Elastic deformation compensation control device for articulated robot

Abstract

This control device (10) for compensating for the elastic deformation of an articulated robot is configured from a joint angle command value calculation unit (100), an axial force torque calculation unit (200), a first dynamic characteristic computing unit (300), a feedback control unit (500), and a motor angle command value calculation unit (600). The first dynamic characteristic computing unit (300) is configured from an interpolation unit configured from an N-ary curve interpolation, and a filter unit configured from an M-ary filter, with N+M being at least 4.

Claims

1. An elastic deformation compensation control device for an articulated robot, the articulated robot including a motor for driving a plurality of joint shafts of the articulated robot and an arm connected to the motor via a speed reducer that elastically deforms, the device driving the joint shafts to cause a tool attached to the articulated robot to perform a desired operation, the device comprising: a joint angle command value calculation unit configured to calculate a joint angle command value lc of each of the joint shafts for realizing a desired tool operation and output the joint angle command value lc; an axial force torque calculation unit configured to calculate an axial force torque fc that is generated when each of the joint shafts operates as instructed by the joint angle command value lc and that is exerted on the joint shaft from the joint angle command value lc on the basis of a kinetic model and output the axial force torque fc; a motor angle command value calculation unit configured to calculate a motor angle command value mc from the joint angle command value lc and the axial force torque fc on the basis of a parameter of the joint shaft including a rigidity parameter and output the motor angle command value mc; a first dynamic characteristic computing unit having a high-frequency cutoff characteristic including a cutoff frequency that is lower than the natural vibration frequency of the robot, the first dynamic characteristic computing unit performing a filtering process on the motor angle command value mc and outputting the motor angle target value md subjected to the filtering process; a motor angle control unit configured to receive the motor angle target value md as a target value for the motor; and a motor current control unit configured to receive, as a target value, a value obtained by adding the axial force torque compensation value fd to a motor torque command value output from the motor angle control unit, wherein the first dynamic characteristic computing unit is configured from an interpolation unit configured by Nth-degree curve interpolation and a filter unit configured by an Mth-order filter, and (N+M) is set to a value greater than or equal to 4.

2. The elastic deformation compensation control device for an articulated robot according to claim 1, wherein the Mth-order filter that constitutes the filter unit is given by the following expression (1): $\begin{array}{cc}\left[\mathrm{Formula}1\right]& \\ \frac{a_0.Math.s^0}{b_M.Math.s^M+b_{M-1}.Math.s^{M-1}+\mathrm{.Math.}+b_1.Math.s^1+b_0.Math.s^0}.& \left(1\right)\end{array}$

3. The elastic deformation compensation control device for an articulated robot according to claim 1, wherein the Mth-order filter that constitutes the filter unit is given by the following expression (2): $\begin{array}{cc}\left[\mathrm{Formula}2\right]& \\ \frac{a_p.Math.s^p+a_{p-1}.Math.s^{p-1}+\mathrm{.Math.}+a_1.Math.s^1+a_0.Math.s^0}{b_{M+p}.Math.s^{M+p}+b_{M+p-1}.Math.s^{M+p-1}+\mathrm{.Math.}+b_1.Math.s^1+b_0.Math.s^0}.& \left(2\right)\end{array}$

4. The elastic deformation compensation control device for an articulated robot according to claim 1, wherein an (M1)th derivative value of a waveform of a step response of the Mth-order filter that constitutes the filter unit is continuous.

5. The elastic deformation compensation control device for an articulated robot according to claim 1, wherein an (M2)th derivative value of a waveform of an impulse response of an Mth-order filter that constitutes the filter unit is continuous.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) FIG. 1 is a block diagram of dynamic characteristics (1) of an elastic deformation compensation control device according to an embodiment of the present invention.

(2) FIG. 2A illustrates the result of control (the operations in the X-axis and Z-axis directions) performed by the dynamic characteristics (1) configured using a technique according to the embodiment (N=4, M=0).

(3) FIG. 2B illustrates the result of control (an enlarged view of the operation in the Z-axis direction) performed by the dynamic characteristics (1) configured using a technique according to the embodiment (N=4, M=0).

(4) FIG. 3A illustrates the result of control (the operations in the X-axis and Z-axis directions) performed by the dynamic characteristics (1) configured using a technique according to the embodiment (N=5, M=0).

(5) FIG. 3B illustrates the result of control (an enlarged view of the operation in the Z-axis direction) performed by the dynamic characteristics (1) configured using a technique according to the embodiment (N=5, M=0).

