JPH0728514A - Machine error deriving method - Google Patents

Abstract

PURPOSE:To unequivocally calculate a derived solution, to increase the calculation speed, and to improve the precision of the derived error at the time of deriving the geometrical error of a robot including a direct-acting shaft, an NC working machine, or the like. CONSTITUTION:The D-H notation is used to make a mechanism, whose front end a working tool is attached to, into a model, and the position and the attitude of this working tool for operation of this mechanism are measured, and the model is used to estimate them, and these measured value (r) and estimated value r' are compared with each other to derive the error of the mechanism. In this case, only parameters to change the coordinates of a driving shaft of the mechanism are used in the model; and when the model is used to estimate the position and the attitude of the working tool, coordinate transform S operation based on the rotation parameter which directs the driving shaft, coordinate transform T operation based on the translation parameter which translates the driving shaft, and inverse transform S<-1> operation of coordinate transform based on the rotation parameter are successively executed.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a machine difference deriving method, and more particularly to a machine difference deriving method for a robot including a linear axis and an NC machine tool.

[0002]

2. Description of the Related Art Generally, when deriving a machine difference of a processing machine or the like, a mechanism modeling method based on the Denabit-Hartenberg notation (hereinafter referred to as DH notation), which is well known as a robot technology, is used. Kaihei 4-21
1806). This expresses the coordinate system of the adjacent drive axes by four parameters of two translation parameters and two rotation parameters. Hereinafter, a 5-axis NC grinder will be described as an example. As shown in Fig. 2, 5-axis NC
The grinder is composed of A axis, X axis, Y axis, Z axis and C axis. FIG. 3 shows a coordinate system of each axis. In the figure, the A axis and C axis are rotation axes, and the X axis, Y axis and Z axis are linear motion axes. According to the general DH notation, the relationship between adjacent axes can be expressed by the above four parameters. When deriving the geometrical error, it is necessary to separate the command value of the axis and the offset amount of the encoder. Therefore, the inter-link distance d _i , the inter-link angle θ _i , the link length a _i , and the twist angle α _i
4 geometrical error parameters and one of the following 1 axis drive parameters (Fig. 4).
(See (a) and (b)). That is, in the DH notation, an arbitrary mechanism is displayed with four parameters between adjacent links. Considering the joints of an actual robot, in the case of the rotary joints of FIG. 4 (a), the inter-link angle θ _i , and FIG.
In the case of the direct acting joint, the link moves by changing the value of the inter-link distance d _i . At this time, if the joint angle of the robot is set to j _i , the following equation is established. Revolving joint: θ _i = j _i + Δθ _i Direct acting joint: d _i = j _i + Δd _{i In the} D-H notation, even if four notations are used, in the actual modeling, the joint angle j _{i of the} robot is set to the above 2 One parameter theta _i, consider that the d _{i contains,} it is necessary to modeling and calculation. Here, the axis drive parameter corresponds to the joint angle j _{i of the} robot, and the encoder offset amount corresponds to Δθ _i or Δd _i . Further, the joint angle j _{i of the} robot is a fixed value at a certain measurement and does not change in the process of deriving the machine difference. FIG. 7 is an explanatory diagram showing a schematic flow in an example of a conventional machine difference derivation method using such a modeling method by the DH notation. As shown in FIG. 7, the conventional machine difference derivation method models a mechanism with a machining tool attached to the tip using the DH notation that expresses various parameters (S1), and the machining tool when the above mechanism is operated. Position / orientation of the machining tool (S2), the position / orientation of the machining tool when the mechanism is operated is estimated using the model (S3), and the measured value r of the position / orientation of the machining tool is calculated. This is a method for deriving the machine difference of the above mechanism by comparing with the estimated value r '. Conventionally, such methods have been used to derive machine differences for processing machines that require absolute positioning accuracy.

