CN118258377A - A bridge rotation monitoring method and system based on three-dimensional orthogonal cursor - Google Patents

Abstract

The present invention discloses a bridge rotation monitoring method and system based on a three-dimensional orthogonal cursor, the method comprising: arranging an orthogonal three-dimensional cursor and an image acquisition device to establish a coordinate system; obtaining an initial posture image of the three-dimensional orthogonal cursor before rotation construction, extracting imaging information of light beam projection, and determining the transformation relationship between various coordinate systems at the initial posture; establishing a mapping relationship between the light beam and the light beam projection, and using the variational principle and numerical iteration method to solve the initial posture of the cursor; continuously collecting posture images of the bridge at different times during the bridge rotation process, and solving the rotation posture of the bridge at different times; calculating the relative rotation matrix of the bridge from the initial posture to the posture at any time, and separating the relative rotation Euler angle therefrom. The method uses a three-dimensional orthogonal cursor as a visual input, can accurately calculate the relative rotation angle of the rotating bridge from the initial posture to any posture, and realizes real-time monitoring of the entire process of bridge rotation, which is accurate, efficient, low-cost, safe, and contactless.

Description

A bridge rotation monitoring method and system based on three-dimensional orthogonal cursor

Technical Field

The invention relates to a bridge rotation monitoring method and system based on a three-dimensional orthogonal cursor, belonging to the technical field of bridge rotation construction monitoring.

Background technique

With the continuous development of my country's infrastructure, the number of grade-separated lines has increased significantly. The problem of how to avoid interference with existing lines during the construction of overpasses has become a hot topic in the engineering community. As a non-interference overpass construction method, the bridge rotation construction method has gradually gained attention and been widely used in recent years. This method has been successfully applied to hundreds of bridges around the world, including continuous beam bridges, arch bridges, cable-stayed bridges, etc. The adoption of the rotation construction method significantly simplifies and accelerates the construction of bridges, and has high economic efficiency and timeliness.

On the one hand, during the rotation and traction process of the bridge, if the bridge rotation exceeds the designed angle, it can only be pushed back by a jack, which puts forward high requirements for accurate rotation. On the other hand, due to the gap between the support legs fixed on the upper structure and the slideway, the beam body rotates around the vertical axis while rotating around the longitudinal and lateral directions of the structure during the rotation process, causing the spatial posture of the rotating structure to change within a certain range. Therefore, in order to ensure "accurate rotation" and realize precise actions such as the rotating bridge crossing obstacles and passing through designated spaces, monitoring the bridge rotation construction process has become a key research issue.

At present, the rotation monitoring of rotating bridges is mainly carried out by traditional contact monitoring methods, such as the turntable pointer method and sensor technology. The turntable pointer method is the most widely used. It uses the "pointer" to align the bridge to monitor the rotation around the vertical axis. It has the function of prompting the rotation process and preventing excessive rotation to a certain extent, but it has the problems of high labor cost, poor real-time performance and insufficient accuracy. The attitude sensor can realize automatic monitoring with high accuracy, but its sensitivity is high and it is easily affected by magnetic field interference and environmental changes. At the same time, the cost is relatively high.

Compared with traditional contact monitoring methods, non-contact rotation monitoring methods have the advantages of all-round measurement and high prediction accuracy, such as satellite positioning method, total station method and other methods. The satellite positioning system (GPS) can realize fully automatic measurement, but its equipment use conditions require high standards, and the communication signal is greatly interfered by the outside world and has poor stability, which is not conducive to the implementation of accurate rotation. The total station method can use the total station to monitor the coordinates of the control points of the rotating bridge, derive the overall structural change characteristics from the local coordinate changes, and indirectly obtain the spatial position of the rotating bridge. However, on-site measurements are greatly affected by factors such as beam rotation, light, and personnel safety, making it difficult to obtain the spatial position of the rotating bridge efficiently and in real time.

In general, the existing bridge rotation construction monitoring methods have shortcomings such as lack of real-time performance and low accuracy, and the entire monitoring process requires manual operation and measurement. Therefore, the rotation monitoring method has become one of the research focuses of bridge rotation construction.

Computer vision monitoring method is a new high-tech monitoring method that is currently popular. It is divided into monocular vision and multi-camera vision according to the number of cameras used. Monocular vision is widely used due to its simple structure, low price and easy deployment. However, since monocular vision imaging will lose depth information, it is usually necessary to combine other sensors or use complex algorithms such as machine learning to accurately obtain the spatial position and posture of moving objects. Machine learning and other methods require a large amount of training data to achieve posture estimation, and the demand for high-quality data is large, the calculation cost is complex, and there is error accumulation. For the problem of bridge rotation, during the rotation process, due to the central limit of the rotating bridge, the beam body only rotates relatively around its own local coordinate system without translation. Therefore, the rotation and translation of the spatial position of the bridge can be separated, and the spatial posture problem related to the bridge rotation can be specifically studied. Therefore, how to apply monocular vision to the field of bridge rotation and realize real-time monitoring of the entire rotation process is one of the problems to be solved in this field.

Summary of the invention

The purpose of the present invention is to solve the shortcomings of existing bridge rotation construction monitoring methods such as insufficient real-time performance and low accuracy, as well as the problem that the entire monitoring process requires manual jog operation and measurement, and to propose a bridge rotation monitoring method and system based on a three-dimensional orthogonal cursor.

The present invention aims to obtain bridge rotation image information based on a three-dimensional orthogonal cursor to inversely calculate the spatial posture of the bridge rotation, and then calculate the relative rotation Euler angle during the bridge rotation process, so as to achieve non-contact, high-precision, and real-time rotation monitoring of the rotating bridge. This technology has important engineering application potential in the field of rotation construction monitoring technology for rotating bridge structures.

In order to solve the above technical problems, the present invention adopts the following technical solutions:

In a first aspect, a bridge rotation monitoring method based on a three-dimensional orthogonal cursor comprises the following steps:

S1, at least one three-dimensional orthogonal cursor capable of emitting light beams is arranged on the rotating bridge, and an image acquisition device is arranged outside the rotating range of the bridge; a local coordinate system of the bridge and a camera coordinate system are established on the rotating bridge and the image acquisition device respectively, and a cursor coordinate system is established with the intersection of the three-dimensional orthogonal cursor light beams as the origin and the directions of the three light beams as the coordinate axes; a local coordinate system of the bridge is established with the center of the spherical joint of the turntable on the bridge as the origin, and the longitudinal, transverse and vertical directions of the bridge as the X _B axis, Y _B axis and Z _B axis respectively; a camera coordinate system is established with the optical center of the image acquisition device as the origin, and the horizontal direction of the image acquisition device is taken to the right, the vertical direction is taken to the downward, and the optical axis directions are taken to the X _C axis, Y _C axis and Z _C axis respectively;

S2, before the bridge rotation construction, the image acquisition device captures and acquires an image containing three-dimensional orthogonal cursor beam rays as an initial posture image, and determines the direction angle and intersection coordinates of the three-dimensional orthogonal cursor beam projected on the imaging plane at the initial posture according to the initial posture image;

S3, using the rigid body space transformation principle to establish the transformation relationship between the cursor coordinate system and the camera coordinate system, and establishing the mapping relationship between the three-dimensional orthogonal cursor beam and the beam projection according to the imaging principle. According to the mapping relationship, the transformation relationship and the direction angle and intersection coordinates of the beam projection at the initial posture obtained in S2, the variational principle and the numerical iteration method are used to solve the initial posture of the three-dimensional orthogonal cursor. According to the initial posture of the three-dimensional orthogonal cursor and the transformation relationship between the cursor coordinate system and the local coordinate system of the bridge, the transformation relationship between the camera coordinate system and the local coordinate system of the bridge at the initial posture is obtained, and then the initial posture of the bridge rotation is determined;

S4, during the bridge rotation construction process, the image acquisition device continuously acquires posture images of the bridge rotation at different times, extracts the direction angles and intersection coordinates of the three-dimensional orthogonal cursor beams projected on the imaging plane at different times from the posture images obtained at different times, and uses the variational principle and numerical iteration method to solve the spatial postures of the three-dimensional orthogonal cursor at different times, and obtains the transformation relationship between the camera coordinate system and the local coordinate system of the bridge at different times during the bridge rotation process, thereby determining the spatial postures of the bridge rotation at different times;

S5, based on the initial posture of the bridge rotation obtained in S3-S4 and the postures at different times during the rotation process, obtain the relative rotation matrix of the postures at different times during the bridge rotation process and the initial posture; set the rotation order of the bridge relative rotation around the local coordinate system of the bridge, and extract the relative rotation Euler angles of the bridge rotation at different times from the relative rotation matrix according to the rotation order.