(6) FIG. 4A illustrates the result of control (the operations in the X-axis and Z-axis directions) performed by the dynamic characteristics (1) configured using a technique according to the embodiment (N=3, M=1).

(7) FIG. 4B illustrates the result of control (an enlarged view of the operation in the Z-axis direction) performed by the dynamic characteristics (1) configured using a technique according to the embodiment (N=3, M=1).

(8) FIG. 5A illustrates the result of control (the operations in the X-axis and Z-axis directions) performed by the dynamic characteristics (1) configured using a technique according to the embodiment (N=2, M=2).

(9) FIG. 5B illustrates the result of control (an enlarged view of the operation in the Z-axis direction) performed by the dynamic characteristics (1) configured using a technique according to the embodiment (N=2, M=2).

(10) FIG. 6A illustrates the result of control (the operations in the X-axis and Z-axis directions) performed by the dynamic characteristics (1) configured using a technique according to the embodiment (N=1, M=3).

(11) FIG. 6B illustrates the result of control (an enlarged view of the operation in the Z-axis direction) performed by the dynamic characteristics (1) configured using a technique according to the embodiment (N=1, M=3).

(12) FIG. 7A illustrates the result of control (the operations in the X-axis and Z-axis directions) performed by the dynamic characteristics (1) configured using a technique according to the embodiment (N=0, M=4).

(13) FIG. 7B illustrates the result of control (an enlarged view of the operation in the Z-axis direction) performed by the dynamic characteristics (1) configured using a technique according to the embodiment (N=0, M=4).

(14) FIG. 8A illustrates the step response of a first-order filter.

(15) FIG. 8B illustrates the first derivative value of the step response of a first-order filter.

(16) FIG. 9A illustrates the moving average weight of a moving average filter corresponding to a first order.

(17) FIG. 9B illustrates the step response of a moving average filter corresponding to a first order.

(18) FIG. 9C illustrates the first derivative value of the step response of the moving average filter corresponding to a first order.

(19) FIG. 10A illustrates the result of control (the operations in the X-axis and Z-axis directions) performed using third-degree interpolation and a moving average filter corresponding to a first order.

(20) FIG. 10B illustrates the result of control (an enlarged view of the operation in the Z-axis direction) performed using third-degree interpolation and a moving average filter corresponding to a first order.

(21) FIG. 11A illustrates the moving average weight of a moving average filter corresponding to a second order.

(22) FIG. 11B illustrates the step response of a moving average filter corresponding to a second order.

(23) FIG. 11C illustrates the first derivative value of the step response of the moving average filter corresponding to a second order.

(24) FIG. 11D illustrates the second derivative value of the step response of the moving average filter corresponding to a second order.

(25) FIG. 12A illustrates the moving average weight of a moving average filter corresponding to a third order.

(26) FIG. 12B illustrates the step response of a moving average filter corresponding to a third order.

(27) FIG. 12C illustrates the first derivative value of the step response of the moving average filter corresponding to a third order.

(28) FIG. 12D illustrates the second derivative value of the step response of the moving average filter corresponding to a third order.

(29) FIG. 12E illustrates the third derivative value of the step response of the moving average filter corresponding to a third order.

(30) FIG. 13 is a block diagram of an elastic deformation compensation control device to which the dynamic characteristics (1) according to the embodiment is applied.

(31) FIG. 14A illustrates the result of control (the operations in the X-axis and Z-axis directions) performed by the dynamic characteristics (1) configured using an existing technique (the zeroth-order hold).

(32) FIG. 14B illustrates the result of control (the operations in the X-axis and Z-axis directions) performed by the dynamic characteristics (1) configured using an existing technique (the first-degree interpolation).

(33) FIG. 14C illustrates the result of control (the operations in the X-axis and Z-axis directions) performed by the dynamic characteristics (1) configured using an existing technique (the second-degree interpolation).

(34) FIG. 14D illustrates the result of control (the operations in the X-axis and Z-axis directions) performed by the dynamic characteristics (1) configured using an existing technique (the third-degree interpolation).

(35) FIG. 14E illustrates the result of control (an enlarged view of the operation in the Z-axis direction) performed by the dynamic characteristics (1) configured using an existing technique (the third-degree interpolation).

(36) FIG. 15 is a block diagram of another elastic deformation compensation control device to which the dynamic characteristics (1) according to the embodiment is applied.

(37) FIG. 16 is a schematic illustration of the architecture of an articulated robot having the elastic deformation compensation control device applied thereto.

