Method for calibrating spatial pose and position of chromatic confocal probe with combined planar and spherical constraints
View Patent ↗A method for calibrating a spatial pose and position of a chromatic confocal probe with combined planar and spherical constraints is provided. The method includes: transforming point information in a contact probe coordinate system into coordinate information in a machine coordinate system, and transforming point information in a chromatic confocal probe coordinate system into the coordinate information in the machine coordinate system; acquiring information of at least two points in each of three planes by using a chromatic confocal probe, and establishing a system of linear equations to solving the system of linear equations to obtain a spatial pose of the chromatic confocal probe; measuring and calculating coordinate information of at least three points on a spherical surface by using the chromatic confocal probe, and establishing an overdetermined system of equations to solve a zero reference position of the chromatic confocal probe.
1 . A method for calibrating a spatial pose of a chromatic confocal probe and position of the chromatic confocal probe with combined planar and spherical constraints, wherein calibration is carried out by a coordinate measuring machine, a contact probe and the chromatic confocal probe are provided on the coordinate measuring machine, the contact probe is a standard part provided on the coordinate measuring machine, and the contact probe and the chromatic confocal probe are synchronously displaced in a three-dimensional direction; and the method for calibrating the spatial pose of the chromatic confocal probe and the position of the chromatic confocal probe with the combined planar and spherical constraints comprises:
step S 1 , establishing a machine coordinate system, a contact probe coordinate system, a chromatic confocal probe coordinate system, and a workpiece coordinate system;
step S 2 , transforming first position information obtained in the contact probe coordinate system by the contact probe upon a measurement by the chromatic confocal probe, into coordinate information in the machine coordinate system; and in consideration of a mounting inclination angle of the chromatic confocal probe, transforming second position information of a point on a workpiece measured in the chromatic confocal probe coordinate system by the chromatic confocal probe into coordinate information in the machine coordinate system;
step S 3 , acquiring coordinate information of two points in one plane of three calibration planes by moving the chromatic confocal probe to measure second position information of the two points respectively, and establishing a linear equation based on the coordinate information of two points in the one plane of the three calibration planes; acquiring coordinate information of two points in each of other two calibration planes, to establish other two linear equation, thereby forming a system of linear equations, wherein the system of linear equations comprises the spatial pose of the chromatic confocal probe; and solving the system of linear equations to obtain the spatial pose of the chromatic confocal probe;
step S 4 , acquiring coordinate information of at least three points on a spherical surface by moving the chromatic confocal probe to measure second position information of the at least three points respectively; substituting the coordinate information of the at least three points into a sphere equation, establishing an overdetermined system of equations, wherein the overdetermined system of equations comprises the spatial pose of the chromatic confocal probe and zero reference position of the chromatic confocal probe, and substituting the spatial pose of the chromatic confocal probe in the step S 3 into the overdetermined system of equations for solution to obtain the zero reference position of the chromatic confocal probe;
placing a target workpiece on a workbench of the coordinate measuring machine, measuring second position information of a point on the target workpiece by using the chromatic confocal probe, and determining coordinate information of the point on the target workpiece in the machine coordinate system based on the spatial pose of the chromatic confocal probe obtained in the step S 3 , the zero reference position of the chromatic confocal probe obtained in the step S 4 , a first position information by the contact probe upon a measurement of the point on the target workpiece by the chromatic confocal probe and the second position information by the chromatic confocal probe.
2 . The method for calibrating the spatial pose of the chromatic confocal probe and the position of the chromatic confocal probe with the combined planar and spherical constraints according to claim 1 , wherein in the step S 2 , the contact probe and the chromatic confocal probe are synchronously displaced, and coordinate information when the contact probe performs measurement is set as a reference value; and
the first position coordinate information on the workpiece measured by the contact probe is substituted into the point on the workpiece measured by the chromatic confocal probe to obtain coordinate information of the point on the workpiece measured by the chromatic confocal probe in the machine coordinate system.
