CN107817003B - External parameter calibration method of distributed large-size space positioning system - Google Patents
External parameter calibration method of distributed large-size space positioning system Download PDFInfo
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Abstract
The invention relates to an external parameter calibration method of a distributed large-size space positioning system, which solves the difficult problems of complicated calibration process of a large-size space measurement system, sensitivity of system global optimization to an external parameter initial value, high cost and the like, and provides a method for realizing the initial calibration of the system by using a two-dimensional calibration rod by assuming that a virtual projection plane exists in front of a transmitter, and then realizing the global calibration of the system by using a Levenberg-Marquardt iterative optimization and a method for minimizing a target function. The method has the advantages of simple operation process and high calibration speed, and can effectively reduce the system cost while improving the system measurement precision and the working efficiency.
Description
Technical Field
The invention relates to an external parameter calibration method for a distributed large-size space positioning system. The principle is as follows: firstly, a virtual projection plane is assumed to exist in front of a transmitter, a virtual transmitter perspective projection model is established, initial calibration of each calibration unit is achieved, and then overall calibration of the system is achieved through a method of Levenberg-Marquardt iterative optimization and objective function minimization.
Background
With the increasing requirements of assembly of large-scale product parts such as aviation, aerospace, ships, automobiles and the like and the requirements of large parts on precision positioning of butt joint pairing and real-time pose measurement and control, large-size space digital measurement systems and application technologies thereof are widely concerned by the industry and academia. At present, the mature large-size measurement technology applied at home and abroad mainly comprises a laser tracker measurement system, a large-view-field vision measurement system, a theodolite measurement system and the like.
The distributed large-size space positioning system is mainly composed of a plurality of measuring base stations, can monitor all parts of a large measured object at the same time, is high in real-time performance and large in measuring range, coordinates contradiction between measuring accuracy and large-size space by means of adding the base stations, and is wide in application prospect. Before measurement, the position relationship between the system world coordinate system and each measurement base station needs to be established, that is, the system external parameter calibration is performed, but the existing external calibration method usually uses other auxiliary measurement devices or needs to add additional constraint conditions, so that additional error sources are easily added, the operation process is complicated, the cost is high, and the field application is not facilitated.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide an external parameter calibration method of a distributed large-size space positioning system, which realizes the quick and accurate calibration of the system, thereby realizing the high-precision and omnibearing large-size space measurement.
The technical scheme adopted by the invention for realizing the purpose is as follows:
1) two near-infrared lasers are installed inside a transmitter rotating platform, the transmitter rotating platform rotates anticlockwise at a constant speed around a rotating shaft under the driving of a servo motor, two fan-shaped laser planes with fixed inclination angles and an LED synchronous optical signal are sent to a measuring space in real time, and the LED synchronous optical signal is used as a zero position signal of a laser plane rotating period;
2) reasonably arranging transmitter networks according to the measurement space, setting fixed rotating speed of each transmitter respectively, sequentially increasing 100r/min for each transmitter by taking 2500r/min as a starting point, and numbering the transmitters in an anticlockwise direction;
3) placing a calibration rod, and establishing a coordinate system of each transmitter, wherein the specific method comprises the steps of taking the intersection point of two laser planes on a rotating shaft as the origin of the coordinate system, taking the intersection line of the laser plane 1 and a vertical Y-axis plane when the laser plane sweeps across a receiver on the left side of the calibration rod as the Z axis, taking the direction pointing to the receiver on the left side as the Z axis forward direction, and determining the X axis direction through a right-hand rule;
4) every two transmitters are used as a calibration unit, the calibration units are numbered, a transmitter coordinate system is used as a world coordinate system, calibration rod with fixed length is used for collecting calibration point data, and a calibration point set is established;
