CN109238199A - A kind of robot rotary shaft kinematic calibration method - Google Patents
A kind of robot rotary shaft kinematic calibration method Download PDFInfo
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- CN109238199A CN109238199A CN201811018214.6A CN201811018214A CN109238199A CN 109238199 A CN109238199 A CN 109238199A CN 201811018214 A CN201811018214 A CN 201811018214A CN 109238199 A CN109238199 A CN 109238199A
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- G—PHYSICS
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- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
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Abstract
The present invention proposes a kind of robot rotary shaft kinematic calibration method, belongs to robot automation's mounting technology field.This method chooses robot to be calibrated first, constructs robot rotary shaft kinematics model；Rotary shaft base coordinate system is registrated by laser tracker, obtains the relationship between laser tracker coordinate system and rotary shaft base coordinate system；The control each rotary shaft of robot rotates different angles, every time after rotation, the terminal angle of robot and the calculated value of position are obtained using robot kinematics' model, the terminal angle of robot after being screened using laser tracker and the measured value of position finally obtain the calculated value and measured value of each rotation shaft angle combination of k group and the combination corresponding robot end's posture and position；It is demarcated by kinematics parameters of the least square method to robot rotary shaft.The method of the present invention is simple to operate, only needs a small amount of utensil that can complete high-precision rotary shaft kinematics parameters identification.
Description
Technical field
The present invention relates to a kind of robot rotary shaft kinematic calibration methods, belong to robot automation's mounting technology
Field.
Background technique
With the development of science and technology, robot has penetrated into the every aspect of human lives, especially as labor
The power substitution mankind receive extensive utilization in the work of high-intensitive high duplication.Many scholars have studied robot inaccuracy
Distribution and source, it is indicated that geometric error is the principal element of influence robot spatial movement error, therefore to the mark of geometric error
Fixed and compensation becomes the important research content for improving robot precision.The measurement of geometric error there are two main classes method, first
It is the individual error direct method of measurement, second is composition error measurement parameter identification method.
Robot is made of multiple joints, and wherein motion profile is that the axis of straight line is known as linear axis, and motion profile is
Circular axis is known as rotary shaft.The common measuring tool of the direct method of measurement of existing robot rotation axis error have dial gauge,
Micrometer and slide calliper rule etc., these tools are used cooperatively, and can complete the detection of all individual errors.But these measurers are not using
Just, low precision, and each error term will independent measurement, constrain the efficiency and precision of rotary shaft error calibration significantly.
The Zhang Zhen people that waits so long proposes a kind of rotary shaft geometric error detection method based on laser tracker measurement, and utilization is homogeneous
Transformation matrix carries out the Kinematic Model of rotary shaft, and provides the relationship of space error Yu each individual error, using laser with
Track instrument obtains rotation shaft end pose to the measurement for 3 target balls for being fixedly arranged at rotation shaft end, carries out parameter identification solution.But
Separate unit laser tracker calibration rotary shaft is used only in the method will appear the problem of precision deficiency.
Wang et al. proposes that a kind of numerically-controlled machine tool rotary shaft using laser tracker timesharing multi-court position measuring principle moves
Learn scaling method.Laser tracker timesharing multi-court position mensuration, is the improvement to multi-path laser tracing measurement system.Multi-path laser
Tracing measurement system in practical applications, needs simultaneously to measure target point with 4 laser trackers, leads to system cost
It is higher, inconvenient, measurement efficiency is not high.The measurement of laser tracker timesharing multi-court position is more with a laser tracker transfer
A erect-position measures same target point, is solved using polygon measuring principle to coordinate of ground point, principle and multichannel
Laser tracking measurement system is identical, but only needs a laser tracker that measurement can be completed, greatly reduce the hardware of system at
This.Since entire measurement process has only used the precision distance measurement value of laser tracker, so timesharing multi-court position measurement method pair
The measurement of spatial point coordinate can achieve very high precision.But due to take multiple measurements, this method time of measuring is long,
Measurement process is complicated, and needs that measurement erect-position is arranged in very large space range, and practical application is very inconvenient, when this external pelivimetry also
It is required that the identical track of lathe repeating motion, requires the repetitive positioning accuracy of lathe very high.
