CN115656986A - Scanning type laser radar additive coefficient error calibration method - Google Patents

Scanning type laser radar additive coefficient error calibration method Download PDF

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CN115656986A
CN115656986A CN202211189404.0A CN202211189404A CN115656986A CN 115656986 A CN115656986 A CN 115656986A CN 202211189404 A CN202211189404 A CN 202211189404A CN 115656986 A CN115656986 A CN 115656986A
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laser radar
point cloud
scanning
reflectivity plate
reflectivity
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周昊
毛庆洲
胡庆武
张学敏
吴安磊
胡雪晴
宋宇飞
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Wuhan University WHU
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Wuhan University WHU
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Abstract

The invention provides a scanning laser radar additive coefficient error calibration method, which comprises three types of rotating mirrors including a single-sided reflector, a multi-sided prism and a multi-sided tower mirror, wherein the error calibration is realized by the following steps: step one, laying a standard reflectivity plate and a laser radar: ensuring that the scanning surface of the laser radar is perpendicular to the standard reflectivity plate as much as possible, and ensuring that the theoretical shape of the standard reflectivity plate in the point cloud is a straight line; the reflectivity plate covers a larger scanning angle as much as possible, so as to obtain a result with higher precision, generally speaking, under the condition that the size of the reflectivity plate is fixed, in order to cover the larger scanning angle, the reflectivity plate needs to be as close to the laser radar as possible; the reflectivity of the standard reflectivity plate has no specific requirement, but the reflectivity plate is still scanned by the laser radar and point cloud is obtained after the reflectivity plate is close to the laser radar, so that the method is suitable for additive coefficient error calibration of most scanning laser radar equipment; the calibration method does not need manual accurate measurement and adjustment, and has high calibration efficiency.

Description

Scanning laser radar additive coefficient error calibration method
Technical Field
The invention belongs to the technical field of laser radar and instrument error calibration, and relates to a scanning laser radar plus coefficient error calibration method.
Background
The laser radar is a new technology applied to the fields of surveying and mapping, road detection, track detection, national defense and the like. The working principle of the system is that laser is emitted, information such as the distance and reflectivity of a target is obtained through information such as time, phase and intensity of a transmitting signal and an echo signal reflected by the surface of an irradiated object, and three-dimensional information of a target reflection point can be obtained through the assistance of angle and position information of a laser radar.
The key point of the laser radar for obtaining the accurate three-dimensional coordinate of the target lies in accurate distance measurement and angle measurement, and in a distance measurement system of the laser radar, various distance measurement system errors can exist, including amplitude phase errors caused by different echo amplitudes, temperature errors influenced by temperature, multiplication coefficient errors caused by clock frequency deviation or using light velocity approximate values and the like, light-emitting delay, adding coefficient errors caused by light path delay and the like.
The additive coefficient error is embodied in the fixed deviation between the laser radar ranging value and the target real distance value. In general, the coordinate origin of the scanning lidar is located inside the system structure, so the real distance between the origin and the target is difficult to accurately measure. The measurement of the true distance generally has two types, one is to directly measure the distance between the target and the laser radar, and the other is to use a tool and a target with known distance, which needs to ensure that the laser is accurately aligned with the target. Both methods require complicated manual adjustment steps, and are inefficient and time-consuming.
At present, the laser radar scanning mode mainly comprises mechanical rotation scanning, MEMS galvanometer scanning and solid-state scanning in Flash or optical phased array mode. The invention provides a method for calibrating an additive coefficient error of a scanning laser radar, aiming at the characteristics of the scanning laser radar.
Disclosure of Invention
The invention aims to provide a method for calibrating an additive coefficient error of a scanning laser radar, which aims to solve the problem that in the background technology, a linear or plane constraint relation of a known plane in a scanning point cloud is utilized to carry out constraint solving on a deformation point cloud caused by the additive coefficient error to obtain the additive coefficient error. By using the method, the measurement work of the real distance between the laser radar and the target or the accurate alignment work of the laser beam can be avoided, the manual measurement debugging process is greatly reduced, and the problem of the efficiency of the additive coefficient error calibration is improved.
