CN101660903B - Extrinsic parameter computing method for measurement robot - Google Patents

Abstract

The invention relates to an extrinsic parameter computing method for a measurement robot; the method mainly aims at computing extrinsic parameters of an industrial robot with a two-dimensional distance-measurement sensor. In the method, a plane target is used as a reference object, a measurement head is firstly driven by the robot to do translational movement along X, Y and Z direction, and the plane target is measured, and a plane target of the extrinsic parameters can be computed according to measurement data and pose data of the robot, and then the end of the robot is controlled to do rotation actions for at least three times, and the plane target is measured, and the translational vector of the extrinsic parameters can be computed according to measurement data and pose data of the robot.

Description

A kind of outer calculation method of parameters that is used for robot measurement

Technical field

The present invention relates to field of measuring technique, definite a kind of outer calculation method of parameters that is used for robot measurement of saying so.

Background technology

Robot is born in the sixties in 20th century, and through the development of decades, Robotics is ripe already.Robot with visual performance is mainly used in industrial circles such as automobile, electronics, machine-building, and wherein most widely used is the Robot Hand-eye coordination function, for example grasps robot, assembly robot and arc welding robot etc.Robot vision has had very proven technique application at processing manufacturing industry.

Along with the development of Robotics, the application of robot in measurement also more and more comes into one's own.The robot measurement has characteristics such as online, flexible, efficient, can realize the measurement to part 100%.Therefore, be particularly suitable for inter process and process measurement in the automated manufacturing system.It is low that cost is measured by robot, realizes that easily measuring speed is fast, automaticity is high, flexible good on-line detecting system.Robot measurement is application from be born to putting into production, begins to show present flourish vital.

Robot measurement is installed distance measuring sensor the robot end usually, drives the measurement that sensor is finished some key parameters by robot.For with robot in the measurement data unification under each attitude under the same coordinate system, need to determine sensor and robot end's annexation, be referred to as the outer parameter of sensor.

Summary of the invention

The purpose of this invention is to provide the outer calculation method of parameters that is applicable to dimension sensor (being that the data that sensor returns are 2-D data).

Principle of the present invention is, with the plane (materials such as metal or pottery are made) of a position the unknown as object of reference, robot drives gauge head and measures this reference planes with specific mode of motion, set up equation of constraint according to the pose of measurement data and robot, find the solution this equation and can obtain outer parameter about outer parameter.

Feature of the present invention is:

A. this method is applicable to the robot measurement system that is made of two-dimentional distance measuring sensor (1), industrial robot (2), plane target drone (3), wherein distance measuring sensor (1) is installed in industrial robot (2) end, and plane target drone (3) places in the visual range of sensor as object of reference.

B. outer CALCULATION OF PARAMETERS step is:

(1) at first drive gauge head along X by robot, Y, three directions of Z are done pure flat shifting movement, and the measurement plane target, can be calculated the rotation matrix of outer parameter by the pose data of measurement data and robot.

(2) the control robot end is done at least three spinning movements then, and measures and the measurement plane target, can be calculated the translation vector of outer parameter by the pose data of measurement data and robot.

Advantage of the present invention is: the common methods of outer CALCULATION OF PARAMETERS has: 1. utilize high-precision three-coordinates measuring machine that sensor clamping instrument is measured; 2. be the outer calculation method of parameters of video camera at sensor, these class methods can not directly apply to displacement transducer; 3. sensor is the one dimension stadimeter, adopts fixed point displacement appearance to carry out outer calculation of parameter.1. cost is higher in the said method, operation inconvenience, and 2. 3. method all is not suitable for dimension sensor.And we are bright at the robot that is used to finish measuring task, only need to use a plane as object of reference, and cost is low, realize easily demarcating automatically.

Description of drawings:

That Fig. 1 is world coordinate system O _w-X _w-Y _w-Z _wWith wrist coordinate system O _g-X _g-Y _g-Z _gAnd gauge head coordinate system O _s-X _s-Y _s-Z _sSynoptic diagram.

Embodiment:

The data of gauge head output are the 2-D datas that comprises the testee depth information, and the position of measured point is to utilize the three-dimensional coordinate in space to describe. realize that three-dimensional measurement must be converted into this 2-D data three-dimensional data, finish the geometric model that this data-switching must be set up measuring system.

For ease of the relation between each link in the research measuring system, at first set up following 3 coordinate systems (seeing accompanying drawing).

(1) world coordinate system O _w-X _w-Y _w-Z _w, measurement data finally should be unified this coordinate system. for simplicity, select the basis coordinates system of world coordinate system and robot to overlap.

(2) wrist coordinate system O _g-X _g-Y _g-Z _g, coordinate origin is determined by the direct kinematics of robot with respect to the attitude of basis coordinates system at the center of ring flange.