Furthermore, in step S1, the three-dimensional orthogonal cursor is arranged as follows:

The three-dimensional orthogonal cursor is composed of three laser emitters connected vertically to each other, with the starting points of the light beams converging at one point. Each laser emitter emits a light beam to form three optical axes. The three laser emitters can respectively emit lasers of different colors, preferably red, green and blue. The emission distance of each laser emitter is preferably greater than or equal to 5m, so that the color of the light beam is prominent and easy to capture by computer vision observation. The three-dimensional orthogonal cursor is preferably installed on a bridge pier or an upper turntable.

Furthermore, in step S1, the image acquisition device is arranged as follows:

There is a height difference between the layout position of the image acquisition device and the layout position of the three-dimensional orthogonal cursor, so that the projections of the three-dimensional orthogonal cursor light beams on the imaging plane of the image acquisition device do not overlap with each other;

During the whole process of bridge rotation construction, the spatial position of the image acquisition device is kept unchanged, and the three-dimensional orthogonal cursor is kept within the viewing range of the image acquisition device.

Further, in step S2, according to the initial posture image (i.e. before the bridge rotates), the direction angle and intersection coordinates of the orthogonal three-dimensional cursor beam projected on the imaging plane of the image acquisition device in the initial posture are obtained by the following method:

Determine the RGB threshold range of the three color light beams, and extract the pixel points corresponding to the three color light beams from the initial posture image according to the corresponding RGB threshold range; use the random sampling consensus method (RANSAC algorithm) to iteratively fit the three groups of pixel points extracted according to the linear function, and obtain several analytical expressions of the corresponding light beam projection fitting lines. When the error of the coordinates of the intersection points of the three fitting lines is less than or equal to 0.1 pixel, the analytical expression of the light beam projection fitting line that meets the accuracy requirement is obtained, and the direction angle of the light beam projection on the imaging plane is obtained, and the average value of the coordinates of the intersection points of the fitting lines is taken as the intersection coordinates of the light beam projection.

Furthermore, in step S3, according to the rigid body space transformation principle, the transformation relationship between the cursor coordinate system and the camera coordinate system is established as follows:

Assuming that the rotation order from the camera coordinate system to the cursor coordinate system is around the XYZ axis, the corresponding rotation Euler angles are α, β, γ, and the corresponding rotation matrices are _RX , _RY , and _RZ , respectively. Then the total rotation transformation matrix _Rc is obtained according to formula (3.1):

Where α, β, γ are the Euler angles of the camera coordinate system rotating around the X, Y, and Z axes respectively; R _X , R _Y , and R _Z are the rotation matrices corresponding to the rotation angles α, β, and γ respectively; R _c is the total rotation transformation matrix from the camera coordinate system to the cursor coordinate system;

According to the rotation transformation matrix R _c , the transformation relationship between the camera coordinate system and the cursor coordinate system is obtained according to formula (3.2):

η _i ＝ _RC Ε＝[r _1i r _2i r _3i ] ^T (3.2)

Wherein, _ηi is the direction vector of the cursor coordinate axis at any moment; _RC is the rotation transformation matrix from the camera coordinate system to the cursor coordinate system at that moment; E is the unit matrix of the camera coordinate system coordinate axis, and the row vectors constituting the unit matrix represent the direction vector of the camera coordinate system coordinate axis; _r1i , _r2i , _r3i are the 1st, 2nd, 3rd row and i-th column elements in the rotation matrix _RC , respectively.

Furthermore, in step S3, according to the imaging principle, the three-dimensional orthogonal cursor beam is centrally projected to the optical center of the camera, that is, the center of the camera coordinate system, and the mapping relationship between the beam and the beam projection is obtained by the following method:

The three-dimensional orthogonal cursor is centrally projected to the optical center of the image acquisition device (center of the camera coordinate system). Assuming that the coordinates of the three-dimensional orthogonal cursor origin _OA in the camera coordinate system are (X ₀ , Y ₀ , Z ₀ ), the image coordinates (x ₀ , y ₀ ) of the three-dimensional orthogonal cursor origin projected to the imaging plane are expressed as follows according to formula (3.3):

Where f is the focal length of the camera;

Assume that the radius vector of the origin _OA of the cursor coordinate system in the camera coordinate system is _t0 = ( _X0 , _Y0 , _Z0 ), _t0 is the translation vector in the camera external parameter matrix, and according to the plane intersection principle, the projection ray l _i of the cursor coordinate system on the imaging plane is the intersection line of the spatial plane determined by the radius vector _t0 and the cursor coordinate axis _ηi with the imaging plane. According to the principle of spatial analytic geometry, the normal vector n _i of the spatial plane determined by the radius vector _t0 and the cursor coordinate axis _ηi is obtained according to formula (3.4):

By solving the plane normal vector, we can get the analytical expression of the space plane where the radius vector _t0 and the cursor coordinate axis _ηi are located, as shown in equation (3.5):

n _i1 x+n _i2 y+n _i3 z＝0 (3.5)

Where n _i1 , n _i2 , and n _i3 are the components of the normal vector _ni of the plane where η _i is located in the directions of the X, Y, and Z axes of the camera coordinate system, that is, the first, second, and third elements of the vector _ni .

According to the principle of spatial analytic geometry, the analytical expression of the spatial plane determined by the radius vector _t0 and the cursor coordinate axis _ηi and the analytical expression of the imaging plane (i.e. z = f) can be solved to obtain the analytical expression of the beam projection l _i on the imaging plane as shown in (3.6):

Where (x, y) is the coordinate of the imaging plane;

According to the analytical expression of the beam projection l _i , the direction angle of the beam projection l _i is solved, and the mapping relationship between the three-dimensional orthogonal cursor beam and the beam projection is obtained as shown in formula (3.7):

θ _i = atan2(fr _2i -y ₀ r _3i ,fr _1i -x ₀ r _3i ) (3.7)

Where _θi is the direction angle of the light beam projection li; atan2(·) is the four-quadrant inverse tangent function.

Further, in step S3, the mapping relationship between the three-dimensional orthogonal cursor beam and the beam projection and the transformation relationship between the cursor coordinate system and the camera coordinate system are solved by a numerical iteration method according to the direction angle and intersection coordinates of the beam projection at the initial posture obtained in S2, so as to obtain the rotation Euler angles α, β, γ corresponding to the three-dimensional orthogonal cursor in the camera coordinate system at the initial posture; the numerical iteration method is preferably a Newton-Raphson numerical iteration method;

According to the solved rotation Euler angles α, β, γ, the transformation relationship between the camera coordinate system and the cursor coordinate system at the initial posture is obtained as shown in formula (3.8):

Where R _c0 is the rotation matrix from the camera coordinate system to the cursor coordinate system at the initial posture; is the direction vector of the coordinate axis of the cursor coordinate system at the initial posture, i=1, 2, 3; E is the unit matrix of the coordinate axis of the camera coordinate system, and the row vectors constituting the unit matrix represent the direction vector of the coordinate axis of the camera coordinate system.