(38) FIG. 17 illustrates Nth-degree interpolation.

DESCRIPTION OF EMBODIMENTS

(39) An elastic deformation compensation control device for an articulated robot according to an embodiment of the present invention is described in detail below with reference to the accompanying drawings. Note that in the description below, the same reference symbol is used to indicate elements which are the same. The name and the functions of the elements are also the same. Accordingly, detailed description of the element is not repeated. In addition, while description below is made with reference to an articulated robot that causes the welding torch serving as an object to be controlled to perform a tilting operation (a weaving operation), the welding torch is only an example. The elastic deformation compensation control device according to the present invention is widely applicable to control of driving of a plurality of joint shafts of an articulated robot including a motor that drives the joint shaft and an arm connected to the motor via the speed reducer that elastically deforms so that a tool attached to the articulated robot performs a desired operation.

Basic Embodiment

(40) A vertical articulated robot (hereinafter also simply referred to as an articulated robot) having the elastic deformation compensation control device according to the embodiment is schematically described first.

(41) FIG. 16 is a schematic illustration of an articulated robot 1 having an elastic deformation compensation control device of the present embodiment applied thereto. The articulated robot 1 is an example of a robot that causes a welding torch to perform a tilting operation (a weaving operation). The articulated robot 1 is a vertical articulated robot and has six joints, that is, joints S1 to S6. The welding torch is attached to the top end of an S6 shaft. Arc welding is executed by a welding wire fed out from the welding torch. The articulated robot 1 is set so as to perform an operation to move in a weld work zone between a predetermined weld start point and a predetermined weld end point in a weld line direction extending from the weld start point to the weld end point and simultaneously tilt the welding wire with a predetermined amplitude and at a predetermined frequency (a weaving operation).

(42) In addition to the body of the articulated robot 1 that is illustrated, the articulated robot 1 includes a control unit (a servo control unit) that has a teach pendant and that servo-controls each of the shafts (not illustrated) and a higher-layer computer (a higher-layer CPU) (not illustrated). The elastic deformation compensation control device according to the present exemplary embodiment is formed by the control unit and the higher-layer computer.

(43) The control unit (the servo control unit) performs control so that the welding torch mounted in the articulated robot 1 moves and performs a weaving operation following the above-described weld line in accordance with a pre-taught program. The teaching program can be generated using a teach pendant connected to the control unit. Alternatively, the teaching program can be generated using an off-line teach system using the higher-layer computer. In either case, the teaching program is pre-generated before an actual operation is performed.

(44) The higher-layer computer generates a weld path or a weaving operation command based on the generated weld path.

(45) FIG. 13 is a block diagram of the control performed by the elastic deformation compensation control device 10 that controls the articulated robot 1 illustrated in FIG. 16. As described above, the elastic deformation compensation control device 10 is configured so as to include a portion realized by the higher-layer CPU and a portion realized by the servo control unit.

(46) The elastic deformation compensation control device 10 drives a plurality of joint shafts so as to cause a tool (the welding torch in the present embodiment) attached to the articulated robot 1 to perform a desired operation (e.g., a weaving operation).

(47) The elastic deformation compensation control device 10 is formed from a joint angle command value calculation unit 100, an axial force torque calculation unit (illustrated as axial force FF) 200, and a motor angle command value calculation unit (illustrated as elastic deformation compensation) 600, each realized by the higher-layer CPU. The elastic deformation compensation control device 10 is further formed from a first dynamic characteristic computing unit (illustrated as dynamic characteristics (1)) 300, a second dynamic characteristic computing unit (illustrated as dynamic characteristics (2)) 400, and a feedback control unit (illustrated as servo control FB characteristics) 500, each realized by the servo control unit. The feedback control unit 500 is configured so as to include a motor angle control unit 510 and a motor current control unit (illustrated as current control) 520. Note that the characteristics of all the element of the control block are dynamic characteristics (even when not stated as dynamic characteristics). In addition, FB stands for feedback, and FF stands for feedforward.

(48) The joint angle command value calculation unit 100 calculates a joint angle command value lc of each of the joint shafts for realizing a weaving operation performed by the welding torch and outputs the joint angle command value lc.

(49) The axial force torque calculation unit 200 calculates an axial force torque fc that is to be exerted on each of the joint shafts and that is generated when the joint shaft operates as instructed by the joint angle command value lc output from the joint angle command value calculation unit 100 using the joint angle command value lc on the basis of a kinetic model. Thereafter, the axial force torque calculation unit 200 outputs the calculated axial force torque fc.

