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 PDF

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CN107627299B
CN107627299B CN201710817308.9A CN201710817308A CN107627299B CN 107627299 B CN107627299 B CN 107627299B CN 201710817308 A CN201710817308 A CN 201710817308A CN 107627299 B CN107627299 B CN 107627299B
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尚伟伟
张飞
丛爽
张彬
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University of Science and Technology of China USTC
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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

A kind of kinematic parameter errors scaling method of rope driving parallel robot
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-Rsps)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-Rsps)bi)T(ai-Ps-Rsps)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=Rcscs)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)cscs) 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:
Rcscs)=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-Rsps)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-Rsps)bi)T(ai-Ps-Rsps)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=Rcscs)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 Rcscs)TRcscs)=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)cscs) 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:
Rcscs)=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-Rsps)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-Rsps)bi)T(ai-Ps-Rsps)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=Rcscs)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)cscs) 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:
Rcscs)=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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