A kind of robot kinematics' parameter calibration method based on laser range finderTechnical field
The invention belongs to information measurement correlative technology field, in particular to a kind of robot motion based on laser range finderLearn parameter calibration method.
Background technique
With the continuous expansion of the installation amount and application range of industrial robot (calling robot in the following text), industrially to robotVarious aspects of performance higher requirements are also raised, the especially pose accuracy of robot, such as absolute fix precision and repeat it is fixedPosition precision.Currently, the repetitive positioning accuracy of industrial robot is very high, 0.1 millimeter can reach, but its absolute fix precision is veryDifference can only achieve centimetre scale, and this precision is far from satisfying the control requirement of industry spot, cause robot localization smartSpending reason not high, that application condition is big is geometric error of the robot in processing, production and assembling process, this fractional error is bigGenerally account for the 90% of all error sources.Robot kinematics' parameter calibration is exactly by the geometric error of identification robot and to itCompensating is the effective means for improving robot absolute fix precision to obtain higher absolute fix precision.Kinematics ginsengNumber calibration is generally divided into 4 modeling, measurement, parameter identification and error compensation steps.
With the development of robot field, researcher both domestic and external proposes many marks to improve the precision of robotDetermine method, mainly include following five kinds of scaling methods:
The first i.e. most popular parameter calibration based on location error model, measures machine with externally measured instrumentPeople end physical location, and make comparisons with robot theoretical position, position is established with the physical location of multiple groups point and theoretical positionThe error differential equation, and then solve error parameter.Commonly measuring instrument such as laser traces instrument, three coordinate measuring machine etc. is allIt is demarcated based on this model, although laser traces instrument and three coordinate measuring machine measurement accuracy are high, expensive, operation is multipleIt is miscellaneous, demarcate low efficiency.
Second is the parameter calibration based on distance error model, and this method utilizes any two points of robot in spaceError model is established the characteristics of being equidistant in robot coordinate system and measurement coordinate system, and then solves kinematics parametersError.The common instrument of this method, such as the caliberating device based on stay wire sensor, industrially use such as dynalog companyCalibration measuring instrument is also based on this principle, however this instrument price is expensive, complicated for operation.
The third is the method using sensor, as the method for inertial sensor plus position sensor, laser sensor addCaliberating device of PSD etc. and the image processing method based on imaging sensor etc., however, the caliberating device that the method usesIt is complicated for operation, it is expensive, and non-large-scale commercial.
4th kind is demarcated using artificial neural network, obtains the parameter error of robot using the above method firstWith the mass data at joint of robot angle, and as exporting and input parameter trains neural network, and then when robot transportsWhen moving a certain position, neural network can calculate kinematic parameter errors herein, and compensate robot in real time and controlIn system.The method can realize the real-time of error compensation, but it is bigger than normal to measure workload.
5th kind is that the method for applying physical constraint to robot end is demarcated, if face constraint or spherical surface constrain,Face constraint or the spherical surface constraint equation of distal point are established, and then solves kinematic parameter errors, such as Zhong (Zhong XL,Lewis J M,Francis L N N.Autonomous robot calibration using a trigger probe[J] .Robotics and Autonomous systems, 1996,18 (4): 395-410.) propose a kind of plane restriction mouldType, but the method is limited to manual operations, leads to the problems such as measurement accuracy is not high, and measurement efficiency is relatively low；For another example Chinese invention(CN104608129A) a kind of robot plane disclosed in constrains scaling method, and this method is utilized to install in robot end and be visitedNeedle, and the plane for keeping prober constraints parallel with robot basis coordinates axis in normal vector then realize robot kinematics' parameterCalibration.But when being demarcated in this way, probe needs are contacted with calibrating block, since probe easily touches calibrating blockCause calibrating block to move, and then results in the need for re-starting calibration, and the motion range very little of robot end's point, machineSufficient movement, calibration point do not concentrate on a certain smaller area of robot working space, are not distributed in machine sufficiently each axis of peopleDevice people's working space；Simultaneously because robot base coordinate sys-tem can not show, it is difficult to accomplish three planes when calibrating block is putNormal vector is substantially parallel with robot base coordinate sys-tem, this generates great error when will lead to calculating, or even can not solve.
