CN109773786A - A kind of industrial robot plane precision scaling method - Google Patents
A kind of industrial robot plane precision scaling method Download PDFInfo
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- CN109773786A CN109773786A CN201811642156.4A CN201811642156A CN109773786A CN 109773786 A CN109773786 A CN 109773786A CN 201811642156 A CN201811642156 A CN 201811642156A CN 109773786 A CN109773786 A CN 109773786A
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- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
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Abstract
The present invention proposes a kind of industrial robot precision calibration method, establishes the relative position error model of robot end, calculates kinematic error by calibration point, and then compensate, and completes robot kinematics' parameter calibration.The present invention improves the plane precision of industrial robot by reducing the relative position error, meet requirement of the robot production task to precision, this method operation is convenient, and cost is relatively low, and robot precision can be effectively improved, most of tandem type industrial robots are suitable for.
Description
Technical field
The invention belongs to robot kinematics calibration technical field, it is related to the industry based on relative positional relationship error model
Robot kinematics calibration method is a kind of industrial robot plane precision scaling method.
Background technique
Robot precision be evaluate robot performance an important indicator, robot precision include repetitive positioning accuracy and
Absolute fix precision.
Robot repetitive positioning accuracy now is higher, but absolute fix precision is very low, and robot reaches in practice
There is certain differences between end pose and theoretical value, cause robot that can not be applied to the higher yard of required precision
It closes.In various error sources, error caused by robot architecture's parameter and joint angles accounts for the 80% of all error sources
More than, therefore the absolute precision that can greatly improve robot is demarcated to robot kinematics' parameter.
It is mostly demarcated using precision measurement equipments such as laser trackers in traditional robot precision's scaling method, such as text
Offering " robot kinematics' parameter calibration method [J] based on laser tracker ", (Ren Yongjie, Zhu, a state in the Zhou Dynasty wait to measure after expensive, Yang Xueyou
Journal, 2008,29 (3): 198-202.) in, it is higher that there are calibration costs, and it is complicated for operation, need to be equipped with professional's operation etc.
Problem.Based on above-mentioned technical situation, the present invention proposes a kind of industrial machine based on relative positional relationship error model of low cost
Device people's plane precision scaling method, can effectively improve the positioning accuracy of robot, and calibration cost is low, calibration process operation letter
Single, calibration is high-efficient, and kinematics model is versatile.
Summary of the invention
The problem to be solved in the present invention is: in existing robot precision's calibration technique, repetitive positioning accuracy is higher, but absolutely
Positioning accuracy is but very low, and calibration cost is higher, complicated for operation, is unable to satisfy the demand of the higher workplace of required precision.
The technical solution of the present invention is as follows: a kind of industrial robot plane precision scaling method, comprising the following steps:
1) establish robot kinematics' model: robot establishes model using improved DH method, includes four fortune in model
It is dynamic to learn parameter: length of connecting rod ai-1, connecting rod corner αi-1, joint bias diWith joint rotation angle θi, the single connecting rod transformation square of robot
Battle array description are as follows:
Ai=Rot (x, αi-1)Trans(x,ai-1)Rot(z,θi)Trans(z,di)
Transformation matrix of robot end's link rod coordinate system relative to basis coordinates system are as follows:
Wherein N indicates the number of robot freedom degree, RNFor 3 × 3 spin matrix, PNFor 3 × 1 excursion matrix；
2) the relative position error model is established: by the connecting rod error differential transformation matrices dA between adjacent two connecting rodiRegard as
It is four kinematic error parameter δ ai-1δαi-1δdiδθiLinear function, letter is ignored when error is sufficiently small according to high number principle
Several higher order terms:
