JPH0643918A - Absolute positioning error correcting device - Google Patents

Abstract

PURPOSE:To obtain an absolute positioning error correcting device capable of highly precise positioning. CONSTITUTION:An error correcting means 2 inputting articulation displacement from an error correcting and reverse converting means 1 which inputs geometric error factors and the target position attitude of an operation coordinate system representing all or some of the geometric error factors as a mathematical expression model and outputs the articulation displacement value (q) of an articulation coordinate system outputs an articulation displacement correction value DELTAq by correcting only error factors which are not modeled with a mathematical expression by the error correcting and reverse converting means 1. Then a target articulation displacement value calculating means 3 adds the articulation displacement value (q) and articulation displacement correction value DELTAq together and outputs a target articulation displacement value qd, so that the absolute positioning error can be corrected with extremely high precision.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an absolute positioning error correction device for improving the absolute positioning accuracy of a work robot which works by an arm composed of a plurality of links.

[0002]

2. Description of the Related Art FIG. 16 shows, for example, Japanese Patent Laid-Open No. 3-175503.
FIG. 17 is a block diagram showing an outline of a conventional positioning error correction device disclosed in Japanese Patent Publication No. JP-A-2004-163200, and in FIG. 16, reference numeral 91 is a target position / orientation value X _d of the robot in the work coordinate system, and joint displacement in the joint coordinate system is input. The coordinate system inverse transforming means for outputting the value q ₀ , 92 receives the target position / orientation value X _d in the work coordinate system as an input, and the joint displacement correction value Δ by the approximation function of the mechanical error formed on the network by learning.
Error correction means for outputting q, 93 is the joint displacement value q ₀
And target joint displacement calculation means for adding the joint displacement correction value Δq.

FIG. 17 is a block diagram during learning of the network which constitutes the error correction means 92. In FIG. 17, 101 is a target position / orientation value X in the work coordinate system.
_This is an error conversion means for inputting the actual work coordinate measurement value x of the industrial robot which is the output of _d and the controller 94 and outputting the joint displacement error value ε _q corresponding to the difference between the two inputs to the error correction means 92. .

The conventional absolute positioning error correction device is constructed as described above. First, the coordinate system inverse transformation means 91 receives the target position / orientation value X _d of the working coordinate system as input, performs coordinate system inverse transformation based on the geometric model of the robot, and outputs the joint displacement value q ₀ in the joint coordinate system. . Since this joint displacement value q ₀ is calculated using the nominal value of the geometric model, it is the same as the target joint displacement when absolute positioning correction is not performed.

On the other hand, the target position / orientation value X _d of the working coordinate system is
It is also input to the network that constitutes the error correction means 92. Learning of the network has been completed in advance, and a joint displacement correction value Δq for correcting all error factors including geometrical error factors such as link length is output. When actually driving the robot, the target joint displacement calculation means 9
3, the joint displacement value q ₀ and the joint displacement correction value Δ
q is added and the output q _d of the target joint displacement calculating means 93 is given to the controller 94 to drive the robot.

When learning the network which constitutes the error correction means 92, the robot is driven to measure the actual work coordinate measurement value x, and the error with the target position / orientation value X _d is obtained by the error conversion means 101. using an inverse matrix of the Jacobian matrix J converts the positioning error in the working coordinate system to the joint displacement error value epsilon _q in the joint coordinate system, the joint displacement error value epsilon _q
Is given to the error correction means 92, and iterative learning is performed so that the joint displacement error value ε _q is minimized.

Therefore, in this conventional apparatus, the actual work coordinate measurement value x must be measured every time learning is performed. Here, the Jacobian matrix J is a small displacement Δq of the joint displacement and a small change Δx of the hand position at a certain joint displacement value q ₀ .
Is a matrix that relates to as in equation (1).

Δx = J · Δq (1)

[0009]

Since the conventional absolute positioning error correction device is constructed as described above, there is a problem in that a very high positioning accuracy cannot be expected. That is, it is considered that the function for calculating the correction amount of the mechanical error of the robot, which includes many factors and influences them in a complicated manner, has an extremely complicated shape. Therefore, as described above, in the conventional absolute positioning error correction device, this complicated function is learned by the network, and all error factors are corrected by the network. However, it is not possible to approximate an arbitrary multi-displacement function with a network in a practical range. Therefore, the conventional device cannot be expected to have very high positioning accuracy.

The present invention has been made to solve the above problems, and an object of the present invention is to obtain an absolute positioning error correction device capable of highly accurate positioning.

[0011]

According to a first aspect of the present invention, there is provided an absolute positioning error correcting apparatus which is a working coordinate system in which all or some of geometrical error factors and non-geometrical error factors are represented by a mathematical model. Error correction inverse transformation means for inputting the target position / orientation value in the joint coordinate system as an output, error correction means for outputting the joint displacement correction value as an input, and the joint displacement value And a target joint displacement calculating means for adding the joint displacement correction value and outputting the target joint displacement value.

In the absolute positioning error correction device according to the second aspect of the present invention, the target position / orientation value in the working coordinate system in which all or some of the geometrical error factors and the non-geometrical error factors are expressed by a mathematical model. Error correction inverse transformation means for outputting the joint displacement value of the joint coordinate system as an input, error correction means for outputting the joint displacement value as an input, and the joint displacement value and the joint displacement correction value And a target joint displacement calculation unit that outputs a target joint displacement value as an output, and the error correction unit, when learning, a value that measures the joint displacement when the tip is in a certain position and orientation,
The approximation function for outputting the joint displacement correction value is obtained by repeatedly using the error with the joint displacement calculated by the error correction inverse conversion means from the measured value of the hand position / orientation as a teacher signal.

