CN107627299B - 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 ropes to drive Kinematics of Parallel Robot parameter error scaling method, include: 1, establish the kinematic parameter errors model that rope drives Kinematics of Parallel Robot model and rope driving parallel robot, 2, parameter error is recognized using optimization algorithm, 3, the positional relationship of the reference frame of the reference frame relative rope driving parallel robot of optimization calibration pose measuring apparatus, 4, in conjunction with 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, to improve the kinematics precision of rope driving parallel robot.
Description
Technical field
The present invention relates to robot kinematics' parameter calibration fields, and in particular to a kind of rope driving based on pose measurement
Kinematics of Parallel Robot parameter error scaling method.
Background technique
Robotic structure inevitably generates some structural parameters errors in processing and assembling process, these knots
The result that the kinematics model that structure parameter error will lead to robot calculates generates error.So in robot production process,
It has to demarcate the kinematic parameter errors of robot.
There are the positions such as camera, laser interferometer and attitude measuring for common calibration tool, these pose measurements
Device can be with the position of robot measurement executor tail end moving platform and posture.Measuring device is using local Coordinate System as reference
The pose of coordinate system robot measurement end effector, so must measuring machine before demarcating robot kinematics' parameter error
Relative positional relationship between device people reference frame and measuring device reference frame.But since the reference of measuring device is surveyed
It measures between position and robot architecture there are error, causes to exist between the relative positional relationship and actual positional relationship of measurement and miss
Difference, so that the robot kinematics' parameter error precision finally demarcated reduces.It is needed in industrial processes to many robots
It is demarcated, conventional method needs to demarcate the positional relationship of measuring device manually, causes calibration speed slow, calibration process
Cumbersome, production efficiency is low.So needing one kind can be demarcated automatically, and the scaling method with degree of precision, with
Phase can be improved production efficiency, expand economic benefit.
Summary of the invention
Present invention place in order to overcome the deficiencies of the prior art, provides 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, 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
1, a kind of kinematic parameter errors scaling method of rope driving parallel robot is to be applied to rope driving parallel connection
In the calibration process of robot, and rope driving parallel robot side is provided with pose measuring apparatus；It is characterized in 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, 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 drives parallel robot, the machine for the rope of the n freedom degree exported for m wire drive
Reference frame O of the people end moving platform in rope driving parallel robotsIn theoretical pose be expressed as Xs=[Ps
Φs]T, wherein PsIndicate the position of robot end's moving platform, ΦsIndicate the posture of robot end's moving platform；
Enable biIndicate reference coordinate of the rope tie point of the i-th wire drive on robot end's moving platform
It is OpOn position, aiIndicate that the rope output point of the i-th wire drive is sat in the reference of rope driving parallel robot
Mark system OsOn position；I=1 ... m；
The closed chain equation of single wire drive is indicated using formula (1):
li=ai-Ps-Rsp(Φs)bi (1)
In formula (1), liIndicate the rope output point of the i-th wire drive to the rope of robot end's moving platform
The rope vector of tie point, RspIndicate the reference frame O on robot end's moving platformpIt is driven to the rope in parallel
The reference frame O of robotsSpin matrix；
Step 2.2, the inverse kinematics equation that 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 the rope lengths vector that formula (2) obtains rope driving parallel robot be 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 is enabled by being machined and the factor of assembling causes robot kinematics' error of the i-th wire drive to be joined
Number is expressed asWherein, Δ biIndicate the rope tie point of the i-th rope driving device in the machine
