CN113296395A - Robot hand-eye calibration method in specific plane - Google Patents
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Abstract
The invention provides a robot hand-eye calibration method in a specific plane, which comprises the following steps: setting a matching template for a calibration object, and acquiring a central pixel coordinate of the matching template; installing a calibration object on a robot flange, teaching the robot to translate for 9 points, and acquiring the world coordinate P of the robot flange at each pointw1～Pw9Obtaining the pixel coordinate P of the template center on the calibration object at each pointp1～Pp9(ii) a Translating the robot flange to any point in the camera view to acquire world coordinates Pw10And pixel coordinate P of the center of the templatep10(ii) a Rotating the calibration object around the center of the flange for 2 times to respectively obtain the pixel coordinate P of the center of the templatep11,Pp12(ii) a According to Pw1～Pw9，Pp1～Pp9Calculating a transformation matrix
According to Pp10，Pp11,Pp12Computing stationAt the centre of the circle, and passing through
Mapping to world coordinates, and flange coordinates Pw10Making a difference to obtain a fixed deviation; will be provided with
Shifting the fixed deviation to obtain the final homography matrix
The homography matrix
The method is used for determining the mapping relation between the world coordinate system and the pixel coordinate system in the plane.
Description
Technical Field
The invention relates to the technical field of robots, in particular to a robot hand-eye calibration method in a specific plane.
Background
Referring to fig. 1, in a robot vision system, a camera is fixed at a point, and a picture is taken by the camera to obtain information of a target, so as to guide a robot to move, which is one of the most common application scenarios. In this scenario, the camera acquires pixel information, and converting the pixel information into motion information of the robot requires that the conversion relationship between the camera coordinate system and the robot coordinate system (world coordinate system) is known, and the goal of robot hand-eye calibration is to determine the relationship between the camera coordinate system and the robot world coordinate system.
The system consisting of camera and robot includes several important coordinate systems, the concept of the relevant coordinate system is as follows:
(1) pixel coordinate system: a coordinate system which takes pixels as units and describes the position information of points on an image; the original point is the upper left corner of the image; the horizontal and vertical coordinates u, v are in pixel units. As shown in fig. 2.
(2) Image physical coordinate system: a coordinate system expressed in physical units (millimeters, meters, etc.) is established under the pixel coordinate system. The origin is located at the principal point, i.e., the center of the image plane, point O1 of fig. 2. x and y are parallel to u and v, respectively.
(3) Camera coordinate system: with the optical center (i.e., the center of the camera lens) as the origin, the Xc axis and the Yc axis are parallel to the x and y axes of the physical coordinate system of the image, respectively, and the Zc axis coincides with the optical axis and is perpendicular to the image plane, as shown in fig. 4.
(4) Robot coordinate system: namely the base coordinate system of the robot, is the reference coordinate system for the robot to perform kinematic solution. The motion information of the robot is all taken as reference by a base coordinate system. The robot coordinate system is the same as the world coordinate system in this patent.
And a conversion relation matrix exists among the coordinate systems, and a certain point is converted from a pixel coordinate system to a world coordinate system:
wherein the content of the first and second substances,
is a transformation matrix from the pixel coordinate system to the camera coordinate system,
is a transformation matrix from the camera coordinate system to the world coordinate system.
Hand-eye calibration of general robot
In the prior art are known
Then, alsoThe conversion process is completed only when the internal reference matrix and the external reference matrix of the camera are accurately calibrated. In many planar vision applications, the coordinate transformation is limited to pixel coordinates and a single specific plane, so that only the relation between the pixel coordinate system and the world coordinate system in the plane needs to be determined, and the coordinate transformation can be directly calibrated at the moment
And
product of (2)
Without separate calibration
When the device is used, the working plane and the calibration plane are overlapped. Through the derivation,
the method for carrying out robot hand-eye calibration on a specific plane is a homography matrix, namely the process of calibrating the homography matrix, and the matrix determines the mapping relation between a world coordinate system and a pixel coordinate system in a certain plane and can be directly used in plane vision application.