In the absolute positioning error correction device according to the third aspect of the present invention, the hand target position / orientation value in the working coordinate system in which all or some of the geometrical error factors and the non-geometrical error factors are expressed by a mathematical model. Error-correction inverse conversion means that receives as input the joint displacement value of the joint coordinate system,
Forward conversion means for inputting the joint displacement value and outputting a hand end command value in a work coordinate system, error correction means for inputting the joint displacement and outputting a hand end command correction value, and the hand end command value and the hand end command It is provided with a hand end command value calculating means for adding a correction value and outputting a new hand end command value, and an inverse converting means for inputting the new hand end command value and outputting a target joint displacement value.

According to a fourth aspect of the present invention, there is provided an absolute positioning error correction device, wherein an inverse transformation means for inputting a true hand target position / posture value and outputting a joint displacement value of a joint coordinate system, and the joint displacement value are inputted. As an input, an error correction means for outputting a hand end target correction value and a hand end target position / orientation value in the work coordinate system are input, and a joint displacement value in the joint coordinate system (target joint displacement)
Error correction reverse conversion means for outputting, and the finger end target value calculation means for adding the true hand end target position / orientation value and the hand end target correction value and supplying the obtained hand end target value to the error correction inverse conversion means. It is equipped with and.

[0015]

In the error correction inverse conversion means according to the present invention, geometrical error factors such as the link length and the offset of the joint displacement gauge and error factors due to the deflection of the joint due to gravity are modeled. Since the correction is performed and the error correction means corrects the remaining error factors that are not modeled by the error correction inverse conversion means, extremely accurate absolute positioning error correction can be performed.

According to the second aspect of the present invention, the error correction means calculates the joint displacement calculated by the error correction inverse conversion means from the measured value of the joint displacement at a certain time and the measured value of the hand position / posture at that time during learning. Since the error between and is repeatedly used as a teacher signal, it is not necessary to measure every learning.
You only need to measure it.

The error correction inverse conversion means according to the third aspect of the present invention uses geometrical error factors such as the link length and the offset of the joint displacement gauge and the error factors that model the error factors due to the deflection of the joint due to gravity. Since the correction is performed and the error correction means corrects the remaining error factors that are not modeled by the error correction inverse conversion means, extremely accurate absolute positioning error correction can be performed.

The error correction inverse conversion means according to the fourth aspect of the present invention uses geometrical error factors such as the link length and the offset of the joint displacement gauge and the error factors modeling the error factors due to the deflection of the joint due to gravity. Since the correction is performed and the error correction means corrects the remaining error factors that are not modeled by the error correction inverse conversion means, extremely accurate absolute positioning error correction can be performed.

[0019]

【Example】

Example 1. An embodiment of the present invention will be described below with reference to the drawings. In FIG. 1, reference numeral 1 denotes an error correction inverse conversion means for inputting a target position / orientation value xd in a work coordinate system and outputting a joint displacement value q corrected for an error factor represented by a mathematical model, and 2 denotes a joint displacement value q. As input, joint displacement correction value Δq
Is a target joint displacement calculating means for adding the joint displacement value q and the joint displacement correction value Δq to output a target joint displacement value qd to be given to the controller 4.

Here, as shown in FIG. 2, a 6-axis robot having a multi-joint arm is constructed by connecting a first link 6 to a sixth link 11 on a base 5 at first joints to sixth joints. An example will be described in which all joints are rotary joints for the sake of simplicity.

First, the first joint rotates about a vertical axis J1, the second joint rotates about a horizontal axis J2, the third joint rotates about a horizontal axis J3, and the fourth joint rotates. Rotates about an axis J4 facing the hand, and the robot has a fifth joint and a sixth joint on its hand, and the fifth joint rotates about an axis J5 orthogonal to the axis J4, The joint rotates about an axis J6 which is orthogonal to the axis J5.

Next, the coordinate system fixed to each link will be described. First, 12 is a robot base coordinate system fixed to the base 5 (0th link coordinate system), 13 is a first link coordinate system fixed to the first link 6, and 14 is a second link coordinate system fixed to the second link 7. , 15 is the third link coordinate system fixed to the third link 8, and 16 is the fourth link system fixed to the fourth link 9.
A link coordinate system, 17 is a fifth link coordinate system fixed to the fifth link 10, and 180 is a sixth link coordinate system fixed to the sixth link coordinate system 11, and is a fourth link coordinate system 16 and a fifth link coordinate system.
The link coordinate system 17 has the same position but different attitude, and the fifth link coordinate system 17 and the sixth link coordinate system 180 have the same position and attitude.

Here, Z _i is the Z-axis of the i-th link coordinate system, and for example, Z ₃ is the Z-axis of the third link coordinate system. Also, the rotation axis of the (i + 1) th joint (that is, J _{i + 1}
Axis) is the Z _i axis, so if Z ₃
Matches the axis of rotation of the joint. Since Z ₆ does not have the 7th joint, it can be used anywhere, and the example shown in the figure corresponds to Z ₅ . Such a coordinate system setting method is often used to set a fixed coordinate system for each link of the robot.