Reference frame O on the moving platform of people endpOn location error, Δ aiIndicate the rope output of i-th wire drive
Reference frame O of the point in rope driving parallel robotsOn location error,Indicate that motor encoder unit turns
Dynamic angle corresponds to the output error in length of rope, then the kinematic parameter errors for needing to recognize share the i-th rope of m 7 × 1 dimension
Robot kinematics' error parameter Cal of driving deviceiComposed kinematic parameter errors Cal=[Cal1 Cal2 …
Cali … Calm]T；
Step 3.2, the pose that N group robot end's moving platform is measured using the pose measuring apparatus, and utilize jth group
The pose of measurement acquires 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 acquired with the pose that jth group measures of expression
Degree, ljThe rope lengths vector that expression is acquired with the pose that jth group measures；Indicate motor encoder in the pose of jth group measurement
Device unit turn angle corresponds to the output error in length of rope；
Step 4 obtains the optimization aim equation as shown in formula (4) as formula (3):
In formula (4), eθIndicate the m motor encoder output angle that the pose of N group robot end's moving platform acquires
The error equation of degree, and have:
Formula (4) is optimized using least square method, obtains the identification of the kinematic parameter errors as shown in formula (5)
Model:
In formula (5),For error equation eθTo the Jacobian matrix of kinematic parameter errors Cal, WtIndicate kinematics ginseng
The normalization matrix of number error Cal；
Step 5, the reference frame O for demarcating pose measuring apparatuscThe reference of the relatively described rope driving parallel robot
Coordinate system OsPositional relationship；
Step 5.1 enables the actual measurement pose of robot end's moving platform be expressed as Xcs=[Pcs Φcs]T,
In, PcsIndicate the reference frame O of the rope driving parallel robotsIn the reference frame O of the pose measuring apparatusc
In position, ΦcsIndicate the reference frame O of rope driving parallel robotsIn the reference coordinate of the pose measuring apparatus
It is OcIn posture；Then indicate robot end's moving platform in the reference coordinate of the pose measuring apparatus using formula (6)
It is OcIn position Pc:
Pc=Rcs(Φcs)Ps+Pcs (6)
In formula (6), RcsIndicate the reference frame O of rope driving parallel robotsRelative to the pose measuring apparatus
Reference frame OcSpin matrix；
Step 5.2, simplified style (6), to establish the reference frame O of pose measuring apparatus using formula (7)cWith the rope
The reference frame O of rope driving parallel robotsPositional relationship equation:
(Pc-Pcs)T(Pc-Pcs)=Ps TPs (7)
The reference frame O of pose measuring apparatus is established using formula (8)cWith the reference of rope driving parallel robot
Coordinate system OsPositional relationship optimization method, recycle L-M algorithm to optimize formula (8), obtain rope driving
The reference frame O of parallel robotsIn the reference frame O of the pose measuring apparatuscIn position Pcs:
minf(Pcs)=| | (Pc-Pcs)T(Pc-Pcs)-(Ps TPs)||2 (8)
Step 5.3 enables Pc-Pcs=A, Ps=B obtains R according to formula (6)cs(Φcs) B=A, then pose is obtained using formula (9)
The reference frame O of measuring devicecWith the reference frame O of rope driving parallel robotsPosture relation equation, then
Formula (9) is optimized using L-M algorithm, obtains the reference frame O of rope driving parallel robotsIn the pose
The reference frame O of measuring devicecIn posture Φcs:
Rcs(Φcs)=ABT(B·BT)-1 (9)
Step 6, combined calibrating kinematic parameter errors；
Step 6.1 measures the square of the pose of N group robot end's moving platform using formula (10) calculating pose measuring apparatus
Error SD:
In formula (10),XcIndicate the reference frame O in pose measuring apparatuscIn, pose measuring apparatus
The attained pose of robot end's moving platform of measurement,Indicate the reference frame O in pose measuring apparatuscIn, robot
The theoretical pose of end moving platform；
Step 6.2, initialization the number of iterations iter=1, kinematic parameter errors Cal, maximum number of iterations iter
max；
Step 6.3, the reference frame O that pose measuring apparatus is calculated using step 5 i-th ter timescIt is driven with the rope
The reference frame O of parallel robotsRelativeness
Step 6.4 utilizes i-th ter times calibration 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 is minimum, then calibration terminates, and is exported
Caliter；If iter > iter max, terminates circulation；If SD > δ and iter < iter max, return step 6.3.
