CN109807937A - A robot hand-eye calibration method based on natural scenes - Google Patents
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Abstract
本发明公开了一种基于自然场景的机器人手眼标定方法，包括三个部分：首先，利用SFM解算定义在一个尺度因子基础上的相机外参数；然后，消除尺度因子，建立改进的手眼标定方程，引入矩阵直积理论参数化标定方程中的旋转矩阵和平移向量；最后，通过最小二乘方法同时求解手眼关系及机器人坐标系与世界坐标系方位关系。本发明的方法基于运动恢复结构算法（Structure From Motion,SFM）求解相机外参数，能够摆脱传统机器人手眼标定过程中对平面靶标的依赖，通过矩阵直积参数法求解消除尺度因子后的手眼标定方程，避免了尺度因子对标定方程求解精度的影响，扩展了手眼标定的应用范围。
The invention discloses a robot hand-eye calibration method based on natural scenes, which includes three parts: firstly, using SFM to solve the camera external parameters defined on the basis of a scale factor; then, eliminating the scale factor and establishing an improved hand-eye calibration equation , the rotation matrix and translation vector in the parameterized calibration equation of the matrix direct product theory are introduced; finally, the hand-eye relationship and the orientation relationship between the robot coordinate system and the world coordinate system are solved simultaneously by the least square method. The method of the invention solves the external parameters of the camera based on the motion recovery structure algorithm (Structure From Motion, SFM), can get rid of the dependence on the plane target in the traditional robot hand-eye calibration process, and solve the hand-eye calibration equation after eliminating the scale factor by the matrix direct product parameter method , which avoids the influence of the scale factor on the solution accuracy of the calibration equation, and expands the application range of hand-eye calibration.
Description
Technical field
The present invention relates to industrial robot vision's calibration technique field more particularly to a kind of robots based on natural scene
Hand and eye calibrating method can be used for articulated arm coordinate measuring machine, robotic surgery, mobile robot technology field.
Background technique
Since First has the intelligent robot Shakey birth of visual sensor in the world within 1966, vision is passed
Sensor is widely used in robot autonomous avoidance and navigation, medical operating, the fields such as automobile manufacture.Utilizing robot vision system
It when system carries out AUTONOMOUS TASK, needs for video camera to be fixed on the end effector of robot arm and constitutes hand-eye system, pass through
Visual sensor provides the function of eye to robot movement-control system.Assess the pass of above-mentioned robotic vision system measurement accuracy
Key step first is that accurately calculating the relative bearing relationship between robot coordinate system and visual sensor coordinate system, i.e. trick
Problem of calibrating.
Major part hand and eye calibrating method is all to solve camera by the object of reference (such as gridiron pattern target) of Accurate Calibration at present
Outer parameter, representative method have the unit quaternion method of the linear dichotomy of Zhuang etc., Horaud etc., Shah etc.
Dual quaterion method, the probability statistics based on Lie Group & Lie Algebra of Li et al. of Matrix Direct Product method, Daniilidis and Ulrich etc.
The synchronization scaling method of the both arms such as global optimization method, the Wu of method, Heller etc. cooperation robot and the polyphaser of Amy etc. change
Dai Fa.However, in some special applications, such as mobile robot and operating robot, it is contemplated that load-carrying and aseptic condition
Limitation is difficult to complete hand and eye calibrating process by traditional calibrated reference, in consideration of it, Andreff etc. proposes that one kind does not need
The hand and eye calibrating improved method of calibrated reference directly obtains the phase of missing scale factor using SFM method from natural scene
Unknown scale factor, hand and eye calibrating equation is substituted into together with trick relationship and is solved by the outer parameter of machine.In recent years, it is this not
The hand and eye calibrating improved method of calibrated reference is needed to obtain the most attention of scholars.For example, in the hand and eye calibrating of Andreff
On the basis of model, Schmidt etc. proposes the nonlinear optimization method extended based on dual quaterion, and Heller and Chen Mingwei etc. are mentioned
Out the propositions such as the global optimization method based on Second-order cone programming, Pachtrachai based on CAD (Computer
Aided Design, CAD) import model micro-wound operation robot hand and eye calibrating method.However, these methods can only calculate hand
Eye relationship and scale factor, cannot solve robot coordinate system and world coordinate system position relation, and by characteristic point simultaneously
Influence with error and space scale factor size variation, often precision is lower for the hand and eye calibrating method based on SFM scene rebuilding,
It is not able to satisfy mobile robot and operating robot vision guided navigation and positions growing accuracy requirement.