Calibrating a transformation matrix from a camera coordinate system to a world coordinate system
Has been started in the 80 th 20 th century, Shiu, Y and Ahmad, S in 1989 given by the relationship of special and general solutions
The closed solution of Tsai, R, and Lenz, R solves the rotation matrix into an equivalent eigen axis solution, and also provides
1991, Chou, J.,&kamel, M. proposesThe method solves the transformation matrix by using quaternion, the above articles decompose the matrix to be solved into a translation part and a rotation matrix part, the rotation matrix part is solved firstly, then the translation is solved, the calculation process is extremely complex, and the precision is not high when the calibration result is used in a single plane. In 1995, Horaud, R. and Dornaika, F. proposed using a non-linear optimal approach while solving for
The rotation and translation part of the method has high complexity, but the precision is not high when the method is applied to a single plane, in 1998, Konstatinos Daniilidis proposes a method for solving a matrix by using dual quaternions, which is a new algorithm for simultaneously solving translation and rotation matrixes, and the method also has the limitations of complex use process and low precision of an industrial scene.
In the calibration
In the literature and the technology, in 2014, a method for calibrating the matrix is introduced in a "quick calibration method of a robot vision system" of opunt automation technology limited in eastern guan, the method determines parameters of the matrix by determining a series of reference points of a world coordinate system, acquiring pixel coordinates of the reference points and the pixel coordinates and using a least square method, and a set of similar principles is introduced in a "automatic calibration device of a robot monocular vision guidance system" patent of xuyin and yangyuan et al
The calibration device of (1). Both methods need to guarantee the accuracy of the world coordinate system reference point coordinates. When determining the coordinates of the reference points, the calibration of the tool needs to be performed manually. For most robot systems, the process of calibrating the tool is complicated, and a large error is introduced in the process of calibrating the tool, which causes a coordinate error of a reference point, and further causes a large error when solving a matrix, and the calibration precision is not high.
Therefore, the methods used in the prior documents and patents have the disadvantages of complicated process and low precision when applied in the industrial field.
Disclosure of Invention
The object of the present invention is to solve at least one of the technical drawbacks mentioned.
Therefore, the invention aims to provide a robot hand-eye calibration method in a specific plane.
In order to achieve the above object, an embodiment of the present invention provides a method for calibrating a robot hand-eye in a specific plane, including the following steps:
step S1, setting a matching template for the calibration object, and acquiring the central pixel coordinate of the matching template;
step S2, installing the calibration object on the robot flange, teaching the robot to translate for 9 points, and acquiring the world coordinate P of the robot flange at each pointw1～Pw9Obtaining a pixel coordinate P of the center of the template on the calibration object at each pointp1～Pp9；
Step S3, translating the robot flange to any point in the camera view to acquire world coordinates Pw10And pixel coordinate P of the center of the templatep10；
Step S4, rotating the calibration object 2 times around the flange center, and respectively obtaining the pixel coordinate P of the template centerp11,Pp12；
Step S5, according to Pw1 Pw9，Pp1 Pp9Calculating a transformation matrix
Such that:
step S6, according to Pp10，Pp11,Pp12Calculating the center pixel coordinate of the circle, and passing
Mapping to world coordinates, and flange coordinates Pw10Making a difference to obtain a fixed deviation;
step S7, will
Shifting the fixed deviation to obtain the final homography matrix
The homography matrix
The method is used for determining the mapping relation between the world coordinate system and the pixel coordinate system in the plane.
Further, in the step S5, a transformation matrix from pixel coordinates to flange coordinate points is established, wherein h is11,h12,h21,h22,h31,h32,p1,p2Is composed of
The elements (c):
further, the calculating the fixed deviation includes the following steps:
the pixel coordinate of the center of a circle is obtained at any point and is B (u)1,v1) Rotating for 2 times around the flange to respectively obtain the pixel coordinate of the center of a circle as A (u)0,v0),C(u2,v2) A circle can be determined by three points which are not on a straight line, and the coordinate of the center of the circle is obtained by calculation as O (u)c,vc) (ii) a Suppose that the world coordinate of the flange is P at this timef(xf,yf) Mixing B (u)1,v1) When the pixel point is converted into the coordinate point of the flange from the conversion matrix, the result is necessarily Pf(xf,yf) Namely:
where s is the corresponding scale factor.
