CN104890013A - Pull-cord encoder based calibration method of industrial robot - Google Patents

Abstract

The invention discloses a pull-cord encoder based calibration method of an industrial robot. The method includes: calculating an error model of the robot according to a kinematic model of the robot and the structure of a pull-cord robot; allowing structural errors of the robot to fully affect rules of an end effector to demonstrate the robot; according to a command of a demonstration program, allowing the robot to move a specified position, and acquiring distances of the pull-cord encoder when the robot is at different positions; according to the acquired measurement data and end positional data of the robot, calculating a reference position of the pull-cord encoder; by means of the calculated reference position and the error model built, calibrating structural parameters of the robot; according to structural errors obtained in the calibration process, correcting the structural parameters of the robot; repeating the steps from five to seven until that the precision is satisfactory. The method is easy to implement and convenient to operate.

Description

A kind of industrial robot calibration algorithm based on draw wire encoder

Technical field

The invention belongs to Industrial Robot Technology field, relate to a kind of industrial robot calibration algorithm based on draw wire encoder.

Background technology

Along with robot is in the extensive utilization of industry-by-industry, industry is had higher requirement to the repetitive positioning accuracy of industrial robot and absolute fix precision.This demand seems particularly outstanding at aerospace field.

On a frame large aircraft, nearly 150 ~ 2,000,000 connectors, the positional precision of connecting hole, surface quality is larger for the machining accuracy impact in hole.At the early process of aircraft development, this some holes position is all by manually carrying out brill riveting.But along with the development of digitizing technique, the brill riveting carrying out position, hole by off-line programing can improve the efficiency of transporation by plane greatly.The absolute fix precision of off-line programing to robot has very high requirement.

Due to the impact of numerous error source, the absolute fix precision of the robot just assembled can not meet the requirement of off-line programing utilization.

But present stage, the repetitive positioning accuracy of robot can reach very high precision. the repetitive positioning accuracy of the R12 robot that company produces can reach the research of Mooring B is that Robot calibration technology has established theoretical foundation.Its research shows the robot high to repetitive positioning accuracy, can be improved the absolute fix precision of robot by scaling method.

Summary of the invention

In order to solve the technical problem existed in prior art, the invention provides a kind of industrial robot calibration algorithm based on draw wire encoder, for using industrial robot widely, provide the algorithm improving its absolute fix precision, this arithmetic accuracy is high, fast convergence rate, and be easy to realize, easy to operate.

Its technical scheme is as follows:

Based on an industrial robot calibration algorithm for draw wire encoder, comprise the following steps:

The first step: the kinematics model setting up robot according to the joint configuration of robot;

Second step: in conjunction with the error model of the kinematics model of robot and the Structure Calculation machine people of draw wire encoder;

3rd step: teaching is carried out to robot with the principle making robot architecture's error fully affect end effector;

4th step: allow robot motion arrive assigned address according to the instruction of tutorial program, and obtain robot distance apart from draw wire encoder when diverse location;

5th step: the reference position calculating draw wire encoder according to the measurement data got and robot end's position data;

6th step: utilize the structural parameters of error model to robot of reference position and the foundation calculated to demarcate;

7th step: according to the structural parameters of the structural failure correction robot that calibration process obtains;

8th step: repeat step 5-seven, until precision meets the demands.

Preferably, following principle should be followed when step 3 carries out teaching to robot:

Robot should move to the peripheral envelope of its working space as far as possible, needs to ensure that each axle has larger movement travel within the scope of its structural limits simultaneously; Not only the position of Yao Shi robot arrival is various, but also will ensure that the end effector of robot has various different attitude.The impact of the structural failure of robot on robot absolute precision can be made like this to reach maximum, improve the stated accuracy of robot.

Compared with prior art, beneficial effect of the present invention: the invention provides and calibrate the structural parameters of robot in producer of robot, to improve the absolute fix precision of robot.Also can find broad application at medium-sized and small enterprises, the loss that Compensating Robot structure causes because of long-term work, for the long-time high reliability work of robot provides quality assurance simultaneously.Relate to for the utilization of industrial robot at industry-by-industry, as aircraft pilot hole, arc-welding, spot welding, spray Tai etc., this arithmetic accuracy is high, fast convergence rate, and is easy to realize, easy to operate.