The purpose of the invention can be realized by the following technical scheme: a scanning laser radar plus coefficient error calibration method comprises three types of rotating mirrors including a single-sided reflector, a polygon prism and a polygon tower mirror, and error calibration is realized by the following steps:
step one, laying a standard reflectivity plate and a laser radar: ensuring that the scanning surface of the laser radar is perpendicular to the standard reflectivity plate as much as possible, and ensuring that the theoretical shape of the standard reflectivity plate in the point cloud is a straight line; the reflectivity plate covers a larger scanning angle as much as possible, so as to obtain a result with higher precision, generally speaking, under the condition that the size of the reflectivity plate is fixed, in order to cover the larger scanning angle, the reflectivity plate needs to be as close to the laser radar as possible; the reflectivity of the standard reflectivity plate has no specific requirement, but the reflectivity plate is still scanned by the laser radar and point cloud is obtained after the reflectivity plate is close to the laser radar;
scanning by using a laser radar and obtaining point clouds of a standard reflectivity plate, wherein point cloud coordinates of the laser radar are finally obtained by using a distance measurement value, an angle value and a scanning model, so that point cloud coordinate calculation modes of different scanning models are different, and linear constraint calculation and coefficient error modes are also different subsequently, and point cloud coordinate calculation formulas of three common scanning types of a single-sided reflector, a polygon prism and a polygon mirror are introduced;
(A) Single-sided mirror and multi-sided tower mirror
The single-sided reflector and the multi-sided tower mirror are characterized in that the rotating shaft is parallel to the laser emitting direction, XOY is the coordinate axis of the laser radar, the Z axis is determined by a right-hand coordinate system, S is the laser emitting point, and P is the distance between the rotating shaft and the laser emitting point 0 Is a plane of a single-sided reflector,
Figure BDA0003868751560000021
is the unit normal vector of the plane, M is the intersection point of the reflecting surface and the X axis,
Figure BDA0003868751560000031
the included angle between the reflecting surface and the Y axis is shown, R is a reflecting point where the laser and the reflecting surface are intersected, A is a coordinate of a target in the point cloud, the rotating shaft of the motor is the X axis, and theta is a rotating angle;
unit normal vector of reflecting surface
Figure BDA0003868751560000032
Can be expressed as:
Figure BDA0003868751560000033
the plane equation of the reflecting surface is:
Figure BDA0003868751560000034
the coordinates of the reflection points are:
Figure BDA0003868751560000035
can be obtained by simultaneous (2) and (3)
Figure BDA0003868751560000036
Then the reflection vector will be
Figure BDA0003868751560000037
In unit vector R = (R) x ,r y ,r z ) T Expressed, its expression is:
Figure BDA0003868751560000038
therefore, there are:
Figure BDA0003868751560000039
the coordinates of the target a in the point cloud are:
Figure BDA00038687515600000310
wherein d is 0 The range values are laser radar range values;
the formula (7) is a point cloud coordinate calculation formula for single-surface mirror scanning, namely a calculation formula of a multi-surface mirror, and is also suitable for a single-surface mirror scanning model for a single surface of the multi-surface mirror;
(B) Polyhedral prism
The scanning of the multi-face prism is characterized in that a rotating shaft is vertical to the laser emitting direction or has a certain included angle, taking the four-face prism as an example, XOY is the coordinate axis of the laser radar, the Z axis is determined by a right-hand coordinate system, S is a laser emitting point, and P is a laser emitting point 0 Is a plane of a single-sided reflector,
Figure BDA0003868751560000041
the normal vector of the plane unit is represented as L, the side length of the four-sided prism is represented as R, a reflection point where the laser and the reflection surface intersect is represented as A, a coordinate of the target in the point cloud is represented as A, a motor rotating shaft is represented as Z axis, and theta is a rotating angle;
unit normal vector of reflecting surface
Figure BDA0003868751560000042
Can be expressed as:
Figure BDA0003868751560000043
the plane equation of the reflecting surface is:
Figure BDA0003868751560000044
the coordinates of the reflection points are:
Figure BDA0003868751560000045
can be obtained by simultaneous (9) and (10)
Figure BDA0003868751560000046
Then the reflection vector will be
Figure BDA0003868751560000047
In unit vector R = (R) x ,r y ,r z ) T Expressed as:
Figure BDA0003868751560000048
therefore, there are:
Figure BDA0003868751560000049
the coordinates of the target a in the point cloud are:
Figure BDA0003868751560000051
wherein d is 0 The range values are laser radar range values;
step three, finding the point cloud of the standard reflectivity plate in the point cloud, and solving the additive coefficient error by using the linear constraint relation of the part of point cloud, wherein the principle is as follows:
for a reflectivity plate plane, the point cloud scanned by the laser radar is theoretically a straight line, and the additive coefficient error R exists a In the case of (2), the reflectance plate is made to be a plateEach measuring point of the point cloud generates fixed distance measurement deviation, so that the point cloud of the reflectivity plate is not a straight line any more and generates certain deviation;
at this moment, the angle of the reflectivity plate occupying the scanning field of view of the laser radar is as follows:
Figure BDA0003868751560000052
wherein L is the length of the reflectivity plate on the scanning surface; d is the distance from the laser radar to the center of the reflectivity plate;
the straightness δ of the reflectivity plate in the point cloud is:
Figure BDA0003868751560000053
from the equation (16), the straightness of the reflectance plate in the point cloud is only equal to the scanning angle α and the additive error R a It is related. Under the condition that the size of the reflectivity plate is fixed, the closer the reflectivity plate is to the laser radar, the larger the occupied scanning angle alpha is, the larger alpha is, and the coefficient error R is added a The greater the influence on the linearity δ, the more the additive error R solved by the linearity constraint a The higher the precision is;
the standard reflectivity plate scanned by the laser radar is theoretically a straight line in the point cloud, and the linear equation of the standard reflectivity plate in the point cloud is set as follows:
Ax+By+1=0 (17)
it should be noted that x and y in the formula (17) are different for different scanning modes, and for the single-sided mirror and the polygon mirror, since the scanning plane is a ZOY plane, there is an additive error R a Thus, x, y in formula (17) are represented as:
Figure BDA0003868751560000061
for a faceted prism, the scan plane is the XOY plane and there is an additive error R a Thus, formula(17) X and y in (1) are expressed as:
Figure BDA0003868751560000062
the parameter to be solved is X = (A, B, R) a ) T Solving parameters by using a Gauss-Newton method;
the equation of the distance from each point in the point cloud of the reflectivity plate to the straight line is
Figure BDA0003868751560000063
The optimization goal is that the sum of the squares of the distances from all points of the reflectivity plate point cloud to the straight line is the minimum, namely:
Figure BDA0003868751560000064
the equation (20) is linearized, and the high-order terms are removed by taylor expansion:
Figure BDA0003868751560000065
in the formula (II), D' i To substitute an approximation of the parameter to be calculated for the value calculated by equation (20), the matrix form is written as:
V=JX+L (23)
V=[D 1 D 2 ...D n ] T (24)
Figure BDA0003868751560000071
x=[ΔA ΔB ΔR a ] T (26)
L=[D′ 1 D′ 2 ...D′ n ] T (27)
the method can be obtained by the principle of least square method:
x=(J T J) -1 J T L (28)
Figure BDA0003868751560000072
in the formula, A k 、B k
Figure BDA0003868751560000073
The parameter to be solved representing the kth iteration is continuously iterated until delta R a Less than a certain value such as Δ R a <10 -5 The iteration can be stopped and the additive error R can be obtained a
Step four, adding coefficient error R obtained in step three a And compensating the laser radar ranging value, and recalculating the coordinates of each point of the point cloud, namely completing the addition coefficient error calibration.
Compared with the prior art, the scanning laser radar coefficient error calibration method has the advantages that: the method is suitable for the additive coefficient error calibration of most scanning laser radar equipment; the manual accurate measurement and adjustment are not needed, and the calibration efficiency is high; the calibration needs few tools and is low in implementation cost.
Drawings
FIG. 1 is a schematic view of the scanning of a single-mirror according to the present invention.
FIG. 2 is a schematic view of a faceted prism scan according to the present invention.
FIG. 3 is a schematic view of a lidar scanning reflectivity plate of the present invention.
FIG. 4 is a schematic diagram showing comparison of point clouds before and after coefficient addition calibration according to the present invention.
Detailed Description
The following are specific embodiments of the present invention and are further described with reference to the accompanying drawings, but the present invention is not limited to these embodiments.