Summary of the invention
Aiming at the above defects or improvement requirements of the prior art, the present invention provides a kind of machines based on laser range finderPeople's kinematic calibration method, based on the work characteristics of existing scaling method, for robot kinematics parameter calibration sideMethod study and has been designed.The calibration tool that robot kinematics' parameter calibration method needs to use is laser range finderAnd test plate, structure is simple, and it is easy for installation, it is easily operated, and cost is relatively low, measurement main component is laser range finder, togetherWhen ensure that the precision of calibration.It, can effective expanding machinery people in addition, test plate is placed in the working space of robotMeasure spatial dimension, it is ensured that sampled point is distributed in space uniform, is conducive to improve precision.
To achieve the above object, the present invention provides a kind of robot kinematics parameter calibration side based on laser range finderMethod, method includes the following steps:
(1) laser range finder and computer are connected to robot to be calibrated, while test plate being placed inIn the working space of the robot；
(2) determine that mapping relations and laser range finder between robot end's coordinate system and robot base coordinate sys-tem are satMapping relations between mark system and robot end's coordinate system；
(3) each axis movement of the robot is controlled, the computer acquisition moves the joint angle of corresponding each axis every timeThe reading value of angle value and the laser range finder, to obtain multiple groups measurement data；
(4) obtain multiple points according to obtained mapping relations and multiple groups measurement data, and according to multiple points of acquisition andCoplanar condition determines the kinematic parameter errors of the robot；
(5) calibration is compensated to the kinematics parameters of the robot using obtained kinematic parameter errors, demarcatedStep (2) are repeated after complete and obtain kinematic parameter errors again to step (4), compare the kinematics parameters that front and back obtains twiceThe size of error optimizes calibration process and goes to step (2) if calibrated kinematic parameter errors dissipate；Otherwise, it usesSecond of kinematic parameter errors obtained compensates calibration to the kinematics parameters of the robot, and calibration is completed.
Further, robot links coordinate system { i } is denoted as relative to the homogeneous transform matrix of link rod coordinate system { i-1 }Then:
In formula, αi, ai, θi, diRespectively indicate connecting rod corner, the length of connecting rod, joint of link rod coordinate system { i } (i=1 ... 6)Angle and connecting rod offset distance.
Further, robot end's coordinate system { E } converts square relative to the pose of robot base coordinate sys-tem { B }Battle arrayAre as follows:
In formula,Indicate module and carriage transformation matrix of the connecting rod i relative to connecting rod i-1；N, o, a are robot end's coordinate systemThe unit vector of { E }；P is position vector of robot end's coordinate origin relative to robot base coordinate sys-tem origin；n,O, a and P is { αi, ai, θi, di(i=1 ... 6) function.
Further, transformation matrix of the laser range finder coordinate system relative to robot end's coordinate system are as follows:
Further, the laser range finder is one-dimensional sensor, then its laser beam projects point is relative to laser range finderThe evolution matrix of coordinate system are as follows:
In formula, l is the measurement distance of laser range finder.
Further, homogeneous coordinates of the laser beam projects point under robot base mark system { B } on plate are tested are as follows:
The differential error expression formula of robot end's point are as follows: Pa-Pn=J Δ ρ, wherein PaIt indicatesThe physical location of distal point, PnIndicate that the theoretical position of distal point, J indicate one 3 × 25 error coefficient matrix, Δ ρ is oneA 25 × 1 geometric error parameter vector.
Further, Δ ρ=[Δ a1 … Δa6 Δd1 … Δd6 Δα1 … Δα6 Δθ1 … Δθ6Δ l],Wherein, Δ αi、Δdi、Δαi、Δθi(i=1 ... 6) is respectively the mistake between theory movement parameter and actual motion parameterDifference.
