CN114505860A - 3D hand-eye calibration method and system - Google Patents

3D hand-eye calibration method and system Download PDF

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CN114505860A
CN114505860A CN202210202349.8A CN202210202349A CN114505860A CN 114505860 A CN114505860 A CN 114505860A CN 202210202349 A CN202210202349 A CN 202210202349A CN 114505860 A CN114505860 A CN 114505860A
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equation set
matrix
coordinate
hand
coordinate system
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侯梦华
陈凯
刘俊锋
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Shenzhen Qiling Image Technology Co ltd
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1694—Programme controls characterised by use of sensors other than normal servo-feedback from position, speed or acceleration sensors, perception control, multi-sensor controlled systems, sensor fusion
    • B25J9/1697—Vision controlled systems
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning

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  • Engineering & Computer Science (AREA)
  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Automation & Control Theory (AREA)
  • Manipulator (AREA)

Abstract

The embodiment of the invention discloses a 3D hand-eye calibration method and a system, wherein the method comprises the following steps: selecting N characteristic points, and acquiring a first coordinate of each characteristic point in a manipulator coordinate system and a second coordinate in a camera coordinate system; substituting the first coordinate and the second coordinate into a mathematical model of a coordinate system conversion matrix to obtain 3N equations, and forming an over-determined equation set by all the equations; and solving the overdetermined equation set by adopting a generalized inverse method of a least square method of the nonlinear equation set to obtain a conversion matrix. The invention solves the overdetermined equation set in the 3D hand-eye calibration method by adopting the generalized inverse method of the least square method of the nonlinear equation set, and can effectively improve the calibration precision, thereby improving the precision of the product out-of-order capture.