(3) the gauge head coordinate system is defined as O _s-X _s-Y _s-Z _s

If the gauge head coordinate system is (R with respect to the attitude (outer parameter) of wrist coordinate system _x, t), the wrist coordinate system is (R with respect to the attitude of the basis coordinates system of robot _w, t _w), a back coordinate system of above 3 coordinate systems is done conversion to previous coordinate system, the geometric model that obtains measuring system is

X _w＝R _w(R _xx _s+t)+t _w (1)

X wherein _w, X _sRepresent measured coordinate respectively at basis coordinates system and gauge head coordinate system.

Set up an office p at gauge head coordinate system O _s-X _s-Y _s-Z _sUnder coordinate be X _s=[x _s, y _s, 0] ^T, this point is at wrist coordinate system O _g-X _g-Y _g-Z _gCoordinate be X _g=[x _g, y _g, z _g] ^T, then

$\left[\begin{array}{c}{x}_g\\ y_g\\ z_g\end{array}\right]=R\left[\begin{array}{c}{x}_s\\ y_s\end{array}\right]+t=\left[\begin{array}{cc}{r}_1& r_2\\ r_4& r_5\\ r_7& r_8\end{array}\right]\left[\begin{array}{c}{x}_s\\ y_s\end{array}\right]+\left[\begin{array}{c}{t}_x\\ t_y\\ t_z\end{array}\right]---\left(2\right)$

(1) finds the solution matrix R

If initial position wrist coordinate system is designated as O _G1-X _G1-Y _G1-Z _G1, the equation of target plane is under this is

${n_1}^T{X}_{g1}+b_1=0---\left(3\right)$

N wherein ₁=[n _1x, n _1y, n _1z] ^TFor target plane at O _G1-X _G1-Y _G1-Z _G1Unit normal vector under the coordinate system.

Wrist-sport during to position j coordinate system be designated as O _Gj-X _Gj-Y _Gj-Z _Gj, this moment, the equation of target plane under this is was

$n_j^T{X}_{\mathrm{gj}}+b_j=0---\left(4\right)$

If X _G1=R _J1X _Gj+ t _J1, substitution (3)

${n_1}^T(R_{j1}{X}_{\mathrm{gj}}+t_{j1})+b_1=0---\left(5\right)$

Relatively (4) and (5) obtain

$n_j^T={n_1}^T{R}_{j1},$ $b_j={n_1}^T{t}_{j1}+b_1---\left(6\right)$

Being located at the data that a bit obtain on j the position gauge head measurement target is X _Sj, then

$n_j^T({\mathrm{RX}}_{\mathrm{sj}}+t)+b_j=0---\left(7\right)$

(6) substitution (7) is got

$\left({n_1}^T{R}_{j1}R\right)X_{\mathrm{sj}}+\left({n_1}^T{R}_{j1}\right)t+{n_1}^T{t}_{j1}+b_1=0---\left(8\right)$

If the motion of wrist is pure flat moving, i.e. R _J1=I, then (8) are

$\left({n_1}^{T}R\right)X_{\mathrm{sj}}+{n_1}^{T}t+{n_1}^T{t}_{j1}+b_1=0---\left(9\right)$

Deduct the equation of initial position with the equation (9) of j position formation $\left({n_1}^{T}R\right)X_{s1}+{n_1}^{T}t+b_1=0$ Obtain

${n_1}^{T}R(X_{\mathrm{sj}}-X_{s1})+{n_1}^T{t}_{j1}=0---\left(10\right)$

Formula (10) is about n ₁With the equation of R, have to draw a conclusion to exist:

(I) if wrist is done pure flat shifting movement at least three times, and these three times move not coplane, then n ₁It is unique definite.

(II) change target direction at least three times, repeat the process of conclusion (I) at every turn, then R is unique determines.

Suppose that wrist has been pure flat shifting movement n time, get the data point that initial position 1 records $X_{s1}={[x_{s1}^1,y_{s1}^1]}^T,$ Two data point [x that i obtains are put in fetch bit _Si ¹, y _Si ¹] T, [x _Si ², y _Si ²] T, then there is following equation to set up at position i according to formula (10).

$t_{i1}^T{n}_1=-[x_{\mathrm{si}}^1-x_{s1}^1,y_{\mathrm{si}}^1-y_{s1}^1]R^T{n}_1---\left(11a\right)$

$t_{i1}^T{n}_1=-[x_{\mathrm{si}}^2-x_{s1}^1,y_{\mathrm{si}}^2-y_{s1}^1]R^T{n}_1---\left(11b\right)$

Order $R^T{n}_1={[k_1^1,k_1^2]}^T,$ Deducting (11a) with (11b) obtains

$\left[\begin{array}{cc}{x}_{\mathrm{si}}^2-x_{\mathrm{si}}^1& y_{\mathrm{si}}^2-y_{\mathrm{si}}^1\end{array}\right]\left[\begin{array}{c}{k}_1^1\\ k_1^2\end{array}\right]=\left[\begin{array}{c}0\\ 0\end{array}\right]---\left(12\right)$

That is $\frac{k_1^1}{k_1^2}=-\frac{y_{\mathrm{si}}^2-y_{\mathrm{si}}^1}{x_{\mathrm{si}}^2-x_{\mathrm{si}}^1}---\left(13\right)$

If the direction of target is certain, then $R^T{n}_1={[k_1^1,k_1^2]}^T$ Be constant, that is to say under the prerequisite that does not change the target direction that if wrist is only done translation motion, the slope of the straight line that measures is consistent.

