CN107627299A - A kind of kinematic parameter errors scaling method of rope driving parallel robot - Google Patents
A kind of kinematic parameter errors scaling method of rope driving parallel robot Download PDFInfo
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Abstract
The invention discloses a kind of rope to drive Kinematics of Parallel Robot parameter error scaling method, including：1st, the kinematic parameter errors model of rope driving Kinematics of Parallel Robot model and rope driving parallel robot is established, 2nd, parameter error is recognized using optimized algorithm, 3rd, the position relationship of the reference frame of the reference frame relative rope driving parallel robot of optimization demarcation pose measuring apparatus, 4, with reference to iteration optimization algorithms combined calibrating kinematic parameter errors.The present invention is capable of the kinematic parameter errors of accurate calibration rope driving parallel robot, so as to improve the kinematics precision of rope driving parallel robot.
Description
Technical field
The present invention relates to robot kinematics' parameter calibration field, and in particular to a kind of rope driving based on pose measurement
Kinematics of Parallel Robot parameter error scaling method.
Background technology
Robotic structure is being processed and is inevitably producing some structural parameters errors in assembling process, these knots
The result that structure parameter error can cause the kinematics model of robot to calculate produces error.So in robot production process,
Have to demarcate the kinematic parameter errors of robot.
There are the positions such as camera, laser interferometer and attitude measuring for conventional calibration tool, these pose measurements
Device can be with the position of robot measurement executor tail end moving platform and posture.Measurement apparatus is to be used as reference using local Coordinate System
The pose of coordinate system robot measurement end effector, so must measuring machine before robot kinematics' parameter error is demarcated
Relative position relation between device people reference frame and measurement apparatus reference frame.But because the reference of measurement apparatus is surveyed
Error be present between amount position and robot architecture, cause to exist between the relative position relation of measurement and actual positional relationship and miss
Difference so that the robot kinematics' parameter error precision finally demarcated reduces.Needed in industrial processes to many robots
Demarcated, conventional method needs to demarcate the position relationship of measurement apparatus manually, causes demarcation speed slow, calibration process
Cumbersome, production efficiency is low.So needing one kind badly can be demarcated automatically, and the scaling method with degree of precision, with
Phase can improve production efficiency, expand economic benefit.
The content of the invention
The present invention is in place of overcome the deficiencies in the prior art, there is provided a kind of kinematics parameters of rope driving parallel robot
Error calibrating method, to be capable of the kinematic parameter errors of accurate calibration rope driving parallel robot, so as to improve rope
Drive the kinematics precision of parallel robot.
The present invention to achieve the above object of the invention, adopts the following technical scheme that：
A kind of kinematic parameter errors scaling method of rope driving parallel robot of the present invention, is to be applied to rope to drive
In the calibration process of parallel robot, and rope driving parallel robot side is provided with pose measuring apparatus；It is special
Point is that the kinematic parameter errors scaling method is carried out according to lower step：
Step 1, in the measurement working range of the pose measuring apparatus, establish rope driving parallel robot
Reference frame Os, the reference frame O on robot end's moving platformp, the reference frame O of pose measuring apparatusc, and will
The reference frame O of the pose measuring apparatuscAs world coordinate system；
Step 2, the kinematics model for establishing the rope driving parallel robot；
Step 2.1, drive parallel robot, the end for the rope of the n frees degree exported for m wire drives
Reference frame O of the moving platform in rope driving parallel robotsIn theoretical pose be expressed as Xs=[Ps Φs]T, its
Middle PsRepresent the position of the end moving platform, ΦsRepresent the posture of the end moving platform；
Make biRepresent reference frame O of i-th wire drive on robot end's moving platformpOn position,
aiRepresent reference frame O of the rope output point on the robot platformsOn position；I=1 ... m；
The closed chain equation of single wire drive is represented using formula (1)：
li=ai-Ps-Rsp(Φs)bi (1)
In formula (1), liRepresent the rope output point of the i-th wire drive to the rope tie point of the end moving platform
