CN103115615B - Fully-automatic calibration method for hand-eye robot based on exponential product model - Google Patents

Abstract

The invention discloses a fully-automatic calibration method for a hand-eye robot based on an exponential product model and particularly relates to a fully-automatic calibration method for achieving synchronization of three parts including a robot body, hands and eyes as well as a camera. The method can be achieved by utilizing a mirror and a plurality of beacon scaffolds instead of additional auxiliary measuring instruments. The fully-automatic calibration method is mainly characterized in that firstly, hand information outside the view field of a terminal camera is converted to a coordinate system of the camera by utilizing mirror reflection principle to finish hand and eye calibration; and secondly, the terminal camera carried by the robot is used as a measuring instrument and a checkerboard on a spacial mirror surface is used as a measuring target, so that the times for shooting the target by using the camera in a rotating process of each joint of the robot are increased, and meanwhile, the camera calibration and the joint parameter calibration are achieved under a special motion strategy. The fully-automatic calibration method for the robot is simple and effective.

Description

A kind of hand-eye machine people full automatic calibration method based on exponent product model

Technical field

The present invention relates to hand-eye machine people and demarcate field, more particularly relate to a kind of hand-eye machine people full automatic calibration method based on exponent product model, to improve the absolute fix precision of hand-eye machine people.

Background technology

Hand-eye machine people refers to and installs camera robot end, plays the effect of eyes, because it is flexible, enjoys people to pay close attention to.The height of its integral calibrating precision determines that this robot can be applied to actual a kind of important indicator, the integral calibrating of hand-eye machine people comprises camera calibration, hand and eye calibrating, robot body demarcation, and wherein camera calibration refers to and demarcates the hard-wired camera intrinsic parameter of robot end.Hand and eye calibrating demarcates the relation between robot end's instrument and camera mounted thereto.It is demarcate each joint parameter of robot that robot body is demarcated, and different kinematics models has different parameter definition.It is all the very important problem in robot vision field that every part is demarcated, all more complicated, therefore a lot of inconvenience is brought to the application of trick robot, people simplify calibration process under the prerequisite ensureing precision as far as possible for this reason, there are camera calibration and hand and eye calibrating to carry out simultaneously, have hand and eye calibrating and robot body to demarcate to carry out simultaneously, also have camera calibration and robot body to demarcate to carry out simultaneously, but also there is no a kind of scaling method three simultaneously carried out, and calibration process complexity needs could realize alternately, therefore a kind of simple in the urgent need to developing, effective automated process realizes the integral calibrating of hand-eye machine people.

Summary of the invention

Task of the present invention is to solve the deficiency that in prior art, hand-eye machine people scaling method exists, and provides a kind of hand-eye machine people full automatic calibration method based on exponent product model.

Its technical solution is:

Based on a hand-eye machine people full automatic calibration method for exponent product model, comprise the following steps:

A provides industrial robot, end binocular camera, one piece of level crossing and some surveyor's beacons; End binocular camera takes detachable connected mode to be installed on robot end, on the minute surface that surveyor's beacon is pasted on level crossing and robot end's tool control point place; Then step b is entered,

B determines the initial position of robot, and select suitable position to be positioned over by the level crossing being pasted with surveyor's beacon in end binocular camera field range, utilize end binocular camera to obtain the mirror image one of level crossing simultaneously, comprise minute surface surveyor's beacon information and the surveyor's beacon information reflexing to the robot end's tool control point place inside mirror in this mirror image, be used for demarcating trick relation; Then step c is entered,

C control rotates one by one from end joint, utilizes end binocular camera certain angular interval in the rotary course of each joint to take minute surface surveyor's beacon image once, until it exceeds end binocular camera field range; Suppose to obtain m in each joint motions process of robot _iwidth image, i=1 ..., n, n are joint of robot number, utilize width image calibration camera and joint of robot parameter.

In above-mentioned steps a, the exponent product motion model of setting robot is:

$g_{\mathrm{wt}}\left(\mathrm{\θ}\right)=e^{{\mathrm{\θ}}_1{\widehat{\mathrm{\ξ}}}_1}{e}^{{\mathrm{\θ}}_2{\widehat{\mathrm{\ξ}}}_2}...e^{{\mathrm{\θ}}_n{\widehat{\mathrm{\ξ}}}_n}$

Wherein g _wt(θ) be that robot is in θ=(θ ₁, θ ₂, θ ₃..., θ _n) time end-of-arm tooling coordinate system T-phase to the transformation relation of world coordinate system W, it is motion spinor exponential matrix;

In above-mentioned steps b, setting trick variation relation is A _ch, wherein A _ocand A _ch'for given data;

