CN104236456A - Robot hand-eye calibration method based on two-degree-of-freedom three-dimensional visual sensor - Google Patents

Abstract

The present invention provides a kind of Robotic Hand-Eye Calibration methods based on two-freedom 3D visual sensor, comprising the following steps: the first step, the calculating of coordinate conversion matrix T0 between initial position visual coordinate system and robot basis coordinates system; Second step, visual sensor from initial position both vertically as well as horizontally respectively rotation angle, θ and Afterwards, the transforming relationship matrix T θ between coordinate system and Calculating; Trick transformational relation matrix can be obtained by the multiplication of each transition matrix in third step; The present invention has many advantages, such as that method is simple, measurement accuracy is high, easy to spread, can effectively meet the needs of Robotic Hand-Eye Calibration.

Description

A kind of Robotic Hand-Eye Calibration method based on two-freedom 3D vision sensor

Technical field

The present invention relates to industrial robot vision's calibration technique field, specifically, it relates to a kind of Robotic Hand-Eye Calibration method based on two-freedom 3D vision sensor.

Background technology

Along with the application & development of 3D vision sensor vision technique, increasing robot is using the important tool of 3D vision sensor as its independent navigation.But, the problem of homing capability by the restriction of 3D vision sensor field range is there is in prior art, the degree of freedom of level, vertical direction must be increased for expanding field range to sensor, driving 3D vision sensor to carry out the scene information collection of more Large visual angle field angle according to this.

Summary of the invention

For deficiency of the prior art, the technical problem to be solved in the present invention is, a kind of Robotic Hand-Eye Calibration method based on two-freedom 3D vision sensor is provided, the method has the features such as computing is simple, measuring accuracy is higher, easy popularization, and effectively can meet the needs of Robotic Hand-Eye Calibration.

In order to solve the problems of the technologies described above, the technical solution adopted in the present invention is: a kind of Robotic Hand-Eye Calibration method based on two-freedom 3D vision sensor, comprises the following steps:

The first step, four points are marked in advance in 3D vision sensor field range, the mutual relationship of these four points be any 3 not conllinear and 4 not coplanar, gather this some cloud information of 4 by the 3D vision sensor be fixed on robot model machine initial position, obtain the D coordinates value of four gauge points relative to 3D vision sensor coordinate system; The measurement of Three-Dimensional Dynamic measuring equipment is adopted to obtain, relative to the D coordinates value of four gauge points in space under basis coordinates system of robot, obtaining transition matrix, obtaining the transformational relation matrix between the coordinate system of 3D vision sensor initial position and basis coordinates system of robot;

Second step, rotate to an angle in the horizontal direction by controlling driven by motor 3D vision sensor, and gather 4 cloud datas under current 3D vision sensor in space, calculate the three-dimensional coordinate of four points, utilize the two group three-dimensional coordinates of 4, space under 3D vision sensor to calculate the turning axle of 3D vision sensor coordinate systems, set up the anglec of rotation and 3D vision sensor and rotates transformational relation matrix afterwards between coordinate system and initial coordinate system; The computing method of the relational matrix that 3D vision sensor is corresponding when vertically rotating are identical;

3rd step, is multiplied by each transition matrix and can obtains trick transformational relation matrix.

Compared with prior art, owing to adopting technique scheme, a kind of Robot Vision Calibration method based on two-freedom 3D vision sensor of the present invention, level must be increased to sensor for expanding field range, the degree of freedom of vertical direction, 3D vision sensor has been driven to carry out the scene information collection of more Large visual angle field angle according to this, solve the problem of homing capability by the restriction of 3D vision sensor field range, and efficiently solve the calculating of sensor coordinate system transformational relation after horizontal vertical direction any rotation and between basis coordinates system of robot, scaling method depends on strict mathematical theory and derives, computational accuracy is high.

The invention has the beneficial effects as follows: have that method is simple, measuring accuracy is high, be easy to the advantages such as popularization, effectively can meet the needs of Robotic Hand-Eye Calibration.