Next, an embodiment of the above construction will be described.
First, the operation of the error correction inverse conversion means 1 will be described. In this error correction inverse transformation means 1, the target position / orientation value x _d in the work coordinate system 18 is input, and the joint displacement value q in which the geometric error factor is corrected is output. Therefore, first, the geometric model of the robot is expressed by a mathematical model.

This time, the modified DH is used as the geometric model.
The model was used. This modified DH model is described in, for example, "Robotics for mechanical systems" issued by Sogo Denshi Publishing. In this geometric model, the coordinate system 13-fixed to each link 6-11 as shown in FIG.
Set 17,180. The relationship between adjacent coordinate systems among these coordinate systems is shown in FIGS. 3, 4, and 5.

Here, a _i is the joint axis of the i-th joint and the i + th joint.
When one joint is parallel, it is the distance between both joints and corresponds to the length of the i-th link. d _i is the link distance in the joint axis direction of the i-th joint, θ _i is the rotation angle of the i-th joint around the joint axis, α _i is the twist angle formed by the joint axes of the i-th joint and the (i + 1) th joint, and β _i
Is a twist angle indicating how much the (i + 1) th joint is twisted with respect to the i-th joint in the plane perpendicular to α _i . The five parameters a _i , d _i , θ _i , α _i , and β _i are called modified DH parameters.

Reference numeral 19 is the i-th joint, 20 is the (i + 1) th joint, and 2
Reference numeral 1 is an i-1th link coordinate system, and 22 is an ith link coordinate system. In FIG. 3, for example, the link 6 in FIG. 2 is a link i−1, the link 7 is a link i, and the link 8 is a link i + 1. Further, x _i-1 , y _i-1 , and z _i-1 are the x-axis, y-axis, z-axis, and x-axis of the i-1th link coordinate system 21, respectively.
_i , y _i , and Z _i are x in the i-th link coordinate system 22, respectively.
Axis, y-axis, Z-axis.

As described above, FIG. 3 shows the relationship between the coordinate system setting method using the modified DH model and the adjacent coordinate system. In FIG. 2, the coordinate system setting method shown in FIG.
It shows what happens when it is applied to an axis robot. Therefore, FIG. 3 shows what kind of coordinate system is set, and FIG. 2 shows a concrete example.

If the offset of the joint displacement gauge of the i-th joint is dθ _i and the measured value of the joint displacement is q _i ,

[0030] _{θ i = q i + dθ i} ····················· (2)

Is satisfied. If these five modified DH parameters are used, the coordinate conversion matrix A _i between the i−1th link coordinate system and the ith link coordinate system is

[0032]

[Equation 1]

It is expressed as follows. Where S _i = sin (θ
_i ), S _ai = sin (α _i ), S _bi = sin (β _i ),
C _i = cos (θ _i ), C _ai = cos (α _i ), C _bi =
cos (β _i ).

Working coordinate system 18 and robot base coordinate system 1
The coordinate conversion matrix between 2 and B is B, and the sixth link coordinate system 180
And the coordinate transformation matrix between the hand coordinate system (the coordinate system fixed to the hand attached to the tip of the sixth link) is H,
The coordinate transformation matrix T between the work coordinate system 18 and the hand coordinate system is

T = BA ₁ A ₂ A ₃ A ₄ A ₅ A ₆ H ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ (4)

Apply. At this time, the hand position in the hand coordinate system is r _h , and the hand position in the work coordinate system 18 is r.

R = Tr _h ... (5)

Is satisfied. The same relational expression holds for the posture.

Therefore, in the work coordinate system 18, the position / orientation value x is determined by the parameters of the coordinate conversion matrices B, H and a _i , d.
A geometrical parameter vector p having _i , dθ _i , α _i , β _i (i = 1, 2, ..., 6) as an element and a joint displacement value q having a joint displacement value q _i of each joint as an element It can be expressed by using equation (6).

X = f (q, p) (6)

Usually, design values are used as the values of geometrical parameters, but in reality they do not follow the design values due to processing errors and assembly errors. Therefore, when the joint displacement value is calculated using the design value of the geometrical parameter, the joint displacement value deviates considerably from the joint displacement value to be calculated.

Therefore, the error correction inverse conversion means 1 does not use the design value but uses the calibrated parameter. Since the calibrated parameters are used, the error due to the error in the geometrical parameter can be corrected by the error correction inverse conversion means 1. The parameter calibration method is, for example, vo of the Robotics Society of Japan, vo
l. 5, No. 4, “Error analysis of robot manipulator by homogeneous transformation” is described in detail. When the target position / orientation value x _d in the work coordinate system is given, the inverse transformation of equation (6) is performed using the calibrated parameter p.

Q = f ₋₁ (x _d , p) (7)

Based on the above, the joint displacement value q in which the geometric error factor is corrected can be obtained. Here, as described above, q is a six-dimensional vector having the joint displacement value q _i (i = 1, 2, ... 6) of each joint as an element. But for a 6-axis robot, calibrating all geometric parameters
Since the 4, 5, and 6 axes do not intersect at one point, the equation (7) cannot be calculated analytically. In such a case, the target position / orientation value is repeatedly corrected, and the corrected target posture value x
_The joint displacement value q is calculated by inversely transforming _t using the nominal value of the parameter.