In view of the above-mentioned problems, set forth herein a kind of Robotic Hand-Eye Calibration method based on natural scene.
Summary of the invention
The Robotic Hand-Eye Calibration method based on natural scene that the purpose of the present invention is to propose to a kind of, this method pass through SFM
Algorithm carries out natural scene reconstruction, under the premise of not needing to calculate scale factor, solves machine simultaneously using Matrix Direct Product method
Manpower eye relationship and robot coordinate system and world coordinate system position relation, to extend the application neck of hand and eye calibrating problem
Domain.
For achieving the above object, the technical scheme is that a kind of Robot Hand-eye mark based on natural scene
Determine method, comprising the following steps:
S1, natural scene reconstruction is carried out by SFM algorithm, sets rotation error threshold value, utilizes adaptive RANSAC algorithm
To nominal data collection CnIn Camera extrinsic number carry out prescreening；
S2, make equivalence transformation to trick calibration equation A (s) X=YB, eliminate calibration equation mesoscale factor s, utilize matrix
Direct product method is the product of matrix and vector the product representation of matrix in trick calibration equation, meets error for what is filtered out in S1
The Camera extrinsic number of threshold requirement substitutes into the hand and eye calibrating equation of parametrization, establishes system of homogeneous linear equations；
S3, the hand and eye calibrating equation parameterized in S2 is solved using singular value decomposition, obtains meeting linear homogeneous
Then orthogonal and unit is added to it and constrains to obtain correct trick relationship X and robot coordinate system by non trivial solution vector value x
With world coordinate system position relation Y.
The present invention is based on exercise recovery structure algorithm (Structure From Motion, SFM) to solve Camera extrinsic number,
Dependence of the traditional robot hand and eye calibrating in the process to ceramic gridiron pattern flat target can be got rid of, is asked by Matrix Direct Product parametric method
Solution eliminates the hand and eye calibrating equation after scale factor, avoids influence of the scale factor to calibration equation solving precision.
The present invention resolves the Camera extrinsic number on the basis of being defined on a scale factor using SFM；Then, eliminate scale because
Son establishes improved hand and eye calibrating equation, the spin matrix being introduced into Matrix Direct Product theoretical parameter calibration equation and is translated towards
Amount；Finally, solving trick relationship and robot coordinate system and world coordinate system position relation simultaneously by least square method.
Detailed description of the invention
Fig. 1 is the flow chart of the Robotic Hand-Eye Calibration method the present invention is based on natural scene；
Fig. 2 is A (s) X=YB hand and eye calibrating basic principle schematic；
Fig. 3 is hand and eye calibrating Experimental equipment；
Fig. 4 is plane target object of reference used in Robotic Hand-Eye Calibration；
Fig. 5 is books object of reference used in Robotic Hand-Eye Calibration；
Fig. 6 is statue object of reference used in Robotic Hand-Eye Calibration；
Fig. 7 is that SFM algorithm carries out natural scene reconstruction effect picture.
Specific embodiment
Below in conjunction with attached drawing, technical scheme in the embodiment of the invention is clearly and completely described.
As shown in Figure 1, a kind of Robotic Hand-Eye Calibration method based on natural scene, which is characterized in that including following step
It is rapid:
S1, natural scene reconstruction is carried out by SFM algorithm, as shown in Fig. 2, setting rotation error threshold value, using adaptive
RANSAC algorithm is to nominal data collection CnIn Camera extrinsic number carry out prescreening；
Camera extrinsic number includes transformation matrix A of the camera coordinate system to reference substance world coordinate systemiIn rotating part
Camera extrinsic number RAi, robot tool coordinate system to robot basis coordinates system transformation matrix BiIn rotating part Camera extrinsic
Number RBi, RAi、RBiScreening technique specifically include:
S1.1, video camera is fixed on end effector of robot, acquires nominal data, driven and imaged using robot
Machine chooses N number of different positions and pose every time and takes pictures imaging to ceramic gridiron pattern flat target, is combined available M=N (N- two-by-two
1)/2 group nominal data collection Cn, the rotating part R in hand and eye calibrating matrix is solved using linear methodXAnd RY；
S1.2, nominal data rotation error screening model is established:
Wherein, eRFor error threshold；
S1.3, using adaptive RANSAC algorithm to nominal data collection CnMiddle Camera extrinsic number RAi、RBiCarry out prescreening.Tool
Body includes: the minimum strong point n=2 of setting, and setting meets error threshold eRIt is required that interior ratio initial value wO=0.5, K sampling
In all samples be bad sample probability z=0.02, rotation error threshold value initial value eR=0.01, terminate the item of RANSAC sampling
Part is to meet error threshold eRNominal data collection CX>=9, it is sampled using adaptive algorithm and updates wOAnd eR, until demarcating number
According to collection CX>=9, write down angle threshold e at this timeh, sampling is terminated, the nominal data collection C that screening is obtainedXSubstitute into S2.