Rope vector, RspRepresent the reference frame O on robot end's moving platformpParallel robot is driven to the rope
Reference frame OsSpin matrix；
Step 2.2, the inverse kinematics equation of rope driving parallel robot is obtained according to formula (2)：
||li||2=(ai-Ps-Rsp(Φs)bi)T(ai-Ps-Rsp(Φs)bi), i=1,2 ..., m (2)
By formula (2) obtain the rope lengths vector of rope driving parallel robot for l=[| | l1||2||l2||2…|
|li||2…||lm||2]T；
Step 3, the kinematic parameter errors model for establishing the rope driving parallel robot；
Step 3.1, order robot kinematics' error parameter as caused by being machined and assemble factor are expressed asWherein, biRepresent reference of i-th wire drive on robot end's moving platform
Coordinate system OpOn site error, aiReference frame O of the rope output point on the robot platform described in representingsOn
Site error,Represent that motor encoder unit turn angle corresponds to the output error in length of rope, then need the fortune recognized
Dynamic parameter error of learning shares 7m Cal=[Cal1 Cal2 … Cali … Calm]T；
Step 3.2, the pose using pose measuring apparatus measurement N group end moving platforms, and utilize the measurement of jth group
Pose tries to achieve the motor encoder output angle θ as shown in formula (3)iError
In formula (3), { θm,jThe actual rotation angle of m motor encoder feedback tried to achieve of the pose that is measured with jth group of expression
Degree, ljThe rope lengths vector that the pose that expression is measured with jth group is tried to achieve；
Step 4, the optimization aim equation as shown in formula (4) obtained as formula (3)：
In formula (4), eθRepresent the mistake for the m motor encoder output angle that the pose of the N group ends moving platform is tried to achieve
Eikonal equation, and have：
Solution is optimized to formula (4) using least square method, obtains the kinematic parameter errors identification as shown in formula (5)
Model：
In formula (5),For error equation eθTo kinematic parameter errors Cal Jacobian matrix, WtRepresent kinematics ginseng
Number error Cal normalization matrix；
Step 5, the reference frame O for demarcating pose measuring apparatuscThe reference of relatively described rope driving parallel robot
Coordinate system OsPosition relationship；
Step 5.1, the actual measurement pose of the end moving platform is made to be expressed as Xcs=[Pcs Φcs]T, wherein, PcsTable
Show the reference frame O of the rope driving parallel robotsIn the reference frame O of the pose measuring apparatuscIn position
Put, ΦcsRepresent the reference frame O of rope driving parallel robotsIn the reference frame O of the pose measuring apparatuscIn
Posture；Then reference frame O of the end moving platform in the pose measuring apparatus is represented using formula (6)cIn position
Pc：
Pc=Rcs(Φcs)Ps+Pcs (6)
In formula (6), RcsRepresent the reference frame O of rope driving parallel robotsRelative to the pose measuring apparatus
Reference frame OcSpin matrix；
Step 5.2, simplified style (6), so as to establish the reference frame O of pose measuring apparatus using formula (7)cWith the rope
Rope drives the reference frame O of parallel robotsPosition relationship equation：
The reference frame O of pose measuring apparatus is established using formula (8)cWith the reference of rope driving parallel robot
Coordinate system OsPosition relationship optimization method, recycle L-M algorithms solution is optimized to formula (8), obtain location parameter Pcs：
Step 5.3, make Pc-Pcs=A, Ps=B, R is obtained according to formula (6)cs(Φcs) B=A, then obtain pose using formula (9)
The reference frame O of measurement apparatuscWith the reference frame O of rope driving parallel robotsPosture relation equation, then
Solution is optimized to formula (9) using L-M algorithms, obtains attitude parameter Φcs：
Rcs(Φcs)=ABT(B·BT)-1 (9)
Step 6, combined calibrating kinematic parameter errors；
Step 6.1, the mean square error that pose measuring apparatus measures the pose of N group end moving platforms is calculated using formula (10)
SD：
In formula (10),XcRepresent the reference frame O in pose measuring apparatuscIn, pose measuring apparatus
The attained pose of robot end's moving platform of measurement,Represent the reference frame O in pose measuring apparatuscIn, robot
The theoretical pose of end moving platform；
Step 6.2, iterations iter=1, kinematic parameter errors Cal are initialized, maximum iteration is
itermax；
Step 6.3, the reference frame O using i-th ter times calculating pose measuring apparatus of step 5cDriven with the rope
The reference frame O of parallel robotsRelativeness
Step 6.4, utilize i-th ter times demarcation kinematic parameter errors Cal of least square methoditer；
Step 6.5, by Caliter+ Cal is assigned to Caliter, iter+1 is assigned to iter；
If step 6.6, SD ＜ ＜ δ and iter ＜ iter max, wherein δ are minimum, then demarcation terminates, and exports
Caliter；If iter ＞ iter max, circulation is terminated；If SD ＞ δ and iter ＜ iter max, return to step 6.3.
