CN104608129A - Planar constraint based robot calibration method - Google Patents

Abstract

The invention relates to a planar constraint based robot calibration method. The planar constraint based robot calibration method specifically comprises the following steps of utilizing a DH and MDH combination method to establish a robot kinematic model, establishing a robot tail end position error model based on a differential conversion principle, establishing a position calibration model of a robot based on planar constraint, setting a calibration block pose position, demonstrating and recording the robot tail end theoretical pose position, calibrating motion parameters of a robot, utilizing a calibration result to perform comparison, and performing re-calibration if the accuracy requirement is not met. The planar constraint based robot calibration method has the advantages of being simple, practical, efficient and low in cost, expensive measurement instruments are not needed, calibration cost is reduced, and positioning accuracy is improved.

Description

Based on the robot calibration method of plane restriction

Technical field

The present invention relates to a kind of robot punctuate method based on plane restriction, relate to the calibration technique field of industrial robot.

Background technology

1. robot localization precision is the important performance indications of of serial manipulator, and being the basis of robot off-line programming, is the important guarantee that robot finishes the work.Complicated along with robot application environment, industrially has higher requirement to robot localization precision, expects that there is very high absolute fix precision in robot.But the impact such as error brought due to robotic part's process and assemble error, robot flexibility distortion inaccuracy, environmental factor, the scope of the absolute fix precision of robot is only ± 100mm to 0.1mm.And robot kinematics calibration improves the most effective approach of robot localization precision, it mainly comprises modeling, measurement, identification, compensation four-stage, real kinematics parameters is picked out, Correction and Control software parameter thus reach the object improving robot localization precision by rational method.

2. but traditional scaling method uses expensive measuring instrument when DATA REASONING, this process operation is complicated, need the human users of specialty, add the cost of demarcation, simultaneously complicated between this process need process surving coordinate system and basis coordinates system of robot transforming relationship, the external error of easy introduction, causes stated accuracy not high, and error increases.

3., for above-mentioned technical situation, the present invention proposes a kind of robot calibration method based on plane restriction.

Summary of the invention

For the deficiency that above-mentioned prior art exists, the invention provides a kind of robot calibration method based on plane restriction, this scaling method has simply, the feature of practical, efficient, low cost, do not need expensive measuring instrument, not only increase robot localization precision, and reduce the overall cost of demarcation.

The technical scheme of invention is:

1., based on a robot calibration method for plane restriction, comprise the following steps:

(1) kinematics model of robot is set up

Set up the kinematics model of robot in conjunction with DH method and MDH method, link rod coordinate system i is set to Ai relative to the homogeneous coordinate transformation of link rod coordinate system i-1, then robot end's coordinate system n is the pose of 0 relative to robot basis coordinates ⁰t _nfor:

⁰T _n＝A ₁A ₂...A _i...A _n

(2) robot end's site error model is set up

Transformed error Δ A between adjacent links coordinate system is drawn according to differential transform principle _ifor:

$\begin{array}{cc}\mathrm{\Δ}{A}_i=\frac{\∂A_i}{\∂\mathrm{\θ}}\mathrm{\Δ\θ}+\frac{\∂A_i}{\∂\mathrm{\α}}\mathrm{\Δ\α}+\frac{\∂A_i}{\∂d}\mathrm{\Δd}+\frac{\∂A_i}{\∂a}\mathrm{\Δa}& \mathrm{\Δ}{A}_i=\frac{\∂A_i}{\∂\mathrm{\θ}}\mathrm{\Δ\θ}+\frac{\∂A_i}{\∂\mathrm{\α}}+\mathrm{\Δ\α}+\frac{\∂A_i}{\∂d}\mathrm{\Δd}+\frac{\∂A_i}{\∂a}\mathrm{\Δa}+\frac{\∂A_i}{\∂\mathrm{\β}}\mathrm{\Δ\β}\end{array}$

Or

Actual homogeneous coordinate transformation A then between each connecting rod of robot, for:

A’＝A _i+ΔA _i

Calculating robot's ending coordinates system relative to the real transform matrix p+ Δ p of basis coordinates system of robot is:

p+Δp＝(A ₁+ΔA ₁)(A ₂+ΔA ₂)···(A _i+ΔA _i)···(A _n+ΔA _n)

Ignore above formula real transform matrix equality right-hand member high-order term and show that robot end's site error model Δ p is:

$\mathrm{\Δp}=\left[\begin{array}{c}{\mathrm{dP}}_x\\ {\mathrm{dP}}_y\\ {\mathrm{dP}}_z\end{array}\right]=\left[\begin{array}{ccccc}{J}_{\mathrm{d\θ}}& J_{\mathrm{dd}}& J_{\mathrm{da}}& J_{\mathrm{d\α}}& J_{\mathrm{d\β}}\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ\θ}\\ \mathrm{\Δd}\\ \mathrm{\Δa}\\ \mathrm{\Δ\α}\\ \mathrm{\Δ\β}\end{array}\right]=\mathrm{J\Δx}$

Wherein, [dP _xdP _ydP _z] be robot location's error matrix, for differential transform Jacobian matrix, Δ x=[Δ θ Δ d Δ a Δ α Δ β] ^tfor link parameters error matrix;

(3) robot location's error identification model is set up based on plane restriction

Based on the character of plane restriction, setting up robot location's error identification model is:

$\mathrm{T\Δx}=\left[\begin{array}{c}{J}_{x1}-J_{x2}\\ J_{y1}-J_{y2}\\ J_{z1}-J_{z2}\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ\θ}\\ \mathrm{\Δd}\\ \mathrm{\Δa}\\ \mathrm{\Δ\α}\\ \mathrm{\Δ\β}\end{array}\right]=\left[\begin{array}{c}{P_{x1}}^N-{P_{x2}}^N\\ {P_{y1}}^N-{P_{y2}}^N\\ {P_{z1}}^N-{P_{z2}}^N\end{array}\right]=D$ Wherein, $T=\left[\begin{array}{c}{J}_{x1}-J_{x2}\\ J_{y1}-J_{y2}\\ J_{z1}-J_{z2}\end{array}\right],D=\left[\begin{array}{c}{P_{x1}}^N-{P_{x2}}^N\\ {P_{y1}}^N-{P_{y2}}^N\\ {P_{z1}}^N-{P_{z2}}^N\end{array}\right],\mathrm{\Δx}=\left[\begin{array}{c}\mathrm{\Δ\θ}\\ \mathrm{\Δd}\\ \mathrm{\Δa}\\ \mathrm{\Δ\α}\\ \mathrm{\Δ\β}\end{array}\right]$

T is identification Jacobian matrix, and Δ x is robot kinematics's parameter error matrix, and D is the matrix of the difference of robot end's any two points theoretical coordinate value;

(4) calibrating block pose

Correct for calibrating block is placed in the working space of robot;

(5) the theoretical pose of teaching recorder robot end

Control makes robot end's difference teaching n point in calibrating block three orthogonal planes, and every teaching point, records theoretical pose corresponding in a controller software;

(6) robot kinematics's parameter error is demarcated

The data that step (5) obtains are updated in robot location's error identification model that step (3) sets up, and calculate real kinematics parameters by least square method robot inaccuracy is compensated;

(7) checking is demarcated, be updated in robot controller software by obtaining robot kinematics's parametric compensation value in step (6), again several points of teaching, relatively whether the theoretical terminal position of robot is constrained in a plane, if not, then continue step (4), (5), (6), until meet required precision;

2., in step described in (1), use DH method when adjacent links axis is not parallel, its homogeneous transforming relationship is:

A _i＝Rot(X,α _i-1)Trans(X,a _i-1)Rot(Z,θi)Trans(Z,d _i)

Use MDH method when adjacent links axis being parallel, its homogeneous transforming relationship is:

A _i＝Rot(X,α _i-1)Trans(X,a _i-1)Rot(Z,θ _i)Trans(Z,d _i)Rot(y,β)

Wherein θ represents joint of robot x _i-1and x _iaround the angle of z-axis; D represents x _i-1and x _ialong the distance of z-axis translation; α represents z _i-1and z _iaround the x-axis anglec of rotation; A represents z _i-1and z _ialong the distance of x-axis translation; β is the angle rotated around Y-axis;

3. the calibrating block used in step described in (4) requires the flatness with more than one-level or one-level;

4. in step described in (4), correct for calibrating block is placed in the working space of robot, guarantees that the normal vector of three mutual vertical planes in calibrating block is parallel with robot base parameter.