If Wrist-sport, obtains the equation of n shape suc as formula (11a) to n position

$\left[\begin{array}{c}{t}_{21}^T\\ t_{31}^T\\ \·\\ \·\\ \·\\ t_{n1}^T\end{array}\right]\left[\begin{array}{c}{n}_{1x}\\ n_{1y}\\ n_{1z}\end{array}\right]=-\begin{array}{}\end{array}\left[\begin{array}{cc}{x}_{s2}^1-x_{s1}^1& y_{s2}^1-y_{s1}^1\\ x_{s3}^1-x_{s1}^1& y_{s3}^1-y_{s1}^1\\ \·& \·\\ \·& \·\\ \·& \·\\ x_{\mathrm{sn}}^1-x_{s1}^1& y_{\mathrm{sn}}^1-y_{s1}^1\end{array}\right]\left[\begin{array}{c}{k}_1^1\\ k_1^2\end{array}\right]---\left(14\right)$

By $\frac{k_1^1}{k_1^2}=-a$ Abbreviation equation (14)

$\left[\begin{array}{c}{t}_{21}^T\\ t_{31}^T\\ \·\\ \·\\ \·\\ t_{n1}^T\end{array}\right]\left[\begin{array}{c}{n}_{1x}\\ n_{1y}\\ n_{1z}\end{array}\right]=-k_1^2\left[\begin{array}{c}{d}_2-d_1\\ d_3-d_1\\ \·\\ \·\\ \·\\ d_n-d_1\end{array}\right]---\left(15\right)$

If k ₁ ¹And k ₁ ²Known, as long as t ₂₁, t ₃₁..., t _N1Three linearly independent vectors, then n are arranged ₁Unique definite:

$n_1=-k_1^2\mathrm{pinv}\left(\left[\begin{array}{c}{t}_{21}^T\\ t_{31}^T\\ \·\\ \·\\ \·\\ t_{n1}^T\end{array}\right]\right)\left[\begin{array}{c}{d}_2{-d}_1\\ d_3-d_1\\ \·\\ \·\\ \·\\ d_n-d_1\end{array}\right]---\left(16\right)$

Pinv () represents the generalized inverse of matrix, again by constraint condition ‖ n ₁‖=1 can unique definite n ₁, k ₁ ¹And k ₁ ².

So far, by n ₁, k ₁ ¹And k ₁ ²Set up a equation of constraint about R $R^T{n}_1={[k_1^1,k_1^2]}^T.$ Only can not obtain R by an equation of constraint, the pose that therefore also needs to change the direction of target or change the robot wrist obtains the more equation of constraint about R.

The direction of bidding target changes m time, has obtained m equation of constraint about R

$R^T{n}_1={[k_1^1,k_1^2]}^T$

$R^T{n}_2={[k_2^1,k_2^2]}^T---\left(17\right)$

$R^T{n}_m={[k_m^1,k_m^2]}^T$

Thus as long as R just can be determined uniquely in m 〉=3.

(2) find the solution translation vector t

Can only obtain a constraint condition about t and b1 according to the corresponding target direction of equation (9), therefore finding the solution t also needs wrist to rotate, and obtains the equation of several shapes suc as formula (8).

Get by formula (9)

$b_1=-\left({n_1}^{T}R\right)X_{\mathrm{si}}-{n_1}^{T}t-{n_1}^T{t}_{i1}---\left(18\right)$

Substitution formula (8)

$({n_1}^T-{n_1}^T{R}_{j1})t=\left({n_1}^T{R}_{j1}R\right)X_{\mathrm{sj}}-\left({n_1}^{T}R\right)X_{\mathrm{si}}+{n_1}^T(t_{j1}-t_{i1})---\left(19\right)$

Claims (1)

1. outer calculation method of parameters that is used for robot measurement, comprise two-dimentional distance measuring sensor (1), industrial robot (2), plane target drone (3), it is characterized in that, wherein two-dimentional distance measuring sensor (1) is installed in industrial robot (2) end, plane target drone (3) places as object of reference in the visual range of two-dimentional distance measuring sensor, and outer CALCULATION OF PARAMETERS step is:

(1) at first drive two-dimentional distance measuring sensor along X by robot, Y, three directions of Z are done pure flat shifting movement, and the measurement plane target, by the go out rotation matrix of parameter of the pose data computation of measurement data and robot,

(2) the control robot end is done at least three spinning movements then, and the measurement plane target, by the go out translation vector of parameter of the pose data computation of measurement data and robot.

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