Accompanying drawing explanation

Fig. 1 is Robot calibration system involved in the present invention;

Fig. 2 is the measure portion of Robot calibration system involved in the present invention;

Fig. 3 is fastening means involved in the present invention;

In Fig. 1: 1 is robot controller, 2 is robots to be calibrated, and 3 is connecting rods, and 4 is draw wire encoder, and 5 is data collecting cards, and 6 is computers.

In Fig. 2: 7 is draw wire encoder, 8 is main rotary shafts of movable pulley, and 9 is movable pulleys, and 10 is fixed pulleys, and 11 is the bases mated with draw wire encoder.

In Fig. 3: 12 is connectors, 13 is fixed bars, and 14 is rotating shafts I, and 15 is rotating shafts II, and 16 is link slots.

Fig. 4 is the industrial robot calibration algorithm flow chart based on draw wire encoder.

Detailed description of the invention

Technical scheme of the present invention is further illustrated below in conjunction with the drawings and specific embodiments.

As shown in Figure 1.Based in the industrial robot calibration algorithm of draw wire encoder, calibration system is by robot controller 1, and robot 2 to be calibrated, connecting rod 3, draw wire encoder 4, data collecting card 5 and computer 6 form.Its basic process industrial robot 1 to be calibrated is arranged on a certain fixed position in workshop, its coordinate system associates with earth coordinates, the end flange of robot is provided with the connecting rod 3 mated with draw wire encoder, draw wire encoder 4 is placed on the centre in robot working range as far as possible, under this principle, the position of draw wire encoder 4 can be any, robot 2 to be calibrated moves to each different position, space under the driving of robot controller 1, the computer 6 that calibration software is housed obtains measurement data by data collecting card 5, finally calculate nominal data.

As shown in Figure 2, draw wire encoder 7 is fixing on the base 11, the end of draw wire encoder 7 is connected firmly by fixed pulley 10 and the connecting rod 3 of movable pulley 9 with Fig. 1, movable pulley 9 can the main rotary shaft 8 of moving pulley rotate, it can ensure that draw wire encoder has a thick-and-thin datum mark in measuring process, and this point is the point of contact of main rotary shaft 8 axis of movable pulley 9 and movable pulley.

As shown in Figure 3, connector 12 and fixed bar 13 connect firmly, fixed bar 13 is connected by the end flange of bolt with robot 2, connector 12 can around two mutually orthogonal and intersect at a point axis rotate, this structure can ensure that the tool center point of robot 2 and the relative position of end flange remain unchanged, and link slot 12 is connected with draw wire encoder end.

The key of this algorithm is exactly the draw wire encoder of measurement is used as a part for robot inaccuracy transmission, and its coordinate defines in the base coordinate system of robot, and can be calculated by algorithm, is designated as datum mark P ₀(x, y, z).

Before Robot calibration, first carry out teaching to robot, the enveloping space motion of object Shi Shi robot as far as possible in its working range of teaching, guarantees that the structural failure of robot is maximum to robot absolute fix Accuracy.Need robot according to instruction campaign assigned position.By draw wire encoder, position, each motor point is measured.

In concrete calibration process, need robot according to the good Sequence motion of teaching to assigned address, note robot motion is P to the coordinate of each its reality of assigned address _i(x _i, y _i, z _i).Measured position, each motor point by draw wire encoder, so by draw wire encoder measurement acquisition is exactly P _ito datum mark P ₀the length l of (x, y, z) _m(0, i), this length is defined by following formula:

$l_M^2(0,i)={(x_i-x)}^2+{(y_i-y)}^2+{(z_i-z)}^2---\left(1\right)$

The present invention's these measurement data of giving chapter and verse calculate datum mark P ₀the discreet value of (x, y, z).

Above formula is launched, the equation in adjacent two motor points is subtracted each other and can set up Least-squares minimization model.