Further, in step S3, according to the transformation relationship between the camera coordinate system and the cursor coordinate system and the transformation relationship between the cursor coordinate system and the local coordinate system of the bridge as shown in formula (3.9), the transformation relationship between the camera coordinate system and the local coordinate system of the bridge at the initial posture is obtained according to formula (3.10), and the initial posture of the bridge rotation is determined according to the transformation relationship (the initial rotation Euler angle based on the camera coordinate system):

[η ₁ ,η ₂ ,η ₃ ] ^T ＝R ₀ [ξ ₁ ,ξ ₂ ,ξ ₃ ] ^T (3.9)

In the formula, is the direction vector of the coordinate axis of the local coordinate system of ^the bridge, i=1, 2, 3; _R0 is the rotation transformation matrix of the local coordinate axis of the bridge to the cursor coordinate system; _R0-1 is the inverse matrix of _R0 ; _η1 , _η2 , _η3 are the direction vectors of the cursor coordinate axis at any time; _ξ1 , _ξ2 , _ξ3 are the direction vectors of the coordinate axis of the local coordinate system of the bridge at any time; _R0-1Rc0 is the ^rotation transformation _matrix of the camera coordinate system to the local coordinate system of the bridge.

Furthermore, in step S4, the transformation relationship between the camera coordinate system and the local coordinate system of the bridge at different times during the bridge rotation process is obtained according to formula (4.1), and the spatial posture of the bridge at different times during the bridge rotation process is determined according to the transformation relationship (the rotation Euler angle based on the camera coordinate system during the rotation):

In the formula, is the direction vector of the coordinate axis of the local coordinate system of the bridge at the kth shooting moment, i=1, 2, ₃ , k=1 ^, 2, 3...; _Rck is the rotation matrix of the camera coordinate system transformed to the cursor coordinate system at the kth shooting moment; _R0-1Rck represents the rotation transformation matrix of the camera coordinate system transformed to the local coordinate system of the bridge at the kth shooting moment, from which the rotational spatial posture (rotation Euler angle) of the rotating bridge based on the camera coordinate system at the kth shooting moment can be extracted.

Further, in step S5, according to the initial posture of the bridge rotation obtained in S3-S4 and the spatial posture at different times during the rotation process, the relative rotation matrix between the posture at different times during the bridge rotation process and the initial posture based on the local coordinate system of the bridge is obtained according to formula (5.1):

ΔR _0k ＝R ₀ ^-1 R _ck R ₀ R _ck ^-1 (5.1)

Where _Rck is the rotation matrix of the camera coordinate system transformed to the cursor coordinate system at the kth shooting moment, k = 1, 2, 3, etc.; _ΔR0k is the relative rotation matrix of the local coordinate system of the rotating bridge from the initial posture to the spatial posture corresponding to the kth shooting moment.

Furthermore, in step S5, the rotation order of the swivel bridge relative to the local coordinate system of the bridge is set to be around the ZYX axis. When the rotation order from the camera coordinate system to the cursor coordinate system is around the XYZ axis, the relative rotation Euler angles Δα, Δβ, Δγ are extracted from the relative rotation matrix ΔR _0k as shown in formula (5.2):

Where Δα, Δβ, and Δγ are the Euler angles of the rotating bridge around the X, Y, and Z axes of the local coordinate system of the bridge, respectively; s _mn (m＝1,2,3; n＝1,2,3) represents the element in the mth row and nth column of the relative rotation matrix.

In a second aspect, a monitoring system for a bridge rotation monitoring method based on a three-dimensional orthogonal cursor comprises:

A cursor module includes a three-dimensional orthogonal cursor fixedly installed on the bridge through a base, wherein the three-dimensional orthogonal cursor is composed of three laser transmitters that are vertically connected to each other and emit light beams of different colors;

An image acquisition module, which uses an image acquisition device to continuously shoot and acquire posture images of a three-dimensional orthogonal cursor installed on the rotating bridge, wherein the posture images include an initial posture image and posture images at different times during the rotation process;

An image processing module extracts the direction angles and intersection coordinates corresponding to the three-dimensional orthogonal cursor beam rays from all the posture images taken by the image acquisition module;

The data processing module calculates the relative rotation Euler angles of the bridge rotation posture at different times relative to the initial posture according to the direction angle and intersection coordinates of the light beam projection obtained by the image processing module;

The data display module displays the relative rotation Euler angles and target rotation Euler angles of the rotating bridge at different times.

The technical principle of the present invention is as follows: since the existing monitoring technology for the construction of a rotating bridge is difficult to accurately obtain the real-time spatial position and posture of the bridge, and considering that the bridge has a center limit during the rotation process, it only rotates around the local coordinate system of the bridge itself without any translation, so the rotation and translation of the bridge are separated; but since the local coordinate system of the bridge is difficult to visualize in the image acquisition device and the monitoring effect is poor, a three-dimensional orthogonal cursor is introduced to convert the bridge rotation problem that is difficult to directly observe into a visualized three-dimensional cursor movement, and the movement monitoring of the three-dimensional orthogonal cursor is equivalently replaced by the monitoring of the bridge rotation movement, providing a new idea for tracking and monitoring the posture of the entire bridge rotation process. ; The present invention establishes a mapping relationship between a three-dimensional orthogonal cursor light beam and a light beam projection based on the imaging principle and the spatial analytical geometry principle, and constructs a conversion relationship between a three-dimensional orthogonal cursor, a bridge, and an image acquisition device based on the rigid body space transformation principle. According to the posture images of the three-dimensional orthogonal cursor at different times during the bridge rotation process acquired by the image acquisition device, the relative rotation Euler angle of the bridge rotation posture at different times relative to the initial posture is finally obtained. By comparing the relative rotation Euler angle with the target rotation Euler angle, the bridge rotation action can be adjusted in real time, thereby realizing real-time monitoring of the entire bridge rotation process, and has the advantages of accuracy, efficiency, low cost, safety, and contactlessness.

Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

(1) Global monitoring: The present invention can realize the whole process monitoring of the rotation process without on-site contact and is not limited by the field of vision position.

(2) High precision: The present invention can accurately calculate the spatial posture of the rotating bridge during its rotation process, and has high precision in monitoring its rotation angle and longitudinal and lateral deflection.

(3) Real-time: The present invention can identify and acquire rotation image information in real time, develop a rotation bridge spatial posture monitoring algorithm, design programmed modules such as data preprocessing, calculation analysis, and parameter output, and realize efficient real-time feedback of monitoring data and results through module integration.

(4) Wide scope of application: The present invention is applicable to the rotation monitoring of rotating bridges in the field of civil engineering, and is particularly applicable to bridge structures with restricted geographical locations.

(5) Great application potential: The present invention can achieve global, high-precision, and real-time monitoring of rotating bridges at extremely low cost and computational effort, which is crucial to the development of computer vision-based structural rotation monitoring methods.

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1 is a flow chart of the method of the present invention;

FIG2 is a schematic diagram of a three-dimensional orthogonal cursor;

FIG3 is a schematic diagram of the layout of a three-dimensional orthogonal cursor;

FIG4 is a schematic diagram of the relative rotation principle of a rotating bridge;

Fig. 5 is a cursor projection plan view;

FIG6 is a schematic diagram of coordinate system transformation.

Detailed ways

In order to make the purpose and technical solution of the embodiment of the present invention clearer, the technical solution of the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings of the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all of the embodiments. Based on the described embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

Embodiment 1;

See Figure 1-6;

The present embodiment provides a bridge rotation monitoring method based on a three-dimensional orthogonal cursor, comprising the following steps:

S1, at least one three-dimensional orthogonal cursor capable of emitting light beams is arranged on the rotating bridge, and an image acquisition device is arranged outside the rotating range of the bridge; a local coordinate system of the bridge is established with the center of the ball joint of the turntable on the bridge as the origin, and the longitudinal, transverse and vertical directions of the bridge are respectively taken as the X _B axis, Y _B axis and Z _B axis; a cursor coordinate system is established with the intersection of the three-dimensional orthogonal cursor light beams as the origin and the directions of the three light beams as the coordinate axes; a camera coordinate system is established with the optical center of the image acquisition device as the origin, and the horizontal direction of the image acquisition device is taken to the right, the vertical direction is taken to be downward, and the optical axis directions are taken as the X _C axis, Y _C axis and Z _C axis;

The 3D orthogonal cursor is arranged as follows:

The three-dimensional orthogonal cursor is composed of three laser emitters connected perpendicularly to each other, the starting points of the light beams converge at one point (i.e., the origin of the three-dimensional orthogonal cursor), the light beam rays form three optical axes, and the starting points of the light beams and the three orthogonal optical axes constitute the cursor coordinate system; the three laser emitters can emit lasers of different colors, preferably red, green, and blue; the emission distance of each laser emitter is preferably greater than or equal to 5m; the three-dimensional orthogonal cursor is preferably installed on a bridge pier or an upper turntable. In a preferred embodiment, the cursor device uses a 4W red laser, a 4W green laser, and a 12W blue laser as beam emitters.

