CN114998422B - High-precision rapid three-dimensional positioning system based on error compensation model - Google Patents
High-precision rapid three-dimensional positioning system based on error compensation model Download PDFInfo
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Abstract
The invention relates to a high-precision rapid three-dimensional positioning system based on an error compensation model, which belongs to the technical field of camera computer vision and comprises system hardware and high-precision three-dimensional positioning software; the system hardware comprises a robot manipulator, a monocular industrial camera, a processor, a marker and an electric lifting base, wherein the monocular industrial camera acquires an initial depth value of a feature circle center of the marker and the monocular industrial camera by capturing a single picture, substitutes a current pixel distance ratio into an error compensation model to obtain a depth error compensation value, adds the depth error compensation value to the initial depth value to realize depth measurement, acquires two-dimensional positioning through a two-dimensional positioning algorithm after depth information is acquired, and finally realizes three-dimensional positioning through high-precision three-dimensional positioning software; the processor provides a carrier. The invention solves the problems of complex design of the marker, lower acquisition precision of depth information, needing other sensors, and the like, simplifies the installation requirement and improves the universality.
Description
Technical Field
The invention relates to a high-precision rapid three-dimensional positioning system based on an error compensation model, and belongs to the technical field of camera computer vision.
Background
With the development of society and the continuous progress of technology, machine vision positioning systems are widely used in various fields such as vision servoing of robots, three-dimensional online dimension measurement, and the like. The current industrial robot vision positioning system is divided into a binocular vision system, a monocular vision system, a structured light vision system and a depth camera system, wherein the monocular camera has the advantages of low price, simple structure and the like, and is widely applied to vision positioning. However, the monocular vision system has difficulty in acquiring depth information, so that a high-precision and rapid depth measurement method is a key for improving the positioning accuracy of the monocular vision system. However, the existing monocular camera positioning technology is largely divided into a two-dimensional positioning method with known depth and a method of designing complex markers to acquire three-dimensional information. The two-dimensional positioning method with known depth is simple, positioning accuracy is high, and the workpiece is positioned and grasped through the infrared sensor and the industrial camera in order to solve the problem that accurate depth information is difficult to obtain by a monocular camera, for example, a monocular vision-based workpiece pose recognition and grasping system. The method mainly obtains the depth information in advance or obtains the depth information through the sensor, increases the industrial cost, has high sensor installation requirements and the like, and does not fundamentally solve the problem that the monocular camera is difficult to obtain the depth information. The method for acquiring the three-dimensional information by designing the complex marker can acquire the three-dimensional information of the workpiece under the world coordinate system without adding any auxiliary equipment. For example, the problem of measuring the three-dimensional distance between a lens of a monocular camera and a target mark is solved by designing a Aruco mark, and the problem of measuring the depth of the monocular camera is realized; lv Re a monocular distance measurement positioning method based on standard balls, calculating camera coordinate values of the standard balls by extracting outlines of the three standard balls, and then realizing distance measurement positioning of the robot on a working machine clamp by a hand-eye calibration transformation matrix. The method is complex in design of the marker, has high requirements on the accuracy of the marker, or obtains depth information in a translation mode, is low in efficiency, and has low obtained three-dimensional positioning accuracy, especially depth information.
In view of the above, the invention provides a high-precision rapid three-dimensional positioning system based on an error compensation model, which solves the problems of complex design of a marker, lower acquisition precision of depth information, the need of other sensors and the like. The method comprises the steps of obtaining the radius of a mark feature circle under a pixel coordinate system and a world coordinate system, calculating a pixel distance ratio, calculating the distance between the feature circle and a camera by using a high-precision and rapid depth measurement algorithm, compensating calculation deviation caused by accidental factors such as installation by means of an error loss model, finally obtaining depth information of the camera, obtaining accurate two-dimensional positioning by a two-dimensional positioning algorithm after obtaining the depth information, and sending deviation values in three directions of XYZ to a controller of a robot for pose adjustment, so that three-dimensional positioning is achieved.