Compared with the prior art, beneficial effects of the present invention are embodied in：
1st, the present invention demarcates robot reference coordinate by establishing kinematic parameter errors model followed by calibration algorithm
Relative position relation between system and measurement apparatus reference frame, kinematic parameter errors then are recognized using optimized algorithm,
So as to improve the kinematic parameter errors stated accuracy of rope driving parallel robot；Due to existing in a calibration process
Measurement error, therefore using the optimized algorithm of iteration, optimization is iterated to kinematic parameter errors calibration process so that it is final
Kinematic error be preferably minimized, substantially increase parameter error stated accuracy.Algorithm can be automatic in whole calibration process
Carry out, it is not necessary to manual intervention, substantially increase demarcation efficiency.
2nd, the present invention establishes the kinematic parameter errors model of rope driving parallel robot, and uses optimized algorithm pair
Error is recognized so that parameter error calibration result is more accurate；
3rd, the present invention demarcates itself reference frame and parallel robot itself of pose measuring apparatus using optimized algorithm
The relative position relation of reference frame, substantially increase the measurement accuracy of pose measuring apparatus.
4th, the present invention uses the parameter error discrimination method of iteration, to itself reference coordinate of the pose measuring apparatus of demarcation
System and parallel robot itself reference frame relative position relation and the kinematic parameter errors of identification are iterated identification, whole
Individual calibration process can perform automatically, it is not necessary to manual intervention, substantially increase demarcation efficiency and kinematic parameter errors identification
Precision.
Brief description of the drawings
Fig. 1 is reference frame schematic diagram in calibration process of the present invention.
Embodiment
In the present embodiment, a kind of rope driving Kinematics of Parallel Robot parameter error demarcation based on position and attitude measurement
Method, it is applied in the calibration process of rope driving parallel robot, rope driving parallel robot side is provided with position
Put attitude measuring；Specifically, the error calibrating method includes：Kinematics of Parallel Robot parameter error identification model,
Position and attitude measurement apparatus coordinate system demarcating module, robot kinematics' parameter error identification module.
There are kinematic parameter errors in rope driving parallel robot, the kinematics model according to parallel robot is established simultaneously
Join robot kinematic parameter errors model；The error measured according to kinematic error parameter model and position and attitude measurement apparatus
Parameter error identification model is obtained, and parameter identification is carried out using this parameter error identification model.
Position and attitude measurement apparatus coordinate system peg model establishes world coordinate system with position and attitude measurement apparatus, with rope
Driving parallel robot establishes reference frame, the parallel robot terminal position posture obtained according to position-measurement device measurement
The relative position relation of demarcation reference frame and world coordinate system is solved with the position and attitude under reference frame.
Robot kinematics' parameter error is recognized module and surveyed with parallel robot parameter error identification model and position and attitude
Based on measuring device coordinate system demarcating module, kinematic error parameter is recognized using parameter identification optimized algorithm.