Further, in step (4), multiple points are determined by obtained multiple groups measurement data；Later, by four in planeThree vectors that point is constituted are coplanar, obtain the equation for meeting coplanar condition, and multiple points sequentially four compositions, one equation then obtainsEquation group comprising multiple equations uses least square method to the solving equations to obtain the kinematics ginseng of the robotNumber error.
Further, the kinematic parameter errors that front and back obtains twice are respectively Δ ρ and Δ ρ2If | | Δ ρ | | < | | Δ ρ2| |, then calibrated kinematic parameter errors diverging.
Further, the computer is connected to the robot and the laser range finder, is used to blame acquisition machinePerson joint's angular data and laser range finder measurement data, and carry out data processing.
In general, through the invention it is contemplated above technical scheme is compared with the prior art, base provided by the inventionIt is mainly had the advantages that in robot kinematics' parameter calibration method of laser range finder
1. the calibration tool that the kinematic calibration method needs to use is laser range finder and test plate, structureSimply, easy for installation, it is easily operated, and cost is relatively low, measurement main component is laser range finder, while ensure that the essence of calibrationDegree；
2. test plate is placed in the working space of robot, can effective expanding machinery people measurement spatial dimension,Ensure that sampled point is distributed in space uniform, is conducive to improve precision；
3. being used to member planar constraint condition using test plate, and robot end is not flat with test in calibration processThe practical contact of plate, ensure that the precision of calibration；
4. using the plane restriction of coplanar condition, at the same avoid multiple measurement coordinate systems and robot base coordinate sys-tem itBetween multiple conversion, effectively reduce calculation amount and error source, ensure that the accuracy of calibration.
Detailed description of the invention
Fig. 1 is robot kinematics' parameter calibration method based on laser range finder that better embodiment of the present invention providesFlow diagram；
Fig. 2 is using being demarcated in Fig. 1 based on robot kinematics' parameter calibration method of laser range finderThe calibration schematic diagram of robot；
Fig. 3 is the planar point schematic diagram for the test plate that the robot in Fig. 2 is related to.
In all the appended drawings, identical appended drawing reference is used to denote the same element or structure, in which: 1- robot sheetBody, 11- end flange, 2- bindiny mechanism, 3- laser range finder, 4- test plate, 5- computer.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, rightThe present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, andIt is not used in the restriction present invention.As long as in addition, technical characteristic involved in the various embodiments of the present invention described belowNot constituting a conflict with each other can be combined with each other.
Please refer to Fig. 1 and Fig. 2, robot kinematics' ginseng based on laser range finder that better embodiment of the present invention providesNumber scaling methods, robot kinematics' parameter calibration method it is easy to operate, the calibration facility price of use is lower, simultaneouslyAlso ensure the high-precision of kinematic calibration.
Robot kinematics' parameter calibration method based on laser range finder that present embodiment provides mainly includes followingStep:
Laser range finder 3 and computer 5 are connected to robot to be calibrated, while will test plate 4 by step 1It is placed in the working space of the robot.The robot includes robot body 1, is connected to the robot bodyEnd flange 11 and the bindiny mechanism 2 for being connected to the end flange 11, the robot body 1 are connected to the computer 5,The bindiny mechanism 2 is fixedly connected with the laser range finder 3.The test plate 4 it is smooth up, and the shiny surfaceFlatness is level-one or level-one or more.The laser beam that the laser range finder 3 issues is radiated at the smooth of the test plate 4On face, the distance between described test plate 4 is maintained in the range of the laser range finder 3.The computer 5 is used forThe range data that the joint angular data and the laser range finder 3 for acquiring the robot measure.In present embodiment, the surveyIt tries plate 4 to be arranged on dampening assembly, to prevent rotation and measure field of the motor of the robot in measurement processThe interference of vibration noise；Angle in measurement process, between the normal vector of the shiny surface of the laser beam and the test plate 4Less than 60 DEG C.