Accompanying drawing explanation

Below by with reference to accompanying drawing describe the present invention particularly in conjunction with example, advantage of the present invention and implementation will be more obvious, wherein content shown in accompanying drawing is only for explanation of the present invention, and does not form restriction of going up in all senses of the present invention, in the accompanying drawings:

Fig. 1 is the calibration process schematic diagram of two-freedom 3D vision sensor of the present invention and basis coordinates system of robot; In figure: (1) is NDI Three-Dimensional Dynamic measuring instrument, (2) be four not coplanar gauge points in space, (3) be basis coordinates system of robot, (4) be 3D vision sensor initial position co-ordinates system, (5) be coordinate system after 3D vision sensor vertically rotates θ, (7) corresponding turning axle is represented, (9) be two points on turning axle with (10), (6) are that 3D vision sensor vertically rotates from position (5) after coordinate system, (8) represent corresponding turning axle, and (11) and (12) are two points on turning axle;

Fig. 2 is the concrete operations process flow diagram of the embodiment of the present invention;

Fig. 3 is the transformational relation schematic diagram between 3D vision sensor initial coordinate system of the present invention and basis coordinates system of robot; In figure: o-xyz is world coordinate system, o _r-x _ry _rz _rfor basis coordinates system of robot, o _v-x _vy _vz _vfor the coordinate system of 3D vision sensor, o _nDI-x _nDIy _nDIz _nDIfor NDI Three-Dimensional Dynamic surveying instrument coordinate system;

Fig. 4 is the transforming relationship schematic diagram of 3D vision sensor coordinate system of the present invention with coordinate system during vertical axis revolving; In figure: 3D vision sensor edge is by P _c1, P _c2coordinate system before and after 2 straight line anglec of rotation θ formed uses o respectively _v1-x _v1y _v1z _v1with o _v2-x _v2y _v2z _v2represent.

Embodiment

The present invention is described further below in conjunction with embodiment and accompanying drawing thereof:

As shown in Figures 1 to 4, a kind of Robotic Hand-Eye Calibration method based on two-freedom 3D vision sensor of the present invention, if robot head vertical direction, horizontal direction are respectively θ relative to the anglec of rotation of initial position, , calibration process is mainly divided into following steps:

The first step, coordinate conversion matrix T between initial position visual coordinate system and basis coordinates system of robot ₀calculating;

Choose four some P not coplanar in space ₁, P ₂, P ₃, P ₄, obtain the three-dimensional coordinate of 4 points under visual coordinate system by vision sensor, be designated as respectively:

P _V1(x _v1，y _v1，z _v1)，P _V2(x _v2，y _v2，z _v2)，P _V3(x _v3，y _v3，z _v3)，P _V4(x _v4，y _v4，z _v4)

By controlling the motion in each joint of arm, and forward kinematics solution obtains the three-dimensional coordinate of these 4 points under basis coordinates system of robot, is designated as respectively:

P _R1(x _r1，y _r1，z _r1)，P _R2(x _r2，y _r2，z _r2)，P _R3(x _r3，y _r3，z _r3)，P _R4(x _r4，y _r4，z _r4)

Calculate transition matrix T ₀

$T_0=\left[\begin{array}{cccc}{x}_{r1}& x_{r2}& x_{r3}& x_{r4}\\ y_{r1}& y_{r2}& y_{r3}& y_{r4}\\ z_{r1}& z_{r2}& z_{r3}& z_{r4}\\ 1& 1& 1& 1\end{array}\right]\·{\left[\begin{array}{cccc}{x}_{v1}& x_{v2}& x_{v3}& x_{v4}\\ y_{v1}& y_{v2}& y_{v3}& y_{v4}\\ z_{v1}& z_{v2}& z_{v3}& z_{v4}\\ 1& 1& 1& 1\end{array}\right]}^{-1}$

Second step, vision sensor from initial position vertically and horizontal direction respectively anglec of rotation θ with after, the transforming relationship matrix T between coordinate system _θwith calculating;

1) four not coplanar points of space are gathered at initial position coordinate is designated as respectively

$P_{V1}^1(x_{v1}^1,y_{v1}^1,z_{v1}^1),P_{V2}^1(x_{v2}^1,y_{v2}^1,z_{v2}^1),P_{V3}^1(x_{v3}^1,y_{v3}^1,z_{v3}^1),P_{V4}^1(x_{v4}^1,y_{v4}^1,z_{v4}^1)$