Compared with the prior art, the beneficial effects of the present invention are embodied in:
1, the present invention demarcates robot reference coordinate followed by calibration algorithm by establishing kinematic parameter errors model
Then relative positional relationship between system and measuring device reference frame recognizes kinematic parameter errors using optimization algorithm,
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 optimization algorithm of iteration, optimization is iterated to kinematic parameter errors calibration process, so that finally
Kinematic error be preferably minimized, substantially increase parameter error stated accuracy.Algorithm can be automatic in entire calibration process
It carries out, does not need manual intervention, substantially increase calibration efficiency.
2, the present invention establishes the kinematic parameter errors model of rope driving parallel robot, and uses optimization algorithm pair
Error is recognized, so that parameter error calibration result is more acurrate；
3, the present invention demarcates itself reference frame and parallel robot itself of pose measuring apparatus using optimization algorithm
The relative positional relationship of reference frame substantially increases the measurement accuracy of pose measuring apparatus.
4, the present invention uses the parameter error discrimination method of iteration, to itself reference coordinate of the pose measuring apparatus of calibration
System and parallel robot itself reference frame relative positional relationship and the kinematic parameter errors of identification are iterated identification, whole
A calibration process can be performed automatically, and not need manual intervention, substantially increase calibration efficiency and kinematic parameter errors identification
Precision.
Detailed description of the invention
Fig. 1 is reference frame schematic diagram in calibration process of the present invention.
Specific embodiment
In the present embodiment, a kind of rope driving Kinematics of Parallel Robot parameter error calibration based on position and attitude measurement
Method is that rope driving parallel robot side is provided with position in the calibration process applied to rope driving parallel robot
Set attitude measuring；Specifically, the error calibrating method include: Kinematics of Parallel Robot parameter error identification model,
Position and attitude measuring device coordinate system demarcating module, robot kinematics' parameter error recognize module.
Rope drives parallel robot there are kinematic parameter errors, and 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 measuring device
Parameter error identification model is obtained, and carries out parameter identification using this parameter error identification model.
Position and attitude measuring device coordinate system peg model establishes world coordinate system with position and attitude measuring device, with rope
Driving parallel robot establishes reference frame, the parallel robot terminal position posture obtained according to position-measurement device measurement
The relative positional relationship of calibration reference frame and world coordinate system is solved with the position and attitude under reference frame.
Robot kinematics' parameter error recognizes module and recognizes model and position and attitude survey with parallel robot parameter error
Based on measuring device coordinate system demarcating module, kinematic error parameter is recognized using parameter identification optimization algorithm.
In the present embodiment, a kind of kinematic parameter errors scaling method of rope driving parallel robot, is to be applied to rope
Rope drives in the calibration process of parallel robot, and rope driving parallel robot side is provided with pose measuring apparatus, position
The measuring device that attitude measuring is general position and attitude is set, position and attitude measuring device measurement is can use and obtains end
The kinematic error of moving platform；Kinematic parameter errors can be recognized during the calibration process, improve rope driving parallel robot fortune
It is dynamic to learn precision；Specifically, which carried out according to lower step:
Step 1, in the measurement working range of pose measuring apparatus, measuring device, which refers to, can measure rope driver device
The device of people end moving platform pose can use laser interferometer, 6D video camera and motion capture system, general to require to survey