Connecting rod error differential matrix of robot end's link rod coordinate system relative to base coordinate system are as follows:
The terminal position error of robot describes are as follows:
Wherein,Bdi、Bai-1And Bαi-1The rest may be inferred,iTN(1,4)It indicatesiTNWhat matrix the first row the 4th arranged
Element
By the terminal position error dP of robottIt is written as follow form:
dPt=[M θ] δ θ+[Md] δ d+ [Ma] δ a+ [M α] δ α
The practical flange extremity coordinate position of robot is expressed as Pt c=Pt+dPt；
It is so practical relative position and name in the relative position error in robot working space between any two points
The difference of relative position:
Derive the relative positional relationship error model of robot are as follows:
dPt1-dPt2=[M θ1-Mθ2]δθ+[Md1-Md2]δd+[Ma1-Ma2]δa+[Mα1-Mα2]δα
3) it chooses suitable calibration point: selecting a robot working face flat as calibration in robot working space
One group of calibration point is chosen in face in calibration plane, and calibration point is evenly distributed in calibration plane, and calibration point number is greater than machine
The number of device people's kinematic error parameter；
4) it data needed for acquisition calibration: allows the end of robot successively to move along each calibration point, keeps robot
Terminal angle is constant, records the joint angles of robot at each calibration point, meanwhile, use distance measuring equipment recorder
The coordinate value of each calibration point of people end in cartesian coordinate system；
5) calculate kinematic error parameter: the initial value of robot kinematics' parameter uses name DH parameter value, simultaneously will
Robot joint angles and collected robot end's coordinate value substitute into robot relative positional relationship error model, pass through
The value of least square method acquisition robot kinematics' error parameter δ a δ α δ d δ θ；
6) it updates robot kinematics' parameter: being joined by the DH that obtained robot kinematics' error parameter value updates robot
Numerical value recalculates robot kinematics' error model, iterates until relative position root-mean-square error meets setting value；
7) robot kinematics' parameter compensates: by the control of the kinematic parameter errors finally picked out compensation to robot
In device, robot kinematics' parameter calibration is completed.
The method of the present invention has the advantages that
1) calibration of robot working face proposed by the invention, robot end carry out the movement of point-to-point, are not required to
Trajectory planning is carried out in advance, and calibration process is easy to operate, while positioning accuracy energy of the calibrated robot in the plane
Access great promotion.
2) robot precision's scaling method proposed by the invention based on relative positional relationship model uses low cost
The relative position distance of distance measuring equipment robot measurement end is adopted compared to using the absolute distances such as laser tracker to demarcate
Collect equipment and carry out robot kinematics' parameter calibration, have calibration cost low, calibration is high-efficient, and calibration facility uses simple etc. excellent
Point.
3) four parameters of use proposed by the invention establish robot kinematics' error model, reduce robot motion
The complexity of error model identification is learned, robot model is versatile, and the practical engineering application value of scaling method is larger.
4) precision calibration method proposed by the invention only needs the relative positional relationship of robot measurement end, avoids
The new error introduced because demarcating robot basis coordinates system.
Detailed description of the invention
Fig. 1 is the Robot calibration process flow diagram flow chart the present invention is based on the relative position error model；
Fig. 2 is robot end's relative positional relationship error schematic diagram of the present invention；
Fig. 3 is robot test platform system architecture diagram of the invention；
Fig. 4 is the robot inaccuracy identification front and back comparison diagram in an example of the invention.
Specific embodiment
The present invention proposes a kind of industrial robot precision calibration method, it is therefore an objective to improve work by reducing the relative position error
The plane precision of industry robot meets requirement of the robot production task to precision, and this method operation is convenient, and cost is relatively low, and
And robot precision can be effectively improved, it is suitable for most of tandem type industrial robots.
