CN117930205A - Sensor relative position calibration device and method based on underwater vision positioning - Google Patents
Sensor relative position calibration device and method based on underwater vision positioning Download PDFInfo
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Abstract
The invention discloses a sensor relative position calibration device and method based on underwater vision positioning, wherein the device comprises: the device comprises a camera A, a camera B, an upper computer, a three-dimensional posture adjusting mechanism of a detected sensor and a three-dimensional posture adjusting mechanism of a detection sensor; the camera A and the camera B are both arranged on the bracket, the shooting directions of the camera A and the camera B are vertically arranged and are used for shooting a detected sensor and a detection sensor, the detected sensor is fixed on the three-dimensional posture adjusting mechanism of the detected sensor, and the detection sensor is fixed on the three-dimensional posture adjusting mechanism of the detection sensor; the upper computer is electrically connected with the camera A and the camera B and is used for collecting images of the camera A and the camera B and processing the images; the upper computer is electrically connected with the three-dimensional posture adjusting mechanism of the detected sensor and the three-dimensional posture adjusting mechanism of the detection sensor and is used for respectively adjusting the relative positions of the detected sensor and the detection sensor. The device can realize high-precision calibration of the relative positions of the detected sensor and the detection sensor.
Description
Technical Field
The invention relates to the technical field of transducer sound field testing, in particular to a sensor relative position calibration device and method based on underwater vision positioning.
Background
Currently, the main method for detecting the sound field of an ultrasonic transducer (hereinafter referred to as a detected sensor) is a hydrophone method, that is, a plane perpendicular to the sound axis (generally referred to as a geometric central axis) of the detected sensor is scanned by using a hydrophone (hereinafter referred to as a detection sensor) to obtain the radiation sound field of the detected sensor in water. When in testing, the central axis of the detection sensor is required to be parallel to the central axis of the detected sensor, and the currently adopted method mainly relies on visual observation to adjust the parallel and central alignment of the detection sensor and the central axis of the detected sensor. In an underwater environment, however, the sensor position is typically three-dimensional, including horizontal displacement, vertical displacement, and attitude. Because of refraction in water, it is difficult for naked eyes to accurately judge the position and orientation of the sensor in three-dimensional space, and factors such as subjective judgment, viewing angle limitation, fatigue and the like of an observer may cause inaccuracy of position observation. However, the sound field detection of the sensor to be detected has high requirements on the test precision, and the sound wave in the high-frequency stage, for example, 5MHz, has the wavelength of only 0.3mm. In addition, for some focusing type detected sensors, the focal domain diameter is only a few millimeters, so that the difficulty of aligning the detection sensor and the detected sensor by naked eyes is high, and the actual operation efficiency is quite low.
Therefore, how to provide a sensor relative position calibration device and a sensor relative position calibration method based on underwater vision positioning, which can realize high-precision calibration of the relative positions of a measured sensor and a detection sensor, is a problem that needs to be solved by those skilled in the art.
Disclosure of Invention
In view of the above, the present invention provides a sensor relative position calibration device and method based on underwater vision positioning, which can realize high-precision calibration of the relative positions of a sensor to be measured and a detection sensor.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
Sensor relative position calibrating device based on vision location under water includes: the device comprises a camera A, a camera B, an upper computer, a three-dimensional posture adjusting mechanism of a detected sensor and a three-dimensional posture adjusting mechanism of a detection sensor;
the camera A and the camera B are both arranged on the bracket and are positioned under water, the shooting directions of the camera A and the camera B are vertically arranged and are used for shooting a detected sensor and a detection sensor, the detected sensor is fixed on the three-dimensional posture adjusting mechanism of the detected sensor, and the detection sensor is fixed on the three-dimensional posture adjusting mechanism of the detection sensor;
the upper computer is electrically connected with the camera A and the camera B and is used for collecting images of the camera A and the camera B in real time and analyzing and processing the images in real time;
The upper computer is electrically connected with the three-dimensional posture adjustment mechanism of the detected sensor and the three-dimensional posture adjustment mechanism of the detection sensor and is used for respectively adjusting the relative positions of the detected sensor and the detection sensor.