The invention has the beneficial effects as follows: a kind of robot calibration method based on plane restriction of the present invention, calibrating block is applied in Robot calibration technical field, by end effector of robot is constrained in plane, thus set up robot location's error identification model, utilize least square method to solve real motion mathematic(al) parameter to improve robot localization precision.The method has simply, the advantage of practical, efficient, low cost, do not need to use expensive measuring instrument, avoid conversion complicated between surving coordinate system and basis coordinates system of robot simultaneously, reduce source of error, ensure that the quality of demarcation, reduce the totle drilling cost of demarcation simultaneously.

Accompanying drawing explanation

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

Fig. 1 is the robot calibration method flow chart based on plane restriction of the present invention;

Tu2Shi robot retrains planar end theoretical position and physical location schematic diagram;

Fig. 3 is that calibrating block is at robot manipulation's space arrangement attitude schematic diagram.

Detailed description of the invention

The technology path of 1,2,3 pair of the present invention's proposition carries out detailed explanation and description by reference to the accompanying drawings, and the example herein applied has more than and is applicable to this example, is applicable to various serial manipulator.

With reference to Fig. 1, the robot calibration method based on plane restriction of the present invention comprises the following steps:

(1) robot kinematics's model is set up

The foundation of robot kinematics's model is the basis of analysis robot performance, mainly the parameterized form of the relation between each connecting rod is showed, modal is represent by DH method, namely four parameter θ are used, d, α, a represent the homogeneous transforming relationship between connecting rod, then between adjacent links coordinate system i-1 and link rod coordinate system i, homogeneous transform matrix is:

A _i＝Rot(X,α _i-1)Trans(X,a _i-1)Rot(Z,θ _i)Trans(Z,d _i)

Wherein θ represents joint of robot x _i-1and x _iaround the angle of z-axis; D represents x _i-1and x _ialong the distance of z-axis translation; α represents z _i-1and z _iaround the x-axis anglec of rotation; A represents z _i-1and z _ialong the distance of x-axis translation;

But during for adjacent links axis being parallel or less parallel, just there will be unusual appearance, so use the DH method of improvement in this case, i.e. MDH method, be exactly increase a parameter beta rotated around Y-axis on the basis of DH method, now between adjacent links coordinate system i-1 and link rod coordinate system i, homogeneous transform matrix is:

A _i＝Rot(X,α _i-1)Trans(X,a _i-1)Rot(Z,θ _i)Trans(Z,d _i)Rot(y,β)

Finally draw robot end's coordinate system position auto―control in basis coordinates system of robot according to the homogeneous transformational relation between connecting rod ⁰t _n:

⁰T _n＝A ₁A ₂...A _i...A _n

(2) robot end's site error model is set up according to differential transform principle

Transformed error Δ A between adjacent links is drawn according to differential transform principle _ifor:

$\begin{array}{cc}\mathrm{\Δ}{A}_i=\frac{\∂A_i}{\∂\mathrm{\θ}}\mathrm{\Δ\θ}+\frac{\∂A_i}{\∂\mathrm{\α}}\mathrm{\Δ\α}+\frac{\∂A_i}{\∂d}\mathrm{\Δd}+\frac{\∂A_i}{\∂a}\mathrm{\Δa}& \mathrm{\Δ}{A}_i=\frac{\∂A_i}{\∂\mathrm{\θ}}\mathrm{\Δ\θ}+\frac{\∂A_i}{\∂\mathrm{\α}}+\mathrm{\Δ\α}+\frac{\∂A_i}{\∂d}\mathrm{\Δd}+\frac{\∂A_i}{\∂a}\mathrm{\Δa}+\frac{\∂A_i}{\∂\mathrm{\β}}\mathrm{\Δ\β}\end{array}$

Or

Actual homogeneous coordinates matrix A then between each connecting rod of robot, for:

A，＝A _i+ΔA _i

Calculating robot's ending coordinates system relative to the real transform matrix of basis coordinates system of robot is:

p+Δp＝(A ₁+ΔA ₁)(A ₂+ΔA ₂)···(A _i+ΔA _i)···(A _n+ΔA _n)

Ignore above formula real transform matrix equality right-hand member high-order term and show that robot end's site error model is:

$\left[\begin{array}{c}{\mathrm{dP}}_x\\ {\mathrm{dP}}_y\\ {\mathrm{dP}}_z\end{array}\right]=\left[\begin{array}{ccccc}{J}_{\mathrm{d\θ}}& J_{\mathrm{dd}}& J_{\mathrm{da}}& J_{\mathrm{d\α}}& J_{\mathrm{d\β}}\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ\θ}\\ \mathrm{\Δd}\\ \mathrm{\Δa}\\ \mathrm{\Δ\α}\\ \mathrm{\Δ\β}\end{array}\right]=\mathrm{J\Δx}$