A scanning laser radar plus coefficient error calibration method comprises three types of rotating mirrors including a single-sided reflector, a polygon prism and a polygon tower mirror, and error calibration is realized by the following steps:
step one, laying a standard reflectivity plate and a laser radar: ensuring that the scanning surface of the laser radar is perpendicular to the standard reflectivity plate as much as possible, and ensuring that the theoretical shape of the standard reflectivity plate in the point cloud is a straight line; the reflectivity plate covers a larger scanning angle as much as possible, so as to obtain a result with higher precision, generally speaking, under the condition that the size of the reflectivity plate is fixed, in order to cover the larger scanning angle, the reflectivity plate needs to be as close to the laser radar as possible; the reflectivity of the standard reflectivity plate has no specific requirement, but the reflectivity plate is still scanned by the laser radar and point cloud is obtained after the reflectivity plate is close to the laser radar;
scanning by using a laser radar and obtaining point clouds of a standard reflectivity plate, wherein point cloud coordinates of the laser radar are finally obtained by using a distance measurement value, an angle value and a scanning model, so that point cloud coordinate calculation modes of different scanning models are different, and linear constraint calculation and coefficient error modes are also different subsequently, and point cloud coordinate calculation formulas of three common scanning types of a single-sided reflector, a polygon prism and a polygon mirror are introduced;
(A) Single-sided reflector and multi-sided tower mirror
The single-sided reflector and the multi-sided tower mirror are characterized in that the rotating shaft is parallel to the laser emitting direction, XOY is the coordinate axis of the laser radar, Z axis is determined by a right-hand coordinate system, S is the laser emitting point, and P is the laser emitting point 0 Is a plane of a single-sided reflector,
Figure BDA0003868751560000081
is the unit normal vector of the plane, M is the intersection point of the reflecting surface and the X axis,
Figure BDA0003868751560000082
the included angle between the reflecting surface and the Y axis is shown, R is a reflecting point where the laser and the reflecting surface are intersected, A is a coordinate of a target in the point cloud, the rotating shaft of the motor is the X axis, and theta is a rotating angle;
unit normal vector of reflecting surface
Figure BDA0003868751560000091
Can be expressed as:
Figure BDA0003868751560000092
the plane equation of the reflecting surface is:
Figure BDA0003868751560000093
the coordinates of the reflection points are:
Figure BDA0003868751560000094
can be obtained by simultaneous (2) and (3)
Figure BDA0003868751560000095
Then the reflection vector will be
Figure BDA0003868751560000096
In unit vector R = (R) x ,r y ,r z ) T Expressed as:
Figure BDA0003868751560000097
therefore, there are:
Figure BDA0003868751560000098
the coordinates of the target a in the point cloud are:
Figure BDA0003868751560000099
wherein d is 0 The range values are laser radar range values;
the formula (7) is a point cloud coordinate calculation formula for single-surface mirror scanning, namely a calculation formula of a multi-surface mirror, and is also suitable for a single-surface mirror scanning model for a single surface of the multi-surface mirror;
(B) Multi-face prism
The scanning of the multi-face prism is characterized in that a rotating shaft is vertical to the laser emitting direction or has a certain included angle, taking the four-face prism as an example, XOY is the coordinate axis of the laser radar, the Z axis is determined by a right-hand coordinate system, S is a laser emitting point, and P is a laser emitting point 0 Is a plane of a single-sided reflector,
Figure BDA0003868751560000101
the normal vector of the plane unit is represented by L, the side length of the four-sided prism is represented by R, the reflection point of the intersection of the laser and the reflection surface is represented by A, the coordinate of the target in the point cloud is represented by A, the rotating shaft of the motor is represented by Z axis, and theta is a rotation angle;
unit normal vector of reflecting surface
Figure BDA0003868751560000102
Can be expressed as:
Figure BDA0003868751560000103
the plane equation of the reflecting surface is:
Figure BDA0003868751560000104