The invention proposes a kind of industrial robot plane precisions based on relative positional relationship error model of low cost
Scaling method, steps are as follows:
(1) establish robot kinematics' model: robot establishes model using improved DH method, includes four fortune in model
It is dynamic to learn parameter: length of connecting rod ai-1, connecting rod corner αi-1, joint bias diWith joint rotation angle θi, model is referring specifically to teaching material " machine
People's technical foundation " (Xiong Youlun, publishing house, the Central China University of Science and Technology), therefore the single connecting rod transformation matrix of robot can describe
Are as follows:
Ai=Rot (x, αi-1)Trans(x,ai-1)Rot(z,θi)Trans(z,di)
AiIt is the transformation matrix of single connecting rod, i.e., transformation matrix of the connecting rod relative to a upper connecting rod, i are indicated i-th
Connecting rod, x, z indicate x coordinate axis z coordinate axis.Rot is rotation transformation, such as Rot (x, α) expression rotates around x axis α angle.Trans
It is translation transformation matrix, such as Trans (z, d) indicates to translate d distance along z-axis.Total connecting rod transformation matrix TNBy single connecting rod
Transformation matrix is multiplied to obtain, transformation matrix of robot end's link rod coordinate system relative to basis coordinates system are as follows:
Wherein N is the number of robot freedom degree, i.e., the robot of N number of freedom degree is exactly by N number of connecting rod transformation matrix phase
It is multiplied to arrive.By TNThe partitioning of matrix, RNFor spin matrix, i.e., by TN3 × 3 matrixes be expressed as RN, PNFor excursion matrix, i.e., by TN
3 × 1 matrixes be expressed as PN。
(2) the relative position error model is established: by the connecting rod error differential transformation matrices dA between adjacent two connecting rodiRegard as
It is four kinematic error parameter δ ai-1δαi-1δdiδθiLinear function, the higher order term of function is ignored when error is sufficiently small:
It is described here it is sufficiently small be a term in high number by the differential of function, such as e^-8~e^-15 is ok
It is sufficiently small for can be regarded as, it should be noted that not being same concept with the error in robot inaccuracy parameter identification here.
Connecting rod error differential matrix of robot end's link rod coordinate system relative to base coordinate system are as follows:
Therefore, the terminal position error of robot can be described as:
Wherein,Bdi、Bai-1And Bαi-1The rest may be inferred.iTN(1,4)It indicatesiTNWhat matrix the first row the 4th arranged
Element,iTN(1,4)、iTN(2,4)、iTN(3,4)It isiTNThe excursion matrix of this homogeneous matrix, i.e., the P mentioned in formula beforeN。
Meanwhile the terminal position error dP of robottForm can be written as follow:
dPt=[M θ] δ θ+[Md] δ d+ [Ma] δ a+ [M α] δ α
The practical flange extremity coordinate position of robot can be expressed as Pt c=Pt+dPt。
Therefore, then the relative position error in robot working space between any two points be practical relative position and
The difference of nominal relative position are as follows:
Wherein, first point is denoted as t1, second point is denoted as t2,Indicate the physical location of first point,Table
Show the physical location of second point, Pt1Indicate the theoretical position of first point, Pt2Indicate the theoretical position of second point.Here
Two o'clock can represent arbitrary two points in the working space of robot, specifically, can be understood as in one group of calibration point
Any two calibration point.
Above formula is integrated, can derive the relative positional relationship error model of robot are as follows:
dPt1-dPt2=[M θ1-Mθ2]δθ+[Md1-Md2]δd+[Ma1-Ma2]δa+[Mα1-Mα2]δα
(3) it chooses suitable calibration point: selecting suitable robot working face as mark in robot working space
Face is allocated, one group of suitable calibration point is chosen in calibration plane, so that it is evenly distributed in the plane.
The suitable plane meets: 1), calibration plane must be in the working space of robot；2) robot, is needed
Precision in which plane domain is improved, and is just demarcated in the plane domain；3), the area of plane is demarcated not
Preferably too large or too small, this does not have specific standard, carries out analysis determination according to actual robot and operating condition.
One group of suitable calibration point meets: " one group " must be greater than the number of robot kinematics' error parameter,
Calibration point number is more, and calibration result is more accurate, but reaches certain number, and stated accuracy would not change.So and
Judgement determination is carried out in conjunction with actual conditions.
(4) it data needed for acquisition calibration: allows the end of robot successively to move along each calibration point, keeps robot
Terminal angle is constant, records the joint angles of robot at each calibration point.Meanwhile using distance measuring equipment recorder
The coordinate value of each calibration point of people end in cartesian coordinate system, common distance measuring equipment have Turbogrid plates, Laser Measuring
Distance meter, visual apparatus etc., depending on the site environment with the suitable measuring device of choice of experimental conditions.
(5) calculate kinematic error parameter: the initial value of robot kinematics' parameter uses name DH parameter value, simultaneously will
Robot joint angles and collected robot end's coordinate value substitute into robot relative positional relationship error model, pass through
The value of least square method acquisition robot kinematics' error parameter δ a δ α δ d δ θ.