Compared with the prior art, the invention discloses a sensor relative position calibration device based on underwater vision positioning, which is used for imaging two corrected objects (a detected sensor and a detection sensor) through two underwater cameras which are vertically arranged to obtain the positions and the postures of the corrected objects in respective projection planes, fitting out the central axes of the two corrected objects and the two-dimensional linear equations of the two corrected objects in the corresponding projection planes through an upper computer, determining the relative deflection angle and the relative offset distance between the two corrected objects through comparing the two-dimensional linear equations of the two corrected objects, and adjusting the positions and the postures of the corrected objects through a three-dimensional posture adjustment mechanism of the detected sensor and a three-dimensional posture adjustment mechanism of the detection sensor so as to finally realize the alignment. Therefore, the underwater positioning technology can accurately measure the position and the orientation of the corrected object in the three-dimensional space, including horizontal displacement, vertical displacement and attitude information, and is more reliable than visual observation. This helps to ensure the relative positional accuracy of the object being corrected; the position correction process is automatically completed through the upper computer, the three-dimensional posture adjustment mechanism of the detected sensor and the three-dimensional posture adjustment mechanism of the detection sensor, so that the possibility of human errors is reduced; the underwater positioning technology can provide real-time or almost real-time position information, so that a user can monitor the relative position of a corrected object at any time and adapt to the rapidly-changing underwater environment. And in the process of position and posture adjustment, real-time monitoring can be performed, and the corrected object can reach the optimal position in a negative feedback adjustment mode.
Further, the bracket includes: the camera comprises a support column, a first cantilever mounting plate and a second cantilever mounting plate, wherein a support plate is fixed at the bottom end of the support column, one end of the first cantilever mounting plate is fixedly connected with the top end of the support column, the camera A is fixed at the other end of the first cantilever mounting plate, one end of the second cantilever mounting plate is fixedly connected with the top end of the support column and is vertically arranged with the first cantilever mounting plate, and the camera B is fixed at the other end of the second cantilever mounting plate.
Further, the support column is of a telescopic structure with adjustable height.
The support comprises a lower support and an upper support, wherein the bottom end of the lower support is fixedly connected with the support plate, the top end of the upper support is fixedly connected with the first cantilever mounting plate and the second cantilever mounting plate, a plurality of first height adjusting holes are formed in the top of the lower support, a plurality of second height adjusting holes are formed in the bottom of the upper support, and connecting bolts are correspondingly arranged in the first height adjusting holes and the second height adjusting holes in a penetrating mode.
The beneficial effects of adopting above-mentioned technical scheme to produce are: the purpose of the height adjustment is to enable the camera A and the camera B to be in close height with the tested sensor and the detection sensor, so that the tested sensor and the detection sensor can be in the visual field of the camera A and the camera B and shot by the camera.
The invention provides a sensor relative position calibration method based on underwater vision positioning, which comprises the following steps of:
S1: two cameras A and B which are vertically installed image the detected sensor and the detection sensor;
S2: the upper computer analyzes and processes the images in real time according to the images of the camera A and the camera B, and extracts the straight line of the edge of the image to fit the central axes of the two images, so as to obtain a two-dimensional straight line equation of the two images in the corresponding projection plane;
S3: determining relative deflection angles and relative offset distances of the detected sensor and the detection sensor according to a two-dimensional linear equation;
S4: the upper computer respectively controls the three-dimensional posture adjustment mechanism of the detected sensor and the three-dimensional posture adjustment mechanism of the detection sensor according to the relative deflection angle and the relative deflection distance to adjust the positions and the postures of the detected sensor and the detection sensor, so that the alignment of the central axes of the detected sensor and the detection sensor is realized.
Further, the step S2 specifically includes: in the world coordinate system, the intersection point of the central axes of the detected sensor and the detection sensor and the z axis is taken as an origin O (0, 0), and the coordinates of the vertexes of the detected sensor and the detection sensor are P (x, y, z), whereinAre vectors of the detected sensor and the detection sensor in a world coordinate system, and the camera A projects the detected sensor and the detection sensor into an xOz plane and images the same to obtain a vector/>Projection in the xOz plane is/>The two-dimensional linear equation is expressed as z=tan α·x, where α is/>An included angle with the x-axis; the camera B projects the detected sensor and the detection sensor into a yOz plane and images the detected sensor and the detection sensor to obtain a vector/>Projection in the yOz plane is/>The two-dimensional linear equation is expressed as z=tan β·y, where β is/>And an angle with the y-axis.