In the present embodiment, a kind of kinematic parameter errors scaling method of rope driving parallel robot, is to be applied to rope
In the calibration process of rope driving parallel robot, and rope driving parallel robot side is provided with pose measuring apparatus, position
The measurement apparatus that attitude measuring is general position and attitude is put, end can be obtained using position and attitude measurement apparatus measurement
The kinematic error of moving platform；Kinematic parameter errors can be recognized in calibration process, improve rope driving parallel robot fortune
It is dynamic to learn precision；Specifically, the kinematic parameter errors scaling method is carried out according to lower step：
Step 1, in the measurement working range of pose measuring apparatus, measurement apparatus, which refers to, can measure rope driver device
The device of people end moving platform pose, laser interferometer, 6D video cameras and motion capture system can be used, it is general to require to survey
The precision of amount device will be far above the precision of robot in itself；Establish the reference frame O of rope driving parallel robots, machine
Reference frame O on the moving platform of device people endp, reference frame OsThe rope in rope driving parallel robot can be established
On the rope output point of drive device so that referential origin and rope output point are easy to establish kinematical equation to coincidence；Machine
Reference frame O on the moving platform of device people endpThe geometric center point in moving platform is established, conveniently establishes kinematics model；Position
The reference frame O of appearance measurement apparatusc, and by the reference frame O of pose measuring apparatuscAs world coordinate system；Reference coordinate
It is OcIt is that measurement apparatus is set, can be marked typically in measurement apparatus；
Step 2, the kinematics model for establishing rope driving parallel robot；
Step 2.1, drive parallel robot for the rope of the n frees degree exported for m wire drives, end is dynamic flat
Reference frame O of the platform in rope driving parallel robotsIn theoretical pose be expressed as Xs=[Ps Φs]T, wherein PsRepresent
The position of end moving platform, ΦsRepresent the posture of end moving platform；
As shown in figure 1, make biRepresent reference frame O of i-th wire drive on robot end's moving platformpOn
Position, aiRepresent reference frame O of the rope output point on robot platformsOn position；I=1 ... m；
The closed chain equation of single wire drive is represented using formula (1)：
li=ai-Ps-Rsp(Φs)bi (1)
In formula (1), liRepresent the rope output point of the i-th wire drive to the rope of the rope tie point of end moving platform
Suo Xiangliang, RspRepresent the reference frame O on robot end's moving platformpTo the reference frame of rope driving parallel robot
OsSpin matrix；
Step 2.2, the inverse kinematics equation of rope driving parallel robot is obtained according to formula (2)：
||li||2=(ai-Ps-Rsp(Φs)bi)T(ai-Ps-Rsp(Φs)bi), i=1,2 ..., m (2)
By formula (2) obtain rope driving parallel robot rope lengths vector for l=[| | l1||2||l2||2…||li|
|2…||lm||2]T；
Step 3, the kinematic parameter errors model for establishing rope driving parallel robot；
Step 3.1, order robot kinematics' error parameter as caused by being machined and assemble factor are expressed asWherein, biRepresent reference frame O of i-th wire drive on robot end's moving platformp
On site error, aiReference frame O of the rope output point of expression on robot platformsOn site error,Table
Show that motor encoder unit turn angle corresponds to the output error in length of rope, general biAnd aiIn respectively have 3 parameters,Have 1
Individual parameter, the then kinematic parameter errors for needing to recognize share 7m Cal=[Cal1 Cal2 … Cali … Calm]T；
Step 3.2, the pose using pose measuring apparatus measurement N group end moving platforms, in order to ensure the Shandong of parameter identification
Rod, it is desirable to which measurement data N number is significantly larger than identified parameters number；Each measurement apparatus can provide 1 equation, so
N × m ＞ ＞ 7m, in order to ensure to demarcate speed, N=20 can make it that；And the pose measured using jth group is tried to achieve such as formula (3) institute
The motor encoder output angle θ showniError
In formula (3), { θm,jThe actual rotation angle of m motor encoder feedback tried to achieve of the pose that is measured with jth group of expression
Degree, ljThe rope lengths vector that the pose that expression is measured with jth group is tried to achieve；
Step 4, the optimization aim equation as shown in formula (4) obtained as formula (3)：
In formula (4), eθRepresent the error side for the m motor encoder output angle that the pose of N group end moving platforms is tried to achieve
Journey, and have：
Solution is optimized to formula (4) using least square method, obtains the kinematic parameter errors identification as shown in formula (5)
Model：
In formula (5),For error equation eθTo kinematic parameter errors Cal Jacobian matrix, WtRepresent kinematics ginseng