[0003]

In the conventional method for deriving a machine difference as described above, the geometrical error constant is uniquely determined, especially when the mechanism for which the machine difference is derived includes a linear axis. No, the solution is derived infinitely. This is because the origin position of the linear motion axis and the encoder offset value have a redundant relationship. That is, in modeling the linear motion axis, the coordinate system after the linear motion axis is simply moved in parallel, so that the origin of the linear motion axis can be set at an arbitrary position. Generally, it is set so that it coincides with the coordinate origin of the adjacent axis. However, when deriving the error, if the modeling of the linear motion axis is expressed by four error parameters, the position of the coordinate origin can be arbitrarily set,
Since the derived equation cannot be uniquely solved, such modeling is not preferable. For example, in FIG. 4C, the origin of the linear motion axis is on the mechanical linear motion axis, but the essence of the problem does not change even if the linear motion axis origin is on the joint i + 1 as shown in FIG. In other words, the linear motion axis does not matter where the coordinate origin position is, and the above redundant relationship occurs. In addition, the linear motion shaft simply translates the mechanism after that axis, but when the DH notation is used, two rotation parameters expressing the moving axis direction of the linear motion shaft are minutely calculated in the machine difference derivation process. Changing it will affect all subsequent coordinate systems, in other words all subsequent parameters. This means that it is difficult to improve the convergence speed and accuracy when deriving the machine difference. In order to solve such a problem in the conventional technique, the present invention improves a method for deriving a machine difference and derives it when deriving a geometrical error of a robot including a linear motion axis and an NC processing machine. It is an object of the present invention to provide a machine-difference deriving method in which a solution is uniquely calculated, a convergence calculation can be speeded up, and the accuracy of a derivation error can be improved.

[0004]

In order to achieve the above object, the present invention operates a mechanism in which a machining tool is attached to the tip thereof is modeled by using the notation of Denabit-Hartenberg which represents various parameters and the mechanism is operated. The position / orientation of the processing tool at the time is measured, the position / orientation of the processing tool when the mechanism is operated is estimated using the model, and the measured value and the estimated value of the position / orientation of the processing tool are calculated. In the machine-difference derivation method for deriving the machine-difference of the mechanism by comparing with, it is configured as a machine-difference derivation method characterized in that only parameters for changing the coordinates of the drive shaft of the mechanism are used in the model. ing. Furthermore, a mechanism with a machining tool attached to the tip is modeled using the Denabit-Hartenberg notation that expresses various parameters, the position and orientation of the machining tool when the mechanism is operated is measured, and the mechanism is operated. A machine difference deriving method for estimating the position / orientation of the machining tool using the above model, and deriving the machine difference of the mechanism by comparing the measured value of the position / orientation of the machining tool with the estimated value. In the above, only parameters for changing the coordinates of the drive shaft of the mechanism are used in the model, and the rotation parameter for orienting the drive shaft when estimating the position / orientation of the machining tool using the model. The coordinate conversion calculation by the above, the coordinate conversion calculation by the translation parameter for translating the drive axis, and the inverse conversion calculation of the coordinate conversion by the rotation parameter are sequentially performed. Is instrumental error derivation method characterized by rows.

[0005]

According to the present invention, the mechanism in which the machining tool is attached to the tip is modeled using the notation of Denabit-Hartenberg, which represents various parameters, and the position / orientation of the machining tool when the mechanism is operated is measured. Then, the position / orientation of the machining tool when the mechanism is operated is estimated using the model, and the machine difference of the mechanism is calculated by comparing the measured value of the position / orientation of the machining tool with the estimated value. When deriving the, only parameters that change the coordinates of the drive axis of the mechanism are used in the model. In this way, by using only the parameters for which the error information is uniquely determined for the geometrical parameter notation of the linear motion axis, the convergence speed when deriving the machine difference can be improved. Further, when estimating the position / orientation of the machining tool using the model, coordinate conversion calculation by a rotation parameter that orients the drive axis, coordinate conversion calculation by a translation parameter that translates the drive axis, and the rotation parameter. And the inverse transformation calculation of the coordinate transformation are sequentially executed. In this way, by modeling so that the parameters after the linear axis are not affected, the parameters can be separated easily, and the measurement error can be cumulatively added when deriving the geometrical parameters. can avoid. This means that the convergence of the geometric error parameter derivation calculation and the accuracy of machine difference derivation can be improved. As a result, when deriving the geometrical error of the robot including the linear motion axis and the NC processing machine, the derived solution can be uniquely calculated, the convergence calculation can be speeded up, and the accuracy of the derived error can be improved. You can get the way.