The light beam can be emitted infinitely within a certain range without being blocked, forming a huge cursor coordinate system with prominent colors, which is convenient for the image acquisition device to observe and capture, thereby improving the shooting effect and image processing accuracy.

It should be noted that in addition to using a laser transmitter to emit a beam to form a three-dimensional orthogonal cursor, a three-dimensional orthogonal physical target with length information can also be used. According to the requirements of cross-railway construction, rotation construction is usually carried out at night. In this case, laser beams are preferred as visual input. If the on-site environment is bright and the laser beam visibility has no obvious advantage, a three-dimensional orthogonal physical target with length information can be used. When using the latter as the visual input of the image acquisition device, it is necessary to ensure that the line of sight between the image acquisition device and the three-dimensional orthogonal target is unobstructed.

The image acquisition device is arranged as follows:

There is a height difference between the placement position of the image acquisition device and the placement position of the three-dimensional orthogonal cursor, so that the projections of the three-dimensional orthogonal cursor light beams on the imaging plane of the image acquisition device do not overlap with each other;

During the whole process of bridge rotation construction, the spatial position of the image acquisition device is kept unchanged, so that the three-dimensional orthogonal cursor is kept within the viewing range of the image acquisition device.

It should be understood that the image acquisition device can be a camera, a camcorder, etc., preferably an industrial camera. The image acquisition device needs to be calibrated before starting to acquire information to obtain the camera's intrinsic parameters required for calculating the spatial posture of the rotating bridge. The calibration method is preferably Zhang's calibration method. When using a camera to take pictures, the camera's frame rate needs to be set in advance to achieve continuous shooting. During the entire process of bridge rotation, the line of sight between the image acquisition device and the orthogonal three-dimensional cursor is kept basically unobstructed without large-area obstruction. Preferably, the distance between the image acquisition device and the three-dimensional orthogonal cursor is within 100m.

S2, before the bridge rotation construction, the image acquisition device captures and acquires an image containing a three-dimensional orthogonal cursor beam as an initial posture image, and determines the direction angle and intersection coordinates of the three-dimensional orthogonal cursor beam projected on the imaging plane at the initial posture according to the initial posture image;

According to the initial posture image (i.e. before the bridge rotates), the direction angle of the orthogonal three-dimensional cursor beam ray projection on the imaging plane of the image acquisition device at the initial posture is obtained by the following method:

In the camera coordinate system, the pixels in the image are traversed and identified based on the set RGB threshold range to extract the pixel information of the light beam. The random sampling consistency method (RANSAC algorithm) is used to iteratively fit the three groups of pixels extracted according to the linear function to obtain several analytical expressions of the corresponding light beam projection fitting lines. When the error of the coordinates of the intersection points of the three fitting lines is less than or equal to 0.1 pixel, the analytical expression of the light beam projection fitting line that meets the accuracy requirement is obtained. Then, the principle of plane analytic geometry is used to obtain the direction angle of the light beam projection on the imaging plane, and the mean value of the coordinates of the intersection points of the fitting lines is used as the intersection coordinates of the light beam projection.

It should be noted that the RANSAC algorithm is a commonly used mathematical method in the field of computer vision. It estimates the parameters of a mathematical model from a set of observed data containing outliers in an iterative manner; RANSAC is a non-deterministic algorithm. The more iterations, the more reasonable the fitting model obtained. In the present invention, the basic idea of the RANSAC algorithm is: taking a certain group of beam projection pixel points as an example, a small amount of random sampling of the pixel point data set is performed as an inlier set and the model is fitted according to a linear function; all pixel points in the data set are predicted using the fitting model, a distance threshold is set, and data points with a degree of model fit higher than the threshold are considered as inliers, the inlier set is updated and the model is fitted again; an inlier ratio threshold is set, and if the number of inliers reaches the threshold, the current model is considered to meet the convergence conditions, and the iteration is stopped, otherwise the previous step is repeated; when the model meets the convergence conditions, the least squares method is used to estimate the model parameters, and an analytical expression of the cursor projection fitting line is obtained.

It should be noted that after the image acquisition device obtains the images/photos of the bridge rotation posture at different times, it is usually necessary to preprocess the images/photos, such as using mean filtering for noise reduction and using morphological opening operation to smooth the photos; image preprocessing is a conventional technical means in this field and will not be repeated here.

In step S2, the bridge rotation posture image is processed, the pixel information is iteratively fitted using the RANSAC algorithm, and constraints are added to improve the fitting accuracy, so as to accurately obtain the two-dimensional image information of the three-dimensional orthogonal cursor on the rotating bridge.

S3, using the rigid body space transformation principle to establish the transformation relationship between the cursor coordinate system and the camera coordinate system, and establishing the mapping relationship between the three-dimensional orthogonal cursor beam and the beam projection according to the imaging principle. According to the mapping relationship, the transformation relationship and the direction angle and intersection coordinates of the beam projection at the initial posture obtained in S2, the variational principle and the numerical iteration method are used to solve the initial posture of the three-dimensional orthogonal cursor. According to the initial posture of the three-dimensional orthogonal cursor and the transformation relationship between the cursor coordinate system and the local coordinate system of the bridge, the transformation relationship between the camera coordinate system and the local coordinate system of the bridge at the initial posture is obtained, and then the initial posture of the bridge rotation is determined;

According to the rigid body space transformation principle and the transformation characteristics of the rotating bridge, the transformation relationship between the cursor coordinate system and the camera coordinate system is established as follows:

The Euler angle is used to describe the posture transformation of the rotating bridge. The beam rotation process is decomposed into three independent rotations around the X, Y, and Z axes, and each rotation is performed with the bridge's own local coordinate system as a reference. Assuming that the rotation order from the camera coordinate system to the bridge's local coordinate system is around the XYZ axes, the corresponding rotation Euler angles are α, β, and γ, respectively, and the corresponding rotation matrices are _RX , _RY , and _RZ , respectively. The total rotation matrix _RC is expressed as follows according to formula (1):

The unit matrix E is used to represent the direction vectors of the three coordinate axes of the camera coordinate system. Taking the camera coordinate system as the observation reference, the direction vectors of the coordinate axes of the camera coordinate system and the direction vectors of the coordinate axes of the cursor coordinate system η _i (i=1, 2, 3) satisfy equation (2):

η _i ＝RC _A Ε＝[r _1i r _2i r _3i ] ^T (2)

Where R _CA is the rotation transformation matrix from the camera coordinate system to the cursor coordinate system; r _1i , r _2i , r _3i are the elements of the 1st, 2nd, and 3rd rows and the i-th column in the rotation matrix R _CA, respectively; E is the coordinate axis matrix of the camera coordinate system, and the row vectors constituting the matrix represent the unit direction vectors of the coordinate axes of the camera coordinate system.

It should be understood that, according to the rigid body space transformation principle, different rotation orders can be used when the camera coordinate system is transformed to the local coordinate system of the bridge, for example, around the X-Z-Y axis. Different rotation orders correspond to different rotation matrices and rotation angles, but the spatial position of the bridge itself before or after rotation will not change due to the change of the rotation order. The rotation order around the X-Y-Z axis cannot be understood as a limitation of the present invention.