5) respectively calibrating the single calibration unit, and calculating the coordinates of the projection points of the calibration points on a virtual projection plane on the assumption that the virtual projection plane exists at a specific position in the forward direction perpendicular to the Z axis of the transmitter, wherein the model is as follows:
wherein P ═ (x y z): the coordinate of a projection point P of the calibration point on the virtual projection plane;
az: the horizontal angle of the calibration point under the transmitter coordinate system;
pa: the pitch angle of the calibration point under the transmitter coordinate system;
d: assuming that a virtual projection plane exists at z ═ d;
6) establishing a virtual transmitter perspective projection model, calculating the coordinates of the projection points of the calibration points on a virtual projection plane, and performing coordinate transformation of a projection point set through translation transformation and scaling transformation, wherein the model comprises the following steps:
p ═ MP and M ═ STS
Wherein, P: according to the projection point coordinates on the virtual projection plane obtained in the step 5;
p': projecting point coordinates on the virtual projection plane after coordinate transformation;
m: a coordinate transformation matrix of the point set;
s: the coordinate scaling transformation matrix of the set of points,
d0the average distance from each point in the point set to the image origin;
TS: the coordinate translation transformation matrix of the set of points,
(Tx Ty)Tis the centroid coordinate of the point set;
7) calculating an essential matrix, and decomposing the essential matrix to obtain possible solutions of a rotation matrix and a unit translation vector, wherein the method comprises the following specific steps:
I. calculating a coefficient matrix according to the projection point coordinates obtained in the step 6 after the coordinate transformation of the point set, taking the calibration unit one as an example, and using the model as follows:
Am＝(a1 a2 … aN)T
wherein Am: coefficient matrix, aiIs the element of the ith in the coefficient matrix Am, and N is the number of the index points;
wherein d in the step 5 is 1;
decomposing the coefficient matrix Am by using singular values to obtain an essential matrix E;
decompose the essence matrix, the model is as follows:
E＝USVT
R1＝UZVTor R2＝UZTVT
t1＝V(0 0 1)TOr t2＝-V(0 0 1)T
Determining possible solutions for the rotation matrix and unit translation vector, the model being as follows:
(R1|t1)
(R1|t2)
(R2|t1)
(R2|t2)
8) and (3) rejecting the pseudo solution in the step 7 by utilizing physical screening and Sampson distance minimum constraint to obtain a unique solution of a rotation matrix and a unit translation vector, wherein the specific steps are as follows:
I. physical screening: ensuring that the index point is in front of both transmitters, i.e. Z1> 0 and Z2＞0；
Sampson distance minimum constraint: ensuring that, in the virtual perspective projection model, the projection point Pi2To a straight line L1Distance of (2) and projection point Pi1To the outer polar line L2The sum of the squared distances of (a) is minimal, the model is as follows:
9) and (3) determining a scale factor according to the unique solution of the rotation matrix and the unit translation vector obtained by screening in the step 8 and taking the length of the calibration rod as a constraint to obtain a translation matrix, wherein the model is as follows:
T＝kt
wherein, k: a scale factor;
l: calibrating the theoretical length of the rod;
l': calculating the length of the calibration rod according to the rotation matrix and the unit translation vector in the step 8;
t: the unit translation vector obtained in the step 8;
t: translating the matrix;
10) and (3) sequentially calculating a rotation matrix and a translation matrix of each calibration unit in the steps 4-9, taking the rotation matrix and the translation matrix as initial values, and minimizing an objective function by using a Levenberg-Marquardt iterative optimization method to obtain a final rotation matrix and a final translation matrix, wherein the model is as follows:
wherein N is the number of the calibration points;
j is the number of times the calibration rod collects data;
l'jis the calculated value of the jth calibration rod length;
l is the theoretical length of the calibration rod.
The method avoids the use of other auxiliary measuring equipment, firstly assumes that a virtual projection plane exists in front of the transmitter, establishes a virtual transmitter perspective projection model, realizes initial calibration of the external parameters by a linear method, then adopts a Levenberg-Marquardt iterative optimization method, minimizes an objective function, realizes global calibration by a nonlinear method, and solves the problems of complicated calibration process, sensitivity of nonlinear optimization to the initial values of the external parameters and the like. The invention ensures that the solving parameters are globally optimal, the solving speed is high, and the optimization result is stable, thereby ensuring the calibration precision of the system parameters.