Disclosure of Invention
The invention aims to provide a high-precision rapid three-dimensional positioning system based on an error compensation model, which solves the problems of complex design of a marker, lower acquisition precision of depth information, need of other sensors and the like; the accurate measurement of depth is realized based on a high-precision and rapid depth measurement algorithm by capturing a single frame image and detecting the circle center and the radius of a feature circle, an error compensation model is established for eliminating errors caused by the fact that a measurement plane is not parallel to a camera imaging plane and the like due to the installation inclination of a camera, accurate two-dimensional positioning is obtained through a two-dimensional positioning algorithm after accurate depth information is obtained, and deviation values in three directions of XYZ are sent to a controller of a robot for pose adjustment, so that the rapid and high-precision measurement of three-dimensional distance is realized.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
The high-precision rapid three-dimensional positioning system based on the error compensation model comprises system hardware and high-precision three-dimensional positioning software; the system hardware comprises a robot manipulator, a monocular industrial camera, a processor, a marker and an electric lifting base, wherein the monocular industrial camera is fixed at the tail end of the robot manipulator, the marker is arranged on the electric lifting base capable of automatically lifting up and down, and the initial position of the marker is located under the monocular industrial camera; the monocular industrial camera acquires the characteristic circle center of the marker and the initial depth value of the monocular industrial camera by capturing a single picture, substitutes the current pixel distance ratio into an error compensation model to obtain a required depth error compensation value in order to solve the problem that an imaging plane and a plane where the marker is positioned are not parallel, adds the depth error compensation value to the initial depth value to realize high-precision and rapid depth measurement, acquires accurate two-dimensional positioning through a two-dimensional positioning algorithm after depth information is acquired, and finally realizes three-dimensional positioning through high-precision three-dimensional positioning software; the processor provides a carrier for data acquisition, storage and initial depth measurement and error compensation model calculation.
The technical scheme of the invention is further improved as follows: the monocular industrial camera includes a camera and a lens for capturing an image of a marker.
The technical scheme of the invention is further improved as follows: the high-precision three-dimensional positioning software comprises two functions of depth measurement and two-dimensional positioning, wherein the depth measurement is used for measuring the depth of a feature circle on a marker, and the two-dimensional positioning is used for calculating the accurate deviation of the xy direction of the feature circle after obtaining the depth information of the feature circle.
The technical scheme of the invention is further improved as follows: the high-precision rapid three-dimensional positioning system realizes the functions by the following steps:
Step 1, fixing a monocular industrial camera at the tail end of a robot manipulator, so that the xy direction of the robot manipulator is parallel to the xy direction of a monocular industrial camera pixel coordinate system;
Step 2, placing the marker under the monocular industrial camera, and automatically controlling the electric lifting base to keep a fixed distance between the surface of the marker and the lens; defining a target position to which the robot manipulator is expected to reach as D i (i=1, 2, …, n), and acquiring an image of a marker of the corresponding position as I i (i=1, 2, …, n);
And 3, in the operation process of the robot, starting a monocular industrial camera after reaching the vicinity of the target position D i each time, adaptively adjusting the exposure degree, acquiring a marker image in real time, and then carrying out three-dimensional high-precision positioning through high-precision three-dimensional positioning software.
