CN103231375A - Industrial robot calibration method based on distance error models - Google Patents

Abstract

The invention discloses an industrial robot calibration method based on distance error models. The method comprises: establishing a robot MDH (modified Denavit-Hartenberg) kinematic model; subjecting the errors of a matrix to homogeneous transformation; establishing a robot distance error calibration model; measuring the end actual pose of a robot; calibrating geometrical parameter errors of every connecting rod of the robot; and performing experimental verification. The industrial robot calibration method based on the distance error models has the advantages of being simple, practical, high-efficiency and rapid, is applicable to any series articulated robots, has a strong commonality, and can improve the positioning accuracy and the distance accuracy of an industrial robot simultaneously.

Description

Industrial robot scaling method based on the range error model

Technical field

The present invention relates to robot calibration technique field, particularly relate to a kind of industrial robot scaling method based on the range error model.

Background technology

Modern manufacturing industry is constantly improving the industrial robot performance demands, and two main evaluation indexes of the performance of robot are: repetitive positioning accuracy and absolute fix precision.The robot repetitive positioning accuracy is than higher now, and the absolute fix precision is but very low, generally differs one more than the order of magnitude, therefore can't reach the requirement of high accuracy processing.Discover that the absolute fix precision mainly is subjected to the influence of connecting rod parameters precision in robot kinematics's model, and calibration technique can be by improving the absolute fix precision of robot to the correction of robot motion's mathematic(al) parameter.Therefore, before using, robot needs it is demarcated.The so-called demarcation is exactly the measurement means of application of advanced and picks out robot model's accurate parameter based on the parameter identification method of model, thereby improves the process of robot absolute precision.

But when the traditional method of application is carried out the demarcation of site error and is compensated, relate to the conversion between measuring system coordinate system and robot base's coordinate system, because this process is difficult to accurately finish, and complicated operation, introduce extraneous error easily, make calibration result inaccurate, can not satisfy requirement of actual application.

Therefore, at above-mentioned technical problem, be necessary to provide a kind of industrial robot scaling method based on the range error model.

Summary of the invention

In view of this, the invention provides a kind of industrial robot scaling method based on the range error model, it has effectively improved positioning accuracy and the range accuracy of industrial robot.

To achieve these goals, the technical scheme that provides of the embodiment of the invention is as follows:

A kind of industrial robot scaling method based on the range error model said method comprising the steps of:

S1, set up the MDH of robot kinematics model;

The error of S2, homogeneous transformation matrix;

S3, set up robot range error peg model;

The measurement of S4, robot end's attained pose;

The demarcation of S5, each connecting rod geometric parameter error of robot;

S6, experimental verification judge whether to satisfy required precision, if, then demarcate and finish, if not, return step S4, with the experimental result iteration, carry out calibration experiment again.

As a further improvement on the present invention, among the described step S1 in the MDH kinematics model the be connected homogeneous transformation defined matrix of coordinate system of connecting rod i-1 and connecting rod i be:

A _i＝Trans(Z,d _i)Rot(Z,θ _i)Trans(X,a _i)Rot(X,α _i)Rot(Y,β _i)，

Wherein, a is length of connecting rod, and α is the connecting rod corner, and d is the connecting rod offset distance, and θ is joint angle, and β is around the Y-axis anglec of rotation;

The base coordinate of robot is always being transformed between B and the tail end connecting rod coordinate system N:

$T_N^B=A_1{A}_2{A}_3\·\·\·A_N.$

As a further improvement on the present invention, described step S2 specifically comprises:

Calculating actual adjacent connecting rod transformation matrix is:

${A_i}^{*}=A_i+d{A}_i;$

Error matrix dA _iBe expressed as with differential form:

$A_i=\frac{\∂A_i}{\∂{\mathrm{\α}}_i}\mathrm{\Δ}{\mathrm{\α}}_i+\frac{\∂A_i}{\∂a_i}\mathrm{\Δ}{a}_i+\frac{\∂A_i}{\∂d_i}\mathrm{\Δ}{d}_i+\frac{\∂A_i}{\∂{\mathrm{\θ}}_i}\mathrm{\Δ}{\mathrm{\θ}}_i+\frac{\∂A_i}{\∂{\mathrm{\β}}_i}\mathrm{\Δ}{\mathrm{\β}}_i;$