The bridge is regarded as a rigid body, and the rigid body motion consists of rotation and translation. Since it is difficult to accurately obtain the spatial position of the rigid body motion with the existing monitoring technology, the inventors consider that the bridge only rotates around its own local coordinate system without translation due to the existence of a center limit during the rotation process, and therefore separate the rotation and translation of the bridge; however, since the local coordinate system of the bridge is difficult to visualize in the image acquisition device, the posture change of the bridge during the rotation process is indirectly determined by means of a three-dimensional orthogonal cursor, and in this process, it is crucial to establish a mapping relationship between the three-dimensional orthogonal cursor beam and its projection on the imaging plane of the image acquisition device;

Taking camera imaging as an example, its imaging principle is briefly described as follows:

Perform central projection on any point in space. Without considering the lens distortion of camera imaging, the transformation relationship between world coordinates ( _XW , _YW , _ZW ), camera coordinates ( _XC , _YC , _ZC ), image coordinates (x, y) and pixel coordinates (u, v) is as shown in formula (3):

Wherein, (u ₀ ,v ₀ ) is the coordinate of the center of the imaging plane of the image acquisition device in the pixel coordinate system; dx and dy represent the lengths of the physical pixels of the photo in the two coordinate axis directions of the pixel coordinate system; K _m is the camera intrinsic parameter matrix; K _T is the camera extrinsic parameter matrix;

K _m is expressed as follows according to formula (4):

In the formula, f is the focal length of the camera, and the camera intrinsic parameters can be obtained through camera calibration.

The camera extrinsic matrix K _T is composed of the rotation matrix R from the camera coordinate system to the world coordinate system and the corresponding translation vector t, which can be expressed as follows according to formula (5):

In this embodiment, the three-dimensional orthogonal cursor is centrally projected onto the optical center of the image acquisition device (the origin of the camera coordinate system). Assuming that the coordinates of the three-dimensional orthogonal cursor origin _OA in the camera coordinate system are (X ₀ , Y ₀ , Z ₀ ), and the camera coordinate system is used as the observation reference, the image coordinates (x ₀ , y ₀ ) of the three-dimensional orthogonal cursor origin projected onto the imaging plane can be expressed as follows according to formula (6):

Assume that the radius vector of the origin _OA of the cursor coordinate system in the camera coordinate system is _t0 = ( _X0 , _Y0 , _Z0 ), _t0 is the translation vector in the camera extrinsic matrix. According to the plane intersection principle, the projection ray l _i of the cursor coordinate system on the imaging plane is the intersection line of the spatial plane determined by the radius vector _t0 and the cursor coordinate axis _ηi with the imaging plane. According to the principle of spatial analytic geometry, the normal vector n _i of the spatial plane determined by the radius vector _t0 and the cursor coordinate axis _ηi can be obtained by formula (7):

According to the normal vector n _i, the analytical expression of the space plane where the radius vector t ₀ and the cursor coordinate axis η _i are located is as follows:

n _i1 x+n _i2 y+n _i3 z＝0 8)

Where n _i1 , n _i2 , and n _i3 are the components of the normal vector _ni of the plane where η _i is located in the X, X, and Z directions of the camera coordinate system, that is, the first, second, and third elements of the normal vector _ni .

According to the plane intersection principle, the mapping information of the cursor coordinate system center projected to the imaging plane is solved, and the analytical expression of the cursor ray projection l _i on the imaging plane is obtained as shown in formula (9):

Since the cursor coordinate system is directional, its projection information is expressed in the form of rays, so the direction angle is used to accurately describe the mapping information. According to the analytical expression of the cursor projection l _i , the mapping relationship between the three-dimensional orthogonal cursor beam and the beam projection is obtained as calculated by (10):

θ _i = atan2(fr _2i -y ₀ r _3i ,fr _1i -x ₀ r _3i ) (10)

Where θ _i is the direction angle of the cursor ray projection l _i ; atan2(·) is the four-quadrant inverse tangent function.

The mapping relationship between the three-dimensional orthogonal cursor beam and the beam projection and the transformation relationship between the cursor coordinate system and the camera coordinate system are formulated as equation (11). According to the direction angle and intersection coordinates of the cursor projection at the initial posture obtained by S2, the simultaneous equations (11) are iteratively solved by using the variational principle and the numerical iteration method to calculate the rotation Euler angles α, β, and γ corresponding to the spatial postures of the three-dimensional orthogonal cursor at different times in the camera coordinate system; the numerical iteration method is preferably the Newton-Raphson numerical iteration method;

According to the solved rotation Euler angles α, β, γ, the rotation matrix R _c0 from the camera coordinate system to the cursor coordinate system at the initial posture of the rotating bridge is determined, and the transformation relationship between the camera coordinate system and the cursor coordinate system at the initial posture of the rotating bridge is obtained as shown in formula (12):

Where R _c0 is the rotation matrix from the camera coordinate system to the cursor coordinate system at the initial posture; is the direction vector of the cursor coordinate system axis at the initial posture, i=1, 2, 3; E is the camera coordinate system axis matrix, and the row vectors constituting the matrix represent the unit direction vector of the camera coordinate system axis.

Using a three-dimensional orthogonal cursor as visual input, the transformation relationship between the cursor coordinate system and the local coordinate system of the bridge is established as shown in formula (13):

[η ₁ ,η ₂ ,η ₃ ] ^T ＝R ₀ [ξ ₁ ,ξ ₂ ,ξ ₃ ] ^T (13)

Wherein: η _i , ζ _i (i=1, 2, 3) represent the direction vectors of the cursor coordinate axis and the bridge local coordinate axis in the same coordinate system respectively; R ₀ is the rotation matrix from the bridge local coordinate system to the cursor coordinate system.

According to the transformation relationship between the camera coordinate system and the cursor coordinate system and the transformation relationship between the cursor coordinate system and the local coordinate system of the rotating bridge, the transformation relationship between the camera coordinate system and the local coordinate system of the bridge at the initial posture is obtained according to formula (14):

In the formula, is the direction vector of the coordinate axis of the local coordinate system of the bridge at the initial posture, i = 1, 2, 3; R ₀ is the rotation transformation matrix of the local coordinate axis of the bridge to the cursor coordinate system at the initial posture, R ₀ satisfies [η ₁ ,η ₂ ,η ₃ ] ^T ＝R ₀ [ξ ₁ ,ξ ₂ ,ξ ₃ ] ^T ; R ₀ ^-1 is the inverse matrix of R ₀ ; R ₀ ^-1 R _c0 represents the rotation transformation matrix of the camera coordinate system to the local coordinate system of the bridge, from which the initial spatial posture of the rotating bridge based on the camera coordinate system can be extracted.

In step S3, an effective mapping relationship solution method is proposed, and a mathematical connection between the three-dimensional orthogonal cursor beam and the image information of its central projection is established, which provides a theoretical basis for the subsequent reconstruction of the spatial posture of the bridge rotation using the three-dimensional orthogonal cursor as a medium.

S4, during the bridge rotation construction process, the image acquisition device continuously acquires the posture images of the bridge rotation at different times, extracts the direction angle and intersection coordinates of the three-dimensional orthogonal cursor beam projected on the imaging plane at different times from the posture images obtained at different times, and uses the variational principle and numerical iteration method to solve the spatial posture of the three-dimensional orthogonal cursor at different times, and obtains the transformation relationship between the camera coordinate system and the local coordinate system of the bridge at different times during the bridge rotation process, and then determines the spatial posture of the bridge rotation at different times (based on the rotation Euler angle of the camera coordinate system);

The transformation relationship between the camera coordinate system and the local coordinate system of the bridge at different times is obtained according to formula (15):

In the formula, is the direction vector of the coordinate axis of the local coordinate system of the bridge at the kth shooting moment, i=1, 2, ₃ , k=1 ^, 2, 3...; _Rck is the rotation matrix of the camera coordinate system transformed to the cursor coordinate system at the kth shooting moment; _R0-1Rck represents the rotation transformation matrix of the camera coordinate system transformed to the local coordinate system of the bridge at the kth shooting moment, from which the rotational spatial posture (rotation Euler angle) of the rotating bridge based on the camera coordinate system at the kth shooting moment can be extracted.