Number error Cal normalization matrix；
Step 5, the reference frame O for demarcating pose measuring apparatuscRelative rope drives the reference coordinate of parallel robot
It is OsPosition relationship；
Step 5.1, the actual measurement pose of end moving platform is made to be expressed as Xcs=[Pcs Φcs]T, wherein, PcsRepresent rope
Rope drives the reference frame O of parallel robotsIn the reference frame O of pose measuring apparatuscIn position, ΦcsRepresent rope
Rope drives the reference frame O of parallel robotsIn the reference frame O of pose measuring apparatuscIn posture；Then utilize formula (6)
Represent reference frame O of the end moving platform in pose measuring apparatuscIn position Pc：
Pc=Rcs(Φcs)Ps+Pcs (6)
In formula (6), RcsRepresent the reference frame O of rope driving parallel robotsRelative to the ginseng of pose measuring apparatus
Examine coordinate system OcSpin matrix；
Step 5.2, due to RcsFor homogeneous matrix, there is Rcs(Φcs)TRcs(Φcs)=1, formula (6) is deformed, so as to utilize formula
(7) the reference frame O of pose measuring apparatus is establishedcWith the reference frame O of rope driving parallel robotsPosition relationship
Equation：
The reference frame O of pose measuring apparatus is established using formula (8)cWith the reference coordinate of rope driving parallel robot
It is OsPosition relationship optimization method, recycle L-M algorithms solution is optimized to formula (8), obtain location parameter Pcs：
Step 5.3, make Pc-Pcs=A, Ps=B, R is obtained according to formula (6)cs(Φcs) B=A, then obtain pose using formula (9)
The reference frame O of measurement apparatuscWith the reference frame O of rope driving parallel robotsPosture relation equation, recycle
L-M algorithms optimize solution to formula (9), obtain attitude parameter Φcs：
Rcs(Φcs)=ABT(B·BT)-1 (9)
Step 6, combined calibrating kinematic parameter errors；
Step 6.1, the mean square error that pose measuring apparatus measures the pose of N group end moving platforms is calculated using formula (10)
SD：
In formula (10),XcRepresent the reference frame O in pose measuring apparatuscIn, pose measuring apparatus
The attained pose of robot end's moving platform of measurement,Represent the reference frame O in pose measuring apparatuscIn, robot
The theoretical pose of end moving platform；
Step 6.2, initialization iterations iter=1, kinematic parameter errors Cal, maximum iteration iter
Max, can be with value iter max=10；
Step 6.3, the reference frame O using i-th ter times calculating pose measuring apparatus of step 5cIt is in parallel with rope driving
The reference frame O of robotsRelativeness
Step 6.4, utilize i-th ter times demarcation kinematic parameter errors Cal of least square methoditer；
Step 6.5, by Caliter+ Cal is assigned to Caliter, iter+1 is assigned to iter；
If step 6.6, SD ＜ ＜ δ and iter ＜ iter max, wherein δ are minimum, δ=10 are taken-6；Then demarcation knot
Beam, export Caliter；If iter ＞ iter max, circulation is terminated；If SD ＞ δ and iter ＜ iter max, are returned
Step 6.3.
Claims (1)
1. a kind of kinematic parameter errors scaling method of rope driving parallel robot, it is to be applied to rope driving parallel manipulator
In the calibration process of people, and rope driving parallel robot side is provided with pose measuring apparatus；It is it is characterized in that described
Kinematic parameter errors scaling method is carried out according to lower step：
Step 1, in the measurement working range of the pose measuring apparatus, establish the reference of rope driving parallel robot
Coordinate system Os, the reference frame O on robot end's moving platformp, the reference frame O of pose measuring apparatusc, and by described in
The reference frame O of pose measuring apparatuscAs world coordinate system；
Step 2, the kinematics model for establishing the rope driving parallel robot；
Step 2.1, drive parallel robot for the rope of the n frees degree exported for m wire drives, the end is dynamic flat
Reference frame O of the platform in rope driving parallel robotsIn theoretical pose be expressed as Xs=[Ps Φs]T, wherein Ps
Represent the position of the end moving platform, ΦsRepresent the posture of the end moving platform；
Make biRepresent reference frame O of i-th wire drive on robot end's moving platformpOn position, aiTable
Show reference frame O of the rope output point on the robot platformsOn position；I=1 ... m；
The closed chain equation of single wire drive is represented using formula (1)：
li=ai-Ps-Rsp(Φs)bi (1)
In formula (1), liRepresent the rope output point of the i-th wire drive to the rope of the rope tie point of the end moving platform
Suo Xiangliang, RspRepresent the reference frame O on robot end's moving platformpTo the ginseng of rope driving parallel robot
Examine coordinate system OsSpin matrix；
Step 2.2, the inverse kinematics equation of rope driving parallel robot is obtained according to formula (2)：
||li||2=(ai-Ps-Rsp(Φs)bi)T(ai-Ps-Rsp(Φs)bi), i=1,2 ..., m (2)
By formula (2) obtain the rope lengths vector of rope driving parallel robot for l=[| | l1||2||l2||2…||li|