In conclusion structure is complicated for robot rotary shaft, error calibration difficulty is larger, individual error direct measuring method
Efficiency is lower, and effect is poor.Error modeling and the method for identification are the main direction of studying of rotary shaft error calibration, some scholars
The rotary shaft error parameter identification method based on instruments such as ball bar, Position-Sensitive Detectors is had studied, but is limited to instrument characteristic,
The practical application of these methods is relatively more limited.Side based on laser tracker measurement and homogeneous transform matrix tectonic kinematics model
Method is using more and more extensive, but for the rotary shaft Kinematic Calibration problem of automatic punching system, due to system structure is complicated,
Volume is larger, leads to laser tracker measurement distance farther out, measurement accuracy is insufficient.And the timesharing multi-court position measurement based on Multi lateration
Method is complicated for operation, and measurement erect-position setting is inconvenient, and has higher requirements to the repetitive positioning accuracy of automatic punching system, actually answers
With very inconvenient.
Summary of the invention
The purpose of the present invention is the shortcomings to overcome prior art, propose a kind of robot rotary shaft kinematics parameters
Scaling method.The method of the present invention is simple to operate, only needs a small amount of utensil that can complete high-precision rotary shaft kinematics ginseng
Number identification.
The present invention proposes a kind of robot rotary shaft kinematic calibration method, which comprises the following steps:
(1) robot to be calibrated is chosen, robot rotary shaft kinematics model is constructed；Specific step is as follows:
(1-1) chooses robot to be calibrated, establishes rotary shaft base coordinate system C to robot rotary shaft pedestal0, enable C0
It is consolidated in straight line shaft end and with linear axis；It sets out from pedestal and correspondence is successively established respectively to each rotary shaft to robot end
Coordinate system be denoted as C respectively1…Cn-1, wherein C1…Cn-1It respectively corresponds from pedestal to each rotary shaft between end, and in machine
The end of device people establishes ending coordinates system and is denoted as Cn；
(1-2) arbitrarily chooses a rotary shaft and is denoted as i, utilizes the rotational angle theta of the rotary shaft of i-th of rotary shafti, torsional angle αi, axis
Length aiWith axle base di4 parameters determine i-th of spin matrixi-1Ti, obtain coordinate system CiTo previous coordinate system Ci-1
Transformational relation, wherein T (zi-1,di) and T (zi-1,θi) it is respectively along (i-1)-th coordinate system Ci-1Z axis movement and rotation, T
(xi,ai) and T (xi,αi) it is respectively along i-th of coordinate system CiX-axis movement and rotation；i-1TiExpression formula is as follows:
(1-3) is by each spin matrixi-1TiIt is decomposed into corresponding one 3 × 3 spin matrixi-1RiWith one 3 × 1
Translation vectori-1ti:
(1-4) calculates ending coordinates system CnWith rotary shaft base coordinate system C0Between relationship, expression formula is as follows:
0Tn=0T1·1T2·…·n-1Tn
According to the targeted attitude V of robot endt=[vx vy vz]T, calculating robot end is in C0Pair under coordinate system
Answer posture Vt 0；Expression formula is as follows:
Vt 0=0R1·1R2·...·n-1Rn·Vt
In formula, VxFor x coordinate of robot end's targeted attitude under ending coordinates system, VyFor robot end's target appearance
Y-coordinate of the state under ending coordinates system, VzFor z coordinate of robot end's targeted attitude under ending coordinates system；
According to robot end target position Pt=[px py pz]TCalculating robot end is in C0Correspondence position under coordinate system
Set Pt 0；Expression formula is as follows:
In formula, PxFor x coordinate of the robot end target position under ending coordinates system, PyFor robot end's target position
Set the y-coordinate under ending coordinates system, PzFor z coordinate of the robot end target position under ending coordinates system；
The building of robot rotary shaft kinematics model finishes；
(2) robot working space is added in laser tracker, by laser tracker to rotary shaft base coordinate system into
Row registration, obtains laser tracker coordinate system CLWith rotary shaft base coordinate system C0Between relationship, obtain laser tracker swash
Light device is in C0The coordinate of coordinate systemWherein, xltFor laser tracker laser in C0X under coordinate system
Coordinate value, yltFor laser tracker laser in C0Y-coordinate value under coordinate system, zltFor laser tracker laser in C0
Z coordinate value under coordinate system；
(3) the control each rotary shaft of robot rotates different angles, every time after rotation, utilizes robot kinematics' model
The terminal angle of robot and the calculated value of position are obtained, the terminal angle of the robot after being screened using laser tracker