According to the method of step S3, _Rck is obtained by the following process:

According to the posture images of the rotating bridge at different times, the direction angle and intersection coordinates of the projection of the three-dimensional orthogonal cursor beam ray on the imaging plane at the corresponding posture are determined; according to the mapping relationship, the transformation relationship and the direction angle and intersection coordinates of the projection of the beam ray at different postures, the postures of the orthogonal three-dimensional cursor at different times are solved by using the variational principle and the numerical iteration method, and the transformation relationship between the camera coordinate system and the cursor coordinate system at the kth shooting time is determined as shown in formula (16):

Where _Rck is the rotation transformation matrix from the camera coordinate system to the cursor coordinate system at the kth shooting moment; is the direction vector of the cursor coordinate system axis at the kth shooting moment, i=1, 2, 3, k=1, 2, 3...; E is the camera coordinate system axis unit matrix, and the row vectors constituting the unit matrix represent the direction vector of the camera coordinate system axis.

S5, according to the initial posture of the bridge rotation and the postures at different times during the rotation process obtained in S3-S4, obtain the relative rotation matrix of the postures at different times during the bridge rotation process and the initial posture; set the rotation order of the rotating bridge relative rotation around the local coordinate system of the bridge, and extract the relative rotation Euler angles of the bridge rotation at different times from the relative rotation matrix according to the rotation order;

Define ΔR _0k as the relative rotation transformation matrix of the local coordinate system of the rotating bridge from the initial state to the kth shooting moment (kth image) corresponding to the spatial posture, then and The relationship is expressed as follows according to formula (17):

In the formula, are the direction vectors of the coordinate axes of the local coordinate system of the bridge at the initial posture and the spatial posture corresponding to the k-th shooting moment, respectively, i=1, 2, 3; ΔR _0k is the relative rotation matrix of the local coordinate system of the rotating bridge from the initial posture to the spatial posture corresponding to the k-th shooting moment.

Based on the transformation relationship between the camera coordinate system and the cursor coordinate system constructed in steps S3-S4 and the transformation relationship between the bridge local coordinate system and the cursor coordinate system, and The relationship is further expressed as follows according to formula (17):

Then the relative rotation transformation matrix ΔR _0k of the rotating bridge from the initial state to the posture transformation is determined according to formula (19):

ΔR _0k ＝R ₀ ^-1 R _ck R ₀ R _c0 ^-1 (19)

According to the characteristics of the rotating bridge, the rotation order of the rotating bridge around its own local coordinate system is set to be around the ZYX axis. When the rotation order from the camera coordinate system to the cursor coordinate system is around the XYZ axis, the unique relative rotation Euler angles Δα, Δβ, Δγ can be extracted from the relative rotation matrix ΔR _0k as shown in formula (20):

Wherein, _rij (i=1,2,3; j=1,2,3) represents the component of the i-th row and j-th column in the rotation matrix _ΔR0k .

In step S5, by introducing a specific rotation mode and rotation order suitable for a rotating bridge, the calculation formula for the relative rotation transformation matrix of the bridge rotation posture at different times and the initial posture is derived, from which the relative rotation Euler angles of the rotating bridge posture at different times and the initial posture are separated, thereby achieving accurate monitoring of the rotating bridge structure and providing a reliable mathematical basis for the rotation monitoring of the rotating bridge structure.

According to the design position and initial posture position of the rotating bridge, the target rotation Euler angle of the rotating bridge is calculated according to the above method. When the Euler angle of the bridge rotation around the vertical axis at any time reaches the target rotation Euler angle, the monitoring is completed. The target rotation Euler angle refers to the rotation Euler angle of the local coordinate system of the bridge around the vertical axis when the bridge is assumed to reach the design rotation position of the bridge after one rotation from the initial posture. During the construction process of the bridge rotation, the bridge is commanded to rotate according to the difference between the bridge rotation data obtained by monitoring and the target rotation angle. At the same time, according to the Euler angles of the rotating bridge around the longitudinal and lateral directions obtained by monitoring, the attitude of the bridge is adjusted in time, so that the bridge is finally accurately rotated to the design position.

Embodiment 2;

The present embodiment provides a monitoring system for a bridge rotation monitoring method based on a three-dimensional orthogonal cursor, including:

A cursor module, comprising a three-dimensional orthogonal cursor installed on the rotating bridge through a base, wherein the three-dimensional orthogonal cursor is composed of three laser emitters which are vertically connected to each other and emit light beams of different colors;

An image acquisition module, which uses an image acquisition device to continuously shoot and acquire posture images of a three-dimensional orthogonal cursor installed on the rotating bridge, wherein the posture images include an initial posture image and posture images at different times during the rotation process;

More specifically, the spatial position of the image acquisition device is adjusted to a suitable position outside the rotation range of the bridge to ensure that the three-dimensional orthogonal cursor does not move out of the camera frame during the rotation of the bridge, and the internal parameters of the image acquisition device are calibrated. After the adjustment, the spatial position of the image acquisition device is kept fixed, and the image acquisition device is controlled to continuously capture the posture image of the three-dimensional orthogonal cursor.

An image processing module extracts the direction angle and intersection coordinates corresponding to the projection of the three-dimensional orthogonal cursor beam from all the posture images taken by the image acquisition module;

More specifically, the image is first smoothed and denoised using mean filtering and morphological opening operations, and then the pixels corresponding to the projection of three different color beams are extracted based on the RGB threshold range. The three groups of pixels are iteratively fitted according to the linear function using the random sampling consistency method to obtain fitting lines, and then the fitting expression is verified according to the orthogonal constraint of the three-dimensional cursor. When the error of the coordinates of the intersections of the three fitting lines is less than or equal to 0.1 pixel units, it is considered that the fitting accuracy requirements are met and the final analytical expression of the beam projection is obtained, and the direction angle of the beam projection is obtained, and the mean value of the intersection coordinates of the fitting function is used as the intersection coordinates of the three beam rays. In other embodiments, the MSAC algorithm, PROSAC algorithm, etc. can also be used.

The data processing module calculates the relative rotation Euler angles of the bridge rotation posture at different times relative to the initial posture according to the direction angle and intersection coordinates of the light beam projection obtained by the image processing module;

It should be noted that image processing and data processing are implemented on the edge computing platform. The edge computing platform can be a microcomputer, a laptop, or other computing platform with computing functions. Processing software, such as matlab software, is installed on the edge computing platform. According to the bridge rotation monitoring method based on orthogonal three-dimensional cursor proposed in the present invention, the program for computing image processing and data processing is compiled into the matlab software of the computing platform, and the image saving path of the image acquisition device is set to the source file specified by the program. Then, the program is started to analyze and identify the image, and the direction angle and intersection coordinates of the beam projection are obtained. The matlab program further calculates the relative rotation Euler angle of the bridge rotation posture at different times relative to the initial posture according to the beam projection information, and obtains the time history data of the target bridge rotation. In a specific embodiment, the CPU of the computing platform is i7-12700@2.10GHz. According to the bridge rotation monitoring method based on orthogonal three-dimensional cursor of the present invention, those skilled in the art can write a corresponding calculation program in matlab software, which will not be repeated here. According to the simulation test of the embodiment, the time from capturing the image to obtaining its corresponding rotation parameters is about 0.15s, which meets the engineering real-time and specification requirements of rotation measurement.

The data display module displays the relative rotation Euler angles and target rotation Euler angles of the rotating bridge at different times; comparing the relative rotation Euler angles with the target rotation Euler angles can guide the bridge rotation construction.

Compared with the existing methods, the shooting and acquisition process of the image acquisition device in this method is continuous and real-time, and then the image information containing the three-dimensional orthogonal cursor is calculated on the edge computing platform through the above method. The calculation time is short, and the relative rotation Euler angle can be obtained at a faster speed, meeting the real-time requirements of the project.