The precision for measuring device will be much higher than the precision of robot 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 OsIt can establish the rope in rope driving parallel robot
On the rope output point of driving device, so that referential origin and rope output point be to coincidence, convenient for establishing kinematical equation；Machine
Reference frame O on the moving platform of device people endpThe geometric center point in moving platform is established, facilitates and establishes kinematics model；Position
The reference frame O of appearance measuring devicec, and by the reference frame O of pose measuring apparatuscAs world coordinate system；Reference coordinate
It is OcIt is that measuring device is set, can be marked generally in measuring device；
Step 2, the kinematics model for establishing rope driving parallel robot；
Step 2.1 drives the rope of the n freedom degree exported for m wire drive parallel robot, and 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 PsIt indicates
The position of end moving platform, ΦsIndicate the posture of end moving platform；
As shown in Figure 1, enabling biIndicate ginseng of the rope tie point of the i-th wire drive on robot end's moving platform
Examine coordinate system OpOn position, aiIndicate reference of the rope output point in rope driving parallel robot of the i-th wire drive
Coordinate system OsOn position；I=1 ... m；
The closed chain equation of single wire drive is indicated using formula (1):
li=ai-Ps-Rsp(Φs)bi (1)
In formula (1), liIndicate that the rope output point of the i-th wire drive is connected to the rope of robot end's moving platform
The rope vector of point, RspIndicate the reference frame O on robot end's moving platformpTo the reference of rope driving parallel robot
Coordinate system OsSpin matrix；
Step 2.2, the inverse kinematics equation that 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 be 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 are expressed as being machined and assembling robot kinematics' error parameter caused by factorWherein Δ biIndicate the rope tie point of the i-th rope driving device on robot end's moving platform
Reference frame OpOn location error, Δ aiIndicate that the rope output point of the i-th wire drive drives parallel manipulator in rope
The reference frame O of peoplesOn location error,Indicate that motor encoder unit turn angle corresponds to the output length of rope
Error, general biAnd aiIn respectively have 3 parameters,Have 1 parameter, then the kinematic parameter errors for needing to recognize share m 7 ×
Robot kinematics' error parameter Cal of i-th wire drive of 1 dimensioniComposed kinematic parameter errors Cal=[Cal1
Cal2 … Cali … Calm]T；
Step 3.2, the pose that N group end moving platform is measured using pose measuring apparatus, in order to guarantee the Shandong of parameter identification
Stick, it is desirable that the number of measurement data N is significantly larger than identified parameters number；Each measuring device can provide 1 equation, so
N × m > > 7m can make N=20 to guarantee to demarcate speed；And it is acquired using the pose that jth group measures such as formula (3) institute
The motor encoder output angle θ showniError
In formula (3), { θm,jThe actual rotation of m motor encoder feedback that is acquired with the pose that jth group measures of expression
Angle, ljThe rope lengths vector that expression is acquired with the pose that jth group measures；Indicate motor in the pose of jth group measurement
Encoder unit turn angle corresponds to the output error in length of rope；
Step 4 obtains the optimization aim equation as shown in formula (4) as formula (3):
In formula (4), eθIndicate the error side for the m motor encoder output angle that the pose of N group end moving platform acquires
Journey, and have:
Formula (4) is optimized using least square method, obtains the identification of the kinematic parameter errors as shown in formula (5)
Model:
In formula (5),For error equation eθTo the Jacobian matrix of kinematic parameter errors Cal, WtIndicate kinematics ginseng
The normalization matrix of number error Cal；
Step 5, the reference frame O for demarcating pose measuring apparatuscThe reference coordinate of relative rope driving parallel robot
It is OsPositional relationship；
Step 5.1 enables the actual measurement pose of end moving platform be expressed as Xcs=[Pcs Φcs]T, wherein PcsIndicate rope
The reference frame O of rope driving parallel robotsIn the reference frame O of pose measuring apparatuscIn position, ΦcsIndicate rope
The reference frame O of rope driving parallel robotsIn the reference frame O of pose measuring apparatuscIn posture；Then utilize formula (6)