With the measured value of position, finally obtain the combination of each rotation shaft angle of k group and the corresponding robot end's posture of the combination and
The calculated value and measured value of position；Specific step is as follows:
(3-1) controls each rotary shaft and rotates different angles, so that positioning after all rotary shaft rotations each time
Angle between face normal vector and measurement light is less than 45 °；
I-th group of each rotation shaft angle combination is substituted into fortune by robot kinematics' model that (3-2) utilizes step (1) to establish
Dynamic initial parameter values of learning carry out the calculated value that i-th group of each rotation shaft angle combination respective ends posture is calculatedIt is denoted as with the calculated value of i-th group of each rotation shaft angle combination respective ends position
WhereinRespective ends Attitude Calculation value is combined in C for i-th group of each rotation shaft angle of robot0Under x coordinate throw
Shadow,Respective ends Attitude Calculation value is combined in C for i-th group of each rotation shaft angle of robot0Under y-coordinate projection,For
Each rotation shaft angle combination respective ends Attitude Calculation value of i-th group of robot is in C0Under z coordinate projection；For robot i-th
Each rotation shaft angle combination respective ends position calculated value of group is in C0Under x coordinate,Shaft angle is respectively rotated for i-th group for robot
Degree combination respective ends position calculated value is in C0Under y-coordinate,For i-th group of each corresponding end of rotation shaft angle combination of robot
End position calculated value is in C0Under z coordinate；
Using the laser of laser tracker in C0Coordinate under coordinate systemCalculate separately i-th group of each rotation shaft angle
Combine the displacement of respective ends position calculated value to laser trackerAnd terminal angle calculated value and measurement radiation direction
Angle ωi, expression formula is as follows:
(3-3) carries out the measurement of terminal position using laser tracker to each group of each rotation shaft angle combination, obtains i-th
The corresponding terminal position measured value of each rotation shaft angle combination of groupChoose ωiThe terminal angle that 45 ° of < measures, and obtains
The terminal angle measured value corresponding to i-th group of each rotation shaft angle combinationFinally obtain each rotation shaft angle combination of k group
And the calculated value and measured value of the combination corresponding robot end's posture and position；
(4) kinematics parameters of robot rotary shaft are demarcated；Specific step is as follows:
(4-1) combines corresponding end X-coordinate error amount f by i-th group of following equation calculations each rotation shaft anglexi, Y sit
Mark error amount fyiWith Z coordinate error amount fzi:
(4-2) is using the laser of laser tracker in C0Coordinate under coordinate system isIn step
(3) any one group of each rotation shaft angle obtained in combines corresponding terminal position measured value and is
Wherein,The x coordinate of corresponding terminal position measured value is combined for i-th group of each rotation shaft angle,It is respectively rotated for i-th group
The y-coordinate of the corresponding terminal position measured value of axis angle combinations,Corresponding end position is combined for i-th group of each rotation shaft angle
The z coordinate for setting measured value, calculate between the terminal position measured value and laser tracker of the group each rotation shaft angle combination away from
From:
Calculate the measured value that each rotation shaft angle of the group combines corresponding measurement radiation direction and each plane included angle of coordinate system
Respectively ψxi, ψyiAnd ψzi；Expression formula is as follows:
Wherein, ψxiThe measured value of the angle of light and yoz plane, ψ are measured for laser trackeryiFor laser tracker survey
Measure the measured value of the angle of light and xoz plane, ψziThe measured value of the angle of light and xoy plane is measured for laser tracker；
(4-3) is demarcated using kinematics parameters of the Least square-fit in following formula to robot rotary shaft, is calculated
Kinematics parameters:
The kinematics parameters for obtaining each rotary shaft are as follows: there are three parameters for first rotary shaft, comprising: torsional angle αi, axial length
Spend aiWith axle base di；There are four parameters for each rotary shaft later, comprising: rotational angle thetai, torsional angle αi, shaft length aiAnd axle base
di。
The features of the present invention and beneficial effect are:
The present invention demarcates the rotary shaft kinematics of robot using the advantage of laser tracker precision distance measurement, with
Improve the precision and efficiency of robot kinematics calibration.