The center coordinate O (u)c,vc) Converting into flange coordinate point Oc(xc,yc) When the temperature of the water is higher than the set temperature,
then
Is a fixed offset from the flange point to the center point.
Further, a homography matrix is calculated
The method comprises the following steps:
will be provided with
And (3) shifting to obtain a final homography matrix:
further, after the step S7, the method further includes the following steps: and (3) carrying out precision verification on the calibration result:
step S71, ensuring the calibration correspondence still on the calibration plane, controlling the robot to move to a certain point, and obtaining the pixel coordinate P of the calibration objectp0；
In step S72, the calibration target specific offset Δ P is translated (Δ X, Δ Y) in the same plane, and the pixel coordinates P of the calibration target are acquired againp1；
Step S73, adding Pp0And Pp1Conversion into world coordinates P by using calibrated matrixw0And Pw1And finding the offset deltap between the world coordinatest＝Pw1-Pw0＝(Δxt,Δyt)；
In step S74, Δ p ═ (Δ X, Δ Y) and Δ p are calculatedt＝(Δxt,Δyt) Component errors in the X-axis direction and the Y-axis direction can be obtained, and the precision condition of the calibration result can be obtained
According to the robot hand-eye calibration method in the specific plane, provided by the embodiment of the invention are an algorithm for calculating a calibration matrix, a calculation method for calibration precision and a complete set of methods for performing hand-eye calibration on the specific plane, and robot calibration is not needed in the calibration process.
The robot eye calibration method in the specific plane of the embodiment of the invention has the following beneficial effects:
(1) in the calibration process, a robot tool is not needed for calibration, the world coordinates of a reference point are not needed to be provided, the complex operation is reduced, and the introduction of human errors is reduced;
(2) in the calibration process, a specially-made calibration plate is not needed, and any object which can be fixed on a robot flange and has obvious characteristics can be used;
(3) the calibration can be completed by controlling 12 points in the motion plane of the robot, so that the calibration is fast and efficient;
(4) the calibration algorithm is simple, and the precision of the calibration result is high. The method provided by the invention and the method for calibrating by using the tool are used for calibrating the same plane of the same system. The calibration results are compared in precision to obtain an attached table 1, and it can be seen that the precision of the method is higher than that of the method based on tool calibration in the aspect of calibration precision.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a schematic diagram of a prior art robot vision system;
FIG. 2 is a schematic diagram of a pixel coordinate system of a prior art robot vision system;
FIG. 3 is a schematic diagram of a camera coordinate system of a prior art robot vision system;
FIG. 4 is a schematic diagram of a robot with a feature of a calibration object mounted on a flange according to an embodiment of the present invention;
FIG. 5 is a diagram illustrating the determination of a fixed offset according to an embodiment of the present invention;
fig. 6 is a flowchart of a robot hand-eye calibration method in a specific plane according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are exemplary and intended to be illustrative of the invention and are not to be construed as limiting the invention.
The basic principle of hand-eye calibration for a specific plane is first explained below:
homography matrix
The method for carrying out robot hand-eye calibration on a specific plane is a process for calibrating the homography matrix, and the matrix determines the mapping relation between a world coordinate system and a pixel coordinate system in a certain plane and can be directly used in plane vision application.
Specifically, the conversion from pixel to world coordinate requires calibration of the homography matrix
The basic form of the homography matrix is:
for convenience of calculation, when the homography matrix is processed, the order h is given33When it is 1
Including 8 unknown parameters. As shown in equation (1), the relationship between the pixel coordinates and the world coordinates is:
where s is a scaling factor, the left coordinate of the equation may be divided by s to be the homogeneous coordinate.