S2, make equivalence transformation to trick calibration equation A (s) X=YB, eliminate calibration equation mesoscale factor s, utilize matrix
Direct product method is the product of matrix and vector the product representation of matrix in trick calibration equation, meets error for what is filtered out in S1
The Camera extrinsic number of threshold requirement substitutes into the hand and eye calibrating equation of parametrization, establishes system of homogeneous linear equations；It specifically includes:
As shown in Fig. 2, defining A is transformation matrix of the object of reference world coordinate system to camera coordinate system, B is expressed as machine
Transformation matrix of people's tool coordinates system to robot basis coordinates system, X expression camera coordinate system to robot tool coordinate system
Transformation matrix, Y indicate robot basis coordinates system to the transformation matrix of object of reference world coordinate system, then hand and eye calibrating equation can be with table
It is shown as:
A (s) X=YB
In formula (1), A, B, X and Y are 4 × 4 matrix, expand into the form of spin matrix and translation vector are as follows:
By formula (2) it is found that only having translation vector part to be influenced by scale factor s in calibration equation, by translation vector portion
Divide both members all multiplied by antisymmetric matrixEliminating scale factor s can obtain:
Wherein
Then the hand and eye calibrating equation in formula (2) can convert are as follows:
Matrix product in formula (3) is expressed as to the form of Matrix Direct Product, establishes system of homogeneous linear equations:
In formula (4), W (A, B) is 18 × 24 matrixes；X is system of homogeneous linear equations solution vector value, is 24 × 1 vector；
Vec (R) is vectorization operator, can be indicated are as follows:
Wherein, r11、r12、…、r1n、r21、r22、…、rnmRepresent R3×3Each of matrix element.
S3, the hand and eye calibrating equation parameterized in S2 is solved using singular value decomposition, obtains meeting linear homogeneous
Then orthogonal and unit is added to it and constrains to obtain correct trick relationship X and robot coordinate system by non trivial solution vector value x
With world coordinate system position relation Y；It specifically includes:
If U=vec-1(x1:9), V=vec-1(x10:18), x1:9It is first 9 of system of homogeneous linear equations solution vector value x,
x10:18For the 10-18 item of system of homogeneous linear equations solution vector value x, non trivial solution RXAnd RYThe ratio differed with solution vector value x because
Sub- β meets:
U=β RX, V=β RY
By above formula reverse scale factor β are as follows:
Therefore, it trick relationship X and robot coordinate system and spin matrix in world coordinate system position relation Y and is translated towards
Amount can indicate are as follows:
Due to measuring the influence of noise,WithAnd it is unsatisfactory for stringent orthogonality, it needs to reuse Schmidt orthogonal
Change carries out equivalence transformation to it.