Vision module, vertically after any rotation, obtains 4, space at the coordinate of current coordinate system by sensor, is designated as respectively

$P_{V1}^2(x_{v1}^2,y_{v1}^2,z_{v1}^2),P_{V2}^2(x_{v2}^2,y_{v2}^2,z_{v2}^2),P_{V3}^2(x_{v3}^2,y_{v3}^2,z_{v3}^2),P_{V4}^2(x_{v4}^2,y_{v4}^2,z_{v4}^2)$

Utilize the principle shown in Fig. 3, calculate corresponding transformed matrix T _t

$T_t=\left[\begin{array}{cccc}{x}_{v1}^1& x_{v2}^1& x_{v3}^1& x_{v4}^1\\ y_{v1}^1& y_{v2}^1& y_{v3}^1& y_{v4}^1\\ z_{v1}^1& z_{v2}^1& z_{v3}^1& z_{v4}^1\\ 1& 1& 1& 1\end{array}\right]\·{\left[\begin{array}{cccc}{x}_{v1}^2& x_{v2}^2& x_{v3}^2& x_{v4}^2\\ y_{v1}^2& y_{v2}^2& y_{v3}^2& y_{v4}^2\\ z_{v1}^2& z_{v2}^2& z_{v3}^2& z_{v4}^2\\ 1& 1& 1& 1\end{array}\right]}^{-1}$

2) transition matrix T is utilized _tcalculate any two points P on turning axle _c1, P _c2, P _c2=(x _c2, y _c2, z _c2) ', P _c2=(x _c2, y _c2, z _c2) '

$\left[\begin{array}{cc}{x}_{c1}& x_{c2}\\ y_{c1}& y_{c2}\\ z_{c1}& z_{c2}\\ 1& 1\end{array}\right]{=T}_t\left[\begin{array}{cc}{x}_{c1}& x_{c2}\\ y_{c1}& y_{c2}\\ z_{c1}& z_{c2}\\ 1& 1\end{array}\right]$

3) by transition matrix T _θ, be divided into rotation and translation two parts to calculate respectively, wherein translational movement d represents, rotation amount R represents, then

$T_{\mathrm{\θ}}=\left[\begin{array}{cc}R& d\\ 0& 1\end{array}\right]$

Vision module initial coordinate system o _v1-x _v1y _v1z _v1be o with the coordinate after stationary shaft anglec of rotation θ _v2-x _v2y _v2z _v2, an O is the center of X-axis rotate to utilize geometry symmetric relation to know.Utilize o _v1o and rotational axis vertical, and O point is on the rotary shaft, these two conditions can set up following equation:

x ₀(x _c2-x _c1)+y ₀(y _c2-y _c1)+z ₀(z _c2-z _c1)＝0

$\frac{x_0-x_{c1}}{x_{c2}-x_{c1}}=\frac{y_0-y_{c1}}{y_{c2}-y_{c1}}=\frac{z_0-z_{c1}}{z_{c2}-z_{c1}}$

Can obtain by solving three equations above:

$\left[\begin{array}{c}{x}_0\\ y_0\\ z_0\end{array}\right]={\left[\begin{array}{ccc}{x}_{c2}-x_{c1}& y_{c2}-y_{c1}& z_{c2}-z_{c1}\\ y_{c2}-y_{c1}& x_{c1}-x_{c2}& 0\\ z_{c2}-z_{c1}& 0& x_{c1}-x_{c2}\end{array}\right]}^{-1}\left[\begin{array}{c}0\\ x_{c1}(y_{c2}-y_{c1})-y_{c1}(x_{c2}-x_{c1})\\ x_{c1}(z_{c2}-z_{c1})-z_{c1}(x_{c2}-x_{c1})\end{array}\right]$

Utilize geometric relationship with the rotary flat motion immovability of coordinate system, can obtain

$\frac{-x_0(d_1-x_0)-y_0(d_2-y_0)-z_0(d_3-z_0)}{\sqrt{x_0^2+y_0^2+z_0^2}+\sqrt{{(d_1-x_0)}^2+{(d_2-y_0)}^2+{(d_3-z_0)}^2}}=\cos \left(\mathrm{\θ}\right)$

d ₁(x _c2-x _c1)+d ₂(y _c2-y _c1)+d ₃(z _c2-z _c1)＝0

${(d_1-x_0)}^2+{(d_2-y_0)}^2+{(d_3-z_0)}^2=x_0^2+y_0^2+z_0^2$

Utilize Mapple software to solve above-mentioned ternary quadratic equation group, its analytic solution can be obtained.