The technical scheme of the invention is further improved as follows: the specific steps of performing three-dimensional high-precision positioning by the high-precision three-dimensional positioning software in the step 3 are as follows:
Step 3.1, calculating an initial value of depth information according to the marker image: after the marker image is acquired, a marker feature circle is extracted by using a circular detection algorithm, and a pixel distance ratio is calculated according to the radius of the feature circle under a world coordinate system and a pixel coordinate system and the pixel coordinate of a circle center, so that preliminary estimation of depth is realized;
step 3.2, compensating errors based on the error compensation model: since the depth information preliminarily estimated in step 3.1 is calculated under the condition that the imaging plane of the camera and the plane of the feature circle are parallel, it is difficult to strictly perform according to the conditions in reality; in order to overcome the problem of precision reduction caused by failure to meet the conditions, adding the compensation value calculated by the proposed error compensation model to the initial depth calculation value, thereby obtaining a high-precision depth calculation result;
Step 3.3, high-precision three-dimensional positioning: after the depth calculation is completed, the target position marker image is acquired according to the monocular industrial camera and is compared with the currently measured depth value, Z-direction deviation is obtained, meanwhile, the accurate deviation in the xy direction is calculated through a two-dimensional plane positioning algorithm, and the deviation values in the three directions of XYZ are sent to a controller of the robot for pose adjustment, so that three-dimensional high-precision positioning of the robot is achieved.
The technical scheme of the invention is further improved as follows: the specific steps of the step 3.1 comprise:
Step 3.1.1, calculating a pixel distance ratio: according to the pinhole imaging model and the camera imaging principle, the radius of a feature circle under a world coordinate system, the radius under a pixel coordinate system and the connecting line of the camera optical center and the circle center form a similar triangle, let H c denote the distance from the optical center of the convex lens to an imaging object, H w denote the distance from the optical center of the convex lens to a real object, X c denote the length of the object in the pixel coordinate system, and X w denote the real size of the object, so that the following relation can be obtained:
under the condition of ensuring that the imaging plane of the camera and the characteristic circle plane of the marker are parallel, the circle center of the characteristic circle at the position a is (u 1, v 1), and the circle center of the characteristic circle at the position b is (u 2, v 2), the pixel distance ratio is:
Step 3.1.2, preliminarily estimating the depth of the feature circle: after the pixel distance ratio is obtained, the depth calculation formula can be expressed as:
f u is the result of camera internal reference calibration.
The technical scheme of the invention is further improved as follows: the specific steps of the step 3.2 comprise:
Step 3.2.1, constructing an error compensation model, wherein the depth information calculated in step 3.1 is calculated under the condition that the imaging plane of the camera and the plane of the feature circle are assumed to be parallel, but is difficult to strictly perform according to the assumption in reality; in order to solve the problem of precision reduction caused by failure to meet the conditions, an error compensation model is constructed to perform error compensation, and the error compensation model is set as follows:
E＝f(Hw) (4)
the evaluation criteria e of the error model are:
e＝E-Er (5)
Wherein E r represents a true error value, E represents a calculated error value, and therefore, curve fitting of error and pixel distance ratio can be carried out through a least square method, so that depth error can be accurately obtained; let the fitting polynomial be:
y＝a0+a1x+a2x2...+ak-1xk-1+akxk (6)
step 3.2.2, simplifying an error compensation model, wherein the value of a i in the above formula ensures that the sum of the distances from each point to the curve is minimum, namely the square sum of deviation R 2 is minimum, and constructing a bias function by the above formula:
the partial derivative of a i is calculated for the above equation, which yields:
simplifying the above into a matrix form:
X*A＝Y (9)
to reduce the amount of computation, only k=3 may be computed, for which the depth measurement can be modified as:
Zr＝zc1+Y (10)
The high-precision rapid depth measurement result can be realized through the formula.
The technical scheme of the invention is further improved as follows: the specific steps of the step 3.3 include:
step 3.3.1, when the robot reaches a specified target position, acquiring a picture, sending the picture to high-precision three-dimensional positioning software, and comparing the picture with a standard picture acquired by the target position;
Step 3.3.2, simultaneously calculating the depth of the target position standard image and the depth measurement result of the current image, and subtracting the depth measurement result and the depth measurement result to obtain Z-direction deviation;
Step 3.3.3, the characteristic circle center of the standard image is marked as C 1＝(Uo,Vo), the circle center of the current image is marked as C n＝(Un,Vn), and the two-dimensional position error can be obtained through the following formula by the pixel distance ratio:
At the moment, the calculated error is sent to a robot controller to control the robot to adjust the pose so as to realize the rapid high-precision three-dimensional positioning of the robot;
The high-precision rapid three-dimensional positioning system based on the error compensation model is used for realizing accurate depth measurement based on a high-precision rapid depth measurement algorithm by capturing a single frame image and detecting the circle center and the radius of a feature circle, and in order to eliminate errors caused by the fact that a camera is installed obliquely and a measurement plane is not parallel to a camera imaging plane and the like, an error compensation model is built, after accurate depth information is obtained, a two-dimensional plane positioning algorithm is used for calculating accurate deviation in an xy direction, and deviation values in three directions of XYZ are sent to a controller of a robot for pose adjustment, so that three-dimensional high-precision positioning of the robot is realized.