[0006]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Embodiments embodying the present invention will be described below with reference to the accompanying drawings for the understanding of the present invention. The following embodiments are examples of embodying the present invention and are not intended to limit the technical scope of the present invention. Here, FIG. 1 is an explanatory view showing a schematic flow of a machine difference deriving method according to an embodiment of the present invention, and FIG. 2 is an explanatory view showing an appearance of a 5-axis NC grinder and its operation direction (shared with a conventional example). , Fig. 3 is an explanatory view of the axis coordinate system of a 5-axis NC grinder (shared with the conventional example),
FIG. 4 is a diagram expressing the joint around of the mechanism by the DH notation (shared with the conventional example), FIG. 5 is a parameter characteristic diagram, and FIG. 6 is an explanatory diagram showing a detailed flow of the machine difference derivation plan. The same reference numerals are used for the elements common to the conventional machine difference deriving method shown in FIG. As shown in FIG. 1, the machine-difference deriving method according to the present embodiment is modeled by using the DH notation in which a mechanism in which a machining tool is attached to the tip is represented by various parameters (S
1 '), the position / orientation of the machining tool when the mechanism is operated is measured (S2'), and the position / orientation of the machining tool when the mechanism is operated is estimated using a model (S).
3 '), which is similar to the conventional example in that the machine difference of the mechanism is derived by comparing the measured value r of the position / orientation of the machining tool with the estimated value r'. However, in this embodiment, only parameters for changing the coordinates of the drive shaft of the mechanism are used in the model, and the drive shaft is used when estimating the position / orientation of the machining tool using the model. Transformation calculation (S3
This is different from the conventional example in that a '), a coordinate conversion calculation (S3b') by a translation parameter for translating the drive shaft, and an inverse conversion calculation (S3c ') by a rotation parameter by the rotation parameter are sequentially executed.

The basic principle of this method will be described below by taking a 5-axis NC grinder similar to the conventional example as an example. First, as shown in FIG. 2, the 5-axis NC grinder has A-axis, X-axis, Y-axis,
It is composed of a Z-axis and a C-axis. FIG. 3 shows the coordinate system of each axis. In the figure, the A axis and the C axis are the rotation axis, the X axis,
The Y axis and the Z axis are linear axes. As described above, according to the general DH notation, the relationship between adjacent axes can be expressed by four parameters. When deriving the geometrical error, it is necessary to separate the command value of the axis and the offset amount of the encoder. Therefore, the inter-link distance d _i , the inter-link angle θ _i , the link length a _i , and the twist angle α _i 4 geometrical error parameters and one axis drive parameter such as the joint angle j _i (FIG. 4 (a),
(See (b)). In such a linear motion axis modeling, since the coordinate system after the linear motion axis is simply moved in parallel, the origin of the linear motion axis can be set at an arbitrary position. Generally, it is set so that it coincides with the coordinate origin of the adjacent axis.
However, when the linear motion axis is modeled by four error parameters when deriving the error, the derived equation cannot be uniquely solved because the position of the coordinate origin can be arbitrarily set, and such modeling is not preferable. The above points are as described above. Therefore, in FIG. 4 (c), the coordinate axis origin position of the linear motion axis may be anywhere, and in the case of the figure, d _i = a _i = 0, which is often convenient for calculation. . In the present invention, since the purpose is to derive the parameters, on the contrary, it is necessary to omit such parameters during modeling. In other words, the linear motion axis parameters that have a factor that changes the origin position are omitted and not considered. Therefore, the parameter a
For the _i-1 and the encoder offset amount [Delta] d _i, not treated as a parameter that changes in order to derive the instrumental error. That is, when deriving the machine difference, the two geometrical parameters representing the translational component of the origin are redundant in the modeling of the linear motion axis and are not considered. When modeling is performed according to the above description, the linear motion axis has two rotation parameters θ _i−1 , α that determine the parallel movement direction of the axis.
_It can be expressed by _i-1 (corresponding to the parameter that changes the coordinate of the drive axis). However, since the axis drive parameter j _i is a fixed value at a certain measurement and is invariable in the process of deriving the machine difference, it is included in the model as a constant at the time of the measurement. Next, modeling will be described.