Drawings
FIG. 1 is a schematic system flow diagram;
FIG. 2 is a schematic diagram of a transmitter architecture;
FIG. 3 is a transmitter numbering diagram;
FIG. 4 is a schematic view of a calibration rod;
FIG. 5 is a schematic diagram of establishing a transmitter coordinate system;
fig. 6 is a schematic view of a virtual transmitter perspective projection model.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings.
An external parameter calibration method of a distributed large-size space positioning system comprises the following steps:
1) as shown in fig. 2, two near-infrared lasers are installed inside a transmitter rotating platform, the transmitter rotating platform rotates counterclockwise around a rotating shaft at a constant speed under the driving of a servo motor, and sends two fan-shaped laser planes with fixed inclination angles and an LED synchronous optical signal to a measurement space in real time, and the LED synchronous optical signal is used as a zero position signal of a laser plane rotating period;
2) as shown in fig. 4, taking four transmitters as an example, a network of transmitters is reasonably arranged according to a measurement space, each transmitter is respectively set with a fixed rotation speed of 2500r/min, 2600r/min, 2700r/min and 2800r/min, and the transmitters are numbered in a counterclockwise direction, which are respectively a first transmitter, a second transmitter, a third transmitter and a fourth transmitter;
3) as shown in fig. 5, a calibration rod is placed in front of a transmitter network, and a coordinate system of each transmitter is established, wherein the specific method is that the intersection point of two laser planes on a rotating shaft is taken as the origin of the coordinate system, the direction of the two laser planes is taken as the forward direction of a Y axis downwards along the rotating shaft of the transmitter, the intersection line of the laser plane 1 which sweeps through a receiver on the left side of the calibration rod and a vertical Y axis plane is taken as a Z axis, the direction pointing to the receiver on the left side is taken as the forward direction of the Z axis, and the direction of the X axis is determined by;
4) numbering the calibration units, taking a transmitter coordinate system as a world coordinate system, taking every two transmitters as a calibration unit, and respectively: the method comprises the following steps that a first transmitter and a second transmitter are calibration units 1, a first transmitter and a third transmitter are calibration units 2, a first transmitter and a fourth transmitter are calibration units 3, calibration rod with fixed lengths are used for collecting calibration point data, and a calibration point set is established;
5) respectively calibrating the single calibration unit, and calculating the coordinates of the projection points of the calibration points on a virtual projection plane on the assumption that the virtual projection plane exists at a specific position in the forward direction perpendicular to the Z axis of the transmitter, wherein the model is as follows:
wherein P ═ (x y z): the coordinate of a projection point P of the calibration point on the virtual projection plane;
az: the horizontal angle of the calibration point under the transmitter coordinate system;
pa: the pitch angle of the calibration point under the transmitter coordinate system;
d: assuming that a virtual projection plane exists at z ═ d;
6) as shown in fig. 6, taking the calibration unit 1 as an example, a virtual transmitter perspective projection model is established, coordinates of a projection point of the calibration point on a virtual projection plane are calculated, and coordinate transformation of a projection point set is performed through translation transformation and scaling transformation, and the model is as follows:
p ═ MP and M ═ STS
Wherein, P: according to the projection point coordinates on the virtual projection plane obtained in the step 5;
p': projecting point coordinates on the virtual projection plane after coordinate transformation;
m: a coordinate transformation matrix of the point set;
s: the coordinate scaling transformation matrix of the set of points,
d0the average distance from each point in the point set to the image origin;
TS: the coordinate translation transformation matrix of the set of points,
(Tx Ty)Tis the centroid coordinate of the point set;
7) calculating an essential matrix, and decomposing the essential matrix to obtain possible solutions of a rotation matrix and a unit translation vector, wherein the method comprises the following specific steps:
I. calculating a coefficient matrix according to the projection point coordinates obtained in the step 6 after the coordinate transformation of the point set, taking the calibration unit one as an example, and using the model as follows:
Am＝(a1 a2 … aN)T
wherein Am: coefficient matrix, aiIs the element of the ith in the coefficient matrix Am, and N is the number of the index points;
wherein d in the step 5 is 1;
decomposing the coefficient matrix Am by using singular values to obtain an essential matrix E;
decompose the essence matrix, the model is as follows:
E＝USVT
R1＝UZVTor R2＝UZTVT
t1＝V(0 0 1)TOr t2＝-V(0 0 1)T
Determining possible solutions for the rotation matrix and unit translation vector, the model being as follows:
(R1|t1)
(R1|t2)
(R2|t1)
(R2|t2)
8) and (3) rejecting the pseudo solution in the step 7 by utilizing physical screening and Sampson distance minimum constraint to obtain a unique solution of a rotation matrix and a unit translation vector, wherein the specific steps are as follows:
I. physical screening: ensuring that the index point is in front of both transmitters, i.e. Z1> 0 and Z2＞0；
Sampson distance minimum constraint: ensuring that, in the virtual perspective projection model, the projection point Pi2To a straight line L1Distance of (2) and projection point Pi1To the outer polar line L2The sum of the squared distances of (a) is minimal, the model is as follows:
9) and (3) determining a scale factor according to the unique solution of the rotation matrix and the unit translation vector obtained by screening in the step 8 and taking the length of the calibration rod as a constraint to obtain a translation matrix, wherein the model is as follows:
T＝kt
wherein, k: a scale factor;
l: calibrating the theoretical length of the rod;
l': calculating the length of the calibration rod according to the rotation matrix and the unit translation vector in the step 8;
t: the unit translation vector obtained in the step 8;
t: translating the matrix;
10) and (3) sequentially calculating a rotation matrix and a translation matrix of each calibration unit in the steps 4-9, taking the rotation matrix and the translation matrix as initial values, and minimizing an objective function by using a Levenberg-Marquardt iterative optimization method to obtain a final rotation matrix and a final translation matrix, wherein the model is as follows:
wherein N is the number of the calibration points;
j is the number of times the calibration rod collects data;
l'jis the calculated value of the jth calibration rod length;
l is the theoretical length of the calibration rod.
Claims (1)
1. An external parameter calibration method of a distributed large-size space positioning system is characterized by comprising the following steps:
1) two near-infrared lasers are installed inside a transmitter rotating platform, the transmitter rotating platform rotates anticlockwise at a constant speed around a rotating shaft under the driving of a servo motor, two fan-shaped laser planes with fixed inclination angles and an LED synchronous optical signal are sent to a measuring space in real time, and the LED synchronous optical signal is used as a zero position signal of a laser plane rotating period;
2) reasonably arranging transmitter networks according to the measurement space, setting fixed rotating speed of each transmitter respectively, sequentially increasing 100r/min for each transmitter by taking 2500r/min as a starting point, and numbering the transmitters in an anticlockwise direction;
3) placing a calibration rod, and establishing a coordinate system of each transmitter, wherein the specific method comprises the steps of taking the intersection point of two laser planes on a rotating shaft as the origin of the coordinate system, taking the intersection line of the laser plane 1 and a vertical Y-axis plane when the laser plane sweeps across a receiver on the left side of the calibration rod as the Z axis, taking the direction pointing to the receiver on the left side as the Z axis forward direction, and determining the X axis direction through a right-hand rule;
4) every two transmitters are used as a calibration unit, the calibration units are numbered, a transmitter coordinate system is used as a world coordinate system, calibration rod with fixed length is used for collecting calibration point data, and a calibration point set is established;
5) respectively calibrating the single calibration unit, and calculating the coordinates of the projection points of the calibration points on a virtual projection plane on the assumption that the virtual projection plane exists at a specific position in the forward direction perpendicular to the Z axis of the transmitter, wherein the model is as follows:
wherein P ═ (x y z): the coordinate of a projection point P of the calibration point on the virtual projection plane;
az: the horizontal angle of the calibration point under the transmitter coordinate system;