By adopting the technical scheme, the invention has the following technical effects:
The invention simplifies the monocular camera positioning process, can realize high-precision rapid three-dimensional distance measurement by capturing a single frame image and detecting the circle center and the radius of the characteristic circle, and omits the need of designing complex markers to acquire the three-dimensional distance information of an object.
According to the invention, the industrial cost can be greatly reduced, the high-precision and rapid three-dimensional distance measurement can be realized only by one industrial camera and the circle center calibration plate, and the extra consumption of acquiring object depth information by installing an infrared range finder is omitted.
The invention uses an error compensation model, does not need absolute parallelism of the imaging plane of the camera and the plane of the calibration plate, simplifies the installation requirement and improves the universality.
Drawings
FIG. 1 is a flow chart of a system method of the present invention;
FIG. 2 is a schematic diagram of the system method of the present invention;
FIG. 3 is a block diagram of a hardware system of the present invention;
The robot comprises a robot manipulator, a monocular industrial camera, a processor, a marker, an electric lifting base and a marker, wherein the robot manipulator, the monocular industrial camera, the processor, the marker and the electric lifting base are arranged in sequence.
Detailed Description
The invention is further described in detail below with reference to the attached drawings and specific examples:
The high-precision rapid three-dimensional positioning system based on the error compensation model is shown in figures 1-3, and comprises system hardware and high-precision three-dimensional positioning software; the system hardware comprises a robot manipulator 1, a monocular industrial camera 2, a processor 3, a marker 4 and an electric lifting base 5, wherein the monocular industrial camera 2 is fixed at a certain position at the tail end of the robot manipulator 1, the marker 4 is arranged on the electric lifting base 5 capable of automatically lifting up and down, and the initial position of the marker 4 is positioned under the monocular industrial camera 2; the monocular industrial camera 2 acquires the characteristic circle center of the marker 4 and the initial depth value of the monocular industrial camera 2 by capturing a single picture, in order to overcome the problem that an imaging plane and a plane where the marker 4 is positioned are not parallel, the calculated depth initial value is added with a compensation value obtained by an error compensation model, the high-precision and rapid depth measurement can be realized by adding the initial depth value with the depth error compensation value, after depth information is obtained, accurate two-dimensional positioning is obtained by a two-dimensional positioning algorithm, and finally three-dimensional positioning is realized by high-precision three-dimensional positioning software; the processor 3 provides a carrier for data acquisition, storage and initial depth measurement and error compensation model calculation.
Preferably, the processor is mainly used for realizing data acquisition, storage and initial depth measurement and providing a carrier for error compensation model calculation. In this embodiment, the processor is a personal PC.
Preferably, the marker 4 is used for an image of the depth measurement of the monocular industrial camera 2, a marker image is captured by the monocular industrial camera 2, and the radius length of the center of a characteristic circle on the marker 4 under an image coordinate system is extracted to realize the depth measurement. In this embodiment, the marker is a circle center calibration plate.
Preferably, the monocular industrial camera 2 is composed of a camera and a lens, and is mainly used for collecting the image of the marker 4. In this embodiment, the camera is a large constant MER-503-20GM-P camera, the resolution is 2448 (H) ×2048 (V), the frame rate is 20fps, and the data interface is GIge.