This method screens the terminal angle for calculating, root according to the angle of cutter positioning face normal vector and measurement light
According to each coordinate direction and measurement radiation direction angle come to terminal position three-dimensional coordinate weight, construct based on laser with
Track instrument measures the rotary shaft Kinematic Calibration method of the coordinate weighting and posture screening of characteristic.
Robot kinematics calibration is robot using preceding very important work, can be substantially reduced due to robot ruler
System position error caused by error is spent, while the utensil that the method for the present invention uses is less, it is only necessary to which a laser tracker is
Can, realize convenient and fast high precision machines people rotary shaft scaling method.
Specific embodiment
The present invention proposes a kind of robot rotary shaft kinematic calibration method, combined with specific embodiments below to this hair
Bright further description is as follows.
The present invention proposes a kind of robot rotary shaft kinematic calibration method, comprising the following steps:
(1) robot to be calibrated is chosen, determines the D-H parameter of the robot motion, building robot rotary shaft movement
Learn model；Specific step is as follows:
(1-1) chooses robot to be calibrated, establishes rotary shaft base coordinate system C to robot rotary shaft pedestal0, enable C0
It is consolidated in straight line shaft end and with linear axis；It sets out from pedestal and correspondence is successively established respectively to each rotary shaft to robot end
Coordinate system be denoted as C respectively1…Cn-1, wherein C1…Cn-1It respectively corresponds from pedestal to each rotary shaft between end, and in machine
The end of device people establishes ending coordinates system and is denoted as Cn；
By taking the robot with 2 rotary shafts as an example, two rotary shafts are denoted as C axis and A axis respectively, wherein the one of C axis
End is fixed on straight line shaft end, realizes the overall movement of two rotary shafts, A the tip of the axis mounting robot end target.In C axis
With corresponding coordinate system C is established on A axis respectively0And C1, and make coordinate system C0It consolidates, and makees in straight line shaft end and with linear axis
For the coordinate system of rotary shaft pedestal.Robot end's target-based coordinate system C is established in A the tip of the axis2(usual robot end makes
Used time can clamp some experiment appliances, for example, if needing robot hole, will clamp cutter, carry out if necessary to robot
Crawl will clamp the crawl equipment of hand or clip etc).