This algorithm is shown in FIG. In FIG. 6, in step ST6-1, the initial value of the target position / posture value xt is set to the target position / posture value xd.
In 2, the equation (7) is calculated using the nominal value of the parameter p ₀ to obtain the joint displacement value q, and in step ST6-3, the calibrated parameter p is used from the joint displacement value q obtained in step ST6-2. Then, the position and orientation value x is calculated by calculating the equation (6).

Position / orientation value x obtained in step ST6-3
Is equal to the target position / orientation value x _d , step ST
The joint displacement value q obtained in 6-2 is the calibrated parameter p
It is a solution of Expression (7) when is used. Therefore, the positioning error Δx is obtained in step ST6-4, and step ST6
At -5, it is determined whether the Euclidean norm ‖Δx‖ of the error Δx is smaller than the minute positive number ε. If it is smaller, the joint displacement value q at that time is output as the target joint displacement value in step ST6-7, and if it is larger, step ST6-6.
Then, the target position / orientation value x which is the input to step ST6-2
Correct _t .

Most industrial robots have 4, 5, 6
Since the axes are designed to intersect at a single point, instead of calibrating all parameters, some parameters are calibrated and nominal values are used, after parameter calibration 4, 5,
If the six axes intersect at one point, the equation (7) can be analytically calculated. Therefore, for example, the calibrated values are used for the geometrical parameters of the 1, 2, and 3 axes, and the geometrical parameters (a ₄ , d ₄ , α ₄ , β ₄ , d θ ₄ ,
a ₅ , d ₅ , α ₅ , β ₅ , dθ ₅ , a ₆ , d ₆ , α ₆ ,
Using the nominal values of β ₆ and dθ ₆ ), the joint displacement value q can be obtained by analytically calculating the equation (7).

Although the case where the geometrical parameters are corrected is shown here, the deflection due to gravity, the gear transmission error and the like can be expressed by a mathematical model and can be similarly corrected.

Next, the operation of the error correction means 2 will be described. The error correction means 2 needs to correct only the remaining error factors that are not represented by the mathematical model in the error correction inverse conversion means 1. For example, when the error correction inverse conversion means 1 corrects the geometrical error factor and the flexure of the joint due to gravity, the remaining error factors include a gear transmission error and a flexure of the link. Further, in the error correction inverse conversion means 1,
When the geometrical error factors of the 1, 2 and 3 axes and the flexure of the joint due to gravity are corrected, the remaining error factors are:
Factors such as geometrical error factors of the 4, 5, and 6 axes, gear transmission error, link deflection, and the like are included.

FIG. 7 shows a three-layer backpropagation type neural network which constitutes the error correction means 2. In FIG. 7, 2a is an input layer, 2b is an intermediate layer, and 2c is an output layer. It is generally known that such a neural network can approximate a multivariable nonlinear function by learning. Here, a correction function for correcting an error factor that is not modeled by the error correction inverse conversion means 1 is learned.

Example 2. FIG. 8 is an example of a block diagram when learning the approximation function used in the error correction means 2. In FIG. 8, reference numeral 81 is a teacher signal generating means, 82 is a joint displacement measuring means, and 83 is a teacher signal / output error output means. The joint displacement value q _n obtained from the error correction inverse transformation means 1 from the measured value x _n of the hand position when the hand of the robot is at a certain position is input, and the joint displacement value q _n and the joint displacement measuring means 82 at that time are input. The error between the measured value q _t and the measured value q _t is learned by the teacher signal generation means 81, and the teacher signal Δq is output.
Then, the teacher signal Δq and the output Δq of the error correction means 2
The difference between and is used as an error signal ε to learn an approximation function that minimizes the error signal ε. The measurement value x _{n of the} hand position used for learning and the joint displacement value q _n are measured prior to learning. This learning is performed by repeatedly using this measured value.

Therefore, it is not necessary to measure every learning as in the learning method shown in the above-mentioned conventional example. Although the three-layer BP is used in this example, a BP other than the three layers may be used, and a computing device (CMAC) imitating the cerebellum, a generalized circular basis function (GRBF), and a counter propagation (Counterp) are used.
ropagation) etc.

Example 3. FIG. 9 is a block diagram showing an outline of the absolute positioning error correction device of the first modification of the above embodiment. In FIG. 9, reference numeral 201 denotes an error correction inverse conversion unit that inputs a target position / orientation value xdd in the work coordinate system and outputs a joint displacement value q that corrects an error factor represented by a mathematical model, and 202 an error correction inverse conversion unit. Error correction means that inputs the joint displacement value q output from 201 and outputs a hand correction command value Δx _rr that corrects an unmodeled error factor, and 203 inputs the joint displacement value q and sets the nominal value of the parameter. Forward conversion means for outputting the hand end command value x _r is used, and reference numeral 204 is a hand end command value calculation means for _resuming the sum of the output x _r of the forward conversion means 203 and the end hand command correction value Δx _rr to be the hand end command value x _s. . Reference numeral 205 denotes an inverse conversion unit that inputs the hand command value x _s and outputs the target joint displacement value q _s using the nominal value of the parameter. The output of the inverse conversion means 205 is input to the controller 206.