Embodiment 3;

In order to verify the real-time monitoring of the bridge rotation posture, a simplified bridge rotation model was constructed in the CAD software for simulation. The model is a rotating T-structure bridge.

The swivel T-structure bridge pier is 16m tall, the upper turntable is a 9m×12m rectangle, and the three-dimensional orthogonal cursor is arranged on the bridge pier base. To simplify the calculation, the cursor coordinate system is completely parallel to the local coordinate system of the bridge. Then the conversion relationship between the local coordinate system of the bridge and the cursor coordinate system is [η ₁ ,η ₂ ,η ₃ ] ^T ＝R ₀ [ξ ₁ ,ξ ₂ ,ξ ₃ ] ^T , where R ₀ is actually the unit matrix. The image acquisition device is a camera, the center of the camera coincides with the center of the coordinate system of the CAD workspace, and the camera focal length f is set to 0.13m. During the simulation, the spatial position of the rotating bridge based on the camera coordinate system (camera coordinate system) at the initial state is set as a range of random values, the random ranges of _{the XC} and _YC coordinates are (-100, 100), and the random range of the _ZC coordinate is (0.13, 100.13), and the spatial posture of the initial state of the rotating bridge relative to the camera coordinate system is randomly given between -90° and 90° (the spatial position parameters of the rotating bridge do not participate in the calculation of the spatial posture and relative rotation, and are only used to simulate the camera layout position). The actual construction monitoring of the bridge rotation is simulated, and the initial posture of the rotating bridge is rotated relative to each other. The rotation Euler angles Δα and Δβ are randomly changed within ±1°, Δγ increases by 0.5° each time, and a random value of ±0.5° is introduced.

For distinction, this embodiment sets three different working conditions as shown in Table 1; taking working condition 1 as an example, in the initial state, the coordinates of the origin of the local coordinate system of the rotating bridge in the camera coordinate system are (57.54m, 9.97m, 96.45m), and the spatial posture relative to the camera coordinate system is α=0.58°, β=-0.40°, γ=0.25°. The relative rotation angle of the rotating bridge relative to the initial state is randomly given as Δα=-0.0162°, Δβ=-0.0017°, Δγ=0.4366°. According to the set working condition group, the direction angle and intersection point coordinates of the orthogonal three-dimensional cursor ray projection are obtained based on the CAD simulation software. Based on steps S3-S5, the relative rotation matrix ΔR _0k is calculated, and the calculated value of the rotation Euler angle is extracted from it. The calculated value is compared with the actual design value to analyze the error. The calculated values of the relative rotation angle under different working conditions are shown in Table 1.

Table 1 Spatial posture of bridge rotation in camera coordinate system

As shown in Table 1, under different working conditions, the calculated values of the relative rotation Euler angles are consistent with the design values, and the calculated errors are within ^10-15 , and the rotation monitoring of the rotating bridge meets the accuracy requirements. The design and calculated values of the rotation angles in Table 1 actually have multiple decimal places, and all data are not provided due to text limitations. For example, for working condition 1, when the design value of the rotation angle α around the X-axis during the first rotation is -0.0162 (rad), the error between the calculated value and the design value is 3.6705* ^10-15 . Based on the acquired projection information of the three-dimensional orthogonal cursor beam in the initial posture and any posture during the rotation process, the test time for solving the relative rotation Euler angle from the initial posture to any posture is about 0.15s, which meets the real-time monitoring requirements of the spatial position of the rotating bridge.

In addition to being used for spatial rotation monitoring of rotating bridges, the monitoring method proposed in this patent can also be widely used in various technical fields for monitoring the spatial posture transformation of target objects. For example, by monitoring the camera's own rotation angle, pitch angle and yaw angle, the camera's posture transformation can be inferred to realize the monocular visual odometer function. This monitoring method can also be extended to the field of aircraft posture estimation technology, posture tracking technology in the field of virtual reality, etc., and has huge application potential.

The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims (10)