Description

3D hand-eye calibration method and system
Technical Field
The invention relates to the field of product positioning, in particular to a 3D hand-eye calibration method and system.
Background
In industrial production, 3D camera positioning is commonly used for disordered grabbing of products, generally, a camera acquires coordinates or a pose of a product in a camera coordinate system, the coordinates or the pose in the camera coordinate system are converted into coordinates or the pose in a manipulator coordinate system by a 3D hand-eye calibration method, the manipulator grabs the product according to the coordinates or the pose in the manipulator coordinate system, and the grabbing precision is directly determined by the precision of the 3D hand-eye calibration method. Therefore, it is necessary to improve the existing 3D hand-eye calibration method to improve the transformation matrix precision, so that the coordinates or pose in the manipulator coordinate system is more accurate, and the capture precision is further improved.
Disclosure of Invention
In view of the above technical problems, embodiments of the present invention provide a 3D hand-eye calibration method and system, which improve the precision of a transformation matrix, and accurately control the transformation relationship between a camera coordinate system and a manipulator coordinate system, thereby improving the grasping precision of a product.
In a first aspect of an embodiment of the present invention, a 3D hand-eye calibration method includes:
selecting N characteristic points, and acquiring a first coordinate of each characteristic point in a manipulator coordinate system and a second coordinate in a camera coordinate system;
substituting the first coordinate and the second coordinate into a mathematical model of a coordinate system conversion matrix to obtain 3N equations, and forming an over-determined equation set by all the equations;
and solving the overdetermined equation set by adopting a generalized inverse method of a least square method of the nonlinear equation set to obtain a conversion matrix.
Preferably, the mathematical model of the coordinate system transformation matrix is:
Figure BDA0003529942370000011
wherein R is3×3For a rotation matrix, T3×1Is a translation matrix.
Preferably, the overdetermined system of equations is represented as:
fi(x0，x1，…，xm-1) 0, 1, …, m-1; m > n formula (2)
Preferably, the solving the over-determined equation set by using a least square method to obtain a transformation matrix specifically includes:
obtaining a Jacobian matrix according to the over-determined equation set as follows:
Figure BDA0003529942370000021
obtaining an iterative formula solved by a least square method of a nonlinear equation set:
x(k+1)＝X(k)-akZkformula (4)
Wherein Z iskIs a linear equation set A(k)Z(k)＝F(k)Solving to obtain alphak，akI.e. the transformation matrix.
Preferably, Z iskIs a linear equation set A(k)Z(k)＝F(k)The linear least-squares solution of (a), is,
Z(k)＝(A(k))+Fk(formula 5)
Wherein the content of the first and second substances,
Figure BDA0003529942370000022
A(k)for k iteration values X(k)Of Jacobian, FkThe left-end function value is the k iteration values.
A second aspect provides a 3D hand-eye calibration system, comprising:
the coordinate acquisition module is used for selecting N characteristic points and acquiring a first coordinate of each characteristic point in a manipulator coordinate system and a second coordinate in a camera coordinate system;
the equation building module is used for substituting the first coordinate and the second coordinate into a mathematical model of a coordinate system conversion matrix to obtain 3N equations, and all the equations form an overdetermined equation set;
and the matrix solving module is used for solving the overdetermined equation set by adopting a generalized inverse method of a least square method of the nonlinear equation set to obtain a conversion matrix.
Preferably, the equation building block includes:
the model building unit is used for building a mathematical model of a conversion matrix of the camera coordinate system and the manipulator coordinate system:
Figure BDA0003529942370000031
wherein R is3×3For a rotation matrix, T3×1Is a translation matrix.
Preferably, the overdetermined system of equations may be expressed as:
fi(x0，x1，...，xm-1) 0, i-0, 1, m-1; m > n formula (2)
Preferably, the matrix calculation unit specifically includes:
obtaining a Jacobian matrix according to the over-determined equation set as follows:
Figure BDA0003529942370000032
obtaining an iterative formula solved by a least square method of a nonlinear equation set:
X(k+1)＝X(k)-akZkformula (4)
Wherein Z iskIs a linear equation set A(k)Z(k)＝F(k)Solving to obtain ak，αkI.e. the transformation matrix.
Preferably, Z iskIs a linear equation set A(k)Z(k)＝F(k)The linear least-squares solution of (a), is,
Z(k)＝(A(k))+Fk(formula 5)
Wherein the content of the first and second substances,
Figure BDA0003529942370000041
A(k)for k iteration values X(k)Of Jacobian, FkThe left-end function value is the k iteration values.
Compared with the prior art, the 3D hand-eye calibration method and the system in the technical scheme provided by the embodiment of the invention adopt the generalized inverse method iteration solution of the least square method of the nonlinear equation system, improve the conversion matrix precision, and accurately control the conversion relation between the camera coordinate system and the manipulator coordinate system, thereby improving the grabbing precision of products.
Drawings
Fig. 1 is a flowchart of a 3D hand-eye calibration method in an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without inventive step based on the embodiments of the present invention, are within the scope of protection of the present invention.
The invention provides a 3D hand-eye calibration method, which is a method for solving a conversion matrix of a 3D camera coordinate system and a manipulator coordinate system during 3D hand-eye calibration. Referring to fig. 1, the following describes in detail specific steps of the 3D hand-eye calibration method according to an embodiment of the present invention:
s1, selecting N feature points, and acquiring a first coordinate of each feature point in a manipulator coordinate system and a second coordinate in a camera coordinate system;
step S2, substituting the first coordinate and the second coordinate into a mathematical model of a coordinate system transformation matrix to obtain 3N equations, and forming an overdetermined equation set by all the equations;
and S3, solving the overdetermined equation set by adopting a generalized inverse method of a least square method of the nonlinear equation set to obtain a conversion matrix.
The method adopts the generalized inverse method iterative solution of least square solution of the nonlinear equation set, improves the accuracy of the transformation matrix through the optimization of the solution method, and effectively solves the accuracy problem of the 3D hand-eye calibration method.
Step S2 is described in detail below:
step S21, constructing a mathematical model of a camera coordinate system and manipulator coordinate system transformation matrix:
Figure BDA0003529942370000051
wherein R is3×3For a rotation matrix, T3×1And the coordinates or the sitting posture in the coordinate system of the mechanical arm can be obtained by rotation and translation calculation for the translation matrix.
According to the mathematical model, an overdetermined equation set can be further constructed, specifically:
and acquiring the coordinates of the N characteristic points in a manipulator coordinate system and a camera coordinate system respectively. When one feature point is selected, three equations can be generated according to the mathematical model, and the rotation matrix has 12 unknowns, so that the transformation matrix can be solved by 12 equations generated by 4 groups of known feature points. And finally, constructing an over-determined equation set by the mathematical model, the coordinates of the manipulator coordinate system and the coordinates in the camera coordinate system, wherein the over-determined equation set comprises a plurality of groups of solutions, and the optimal solution is solved for improving the calibration precision requirement.
Specifically, the final obtained overdetermined system of equations may be expressed as:
fi(x0x1，...，xm-1) 0, 1, …, m-1; m > n formula (2)
After the over-determined equation set is obtained, the over-determined equation set is solved by adopting a least square method to obtain a conversion matrix, and the over-determined equation is solved by adopting the least square method in the solving process, so that the calibration precision is effectively improved.
Figure BDA0003529942370000052
Obtaining an iterative formula solved by a least square method of a nonlinear equation set:
X(k+1)＝X(k)-αkZkformula (4)
Wherein Z iskIs a linear equation set A(k)Z(k)＝F(k)Solving to obtain ak，akI.e. the transformation matrix.
The specific solving process is as follows:
Zkis a linear equation set A(k)Z(k)＝F(k)Linear minimum two-component solution of (i.e.
Z(k)＝(A(k))+Fk(formula 5)
Wherein the content of the first and second substances,
Figure BDA0003529942370000061
A(k)for k iteration values X(k)Of Jacobian, FkLeft-end function value of k iteration values, akAs a unary function of a
Figure BDA0003529942370000062
Point of reaching minimum value, akI.e. the transformation matrix.
The invention also provides a 3D camera positioning system, comprising:
the system comprises a mark acquisition module, a marking module and a marking module, wherein the mark acquisition module is used for selecting N characteristic points and acquiring a first coordinate of each characteristic point in a manipulator coordinate system and a second coordinate in a camera coordinate system;
the equation building module is used for substituting the first coordinate and the second coordinate into a mathematical model of a coordinate system conversion matrix to obtain 3N equations, and all the equations form an overdetermined equation set;
and the matrix solving module is used for solving the overdetermined equation set by adopting a generalized inverse method of a least square method of the nonlinear equation set to obtain a conversion matrix.
Preferably, the equation building block includes:
the model building unit is used for building a mathematical model of a conversion matrix of the camera coordinate system and the manipulator coordinate system:
Figure BDA0003529942370000063
wherein R is3×3For a rotation matrix, T3×1Is a translation matrix.
Preferably, the overdetermined system of equations may be expressed as:
fi(x0，x1，...，xm-1) 0, 1, …, m-1; m > n formula (2)
Preferably, the matrix calculation unit specifically includes:
obtaining a Jacobian matrix according to the over-determined equation set as follows:
Figure BDA0003529942370000071
obtaining an iterative formula solved by a least square method of a nonlinear equation set:
X(k+1)＝X(k)-akZkformula (4)
Wherein Z iskIs a linear equation set A(k)Z(k)＝F(k)Solving to obtain ak，αkI.e. the transformation matrix.
Preferably, Z iskIs a linear equation set A(k)Z(k）＝F(k)The linear least-squares solution of (a), is,
Z(k)＝(A(k))+Fk(formula 5)
Wherein the content of the first and second substances,
Figure BDA0003529942370000072
A(k)for k iteration values X(k)Of Jacobian, FkThe left-end function value is the k iteration values.
Compared with the prior art, the 3D hand-eye calibration method and the system in the technical scheme provided by the embodiment of the invention adopt the generalized inverse method iteration solution of the least square method of the nonlinear equation system, improve the conversion matrix precision, and accurately control the conversion relation between the camera coordinate system and the manipulator coordinate system, thereby improving the grabbing precision of products.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, apparatus, or computer program product. Accordingly, embodiments of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, embodiments of the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
Embodiments of the present invention are described with reference to flowchart illustrations and/or block diagrams of methods, electronic devices (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing electronic device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing electronic device, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing electronic devices to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing electronic device to cause a series of operational steps to be performed on the computer or other programmable electronic device to produce a computer implemented process such that the instructions which execute on the computer or other programmable electronic device provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While preferred embodiments of the present invention have been described, additional variations and modifications of these embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the embodiments of the invention.
Finally, it should also be noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or electronic device that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or electronic device. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or electronic device that comprises the element.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (10)