The operation of the error correction inverse conversion means 201 is as follows.
Similar to the error correction inverse transformation means 1 in the above-mentioned embodiment, the hand target position / posture value x _dd in the work coordinate system 18 is input, and the joint displacement value q in which the geometric error factor is corrected is output. In this case, the error correction inverse transformation means 201 does not use the design value of the geometrical parameter but uses the calibrated parameter. By using the calibrated parameters, the error due to the error of the geometrical parameter can be corrected by the error correction inverse transformation means 201.
When the hand target position / orientation value x _dd in the work coordinate system 18 is given, the joint displacement value q in which the geometric error factor is corrected can be obtained based on the inverse transformation of the equation (6) using the calibrated parameter p.

In order to obtain the joint displacement value q by analytically calculating the equation (7), for example, the geometric parameters of the 1, 2, and 3 axes and the joint displacement meter of the 4, 5, and 6 axes are used. The calibrated values are used for the offsets of the geometrical parameters (a ₄ , d ₄ , α ₄ ,
β ₄ , a ₅ , d ₅ , α ₅ , β ₅ , a ₆ , d ₆ , α ₆ , β
₆ ) may use the nominal value.

The operation of the error correction means 202 is the same as that of the error correction means 2 in the above embodiment, and the error correction inverse conversion means 201 corrects only the remaining error factors which are not expressed by the mathematical model. For example, when the error correction inverse conversion means 201 corrects the geometrical error factor and the flexure of the joint due to gravity, the remaining error factors include the gear transmission error and the flexure of the link.

FIG. 10 shows the structure of the error correction means 202.
FIG. 8 is a diagram showing a neural network of a layer back propagation type, which is similar to the neural network of a three layer back propagation type forming the error correction means 2 shown in FIG. 7. In FIG. 10, 202a is an input layer, 202b is an intermediate layer, and 202c is an output layer. In this circuit network, a correction function for correcting an error factor that is not modeled by the error correction inverse conversion means 201 is learned.

FIG. 11 is an example of a block diagram for learning the approximate function used by the error correction means 202. In FIG. 11, 207 is a teacher signal generation means, 208 is a joint displacement measurement means, 209 is a forward conversion means, and 210 is a teacher signal / output error output means.

The hand of the robot is brought close to a plurality of points, and the measured value of the robot's hand at each point (measured value of hand position / posture) x _n and the measured value of the joint displacement measuring means 208 (measured value of joint displacement) q Measure _n and. Then, the output of the error correction inverse conversion means 201 when the measured hand position / orientation measurement value x _n is input is set to q, and this output q
The output obtained by the forward conversion by the forward conversion means 203 is x _r . On the other hand, the measured values q _n of the joint displacement when the hand position and orientation measurements x _n, the measured values q _n of the forward converter 209
Let x ₁ be the output obtained by forward conversion with.

Then, the output x _r of the forward conversion means 203,
The difference (x ₁ −x _r ) from the output x ₁ of the forward conversion means 209 is Δ.
x _r, and this Δx _r and the output q of the error correction means 202 when the output q of the error correction inverse conversion means 201 is input.
_The calculation of the difference ε from _rr is performed by the teacher signal / output error output means 210. Then, iterative learning is performed so that this difference ε is minimized. The hand position / posture measurement value x _n and joint displacement measurement value q _n used for learning are measured prior to learning. This learning is performed by repeatedly using this measurement. Also, the parameters of the mathematical model of the error correction inverse transformation means 201 are calibrated in advance.

Therefore, also in this modification 1, it is not necessary to perform measurement every time learning is performed, unlike the learning method shown in the above-mentioned conventional example. Also, in this modification 1, the three-layer BP is used, but a BP other than the three layers may be used, and an arithmetic device imitating a cerebellum, a generalized circular basis function, counter propagation, or the like may be used.

Example 4. FIG. 12 shows a modification 2 of the above embodiment.
3 is a block diagram showing an outline of the absolute positioning error correction device of FIG. In FIG. 12, reference numeral 220 denotes an error correction inverse conversion means 221 for inputting a hand end target value (hand end target position / orientation value) x _p and outputting a joint displacement value q _{s in} which an error factor expressed by a mathematical model is corrected. Inverse transformation means 222 for inputting the hand target position / orientation value x _dc and calculating the joint displacement value q ₀ using the nominal value of the parameter, and 222 for inputting the joint displacement value q ₀ , and the error correction inverse transformation means 220 for the model The error correction means 223 for outputting the hand target correction value Δx _dcr for correcting the error factor which has not been converted into a new hand target position / posture value x _p is the sum of the true hand target position / posture x _dc and the hand target correction value Δx _dcr. It is a hand target value calculation means for outputting.

The operation of the error correction inverse conversion means 220 is as follows.
The hand target position / posture value x _p in the work coordinate system 18 is input, and the joint displacement value q _{s in} which the geometric error factor is corrected is output. The calculation of the joint displacement value q _s is the same as in the above-mentioned embodiment. In this case, the error correction inverse conversion means 220 does not use the design value but uses the calibrated parameter as in the above embodiment. By using the calibrated parameters, the error due to the error of the geometrical parameters can be corrected by the error correction inverse conversion means 220. Working coordinate system 18
When the hand target position / orientation value x _{p at} is given, the inverse transformation q _s = f ₋₁ (x _p , p) of the equation (6) using the calibrated parameter p.・ ・ ・ ・ ・ ・ ・ (8)

Based on the above, the target joint displacement value q _{s in} which the geometrical error factor is corrected can be obtained. The joint displacement value q _s is a 6-dimensional vector having the joint displacement value q _i (i = 1, 2, ... 6) of each joint as an element, but in the case of a 6-axis robot, all geometrical values are calculated. Calibrating the dynamic parameters,
Since the 4, 5 and 6 axes do not intersect at one point, the equation (8) cannot be analytically calculated. Therefore, the target position / orientation value is repeatedly corrected in the same manner as in the above-described embodiment, and the corrected target position / orientation value x _t is inversely converted using the nominal value of the parameter to calculate the joint displacement value q _s . To do.