The model notation in the DH notation is expressed by the product of coordinate homogeneous transformation matrices corresponding to the respective parameters. Here, considering the physical function of the linear motion axis, it is only a parallel movement, and should not affect the posture of any link attached to its tip. When the parameter expression by the DH notation is performed, the position / orientation of the tip of the machining tool changes when the rotation parameter that determines the moving direction of the linear motion axis is changed. On the contrary, in order to maintain the position and orientation of the tip even if the rotation parameters of the linear motion axis are changed, all parameters after the linear motion axis must be changed. Thus, the more one parameter affects the other, the worse the convergence in deriving the error. Therefore, in the present invention, a rotational coordinate transformation S (corresponding to coordinate transformation by a rotation parameter) that determines the moving direction of the linear axis, and a coordinate transformation T that translates by the command value of the linear axis.
After performing (corresponding to coordinate conversion by translation parameter),
By multiplying the inverse matrix S ⁻¹ of the rotational coordinate transformation described above (corresponding to the inverse transformation of the coordinate transformation based on the rotation parameter), the influence of the parameter change on the linear axis is prevented from propagating to the subsequent parameters.

That is, D- of an NC grinder as shown in FIG.
The coordinate system of the mechanical model using the H notation is expressed by the following coordinate conversion determinant.

[Equation 1] Here, the A, X, Y, Z, and C axes are sequentially numbered as 0 to 4, 5 is a coordinate system of a grindstone (processing tool), and w is a work coordinate system. Further, ^w Σ ₀ is the A-axis coordinate system viewed from the work coordinate system, ⁰ Σ ₁ is the X coordinate system viewed from the A coordinate system, ¹ Σ ₂ is the Y axis coordinate system viewed from the X coordinate system, ..., ⁴ Σ ₅ is a grindstone coordinate system viewed from the C coordinate system. The rotation coordinate conversion S is Ro around the X axis.
Rotz around tx and Z axis, translational coordinate conversion T is Tr
The inverse transformation S ^{−1 in} ans is represented by making the parameter negative, and the parameters are represented by P1 to P18. After all, ^W Σ ₅ = ^W Σ ₀ · ⁰ Σ ₁ · ¹ Σ ₂ · ² Σ
_{^{3 · 3 Σ 4 · 4 Σ}} 5 is grindstone coordinate system as viewed from the workpiece coordinate system. Next, the convergence calculation will be described. To actually derive the machine difference parameter, combine the command values of the n axes.

[Equation 2] With respect to the position and orientation of the tip processing tool

[Equation 3] To measure. For the actually measured position vector ri,
The difference Δri = ri-ri ′ between the geometrical parameter and the position vector ri ′ calculated from the command value qi of the axis is the error at the tip of the machining tool. This error is caused by the error in the parameters of the geometrical mechanism. The given or estimated geometrical parameter, the error of the true geometrical parameter, and the error of the machining tool tip are calculated using the Jacobian matrix J _i (i = 1, 2, ...) It can be expressed by a relational expression.

[Equation 4] When there are n measurement points, the following equations can be created by arranging the above equations in order from i = 1 to n.

[Equation 5]

By multiplying both sides by the transposed matrix of the Jacobian matrix J _i , the parameter error can be calculated as follows using the nonlinear least squares method.