1. A3D hand-eye calibration method is characterized by comprising the following steps:
selecting N characteristic points, and acquiring a first coordinate of each characteristic point in a manipulator coordinate system and a second coordinate in a camera coordinate system;
substituting the first coordinate and the second coordinate into a mathematical model of a coordinate system conversion matrix to obtain 3N equations, and forming an over-determined equation set by all the equations;
and solving the overdetermined equation set by adopting a generalized inverse method of a least square method of the nonlinear equation set to obtain a conversion matrix.
2. The 3D hand-eye calibration method according to claim 1, wherein the mathematical model of the coordinate system transformation matrix is:
Figure FDA0003529942360000011
wherein R is3×3For a rotation matrix, T3×1Is a translation matrix.
3. The 3D hand-eye calibration method according to claim 2, wherein the over-determined system of equations is expressed as:
fi(x0，x1，…，xm-1) 0, 1, …, m-1; m > n formula (2)
4. The 3D hand-eye calibration method according to claim 2, wherein the solving of the overdetermined system of equations by using the generalized inverse of the least squares method of the nonlinear system of equations to obtain the transformation matrix specifically comprises:
obtaining a Jacobian matrix according to the over-determined equation set as follows:
Figure FDA0003529942360000012
obtaining an iterative formula solved by a least square method of a nonlinear equation set:
X(k+1)＝X(k)-akZkformula (4)
Wherein, ZkIs a linear equation set A(k)Z(k)＝F(k)A linear least-squares solution of (a),solving to obtain ak，akI.e. the transformation matrix.
5. The 3D hand-eye calibration method according to claim 4, wherein Z iskIs a linear equation set A(k)Z(k)＝F(k)The linear least-squares solution of (a), is,
Z(k)＝(A(k))+Fk(formula 5)
Wherein the content of the first and second substances,
Figure FDA0003529942360000021
A(k)for k iteration values X(k)Jacobian matrix of FkThe left-end function value is the k iteration values.
6. A 3D hand-eye calibration system, comprising:
the coordinate acquisition module is used for selecting N characteristic points and acquiring a first coordinate of each characteristic point in a manipulator coordinate system and a second coordinate in a camera coordinate system;
the equation building module is used for substituting the first coordinate and the second coordinate into a mathematical model of a coordinate system conversion matrix to obtain 3N equations, and all the equations form an overdetermined equation set;
and the matrix solving module is used for solving the overdetermined equation set by adopting a generalized inverse method of a least square method of the nonlinear equation set to obtain a conversion matrix.
7. The 3D hand-eye calibration system of claim 6, wherein the equation building module comprises:
the model building unit is used for building a mathematical model of a conversion matrix of the camera coordinate system and the manipulator coordinate system:
Figure FDA0003529942360000022
wherein R is3×3For a rotation matrix, T3×1Is a translation matrix.
8. The 3D hand-eye calibration system according to claim 7, wherein the over-determined system of equations is expressed as:
fi(x0，x1，…，xm-1) 0, 1, …, m-1; m > n formula (2)
9. The 3D hand-eye calibration system according to claim 7, wherein the matrix calculation unit specifically comprises:
obtaining a Jacobian matrix according to the over-determined equation set as follows:
Figure FDA0003529942360000031
obtaining an iterative formula solved by a least square method of a nonlinear equation set:
X(k+1)＝X(k)-akZkformula (4)
Wherein Z iskIs a linear equation set A(k)Z(k)＝F(k)Solving to obtain ak，akI.e. the transformation matrix.
10. The 3D hand-eye calibration system of claim 9, wherein Z iskIs a linear equation set A(k)Z(k)＝F(k)The linear least-squares solution of (a), is,
Z(k)＝(A(k))+Fk(formula 5)
Wherein the content of the first and second substances,
Figure FDA0003529942360000032
A(k)for k iteration values X(k)Jacobian matrix of FkThe left-end function value is the k iteration values.
CN202210202349.8A 2022-03-03 2022-03-03 3D hand-eye calibration method and system Pending CN114505860A (en)