|2…||lm||2]T；
Step 3, the kinematic parameter errors model for establishing the rope driving parallel robot；
Step 3.1, order robot kinematics' error parameter as caused by being machined and assemble factor are expressed asWherein, biRepresent reference of i-th wire drive on robot end's moving platform
Coordinate system OpOn site error, aiReference frame O of the rope output point on the robot platform described in representingsOn
Site error,Represent that motor encoder unit turn angle corresponds to the output error in length of rope, then need the fortune recognized
Dynamic parameter error of learning shares 7m Cal=[Cal1 Cal2 … Cali … Calm]T；
Step 3.2, the pose using pose measuring apparatus measurement N group end moving platforms, and utilize the pose of jth group measurement
Try to achieve the motor encoder output angle θ as shown in formula (3)iError
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The rope lengths vector that the pose that expression is measured with jth group is tried to achieve；
Step 4, the optimization aim equation as shown in formula (4) obtained as formula (3)：
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Solution is optimized to formula (4) using least square method, obtains the kinematic parameter errors identification mould as shown in formula (5)
Type：
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Cal normalization matrix；
Step 5, the reference frame O for demarcating pose measuring apparatuscThe reference frame of relatively described rope driving parallel robot
OsPosition relationship；
Step 5.1, the actual measurement pose of the end moving platform is made to be expressed as Xcs=[Pcs Φcs]T, wherein, PcsRepresent institute
State the reference frame O of rope driving parallel robotsIn the reference frame O of the pose measuring apparatuscIn position,
ΦcsRepresent the reference frame O of rope driving parallel robotsIn the reference frame O of the pose measuring apparatuscIn appearance
State；Then reference frame O of the end moving platform in the pose measuring apparatus is represented using formula (6)cIn position Pc：
Pc=Rcs(Φcs)Ps+Pcs (6)
In formula (6), RcsRepresent the reference frame O of rope driving parallel robotsRelative to the ginseng of the pose measuring apparatus
Examine coordinate system OcSpin matrix；
Step 5.2, simplified style (6), so as to establish the reference frame O of pose measuring apparatus using formula (7)cDriven with the rope
The reference frame O of dynamic parallel robotsPosition relationship equation：
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It is OsPosition relationship optimization method, recycle L-M algorithms solution is optimized to formula (8), obtain location parameter Pcs：
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<msup>
<mrow>
<mo>(</mo>
<msub>
<mi>P</mi>
<mi>c</mi>
</msub>
<mo>-</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>c</mi>
<mi>s</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mi>T</mi>
</msup>
<mrow>
<mo>(</mo>
<msub>
<mi>P</mi>
<mi>c</mi>
</msub>
<mo>-</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>c</mi>
<mi>s</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mrow>
<mo>(</mo>
<msubsup>
<mi>P</mi>
<mi>s</mi>
<mi>T</mi>
</msubsup>
<msub>
<mi>P</mi>
<mi>s</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>|</mo>
<msub>
<mo>|</mo>
<mn>2</mn>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
Step 5.3, make Pc-Pcs=A, Ps=B, R is obtained according to formula (6)cs(Φcs) B=A, then obtain pose measurement using formula (9)
The reference frame O of devicecWith the reference frame O of rope driving parallel robotsPosture relation equation, recycle
L-M algorithms optimize solution to formula (9), obtain attitude parameter Φcs：
Rcs(Φcs)=ABT(B·BT)-1 (9)
Step 6, combined calibrating kinematic parameter errors；
Step 6.1, the mean square error SD that pose measuring apparatus measures the pose of N group end moving platforms is calculated using formula (10)：
<mrow>
<mi>S</mi>
<mi>D</mi>
<mo>=</mo>
<msqrt>
<mfrac>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msup>
<mi>eX</mi>
<mi>T</mi>
</msup>
<mi>e</mi>
<mi>X</mi>
</mrow>
<mi>N</mi>
</mfrac>
</msqrt>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (10),XcRepresent the reference frame O in pose measuring apparatuscIn, pose measuring apparatus measurement
Robot end's moving platform attained pose,Represent the reference frame O in pose measuring apparatuscIn, robot end
The theoretical pose of moving platform；
Step 6.2, initialization iterations iter=1, kinematic parameter errors Cal, maximum iteration itermax；
Step 6.3, the reference frame O using i-th ter times calculating pose measuring apparatus of step 5cIt is in parallel with rope driving
The reference frame O of robotsRelativeness
Step 6.4, utilize i-th ter times demarcation kinematic parameter errors Cal of least square methoditer；
Step 6.5, by Caliter+ Cal is assigned to Caliter, iter+1 is assigned to iter；
If step 6.6, SD ＜ ＜ δ and iter ＜ itermax, wherein δ are minimum, then demarcation terminates, and exports Caliter；Such as
Fruit iter ＞ itermax, then terminate circulation；If SD ＞ δ and iter ＜ itermax, return to step 6.3.