Wherein, [dP _xdP _ydP _z] be robot location's error, for differential transform Jacobian matrix, Δ x=[Δ θ Δ d Δ a Δ α Δ β [ ^tfor link parameters error matrix;

(3) robot location's error identification model is set up based on plane restriction

With reference to Fig. 2, time in the plane constraining in normal vector and robot basis coordinates axis being parallel according to end effector of robot, its end actual position coordinate value is equal in the projection of this normal, that is:

$P_j^R=P_j^R$

And any two points theoretical position and physical location in the difference of the projection of this normal are on robot end's track:

$\left[\begin{array}{c}{\mathrm{dx}}_i-{\mathrm{dx}}_j\\ {\mathrm{dy}}_i-{\mathrm{dy}}_j\\ {\mathrm{dz}}_i-{\mathrm{dz}}_j\end{array}\right]=\left[\begin{array}{c}{P_{x1}}^N-{P_{x2}}^N\\ {P_{y1}}^N-{P_{y2}}^N\\ {P_{z1}}^N-{P_{z2}}^N\end{array}\right]$

The final difference equaling these 2 these direction theoretical coordinate values according to the difference of the site error of any two points on track on plane normal direction, thus set up robot location's error identification model and be:

$\mathrm{T\Δx}=\left[\begin{array}{c}{J}_{x1}-J_{x2}\\ J_{y1}-J_{y2}\\ J_{z1}-J_{z2}\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ\θ}\\ \mathrm{\Δd}\\ \mathrm{\Δa}\\ \mathrm{\Δ\α}\\ \mathrm{\Δ\β}\end{array}\right]=\left[\begin{array}{c}{P_{x1}}^N-{P_{x2}}^N\\ {P_{y1}}^N-{P_{y2}}^N\\ {P_{z1}}^N-{P_{z2}}^N\end{array}\right]=D$ Wherein, $T=\left[\begin{array}{c}{J}_{x1}-J_{x2}\\ J_{y1}-J_{y2}\\ J_{z1}-J_{z2}\end{array}\right],D=\left[\begin{array}{c}{P_{x1}}^N-{P_{x2}}^N\\ {P_{y1}}^N-{P_{y2}}^N\\ {P_{z1}}^N-{P_{z2}}^N\end{array}\right],\mathrm{\Δx}=\left[\begin{array}{c}\mathrm{\Δ\θ}\\ \mathrm{\Δd}\\ \mathrm{\Δa}\\ \mathrm{\Δ\α}\\ \mathrm{\Δ\β}\end{array}\right]$

T is identification Jacobian matrix, and Δ x is robot kinematics's parameter error matrix, and D is the matrix of the difference of 2 theoretical coordinate values on robot end's track.The matrix D of the difference of identification Jacobian matrix T and two position can calculate according to the mathematical point pose of robot records, Δ x=[Δ θ Δ d Δ a Δ α Δ β [ ^tit is the matrix of unknown parameters needing to solve;

(4) calibrating block pose

With reference to Fig. 3, putting of calibrating block pose is a vital step in whole calibration process, first to guarantee that each plane of calibrating block has the flatness of more than one-level or one-level, to guarantee that robot end constrains in same plane, reduce the error brought by flatness, correct for calibrating block is placed in the working space of robot, guarantees that the normal vector of orthogonal three planes in calibrating block is parallel with basis coordinates system of robot axle;

(5) the theoretical pose of teaching recorder robot end

Control carries out teaching to the calibrating block be placed in robot working space, mainly in calibrating block, distinguishes teaching n point in orthogonal three planes, every teaching point, records theoretical pose corresponding in a controller software;

(6) robot kinematics's parameter error is demarcated

The theoretical pose of the robot that step (5) teaching is obtained, and the joint rotation angle value of correspondence is updated in robot location's error identification model that step (3) sets up, calculate real kinematics parameters by least square method, substituted into robot controller to improve robot precision;

(7) be updated in robot controller software by obtaining robot kinematics's parametric compensation value in step (6), again several points of teaching, relatively whether the theoretical distal point position of robot is constrained in a plane, if not, then continue step (4), (5), (6), until meet required precision;

The present invention has following beneficial effect:

First be used robot kinematics's model be the modeling method that DH method combines with MDH method, avoid when being used alone DH modeling, the unusual appearance occurred during the parallel or less parallel of adjacent links, combines the advantage of two kinds of modeling methods.