the coordinates of the reflection points are:
Figure BDA0003868751560000105
can be obtained by simultaneous (9) and (10)
Figure BDA0003868751560000106
Then the reflection vector will be
Figure BDA0003868751560000107
In unit vector R = (R) x ,r y ,r z ) T Expressed, its expression is:
Figure BDA0003868751560000108
therefore, there are:
Figure BDA0003868751560000109
the coordinates of the target a in the point cloud are:
Figure BDA00038687515600001010
wherein d is 0 The range values are laser radar range values;
step three, finding the point cloud of the standard reflectivity plate in the point cloud, and solving the additive coefficient error by using the linear constraint relation of the part of point cloud, wherein the principle is as follows:
for a reflectivity plate plane, the point cloud scanned by the laser radar is theoretically a straight line, and the additive coefficient error R exists a Under the condition (2), each measuring point of the reflectivity plate point cloud generates fixed distance measurement deviation, so that the reflectivity plate point cloud is not a straight line any more and generates certain deviation;
at this moment, the angle of the reflectivity plate occupying the scanning field of view of the laser radar is as follows:
Figure BDA0003868751560000111
wherein L is the length of the reflectivity plate on the scanning surface; d is the distance from the laser radar to the center of the reflectivity plate;
the straightness δ of the reflectivity plate in the point cloud is:
Figure BDA0003868751560000112
from the equation (16), the straightness of the reflectance plate in the point cloud is only equal to the scanning angle α and the additive error R a It is related. Under the condition that the size of the reflectivity plate is fixed, the closer the reflectivity plate is to the laser radar, the larger the occupied scanning angle alpha is, the larger alpha is, and the coefficient error R is added a The greater the influence on the linearity δ, so the additive coefficient error R solved by the straight-line constraint a The higher the precision is;
the standard reflectivity plate scanned by the laser radar is theoretically a straight line in the point cloud, and the equation of the straight line of the standard reflectivity plate in the point cloud is set as follows:
Ax+By+1=0 (17)
it should be noted that x and y in the formula (17) are different for different scanning modes, and for the single-sided mirror and the polygon mirror, since the scanning plane is a ZOY plane, there is an additive error R a Therefore, x and y in formula (17) are represented as:
Figure BDA0003868751560000121
for a faceted prism, the scan plane is the XOY plane and there is an additive error R a Therefore, x and y in formula (17) are represented as:
Figure BDA0003868751560000122
the parameter to be solved is X = (A, B, R) a ) T Solving parameters by using a Gauss-Newton method;
the equation of the distance from each point in the point cloud of the reflectivity plate to the straight line is
Figure BDA0003868751560000123
The optimization goal is that the sum of the squared distances of all points of the reflectivity plate point cloud to the straight line is minimal, i.e.:
Figure BDA0003868751560000124
the linearization of equation (20) with taylor expansion and the truncation of higher order terms is:
Figure BDA0003868751560000125
in the formula (II), D' i To substitute an approximation of the parameter to be calculated for the value calculated by equation (20), the matrix form is written as:
V=JX+L (23)
V=[D 1 D 2 ...D n ] T (24)
Figure BDA0003868751560000131
x=[ΔA ΔB ΔR a ] T (26)
L=[D′ 1 D′ 2 ...D′ n ] T (27)
the method can be obtained by the principle of least square method:
X=(J T J) -1 J T L (28)
Figure BDA0003868751560000132
in the formula, A k 、B k
Figure BDA0003868751560000133
The parameter to be solved representing the kth iteration is continuously iterated until delta R a Less than a certain value, e.g. Δ R a <10 -5 The iteration can be stopped and the additive error R can be obtained a
Step four,By adding the coefficient error R obtained in step three a And compensating the laser radar ranging value, and recalculating the coordinates of each point of the point cloud, namely completing the error calibration by adding the coefficient.
Those not described in detail in this specification are within the skill of the art. The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments, or alternatives may be employed, by those skilled in the art, without departing from the spirit or ambit of the invention as defined in the appended claims.