4) the translation vector d calculated is utilized, and the character that on turning axle, the coordinate figure of any point does not change with rotation, following equation can be obtained:

$\left[\begin{array}{cc}{x}_{c1}& x_{c2}\\ y_{c1}& y_{c2}\\ z_{c1}& z_{c2}\\ 1& 1\end{array}\right]=\left[\begin{array}{cc}R& d\\ 0& 1\end{array}\right]\left[\begin{array}{cc}{x}_{c1}& x_{c2}\\ y_{c1}& y_{c2}\\ z_{c1}& z_{c2}\\ 1& 1\end{array}\right]$

By solving above-mentioned system of linear equations, corresponding rotation matrix R can be obtained, comprehensive 1) to 4) transition matrix T can be obtained _θ;

Vision sensor is from the initial position anglec of rotation in the horizontal direction after, the transforming relationship matrix between coordinate system above-mentioned identical step can be adopted to calculate;

3rd step, each transition matrix is multiplied and can obtains trick transformational relation matrix; Press three steps above and calculate transition matrix T ₀, T _θ, after, the arbitrfary point (x, y, z) in the field range that sensor obtains ', calculate its coordinate under robot coordinate system by following conversion formula.

Although invention has been described by reference to the accompanying drawings above; but the present invention is not limited to above-mentioned embodiment; above-mentioned embodiment is only schematic; instead of it is restrictive; those of ordinary skill in the art is under enlightenment of the present invention; when not departing from present inventive concept, can also make a lot of distortion, these all belong within protection of the present invention.

Claims (2)

1., based on a Robotic Hand-Eye Calibration method for two-freedom 3D vision sensor, it is characterized in that, comprise the following steps:

The first step, coordinate conversion matrix T between initial position visual coordinate system and basis coordinates system of robot ₀calculating; Four points are marked in advance in 3D vision sensor field range, the mutual relationship of these four points be any 3 not conllinear and 4 not coplanar, gather this some cloud information of 4 by the 3D vision sensor be fixed on robot model machine initial position, obtain the D coordinates value of four gauge points relative to 3D vision sensor coordinate system; The measurement of Three-Dimensional Dynamic measuring equipment is adopted to obtain, relative to the D coordinates value of four gauge points in space under basis coordinates system of robot, obtaining transition matrix, obtaining the transformational relation matrix T between the coordinate system of 3D vision sensor initial position and basis coordinates system of robot ₀;

Second step, vision sensor from initial position vertically and horizontal direction respectively anglec of rotation θ with after, the transforming relationship matrix T between coordinate system _θwith calculating; By controlling driven by motor 3D vision sensor vertically any rotation θ, and gather 4 cloud datas under current 3D vision sensor in space, calculate the three-dimensional coordinate of four points, utilize the two group three-dimensional coordinates of 4, space under 3D vision sensor to calculate the turning axle of 3D vision sensor coordinate systems, set up the anglec of rotation and 3D vision sensor and rotates transformational relation matrix T afterwards between coordinate system and initial coordinate system _θ; 3D vision sensor any rotation in the horizontal direction time, corresponding relational matrix computing method with calculate T _θmethod identical;

3rd step, is multiplied by each transition matrix and can obtains trick transformational relation matrix; When vision module does vertical and horizontal direction rotary motion relative to basis coordinates system of robot, its relation transition matrix corresponding to robot basis coordinates is

2. the Robotic Hand-Eye Calibration method based on having two-freedom 3D vision sensor according to claim 1, it is characterized in that, 3D vision sensor does horizontal or vertical direction and rotates timing signal, two points on turning axle, try to achieve by utilizing the characteristic that on turning axle, the D coordinates value of arbitrfary point under 3D sensor coordinate system does not change with rotation.