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Cited By (13)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109241675A (en) * | 2018-10-17 | 2019-01-18 | 清华大学 | A kind of Dynamics calibration method for parallel architecture main tapping |
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Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0546776B1 (en) * | 1991-12-07 | 1997-07-30 | Pohang Iron & Steel Co., Ltd. | Method of Orientating Axes of a Robot Wrist having an Offset |
| CN1727861A (en) * | 2005-07-22 | 2006-02-01 | 浙江大学 | Device for calibrating parallel force transducer in six dimensions |
| CN103267112A (en) * | 2013-05-29 | 2013-08-28 | 哈尔滨工业大学 | Device used for carrying out rope performance study on tandem type rope sheave structure |
| CN103934823A (en) * | 2014-04-28 | 2014-07-23 | 哈尔滨工程大学 | Six-PTRT type parallel robot with self-calibration function |
| CN203831398U (en) * | 2014-04-28 | 2014-09-17 | 哈尔滨工程大学 | 6-PTRT type parallel-connected robot with automatic calibrating function |
| CN107009348A (en) * | 2017-04-18 | 2017-08-04 | 中国科学技术大学 | A kind of multi-configuration rope driving parallel robot and its spatial pose method for solving |
-
2017
- 2017-09-12 CN CN201710817308.9A patent/CN107627299B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0546776B1 (en) * | 1991-12-07 | 1997-07-30 | Pohang Iron & Steel Co., Ltd. | Method of Orientating Axes of a Robot Wrist having an Offset |
| CN1727861A (en) * | 2005-07-22 | 2006-02-01 | 浙江大学 | Device for calibrating parallel force transducer in six dimensions |
| CN103267112A (en) * | 2013-05-29 | 2013-08-28 | 哈尔滨工业大学 | Device used for carrying out rope performance study on tandem type rope sheave structure |
| CN103934823A (en) * | 2014-04-28 | 2014-07-23 | 哈尔滨工程大学 | Six-PTRT type parallel robot with self-calibration function |
| CN203831398U (en) * | 2014-04-28 | 2014-09-17 | 哈尔滨工程大学 | 6-PTRT type parallel-connected robot with automatic calibrating function |
| CN107009348A (en) * | 2017-04-18 | 2017-08-04 | 中国科学技术大学 | A kind of multi-configuration rope driving parallel robot and its spatial pose method for solving |
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|---|---|---|---|---|
| CN109241675A (en) * | 2018-10-17 | 2019-01-18 | 清华大学 | A kind of Dynamics calibration method for parallel architecture main tapping |
| WO2020215385A1 (en) * | 2019-04-26 | 2020-10-29 | 哈尔滨工业大学（深圳） | Kinematics test system for rope-driven flexible robot |
| CN110861081A (en) * | 2019-10-14 | 2020-03-06 | 北京航空航天大学 | Autonomous positioning method for under-constrained cable parallel robot end effector |
| CN110871434A (en) * | 2019-11-25 | 2020-03-10 | 清华大学 | Kinematics calibration method of parallel processing equipment |
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