the formula four is rewritten in the form of a homogeneous equation as:
the formula five,
Figure FDA0003410021500000026
The number of points on the calibration plate is more than 9, the physical coordinates of the calibration plate and the corresponding image coordinates of each point are substituted into a formula five, b is solved through the formula five, and after an A matrix is obtained, a position matrix H of the camera is obtained through an equation1：
Figure FDA0003410021500000027
r3＝r1×r2
Figure FDA0003410021500000028
H1＝[r1 r2 r3 t]。
5. The calibration plate-based spatial rotation axis solving method according to claim 1, wherein: in the step (4), the position matrix H2Is calculated by the method and the position matrix H1The same is true.
6. The calibration plate-based spatial rotation axis solving method according to claim 1, wherein: in the step (5), the rotation matrix is calculated in the manner of H1,H2For a full rank invertible matrix, then:
Hrot＝H2 -1H1；
from HrotDecomposing a three-dimensional rotating part R:
Figure FDA0003410021500000031
7. the calibration plate-based spatial rotation axis solving method according to claim 1, wherein: the method for calculating the rotation axis V and the rotation angle Theta is to set four elements q ═ (q ═ q)0，q1，q2，q3)；
Solving the corresponding rotation matrix R according to the definition of the shaft angleqComprises the following steps:
Figure FDA0003410021500000032
with rotation of R and RqThe matrix equality correspondence yields:
Figure FDA0003410021500000033
any one of q0 to q4 is calculated, and the values of the remaining 3 components are obtained in accordance with the above correspondence relationship, and the rotation axis V is [ q ] - [ q ]1 q2 q3]Rotation angle Theta ═ q0。
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