The real transform matrix that calculating robot's tail end connecting rod with respect to base coordinate is:

$T_N^{B*}=T_N^B+d{T}_N^B=T_N^B+T_N^B\mathrm{\δ}{T}_N^B$

$={A_1}^{*}{A_2}^{*}\·\·\·{A_N}^{*}$

Calculate Error matrix

$\mathrm{\δ}{T}_N^B=\left(\begin{array}{cccc}0& -{\mathrm{\δ}}_z^N& {\mathrm{\δ}}_y^N& d_x^N\\ {\mathrm{\δ}}_z^N& 0& -{\mathrm{\δ}}_x^N& d_y^N\\ -{\mathrm{\δ}}_y^N& {\mathrm{\δ}}_x^N& 0& d_z^N\\ 0& 0& 0& 0\end{array}\right);$

Calculating robot's terminal position error vector $\mathrm{dP}={\left(\begin{array}{ccc}{d}_x^N& d_y^N& d_z^N\end{array}\right)}^T$ Matrix.

As a further improvement on the present invention, the formula of robot range error peg model is among the described step S3:

$\mathrm{\Δl}(i,j)=(\frac{x_B\left(j\right)-x_B\left(i\right)}{l_B(i,j)},\frac{y_B\left(j\right)-y_B\left(i\right)}{l_B(i,j)},\frac{z_B\left(j\right)-z_B\left(i\right)}{l_B(i,j)})(B_j-B_i)\mathrm{\Δq};$

I and j are robot point arbitrarily in three dimensions, l _B(i, j), l _L(i, j) being respectively at 2 is B and the distance of measuring among the coordinate system L in the robot basis coordinates, (i j) is range error to Δ l.

As a further improvement on the present invention, described step S4 is specially:

In the robot working space, specify n point arbitrarily, record the cartesian coordinate value of described n point, when the robot end moves to specified point, note corresponding joint rotation angle value, measure corresponding robot end's attained pose coordinate figure simultaneously with laser tracker.

As a further improvement on the present invention, described step S5 is specially:

One group of joint rotation angle value of each the specified point correspondence among the step S4 and the corresponding robot end's who is measured by laser tracker thereof attained pose coordinate figure is updated to the formula of the robot range error peg model among the step S3;

Obtain n-1 equation by n point, form an equation group;

Equation group is rewritten into matrix form, adopts the basic theories of generalized inverse matrix to try to achieve least square solution, i.e. each connecting rod geometric parameter error amount Δ α of robot ₁, Δ a ₁, Δ d ₁, Δ θ ₁, Δ β ₁, Δ α ₂..., Δ β _N

According to each connecting rod geometric parameter error amount of the robot of trying to achieve, (i is j) with site error dP to obtain corresponding range error Δ l.

As a further improvement on the present invention, the experimental verification among the described step S6 is specially:

Revise according to each the connecting rod geometric parameter of the robot of Δ q that calculates among the step S5, the connecting rod geometric parameter of use the revising checking that experimentizes, be input to the coordinate figure of n point among the step S4 in the robot controller again, note corresponding one group of joint rotation angle value and the corresponding robot end's who is measured by laser tracker thereof attained pose coordinate figure, interpretation of result after the experiment is calculated, (i is j) with site error dP to try to achieve the range error Δ l that this time tests.

The invention has the beneficial effects as follows: the industrial robot scaling method based on the range error model provided by the invention has simply, practical, efficiently, advantage efficiently, be applicable to any series connection revolute robot, highly versatile can improve industrial robot positioning accuracy and range accuracy simultaneously.