Claims (1)

1. A scanning laser radar additive coefficient error calibration method is characterized by comprising three types of rotating mirrors including a single-sided reflector, a multi-sided prism and a multi-sided tower mirror, wherein error calibration is realized by the following steps:
step one, laying a standard reflectivity plate and a laser radar: ensuring that the scanning surface of the laser radar is perpendicular to the standard reflectivity plate as much as possible, and ensuring that the theoretical shape of the standard reflectivity plate in the point cloud is a straight line; the reflectivity plate covers a larger scanning angle as much as possible so as to obtain a result with higher precision, generally speaking, under the condition that the size of the reflectivity plate is fixed, in order to cover the larger scanning angle, the reflectivity plate needs to be as close to the laser radar as possible; the reflectivity of the standard reflectivity plate has no specific requirement, but the reflectivity plate is still scanned by the laser radar and point cloud is obtained after the reflectivity plate is close to the laser radar;
scanning by using a laser radar and obtaining point clouds of a standard reflectivity plate, wherein point cloud coordinates of the laser radar are finally obtained by using a distance measurement value, an angle value and a scanning model, so that point cloud coordinate calculation modes of different scanning models are different, and linear constraint calculation and coefficient error modes are also different subsequently, and point cloud coordinate calculation formulas of three common scanning types of a single-sided reflector, a polygon prism and a polygon mirror are introduced;
(A) Single-sided mirror and multi-sided tower mirror
Single sided reflectionThe mirror and the polygon mirror are characterized in that the rotation axis is parallel to the laser emitting direction, XOY is the laser radar coordinate axis, the Z axis is determined by the right-hand coordinate system, s is the laser emitting point, P is the distance between the laser emitting point and the X axis 0 Is a plane of a single-sided reflector,
Figure FDA0003868751550000011
is the unit normal vector of the plane, M is the intersection point of the reflecting surface and the X axis,
Figure FDA0003868751550000012
the included angle between the reflecting surface and the Y axis is shown, R is a reflecting point where the laser and the reflecting surface are intersected, A is a coordinate of a target in the point cloud, the rotating shaft of the motor is the X axis, and theta is a rotating angle;
unit normal vector of reflecting surface
Figure FDA0003868751550000013
Can be expressed as:
Figure FDA0003868751550000021
the plane equation of the reflecting surface is:
Figure FDA0003868751550000022
the coordinates of the reflection points are:
Figure FDA0003868751550000023
can be obtained by simultaneous (2) and (3)
Figure FDA0003868751550000024
Then the reflection vector will be
Figure FDA0003868751550000025
In unit vector R = (R) x ,r y ,r z ) T Expressed, its expression is:
Figure FDA0003868751550000026
therefore, the following are provided:
Figure FDA0003868751550000027
the coordinates of the target a in the point cloud are:
Figure FDA0003868751550000028
wherein d is 0 The range values are laser radar range values;
the formula (7) is a point cloud coordinate calculation formula for single-surface mirror scanning, namely a calculation formula of a multi-surface mirror, and is also suitable for a single-surface mirror scanning model for a single surface of the multi-surface mirror;
(B) Polyhedral prism
The scanning of the multi-surface prism is characterized in that the rotating shaft is vertical to the laser emitting direction or has a certain included angle, taking the four-surface prism as an example, XOY is the coordinate axis of the laser radar, the Z axis is determined by a right-hand coordinate system, S is the laser emitting point, and P is the laser emitting point 0 Is a plane of a single-sided reflector,
Figure FDA0003868751550000029
the normal vector of the plane unit is represented as L, the side length of the four-sided prism is represented as R, a reflection point where the laser and the reflection surface intersect is represented as A, a coordinate of the target in the point cloud is represented as A, a motor rotating shaft is represented as Z axis, and theta is a rotating angle;
unit normal vector of reflecting surface
Figure FDA0003868751550000031
Can be expressed as:
Figure FDA0003868751550000032
the plane equation of the reflecting surface is:
Figure FDA0003868751550000033
the coordinates of the reflection points are:
Figure FDA0003868751550000034
can be obtained by simultaneous (9) and (10)
Figure FDA0003868751550000035
Then the reflection vector will be
Figure FDA0003868751550000036
In unit vector R = (R) x ,r y ,r z ) T Expressed, its expression is:
Figure FDA0003868751550000037
therefore, the following are provided:
Figure FDA0003868751550000038
the coordinates of the target a in the point cloud are:
Figure FDA0003868751550000039
wherein d is 0 The range values are laser radar range values;