Step 2 determines mapping relations and laser ranging between robot end's coordinate system and robot base coordinate sys-temMapping relations between instrument coordinate system and robot end's coordinate system.Specifically, the kinematics mould of the robot is establishedType, the modeling method of common robot kinematics' model have classical DH method, 5 parameter MDH methods, CPC model, S model and POE mouldType etc., classical DH method is because its principle is simple, is readily appreciated that, compared to other modeling methods answering in industrial robot fieldWith the most extensively, present embodiment also establishes the DH model of the robot using classics DH method.
DH model on each link joint of industrial robot by establishing joint coordinate system, and with four parameter characterizationsEach connecting rod, to establish the space coordinates of each connecting rod of robot.It is opposite that robot links coordinate system { i } is obtained by DH modelIt is denoted as in the homogeneous transform matrix of link rod coordinate system { i-1 }Then:
In formula, αi, ai, θi, diThe connecting rod respectively indicated in the DH model parameter of link rod coordinate system { i } (i=1 ... 6) turnsAngle, length of connecting rod, joint angle and connecting rod offset distance.
Module and carriage transformation matrix of the robot end's coordinate system { E } relative to robot base coordinate sys-tem { B }Are as follows:
In formula,Indicate module and carriage transformation matrix of the connecting rod i relative to connecting rod i-1；N, o, a are robot end's coordinate systemThe unit vector of { E }, P are position vector of robot end's coordinate origin relative to robot base coordinate sys-tem origin；n,O, a and P is { αi, ai, θi, di(i=1 ... 6) function.In present embodiment, robot end's coordinate system { E } be withThe coordinate system that the end flange center of robot is established, the robot base coordinate sys-tem { B } is the base center with robotThe coordinate system of foundation；Laser range finder coordinate system { T } is built upon the coordinate system on laser range finder 3, coordinate origin settingIn the eye point of laser beam.
Transformation matrix of the laser range finder coordinate system relative to robot end's coordinate system are as follows:
The laser range finder 3 is one-dimensional sensor, and laser beam projects are on the test plate 4, then its laser beamEvolution matrix of the incident point relative to laser range finder coordinate system are as follows:
In formula, l is the measurement distance of laser range finder.
Homogeneous coordinates of the laser beam transmission point under robot base mark system { B } are as follows:
The differential error expression formula of robot end's point are as follows:
Pa-Pn=J Δ ρ (6)
In formula, PaIndicate the physical location of distal point, PnIndicate that the theoretical position of distal point, J indicate one 3 × 25 mistakePoor coefficient matrix, it may be assumed that
Δ ρ is one 25 × 1 geometric error parameter vector, it may be assumed that
Δ ρ=[Δ α1 … Δα6 Δd1 … Δd6 Δα1 … Δα6 Δθ1 … Δθ6 Δl] (8)
Wherein, Δ αi、Δdi、Δαi、Δθi(i=1 ... 6) is respectively theory movement parameter and actual motion parameterBetween error amount.
Step 3, controls each axis movement of the robot, and the computer acquisition moves the pass of corresponding each axis every timeThe reading value of angle value and the laser range finder 3 is saved, to obtain multiple groups measurement data.Specifically, the robot is controlledEach axis movement, it is mobile on a large scale that the robot end drives the laser range finder 3 to do repeatedly, keeps institute while mobileThe laser beam projects of the transmitting of laser range finder 3 are stated on the test plate 5, record the Laser Measuring when movement stops every timeThe reading value l of distance meter 3 at this timeiAnd the joint angle angle value q of each axis of robot at this timei={ θ1, θ2, θ3, θ4, θ5, θ6, it is recorded asOne group of measurement data；Duplicate measurements is to obtain n group measurement data, and wherein n is more than or equal to 25+3, and it is 50 that present embodiment, which takes n,.