(50) The motor angle command value calculation unit 600 calculates a motor angle command value mc from the joint angle command value lc and the axial force torque fc on the basis of a parameter including a rigidity parameter of the joint shaft and outputs the calculated motor angle command value mc.

(51) More specifically, the axial force torque calculation unit 200 calculates the axial force torque fc to be exerted on each of the joint shafts when the joint shaft operates as instructed by the joint angle command value lc on the basis of the joint angle command value lc. The motor angle command value calculation unit 600 calculates the amount of elastic deformation ec from the axial force torque fc on the basis of a shaft rigidity K and a viscosity B (the viscosity is negligible since the viscosity is small) and, thereafter, calculates the motor angle command value mc from the joint angle command value lc and the elastic deformation ec.

(52) The first dynamic characteristic computing unit 300 performs a filtering process on the motor angle command value mc output from the motor angle command value calculation unit 600 and outputs a motor angle target value md subjected to the filtering process. The first dynamic characteristic computing unit 300 has a high-frequency cutoff characteristic so as to have a cutoff frequency that is lower than the natural vibration frequency of the articulated robot 1.

(53) The second dynamic characteristic computing unit 400 performs a filtering process on at least one of the input to the axial force torque calculation unit 200 and the output from the axial force torque calculation unit 200 and outputs an axial force torque compensation value fd subjected to the filtering process. In FIG. 13, the second dynamic characteristic computing unit 400 performs a filtering process on the output from the axial force torque calculation unit 200. The second dynamic characteristic computing unit 400 has a high-frequency cutoff characteristic so as to have a cutoff frequency that is lower than or equal to the cutoff frequency of the first dynamic characteristic computing unit 300.

(54) Note that the first dynamic characteristic computing unit 300 and the second dynamic characteristic computing unit 400 may have the same characteristics. If the first dynamic characteristic computing unit 300 and the second dynamic characteristic computing unit 400 have the same characteristics, the first dynamic characteristic computing unit 300 is equivalent to the elastic deformation compensation control device disposed on the output side of the joint angle command value calculation unit 100. The technique of the present invention (described in detail below) is applicable to even such an elastic deformation compensation control device.

(55) The motor angle target value md is input to the motor angle control unit 510 as a target value for the motor. The motor angle control unit 510 has speed feedforward control and/or acceleration feedforward control. Gda and Gdv indicate an acceleration feedforward gain and a speed feedforward gain, respectively. Each of Gda and Gdv is in the range from 0 to 1.

(56) A value obtained by adding the axial force torque compensation value fd output from the second dynamic characteristic computing unit 400 to the motor torque command value output from the motor angle control unit 510 is input to the motor current control unit 520 as a target value.

(57) The elastic deformation compensation control device 10 illustrated in the block diagram of FIG. 13 has the following features.

(58) That is, the second dynamic characteristic computing unit 400, which serves as a non-linear term, is disposed on the upstream and/or downstream of the axial force torque calculation unit 200 (only on the downstream in this example). The second dynamic characteristic computing unit 400 has a high-frequency cutoff characteristic that cuts off a high-frequency band higher than or equal to that of the first dynamic characteristic computing unit 300. That is, the cutoff frequency of the second dynamic characteristic computing unit 400 is lower than or equal to the cutoff frequency of the first dynamic characteristic computing unit 300.

(59) According to such a configuration, a high frequency including a natural vibration component contained in the joint angle command value lc can be prevented by the first dynamic characteristic computing unit 300. In addition, a high frequency including the natural vibration component contained in the axial force torque fc can be prevented by the second dynamic characteristic computing unit 400. In this manner, a high-frequency vibration occurring in the articulated robot 1 can be prevented.

(60) In addition, even when the articulated robot 1 is operated in the XYZ space at a low frequency, a high frequency that turns into double or triple high-frequency component of a joint angle is generated at a position at which Jacobian abruptly changes (e.g., in the vicinity of a singular point). Furthermore, even when the articulated robot 1 is operated in a joint angle space at low frequency, a high frequency that is a double or triple component of the joint angle is generated, since the non-linear term includes a squared term of the speed. Accordingly, by processing the axial force torque fc, which is a non-linear term output from the axial force torque calculation unit 200, using the second dynamic characteristic computing unit 400 having the high-frequency cutoff characteristic higher than or equal to the high-frequency cutoff characteristic of the first dynamic characteristic computing unit 300 and by using the resultant value as the axial force torque compensation value fd, high-frequency vibration occurring in the articulated robot 1 is further reduced.