The equation is known from equation (3):
s＝h31u+h32v+1
sx＝h11u+h12v+h13
sy＝h21u+h22v+h23 (3)
and (4) substituting s into the following two formulas of (4) to obtain:
h11u+h12v+h13-h31ux-h32vx＝x
h21u+h22v+h23-h31uy-h32vy＝y (4)
the form of the conversion into matrix multiplication is:
finding a pair of corresponding points can provide 2 equations, and the solved homography matrix contains 8 unknown parameters, so at least 4 pairs of corresponding points are needed to solve. In actual calculation, errors exist in pixel and world coordinate point data, and when the number of corresponding points is more than 4, the optimal solution can be obtained through a least square optimization method.
As shown in fig. 1, the method for calibrating the hands and eyes of the robot in a specific plane according to the embodiment of the present invention includes the following steps:
step S1, setting a matching template for the calibration object, and acquiring the central pixel coordinate of the matching template;
step S2, installing the calibration object on the robot flange, teaching the robot to translate for 9 points, and acquiring the world coordinate P of the robot flange at each pointw1～Pw9Obtaining a pixel coordinate P of the center of the template on the calibration object at each pointp1～Pp9；
Step S3, translating the robot flange to any point in the camera view to acquire world coordinates Pw10And pixel coordinate P of the center of the templatep10；
Step S4, rotating the calibration object 2 times around the center of the flange, and respectively obtaining the pixel coordinate P of the center of the templatep11,Pp12；
Step S5, according to Pw1～Pw9，Pp1～Pp9Calculating a transformation matrix
Such that:
establishing a conversion matrix from pixel coordinates to flange coordinate points, wherein h11,h12,h21,h22,h31,h32,p1,p2Is composed of
The elements (c):
step S6, according to Pp10，Pp11,Pp12Calculating the center pixel coordinate of the circle, and passing
Mapping toWorld coordinate, and flange coordinate Pw10Making a difference to obtain a fixed deviation;
calculating the fixation deviation, comprising the steps of:
the pixel coordinate of the center of a circle is obtained at any point and is B (u)1,v1) Rotating for 2 times around the flange to respectively obtain the pixel coordinate of the center of a circle as A (u)0,v0),C(u2,v2) A circle can be determined by three points which are not on a straight line, and the coordinate of the center of the circle is obtained by calculation as O (u)c,vc) (ii) a Suppose that the world coordinate of the flange is P at this timef(xf,yf) Mixing B (u)1,v1) When the pixel point is converted into the coordinate point of the flange from the conversion matrix, the result is necessarily Pf(xf,yf) Namely:
where s is the corresponding scale factor.
The center coordinate O (u)c,vc) Converting into flange coordinate point Oc(xc,yc) When the temperature of the water is higher than the set temperature,
then
Is a fixed offset from the flange point to the center point.
Step S7, will
Shifting the fixed deviation to obtain the final homography matrix
Homography matrix
The method is used for determining the mapping relation between the world coordinate system and the pixel coordinate system in the plane.
Generally, calibrating a certain tool mounted on a robot means that the origin of the tool is pointed to the same fixed point in multiple postures, and then the offset and the angle of the tool relative to a flange are calculated, so that the coordinate of the origin of the tool relative to the robot can be determined, that is, the world coordinate of the origin of the tool can be obtained, and the process is called tool calibration.
When the hand-eye calibration is performed, a calibration object with characteristics is installed on a flange of the robot, and the calibration object can be a self-made calibration plate, as shown in fig. 4, or can be a part with obvious characteristics. In the introduction of the above principle, at least 4 pairs of corresponding pixels and world coordinate points in a specific plane are required, and the pixel points can be directly obtained by a camera.
For the coordinate point, the existing method is to install a calibration object on a flange of a robot, and determine the coordinate of the origin of a tool in a world coordinate system by calibrating the tool of the robot. For example, the center of a circle on the calibration plate is calibrated by a tool, so that the world coordinates of the center of the circle are determined. However, the process of tool calibration is cumbersome and calibration errors can be introduced.