Feasibility of the above method in actual measurement is verified with validity below by way of specific experiment, such as
Shown in Fig. 3, DENSO robot, Japan electric coating company VS-6577GM, company, Daheng MER-500-14GM/GC model are utilized
CMOS industrial camera builds actual measurement experiment porch.As Figure 4-Figure 6, made respectively using ceramic gridiron pattern flat target, books, statue
Hand and eye calibrating equation is solved for object of reference.The repetitive positioning accuracy of DENSO robot all directions is ± 0.020mm, each joint angle
Resolution ratio is 5 ", camera resolution is 2592 × 1944pixels, and pixel dimension is 2.2 μm of 2.2 μ m, and lens focus is
Video camera is first fixed tightly on end effector of robot ring flange by 12mm before experiment.Due to actual measurement experiment in can not be direct
The absolute true value for measuring trick relationship X and robot orientation Y, in order to verify the precision and reliability of the method for the present invention, with tradition
Using ceramic gridiron pattern flat target as the result X of the hand and eye calibrating method of object of referencebarAnd YbarIt is for true value, it is upper with utilization
The carry out trick relationship X that the method for stating is calculatedsceneWith robot orientation YsceneIt is worth comparative analysis.Detailed process are as follows:
1, it defines trick relationship and robot azimuthal error is respectively as follows:
EX=| | Xbar-Xscene||2 EY=| | Ybar-Yscene||2
2, drive industrial camera centered on ceramic gridiron pattern flat target origin using robot, radius is about 600mm
Hemisphere face on 9 different positions take pictures imaging to 11mm × 11mm ceramics gridiron pattern flat target shown in Fig. 4, recorder
People's tool coordinates system is to robot basis coordinates system transformation matrix；
3, with Zhang Zhengyou method calibration for cameras intrinsic parameter, Camera extrinsic number is solved, the tradition based on target object of reference is used
Scaling method calculates trick relationship XbarWith robot orientation Ybar；
4, it is taken pictures imaging with books or statue, previous step camera internal reference numerical value obtained by calibrating and SFM algorithm is utilized to calculate
The Camera extrinsic number for lacking scale factor, obtains space characteristics point by Feature Points Matching, triangulation and beam optimum adjustment
Three-dimensional information, be illustrated in figure 7 in Fig. 5 object of reference 5035 characteristic points rebuild after result.Using based on nature field
The Robotic Hand-Eye Calibration method of scape solves trick relationship XsceneWith robot orientation Yscene, calculate trick relationship and robot
Azimuthal error EXAnd EY。
In order to verify the reliability of the method for the present invention, 10 groups of completely self-contained calibration experiments are repeated, are averaged
It is compared analysis, as shown in table 1:
1 natural scene object of reference hand and eye calibrating experimental result (unit: mm) of table
As known from Table 1: 2 kinds of different types of natural scene objects of reference are directed to, it is proposed by the present invention based on natural scene
The trick relationship X that Robotic Hand-Eye Calibration improved method is calculatedsceneWith robot orientation YsceneValue is close to based on ceramics
The trick relationship X that gridiron pattern flat target is calculatedbarWith robot orientation YbarValue.Show in no calibrated reference as empty
Between constrain under conditions of, method of the invention is it is also ensured that certain stated accuracy and reliability.
Described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.Based on the present invention
In embodiment, every other implementation obtained by those of ordinary skill in the art without making creative efforts
Example, belongs to the scope of the present invention.
Claims (5)
1. a kind of Robotic Hand-Eye Calibration method based on natural scene, which comprises the following steps:
S1, natural scene reconstruction is carried out by SFM algorithm, rotation error threshold value is set, using adaptive RANSAC algorithm to mark
Determine data set CnIn Camera extrinsic number carry out prescreening；
S2, make equivalence transformation to trick calibration equation A (s) X=YB, eliminate calibration equation mesoscale factor s, utilize Matrix Direct Product
Method is the product of matrix and vector the product representation of matrix in trick calibration equation, meets error threshold for what is filtered out in S1
It is required that Camera extrinsic number substitute into parametrization hand and eye calibrating equation, establish system of homogeneous linear equations；
S3, the hand and eye calibrating equation parameterized in S2 is solved using singular value decomposition, obtains meeting homogeneous linear equations
Solution vector value x, orthogonal and unit is then added to it and constrains to obtain correct trick relationship X and robot coordinate system and generation
Boundary coordinate system position relation Y.
2. a kind of Robotic Hand-Eye Calibration method based on natural scene as described in claim 1, which is characterized in that the S1
Middle Camera extrinsic number includes transformation matrix A of the camera coordinate system to reference substance world coordinate systemiIn rotating part camera outside
Parameter RAi, robot tool coordinate system to robot basis coordinates system transformation matrix BiIn rotating part Camera extrinsic number RBi,
RAi、RBiScreening technique specifically include:
S1.1, video camera is fixed on end effector of robot, acquires nominal data, drive video camera every using robot
It is secondary to choose N number of different positions and pose and take pictures imaging to ceramic gridiron pattern flat target, it is combined available M=N (N-1)/2 group two-by-two
Nominal data collection Cn, the rotating part R in hand and eye calibrating matrix is solved using linear methodXAnd RY；
S1.2, nominal data rotation error screening model is established:
Wherein, eRFor error threshold；
S1.3, using adaptive RANSAC algorithm to nominal data collection CnMiddle Camera extrinsic number RAi、RBiCarry out prescreening.