First Embodiment

(61) By using the elastic deformation compensation control device 10 described above, the articulated robot 1 can compensate for the adverse effect of elastic deformation of each of the shafts and perform an operation, such as weaving, with high accuracy of trajectory. However, the present inventors discovered that vibration of the top end of the welding torch occurs if the elastic deformation compensation and the feedforward control are performed without appropriate design of the dynamic characteristics (1) provided in the elastic deformation compensation control device 10 illustrated in the block diagram of FIG. 13, that is, without appropriate design of the first dynamic characteristic computing unit 300. The same situation occurs even when the first dynamic characteristic computing unit 300 is disposed on the input side of the axial force torque calculation unit 200. In addition, the same situation occurs even when the first dynamic characteristic computing unit 300 separates into two dynamic characteristic portions and, thereafter, one of the dynamic characteristic portions is disposed at the position of the first dynamic characteristic computing unit 300 illustrated in FIG. 13 and the other is disposed on the input side of the axial force torque calculation unit 200.

(62) To address such an issue, the applicants for the present application configure the first dynamic characteristic computing unit 300 from an interpolating unit 301 that interpolates a rough trajectory (a control trajectory) of the welding tool calculated by the higher-layer CPU with a finer scale and a filter unit 302 that performs filtering on the output of the interpolating unit 301, as illustrated in FIG. 1. The interpolating unit 301 employs Nth-degree curve interpolation, and the filter unit 302 employs an Mth-order filter.

(63) The term Nth-degree curve interpolation performed by the interpolating unit 301 refers to interpolation performed between two adjacent points of a point sequence obtained from a coarse sampling using an Nth-degree function (curve). The most widely used Nth-degree curve interpolation is zeroth-order hold, where N=0, and a first-degree interpolation, where N=1. Second-degree or higher interpolation can be performed using, for example, a technique described in Japanese Patent No. 4119011. FIG. 17 illustrates an example of fifth-degree interpolation.

(64) Despite the above description, the present inventor discovered that as illustrated in FIGS. 14A to 14E, vibration of the top end of the welding torch (in particular, vibration in the Z direction) occurs unless the number N for the Nth-degree curve and the number M for the Mth-order filter are appropriate. Accordingly, the present inventors made further study on the basis of the discovery.

(65) As a result, the present inventors found that it is desirable that the elastic deformation compensation control device 10 (a control system that performs position control using elastic deformation compensation) include the first dynamic characteristic computing unit 300 formed from the interpolating unit 301 configured by Nth-degree curve interpolation and the filter unit 302 configured by an Mth-order filter and, in addition, (N+M) be greater than or equal to 4. In this manner, the occurrences of the vibration of the top end of the welding torch illustrated in FIGS. 14A to 14E can be prevented. Thus, the adverse effect of the elastic deformation of each of the shafts can be compensated for, and an operation such as weaving can be performed with high accuracy of trajectory.

(66) It is desirable that a filter applied to the filter unit 302 be a filter given by the following expression (1):

(67) $\begin{array}{cc}\left[\mathrm{Formula}3\right]& \\ \frac{a_0.Math.s^0}{b_M.Math.s^M+b_{M-1}.Math.s^{M-1}+\mathrm{.Math.}+b_1.Math.s^1+b_0.Math.s^0}& \left(1\right)\end{array}$

(68) In addition, an Mth-order filter given by the following expression (2) having a difference in the order between the denominator and the numerator is M may be employed:

(69) $\begin{array}{cc}\left[\mathrm{Formula}4\right]& \\ \frac{a_p.Math.s^p+a_{p-1}.Math.s^{p-1}+\mathrm{.Math.}+a_1.Math.s^1+a_0.Math.s^0}{b_{M+p}.Math.s^{M+p}+b_{M+p-1}.Math.s^{M+p-1}+\mathrm{.Math.}+b_1.Math.s^1+b_0.Math.s^0}& \left(2\right)\end{array}$

(70) FIG. 2A to FIG. 7B illustrate the result of control using the first dynamic characteristic computing unit 300 configured from the interpolating unit 301 configured by Nth-degree curve interpolation and the filter unit 302 configured by an Mth-order filter (where, N+M4).

(71) FIGS. 2A and 2B illustrate the result of control using the first dynamic characteristic computing unit 300 configured from only the interpolating unit 301 configured by fourth-degree curve interpolation. As illustrated in FIGS. 14A to 14E, in the existing technique, when a welding torch is moved in the Z direction by 310.sup.3 m, vibration with a significantly large amplitude of 2010.sup.3 m is generated in the Z direction. However, by performing fourth-degree curve interpolation using the interpolating unit 301, the amplitude of the vibration can be decreased to a value less than or equal to 110.sup.5 m in the Z direction, as illustrated in FIG. 2B.