Secondly, based on the measurement not relating to robot end's actual position coordinate in robot end's site error peg model that plane restriction is set up, the complexity avoided between surving coordinate system and basis coordinates system of robot is changed, reduce the possibility introducing external error, save the time that operation consumes simultaneously.

Finally the robot calibration method based on plane restriction in this paper have simply, the advantage of practical, efficient, low cost, do not need to use expensive measuring instrument, avoid conversion complicated between surving coordinate system and basis coordinates system of robot simultaneously, reduce source of error, ensure that the quality of demarcation, reduce the totle drilling cost of demarcation simultaneously.

Claims (4)

1., based on a Robot calibration method method for plane restriction, it is characterized in that: comprise the following steps:

(1) kinematics model of robot is set up

Set up the kinematics model of robot in conjunction with DH method and MDH method, link rod coordinate system i is set to A relative to the homogeneous coordinate transformation of link rod coordinate system i-1 _i, then robot end's coordinate system n is the pose of 0 relative to robot basis coordinates ⁰t _nfor:

⁰T _n＝A ₁A ₂...A _i...A _n

(2) robot end's site error model is set up

Transformed error Δ A between adjacent links coordinate system is drawn according to differential transform principle _ifor:

Or

Actual homogeneous coordinate transformation A then between each connecting rod of robot, for:

A,＝A _i+ΔA _i

Calculating robot's ending coordinates system relative to the real transform matrix p+ Δ p of basis coordinates system of robot is:

The high-order term ignored on the right side of above formula real transform matrix equality show that robot end's site error model Δ p is:

Wherein, [dP _xdP _ydP _z] be robot location's error matrix, J=[J _{d θ}j _ddj _daj _{d α}j _{d β}] be differential transform Jacobian matrix, Δ x=[Δ θ Δ d Δ a Δ α Δ β] ^tfor link parameters error matrix;

(3) robot location's error identification model is set up based on plane restriction

Based on the character of plane restriction, setting up robot location's error identification model is:

wherein,

T is identification Jacobian matrix, and Δ x is robot kinematics's parameter error matrix, and D is the matrix of the difference of 2 theoretical coordinate values on robot end's track;

(4) calibrating block pose

Correct for calibrating block is placed in the working space of robot;

(5) the theoretical pose of teaching recorder robot end

Control makes robot end's difference teaching n point in calibrating block three orthogonal planes, and every teaching point, records theoretical pose corresponding in a controller software;

(6) robot kinematics's parameter error is demarcated

The data that step (5) obtains are updated in robot location's error identification model that step (3) sets up, and calculate real kinematics parameters by least square method robot inaccuracy is compensated;

(7) checking is demarcated, be updated in robot controller software by obtaining robot kinematics's parametric compensation value in step (6), again several points of teaching, relatively whether the theoretical terminal position of robot is constrained in a plane, if not, then continue step (4), (5), (6), until meet required precision.

2. a kind of robot calibration method based on plane restriction according to claim 1, is characterized in that: in described step (1), and use DH method when adjacent links axis is not parallel, its homogeneous coordinate transformation is: A _i=Rot (X, α _i-1) Trans (X, a _i-1) Rot (Z, θ _i) Trans (Z, d _i)

Use MDH method when adjacent links axis being parallel, its homogeneous coordinate transformation is: A _i=Rot (X, α _i-1) Trans (X, a _i-1) Rot (Z, θ _i) Trans (Z, d _i) Rot (y, β)

Wherein: θ represents joint of robot x _i-1and x _iaround the angle of z-axis; D represents x _i-1and x _ialong the distance of z-axis translation; α represents z _i-1and z _iaround the x-axis anglec of rotation; A represents z _i-1and z _ialong the distance of x-axis translation; β is the angle rotated around Y-axis.

3. a kind of robot calibration method based on plane restriction according to claim 1, is characterized in that: the calibrating block used requires the flatness with more than one-level or one-level.

4. a kind of robot calibration method based on plane restriction according to claim 1, it is characterized in that: in described step (4), calibrating block is placed in the working space of robot, guarantees that the normal vector of calibrating block three mutual vertical planes is parallel with robot base parameter.