Preferably, the high-precision three-dimensional positioning software is mainly divided into two functions of depth measurement and two-dimensional positioning, wherein the depth measurement is mainly used for measuring the depth of the feature circle on the marker, and the two-dimensional positioning function is mainly used for calculating the accurate deviation of the xy direction of the feature circle after obtaining the depth information.
Preferably, the electric lifting base 5 is mainly used for supporting the marker, and automatically controls the electric lifting base to keep a fixed distance between the surface of the marker and the lens.
The high-precision rapid three-dimensional positioning system realizes the functions by the following steps:
step 1, fixing a monocular industrial camera 2 at the tail end of a robot manipulator 1, so that the xy direction in a coordinate system of the robot manipulator 1 is parallel to the xy direction of a camera pixel coordinate system; in this embodiment, the manipulator is a four-degree-of-freedom serial-parallel mechanism, and the included angle between the manipulator coordinate system and the camera pixel coordinate system is compensated by the rotating motor of the four-degree-of-freedom serial-parallel mechanism, and the compensated included angle is 81.5 °.
Step 2, placing the marker 4 under the monocular industrial camera 2, and automatically controlling the electric lifting base 5 to keep a fixed distance between the surface of the marker 4 and the lens; defining a target position to which the robot manipulator 1 is expected to reach as D i (i=1, 2, …, n), and acquiring an image of the marker 4 at the corresponding position as I i (i=1, 2, …, n); in this embodiment, the number of target positions is 5, 5 marker images corresponding to the positions are collected, and the marker images are stored in a database.
And 3, in the operation process of the robot, starting the monocular industrial camera 2 after reaching the vicinity of the target position D i each time, adaptively adjusting the exposure degree, acquiring a marker image in real time, and then carrying out three-dimensional high-precision positioning through high-precision three-dimensional positioning software.
Step 3.1, calculating an initial value of depth information according to the marker image: after the marker image is acquired, a marker feature circle is extracted by using a circular detection algorithm, and a pixel distance ratio is calculated according to the radius of the feature circle under a world coordinate system and a pixel coordinate system and the pixel coordinate of a circle center, so that preliminary estimation of depth is realized; in the embodiment, the camera stores the image with the marker, and utilizes EDcircle circle detection algorithm to realize calculation of the radius and center coordinates of the feature circle, wherein the distance between two feature circles in the pixel coordinate system is 102.3pixel, the distance between two feature circles in the world coordinate system is 7.5mm, and therefore the pixel distance ratio is 13.64pixel/mm. By camera calibration, fu is 3520.7431, the current depth is 258.0mm.
The specific steps of the step 3.1 comprise:
Step 3.1.1, calculating a pixel distance ratio: according to the pinhole imaging model and the camera imaging principle, the radius of a feature circle under a world coordinate system, the radius under a pixel coordinate system and the connecting line of the camera optical center and the circle center form a similar triangle, let H c denote the distance from the optical center of the convex lens to an imaging object, H w denote the distance from the optical center of the convex lens to a real object, X c denote the length of the object in the pixel coordinate system, and X w denote the real size of the object, so that the following relation can be obtained:
under the condition of ensuring that the imaging plane of the camera and the characteristic circle plane of the marker are parallel, the circle center of the characteristic circle at the position a is (u 1,v1), the circle center of the characteristic circle at the position b is (u 2,v2), and the pixel distance ratio is:
Step 3.1.2, preliminarily estimating the depth of the feature circle: after the pixel distance ratio is obtained, the depth calculation formula can be expressed as:
f u is the result of camera internal reference calibration.