3 . The method for calibrating the spatial pose of the chromatic confocal probe and the position of the chromatic confocal probe with the combined planar and spherical constraints according to claim 2 , wherein the coordinate information of the point on the workpiece measured by the chromatic confocal probe in the machine coordinate system in the step S 2 is acquired as follows:
causing directions of three axes of X, Y, and Z in the machine coordinate system, the contact probe coordinate system, and the chromatic confocal probe coordinate system to be parallel to and consistent with each other, respectively;
establishing homogeneous transformation matrices from the machine coordinate system to an X-axis coordinate system, from the X-axis coordinate system to a Y-axis coordinate system, and from the Y-axis coordinate system to a Z-axis coordinate system, respectively;
setting a direction vector of the contact probe with respect to an origin of the machine coordinate system as {right arrow over (O C O T )}=(δx, δy, δz) to obtain a homogeneous transformation matrix from the Z-axis coordinate system to the chromatic confocal probe coordinate system;
setting the second position information of the chromatic confocal probe as d to obtain a homogeneous transformation matrix from the chromatic confocal probe coordinate system to the workpiece coordinate system;
obtaining a homogeneous transformation matrix from the machine coordinate system to the workpiece coordinate system according to the homogeneous transformation matrix from the machine coordinate system to the X-axis coordinate system, the homogeneous transformation matrix from the X-axis coordinate system to the Y-axis coordinate system, the homogeneous transformation matrix from the Y-axis coordinate system to the Z-axis coordinate system, the homogeneous transformation matrix from the Z-axis coordinate system to the chromatic confocal probe coordinate system, and the homogeneous transformation matrix from the chromatic confocal probe coordinate system to the workpiece coordinate system;
obtaining a theoretical coordinate of the point on the workpiece in the machine coordinate system according to a homogeneous transformation principle; and
setting included angles between an optical axis of the chromatic confocal probe and three coordinate axes to obtain coordinates of the point on the workpiece measured by the chromatic confocal probe in the machine coordinate system.
4 . The method for calibrating the spatial pose of the chromatic confocal probe and the position of the chromatic confocal probe with the combined planar and spherical constraints according to claim 3 , wherein forming the system of linear equations in the step S 3 comprises:
step S 301 , setting a calibration plane on the coordinate measuring machine, wherein the calibration plane is not parallel to each of X-axis, Y-axis, and Z-axis in the machine coordinate system, and establishing a plane equation, wherein the plane equation is established with four points in the calibration plane;
step S 302 , obtaining coordinate information of a first point on the calibration plane by using the chromatic confocal probe, moving the chromatic confocal probe to obtain coordinate information of a second point in the calibration plane, substituting the coordinate information of the first point and the coordinate information of the second point into the plane equation and subtracting the information of the first point and the information of the second point to obtain an equation with the zero reference position eliminated;
step S 303 , selecting other two calibration planes, and repeating the step S 302 to obtain other two equations, wherein in each of the other two equations, information of two points is subtracted; and
step S 304 , combining the equation in the step S 302 and the other two equations in the step S 303 to establish the system of linear equations, and solving the system of linear equations to obtain the spatial pose of the chromatic confocal probe.
5 . The method for calibrating the spatial pose of the chromatic confocal probe and the position of the chromatic confocal probe with the combined planar and spherical constraints according to claim 4 , wherein the theoretical coordinate of the point on the workpiece in the machine coordinate system is calculated as follows:
expressing the homogeneous transformation matrix from the machine coordinate system to the X-axis coordinate system, the homogeneous transformation matrix from the X-axis coordinate system to the Y-axis coordinate system, and the homogeneous transformation matrix from the Y-axis coordinate system to the Z-axis coordinate system are respectively as follows:
X
B
T
i
=
[
1
0
0
x
m
0
1
0
0
0
0
1
0
0
0
0
1
]
,
(
1
)
Y
X
T
i
=
[
1
0
0
0
0
1
0
y
m
0
0
1
0
0
0
0
1
]
,
Z
Y
T
i
=
[
1
0
0
0
0
1
0
0
0
0
1
z
m
0
0
0
1
]
;
where X m , Y m and z m are first position information of the contact probe;
setting the direction vector of the contact probe with respect to the origin of the machine coordinate system as {right arrow over (O C O T )}=(δx, δy, δz) to obtain the homogeneous transformation matrix from the Z-axis coordinate system to the chromatic confocal probe coordinate system as follows:
S
Z
T
i
=
[
1
0
0
δ
x
0
1
0
δ
y
0
0
1
δ
z
0
0
0
1
]
;
(
2
)
setting the second position information of the chromatic confocal probe as d to obtain the homogeneous transformation matrix from the chromatic confocal probe coordinate system to the workpiece coordinate system as follows:
B
S
T
i
=
[
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
]
;
(
3
)
obtaining the homogeneous transformation matrix from the machine coordinate system to the workpiece coordinate system as follows:
W
B
T
i
=
X
B
T
i
·
Y
X
T
i
·
Z
Y
T
i
·
S
Z
T
i
·
W
S
T
i
=
[
1
0
0
x
m
+
δ
x
0
1
0
y
m
+
δ
y
+
d
0
0
1
z
m
+
δ
z
0
0
0
1
]
;
(
4
)
and
obtaining the coordinates of the point on the workpiece in the machine coordinate system by using a homogeneous coordinate transformation principle, as follows:
P B =( x m +δx,y m +δy+d,z m +δz ) (5).