Indicate robot end's moving platform in the reference frame O of pose measuring apparatuscIn position Pc:
Pc=Rcs(Φcs)Ps+Pcs (6)
In formula (6), RcsIndicate the reference frame O of rope driving parallel robotsGinseng relative to pose measuring apparatus
Examine coordinate system OcSpin matrix；
Step 5.2, due to RcsFor homogeneous matrix, there is Rcs(Φcs)TRcs(Φcs)=1 deforms formula (6), to utilize formula
(7) the reference frame O of pose measuring apparatus is establishedcWith the reference frame O of rope driving parallel robotsPositional relationship
Equation:
(Pc-Pcs)T(Pc-Pcs)=Ps TPs (7)
The reference frame O of pose measuring apparatus is established using formula (8)cWith the reference coordinate of rope driving parallel robot
It is OsPositional relationship optimization method, recycle L-M algorithm formula (8) is optimized, obtain rope driving parallel manipulator
The reference frame O of peoplesIn the reference frame O of pose measuring apparatuscIn position Pcs:
minf(Pcs)=| | (Pc-Pcs)T(Pc-Pcs)-(Ps TPs)||2 (8)
Step 5.3 enables Pc-Pcs=A, Ps=B obtains R according to formula (6)cs(Φcs) B=A, then pose is obtained using formula (9)
The reference frame O of measuring devicecWith the reference frame O of rope driving parallel robotsPosture relation equation, recycle
L-M algorithm optimizes formula (9), obtains the reference frame O of rope driving parallel robotsIn pose measuring apparatus
Reference frame OcIn posture Φcs:
Rcs(Φcs)=ABT(B·BT)-1 (9)
Step 6, combined calibrating kinematic parameter errors；
Step 6.1 calculates the mean square error that pose measuring apparatus measures the pose of N group end moving platform using formula (10)
SD:
In formula (10),XcIndicate the reference frame O in pose measuring apparatuscIn, pose measuring apparatus
The attained pose of robot end's moving platform of measurement,Indicate the reference frame O in pose measuring apparatuscIn, robot
The theoretical pose of end moving platform；
Step 6.2, initialization the number of iterations iter=1, kinematic parameter errors Cal, maximum number of iterations iter
Max, can be with value iter max=10；
Step 6.3, the reference frame O that pose measuring apparatus is calculated using step 5 i-th ter timescIt is in parallel with rope driving
The reference frame O of robotsRelativeness
Step 6.4 utilizes i-th ter times calibration 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 is minimum, takes δ=10-6；Then demarcate knot
Beam exports Caliter；If iter > iter max, terminates circulation；If SD > δ and iter < iter max, return
Step 6.3.
Claims (1)
1. a kind of kinematic parameter errors scaling method of rope driving parallel robot is to be applied to rope to drive parallel manipulator
In the calibration process of people, and rope driving parallel robot side is provided with pose measuring apparatus；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, reference frame O on robot end's moving platformp, the reference frame O of pose measuring apparatusc, and will be described
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 drives the rope of the n freedom degree exported for m wire drive at parallel robot, the robot end
Hold moving platform in the reference frame O of rope driving parallel robotsIn theoretical pose be expressed as Xs=[Ps Φs]T,
Wherein PsIndicate the position of robot end's moving platform, ΦsIndicate the posture of robot end's moving platform；
Enable biIndicate reference frame O of the rope tie point of the i-th wire drive on robot end's moving platformp
On position, aiIndicate reference coordinate of the rope output point in rope driving parallel robot of the i-th wire drive
It is OsOn position；I=1 ... m；
The closed chain equation of single wire drive is indicated using formula (1):
li=ai-Ps-Rsp(Φs)bi (1)
In formula (1), liIndicate that the rope output point of the i-th wire drive is connected to the rope of robot end's moving platform
The rope vector of point, RspIndicate the reference frame O on robot end's moving platformpParallel manipulator is driven to the rope
The reference frame O of peoplesSpin matrix；
Step 2.2, the inverse kinematics equation that 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 the rope lengths vector that formula (2) obtains rope driving parallel robot be 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 is enabled by being machined and the factor of assembling leads to robot kinematics' error parameter table of the i-th wire drive
It is shown asWherein, Δ biIndicate the rope tie point of the i-th rope driving device at the robot end
Hold the reference frame O on moving platformpOn location error, Δ aiIndicate that the rope output point of i-th wire drive exists