Further, the step S3 specifically includes: taking projections of the detected sensor and the detection sensor on an xOz plane according to the image shot by the camera AThe length of the two axes is a, and the included angles between the two axes are epsilon and alpha; taking projections/>, on the yOz plane, of the detected sensor and the detection sensor according to the image shot by the camera BThe length of the sensor is b, the included angles between the sensor and between the sensor and the sensor are lambda and beta, and the coordinates of the sensor to be detected and the sensor to be detected on the camera plane can be obtained according to the information:
Length c of (c) is:
And/> The included angle theta of (2) is as follows:
And/> The included angle mu is:
included angle lambda,/>, with y-axis And/>The included angle mu of the sensor to be detected is the relative deflection angle of the sensor to be detected and the detection sensor, and the axis of the sensor to be detected can be corrected and adjusted to be parallel to the z axis according to the information;
For the relative offset distance, specifically, on the basis of the known relative deflection angle, the projections of the detected sensor and the detection sensor on the xOy plane are points A and B respectively;
the coordinates of the point A are as follows:
The coordinates of the point B are as follows:
The distance l between the point A and the point B is as follows:
and the distance l between the point A and the point B is the relative offset distance between the central axes of the detected sensor and the detection sensor.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required to be used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only embodiments of the present invention, and that other drawings can be obtained according to the provided drawings without inventive effort for a person skilled in the art.
Fig. 1 is a schematic structural diagram of a sensor relative position calibration device based on underwater vision positioning.
Fig. 2 is a schematic structural view of the bracket.
Fig. 3 is a schematic side view of the bracket.
FIG. 4 is a schematic view of the sensor under test aligned and coaxial with the probe sensor.
Fig. 5 is a schematic view of the projection of the object (sensor under test and detection sensor) in world coordinate system.
Fig. 6 is a schematic view of the projection of the object (sensor under test and detection sensor) on the xOy plane.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1 to 6, an embodiment of the present invention discloses a sensor relative position calibration device based on underwater vision positioning, including: the camera A1, the camera B2, the upper computer 3, the three-dimensional posture adjustment mechanism 4 of the detected sensor and the three-dimensional posture adjustment mechanism 5 of the detection sensor (the three-dimensional posture adjustment mechanism 4 of the detected sensor and the three-dimensional posture adjustment mechanism 5 of the detection sensor can all adopt the existing multi-axis adjustment platform, and the multi-axis adjustment platform comprises a travelling mechanism along the three axial directions of X, Y and Z and a rotating mechanism around the X, Y and Z axes);
The camera A1 and the camera B2 are both arranged on the bracket 6 and are positioned under water, the shooting directions of the camera A1 and the camera B2 are vertically arranged and are used for shooting a detected sensor 7 and a detection sensor 8, the detected sensor 7 is fixed on the detected sensor three-dimensional posture adjusting mechanism 4, and the detection sensor 8 is fixed on the detection sensor three-dimensional posture adjusting mechanism 5;
The upper computer 3 is electrically connected with the camera A1 and the camera B2 and is used for collecting images of the camera A1 and the camera B2 in real time and analyzing and processing the images in real time;
The upper computer 3 is electrically connected with the three-dimensional posture adjustment mechanism 4 of the detected sensor and the three-dimensional posture adjustment mechanism 5 of the detection sensor and is used for respectively adjusting the relative positions of the detected sensor 7 and the detection sensor 8.
Wherein the bracket 6 comprises: the camera comprises a support column 61, a first cantilever mounting plate 62 and a second cantilever mounting plate 63, wherein a support plate 611 is fixed at the bottom end of the support column 61, one end of the first cantilever mounting plate 62 is fixedly connected with the top end of the support column 61, a camera A1 is fixed on the other end of the first cantilever mounting plate 62, one end of the second cantilever mounting plate 63 is fixedly connected with the top end of the support column 61 and is vertically arranged with the first cantilever mounting plate 62, and a camera B2 is fixed on the other end of the second cantilever mounting plate 63.