Step 3.2, compensating errors based on the error compensation model: since the depth information preliminarily estimated in step 3.1 is measured under the condition that the imaging plane of the camera and the plane of the feature circle are parallel, it is difficult to strictly perform according to the conditions in reality; in order to overcome the problem of precision reduction caused by failure to meet the conditions, the error calculated by the error compensation model is added to the initial depth calculation value, so that a high-precision depth calculation result is obtained; in this embodiment, the inclination angle of the camera imaging plane and the plane on which the feature circle is located in the X direction is 2.43 ° and the inclination angle of the Y direction is 1.98 °. The error compensation model is fitted through the pixel distance ratio and the calculated error through a least square method, and although the higher the order of the model is, the higher the accuracy is, the more complex the calculation process is, for this purpose, the two orders are generally selected, and the parameters of the model are K 1＝0.2144,K2＝-5.584,K3 = 36.28 respectively.
The specific steps of the step 3.2 comprise:
Step 3.2.1, constructing an error compensation model, wherein the depth information calculated in step 3.1 is calculated under the condition that the imaging plane of the camera and the plane of the feature circle are assumed to be parallel, but is difficult to strictly perform according to the assumption in reality; in order to solve the problem of precision reduction caused by failure to meet the conditions, an error compensation model is constructed to perform error compensation, and the error compensation model is set as follows:
E＝f(Hw) (4)
the evaluation criteria e of the error model are:
e＝E-Er (5)
Wherein E r represents a true error value, E represents a calculated error value, and therefore, curve fitting of error and pixel distance ratio can be carried out through a least square method, so that depth error can be accurately obtained; let the fitting polynomial be:
y＝a0+a1x+a2x2...+ak-1xk-1+akxk (6)
step 3.2.2, simplifying an error compensation model, wherein the value of a i in the above formula ensures that the sum of the distances from each point to the curve is minimum, namely the square sum of deviation R 2 is minimum, and constructing a bias function by the above formula:
the partial derivative of a i is calculated for the above equation, which yields:
simplifying the above into a matrix form:
X*A＝Y (9)
to reduce the amount of computation, only k=3 may be computed, for which the depth measurement can be modified as:
Zr＝zc1+Y (10)
The high-precision rapid depth measurement result can be realized through the formula.
Step 3.3, high-precision three-dimensional positioning: after the depth estimation is completed, the target position marker image is acquired according to the monocular industrial camera 2 and is compared with the currently measured depth value, Z-direction deviation is obtained, meanwhile, the accurate deviation in the xy direction is calculated through a two-dimensional plane positioning algorithm, and the deviation values in the three directions of XYZ are sent to a controller of the robot for pose adjustment, so that three-dimensional high-precision positioning of the robot is realized. In the embodiment, the deviation in the Z direction is calculated to be 0.35mm, the deviation in the X direction is calculated to be 0.48mm, the deviation in the y direction is calculated to be-1.01 mm, the deviation is sent to a four-degree-of-freedom serial-parallel mechanism, and three-dimensional error compensation is realized through movement of three motors.
The specific steps of the step 3.3 include:
step 3.3.1, when the robot reaches a specified target position, acquiring a picture, sending the picture to high-precision three-dimensional positioning software, and comparing the picture with a standard picture acquired by the target position;
Step 3.3.2, simultaneously calculating the depth of the target position standard image and the depth measurement result of the current image, and subtracting the depth measurement result and the depth measurement result to obtain Z-direction deviation;
Step 3.3.3, the characteristic circle center of the standard image is marked as C 1＝(Uo,Vo), the circle center of the current image is marked as C n＝(Un,Vn), and the two-dimensional position error can be obtained through the following formula by the pixel distance ratio:
At the moment, the calculated error is sent to a robot controller to control the robot to adjust the pose so as to realize the rapid high-precision three-dimensional positioning of the robot;
The high-precision rapid three-dimensional positioning system based on the error compensation model is used for realizing accurate depth measurement based on a high-precision rapid depth measurement algorithm by capturing a single frame image and detecting the circle center and the radius of a feature circle, and in order to eliminate errors caused by the fact that a camera is installed obliquely and a measurement plane is not parallel to a camera imaging plane and the like, an error compensation model is built, after accurate depth information is obtained, a two-dimensional plane positioning algorithm is used for calculating accurate deviation in an xy direction, and deviation values in three directions of XYZ are sent to a controller of a robot for pose adjustment, so that three-dimensional high-precision positioning of the robot is realized.