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Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102589437A (en) * 2012-03-09 2012-07-18 天津大学 Calibration method for measuring head center position in light pen-type portable three-coordinate measuring system
CN104376572A (en) * 2014-12-02 2015-02-25 成都理工大学 Mobile terminal camera calibrating method
CN107545591A (en) * 2016-06-29 2018-01-05 沈阳新松机器人自动化股份有限公司 A kind of Robotic Hand-Eye Calibration method based on 6 contact methods
CN108122257A (en) * 2016-11-28 2018-06-05 沈阳新松机器人自动化股份有限公司 A kind of Robotic Hand-Eye Calibration method and device
US20190147622A1 (en) * 2016-12-09 2019-05-16 Sun Yat-Sen University Unmanned aerial vehicle calibration method and system based on colour 3d calibration object
CN113052974A (en) * 2019-12-11 2021-06-29 清华大学 Method and device for reconstructing three-dimensional surface of object

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102589437A (en) * 2012-03-09 2012-07-18 天津大学 Calibration method for measuring head center position in light pen-type portable three-coordinate measuring system
CN104376572A (en) * 2014-12-02 2015-02-25 成都理工大学 Mobile terminal camera calibrating method
CN107545591A (en) * 2016-06-29 2018-01-05 沈阳新松机器人自动化股份有限公司 A kind of Robotic Hand-Eye Calibration method based on 6 contact methods
CN108122257A (en) * 2016-11-28 2018-06-05 沈阳新松机器人自动化股份有限公司 A kind of Robotic Hand-Eye Calibration method and device
US20190147622A1 (en) * 2016-12-09 2019-05-16 Sun Yat-Sen University Unmanned aerial vehicle calibration method and system based on colour 3d calibration object
CN113052974A (en) * 2019-12-11 2021-06-29 清华大学 Method and device for reconstructing three-dimensional surface of object

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