The support 61 is a telescopic structure with adjustable height.
The support column 61 comprises a lower support column 612 and an upper support column 613, the bottom end of the lower support column 612 is fixedly connected with the support plate 611, the top end of the upper support column 613 is fixedly connected with the first cantilever mounting plate 62 and the second cantilever mounting plate 63, a plurality of first height adjusting holes 6121 are formed in the top of the lower support column 612, a plurality of second height adjusting holes 6131 are formed in the bottom of the upper support column 613, and connecting bolts are arranged in the corresponding first height adjusting holes 6121 and second height adjusting holes 6131 in a penetrating mode. The heights of the support posts can be adjusted through the connecting bolts penetrating through the corresponding first height adjusting holes 6121 and the second height adjusting holes 6131, so that the camera A and the camera B on the support can be positioned at proper positions, and the detected sensor 7 and the detection sensor 8 can be conveniently shot.
The invention relates to a sensor relative position calibration method based on underwater vision positioning, which comprises the following steps of:
S1: two cameras A1 and B2 which are vertically arranged image the detected sensor 7 and the detection sensor 8;
S2: the upper computer 3 analyzes and processes the images in real time according to the images of the camera A1 and the camera B2, extracts the straight lines of the edges of the images to fit the central axes of the images and obtain a two-dimensional straight line equation of the images in the corresponding projection plane;
S3: determining the relative deflection angle and the relative offset distance of the detected sensor 7 and the detection sensor 8 according to a two-dimensional linear equation;
s4: the upper computer 3 respectively controls the three-dimensional posture adjustment mechanism 4 of the detected sensor and the three-dimensional posture adjustment mechanism 5 of the detection sensor according to the relative deflection angle and the relative deflection distance to adjust the positions and the postures of the detected sensor 7 and the detection sensor 8, so that the alignment of the central axes of the detected sensor 7 and the detection sensor 8 is realized.
The step S2 specifically includes: in the world coordinate system, the intersection point of the central axes of the detected sensor 7 and the detecting sensor 8 and the z-axis is taken as an origin O (0, 0), and the coordinates of the vertexes of the detected sensor 7 and the detecting sensor 8 are P (x, y, z), whereinAre vectors of the detected sensor 7 and the detection sensor 8 in a world coordinate system, and the camera A1 projects the detected sensor 7 and the detection sensor 8 into an xOz plane and images the same to obtain a vector/>Projection in the xOz plane is/>The two-dimensional linear equation is expressed as z=tan α·x, where α is/>An included angle with the x-axis; the camera B2 projects and images both the detected sensor 7 and the detection sensor 8 into the yOz plane to obtain a vector/>Projection in the yOz plane is/>The two-dimensional linear equation is expressed as z=tan β·y, where β is/>And an angle with the y-axis.
The step S3 specifically comprises the following steps: taking projections of the detected sensor 7 and the detection sensor 8 on the xOz plane according to the image shot by the camera A1The length of the two axes is a, and the included angles between the two axes are epsilon and alpha; taking projections/>, in the yOz plane, of the sensor 7 under test and the detection sensor 8 from the image taken by the camera B2The length of the sensor 7 is b, the included angles with the y axis and the z axis are lambda and beta, and the coordinates of the detected sensor 7 and the detection sensor 8 on the camera plane can be obtained according to the information:
Length c of (c) is:
And/> The included angle theta of (2) is as follows:
And/> The included angle mu is:
included angle lambda,/>, with y-axis And/>The included angle mu of the sensor 7 to be detected and the detection sensor 8 are relative deflection angles, and the axis of the sensor can be corrected and adjusted to be parallel to the z axis according to the information;
for the relative offset distance, specifically, on the basis of the known relative deflection angle, the projections of the detected sensor 7 and the detection sensor 8 on the xOy plane are all a point, and are respectively a point A and a point B;
the coordinates of the point A are as follows:
The coordinates of the point B are as follows:
The distance l between the point A and the point B is as follows:
the distance l between the point A and the point B is the relative offset distance between the central axes of the detected sensor 7 and the detection sensor 8.