Step 4 obtains the point of identical quantity, and the point according to acquisition according to the multi-group data and mapping relations that obtainAnd coplanar condition determines kinematic parameter errors.50 point P can be obtained by 50 groups of data that formula (5) obtaini(xi yi zi)i∈ [0,50], it may be assumed that
It can be obtained in conjunction with formula (6) and formula (9):
In formula, PiaIndicate i-th point of physical location；PinIndicate i-th point of nominal position, JiIt indicates at i-th of pointDifferential Jacobi coefficient matrix；[…]TRepresenting matrix transposition.
Formula (11) progress difference vector is normalized to obtain:
It may be constructed three vectors by four points in plane, and three vectors meet coplanar condition and obtain formula (13):
Formula (13) are unfolded and are obtained after casting out second order and higher order term:
Note
Then it can be obtained:
HiΔρ+Xi=0 (15)
Four points can construct the equation shaped like formula (15), and sequentially 4 points constitute an equation to 50 points, then may be usedOne equation group comprising 47 equations of construction:
H Δ ρ+X=0 (16)
Wherein, H=[H1, H2... H47]T, X=[X1, X2... X47]T。
Overdetermined equation (16) are solved using least square method to obtain:
Δ ρ=- H-1·X (17)
Obtained result is kinematic parameter errors.
Step 5 compensates calibration using kinematics parameters of the obtained kinematic parameter errors to the robot,Step 2 is repeated after having demarcated to step 4 to obtain kinematic parameter error again, compares the kinematics parameters that front and back obtains twiceThe size of error optimizes calibration process and goes to step 2 if calibrated kinematic parameter errors dissipate；Otherwise, it usesSecond of kinematic parameter errors obtained compensates calibration to the kinematics parameters of the robot, and calibration is completed.
Specifically, obtained kinematic parameter errors are compensated into kinematics model with the kinematics parameters to robotCalibration is compensated, step 2 is repeated later to step 4 to obtain new kinematic parameter errors, is denoted as Δ ρ2。
Then, compare the size for the kinematic parameter errors that front and back obtains twice, if | | Δ ρ | | > | | Δ ρ2| |, then it is defeatedThe kinematic parameter errors Δ ρ obtained for the second time out2, i.e., using the kinematic parameter errors obtained for the second time to the fortune of robotDynamic parameter of learning compensates calibration；If | | Δ ρ | | < | | Δ ρ2| |, i.e. calibrated kinematic parameter errors diverging, then secondThe kinematic parameter errors that secondary operating process is obtained there are large error or for the first time are wrong, should optimize kinematics model at this timeAnd solution procedure (calibration process), and step 2 is gone to until obtaining satisfactory kinematic parameter errors.
Referring to Fig. 3, incident point of the laser range finder 3 on the test plate 5 is denoted as P1 point under a certain posture,The reading l of the laser range finder 3 of record at this time1With joint angle q1={ θ1, θ2, θ3, θ4, θ5, θ6It is one group of data, changeThe pose of the robot, repeats a upper process, available P2, P3, P4 ... Pn and n group data.The number of 4 points in N number of pointAccording to a composable equation, if the data of P1, P2, P3, P4 may make up first equation, the data of P2, P3, P4, P5 be may make upSecond equation；In n point, sequentially 4 points form an equation for front and back, amount to (n-3) a equation, because unknown errors parameter has25, therefore should ensure that (n-3) > 25 when operation.
Robot kinematics' parameter calibration method provided by the invention based on laser range finder, the kinematics parameters markDetermining the calibration tool that method needs to use is laser range finder and test plate, and structure is simple, easy for installation, easily operated, andCost is relatively low, and measurement main component is laser range finder, while ensure that the precision of calibration.In addition, test plate is placed onIn the working space of robot, can effective expanding machinery people measurement spatial dimension, it is ensured that sampled point is distributed in space uniform, is hadConducive to raising precision.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not toThe limitation present invention, any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should all includeWithin protection scope of the present invention.