(1-2) arbitrarily chooses a rotary shaft and is denoted as i, utilizes the rotational angle theta of the rotary shaft of i-th of rotary shafti, torsional angle αi, axis
Length aiWith axle base di(above 4 parameters directly can use measuring tool (such as ruler etc.) to measure to 4 parameters, herein
Only need a not particularly accurate estimated value) determine i-th of spin matrixi-1Ti, obtain coordinate system CiIt is previous to its
Coordinate system Ci-1Transformational relation, wherein T (zi-1,di) and T (zi-1,θi) it is respectively along (i-1)-th coordinate system Ci-1Z axis shifting
Dynamic and rotation, T (xi,ai) and T (xi,αi) it is respectively along i-th of coordinate system CiX-axis movement and rotation.i-1TiExpression formula is such as
Under:
(1-3) is by each spin matrixi-1TiIt is decomposed into corresponding one 3 × 3 spin matrixi-1RiWith one 3 × 1
Translation vectori-1ti:
(1-4) calculates ending coordinates system CnWith rotary shaft base coordinate system C0Between relationship, expression formula is as follows:
0Tn=0T1·1T2·····n-1Tn
And according to the targeted attitude V of robot endt=[vx vy vz]T, calculating robot end is in C0Under coordinate system
Corresponding posture Vt 0；Expression formula is as follows:
Vt 0=0R1·1R2·...·n-1Rn·Vt
In formula, VxFor x coordinate of robot end's targeted attitude under ending coordinates system, VyFor robot end's target appearance
Y-coordinate of the state under ending coordinates system, VzFor z coordinate of robot end's targeted attitude under ending coordinates system；
According to robot end target position Pt=[px py pz]TCalculating robot end is in C0Correspondence position under coordinate system
Set Pt 0；Expression formula is as follows:
In formula, PxFor x coordinate of the robot end target position under ending coordinates system, PyFor robot end's target position
Set the y-coordinate under ending coordinates system, PzFor z coordinate of the robot end target position under ending coordinates system；
The building of robot rotary shaft kinematics model finishes.
(2) laser tracker (can be disposable type, the concrete model LeicaAT-960 of the present embodiment) be adjusted, and will
Robot working space is added in laser tracker, is registrated, is swashed to rotary shaft base coordinate system by laser tracker
Optical tracker system coordinate system CLWith rotary shaft base coordinate system C0Between relationship, obtain the laser of laser tracker in C0Coordinate
The coordinate of systemWherein, xltFor laser tracker laser in C0X-coordinate value under coordinate system, yltFor
The laser of laser tracker is in C0Y-coordinate value under coordinate system, zltFor laser tracker laser in C0Z under coordinate system
Coordinate value.
(3) it controls each rotary shaft and rotates different angles, every time after rotation, obtain machine using robot kinematics' model
The terminal angle of device people and the calculated value of position screen terminal angle according to angle, obtain robot using laser tracker
The measured value of terminal angle and position finally obtains each rotation shaft angle combination of k group and the corresponding robot end of the combination
Hold the calculated value and measured value of posture and position；Specific step is as follows:
(3-1) controls each rotary shaft (being C axis and A axis in embodiment) different angle of rotation, so that owning each time
Rotary shaft rotation finishes the angle between rear-locating face normal vector and measurement light less than 45 °, and number of revolutions is 8 times of rotation number of axle
Amount is above (to be 2 rotary shafts in the present embodiment, then at least carry out 16 rotations, be 17 times in the present embodiment), revolve every time
It is preferably such that all rotary shafts are rotated when turning, so that measurement range is more evenly distributed；
I-th group of each rotation shaft angle combination is substituted into fortune by robot kinematics' model that (3-2) utilizes step (1) to establish
Dynamic initial parameter values of learning carry out the calculated value that i-th group of each rotation shaft angle combination respective ends posture is calculatedIt is denoted as with the calculated value of i-th group of each rotation shaft angle combination respective ends position
WhereinRespective ends Attitude Calculation value is combined in C for i-th group of each rotation shaft angle of robot0Under x coordinate throw
Shadow,Respective ends Attitude Calculation value is combined in C for i-th group of each rotation shaft angle of robot0Under y-coordinate projection,For
Each rotation shaft angle combination respective ends Attitude Calculation value of i-th group of robot is in C0Under z coordinate projection；
In following embodiment for by i-th group of C axis and A shaft angle degree combination bring into kinematics parameters initial value as a result, obtaining down
Formula:
In formula, C, S are respectively the abbreviation of cos and sin, θAi,θCiRespectively i-th group of A axis, C axis are controlled by shaft rotating motor