In above-mentioned steps c, suppose that the point that end binocular camera is measured in i-th joint rotary course is designated as x _ij∈ R ^{4 × num}for space three-dimensional homogeneous coordinates, m _ibe the number of times of camera measurement data in the i-th joint rotary course, num is the number of measured point, space, and joint parameter solution formula is:

$x_{i,a}=e^{{\mathrm{\θ}}_{\mathrm{ij}}{\widehat{\mathrm{\ξ}}}_{\mathrm{ij}}}{x}_{i,b},i=1,...,n,j=\mathrm{1,2,3},...,m_i,a,b\∈\{1,...,m_i\},$

Wherein x _i,aand x _i,bx _iin the homogeneous coordinates value of any two groups of data, can directly obtain spinor parameter ξ according to above formula _ij, then pass through X _iin m _igroup measurement data, every two groups are obtained one group of solution, are obtained by combination of two group is separated, will group solution is averaged as final joint parameter, that is:

${\mathrm{\ξ}}_i=\frac{1}{C_{m_i}^2}\underset{j=1}{\overset{C_{m_i}^2}{\mathrm{\Σ}}}{\mathrm{\ξ}}_{\mathrm{ij}}$

Wherein ξ _ifor motion spinor coordinate.

The present invention has following Advantageous Effects:

1, realize simply.Do not need extra measuring equipment, only utilize self-contained end camera to obtain in robot each joint rotary course trick, camera, body can all be demarcated by width image.

2, error is introduced little.Error source only has measuring accuracy index of end camera.

3, precision is high.Error source is few, and utilizes the image calibration joint of robot parameter of calibration for cameras, and its degree of accuracy is higher.

Accompanying drawing explanation

Below in conjunction with accompanying drawing and embodiment, the present invention is further described:

Fig. 1 is the robot kinematics's illustraton of model in the present invention.

Fig. 2 is the trick relation calibration principle figure in the present invention.

Fig. 3 is the calibration principle figure in the present invention.

Embodiment

Shown in Fig. 1 is robot kinematics's illustraton of model.During initial position, world coordinate system W and tool coordinates system T is based upon on robot end's camera, world coordinates ties up to initial position and maintains static, and tool coordinates is moved along with the motion of robot, assuming that there be n rotary joint of connecting in robot, then the exponent product motion model of robot is:

$g_{\mathrm{wt}}\left(\mathrm{\θ}\right)=e^{{\mathrm{\θ}}_1{\widehat{\mathrm{\ξ}}}_1}{e}^{{\mathrm{\θ}}_2{\widehat{\mathrm{\ξ}}}_2}...e^{{\mathrm{\θ}}_n{\widehat{\mathrm{\ξ}}}_n}---\left(1\right)$

Wherein g _wt(θ) be that robot is in θ=(θ ₁, θ ₂, θ ₃..., θ _n) time end-of-arm tooling coordinate system T-phase to the transformation relation of world coordinate system W. it is motion spinor exponential matrix, be specifically expressed as follows:

$e^{\mathrm{\θ}\widehat{\mathrm{\ξ}}}=\left[\begin{array}{cc}{e}^{\mathrm{\θ}\widehat{\mathrm{\ω}}}& (I-e^{\mathrm{\θ}\widehat{\mathrm{\ω}}})r\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}{R}_{3\×3}& t_{3\×1}\\ 0& 1\end{array}\right],\mathrm{\ω}\≠0---\left(2\right)$

$\widehat{\mathrm{\ω}}=\left[\begin{array}{ccc}0& -{\mathrm{\ω}}_3& {\mathrm{\ω}}_2\\ {\mathrm{\ω}}_3& 0& -{\mathrm{\ω}}_1\\ -{\mathrm{\ω}}_2& {\mathrm{\ω}}_1& 0\end{array}\right]$

for the antisymmetric matrix of ω.ξ _ifor motion spinor coordinate, can be expressed as:

${\mathrm{\ξ}}_i=\left[\begin{array}{c}{\mathrm{\ω}}_i\\ {\mathrm{\ω}}_i\×r_i\end{array}\right]\∈R^6---\left(3\right)$

Wherein ω _iand r _i∈ R ³, i=1 ..., n is the position vector of turning axle unit direction, joint under world coordinate system and turning axle, is collectively referred to as spinor parameter, also referred to as joint parameter.And the coordinate of spatial point under world coordinate system can obtain according to following formula:

X _w＝g _wt(θ)X _t (4)

Wherein X _t, X _w∈ R ^{4 × 1}be respectively the homogeneous coordinates of spatial point under tool coordinates system and world coordinate system.