Description of drawings

In order to be illustrated more clearly in the embodiment of the invention or technical scheme of the prior art, to do to introduce simply to the accompanying drawing of required use in embodiment or the description of the Prior Art below, apparently, the accompanying drawing that describes below only is some embodiment that put down in writing among the present invention, for those of ordinary skills, under the prerequisite of not paying creative work, can also obtain other accompanying drawing according to these accompanying drawings.

Fig. 1 is the particular flow sheet that the present invention is based on the industrial robot scaling method of range error model;

Fig. 2 is the MDH kinematics model coordinate system figure of six-shaft industrial robot in the embodiment of the invention;

Fig. 3 is that the range error of robot in the embodiment of the invention is described figure;

Fig. 4 is the site error figure of robot in the embodiment of the invention.

The specific embodiment

In order to make those skilled in the art person understand technical scheme among the present invention better, below in conjunction with the accompanying drawing in the embodiment of the invention, technical scheme in the embodiment of the invention is clearly and completely described, obviously, described embodiment only is the present invention's part embodiment, rather than whole embodiment.Based on the embodiment among the present invention, those of ordinary skills should belong to the scope of protection of the invention not making the every other embodiment that obtains under the creative work prerequisite.

Join shown in Figure 1ly, Fig. 1 may further comprise the steps for the industrial robot scaling method based on the range error model in the embodiment of the invention:

S1, set up the MDH of robot kinematics model;

The DH model is that basic exercise is learned model at present, and it is according to certain rule the member coordinate system to be embedded in each linkage of robot, thereby sets up the space coordinates of each connecting rod of robot.The DH kinematics model comprises 4 geometric parameters: length of connecting rod a, connecting rod corner α, connecting rod offset distance d and joint angle θ.The weak point of DH model is that when adjacent two joints axes are parallel, the little deviation of the depth of parallelism will cause the position of actual common normal and the position of theoretical common normal to have very big deviation.Therefore, on the DH model based, the MDH kinematics model of correction has increased the β parameter of rotating around Y-axis.

Join shown in Figure 2ly, present embodiment adopts the MDH kinematics model, according to certain rule the member coordinate system is embedded in each linkage of robot, thereby sets up the space coordinates of each connecting rod of robot.The MDH kinematics model comprises 5 geometric parameter: α, a, d, θ, β.Be the be connected homogeneous transformation defined matrix of coordinate system of connecting rod i-1 and connecting rod i:

A _i=Trans(Z,d _i)Rot(Z,θ _i)Trans(X,a _i)Rot(X,α _i)Rot(Y,β _i)，

The base coordinate of robot is always being transformed between B and the tail end connecting rod coordinate system N:

$T_N^B=A_1{A}_2{A}_3\·\·\·A_N.$

The error of S2, homogeneous transformation matrix;

Because have deviation between the actual geometric parameter of joint of robot and the theoretical parameter value in manufacturing and the installation process, the adjacent connecting rod transformation matrix on historical facts or anecdotes border is:

${A_i}^{*}=A_i+d{A}_i;$

Error mainly be that geometric parameter error by each connecting rod causes, simultaneously because each parameter error is smaller, so error matrix dA _iBe expressed as with differential form:

$A_i=\frac{\∂A_i}{\∂{\mathrm{\α}}_i}\mathrm{\Δ}{\mathrm{\α}}_i+\frac{\∂A_i}{\∂a_i}\mathrm{\Δ}{a}_i+\frac{\∂A_i}{\∂d_i}\mathrm{\Δ}{d}_i+\frac{\∂A_i}{\∂{\mathrm{\θ}}_i}\mathrm{\Δ}{\mathrm{\θ}}_i+\frac{\∂A_i}{\∂{\mathrm{\β}}_i}\mathrm{\Δ}{\mathrm{\β}}_i$

Robot end's connecting rod with respect to the real transform matrix of base coordinate is:

$T_N^{B*}=T_N^B+d{T}_N^B=T_N^B+T_N^B\mathrm{\δ}{T}_N^B$

${=A_1}^{*}{A_2}^{*}\·\·\·{A_N}^{*};$

Be Error matrix, its expression formula is:

$\mathrm{\δ}{T}_N^B=\left(\begin{array}{cccc}0& -{\mathrm{\δ}}_z^N& {\mathrm{\δ}}_y^N& d_x^N\\ {\mathrm{\δ}}_z^N& 0& -{\mathrm{\δ}}_x^N& d_y^N\\ -{\mathrm{\δ}}_y^N& {\mathrm{\δ}}_x^N& 0& d_z^N\\ 0& 0& 0& 0\end{array}\right);$

According to top described formula, can derive robot end's position error vector $\mathrm{dP}={\left(\begin{array}{ccc}{d}_x^N& d_y^N& d_z^N\end{array}\right)}^T$ Matrix express formula.

S3, set up robot range error peg model;

Join shown in Figure 3ly, in three dimensions, put i and some j arbitrarily for robot, though they are that coordinate figure among B and the measurement coordinate system L is different in the robot basis coordinates, these 2 the robot basis coordinates be among the B apart from l _B(i, j) and in measuring coordinate system L apart from l _L(i is identical j).Utilize this characteristics, set up robot range error peg model.Join shown in Figure 4, robot end's position error vector dP and range error Δ l in this model (i, relational expression j) is:

$\mathrm{\Δl}(i,j)=l_L(i,j)-l_B(i,j)$

$=(\frac{x_B\left(j\right)-x_B\left(i\right)}{l_B(i,j)},\frac{y_B\left(j\right)-y_B\left(i\right)}{l_B(i,j)},\frac{z_B\left(j\right)-z_B\left(i\right)}{l_B(i,j)})(d{P}_j-d{P}_i);$

Robot end's position error vector dP _iCan further be expressed as:

dP _i=B _iΔq，

Wherein, Δ q=(Δ α ₁, Δ a ₁, Δ d ₁, Δ θ ₁, Δ β ₁, Δ α ₂..., Δ β _N) ^TBeing the error vector that the robot intrinsic systematic error of each connecting rod parameter constitutes, is the unknown quantity that need find the solution; B _iBe 3 * 5N (N is number of degrees of freedom) coefficient matrix, determine concrete numerical value according to the formula among the step S2.

According to above-mentioned each formula, the formula of robot range error peg model can be expressed as:

$\mathrm{\Δl}(i,j)=(\frac{x_B\left(j\right)-x_B\left(i\right)}{l_B(i,j)},\frac{y_B\left(j\right)-y_B\left(i\right)}{l_B(i,j)},\frac{z_B\left(j\right)-z_B\left(i\right)}{l_B(i,j)})(B_j-B_i)\mathrm{\Δq}.$

The measurement of S4, robot end's attained pose;

In the robot working space, specify n point arbitrarily, the cartesian coordinate value of this n point is imported the control panel of robot, when the robot end moves to specified point, note corresponding joint rotation angle value, measure corresponding robot end's attained pose coordinate figure simultaneously with laser tracker.

The demarcation of S5, each connecting rod geometric parameter error of robot;

One group of joint rotation angle value of each the specified point correspondence among the step S4 and the corresponding robot end's who is measured by laser tracker thereof attained pose coordinate figure is updated to the formula of the robot range error peg model among the step S3;

Obtain n-1 equation by n point, form an equation group;

Equation group is rewritten into matrix form, adopts the basic theories of generalized inverse matrix to try to achieve least square solution, i.e. each connecting rod geometric parameter error amount Δ α of robot ₁, Δ a ₁, Δ d ₁, Δ θ ₁, Δ β ₁, Δ α ₂..., Δ β _N

According to each connecting rod geometric parameter error amount of the robot of trying to achieve, (i is j) with site error dP to obtain corresponding range error Δ l.

The equation number will be enough to solve parameter to be revised in this step.

S6, experimental verification judge whether to satisfy required precision, if, then demarcate and finish, if not, return step S4, with the experimental result iteration, carry out calibration experiment again.