Corner, α1,α2Respectively A axis, the torsional angle that the mechanical arm itself of C axis connection generates, θ2It is produced for A axis and the mechanical arm of C axis connection
Raw corner, d1,d2Respectively A axis, axle base caused by the mechanical arm of C axis connection, a1,a2Respectively A axis, the axial length of C axis
Degree
The calculated value that i-th group of each rotation shaft angle combines corresponding terminal position is denoted asIts
In,Respective ends position calculated value is combined in C for i-th group of each rotation shaft angle of robot0Under x coordinate,For machine
I-th group of people each rotation shaft angle combination respective ends position calculated value is in C0Under y-coordinate,It is respectively rotated for i-th group for robot
Axis angle combinations respective ends position calculated value is in C0Under z coordinate；
The present embodiment calculation expression is as follows
Using the laser of laser tracker in C0Coordinate under coordinate systemCalculate separately i-th group of each rotation shaft angle
Combine the displacement of respective ends position calculated value to laser trackerAnd the folder of terminal angle calculated value and measurement radiation direction
Angle ωi, expression formula is as follows:
(3-3) is using laser tracker to each group of each rotation shaft angle (being C axis and A shaft angle degree in the present embodiment) combination
The measurement for carrying out terminal position obtains i-th group of corresponding terminal position measured value of each rotation shaft angle combinationBut it is right
The angle ω so that between positioning surface normal vector and measurement light is only chosen in the measurement of terminal angleiThe terminal angle that 45 ° of < into
Row measurement obtains i-th group of corresponding terminal angle measured value of each rotation shaft angle combinationFinally obtain each rotation of k group
The calculated value and measured value of axis angle combinations and the combination corresponding robot end's posture and position.
In the present embodiment,
Wherein,To be measured using laser tracker in coordinate system C0Under obtain i-th group
The corresponding terminal angle measured value of each rotation shaft angle combination；, terminal positionTo utilize
Laser tracker is measured in coordinate system C0Obtain i-th group of corresponding terminal position measured value of each rotation shaft angle combination；WhereinRespective ends attitude measurement value is combined in C for i-th group of each rotation shaft angle of robot0Under x coordinate projection,For machine
I-th group of device people each rotation shaft angle combination respective ends attitude measurement value is in C0Under y-coordinate projection,For i-th group of robot
Each rotation shaft angle combination respective ends targeted attitude measured value is in C0Under z coordinate projection；It is respectively revolved for i-th group for robot
Shaft angle combinations respective ends position measurements are in C0Under x coordinate,For i-th group of each rotation shaft angle combination of robot
Respective ends position measurements are in C0Under y-coordinate,Respective ends position is combined for i-th group of each rotation shaft angle of robot
Measured value is in C0Under z coordinate；
(4) kinematics parameters of robot rotary shaft are demarcated；Specific step is as follows:
(4-1) noteIt is that i-th group of each rotation shaft angle combination (being C axis and A axis angle combinations in the present embodiment) is right
The terminal position measured value answered,It is the calculated value of terminal position, passes through i-th group of each rotation shaft angle group of following equation calculations
Close corresponding end X-coordinate error amount fxi, Y coordinate error amount fyiWith Z coordinate error amount fzi:
(4-2) is using the laser of laser tracker in C0Coordinate under coordinate system isIn step
(3) the corresponding terminal position of each rotation shaft angle combination of any one group obtained (being C axis and A axis angle combinations in the present embodiment)
Measured value isThe terminal position calculated value and laser for calculating each rotation shaft angle combination of the group track
The distance between instrument:
And then calculate the survey that each rotation shaft angle of the group combines corresponding measurement radiation direction and each plane included angle of coordinate system
Magnitude is respectively ψxi, ψyiAnd ψzi；Expression formula is as follows:
Wherein, ψxiThe measured value of the angle of light and yoz plane, ψ are measured for laser trackeryiFor laser tracker survey
Measure the measured value of the angle of light and xoz plane, ψziThe measured value of the angle of light and xoy plane is measured for laser tracker.
(4-3) is demarcated using kinematics parameters of the Least square-fit in following formula to robot rotary shaft, is calculated
Kinematics parameters:
Wherein, k is the group number of each rotation angle of rotating shaft combination obtained by step (3) screening, the present embodiment 17.