This algorithm is shown in FIG. FIG.
In step ST7-1, the target position / orientation value x _t
Is set to the hand target position / orientation value x _p , and the nominal value p _{0 of the} parameter is used in step ST7-2 (8).
The formula is calculated to obtain the joint displacement value q, and step ST7-3
Then, the position and orientation value x is calculated by calculating the equation (6) using the calibrated parameters from the joint displacement value q obtained in step ST7-2.

Position / orientation value x obtained in step ST7-3
If is coincident with the hand target position / orientation value x _p , the joint displacement value q obtained in step ST7-2 is the solution of the equation (8) when the calibrated parameter p is used. Therefore, the positioning error Δx is calculated in step ST7-4, and
At T7-5, it is determined whether or not the Euclidean norm ‖Δx‖ of the error Δx is smaller than the minute positive number ε. If it is smaller, the joint displacement value q at that time is output as the target joint displacement value in step ST7-7, and if it is larger, step ST7.
At -6, the target position / orientation value x _t which is the input to step ST7-2 is corrected.

In order to obtain the target joint displacement value q _s by analytically calculating the equation (8), for example, geometric parameters of the 1st, 2nd and 3rd axes and joints of the 4th, 5th and 6th axes are used. The offset of the displacement meter uses the calibrated value, and the geometric parameters (a ₄ , d ₄ ,
α ₄ , β ₄ , a ₅ , d ₅ , α ₅ , β ₅ , a ₆ , d ₆ , α
Nominal values may be used for ₆ , ₆ ).

In the fourth embodiment, the case of correcting the geometrical parameter has been described, but the deflection due to gravity, the gear transmission error, etc. can be expressed by a mathematical model and can be similarly corrected.

The operation of the error correction means 222 is similar to that of the error correction means 2 in the above embodiment, and the error correction inverse conversion means 220 corrects only the remaining error factors that are not expressed by the mathematical model. For example, when the error correction inverse conversion means 220 corrects the geometrical error factors and the flexure of the joint due to gravity, the remaining error factors include a gear transmission error and a flexure of the link.

FIG. 14 is a block diagram of the error compensating means 222.
FIG. 8 is a diagram showing a neural network of a layer back propagation type, which is similar to the neural network of a three layer back propagation type forming the error correction means 2 shown in FIG. 7. In FIG. 14, 222a is an input layer, 222b is an intermediate layer, and 222c is an output layer. In this circuit network, a correction function for correcting an error factor that is not modeled by the error correction inverse conversion means 220 is learned.

FIG. 15 is an example of a block diagram for learning the approximate function used by the error correction means 222. In FIG. 15, reference numeral 230 is a teacher signal generating means, 231 is a joint displacement measuring means, 232 is an error correction order conversion means for performing coordinate system order conversion using the calibration values of the parameters of the mathematical model of the error correction inverse conversion means 220, 233. Is a teacher signal / output error output means.

The hands of the robot are respectively brought close to a plurality of points, and the measured value of the robot's hand at each point (measured value of hand position / posture) x _n and the measured value of the joint displacement measuring means 208 (measured value of joint displacement) q Measure _n and. Then, the difference between x ₂ obtained by forward conversion of the joint displacement measurement value q _n when the hand is at x _n by the error correction forward conversion 232 and the hand position / posture measurement value x _n is Δx _d, and this Δx the difference between the output [Delta] x _d of _d and error correcting unit 222 epsilon performs iterative learning to minimize. The hand position / posture measurement value x _n and joint displacement measurement value q _n used for learning are measured prior to learning. This learning is performed by repeatedly using this measurement. Further, the parameters of the mathematical model of the error correction order conversion means 230 are calibrated in advance.

Therefore, also in the fourth embodiment, it is not necessary to perform the measurement every time the learning is performed, unlike the learning method shown in the above-mentioned conventional example. Further, although the three-layer BP is used also in the fourth embodiment, a BP other than the three layers may be used, and a computing device imitating a cerebellum, a generalized circular basis function, counter propagation, etc. may be used.

[0074]

As described above, according to the first aspect of the present invention, since the error factor which can be expressed by the mathematical model is corrected by the error correcting means, the absolute positioning error can be corrected with extremely high accuracy. effective.

According to the second aspect of the invention, the error between the joint displacement calculated by the error correction inverse transforming means from the measured value of the joint displacement at a certain time and the measured value of the hand position / posture at that time is taught. Since it is repeatedly used as a signal, it is not necessary to measure every learning, and it is sufficient to measure once before learning.

According to the invention described in claim 3, since the error factor which can be expressed by the mathematical model is corrected by the error correction means, the same effect as that of the invention described in claim 1 can be obtained. To be

According to the invention described in claim 4, since the error factor which can be represented by the mathematical model is corrected by the error correction means, the same effect as that of the invention described in claim 1 can be obtained. To be

[Brief description of drawings]

FIG. 1 is a block diagram of an absolute positioning error correction device according to an embodiment of the present invention.

