CN103115615A - 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 the hand-eye machine people and demarcate the field, more particularly relate to a kind of hand-eye machine people full automatic calibration method based on exponent product model, to improve hand-eye machine people's absolute fix precision.

Background technology

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

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 a kind of hand-eye machine people full automatic calibration method based on exponent product model is provided.

Its technical solution is:

A kind of hand-eye machine people full automatic calibration method based on exponent product model comprises the following steps:

A provides industrial robot, end binocular camera, a level crossing and some surveyor's beacons; The end binocular camera takes the detachable connected mode to be installed on the robot end, and surveyor's beacon is pasted on the minute surface of level crossing and place, robot end's instrument reference mark; Then enter step b,

B determines the initial position of robot, and the level crossing of selecting suitable position will be pasted with surveyor's beacon is positioned in end binocular camera field range, utilize simultaneously the end binocular camera to obtain one of the mirror image of level crossing, comprise minute surface surveyor's beacon information in this mirror image and reflex to the surveyor's beacon information that the end hand of mirror the inside is grabbed, be used for demarcating the trick relation; Then enter step c,

The c control begins to rotate one by one from the end joint, utilizes end binocular camera interval certain angle in each joint rotary course to take minute surface surveyor's beacon image once, until it exceeds the viewing field of camera scope; Suppose to obtain m in each joint motions process of robot _iThe width image, i=1 ..., n, n are the 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:

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

G wherein _WT(θ) that robot is in θ=(θ ₁, θ ₂, θ ₃..., θ _n) time end-of-arm tooling coordinate system T relative world coordinate system W transformation relation,

It is the motion spinor

Exponential matrix;

In above-mentioned steps b, setting the trick variation relation is A _ch,

A wherein _ocAnd A _{Ch '}Be given data;

In above-mentioned steps c, suppose that the point that the end binocular camera is measured is designated as X in i joint rotary course _i=(x _i1, x _i2..., x _im), i=1 ..., n, x _ij∈ R ^{4 * num}Be space three-dimensional homogeneous coordinates, m _iBe the number of times of camera measurement data in the rotary course of i joint, num is the number of measured point, space, and the joint parameter solution formula is:

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

X wherein _i,aAnd x _i,bX _iIn the homogeneous coordinates value of any two groups of data, can directly obtain spinor parameter ξ according to following formula _ij, then pass through X _iIn m _iThe group measurement data, every two groups obtain one group of solution, obtain by combination in twos

Group is separated, will

The group solution is averaged as final joint parameter, that is:

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

ξ wherein _iBe motion spinor coordinate.

The present invention has following useful technique effect:

1, realize simply.Do not need extra measuring equipment, only utilize self-contained end camera in each joint rotation of robot

Obtain in process

The width image can all be demarcated trick, camera, body.

2, the introducing error is little.Error source only has index of measuring accuracy 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.Description of drawings

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 that the trick in the present invention concerns calibration principle figure.

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 are that 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 machine human motion, supposes that there is the rotary joint of n series connection in robot, and the exponent product motion model of robot is:

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

G wherein _WT(θ) that robot is in θ=(θ ₁, θ ₂, θ ₃..., θ _n) time end-of-arm tooling coordinate system T relative world coordinate system W transformation relation.

It is the motion spinor

Exponential matrix, specifically be expressed as follows:

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

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

Antisymmetric matrix for ω.ξ _iBe motion spinor coordinate, can be expressed as:

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

ω wherein _iAnd r _i∈ R ³, i=1 ..., n is joint turning axle unit's direction under world coordinate system and the position vector of turning axle, is collectively referred to as the 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) X wherein _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 the hand and eye calibrating schematic diagram.At first select a suitable attitude as robot initial position, and obtain the mirror image of the level crossing in field range, comprised minute surface surveyor's beacon information in this mirror image and reflexed to the surveyor's beacon information that the end hand of mirror the inside is grabbed.Namely utilize this two parts information acquisition trick relation, concrete grammar is as follows:

Consider the robot end at camera not within sweep of the eye, can utilize mirror 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 the space a bit, its virtual image is X '.Before introducing the hand and eye calibrating process, two propositions of given first:

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

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

Postulated point X ' and the odd coordinate of X under camera C and O coordinate system are expressed as respectively

X _cAnd X _o, the coordinate transform between coordinate system O and C, C and C ', C and H ', C ' and H ', C and H is respectively A _oc, A _{Cc '}, A _{Ch '}, A _{C ' h '}, A _ch, A wherein _ocAnd A _{Ch '}Be given data, A _chThe trick transformation relation of finding the solution for needs.