Claims (7)
1. A high-precision rapid three-dimensional positioning system based on an error compensation model is characterized in that: the high-precision rapid three-dimensional positioning system comprises system hardware and high-precision three-dimensional positioning software; the system hardware comprises a robot manipulator (1), a monocular industrial camera (2), a processor (3), a marker (4) and an electric lifting base (5), wherein the monocular industrial camera (2) is fixed at the tail end of the robot manipulator (1), the marker (4) is arranged on the electric lifting base (5) capable of automatically lifting up and down, and the initial position of the marker (4) is located under the monocular industrial camera (2); the monocular industrial camera (2) acquires the characteristic circle center of the marker (4) and the initial depth value of the monocular industrial camera (2) by capturing a single picture, substitutes the current pixel distance ratio into an error compensation model to obtain a required depth error compensation value in order to solve the problem that an imaging plane and the plane where the marker (4) is positioned are not parallel, adds the depth error compensation value into the initial depth value to realize high-precision and rapid depth measurement, obtains accurate two-dimensional positioning through a two-dimensional positioning algorithm after obtaining depth information, and finally realizes three-dimensional positioning through high-precision three-dimensional positioning software; the processor (3) provides a carrier for data acquisition, storage and initial depth measurement and error compensation model calculation,
The specific steps of adding the initial depth value with the depth error compensation value to realize high-precision and rapid depth measurement are as follows:
Constructing an error compensation model, and setting the error compensation model as follows:
E＝f(Hw) (4)
the evaluation criteria e of the error model are:
e＝E-Er (5)
Wherein E r represents a true error value, E represents a calculated error value, and therefore, curve fitting of error and pixel distance ratio can be carried out through a least square method, so that depth error can be accurately obtained; let the fitting polynomial be:
y＝a0+a1x+a2x2...+ak-1xk-1+akxk (6)
Simplifying an error compensation model, wherein the value of a i in the above formula ensures that the sum of the distances from each point to the curve is minimum, namely the square sum of deviation R 2 is minimum, and constructing a bias function by the above formula:
the partial derivative of a i is calculated for the above equation, which yields:
simplifying the above into a matrix form:
X*A＝Y (9)
to reduce the amount of computation, only k=3 may be computed, for which the depth measurement can be modified as:
Zr＝zc1+Y (10)
The high-precision rapid depth measurement result can be realized through the formula.
2. The high-precision rapid three-dimensional positioning system based on the error compensation model as claimed in claim 1, wherein: the monocular industrial camera (2) comprises a camera and a lens for capturing images of the markers (4).
3. The high-precision rapid three-dimensional positioning system based on the error compensation model as claimed in claim 1, wherein: the high-precision three-dimensional positioning software comprises two functions of depth measurement and two-dimensional positioning, wherein the depth measurement is used for measuring the depth of a feature circle on a marker (4), and the two-dimensional positioning is used for calculating the accurate deviation of the xy direction of the feature circle after obtaining the depth information of the feature circle.
4. The high-precision rapid three-dimensional positioning system based on the error compensation model as claimed in claim 2, wherein: the high-precision rapid three-dimensional positioning system realizes the functions by the following steps:
Step 1, fixing a monocular industrial camera (2) at the tail end of a robot manipulator (1) so that the xy direction of the robot manipulator (1) is parallel to the xy direction of a pixel coordinate system of the monocular industrial camera (2);
Step 2, placing the marker (4) under the monocular industrial camera (2), and automatically controlling the electric lifting base (5) to keep a fixed distance between the surface of the marker (4) and the lens; defining a target position to which the robot manipulator (1) is expected to reach as D i (i=1, 2, …, n), and acquiring an image of a marker (4) at the corresponding position as I i (i=1, 2, …, n);
And 3, in the operation process of the robot, starting the monocular industrial camera (2) after reaching the vicinity of the target position D i each time, adaptively adjusting the exposure degree, acquiring a marker image in real time, and then carrying out three-dimensional high-precision positioning through high-precision three-dimensional positioning software.