The kinematics parameters for obtaining each rotary shaft are as follows: there are three parameters for first rotary shaft, comprising: torsional angle αi, axial length
Spend aiWith axle base di；There are four parameters for each rotary shaft later, comprising: rotational angle thetai, torsional angle αi, shaft length aiAnd axle base
di。
Claims (1)
1. a kind of robot rotary shaft kinematic calibration method, which comprises the following steps:
(1) robot to be calibrated is chosen, robot rotary shaft kinematics model is constructed；Specific step is as follows:
(1-1) chooses robot to be calibrated, establishes rotary shaft base coordinate system C to robot rotary shaft pedestal0, enable C0Straight
Spool end and with linear axis consolidate；It sets out from pedestal and corresponding seat is successively established respectively to each rotary shaft to robot end
Mark system is denoted as C respectively1…Cn-1, wherein C1…Cn-1It respectively corresponds from pedestal to each rotary shaft between end, and in robot
End establish ending coordinates system and be denoted as Cn；
(1-2) arbitrarily chooses a rotary shaft and is denoted as i, utilizes the rotational angle theta of the rotary shaft of i-th of rotary shafti, torsional angle αi, shaft length
aiWith axle base di4 parameters determine i-th of spin matrixi-1Ti, obtain coordinate system CiTo previous coordinate system Ci-1Turn
Relationship is changed, wherein T (zi-1,di) and T (zi-1,θi) it is respectively along (i-1)-th coordinate system Ci-1Z axis movement and rotation, T (xi,
ai) and T (xi,αi) it is respectively along i-th of coordinate system CiX-axis movement and rotation；i-1TiExpression formula is as follows:
(1-3) is by each spin matrixi-1TiIt is decomposed into corresponding one 3 × 3 spin matrixi-1RiWith one 3 × 1 translation
Vectori-1ti:
(1-4) calculates ending coordinates system CnWith rotary shaft base coordinate system C0Between relationship, expression formula is as follows:
0Tn=0T1·1T2·····n-1Tn
According to the targeted attitude V of robot endt=[vx vy vz]T, calculating robot end is in C0Correspondence appearance under coordinate system
State Vt 0；Expression formula is as follows:
Vt 0=0R1·1R2·…·n-1Rn·Vt
In formula, VxFor x coordinate of robot end's targeted attitude under ending coordinates system, VyExist for robot end's targeted attitude
Y-coordinate under ending coordinates system, VzFor z coordinate of robot end's targeted attitude under ending coordinates system；
According to robot end target position Pt=[px py pz]TCalculating robot end is in C0Corresponding position under coordinate system
Pt 0；Expression formula is as follows:
In formula, PxFor x coordinate of the robot end target position under ending coordinates system, PyExist for robot end target position
Y-coordinate under ending coordinates system, PzFor z coordinate of the robot end target position under ending coordinates system；
The building of robot rotary shaft kinematics model finishes；
(2) robot working space is added in laser tracker, rotary shaft base coordinate system is matched by laser tracker
Standard obtains laser tracker coordinate system CLWith rotary shaft base coordinate system C0Between relationship, obtain the laser of laser tracker
In C0The coordinate of coordinate systemWherein, xltFor laser tracker laser in C0X-coordinate under coordinate system
Value, yltFor laser tracker laser in C0Y-coordinate value under coordinate system, zltFor laser tracker laser in C0Coordinate
Z coordinate value under system；
(3) the control each rotary shaft of robot rotates different angles, every time after rotation, is obtained using robot kinematics' model
The terminal angle of robot and the calculated value of position, the terminal angle of the robot after being screened using laser tracker and position
The measured value set finally obtains each rotation shaft angle combination of k group and the corresponding robot end's posture of the combination and position
Calculated value and measured value；Specific step is as follows:
(3-1) controls each rotary shaft and rotates different angles, so that all rotary shaft rotations finish rear-locating face method each time
Angle between vector and measurement light is less than 45 °；
I-th group of each rotation shaft angle combination is substituted into kinematics by robot kinematics' model that (3-2) utilizes step (1) to establish