[Equation 6] If the parameter error ΔP can be derived, P + ΔP is updated as a new geometric parameter,

[Equation 7] Perform convergence calculation until. That is,

[Equation 8] Next, parameter separation will be described. In fact, when deriving the geometrical error parameter by the convergence calculation, the smaller the number of columns and rows of the Jacobian matrix J, the faster the calculation speed. In addition, the amount of calculation is small, and the truncation errors that occur during calculation are less likely to accumulate, improving the calculation accuracy. For this reason, it is effective to divide the parameters into several properties and perform the convergence calculation.
Considering the tip of the processing tool, the rotation parameter affects only the position and orientation, and the translation parameter affects only the position. From this, it is general to obtain the rotation parameter from the posture information and the translation parameter from the position information. In the case of the present embodiment, the rotation parameter relating to the linear motion axis can be obtained from the translational movement direction itself of the linear motion axis, and the parameters can be grouped to improve the calculation accuracy and the calculation speed. Specifically, the parameters represented by Expression 1 can be separated as shown in FIG. The detailed flow of this calculation is shown in FIG. By using such a method, it is possible to quickly and accurately derive the machine difference. In other words, in a robot including a linear motion axis, an NC machine tool, etc., geometrical error parameters can be uniquely separated, and parameter separation can be performed so as not to affect the error derivation. The convergence of calculation and the accuracy of derivation of machine differences are improved. For this reason, the absolute positioning accuracy is finally improved, which can lead to FA and FMS of the line.

[0011]

Since the machine difference deriving method according to the present invention is configured as described above, in a robot including a linear motion axis, an NC machine tool, etc., a geometrical error parameter is uniquely derived and the error is derived. The parameters can be separated so that they do not affect each other. This improves the convergence of the machine difference derivation calculation and the machine difference derivation accuracy,
Ultimately, the absolute positioning accuracy is improved, which can lead to FA and FMS of the line.

[Brief description of drawings]

FIG. 1 is an explanatory diagram showing a schematic flow of a machine difference deriving method according to an embodiment of the present invention.

FIG. 2 is an explanatory view showing the outer appearance of a 5-axis NC grinding machine and its operating direction.

FIG. 3 is an explanatory diagram of an axial coordinate system of a 5-axis NC grinder.

FIG. 4 is a diagram expressing a joint around a mechanism by a DH notation.

FIG. 5 is a parameter characteristic diagram.

FIG. 6 is an explanatory diagram showing a detailed flow of a machine difference derivation plan.

FIG. 7 is an explanatory diagram showing a schematic flow in an example of a conventional machine difference deriving method.

[Explanation of symbols]

r (ri) ... Measured value of machining tool position / orientation r '(ri') ... Estimation of machining tool position / orientation S ... Rotation coordinate conversion (corresponding to coordinate conversion by rotation parameter) T ... Translation coordinate conversion (translation) Corresponding to coordinate conversion by parameter) S ^-1 ... Inverse conversion (corresponding to inverse conversion of coordinate conversion by rotation parameter)

─────────────────────────────────────────────────── ─── Continuation of front page (51) Int.Cl. ⁶ Identification code Internal reference number FI technical display location G05B 19/18 // B25J 17/02 8611-3F G05B 13/04 9131-3H

Claims (2)

[Claims] 1. A mechanism in which a machining tool is attached to the tip is modeled using the notation of Denabit-Hartenberg, which represents various parameters, and the position and orientation of the machining tool when the mechanism is operated are measured, A machine for deriving the machine difference of the mechanism by estimating the position / orientation of the machining tool when the tool is operated using the model, and comparing the measured value of the position / orientation of the machining tool with the estimated value. In the difference deriving method, the machine difference deriving method is characterized in that only parameters for changing the coordinates of the drive shaft of the mechanism are used in the model. 2. A mechanism in which a machining tool is attached to the tip is modeled using the notation of Denabit-Hartenberg, which represents various parameters, and the position and orientation of the machining tool when the mechanism is operated are measured, A machine for deriving the machine difference of the mechanism by estimating the position / orientation of the machining tool when the tool is operated using the model, and comparing the measured value of the position / orientation of the machining tool with the estimated value. In the difference deriving method, only parameters that change the coordinates of the drive axis of the mechanism are used in the model, and
When estimating the position / orientation of the machining tool using the model, coordinate conversion calculation by a rotation parameter for orienting the drive axis, coordinate conversion calculation by a translation parameter for translating the drive axis, and coordinate by the rotation parameter A method of deriving a machine difference, characterized in that an inverse transformation operation of transformation is sequentially executed.