step three, finding the point cloud of the standard reflectivity plate in the point cloud, and solving the additive coefficient error by utilizing the linear constraint relation of the part of the point cloud, wherein the principle is as follows:
for a reflectivity plate plane, the point cloud scanned by the laser radar is theoretically a straight line, and the additive coefficient error R exists a Under the condition (2), each measuring point of the reflectivity plate point cloud generates fixed distance measurement deviation, so that the reflectivity plate point cloud is not a straight line any more and generates certain deviation;
at this moment, the angle of the reflectivity plate occupying the scanning field of view of the laser radar is as follows:
Figure FDA0003868751550000041
wherein L is the length of the reflectivity plate on the scanning surface; d is the distance from the laser radar to the center of the reflectivity plate;
the straightness δ of the reflectivity plate in the point cloud is:
Figure FDA0003868751550000042
from the equation (16), the straightness of the reflectance plate in the point cloud is only equal to the scanning angle α and the additive error R a It is related. Under the condition that the size of the reflectivity plate is fixed, the closer the reflectivity plate is to the laser radar, the larger the occupied scanning angle alpha is, the larger alpha is, and the coefficient error R is added a The greater the influence on the linearity δ, the more the additive error R solved by the linearity constraint a The higher the precision is;
the standard reflectivity plate scanned by the laser radar is theoretically a straight line in the point cloud, and the linear equation of the standard reflectivity plate in the point cloud is set as follows:
Ax+By+1=0 (17)
in which it is to be noted that,the x and y in the formula (17) are different for different scanning modes, and for a single-sided mirror and a multi-sided tower mirror, the scanning plane is a ZOY plane, and an additive coefficient error R exists a Therefore, x and y in formula (17) are represented as:
Figure FDA0003868751550000051
for a faceted prism, the scan plane is the XOY plane and there is an additive error R a Thus, x, y in formula (17) are represented as:
Figure FDA0003868751550000052
the parameter to be solved is X = (A, B, R) a ) T Solving parameters by using a Gauss-Newton method;
the equation of the distance from each point in the point cloud of the reflectivity plate to the straight line is
Figure FDA0003868751550000053
The optimization goal is that the sum of the squares of the distances from all points of the reflectivity plate point cloud to the straight line is the minimum, namely:
Figure FDA0003868751550000054
the linearization of equation (20) with taylor expansion and the truncation of higher order terms is:
Figure FDA0003868751550000055
in formula (II) to' i To substitute an approximation of the parameter to be calculated for the value calculated by equation (20), the matrix form is written as:
V=JX+L (23)
V=[D 1 D 2 … D n ] T (24)
Figure FDA0003868751550000056
X=[ΔA ΔB ΔR a ] T (26)
L=[D′ 1 D′ 2 … D′ n ] T (27)
the method can be obtained by the principle of least square method:
X=(J T J) -1 J T L (28)
Figure FDA0003868751550000061
in the formula, A k 、B k
Figure FDA0003868751550000062
The parameter to be solved representing the kth iteration is continuously iterated until delta R a Less than a certain value such as Δ R a <10 -5 The iteration can be stopped and the additive error R can be obtained a
Step four, adding the coefficient error R obtained in the step three a And compensating the laser radar ranging value, and recalculating the coordinates of each point of the point cloud, namely completing the error calibration by adding the coefficient.
CN202211189404.0A 2022-09-28 2022-09-28 Scanning type laser radar additive coefficient error calibration method Pending CN115656986A (en)

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115953905A (en) * 2023-03-15 2023-04-11 河北博士林科技开发有限公司 Laser radar-based vehicle and road cooperative control system
CN116540219A (en) * 2023-07-04 2023-08-04 北醒(北京)光子科技有限公司 Method and device for correcting radar emergent light angle, storage medium and electronic equipment
CN117419681A (en) * 2023-12-18 2024-01-19 华云敏视达雷达(北京)有限公司 Positioning processing method, system, storage medium and electronic equipment

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115953905A (en) * 2023-03-15 2023-04-11 河北博士林科技开发有限公司 Laser radar-based vehicle and road cooperative control system
CN115953905B (en) * 2023-03-15 2023-05-16 河北博士林科技开发有限公司 Vehicle-road cooperative control system based on laser radar
CN116540219A (en) * 2023-07-04 2023-08-04 北醒(北京)光子科技有限公司 Method and device for correcting radar emergent light angle, storage medium and electronic equipment
CN116540219B (en) * 2023-07-04 2023-09-22 北醒(北京)光子科技有限公司 Method and device for correcting radar emergent light angle, storage medium and electronic equipment
CN117419681A (en) * 2023-12-18 2024-01-19 华云敏视达雷达(北京)有限公司 Positioning processing method, system, storage medium and electronic equipment
CN117419681B (en) * 2023-12-18 2024-03-08 华云敏视达雷达(北京)有限公司 Positioning processing method, system, storage medium and electronic equipment

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