pa: the pitch angle of the calibration point under the transmitter coordinate system;
d: assuming that a virtual projection plane exists at z ═ d;
6) establishing a virtual transmitter perspective projection model, calculating the coordinates of the projection points of the calibration points on a virtual projection plane, and performing coordinate transformation of a projection point set through translation transformation and scaling transformation, wherein the model comprises the following steps:
p ═ MP and M ═ STS
Wherein, P: according to the projection point coordinates on the virtual projection plane obtained in the step 5;
p': projecting point coordinates on the virtual projection plane after coordinate transformation;
m: a coordinate transformation matrix of the point set;
s: the coordinate scaling transformation matrix of the set of points,
d0the average distance from each point in the point set to the image origin;
TS: the coordinate translation transformation matrix of the set of points,
(Tx Ty)Tis the centroid coordinate of the point set;
7) calculating an essential matrix, and decomposing the essential matrix to obtain possible solutions of a rotation matrix and a unit translation vector, wherein the method comprises the following specific steps:
I. calculating a coefficient matrix according to the projection point coordinates obtained in the step 6 after the coordinate transformation of the point set, taking the calibration unit one as an example, and using the model as follows:
Am＝(a1 a2 … aN)T
wherein Am: coefficient matrix, aiIs the element of the ith in the coefficient matrix Am, and N is the number of the index points;
wherein d in the step 5 is 1;
decomposing the coefficient matrix Am by using singular values to obtain an essential matrix E;
decompose the essence matrix, the model is as follows:
E＝USVT
R1＝UZVTor R2＝UZTVT
t1＝V(001)TOr t2＝-V(001)T
Determining possible solutions for the rotation matrix and unit translation vector, the model being as follows:
(R1|t1)
(R1|t2)
(R2|t1)
(R2|t2)
8) and (3) rejecting the pseudo solution in the step 7 by utilizing physical screening and Sampson distance minimum constraint to obtain a unique solution of a rotation matrix and a unit translation vector, wherein the specific steps are as follows:
I. physical screening: ensuring that the index point is in front of both transmitters, i.e. Z1> 0 and Z2＞0；
Sampson distance minimum constraint: ensuring that, in the virtual perspective projection model, the projection point Pi2To a straight line L1Distance of (2) and projection point Pi1To the outer polar line L2The sum of the squared distances of (a) is minimal, the model is as follows:
9) and (3) determining a scale factor according to the unique solution of the rotation matrix and the unit translation vector obtained by screening in the step 8 and taking the length of the calibration rod as a constraint to obtain a translation matrix, wherein the model is as follows:
T＝kt
wherein, k: a scale factor;
l: calibrating the theoretical length of the rod;
l': calculating the length of the calibration rod according to the rotation matrix and the unit translation vector in the step 8;
t: the unit translation vector obtained in the step 8;
t: translating the matrix;
10) and (3) sequentially calculating a rotation matrix and a translation matrix of each calibration unit in the steps 4-9, taking the rotation matrix and the translation matrix as initial values, and minimizing an objective function by using a Levenberg-Marquardt iterative optimization method to obtain a final rotation matrix and a final translation matrix, wherein the model is as follows:
wherein N is the number of the calibration points;
j is the number of times the calibration rod collects data;
l'jis the calculated value of the jth calibration rod length;
l is the theoretical length of the calibration rod.
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| CN109884658B (en) * | 2019-03-04 | 2020-11-27 | 北京工业大学 | Laser tracker station position method based on laser tracker multi-station position measuring system |
| CN110006459B (en) * | 2019-04-30 | 2020-11-10 | 西安交通大学 | Self-correcting system and method for R-LATs measurement network in workshop dynamic operation environment |
| CN110654571B (en) * | 2019-11-01 | 2023-10-20 | 西安航通测控技术有限责任公司 | Nondestructive testing robot system and method for surface defects of aircraft skin |
| CN111622114B (en) * | 2020-05-08 | 2021-08-10 | 中铁大桥科学研究院有限公司 | Bridge segment prefabrication construction line shape error adjusting method |
| CN113158846B (en) * | 2021-04-06 | 2024-02-20 | 中航航空电子有限公司 | Anti-interference sight tracking method for head-mounted waveguide display device |
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