Shown in Fig. 2 is hand and eye calibrating schematic diagram.First select a suitable attitude as robot initial position, and obtain the mirror image of the level crossing in field range, contain minute surface surveyor's beacon information in this mirror image and reflex to the surveyor's beacon information that the end hand inside mirror grabs.Namely utilize this two parts information acquisition trick relation, concrete grammar is as follows:

Consider robot end at camera not within sweep of the eye, mirror can be utilized to reflect it to it within sweep of the eye, as shown in Figure 2, C, H, O are respectively camera coordinates system, hand coordinate system and minute surface coordinate system, C', H' are corresponding virtual image coordinate system, X be space a bit, its virtual image is X'.Before introducing hand and eye calibrating process, first provide two propositions:

Proposition 1: by specularly reflected jiong coordinate system, if the left-handed system of being originally, be right-handed system after reflection, vice versa;

Proposition 2: due to point and the duality of camera, at the camera observation station X' at a C place, be equivalent to the camera observation station X at a C' place.

The homogeneous coordinates of postulated point X' and X under camera C and O coordinate system are expressed as X ' _c, X' _o, X _cand X _o, coordinate system O and C, C and C', C and H', coordinate transform between C' and H', C and H are respectively A _oc, A _cc', A _ch', A _c'h', A _ch, wherein A _ocand A _ch'for given data, A _chfor needing the trick transformation relation solved.Then X ' _cwith X' _o, X _cwith X _obetween there is following relation:

X' _o＝A _ocX′ _c (5)

X _o＝A _ocX _c (6)

According to proposition 1:

$X_o=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& -1& 0\\ 0& 0& 0& 1\end{array}\right]X_o^{\′}={\mathrm{BX}}_o^{\′},B=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& -1& 0\\ 0& 0& 0& 1\end{array}\right]---\left(7\right)$

Bring formula (5) and (6) into (7) to arrange:

$X_c=A_{\mathrm{oc}}^{-1}{\mathrm{BA}}_{\mathrm{oc}}{X}_c^{\′}---\left(8\right)$

If note X _c'for the homogeneous coordinates of X under coordinate system C', according to the known X ' of proposition 2 _c=X _c', then formula (8) can be changed into:

$X_c=A_{\mathrm{oc}}^{-1}{\mathrm{BA}}_{\mathrm{oc}}{X}_{c\′}---\left(9\right)$

Transformation relation A then between known camera coordinates system C and C ' _cc'for:

$A_{\mathrm{cc}\′}=A_{\mathrm{oc}}^{-1}{\mathrm{BA}}_{\mathrm{oc}}---\left(10\right)$

Again according to the transformation relation in Fig. 2 between coordinate:

$A_{c\′h\′}=A_{\mathrm{cc}\′}^{-1}{A}_{\mathrm{ch}\′}---\left(11\right)$

In addition, according to proposition 2:

A _ch＝A _c'h' (12)

Formula (10) and (11) are brought in formula (12), can obtain:

$A_{\mathrm{ch}}=A_{\mathrm{oc}}^{-1}{\mathrm{BA}}_{\mathrm{oc}}{A}_{\mathrm{ch}\′}---\left(13\right)$

Then trick relativeness A _chuniquely can be determined by formula (13).

As Fig. 3, the present invention does not need extra surveying instrument, only need utilize mirror and some surveyor's beacons.Its principal feature is: one is, under extraneous for end camera fields of view hand information is transformed into camera coordinates system by the principle of reflection that make use of mirror, complete hand and eye calibrating; Two is as surveying instrument using end camera self-contained for robot, with the gridiron pattern (surveyor's beacon) on the minute surface of space for measurement target, using the point of fixity within the scope of spatial field of view as impact point, then in robot single joint rotary course, impact point is taken, first utilize these image calibration camera intrinsic parameters, to reentry the 3 d space coordinate value of impact point, wherein end binocular camera intrinsic parameter is that the planar approach utilizing Zhang Zhengyou to propose carries out demarcating, and the scaling method of joint of robot parameter is as follows:

Suppose that the point that end camera is measured in i-th joint rotary course is designated as x _ij∈ R ^{4 × num}for space three-dimensional homogeneous coordinates, m _ibe the number of times of camera measurement data in the i-th joint rotary course, num is the number of measured point, space, then joint parameter solution formula is:

$x_{i,a}=e^{{\mathrm{\θ}}_{\mathrm{ij}}{\widehat{\mathrm{\ξ}}}_{\mathrm{ij}}}{x}_{i,b},i=1,...,n,j=\mathrm{1,2,3},...,m_i,a,b\∈\{1,...,m_i\}---\left(14\right)$