FIG. 2 is an explanatory diagram of a coordinate system set for each joint in the embodiment of the present invention.

FIG. 3 is an explanatory diagram of a geometric model according to an embodiment of the present invention.

FIG. 4 is a front view of a geometric model according to an embodiment of the present invention.

FIG. 5 is a front view of a geometric model according to an embodiment of the present invention.

FIG. 6 is a flowchart of joint displacement calculation in an embodiment of the present invention.

FIG. 7 is an explanatory diagram of a neural network used in the error correction means according to the embodiment of the present invention.

FIG. 8 is a block diagram at the time of learning of the error correction means in the embodiment of the present invention.

FIG. 9 is a block diagram of an absolute positioning error correction device according to a third embodiment of the present invention.

FIG. 10 is an explanatory diagram of a neural network used in the error correcting means according to the third embodiment of the present invention.

FIG. 11 is a block diagram at the time of learning of the error correction means according to the third embodiment of the present invention.

FIG. 12 is a block diagram of an absolute positioning error correction device according to a fourth embodiment of the present invention.

FIG. 13 is a flowchart of joint displacement calculation according to the fourth embodiment of the present invention.

FIG. 14 is an explanatory diagram of a neural network used in the error correcting means according to the fourth embodiment of the present invention.

FIG. 15 is a block diagram at the time of learning of the error correction means according to the fourth embodiment of the present invention.

FIG. 16 is a block diagram showing a conventional absolute positioning error correction device.

FIG. 17 is a block diagram at the time of learning of error correction means in a conventional absolute positioning error correction device.

[Explanation of symbols]

1, 201, 220 Error correction inverse conversion means 2, 202, 222 Error correction means 3 Target joint displacement calculation means 83 Teacher signal / output error output means 203 Forward conversion means 204 Hand command value calculation means 205, 221 Inverse conversion means 223 Hand target value calculation means x _d Target position / posture value x _dd Hand target position / posture value x _dc True hand target position / posture value x _s Hand command value x _p Hand target position / posture value x _r Hand command value Δx _rr Hand command correction value Δx _dcr Hand target correction value q Joint displacement value output by error correction inverse conversion means _Δq Joint displacement correction value output by error correction means q _d Target joint displacement value

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[Procedure amendment]

[Submission date] January 21, 1993

[Procedure Amendment 1]

[Document name to be amended] Statement

[Name of item to be corrected] 0015

[Correction method] Change

[Correction content]

[0015]

Error correction reverse conversion means of the invention of the effects] according to claim 1, for example the length of the link and the joints by geometrical error factors and gravity, such as offset of the joint displacement meter deflection such as model <br/> Dell of the error The error correcting means corrects the remaining error factors that are not modeled by the error correction inverse converting means, so that extremely accurate absolute positioning error correction can be performed.

[Procedure Amendment 2]

[Document name to be amended] Statement

[Correction target item name] 0017

[Correction method] Change

[Correction content]

The error correction inverse conversion means in the third aspect of the invention is, for example, a geometrical error factor such as a link length or an offset of the joint displacement meter, or a deflection of the joint due to gravity.
Since the modeled error factors are corrected and the error correction means corrects the remaining error factors which are not modeled by the error correction inverse conversion means, extremely accurate absolute positioning error correction can be performed.

[Procedure 3]

[Document name to be amended] Statement

[Correction target item name] 0018

[Correction method] Change

[Correction content]

The error correction inverse conversion means in the invention of claim 4 is, for example, a geometrical error factor such as a link length or an offset of the joint displacement gauge, or a deflection of the joint due to gravity.
Since the modeled error factors are corrected and the error correction means corrects the remaining error factors which are not modeled by the error correction inverse conversion means, extremely accurate absolute positioning error correction can be performed.

[Procedure amendment 4]

[Document name to be amended] Statement

[Correction target item name] 0051

[Correction method] Change

[Correction content]

Example 2. FIG. 8 is an example of a block diagram when learning the approximation function used in the error correction means 2. In FIG. 8, reference numeral 81 is a teacher signal generating means, 82 is a joint displacement measuring means, and 83 is a teacher signal / output error output means. The joint displacement value q _n obtained from the error correction inverse transformation means 1 from the measured value x _n of the hand position when the hand of the robot is at a certain position is input, and the joint displacement value q _n and the joint displacement measuring means 82 at that time are input. The error between the measured value q _t and the measured value q _t is learned by the teacher signal generation unit 81, and the teacher signal Δq _t is output. Then, the difference between the teacher signal Δq _t and the output Δq of the error correction means 2 is used as an error signal ε to learn an approximate function that minimizes the error signal ε. The measurement value x _{n of the} hand position used for learning and the joint displacement value q _n are measured prior to learning. This learning is performed by repeatedly using this measured value.

[Procedure Amendment 5]

[Document name to be amended] Statement

[Correction target item name] 0060

[Correction method] Change

[Correction content]

Then, the output x _r of the forward conversion means 203,
The difference (x ₁ −x _r ) from the output x ₁ of the forward conversion means 209 is Δ.
x _r, and this Δx _r and the output q of the error correction means 202 when the output q of the error correction inverse conversion means 201 is input.
_The calculation of the difference ε from _rr is performed by the teacher signal / output error output means 210. Then, iterative learning is performed so that this difference ε is minimized. The hand position / posture measurement value x _n and the joint displacement measurement value q _n used for learning are measured prior to learning. This learning is performed by repeatedly using this measured value . Also, the parameters of the mathematical model of the error correction inverse transformation means 201 are calibrated in advance.