Revise according to each the connecting rod geometric parameter of the robot of Δ q that calculates among the step S5, the connecting rod geometric parameter of use the revising checking that experimentizes, be input to the coordinate figure of n point among the step S4 in the robot controller again, note corresponding one group of joint rotation angle value and the corresponding robot end's who is measured by laser tracker thereof attained pose coordinate figure, interpretation of result after the experiment is calculated, (i is j) with site error dP to try to achieve the range error Δ l that this time tests.Compare with the permissible accuracy standard, as do not reach required precision, then in the data substitution range error peg model formula with this experiment, carry out secondary and demarcate, until reaching required precision.

Compared with prior art, the present invention has following beneficial effect:

Verification step among the present invention can carry out repeatedly, do not reach requirement as positioning accuracy, formula with the robot range error peg model among the parameter correction value replacement theoretical parameter value substitution step S3 repeats step S4～S6, makes the positioning accuracy of demarcation and range accuracy higher;

The scaling method of industrial robot positioning accuracy and range accuracy adopts the 5 parameter MDH kinematics models of revising, and has overcome the weak point that occurs unusual appearance in the DH kinematics model when adjacent two joints axes are parallel, makes kinematics model more accurate;

This scaling method has been avoided the robot coordinate system and has been measured the error that the coordinate system conversion brings based on the range error peg model, and it is little to introduce extraneous error.Experimental implementation is simple, and direct point coordinates value control robot end in robot controller input service space moves to specified point, does not need to plan in advance specific track.

The processing procedure of the experimental data of this scaling method is simple, in experimental data substitution formula, obtains polynary linear function group, uses mathematical analysis softwares such as Matlab, can obtain experimental result fast.

In sum, industrial robot scaling method based on the range error model provided by the invention has simply, practical, efficiently, advantage efficiently, be applicable to any series connection revolute robot, highly versatile can improve industrial robot positioning accuracy and range accuracy simultaneously.

To those skilled in the art, obviously the invention is not restricted to the details of above-mentioned one exemplary embodiment, and under the situation that does not deviate from spirit of the present invention or essential characteristic, can realize the present invention with other concrete form.Therefore, no matter from which point, all should regard embodiment as exemplary, and be nonrestrictive, scope of the present invention is limited by claims rather than above-mentioned explanation, therefore is intended to include in the present invention dropping on the implication that is equal to important document of claim and all changes in the scope.Any Reference numeral in the claim should be considered as limit related claim.

In addition, be to be understood that, though this specification is described according to embodiment, but be not that each embodiment only comprises an independently technical scheme, this narrating mode of specification only is for clarity sake, those skilled in the art should make specification as a whole, and the technical scheme among each embodiment also can form other embodiments that it will be appreciated by those skilled in the art that through appropriate combination.

Claims (7)

1. the industrial robot scaling method based on the range error model is characterized in that, said method comprising the steps of:

S1, set up the MDH of robot kinematics model;

The error of S2, homogeneous transformation matrix;

S3, set up robot range error peg model;

The measurement of S4, robot end's attained pose;

The demarcation of S5, each connecting rod geometric parameter error of robot;

S6, experimental verification judge whether to satisfy required precision, if, then demarcate and finish, if not, return step S4, with the experimental result iteration, carry out calibration experiment again.

2. method according to claim 1 is characterized in that, among the described step S1 in the MDH kinematics model the be connected homogeneous transformation defined matrix of coordinate system of connecting rod i-1 and connecting rod i be:

A _i=Trans(Z,d _i)Rot(Z,θ _i)Trans(X,a _i)Rot(X,α _i)Rot(Y,β _i)，

Wherein, a is length of connecting rod, and α is the connecting rod corner, and d is the connecting rod offset distance, and θ is joint angle, and β is around the Y-axis anglec of rotation;

The base coordinate of robot is always being transformed between B and the tail end connecting rod coordinate system N:

$T_N^B=A_1{A}_2{A}_3\·\·\·A_N.$

3. method according to claim 2 is characterized in that, described step S2 specifically comprises:

Calculating actual adjacent connecting rod transformation matrix is:

${A_i}^{*}=A_i+d{A}_i;$

Error matrix dA _iBe expressed as with differential form:

$d{A}_i=\frac{\∂A_i}{\∂{\mathrm{\α}}_i}\mathrm{\Δ}{\mathrm{\α}}_i+\frac{\∂A_i}{\∂a_i}\mathrm{\Δ}{a}_i+\frac{\∂A_i}{\∂d_i}\mathrm{\Δ}{d}_i+\frac{\∂A_i}{\∂{\mathrm{\θ}}_i}\mathrm{\Δ}{\mathrm{\θ}}_i+\frac{\∂A_i}{\∂{\mathrm{\β}}_i}\mathrm{\Δ}{\mathrm{\β}}_i;$

The real transform matrix that calculating robot's tail end connecting rod with respect to base coordinate is:

$T_N^{B*}=T_N^B+d{T}_N^B=T_N^B+T_N^B\mathrm{\δ}{T}_N^B$ $={A_1}^{*}{A_2}^{*}\·\·\·{A_N}^{*}$

Calculate Error matrix

$\mathrm{\δ}{T}_N^B=\left(\begin{array}{cccc}0& -{\mathrm{\δ}}_z^N& {\mathrm{\δ}}_y^N& d_x^N\\ {\mathrm{\δ}}_z^N& 0& -{\mathrm{\δ}}_x^N& d_y^N\\ -{\mathrm{\δ}}_y^N& {\mathrm{\δ}}_x^N& 0& d_z^N\\ 0& 0& 0& 0\end{array}\right);$

Calculating robot's terminal position error vector ${\mathrm{dP}=\left(\begin{array}{ccc}{d}_x^N& d_y^N& d_z^N\end{array}\right)}^T$ Matrix.

4. method according to claim 3 is characterized in that, the formula of robot range error peg model is among the described step S3:

$\mathrm{\Δl}(i,j)=(\frac{x_B\left(j\right)-x_B\left(i\right)}{l_B(i,j)},\frac{y_B\left(j\right)-y_B\left(i\right)}{l_B(i,j)},\frac{z_B\left(j\right)-z_B\left(i\right)}{l_B(i,j)})(B_j-B_i)\mathrm{\Δq};$

I and j are robot point arbitrarily in three dimensions, l _B(i, j), l _L(i, j) being respectively at 2 is B and the distance of measuring among the coordinate system L in the robot basis coordinates, (i j) is range error to Δ l.

5. method according to claim 4 is characterized in that, described step S4 is specially:

In the robot working space, specify n point arbitrarily, record the cartesian coordinate value of described n point, when the robot end moves to specified point, note corresponding joint rotation angle value, measure corresponding robot end's attained pose coordinate figure simultaneously with laser tracker.

6. method according to claim 5 is characterized in that, described step S5 is specially:

One group of joint rotation angle value of each the specified point correspondence among the step S4 and the corresponding robot end's who is measured by laser tracker thereof attained pose coordinate figure is updated to the formula of the robot range error peg model among the step S3;

Obtain n-1 equation by n point, form an equation group;

Equation group is rewritten into matrix form, adopts the basic theories of generalized inverse matrix to try to achieve least square solution, i.e. each connecting rod geometric parameter error amount Δ α of robot ₁, Δ a ₁, Δ d ₁, Δ θ ₁, Δ β ₁, Δ α ₂..., Δ β _N

According to each connecting rod geometric parameter error amount of the robot of trying to achieve, (i is j) with site error dP to obtain corresponding range error Δ l.

7. method according to claim 6 is characterized in that, the experimental verification among the described step S6 is specially:

Revise according to each the connecting rod geometric parameter of the robot of Δ q that calculates among the step S5, the connecting rod geometric parameter of use the revising checking that experimentizes, be input to the coordinate figure of n point among the step S4 in the robot controller again, note corresponding one group of joint rotation angle value and the corresponding robot end's who is measured by laser tracker thereof attained pose coordinate figure, interpretation of result after the experiment is calculated, (i is j) with site error dP to try to achieve the range error Δ l that this time tests.