3. a kind of Robotic Hand-Eye Calibration method based on natural scene as claimed in claim 2, which is characterized in that described
S1.3 is specifically included: setting minimum strong point n=2, setting meets error threshold eRIt is required that interior ratio initial value w0=0.5, K
All samples are the probability z=0.02 of bad sample, rotation error threshold value initial value e in secondary samplingR=0.01, it terminates RANSAC and takes out
The condition of sample is to meet error threshold eRNominal data collection CX>=9, it is sampled using adaptive algorithm and updates w0And eR, until
Nominal data collection CX>=9, write down angle threshold e at this timeh, sampling is terminated, the nominal data collection C that screening is obtainedXSubstitute into S2.
4. a kind of Robotic Hand-Eye Calibration method based on natural scene as described in claim 1, which is characterized in that the S2
In establish system of homogeneous linear equations and specifically include:
Defining A is transformation matrix of the object of reference world coordinate system to camera coordinate system, and B is expressed as robot tool coordinate system and arrives
The transformation matrix of robot basis coordinates system, X indicate camera coordinate system to the transformation matrix of robot tool coordinate system, Y expression
Robot basis coordinates system is to the transformation matrix of object of reference world coordinate system, then hand and eye calibrating equation can indicate are as follows:
A (s) X=YB
In formula (1), A, B, X and Y are 4 × 4 matrix, expand into the form of spin matrix and translation vector are as follows:
RAtX+stA=RYtB+tY (2)
By formula (2) it is found that only having translation vector part to be influenced by scale factor s in calibration equation, by translation vector part etc.
Formula both sides are all multiplied by antisymmetric matrixEliminating scale factor s can obtain:
Wherein
Then the hand and eye calibrating equation in formula (2) can convert are as follows:
Matrix product in formula (3) is expressed as to the form of Matrix Direct Product, establishes system of homogeneous linear equations:
In formula (4), W (A, B) is 18 × 24 matrixes；X is system of homogeneous linear equations solution vector value, is 24 × 1 vector；vec(R)
For vectorization operator, can indicate are as follows:
Vec (R)=[r11,r12,…,r1n,r21,r22..., rmn]T, vec-1(vec (R))=R
Wherein, r11、r12、…、r1n、r21、r22、…、rnmRepresent R3×3Each of matrix element.
5. a kind of Robotic Hand-Eye Calibration method based on natural scene as described in claim 1, which is characterized in that the S3
It is middle to calculate correct trick relationship X and robot coordinate system specifically includes with world coordinate system position relation Y:
If U=vec-1(x1:9), V=vec-1(x10:18), x1:9It is first 9 of system of homogeneous linear equations solution vector value x, x10:18For
The 10-18 item of system of homogeneous linear equations solution vector value x, non trivial solution RXAnd RYThe scale factor β differed with solution vector value x meets:
U=β RX, V=β RY
By above formula reverse scale factor β are as follows:
Therefore, trick relationship X and robot coordinate system can with spin matrix in world coordinate system position relation Y and translation vector
To indicate are as follows:
Due to measuring the influence of noise,WithAnd it is unsatisfactory for stringent orthogonality, it needs to reuse Schimidt orthogonalization pair
It carries out equivalence transformation.
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| CN112700505A (en) * | 2020-12-31 | 2021-04-23 | 山东大学 | Binocular three-dimensional tracking-based hand-eye calibration method, equipment and storage medium |
| CN112729344A (en) * | 2020-12-30 | 2021-04-30 | 珠海市岭南大数据研究院 | Sensor external reference calibration method without reference object |
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| CN112700505A (en) * | 2020-12-31 | 2021-04-23 | 山东大学 | Binocular three-dimensional tracking-based hand-eye calibration method, equipment and storage medium |
| CN115582829A (en) * | 2021-07-05 | 2023-01-10 | 腾讯科技（深圳）有限公司 | Method and device for determining position of mechanical arm, electronic equipment and storage medium |
| CN113787515A (en) * | 2021-08-12 | 2021-12-14 | 佛山缔乐视觉科技有限公司 | Loading and unloading method and device based on mobile robot and storage medium |
| CN115502983A (en) * | 2022-10-31 | 2022-12-23 | 深圳市凌云视迅科技有限责任公司 | Robot eye calibration method and device, computer equipment and medium |
| CN116352710A (en) * | 2023-03-24 | 2023-06-30 | 电子科技大学 | A robot automatic calibration and three-dimensional measurement method for large aerospace components |
| CN116352710B (en) * | 2023-03-24 | 2025-03-25 | 电子科技大学 | A robot automatic calibration and three-dimensional measurement method for large aerospace components |
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