The specific step of the step S4 is that according to the relative deflection angle and the relative deflection distance between two corrected objects obtained in the step S3, the detection sensor is firstly rotated towards the negative direction of the x axis by taking the O point as a rotation center, and the rotation angle is mu; and then the rotation angle is lambda by taking the O point as the rotation center along the negative direction of the y axis. The same operation is performed on the sensor under test. And translating one of the corrected objects towards the other corrected object by a distance of l, so that the two corrected objects can be aligned.
In actual operation, the underwater camera A is arranged on the side face, the underwater camera B is vertically arranged at 90 degrees with the camera A on the front face, the detected sensor and the detection sensor are shot, and the distance sensor is about 500mm. The image of the camera is acquired in real time through the upper computer, the image is analyzed and processed in real time, and the edge of the image is extracted by adopting a related algorithm. And then the central axis of the measured sensor is calculated according to the straight line of the edge of the measured sensor, and the central axis of the measured sensor is obtained by fitting the central axis of the measured sensor in each camera: y=k 1x+b1. The same operation is carried out on the edge of the detection sensor, and the central axis of the detection sensor is obtained by fitting the edge of the detection sensor:
y＝k2x+b2。
If k 1 and k 2,b1 are approximately equal to b 2 in a certain range, it is indicated that the central axis of the measured sensor is in a straight line with the central axis of the detecting sensor, and alignment of the two sensors can be achieved, as shown in fig. 3. If both camera a and camera B yield such a result, it is stated that both are coaxial. If the two sensors are not coaxial, the relative deflection angle and the relative offset distance of the detection sensor and the detected sensor can be calculated through pictures of the camera A and the camera B, and the relative positions among the sensors are adjusted.
The camera A and the camera B are underwater cameras, the models of the cameras are the same, and parameters to be met are as follows: the resolution is 4024×3036 (1200 ten thousand pixels), the pixel size is 1.85 μm×1.85 μm, the frame rate is 9fps, the interface is Gigabit Ethernet (Gigabit network), the shooting distance is less than 500mm, the focal length is 12mm, and the shooting precision is 0.28mm.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (7)
1. Sensor relative position calibrating device based on vision location under water, its characterized in that includes: the device comprises a camera A (1), a camera B (2), an upper computer (3), a three-dimensional posture adjusting mechanism (4) of a detected sensor and a three-dimensional posture adjusting mechanism (5) of a detection sensor;
The camera A (1) and the camera B (2) are both arranged on the bracket (6) and are positioned under water, the shooting directions of the camera A and the camera B are vertically arranged and are used for shooting a detected sensor (7) and a detection sensor (8), the detected sensor (7) is fixed on the detected sensor three-dimensional posture adjusting mechanism (4), and the detection sensor (8) is fixed on the detection sensor three-dimensional posture adjusting mechanism (5);
The upper computer (3) is electrically connected with the camera A (1) and the camera B (2) and is used for collecting images of the camera A (1) and the camera B (2) in real time and analyzing and processing the images in real time;
The upper computer (3) is electrically connected with the three-dimensional posture adjustment mechanism (4) of the detected sensor and the three-dimensional posture adjustment mechanism (5) of the detection sensor, and is used for respectively adjusting the relative positions of the detected sensor (7) and the detection sensor (8).
2. Sensor relative position calibration device based on underwater vision positioning according to claim 1, characterized in that the bracket (6) comprises: support column (61), first cantilever mounting panel (62) and second cantilever mounting panel (63), support column (61) bottom mounting has extension board (611), first cantilever mounting panel (62) one end with support column (61) top fixed connection, camera A (1) are fixed on first cantilever mounting panel (62) other end, second cantilever mounting panel (63) one end with support column (61) top fixed connection, and with first cantilever mounting panel (62) are arranged perpendicularly, camera B (2) are fixed on second cantilever mounting panel (63) other end.
3. The underwater vision positioning based sensor relative position calibration device according to claim 2, characterized in that the support (61) is a telescopic structure with adjustable height.