(6) it updates robot kinematics' parameter: updating the name of robot by obtained robot kinematics' error parameter value
Adopted parameter recalculates robot kinematics' error model.It iterates until relative position root-mean-square error meets setting value,
It can be obtained by result general iteration 2~4 times.At this point, precision of the robot in the plane is greatly improved, usual energy
Reach two to three orders of magnitude.
(7) robot kinematics' parameter compensates: by the control of the kinematic parameter errors finally picked out compensation to robot
In device processed, robot kinematics' parameter calibration is completed.
Illustrate implementation of the invention below by specific embodiment.
(1) establish robot kinematics' model: by taking six-joint robot as an example, robot establishes mould using improved DH method
The connecting rod transformation matrix of type, robot can be described as:
Ai=Rot (x, αi-1)Trans(x,ai-1)Rot(z,θi)Trans(z,di)
The nominal DH parameter of robot is referring to table 1.
1 robot name DH parameter of table
| Joint | α(°) | a(mm) | d(mm) | θ(°) |
| 1 | 0 | 0 | 310 | θ1 |
| 2 | -90 | 160 | 0 | θ2 |
| 3 | 0 | 780 | 0 | θ3 |
| 4 | -90 | 196 | 690 | θ4 |
| 5 | 90 | 0 | 0 | θ5 |
| 6 | -90 | 0 | 60 | θ6 |
Transformation matrix of robot end's link rod coordinate system relative to basis coordinates system can be found out are as follows:
T6=A1·A2…A6
(2) the relative position error model: robot end's nominal position P is establishedt=F (a, α, d, θ), robot end are real
Border position is Pt c=F (a+ Δ a, α+Δ α, d+ Δ d, θ+Δ θ).The relative position error between the two o'clock of robot are as follows:
Robot the relative position error model is established with this:
dPt1-dPt2=[M θ1-Mθ2]δθ+[Md1-Md2]δd+[Ma1-Ma2]δa+[Mα1-Mα2]δα
(3) it chooses suitable calibration point: choosing the plane of a 240*240mm in the working space of robot as machine
The working face of robot is divided into the square of the identical 80*80mm of size by the working face of device people, by each small pros
Calibration point of the vertex of shape as robot.
(4) it data needed for acquisition calibration: allows the end of robot successively to move along each calibration point, keeps robot
Terminal angle is constant, records the joint angles of robot at each calibration point.Meanwhile using Turbogrid plates recorder people end
The coordinate value of each calibration point in cartesian coordinate system.
(5) it calculates kinematic error parameter: obtaining the value of the error parameter δ a δ α δ d δ θ of robot using least square method.
(6) it updates robot kinematics' parameter: robot is arrived into the compensation of obtained robot kinematics' error parameter value
In nominal parameter, robot kinematics' error model is recalculated, by 2 iteration, relative position root-mean-square error value is i.e. full
Sufficient setting value.It finally obtains compensated robot kinematics' parameter and is shown in Table 2.
The compensated robot DH parameter of table 2
| Joint | α(°) | a(mm) | d(mm) | θ(°) |
| 1 | 0 | 0 | 310 | θ1+0.0017 |
| 2 | -90 | 156.7173 | 0.0377 | θ2-0.0625 |
| 3 | 0 | 781.3731 | 0 | θ3-0.0364 |
| 4 | -90 | 196 | 683.5724 | θ4-0.0717 |
| 5 | 90 | 0 | 2.4924 | θ5+0.0072 |
| 6 | -90 | 0 | 60 | θ6 |
(7) robot kinematics' parameter compensates: by the control of the kinematic parameter errors finally picked out compensation to robot
It in device processed, is verified again, verification result is shown in Table 3.
The comparison of 3 Robot calibration front-rear position error of table
| Worst error | Mean error | |
| Before calibration | 23.2522 | 12.1091 |
| After calibration | 1.4514 | 0.4841 |
The location error identification front and back comparison of robot is as shown in Figure 4, it can be seen that by calibration, the precision of robot is obtained
Great raising is arrived.
The present invention can simplify calibration measurement using the working face of robot as the acquisition target of Robot calibration data
Step, essence while precision of the calibrated robot in its working space is greatly improved, in its working face
Degree can be optimal.