6 . The method for calibrating the spatial pose of the chromatic confocal probe and the position of the chromatic confocal probe with the combined planar and spherical constraints according to claim 5 , wherein the coordinates of the point on the workpiece measured by the chromatic confocal probe in the machine coordinate system is calculated as follows:
setting the included angles between the optical axis of the chromatic confocal probe and the three coordinate axes as α, β, γ, and expressing a unit direction vector of the optical axis in the chromatic confocal probe coordinate system as
l
¯
=
(
cos
α
,
cos
β
,
cos
γ
)
=
(
a
,
b
,
c
)
substituting the unit direction vector into the homogeneous transformation matrix from the machine coordinate system to the workpiece coordinate system:
W
B
T
i
=
X
B
T
i
·
Y
X
T
i
·
Z
Y
T
i
·
X
B
T
i
·
W
S
T
i
=
[
1
0
0
x
m
+
δ
x
+
d
·
a
0
1
0
y
m
+
δ
y
+
d
·
b
0
0
1
z
m
+
δ
z
+
d
·
c
0
0
0
1
]
;
(
6
)
and
obtaining the coordinates of the point on the workpiece measured by the chromatic confocal probe in the machine coordinate system by using the homogeneous coordinate transformation principle:
P B =( X m +δx+d·a,y m +δy+d·b,z m +δz+d·c ) (7).
7 . The method for calibrating the spatial pose of the chromatic confocal probe and the position of the chromatic confocal probe with the combined planar and spherical constraints according to claim 6 , wherein establishing the system of linear equations in the step S 3 is as follows:
expressing the plane equation as follows:
Ax+By+Cz+D= 0; (8)
where A, B, C, and D are parameters of spatial positions in the one calibration plane, respectively;
denoting second position information measured by the chromatic confocal probe as d 1 , first position information measured by the contact probe as x 1 , y 1 , and z 1 , and obtaining first point coordinates of (x 1 +δx+d 1 ·a, y 1 +δy+d 1 ·b, z 1 +δz+d 1 ·c) according to formula (7);
substituting the first point coordinates into the plane equation to obtain formula (9):
A 1 ·( x 1 +δx+d 1 ·a )+ B 1 ·( y 1 +δy+d 1 ·b )+ C 1 ·( z 1 +δz+d 1 ·c )+ D 1 =0; (9)
moving the chromatic confocal probe to measure the second point on the one calibration plane, wherein the second point is not the same as the first point, denoting second position information of the second point measured by the chromatic confocal probe as d 2 , first position information measured by the contact probe as x 2 , y 2 and z 2 to obtain second point coordinates (x 2 +δx+d 2 ·a, y 2 +δy+d 2 ·b, z 2 +δz+d 2 ·c), and substituting the second point coordinates into the plane equation to obtain formula (10):
A 1 ·( x 2 +δx+d 2 ·a )+ B 1 ·( y 2 +δy+d 2 ·b )+ C 1 ·( z 2 +δz+d 2 ·c )+ D 1 =0; (10)
subtracting formula (10) from formula (9) obtain:
[
A
1
·
(
d
1
-
d
2
)
B
1
·
(
d
1
-
d
2
)
C
1
·
(
d
1
-
d
2
)
]
·
[
a
b
c
]
=
[
A
1
·
(
x
1
-
x
2
)
+
B
1
·
(
x
1
-
x
2
)
+
C
1
·
(
x
1
-
x
2
)
]
.
(
11
)
8 . The method for calibrating the spatial pose of the chromatic confocal probe and the position of the chromatic confocal probe with the combined planar and spherical constraints according to claim 7 , wherein in the step S 303 , the other two equations from the coordinate information of two points in each of the other two calibration planes are as follows:
[
A
2
·
(
d
3
-
d
4
)
B
2
·
(
d
3
-
d
4
)
C
2
·
(
d
3
-
d
4
)
]
·
[
a
b
c
]
=
(
12
)
[
A
2
·
(
x
3
-
x
4
)
+
B
2
·
(
x
3
-
x
4
)
+
C
2
·
(
x
3
-
x
4
)
]
;
[
A
3
·
(
d
5
-
d
6
)
B
3
·
(
d
5
-
d
6
)
C
3
·
(
d
5
-
d
6
)
]
·
[
a
b
c
]
=
(
13
)
[
A
3
·
(
x
5
-
x
6
)
+
B
3
·
(
x
3
-
x
4
)
+
C
3
·
(
x
5
-
x
6
)
]
;
and
formula (11), formula (12), and formula (13) are combined to obtain the system of linear equations:
[
A
1
(
d
1
-
d
2
)
B
1
·
(
d
1
-
d
2
)
C
1
·
(
d
1
-
d
2
)
A
2
·
(
d
3
-
d
4
)
B
2
·
(
d
3
-
d
4
)
C
2
·
(
d
3
-
d
4
)
A
3
·
(
d
5
-
d
6
)
B
3
·
(
d
5
-
d
6
)
C
3
·
(
d
5
-
d
6
)
]
·
[
a
b
c
]
=
[
A
1
·
(
x
1
-
x
2
)
+
B
1
·
(
x
1
-
x
2
)
+
C
1
·
(
x
1
-
x
2
)
A
2
·
(
x
3
-
x
4
)
+
B
2
·
(
x
3
-
x
4
)
+
C
2
·
(
x
3
-
x
4
)
A
3
·
(
x
5
-
x
6
)
+
B
3
·
(
x
5
-
x
6
)
+
C
3
·
(
x
5
-
x
6
)
]
.