The reference frame O of the rope driving parallel robotsOn location error,Indicate motor encoder unit turn angle
The output error in length of corresponding rope, then the i-th rope that the kinematic parameter errors for needing to recognize share m 7 × 1 dimension drive dress
The robot kinematics' error parameter Cal setiComposed kinematic parameter errors Cal=[Cal1 Cal2 … Cali …
Calm]T；
Step 3.2 is measured using the pose of pose measuring apparatus measurement N group robot end's moving platform, and using jth group
Pose acquire 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 that is acquired with the pose that jth group measures of expression, lj
The rope lengths vector that expression is acquired with the pose that jth group measures；Indicate motor encoder list in the pose of jth group measurement
Position rotational angle corresponds to the output error in length of rope；
Step 4 obtains the optimization aim equation as shown in formula (4) as formula (3):
In formula (4), eθIndicate the mistake for the m motor encoder output angle that the pose of N group robot end's moving platform acquires
Eikonal equation, and have:
Formula (4) is optimized using least square method, obtains the identification mould of the kinematic parameter errors as shown in formula (5)
Type:
In formula (5),For error equation eθTo the Jacobian matrix of kinematic parameter errors Cal, WtIndicate that kinematics parameters are missed
The normalization matrix of poor Cal；
Step 5, the reference frame O for demarcating pose measuring apparatuscThe reference frame of the relatively described rope driving parallel robot
OsPositional relationship；
Step 5.1 enables the actual measurement pose of robot end's moving platform be expressed as Xcs=[Pcs Φcs]T, wherein Pcs
Indicate the reference frame O of the rope driving parallel robotsIn the reference frame O of the pose measuring apparatuscIn position
It sets, ΦcsIndicate the reference frame O of rope driving parallel robotsIn the reference frame O of the pose measuring apparatuscIn
Posture；Then indicate robot end's moving platform in the reference frame O of the pose measuring apparatus using formula (6)cIn
Position Pc:
Pc=Rcs(Φcs)Ps+Pcs (6)
In formula (6), RcsIndicate the reference frame O of rope driving parallel robotsGinseng relative to the pose measuring apparatus
Examine coordinate system OcSpin matrix；
Step 5.2, simplified style (6), to establish the reference frame O of pose measuring apparatus using formula (7)cIt is driven with the rope
The reference frame O of dynamic parallel robotsPositional relationship equation:
(Pc-Pcs)T(Pc-Pcs)=Ps TPs (7)
The reference frame O of pose measuring apparatus is established using formula (8)cWith the reference coordinate of rope driving parallel robot
It is OsPositional relationship optimization method, recycle L-M algorithm to optimize formula (8), it is in parallel to obtain rope driving
The reference frame O of robotsIn the reference frame O of the pose measuring apparatuscIn position Pcs:
minf(Pcs)=| | (Pc-Pcs)T(Pc-Pcs)-(Ps TPs)||2 (8)
Step 5.3 enables Pc-Pcs=A, Ps=B obtains R according to formula (6)cs(Φcs) B=A, then pose measurement is obtained using formula (9)
The reference frame O of devicecWith the reference frame O of rope driving parallel robotsPosture relation equation, recycle
L-M algorithm optimizes formula (9), obtains the reference frame O of rope driving parallel robotsIn the pose measurement
The reference frame O of devicecIn posture Φcs:
Rcs(Φcs)=ABT(B·BT)-1 (9)
Step 6, combined calibrating kinematic parameter errors；
Step 6.1 calculates the mean square error that pose measuring apparatus measures the pose of N group robot end's moving platform using formula (10)
SD:
In formula (10),XcIndicate the reference frame O in pose measuring apparatuscIn, pose measuring apparatus measurement
Robot end's moving platform attained pose,Indicate the reference frame O in pose measuring apparatuscIn, robot end
The theoretical pose of moving platform；
Step 6.2, initialization the number of iterations iter=1, kinematic parameter errors Cal, maximum number of iterations itermax；
Step 6.3, the reference frame O that pose measuring apparatus is calculated using step 5 i-th ter timescIt is in parallel with rope driving
The reference frame O of robotsRelativeness
Step 6.4 utilizes i-th ter times calibration 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 is minimum, then calibration terminates, and exports Caliter；Such as
Fruit iter > itermax, then terminate circulation；If SD > δ and iter < itermax, return step 6.3.
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