The present invention can obtain the relative positional relationship of robot end using the distance measuring equipment of low cost, including
But it is not limited to the equidistant measuring device of Turbogrid plates, laser range finder, visual apparatus, expensive absolute distance measurement is not needed and sets
It is standby, reduce calibration cost.
The working face of robot is chosen to be measurement object by the present invention, the plane precision of robot can achieve it is optimal,
Relatively inexpensive distance measuring equipment can be used simultaneously, reduce calibration cost.It is excellent that above example is only used as of the invention one
Example is selected, all without departing from technical spirit of the invention, made any modification, replacement, improvement etc. belong to guarantor of the invention
Protect range.
Claims (3)
1. a kind of industrial robot plane precision scaling method, it is characterized in that the following steps are included:
1) establish robot kinematics' model: robot establishes model using improved DH method, includes four kinematics in model
Parameter: length of connecting rod ai-1, connecting rod corner αi-1, joint bias diWith joint rotation angle θi, the single connecting rod transformation matrix of robot retouches
It states are as follows:
Ai=Rot (x, αi-1)Trans(x,ai-1)Rot(z,θi)Trans(z,di)
Transformation matrix of robot end's link rod coordinate system relative to basis coordinates system are as follows:
Wherein N indicates the number of robot freedom degree, RNFor 3 × 3 spin matrix, PNFor 3 × 1 excursion matrix；
2) the relative position error model is established: by the connecting rod error differential transformation matrices dA between adjacent two connecting rodiRegard four as
Kinematic error parameter δ ai-1 δαi-1 δdi δθiLinear function, function is ignored when error is sufficiently small according to high number principle
Higher order term:
Connecting rod error differential matrix of robot end's link rod coordinate system relative to base coordinate system are as follows:
The terminal position error of robot describes are as follows:
Wherein,Bdi、Bai-1And Bαi-1The rest may be inferred,iTN(1,4)It indicatesiTNThe element that matrix the first row the 4th arranges
By the terminal position error dP of robottIt is written as follow form:
dPt=[M θ] δ θ+[Md] δ d+ [Ma] δ a+ [M α] δ α
The practical flange extremity coordinate position of robot is expressed as Pt c=Pt+dPt；
It is so that practical relative position is opposite with name in the relative position error in robot working space between any two points
The difference of position:
Derive the relative positional relationship error model of robot are as follows:
dPt1-dPt2=[M θ1-Mθ2]δθ+[Md1-Md2]δd+[Ma1-Ma2]δa+[Mα1-Mα2]δα
3) it chooses suitable calibration point: select one robot working face as demarcating plane in robot working space,
One group of calibration point is chosen in calibration plane, calibration point is evenly distributed in calibration plane, and calibration point number is greater than machine
The number of people's kinematic error parameter；
4) it data needed for acquisition calibration: allows the end of robot successively to move along each calibration point, keeps robot end
Posture is constant, records the joint angles of robot at each calibration point, meanwhile, use distance measuring equipment recorder people end
The coordinate value of each calibration point of end in cartesian coordinate system；
5) calculate kinematic error parameter: the initial value of robot kinematics' parameter uses name DH parameter value, while by machine
Person joint's angle and collected robot end's coordinate value substitute into robot relative positional relationship error model, pass through minimum
The value of square law acquisition robot kinematics' error parameter δ a δ α δ d δ θ；
6) it updates robot kinematics' parameter: updating the DH parameter of robot by obtained robot kinematics' error parameter value
Value, recalculates robot kinematics' error model, iterates until relative position root-mean-square error meets setting value；
7) robot kinematics' parameter compensates: by the controller of the kinematic parameter errors finally picked out compensation to robot
In, complete robot kinematics' parameter calibration.
2. a kind of industrial robot plane precision scaling method according to claim 1, it is characterized in that being used in step 4)
Distance measuring equipment include Turbogrid plates, laser range finder and visual apparatus, it is suitable with choice of experimental conditions depending on the site environment
Measuring device.
3. a kind of industrial robot plane precision scaling method according to claim 1, it is characterized in that selection in step 3)
Selection principle when the calibration plane of robot are as follows: 1), calibration plane must be in the working space of robot；2) machine, is needed
Precision of the people in which plane domain improves, just the selection calibration plane in the plane domain；3) plane, is demarcated
Area is determined according to actual robot and operating condition.
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