(
14
)
9 . The method for calibrating the spatial pose of the chromatic confocal probe and the position of the chromatic confocal probe with the combined planar and spherical constraints according to claim 1 , wherein establishing the overdetermined system of equations in the step S 4 is as follows:
setting coordinates of a spherical center, a point O, of the spherical surface in the machine coordinate system as (x 0 , Y 0 , z 0 ), setting the included angles between the optical axis of the chromatic confocal probe and the three coordinate axes of the machine coordinate system as α, β, γ, and setting a unit direction vector of the optical axis as
I
_
=
(
cos
α
,
cos
β
,
cos
γ
)
=
(
a
,
b
,
c
)
;
setting second position information measured by the chromatic confocal probe as d 7 , first position information of the contact probe as x 7 , y 7 and z 7 , and coordinates of a point S on the spherical surface in the machine coordinate system as S C :
( x 7 +δx+d 7 ·a,y 7 +δy+d 7 ·b,z 7 +δz+d 7 ·c );
substituting the coordinates of the point S and coordinates of the point O into the sphere equation, wherein the point S is located on the spherical surface, and
SO
→
=
R
:
f
1
=
(
x
7
+
δ
x
+
d
7
·
a
-
X
0
)
2
+
(
y
7
+
δ
y
+
d
7
·
b
-
Y
0
)
2
+
(
z
7
+
δ
z
+
d
7
·
c
-
Z
0
)
2
-
R
2
=
0
;
(
15
)
measuring a point T on the spherical surface by using the chromatic confocal probe, to obtain coordinates of the point T in the machine coordinate system as T C :
( x 8 +δx+d 8 ·a,y 8 +δy+d 8 ·b,z 8 +δz+d 8 ·c );
substituting the coordinates of the point T and the coordinates of the point O into the sphere equation, wherein the point T is located on the spherical surface and
TO
→
=
R
:
f
2
=
(
x
8
+
δ
x
+
d
8
·
a
-
X
0
)
2
+
(
y
8
+
δ
y
+
d
8
·
b
-
Y
0
)
2
+
(
z
8
+
δ
z
+
d
8
·
c
-
Z
0
)
2
-
R
2
=
0
;
(
16
)
measuring coordinate information of a plurality of points on the spherical surface by using the chromatic confocal probe, assuming second position information of the chromatic confocal probe as d i , and first position information of the contact probe as x i , y i , and z i and obtaining the overdetermined system of equations as follows:
{
(
x
7
+
δ
x
+
d
2
·
a
-
X
0
)
2
+
(
y
7
+
δ
y
+
d
2
·
b
-
Y
0
)
2
+
(
z
7
+
δ
z
+
d
2
·
c
-
Z
0
)
2
-
r
2
=
0
(
x
7
+
δ
x
+
d
2
·
a
-
X
0
)
2
+
(
y
7
+
δ
y
+
d
2
·
b
-
Y
0
)
2
+
(
z
7
+
δ
z
+
d
2
·
c
-
Z
0
)
2
-
r
2
=
0
⋮
⋮
(
x
7
+
δ
x
+
d
2
·
a
-
X
0
)
2
+
(
y
7
+
δ
y
+
d
2
·
b
-
Y
0
)
2
+
(
z
7
+
δ
z
+
d
2
·
c
-
Z
0
)
2
-
r
2
=
0
;
(
17
)
and
wherein a constraint condition of formula (17) is as follows:
{
a
2
+
b
2
+
c
2
=
1
-
1
≤
a
,
b
,
c
≤
1
.
(
18
)
10 . The method for calibrating the spatial pose of the chromatic confocal probe and the position of the chromatic confocal probe with the combined planar and spherical constraints according to claim 9 , wherein formula (17) is solved by a Levenberg-Marquardt (LM) iterative algorithm to obtain the zero reference position of the chromatic confocal probe.