The i-th+1 equation and i-th equation subtract each other and can obtain:

$2(x_i-x_{i+1})x+2(y_i-y_{i+1})y+2(z_i-z_{i+1})z=l_M^2(0,i+1)-l_M^2(0,i)+|P_i{|}^2-|P_{i+1}{|}^2---\left(2\right)$

Wherein | P _i| ²=x _i ²+ y _i ²+ z _i ²

Might as well suppose in calibration process, to have collected m length data.Following variable can be defined:

$\begin{array}{cc}\mathrm{\λ}=\left[\begin{array}{c}x\\ y\\ z\end{array}\right]& b=\left[\begin{array}{c}{l}_M^2(0,2)-l_M^2(0,1)+|P_1{|}^2-|P_2{|}^2\\ l_M^2(0,2)-l_M^2(0,1)+|P_2{|}^2-|P_3{|}^2\\ ...\\ l_M^2(0,m)-l_M^2(0,m-1)+|P_{m-1}{|}^2-|P_m{|}^2\end{array}\right]\end{array}$

$A=\left[\begin{array}{ccc}2(x_1-x_2)& 2(y_1-y_2)& 2(x_1-x_2)\\ 2(x_2-x_3)& 2(y_2-y_3)& 2(z_2-z_3)\\ ...& ...& ...\\ 2(x_{m-1}-x_m)& 2(y_{m-1}-y_m)& 2(z_{m-1}-z_m)\end{array}\right]$

Can obtain according to least square method

A ^HAλ＝A ^Hb (3)

λ can be tried to achieve, i.e. the position of datum mark coordinate by above formula.

P in Practical Calculation process _i(x _i, y _i, z _i) coordinate cannot learn, therefore the present invention sets up a high-precision error model, can ensure to remove identification machine ginseng number and obtain theoretical position by robot parameter to go to mutually promote between Calculation Basis point by datum mark, namely can be restrained effect preferably by iteration.

Set up error model, first need the kinematics model setting up robot.

The present invention uses D-H model to carry out Kinematic Model to robot.

D-H model uses 4 independently parameter θ to adjacent segment _i, a _i, a _i, d _irepresent its transformation relation, the θ when joint of robot is rotary joint _ifor variable, when it is d during translation joint _ibecome variable.Transformation matrix between adjacent segment is expressed as represent the transformation matrix of the (n-1)th joint to the n-th joint.

For serial manipulator, its total transformation matrix can be expressed as

$T_0^n({\mathrm{\θ}}_1,{\mathrm{\α}}_1,a_1,d_1,{\mathrm{\θ}}_2,{\mathrm{\α}}_2,a_2,d_2...{\mathrm{\θ}}_n,{\mathrm{\α}}_n,a_n,d_n)=T_0^{1}T_1^{2}T_2^{3}nT_{n-1}^n---\left(4\right)$

Slight error is imposed to the parameter in each joint, uses the transformation matrix in Taylor expansion (giving up higher order term) then i-th joint to become

$\begin{array}{c}T_{i-1}^i({\mathrm{\θ}}_i+{\mathrm{\Δ\θ}}_i,{\mathrm{\α}}_i+{\mathrm{\Δ\α}}_i,a_i+{\mathrm{\Δa}}_i,d_i+{\mathrm{\Δd}}_i)=T_{i-1}^i+\frac{\∂T_{i-1}^i}{\∂{\mathrm{\θ}}_i}{\mathrm{\Δ\θ}}_i\frac{\∂T_{i-1}^i}{\∂{\mathrm{\α}}_i}{\mathrm{\Δ\α}}_i+\frac{\∂T_{i-1}^i}{\∂a_i}{\mathrm{\Δa}}_i+\frac{\∂T_{i-1}^i}{\∂d_i}{\mathrm{\Δd}}_i\\ =T_{i-1}^i+dT_{i-1}^i\end{array}$

Namely $dT_{i-1}^i+\frac{\∂T_{i-1}^i}{\∂{\mathrm{\θ}}_i}{\mathrm{\Δ\θ}}_i\frac{\∂T_{i-1}^i}{\∂{\mathrm{\α}}_i}{\mathrm{\Δ\α}}_i+\frac{\∂T_{i-1}^i}{\∂a_i}{\mathrm{\Δa}}_i+\frac{\∂T_{i-1}^i}{\∂d_i}{\mathrm{\Δd}}_i---\left(5\right)$