Initial parameter values carry out the calculated value that i-th group of each rotation shaft angle combination respective ends posture is calculatedIt is denoted as with the calculated value of i-th group of each rotation shaft angle combination respective ends position
WhereinRespective ends Attitude Calculation value is combined in C for i-th group of each rotation shaft angle of robot0Under x coordinate projection,Respective ends Attitude Calculation value is combined in C for i-th group of each rotation shaft angle of robot0Under y-coordinate projection,For machine
I-th group of people each rotation shaft angle combination respective ends Attitude Calculation value is in C0Under z coordinate projection；It is each for i-th group of robot
Rotation shaft angle combines respective ends position calculated value in C0Under x coordinate,For i-th group of each rotation shaft angle group of robot
Respective ends position calculated value is closed in C0Under y-coordinate,Respective ends position is combined for i-th group of each rotation shaft angle of robot
Calculated value is set in C0Under z coordinate；
Using the laser of laser tracker in C0Coordinate under coordinate systemCalculate separately i-th group of each rotation shaft angle combination
Displacement of the respective ends position calculated value to laser trackerAnd the angle of terminal angle calculated value and measurement radiation direction
ωi, expression formula is as follows:
(3-3) carries out measurement of terminal position using laser tracker to each group of each rotation shaft angle combination, obtain i-th group it is each
The corresponding terminal position measured value of rotation shaft angle combinationChoose ωiThe terminal angle that 45 ° of < measures, and obtains
The corresponding terminal angle measured value of each rotation shaft angle combination of i groupIt finally obtains each rotation shaft angle combination of k group and is somebody's turn to do
Combine the calculated value and measured value of corresponding robot end's posture and position；
(4) kinematics parameters of robot rotary shaft are demarcated；Specific step is as follows:
(4-1) combines corresponding end X-coordinate error amount f by i-th group of following equation calculations each rotation shaft anglexi, Y coordinate miss
Difference fyiWith Z coordinate error amount fzi:
(4-2) is using the laser of laser tracker in C0Coordinate under coordinate system isIn step (3)
Each rotation shaft angle of any one group obtained combines corresponding terminal position measured valueWherein,The x coordinate of corresponding terminal position measured value is combined for i-th group of each rotation shaft angle,Shaft angle is respectively rotated for i-th group
Degree combines the y-coordinate of corresponding terminal position measured value,Corresponding terminal position is combined for i-th group of each rotation shaft angle to survey
The z coordinate of magnitude calculates the distance between terminal position measured value and laser tracker of each rotation shaft angle combination of the group:
Calculate the measured value difference that each rotation shaft angle of the group combines corresponding measurement radiation direction and each plane included angle of coordinate system
For ψxi, ψyiAnd ψzi；Expression formula is as follows:
Wherein, ψxiThe measured value of the angle of light and yoz plane, ψ are measured for laser trackeryiLight is measured for laser tracker
With the measured value of the angle of xoz plane, ψziThe measured value of the angle of light and xoy plane is measured for laser tracker；
(4-3) is demarcated using kinematics parameters of the Least square-fit in following formula to robot rotary shaft, calculates movement
Learn parameter:
The kinematics parameters for obtaining each rotary shaft are as follows: there are three parameters for first rotary shaft, comprising: torsional angle αi, shaft length aiWith
Axle base di；There are four parameters for each rotary shaft later, comprising: rotational angle thetai, torsional angle αi, shaft length aiWith axle base di。
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| CN112631199B (en) * | 2020-11-27 | 2021-10-01 | 上海柏楚电子科技股份有限公司 | Method and device for calibrating structural parameters of machine tool and machine tool control system |
| CN113568369A (en) * | 2021-07-16 | 2021-10-29 | 英诺威讯智能科技（杭州）有限公司 | Method for measuring relative precision of built-in system for zero calibration of full-automatic robot |
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