The invention does not need a method for calibrating a tool, is simple and does not introduce errors. In a robot system, it is simple to acquire world coordinates of a flange, which is a basic function of a robot. During calibration, the calibration board shown in the figure 4 is installed on the flange, the robot is controlled to move at least 4 points, the pixel coordinate of the circle center is obtained at each point through the camera, the world coordinate of the flange can be obtained through the robot control system, and a conversion matrix from the pixel coordinate to the flange coordinate point is established through the basic principle stated by 3.1, wherein h is11,h12,h21,h22,h31,h32,p1,p2Is composed of
The elements (c):
as shown in fig. 5, there is a fixed offset between the flange coordinate point and the actual center point, and assuming that this offset can be found, it will be
And shifting to obtain a conversion matrix from the pixel to the world coordinate point. The following describes how to find the fixed offset without calibration of the tool.
The pixel coordinate of the center of a circle is obtained at any point and is B (u)1,v1) Rotating for 2 times around the flange to respectively obtain the pixel coordinate of the center of a circle as A (u)0,v0),C(u2,v2) A circle can be determined by three points which are not on a straight line, and the coordinate of the center of the circle is obtained by calculation as O (u)c,vc). Suppose that the world coordinate of the flange is P at this timef(xf,yf) Mixing B (u)1,v1) When the pixel point is converted into the coordinate point of the flange by the formula (7), the result is necessarily Pf(xf,yf) Namely:
the center coordinate O (u)c,vc) Converting into flange coordinate point Oc(xc,yc) When the temperature of the water is higher than the set temperature,
then
Is a fixed offset from the flange point to the center point.
Will be provided with
And (3) shifting to obtain a final homography matrix:
after step S7, the method further includes the following steps: and carrying out precision verification on the calibration result.
The accuracy of the calibration result is one of the important criteria for determining whether the calibration result is usable. The common method is that points used in the calibration process are mapped into a pixel coordinate system through a homography matrix obtained by calibration, and the root mean square error (RMS) of the mapped coordinates and pixel coordinates used in calibration is obtained, wherein the error is the error of a theoretical calculation level, and the smaller the error is, the higher the precision of the matrix obtained by data points is. Such errors do not have a meaning of measuring actual errors because the RMS is small even if the data used in calculating the matrix itself has errors.
The invention carries out precision verification on the calibration result, and comprises the following steps:
step S71, ensuring the calibration correspondence still on the calibration plane, controlling the robot to move to a certain point, and obtaining the pixel coordinate P of the calibration objectp0；
In step S72, the calibration target specific offset Δ P is translated (Δ X, Δ Y) in the same plane, and the pixel coordinates P of the calibration target are acquired againp1；
Step S73, adding Pp0And Pp1Conversion into world coordinates P by using calibrated matrixw0And Pw1And finding the offset deltap between the world coordinatest＝Pw1-Pw0＝(Δxt,Δyt)；
In step S74, Δ p ═ (Δ X, Δ Y) and Δ p are calculatedt＝(Δxt,Δyt) The component errors in the X-axis direction and the Y-axis direction can obtain the precision condition of the calibration result.
According to the robot hand-eye calibration method in the specific plane, provided by the embodiment of the invention are an algorithm for calculating a calibration matrix, a calculation method for calibration precision and a complete set of methods for performing hand-eye calibration on the specific plane, and robot calibration is not needed in the calibration process.
The robot eye calibration method in the specific plane of the embodiment of the invention has the following beneficial effects:
(1) in the calibration process, a robot tool is not needed for calibration, the world coordinates of a reference point are not needed to be provided, the complex operation is reduced, and the introduction of human errors is reduced;
(2) in the calibration process, a specially-made calibration plate is not needed, and any object which can be fixed on a robot flange and has obvious characteristics can be used;
(3) the calibration can be completed by controlling 12 points in the motion plane of the robot, so that the calibration is fast and efficient;
(4) the calibration algorithm is simple, and the precision of the calibration result is high. The method provided by the invention and the method for calibrating by using the tool are used for calibrating the same plane of the same system. The calibration results are compared in precision to obtain an attached table 1, and it can be seen that the precision of the method is higher than that of the method based on tool calibration in the aspect of calibration precision.