Total transformation matrix of robot is represented by (4) formula, might as well suppose that four parameters in each joint of robot have slight error, and so the total transformation matrix applied after error becomes

$T_0^n+dT_0^n=\underset{i=1}{\overset{n}{\Π}}(T_{i-1}^i+dT_{i-1}^i)---\left(6\right)$

(6) formula is launched, obtains after casting out high-order small quantity

$T_0^n+dT_0^n=T_0^{1}T_1^2\mathrm{...}T_{n-1}^n+\underset{i=1}{\overset{n}{\Σ}}\[T_0^1\mathrm{...}T_{i-2}^{i-1}\left(dT_{i-1}^i\right)T_i^{i+1}\mathrm{...}T_{n-1}^n\]---\left(7\right)$

(7) formula of substitution can obtain

$\begin{array}{c}dT_0^n\underset{i=1}{\overset{n}{\Σ}}\[T_0^1\mathrm{...}T_{i-2}^{i-1}(\frac{\∂T_{i-1}^i}{\∂{\mathrm{\θ}}_i}{\mathrm{\Δ\θ}}_i\frac{\∂T_{i-1}^i}{\∂{\mathrm{\α}}_i}{\mathrm{\Δ\α}}_i+\frac{\∂T_{i-1}^i}{\∂a_i}{\mathrm{\Δa}}_i+\frac{\∂T_{i-1}^i}{\∂d_i}{\mathrm{\Δd}}_i)T_i^{i+1}\mathrm{...}T_{n-1}^n\]\\ =\underset{i=1}{\overset{n}{\Σ}}(T_0^1\mathrm{...}T_{i-2}^{i-1}\frac{\∂T_{i-1}^i}{\∂{\mathrm{\θ}}_i}{\mathrm{\Δ\θ}}_{i}T_i^{i+1}\mathrm{...}T_{n-1}^n+T_0^1\mathrm{...}T_{i-2}^{i-1}\frac{\∂T_{i-1}^i}{\∂{\mathrm{\α}}_i}{\mathrm{\Δ\α}}_{i}T_i^{i+1}\mathrm{...}T_{n-1}^n\\ +T_0^1\mathrm{...}T_{i-2}^{i-1}\frac{\∂T_{i-1}^i}{\∂a_i}{\mathrm{\Δa}}_{i}T_i^{i+1}\mathrm{...}T_{n-1}^n+T_0^1\mathrm{...}T_{i-2}^{i-1}\frac{\∂T_{i-1}^i}{\∂d_i}{\mathrm{\Δd}}_{i}T_i^{i+1}\mathrm{...}T_{n-1}^n)\end{array}---\left(8\right)$

In order to improve the precision of demarcation, and being convenient to the connection of robot and draw wire encoder, the present invention relates to the feature for robot, devise the connecting rod as Fig. 3.

This connecting rod head end and robot end's flange are bolted, tip designs have special can the mutually orthogonal and axis intersecting at a point rotates around two structure, this structure can ensure that the relative position of robot tooling center points and end flange remains unchanged, and tool center point can pass through the coordinate of end flange and the homogeneous transform matrix of a constant represent.

In conjunction with (4) formula and (8) formula, final error can be obtained as follows:

$\begin{array}{c}dT_0^{n+1}\underset{i=1}{\overset{n}{\Σ}}\[T_0^1\mathrm{...}T_{i-2}^{i-1}(\frac{\∂T_{i-1}^i}{\∂{\mathrm{\θ}}_i}{\mathrm{\Δ\θ}}_i\frac{\∂T_{i-1}^i}{\∂{\mathrm{\α}}_i}{\mathrm{\Δ\α}}_i+\frac{\∂T_{i-1}^i}{\∂a_i}{\mathrm{\Δa}}_i+\frac{\∂T_{i-1}^i}{\∂d_i}{\mathrm{\Δd}}_i)T_i^{i+1}\mathrm{...}T_{n-1}^{n}T_n^{n+1}\]\\ =\underset{i=1}{\overset{n}{\Σ}}(T_0^1\mathrm{...}T_{i-2}^{i-1}\frac{\∂T_{i-1}^i}{\∂{\mathrm{\θ}}_i}{\mathrm{\Δ\θ}}_{i}T_i^{i+1}\mathrm{...}T_{n-1}^n+T_n^{n+1}+T_0^1\mathrm{...}T_{i-2}^{i-1}\frac{\∂T_{i-1}^i}{\∂{\mathrm{\α}}_i}{\mathrm{\Δ\α}}_{i}T_i^{i+1}\mathrm{...}T_{n-1}^{n}T_n^{n+1}\\ +T_0^1\mathrm{...}T_{i-2}^{i-1}\frac{\∂T_{i-1}^i}{\∂a_i}{\mathrm{\Δa}}_{i}T_i^{i+1}\mathrm{...}T_{n-1}^{n}T_n^{n+1}+T_0^1\mathrm{...}T_{i-2}^{i-1}\frac{\∂T_{i-1}^i}{\∂d_i}{\mathrm{\Δd}}_{i}T_i^{i+1}\mathrm{...}T_{n-1}^{n}T_n^{n+1})\end{array}---\left(9\right)$

According to the model that prior art proposes, there is following relation with its range error in the absolute position error of robot under programmed instruction between actual in-position and theoretical position:

$\mathrm{\Δ}l(i,i+1)=\[\frac{x_R(i+1)-x_R\left(i\right)}{l_R(i,i+1)},\frac{y_R(i+1)-y_R\left(i\right)}{l_R(i,i+1)},\frac{z_R(i+1)-z_R\left(i\right)}{l_R(i,i+1)}\]\·({\mathrm{dP}}_{i+1}-{\mathrm{dP}}_i)---\left(10\right)$

Wherein

△ l (i, i+1) be i-th with the difference of the distance of the i-th+1 instruction theoretical position and robot actual motion in-position, can be obtained by the computing of measuring system and robot gross data;

X _r(i), y _r(i), z _ri () is the theoretical position point that robot instruction defines;

L _rthe distance of i-th mathematical point that (i, i+1) represents for robot instruction and the i-th+1 mathematical point;

DP _ithe position error vector of i-th, by the 4th row first three rows definition, " d " represent differentiate.

According to the datum mark that step 5 calculates, using datum mark as the part compared at every turn, be designated as the 0th point, namely take the position of the actual arrival of robot and the position of datum mark to carry out application condition.DP can be obtained like this ₀=0, therefore (10) formula becomes:

$l_M(0,i)-l_R(0,i)=\[\frac{x_R\left(i\right)-x_R\left(0\right)}{l_R(0,i)},\frac{y_R\left(i\right)-y_R\left(0\right)}{l_R(0,i)},\frac{z_R\left(i\right)-z_R\left(0\right)}{l_R(0,i)}\]\·{\mathrm{dP}}_i---\left(11\right)$

Wherein

L _m(0, i) for measuring i-th point obtaining length to datum mark,

L _r(0, i) for robot theoretical position is to the length of datum mark,

Other identical with the meaning that (10) formula represents.

DP _ifor the site error function of robot, to the robot of D-H model, this function can be expressed as ${\mathrm{dP}}_i({\mathrm{\θ}}_1,{\mathrm{\α}}_1,a_1,d_1,{\mathrm{\θ}}_2,{\mathrm{\α}}_2,a_2,d_2...{\mathrm{\θ}}_n,{\mathrm{\α}}_n,a_n,d_n)=\underset{i=1}{\overset{n}{\Σ}}(k^{\mathrm{\θ}i}{\mathrm{\Δ\θ}}_i+k^{\mathrm{\α}i}{\mathrm{\Δ\α}}_i+k^{ai}{\mathrm{\Δa}}_i+k^{di}{\mathrm{\Δd}}_i),$ As follows by matrix notation:

${\mathrm{dP}}_i=\left[\begin{array}{ccccccc}{k}_x^{\mathrm{\θ}1}& k_x^{\mathrm{\α}1}& k_x^{a1}& k_x^{d1}& k_x^{\mathrm{\θ}2}& \mathrm{...}& k_x^{dn}\\ k_y^{\mathrm{\θ}1}& k_y^{\mathrm{\α}1}& k_y^{a1}& k_y^{d1}& k_y^{\mathrm{\θ}2}& \mathrm{...}& k_y^{dn}\\ k_z^{\mathrm{\θ}1}& k_z^{\mathrm{\α}1}& k_z^{a1}& k_z^{d1}& k_z^{\mathrm{\θ}2}& \mathrm{...}& k_z^{dn}\end{array}\right]\·\left[\begin{array}{c}\mathrm{\Δ}\mathrm{\θ}1\\ \mathrm{\Δ}\mathrm{\α}1\\ \mathrm{\Δ}a1\\ \mathrm{\Δ}d1\\ \mathrm{\Δ}\mathrm{\θ}2\\ \mathrm{...}\\ \mathrm{\Δ}dn\end{array}\right]=B_i\·\mathrm{\Δ}q---\left(12\right)$

Wherein

B _irefer to i-th coefficient matrix relevant with robot theoretical position, exponent number is 3 × 4n;

△ q then represents the error of robot links parameter, is the amount finally required;

DP _iwhat represent is the site error of tool focus, for the 4th row first three rows

According to identical character, B can be obtained _ithe k of matrix ^qithe corresponding above formula i-th joint △ q of coefficient _ithe coefficient of parameter error, such as k ^{θ 2}corresponding the first three rows that matrix the 4th arranges.

So far combination (11) formula and (12) formula can obtain the error model of robot:

$l_M(0,i)-l_R(0,i)=\[\frac{x_R\left(i\right)-x_R\left(0\right)}{l_R(0,i)},\frac{y_R\left(i\right)-y_R\left(0\right)}{l_R(0,i)},\frac{z_R\left(i\right)-z_R\left(0\right)}{l_R(0,i)}\]\·B_i.\left[\begin{array}{c}\mathrm{\Δ}\mathrm{\θ}1\\ \mathrm{\Δ}\mathrm{\α}1\\ \mathrm{\Δ}a1\\ \mathrm{\Δ}d1\\ \mathrm{\Δ}\mathrm{\θ}2\\ ...\\ \mathrm{\Δ}dn\end{array}\right]---\left(13\right)$

Clearly accurate reference point location can ensure the precision of the parameter error that this error model identification obtains; Simultaneously by after calibration compensation robot architecture parameter, the precision of the datum mark of calculating can be improved, therefore at the beginning of Calculation Basis point, the mathematical point position replacement P of instruction arrival can be performed with robot _i(x _i, y _i, z _i), the structural parameters error of datum mark and robot is ensured eventually through alternative manner.

The above, be only best mode for carrying out the invention, is anyly familiar with those skilled in the art in the technical scope that the present invention discloses, and the simple change of the technical scheme that can obtain apparently or equivalence are replaced and all fallen within the scope of protection of the present invention.

Claims (2)

1., based on an industrial robot calibration algorithm for draw wire encoder, it is characterized in that, comprise the following steps:

The first step: the kinematics model setting up robot according to the joint configuration of robot;

Second step: in conjunction with the error model of the kinematics model of robot and the Structure Calculation machine people of draw wire encoder;

3rd step: teaching is carried out to robot with the principle making robot architecture's error fully affect end effector;

4th step: allow robot motion arrive assigned address according to the instruction of tutorial program, and obtain robot distance apart from draw wire encoder when diverse location;

5th step: the reference position calculating draw wire encoder according to the measurement data got and robot end's position data;

6th step: utilize the structural parameters of error model to robot of reference position and the foundation calculated to demarcate;

7th step: according to the structural parameters of the structural failure correction robot that calibration process obtains;

8th step: repeat step 5-seven, until precision meets the demands.

2. the industrial robot calibration algorithm based on draw wire encoder according to claim 1, is characterized in that, should follow following principle when step 3 carries out teaching to robot:

Robot should move to the peripheral envelope of its working space as far as possible, needs to ensure that each axle has larger movement travel within the scope of its structural limits simultaneously; Not only the position of Yao Shi robot arrival is various, but also will ensure that the end effector of robot has various different attitude, makes the impact of the structural failure of robot on robot absolute precision reach maximum like this, thus improves the stated accuracy of robot.