[Procedure correction 6]

[Document name to be amended] Statement

[Name of item to be corrected] 0072

[Correction method] Change

[Correction content]

The hands of the robot are respectively brought close to a plurality of points, and the measured values of the robot's hand positions at the respective points (measured values of the hand position / posture) x _n and the measured values of the joint displacement measuring means 231 (measured values of the joint displacement) q Measure _n and. Then, the difference between x ₂ obtained by forward conversion of the joint displacement measurement value q _n when the hand is at x _n by the error correction forward conversion 232 and the hand position / posture measurement value x _n is Δx _d, and this Δx the difference between the output [Delta] x _d of _d and error correcting unit 222 epsilon performs iterative learning to minimize. The hand position / posture measurement value x _n and joint displacement measurement value q _n used for learning are measured prior to learning. This learning is performed by repeatedly using this measured value .
Further, the parameters of the mathematical model of the error correction order conversion means 230 are calibrated in advance.

[Procedure Amendment 7]

[Document name to be amended] Statement

[Correction target item name] 0074

[Correction method] Change

[Correction content]

[0074]

As described above, according to the first aspect of the invention, the error factor that can be expressed by the mathematical model is the error correction.
Since the correction is performed by the inverse conversion means , the absolute positioning error can be corrected with extremely high accuracy.

[Procedure Amendment 8]

[Document name to be amended] Statement

[Correction target item name] 0076

[Correction method] Change

[Correction content]

According to the third aspect of the invention, the error factor that can be represented by the mathematical model is the error correction inverse transformation method.
Since the correction is made in stages , the same effect as the effect of the first aspect of the invention can be obtained.

[Procedure Amendment 9]

[Document name to be amended] Statement

[Correction target item name] 0077

[Correction method] Change

[Correction content]

Further, according to the invention described in claim 4, the error factor which can be expressed by the mathematical model is the error correction inverse conversion procedure.
Since the correction is made in stages , the same effect as the effect of the first aspect of the invention can be obtained.

[Procedure Amendment 10]

[Document name to be corrected] Drawing

[Name of item to be corrected] Figure 3

[Correction method] Change

[Correction content]

[Figure 3]

[Procedure Amendment 11]

[Document name to be corrected] Drawing

[Correction target item name] Figure 8

[Correction method] Change

[Correction content]

[Figure 8]

[Procedure Amendment 12]

[Document name to be corrected] Drawing

[Name of item to be corrected] Fig. 13

[Correction method] Change

[Correction content]

[Fig. 13]

Claims (4)

[Claims] 1. A target position / orientation value in a work coordinate system in which all or part of geometrical error factors and non-geometrical error factors are expressed by a mathematical model is input, and a joint displacement value in a joint coordinate system is output. An error correction inverse conversion means, an error correction means for inputting the joint displacement value and correcting an error factor which is not mathematically modeled in the error correction inverse conversion means and outputting a joint displacement correction value, and the joint displacement value And a target joint displacement calculating means for adding the joint displacement correction value and outputting a target joint displacement value. 2. A target position / orientation value in a work coordinate system in which all or part of geometrical error factors and non-geometrical error factors are expressed by a mathematical model, and a joint displacement value in a joint coordinate system is output. An error correction inverse conversion means, an error correction means for inputting the joint displacement value, and correcting an error factor not mathematically modeled in the error correction inverse conversion means and outputting a joint displacement correction value, and the joint displacement value And a target joint displacement calculating means for adding the joint displacement correction value and outputting a target joint displacement value, and a learning value of the correction value of the error correcting means, when learning a correction value of the hand position / posture at a certain time, the error correcting reverse conversion The difference between the joint displacement value calculated by the means and the joint displacement measurement value at that time is used as a teacher signal, and the difference between the teacher signal and the output of the error correction means is used as an error signal,
An absolute positioning error correction device comprising: a teacher signal / output error output means for performing repetitive learning. 3. An error for outputting a joint displacement value of a joint coordinate system from a target hand position / orientation value in a work coordinate system in which all or part of geometrical error factors and non-geometrical error factors are expressed by a mathematical model. Correction inverse conversion means, forward conversion means for inputting the joint displacement value and outputting a hand end command value,
Error correction means for inputting the joint displacement value and correcting an error factor not mathematically modeled in the error correction inverse conversion means and outputting a hand end command correction value, and the hand end command value and the hand end command correction value are added. Then, a hand end command value calculation means for outputting a new hand end command value, and an inverse conversion means for inputting the hand end command value output from the hand end command value calculation means and outputting a target joint displacement value are provided. Characteristic absolute positioning error correction device. 4. A target hand position / orientation value in a work coordinate system in which all or part of geometrical error factors and non-geometrical error factors are expressed by a mathematical model, and a joint displacement value in a joint coordinate system is output. Error correction inverse transformation means, an inverse transformation means for inputting a true hand target position / orientation value and outputting a joint displacement value, and a joint displacement value output from the inverse transformation means for inputting the error correction inverse transformation. Error correction means for outputting a hand target correction value for correcting an error factor not modeled in the means, and a hand target value obtained by adding the true hand target position / orientation value and the hand target correction value to the error correction inverse. An absolute positioning error correction device comprising: a hand target value calculation means for supplying to a conversion means.