TABLE 1 comparison of the two calibration methods for accuracy
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made in the above embodiments by those of ordinary skill in the art without departing from the principle and spirit of the present invention. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (5)
1. A robot hand-eye calibration method in a specific plane is characterized by comprising the following steps:
step S1, setting a matching template for the calibration object, and acquiring the central pixel coordinate of the matching template;
step S2, installing the calibration object on the robot flange, teaching the robot to translate for 9 points, and acquiring the world coordinate P of the robot flange at each pointw1～Pw9Obtaining the pixel coordinate P of the template center on the calibration object at each pointp1～Pp9；
Step S3, translating the robot flange to any point in the camera view to acquire world coordinates Pw10And pixel coordinate P of the center of the templatep10；
Step S4, rotating the calibration object 2 times around the flange center, and respectively obtaining the pixel coordinate P of the template centerp11,Pp12；
Step S5, according to Pw1 Pw9，Pp1 Pp9Calculating a transformation matrix
Such that:
step S6, according to Pp10，Pp11,Pp12Calculating the center pixel coordinate of the circle, and passing
Mapping to world coordinates, and flange coordinates Pw10Making a difference to obtain a fixed deviation;
step S7, will
Shifting the fixed deviation to obtain the final homography matrix
The homography matrix
The method is used for determining the mapping relation between the world coordinate system and the pixel coordinate system in the plane.
2. A robot eye calibration method in a specific plane according to claim 1, wherein in said step S5, a transformation matrix from pixel coordinates to flange coordinate points is established, wherein h is11,h12,h21,h22,h31,h32,p1,p2Is composed of
The elements (c):
3. a method for calibrating a robotic eye in a particular plane as defined in claim 1, wherein said calculating a fixation deviation comprises the steps of:
the pixel coordinate of the center of a circle is obtained at any point and is B (u)1,v1) Rotate 2 times around the flange to obtain circles respectivelyThe pixel coordinate of the heart is A (u)0,v0),C(u2,v2) A circle can be determined by three points which are not on a straight line, and the coordinate of the center of the circle is O (u) through calculationc,vc) (ii) a Suppose that the world coordinate of the flange is P at this timef(xf,yf) Mixing B (u)1,v1) When the pixel point is converted into the coordinate point of the flange by the conversion matrix, the result is necessarily Pf(xf,yf) Namely:
where s is the corresponding scale factor.
The center coordinate O (u)c,vc) Converting into flange coordinate point Oc(xc,yc) When the temperature of the water is higher than the set temperature,
then
Is a fixed offset from the flange point to the center point.
4. A method for calibration of a robot eye in a specific plane according to claim 3, characterised by calculating a homography matrix
The method comprises the following steps:
will be provided with
And (3) shifting to obtain a final homography matrix:
5. a method for calibrating a robot eye in a specific plane according to claim 1, further comprising the following steps after said step S7: and (3) carrying out precision verification on the calibration result:
step S71, ensuring the calibration correspondence still on the calibration plane, controlling the robot to move to a certain point, and obtaining the pixel coordinate P of the calibration objectp0；
In step S72, the calibration target specific offset Δ P is translated (Δ X, Δ Y) in the same plane, and the pixel coordinates P of the calibration target are acquired againp1；
Step S73, adding Pp0And Pp1Conversion into world coordinates P by using calibrated matrixw0And Pw1And finding the offset deltap between the world coordinatest＝Pw1-Pw0＝(Δxt,Δyt)；
In step S74, Δ p ═ (Δ X, Δ Y) and Δ p are calculatedt＝(Δxt,Δyt) The component errors in the X-axis direction and the Y-axis direction can obtain the precision condition of the calibration result.
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