4. The sensor relative position calibration device based on underwater vision positioning according to claim 3, wherein the support column (61) comprises a lower support column (612) and an upper support column (613), the bottom end of the lower support column (612) is fixedly connected with the support plate (611), the top end of the upper support column (613) is fixedly connected with the first cantilever mounting plate (62) and the second cantilever mounting plate (63), a plurality of first height adjusting holes (6121) are formed in the top of the lower support column (612), a plurality of second height adjusting holes (6131) are formed in the bottom of the upper support column (613), and connecting bolts are arranged in the corresponding first height adjusting holes (6121) and second height adjusting holes (6131) in a penetrating mode.
5. A method for calibrating the relative position of a sensor based on underwater vision positioning, characterized in that the following steps are performed by using a calibrating device according to any of claims 1-4:
S1: two cameras A (1) and B (2) which are vertically installed image the detected sensor (7) and the detection sensor (8);
S2: the upper computer (3) analyzes and processes the images in real time according to the images of the camera A (1) and the camera B (2), and extracts the straight line of the edge of the image to fit the central axes of the two images, so as to obtain a two-dimensional straight line equation of the two images in the corresponding projection plane;
S3: determining the relative deflection angle and the relative offset distance of the detected sensor (7) and the detection sensor (8) according to a two-dimensional linear equation;
S4: the upper computer (3) respectively controls the three-dimensional posture adjustment mechanism (4) of the detected sensor and the three-dimensional posture adjustment mechanism (5) of the detection sensor to adjust the positions and the postures of the detected sensor (7) and the detection sensor (8) according to the relative deflection angle and the relative offset distance, so that the alignment of the central axes of the detected sensor (7) and the detection sensor (8) is realized.
6. The method for calibrating relative positions of sensors based on underwater vision positioning according to claim 5, wherein step S2 is specifically: in the world coordinate system, the intersection point of the central axes of the detected sensor (7) and the detection sensor (8) and the z axis is taken as an origin O (0, 0), and the coordinates of the vertexes of the detected sensor (7) and the detection sensor (8) are P (x, y, z), whereinAre vectors of the detected sensor (7) and the detection sensor (8) in a world coordinate system, and the camera A (1) projects the detected sensor (7) and the detection sensor (8) into an xOz plane and images the same to obtain a vector/>Projection in the xOz plane is/>The two-dimensional linear equation is expressed as z=tan α·x, where α is/>An included angle with the x-axis; the camera B (2) projects the detected sensor (7) and the detection sensor (8) into a yOz plane and images the detected sensor and the detection sensor to obtain a vector/>Projection in the yOz plane is/>The two-dimensional linear equation is expressed as z=tan β·y, where β is/>And an angle with the y-axis.
7. The method for calibrating relative positions of sensors based on underwater vision positioning according to claim 6, wherein step S3 is specifically: taking projections of the detected sensor (7) and the detection sensor (8) on an xOz plane according to the image shot by the camera A (1)The length of the two axes is a, and the included angles between the two axes are epsilon and alpha; taking the projection/>, in the yOz plane, of the sensor under test (7) and of the detection sensor (8) from the image taken by the camera B (2)The length of the sensor (7) to be detected and the coordinates of the detection sensor (8) on the camera plane can be obtained according to the information, wherein the included angles between the sensor (7) and the y axis and the z axis are lambda and beta, and the coordinates of the sensor (8) to be detected on the camera plane are:
Length c of (c) is:
And/> The included angle theta of (2) is as follows:
And/> The included angle mu is:
included angle lambda,/>, with y-axis And/>The included angle mu of the sensor (7) to be detected and the detection sensor (8) are relative deflection angles, and the axis of the sensor can be corrected and adjusted to be parallel to the z axis according to the information;
for the relative offset distance, specifically, on the basis of the known relative deflection angle, the projections of the detected sensor (7) and the detection sensor (8) on the xOy plane are all a point and are respectively an A point and a B point;
the coordinates of the point A are as follows:
The coordinates of the point B are as follows:
The distance l between the point A and the point B is as follows:
the distance l between the point A and the point B is the relative offset distance between the central axes of the detected sensor (7) and the detection sensor (8).
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