With , X _cWith X _oBetween have a following relation:

$X_o^{\′}=A_{\mathrm{oc}}{X}_c^{\′}---\left(5\right)$

X _o=A _ocX _c（6）

According to proposition 1 as can be known:

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

Bringing formula (5) and (6) into (7) arranges:

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

If note X _c′Odd coordinate for X under coordinate system C ', according to proposition 2 as can be known

, formula (8) can be changed into:

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

Camera coordinates is transformation relation A between C and C ' as can be known _{Cc '}For:

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

Again according to the transformation relation between coordinate in Fig. 2 as can be known:

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

In addition, according to proposition 2 as can be known:

A _ch=A _{C ' h '}(12) formula (10) and (11) are brought in formula (12), can be got:

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

Trick relativeness A _chCan determine by formula (13) is unique.

As Fig. 3, the present invention does not need extra surveying instrument, only need utilize mirror and some surveyor's beacons to get final product.Its principal feature is: the one, and the principle of reflection of the having utilized mirror hand information that end camera field range is outer is transformed under camera coordinates system,

Complete hand and eye calibrating; The 2nd, the end camera that robot is self-contained is as surveying instrument, gridiron pattern (surveyor's beacon) on the minute surface of space is as measurement target, with the point of fixity in the field range of space as impact point, then in robot simple joint rotary course, impact point is taken, first utilize these image calibration camera intrinsic parameters, the reentry 3 d space coordinate value of impact point, wherein end binocular camera intrinsic parameter is that the planar approach of utilizing Zhang Zhengyou to propose is demarcated, and the scaling method of joint of robot parameter is as follows:

Suppose that the point that the end camera is measured is designated as X in i joint rotary course _i=(x _i1, x _i2..., x _im), i=1 ..., n, x _ij∈ R ^{4 * num}Be space three-dimensional homogeneous coordinates, m _iBe the number of times of camera measurement data in the rotary course of i joint, num is the number of measured point, space, and the joint parameter solution formula is:

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

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 following formula _ijDue to X _iIn m is arranged _iThe group measurement data, every two groups can obtain one group of solution, can obtain by combination in twos

Group is separated, with this

The group solution is averaged as final joint parameter, that is:

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

The relevant technologies content of not addressing in aforesaid way is taked or is used for reference prior art and can realize.

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

Claims (2)

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

A provides industrial robot, end binocular camera, a level crossing and some surveyor's beacons; The end binocular camera takes the detachable connected mode to be installed on the robot end, and surveyor's beacon is pasted on the minute surface of level crossing and place, robot end's instrument reference mark; Then enter step b,

B determines the initial position of robot, and the level crossing of selecting suitable position will be pasted with surveyor's beacon is positioned in end binocular camera field range, utilize simultaneously the end binocular camera to obtain one of the mirror image of level crossing, comprise minute surface surveyor's beacon information in this mirror image and reflex to the surveyor's beacon information that the end hand of mirror the inside is grabbed, be used for demarcating the trick relation; Then enter step c,

The c control begins to rotate one by one from the end joint, utilizes end binocular camera interval certain angle in each joint rotary course to take minute surface surveyor's beacon image once, until it exceeds the viewing field of camera scope; Suppose to obtain m in each joint motions process of robot _iThe width image, i=1 ..., n, n are the joint of robot number, utilize

Width image calibration 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:

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

G wherein _WT(θ) that robot is in θ=(θ ₁, θ ₂, θ ₃..., θ _n) time end-of-arm tooling coordinate system T relative world coordinate system W transformation relation, It is the motion spinor

Exponential matrix;

In above-mentioned steps b, setting the trick variation relation is A _ch, A wherein _ocAnd A _{Ch '}Be given data;

In above-mentioned steps c, suppose that the point that the end binocular camera is measured is designated as X in i joint rotary course _i=(x _i1, x _i2..., x _im), i=1 ..., n, x _ij∈ R ^{4 * num}Be space three-dimensional homogeneous coordinates, m _iBe the number of times of camera measurement data in the rotary course of i joint, num is the number of measured point, space, and the joint parameter solution formula is:

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

X wherein _i,aAnd x _i,bX _iIn the homogeneous coordinates value of any two groups of data, can directly obtain spinor parameter ξ according to following formula _ij, then pass through X _iIn m _iThe group measurement data, every two groups obtain one group of solution, obtain by combination in twos

Group is separated, will

The group solution is averaged as final joint parameter, that is:

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

ξ wherein _iBe motion spinor coordinate.

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