X _i,aand x _i,bx _iin the homogeneous coordinates value of any two groups of data, can directly obtain spinor parameter ξ according to above formula _ij.Due to X _iin have m _igroup measurement data, every two groups can be obtained one group of solution, can be obtained by combination of two group is separated, by this group solution is averaged as final joint parameter, that is:

${\mathrm{\ξ}}_i=\frac{1}{C_{m_i}^2}\underset{j=1}{\overset{C_{m_i}^2}{\mathrm{\Σ}}}{\mathrm{\ξ}}_{\mathrm{ij}}---\left(15\right)$

The relevant technologies content do not addressed in aforesaid way is taked or uses for reference prior art to realize.

It should be noted that, under the instruction of this instructions, those skilled in the art can also make such or such easy variation pattern, such as equivalent way, or obvious mode of texturing.Above-mentioned variation pattern all should within protection scope of the present invention.

Claims (2)

1., based on a hand-eye machine people full automatic calibration method for exponent product model, it is characterized in that comprising the following steps:

A provides industrial robot, end binocular camera, one piece of level crossing and some surveyor's beacons; End binocular camera takes detachable connected mode to be installed on robot end, on the minute surface that surveyor's beacon is pasted on level crossing and robot end's tool control point place; Then step b is entered,

B determines the initial position of robot, and select suitable position to be positioned over by the level crossing being pasted with surveyor's beacon in end binocular camera field range, utilize end binocular camera to obtain the mirror image one of level crossing simultaneously, comprise minute surface surveyor's beacon information and the surveyor's beacon information reflexing to the robot end's tool control point place inside mirror in this mirror image, be used for demarcating trick relation; Then step c is entered,

C control rotates one by one from end joint, utilizes end binocular camera certain angular interval in the rotary course of each joint to take minute surface surveyor's beacon image once, until it exceeds end binocular camera field range; Suppose to obtain m in each joint motions process of robot _iwidth image, i=1 ..., n, n are joint of robot number, utilize width image calibration end binocular camera and joint of robot parameter.

2. a kind of hand-eye machine people full automatic calibration method based on exponent product model according to claim 1, is characterized in that:

In above-mentioned steps a, the exponent product motion model of setting robot is:

$g_{\mathrm{wt}}\left(\mathrm{\θ}\right)=e^{{\mathrm{\θ}}_1{\widehat{\mathrm{\ξ}}}_1}{e}^{{\mathrm{\θ}}_2{\widehat{\mathrm{\ξ}}}_2}...e^{{\mathrm{\θ}}_n{\widehat{\mathrm{\ξ}}}_n}$

Wherein g _wt(θ) be that robot is in θ=(θ ₁, θ ₂, θ ₃..., θ _n) time end-of-arm tooling coordinate system T-phase to the transformation relation of world coordinate system W, it is motion spinor exponential matrix;

In above-mentioned steps b, setting trick variation relation is A _ch, wherein A _ocand A _ch'for given data; A _ocrepresent the coordinate conversion relation between minute surface and end binocular camera, a _ocinverse matrix; A _ch'for the coordinate conversion relation between end binocular camera and robot end's virtual image, A _ocand A _ch'directly can obtain by measuring, $B=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& -1& 0\\ 0& 0& 0& 1\end{array}\right];$

In above-mentioned steps c, suppose that the point that end binocular camera is measured in i-th joint rotary course is designated as i=1 ..., n, x _ij∈ R ^{4 × num}for space three-dimensional homogeneous coordinates, m _ibe the number of times of end binocular camera measurement data in the i-th joint rotary course, num is the number of measured point, space, and joint parameter solution formula is:

$x_{i,a}=e^{{\mathrm{\θ}}_{\mathrm{ij}}{\widehat{\mathrm{\ξ}}}_{\mathrm{ij}}}{x}_{i,b},i=1,...,n,$ j＝1,2,3,...,m _i，a,b∈{1,...,m _i}，

Wherein x _i,aand x _i,bx _iin the homogeneous coordinates value of any two groups of data, can directly obtain spinor parameter ξ according to above formula _ij, then pass through X _iin m _igroup measurement data, every two groups are obtained one group of solution, are obtained by combination of two group is separated, will group solution is averaged as final joint parameter, that is:

${\mathrm{\ξ}}_i=\frac{1}{C_{m_i}^2}\underset{j=1}{\overset{C_{m_i}^2}{\mathrm{\Σ}}}{\mathrm{\ξ}}_{\mathrm{ij}}$

Wherein ξ _ifor motion spinor coordinate.