5. The high-precision rapid three-dimensional positioning system based on the error compensation model according to claim 4, wherein: the specific steps of performing three-dimensional high-precision positioning by the high-precision three-dimensional positioning software in the step 3 are as follows:
Step 3.1, calculating an initial value of depth information according to the marker image: after the marker image is acquired, a marker feature circle is extracted by using a circular detection algorithm, and a pixel distance ratio is calculated according to the radius of the feature circle under a world coordinate system and a pixel coordinate system and the pixel coordinate of a circle center, so that preliminary estimation of depth is realized;
step 3.2, compensating errors based on the error compensation model: adding the compensation value calculated by the proposed error compensation model to the initial depth calculation value, thereby obtaining a high-precision depth calculation result;
Step 3.3, high-precision three-dimensional positioning: after the depth calculation is completed, a target position marker image is acquired according to a monocular industrial camera (2) and is compared with a currently measured depth value, Z-direction deviation is obtained, meanwhile, through a two-dimensional plane positioning algorithm, the accurate deviation in the xy direction is calculated, and the deviation values in the three directions of XYZ are sent to a controller of the robot for pose adjustment, so that three-dimensional high-precision positioning of the robot is realized.
6. The high-precision rapid three-dimensional positioning system based on the error compensation model according to claim 5, wherein the system comprises: the specific steps of the step 3.1 comprise:
Step 3.1.1, calculating a pixel distance ratio: according to the pinhole imaging model and the camera imaging principle, the radius of a feature circle under a world coordinate system, the radius under a pixel coordinate system and the connecting line of the camera optical center and the circle center form a similar triangle, let H c denote the distance from the optical center of the convex lens to an imaging object, H w denote the distance from the optical center of the convex lens to a real object, X c denote the length of the object in the pixel coordinate system, and X w denote the real size of the object, so that the following relation can be obtained:
under the condition of ensuring that the imaging plane of the camera and the characteristic circle plane of the marker are parallel, the circle center of the characteristic circle at the position a is (u 1,v1), the circle center of the characteristic circle at the position b is (u 2,v2), and the pixel distance ratio is:
Step 3.1.2, preliminarily estimating the depth of the feature circle: after the pixel distance ratio is obtained, the depth calculation formula can be expressed as:
f u is the result of camera internal reference calibration.
7. The high-precision rapid three-dimensional positioning system based on the error compensation model according to claim 5, wherein the system comprises: the specific steps of the step 3.3 include:
step 3.3.1, when the robot reaches a specified target position, acquiring a picture, sending the picture to high-precision three-dimensional positioning software, and comparing the picture with a standard picture acquired by the target position;
Step 3.3.2, simultaneously calculating the depth of the target position standard image and the depth measurement result of the current image, and subtracting the depth measurement result and the depth measurement result to obtain Z-direction deviation;
Step 3.3.3, the characteristic circle center of the standard image is marked as C 1＝(Uo,Vo), the circle center of the current image is marked as C n＝(Un,Vn), and the two-dimensional position error can be obtained through the following formula by the pixel distance ratio:
At the moment, the calculated error is sent to a robot controller to control the robot to adjust the pose so as to realize the rapid high-precision three-dimensional positioning of the robot;
The high-precision rapid three-dimensional positioning system based on the error compensation model is used for realizing depth accurate measurement based on a high-precision rapid depth measurement algorithm by capturing a single frame image and detecting the circle center and the radius of a feature circle, establishing the error compensation model, calculating accurate deviation in the xy direction by using a two-dimensional plane positioning algorithm after obtaining accurate depth information, and sending deviation values in the three directions of XYZ to a controller of a robot for pose adjustment, so that the three-dimensional high-precision positioning of the robot is realized.
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