1. A bridge rotation monitoring method based on three-dimensional orthogonal cursors, characterized in that it includes the following steps: S1, deploy at least one three-dimensional orthogonal cursor capable of emitting light beams on the rotating bridge, and deploy an image acquisition device outside the rotating range of the bridge; establish a bridge local coordinate system and a camera coordinate system on the bridge and the image acquisition device respectively, and establish a cursor coordinate system with the intersection of the three-dimensional orthogonal cursor light beams as the origin and the three light beam directions as the coordinate axes; S2, before the bridge rotation construction, the image acquisition device captures and acquires an image containing three-dimensional orthogonal cursor beam rays as an initial posture image, and extracts the direction angle and intersection coordinates of the three-dimensional orthogonal cursor beam projected on the imaging plane at the initial posture from the initial posture image; S3, using the rigid body space transformation principle to establish the transformation relationship between the cursor coordinate system and the camera coordinate system, and establishing the mapping relationship between the three-dimensional orthogonal cursor light beam and the light beam projection according to the imaging principle. According to the transformation relationship, the mapping relationship and the direction angle and the intersection coordinates of the light beam projection at the initial posture obtained in S2, the initial posture of the three-dimensional orthogonal cursor is solved by using the variational principle and the numerical iteration method. According to the initial posture of the three-dimensional orthogonal cursor and the transformation relationship between the cursor coordinate system and the local coordinate system of the bridge, the transformation relationship between the camera coordinate system and the local coordinate system of the bridge at the initial posture is obtained, and then the initial posture of the bridge rotation is determined; S4, during the bridge rotation construction process, the image acquisition device continuously acquires posture images of the bridge rotation at different times, extracts the direction angles and intersection coordinates of the three-dimensional orthogonal cursor beams projected on the imaging plane at different times from the posture images obtained at different times, and uses the variational principle and numerical iteration method to solve the spatial postures of the three-dimensional orthogonal cursor at different times, and obtains the transformation relationship between the camera coordinate system and the local coordinate system of the bridge at different times during the bridge rotation process, thereby determining the spatial postures of the bridge rotation at different times; S5, based on the initial posture of the bridge rotation obtained in S3-S4 and the spatial posture at different times during the rotation process, obtain the relative rotation matrix of the posture of the bridge at different times during the rotation process and the initial posture; set the rotation order of the bridge relative rotation around its own local coordinate system, and extract the relative rotation Euler angles of the bridge rotation at different times from the relative rotation matrix according to the rotation order. 2. The bridge rotation monitoring method based on a three-dimensional orthogonal cursor according to claim 1 is characterized in that: in step S1, the three-dimensional orthogonal cursor is composed of three laser emitters connected vertically to each other; the three laser emitters respectively emit lasers of different colors; There is a height difference between the layout position of the image acquisition device and the layout position of the three-dimensional orthogonal cursor; during the entire process of bridge rotation construction, the spatial position of the image acquisition device is kept unchanged, so that the three-dimensional orthogonal cursor is kept within the field of view of the image acquisition device. 3. The bridge rotation monitoring method based on three-dimensional orthogonal cursor according to claim 1 is characterized in that the direction angle and intersection coordinates of the orthogonal three-dimensional cursor beam projected on the imaging plane are obtained by the following method: Determine the RGB threshold range of the three color light beams, and extract the pixel points corresponding to the three color light beams from the posture image according to the corresponding RGB threshold range; use the random sampling consensus algorithm to iteratively fit the three groups of pixel points extracted according to the linear function, and obtain several analytical expressions of the corresponding light beam projection fitting lines. When the error of the coordinates of the intersection points of the three fitting lines is less than or equal to 0.1 pixel, the analytical expression of the light beam projection fitting line that meets the accuracy requirement is obtained, and the direction angle of the light beam projection on the imaging plane is obtained, and the average value of the coordinates of the intersection points of the fitting lines is taken as the intersection coordinates of the light beam projection. 4. The bridge rotation monitoring method based on three-dimensional orthogonal cursor according to claim 1 is characterized in that: in step S3, according to the imaging principle, the mapping relationship between the light beam and the light beam projection is obtained by the following method: Project the 3D orthogonal cursor to the center of the camera coordinate system. Assuming that the coordinates of the 3D orthogonal cursor origin _OA in the camera coordinate system are (X ₀ , Y ₀ , Z ₀ ), and the radius vector t ₀ = (X ₀ , Y ₀ , Z ₀ ), the image coordinates (x ₀ , y ₀ ) of the 3D orthogonal cursor origin projected to the imaging plane are expressed as follows according to formula (3.1): Where f is the focal length of the camera; According to the principles of spatial analytic geometry, the normal vector n _i of the spatial plane determined by the radius vector t ₀ and the cursor coordinate axis η _i is obtained according to formula (3.2): Where r _1i , r _2i , and r _3i are the elements of the 1st, 2nd, and 3rd rows and the i-th column in the rotation transformation matrix from the camera coordinate system to the cursor coordinate system; The analytical expression of the space plane where the radius vector _t0 and the cursor coordinate axis _ηi are located is as follows: n _i1 x+n _i2 y+n _i3 z＝0 (3.3) Where n _i1 , n _i2 , and n _i3 are the first, second, and third elements of the normal vector n _i , respectively; By combining the analytical expression of the space plane determined by the radius vector _t0 and the cursor coordinate axis _ηi with the analytical expression of the imaging plane, the analytical expression of the beam projection l _i on the imaging plane can be obtained as (3.4): Where (x, y) is the coordinate of the imaging plane; According to the analytical expression of the beam projection l _i , the direction angle of the beam projection l _i is obtained, and the mapping relationship between the three-dimensional orthogonal cursor beam and the beam projection is obtained as shown in formula (3.5): θ _i = atan2(fr _2i -y ₀ r _3i ,fr _1i -x ₀ r _3i ) (3.5) Where _θi is the direction angle of the light beam projection li; atan2(·) is the four-quadrant inverse tangent function. 5. The bridge rotation monitoring method based on the three-dimensional orthogonal cursor as claimed in claim 1 is characterized in that: in step S3, the mapping relationship between the three-dimensional orthogonal cursor light beam and the light beam projection and the transformation relationship between the cursor coordinate system and the camera coordinate system are solved by the simultaneous equations, and the direction angle and intersection coordinates of the light beam projection at the initial posture obtained in step S2 are used to solve the simultaneous equations by using the numerical iteration method to obtain the rotation Euler angles α, β, γ corresponding to the three-dimensional orthogonal cursor in the camera coordinate system at the initial posture; According to the solved rotation Euler angles α, β, γ, the transformation relationship between the camera coordinate system and the cursor coordinate system at the initial posture is obtained as shown in formula (3.6): Where R _c0 is the rotation matrix from the camera coordinate system to the cursor coordinate system at the initial posture; is the direction vector of the coordinate axis of the cursor coordinate system at the initial posture, i=1, 2, 3; E is the unit matrix of the coordinate axis of the camera coordinate system, and the row vectors constituting the unit matrix represent the direction vector of the coordinate axis of the camera coordinate system. 6. The bridge rotation monitoring method based on three-dimensional orthogonal cursor as described in claim 1 is characterized in that: in step S3, according to the transformation relationship between the camera coordinate system and the cursor coordinate system and the transformation relationship between the cursor coordinate system and the local coordinate system of the bridge as shown in formula (3.7), the transformation relationship between the camera coordinate system and the local coordinate system of the bridge at the initial posture is obtained according to formula (3.8), and the initial posture of the bridge rotation is determined according to the transformation relationship: [η ₁ ,η ₂ ,η ₃ ] ^T ＝R ₀ [ξ ₁ ,ξ ₂ ,ξ ₃ ] ^T (3.7) In the formula, is the direction vector of the coordinate axis of the local coordinate system of ^the bridge, i=1, 2, 3; _R0 is the rotation transformation matrix of the local coordinate axis of the bridge to the cursor coordinate system; _R0-1 is the inverse matrix of _R0 ; _η1 , _η2 , _η3 are the direction vectors of the cursor coordinate axis at any time; _ξ1 , _ξ2 , _ξ3 are the direction vectors of the coordinate axis of the local coordinate system of the bridge at any time; _R0-1Rc0 is the ^rotation _{transformation} matrix of the camera coordinate system to the local coordinate system of the bridge; E is the unit matrix of the camera coordinate system, and the row vectors constituting the unit matrix represent the direction vectors of the coordinate axes of the camera coordinate system. 7. The bridge rotation monitoring method based on three-dimensional orthogonal cursor as claimed in claim 1 is characterized in that: in step S4, the transformation relationship between the camera coordinate system and the bridge local coordinate system at different times during the bridge rotation process is obtained according to formula (4.1), and the spatial posture at different times during the bridge rotation process is determined according to the transformation relationship: In the formula, is the direction vector of the coordinate axis of the local coordinate system of the bridge at the kth shooting moment, i=1, 2, ³ , k=1, 2, 3...; _R0 is the rotation transformation matrix of the local coordinate axis of the bridge to the cursor coordinate system; _R0-1 is the inverse matrix of _R0 ; _Rck is the rotation matrix of the camera coordinate system to the cursor coordinate system at the kth shooting moment; _{R0-1 Rck} represents the rotation transformation matrix of the camera coordinate system to the local coordinate system of ^the bridge at the kth shooting moment; E is the unit matrix of the camera coordinate system, and the row vectors constituting the unit matrix represent the direction vector of the coordinate axis of the camera coordinate system. 8. The bridge rotation monitoring method based on three-dimensional orthogonal cursor as claimed in claim 1 is characterized in that: in step S5, according to the initial posture of the bridge rotation obtained in S3-S4 and the spatial posture at different times during the rotation process, during the bridge rotation process, the relative rotation matrix of the bridge local coordinate system between the posture at different times and the initial posture is obtained according to formula (5.1): ΔR _0k ＝R ₀ ^-1 R _ck R ₀ R _ck ^-1 (5.1) Wherein, R ₀ is the rotation transformation matrix of the local coordinate axis of the bridge to the cursor coordinate system; R ₀ ^-1 is the inverse matrix of R ₀ ; R _ck is the rotation matrix of the camera coordinate system to the cursor coordinate system at the kth shooting moment, k = 1, 2, 3, etc.; ΔR _0k is the relative rotation matrix of the local coordinate system of the rotating bridge from the initial posture to the spatial posture corresponding to the kth shooting moment. 9. The bridge rotation monitoring method based on three-dimensional orthogonal cursor as claimed in claim 1 is characterized in that: in step S5, the rotation order of the rotating bridge around the local coordinate system of the bridge is set to be around the Z-Y-X axis, and when the rotation order from the camera coordinate system to the cursor coordinate system is around the X-Y-Z axis, the relative rotation Euler angles Δα, Δβ, Δγ are extracted from the relative rotation matrix as shown in formula (5.2): Where Δα, Δβ, and Δγ are the Euler angles of the rotating bridge around the X, Y, and Z axes of the local coordinate system of the bridge, respectively; s _mn is the element in the mth row and nth column of the relative rotation matrix, m = 1, 2, 3; n = 1, 2, 3. 10. The monitoring system of the bridge rotation monitoring method based on three-dimensional orthogonal cursor according to any one of claims 1 to 9, characterized in that it comprises: A cursor module includes a three-dimensional orthogonal cursor fixedly installed on the bridge through a base, wherein the three-dimensional orthogonal cursor is composed of three laser transmitters that are vertically connected to each other and emit light beams of different colors; An image acquisition module, which uses an image acquisition device to continuously shoot and acquire posture images of a three-dimensional orthogonal cursor installed on the rotating bridge, wherein the posture images include an initial posture image and posture images at different times during the rotation process; An image processing module extracts the direction angle and intersection coordinates corresponding to the projection of the three-dimensional orthogonal cursor beam from all the posture images taken by the image acquisition module; The data processing module calculates the relative rotation Euler angles of the bridge rotation posture at different times relative to the initial posture according to the direction angle and intersection coordinates of the light beam projection obtained by the image processing module; The data display module displays the relative rotation Euler angles and target rotation Euler angles of the rotating bridge at different times.