(72) FIGS. 3A and 3B illustrate the result of control using the first dynamic characteristic computing unit 300 configured from only the interpolating unit 301 configured by fifth-degree curve interpolation. Even in such a case, the amplitude of the vibration can be decreased to a value less than or equal to 110.sup.5 m in the Z direction.

(73) FIGS. 4A and 4B illustrate the result of control using the first dynamic characteristic computing unit 300 configured from the interpolating unit 301 configured by third-degree curve interpolation and the filter unit 302 that employs a first-order filter. Even in such a case, the amplitude of the vibration can be decreased to a value less than or equal to 110.sup.5 m in the Z direction.

(74) FIGS. 5A and 5B illustrate the result of control using the first dynamic characteristic computing unit 300 configured from the interpolating unit 301 configured by second-degree curve interpolation and the filter unit 302 that employs a second-order filter. Even in such a case, the amplitude of the vibration can be decreased to a value less than or equal to 110.sup.5 m in the Z direction.

(75) FIGS. 6A and 6B illustrate the result of control using the first dynamic characteristic computing unit 300 configured from the interpolating unit 301 configured by first-degree curve interpolation and the filter unit 302 that employs a third-order filter. Even in such a case, the amplitude of the vibration can be decreased to a value less than or equal to 110.sup.5 m in the Z direction.

(76) FIGS. 7A and 7B illustrate the result of control using the first dynamic characteristic computing unit 300 configured from only the filter unit 302 configured by a fourth-order filter. In such a case, the amplitude of the vibration is about 110.sup.5 m in the Z direction. The results illustrated in FIGS. 7A and 7B are slightly inferior to the results illustrated in FIG. 2A to FIG. 6B, but the amplitude of the vibration is apparently smaller than the results due to the existing technique illustrated in FIGS. 12A to 12E.

(77) As described above, by configuring the first dynamic characteristic computing unit 300 from the interpolating unit 301 configured by the Nth-degree curve interpolation and the filter unit 302 configured by the Mth-order filter and setting (N+M) to a value greater than or equal to 4, vibration of the top end of the welding torch illustrated in FIGS. 14A to 14E can be reliably prevented and, thus, the adverse effect of the elastic deformation of each of the shafts can be compensated for, and an operation such as weaving can be performed with high accuracy of trajectory.

Second Embodiment

(78) Note that the waveform of the Mth-order filter applied to the filter unit 302 may have a continuous (M1)th derivative value in terms of a waveform of a step response of the Mth-order filter. In contrast, the waveform of the Mth-order filter applied to the filter unit 302 may have a continuous (M2)th derivative value in terms of a waveform of an impulse response of the Mth-order filter.

(79) That is, while the first embodiment above has been described with reference to the Mth-order filter (expression (1)) that can be expressed as the transfer function of continuous time, the Mth-order filter can be approximated by a moving average filter if the Mth-order filter is subjected to impulse response approximation. In addition, if the Mth-order filter can be expressed in the form of a fraction, the difference in the order between the denominator and the numerator is M. Thus, a derivative value up to the (M1)th derivative value of a step response is continuous, and the Mth derivative value is non-continuous. That is, a variety of filters including a moving average filter have characteristic that is the same as the Mth-order filter due to the above-described characteristics. A filter having continuous derivative value up to the (M1)th derivative value of step response can be equivalent to the Mth-order filter. Such an equivalent filter can be employed for the filter unit 302 that provides the operation and effect that are substantially the same as those of the first embodiment.

(80) FIGS. 8A and 8B, FIGS. 9A and 9B, FIGS. 11A to 11D, and FIGS. 12A to 12E illustrate the waveforms of the filters applied to the filter unit 302 according to the second embodiment.

(81) FIGS. 8A and 8B relate to the first-order filter according to the first embodiment. A graph in FIG. 8A illustrates the waveform of a step response of the first-order filter. Although the waveform is continuous, the waveform of the first derivative value of the step response waveform is non-continuously changed at a time 0, as illustrated by the graph of FIG. 8B.

(82) FIGS. 9A and 9B illustrate an example of a moving average filter corresponding to the first order. Since N1=0, the (N1)th derivative value of a step response, that is, even a step response itself that is not differentiated is continuous, and the Nth derivative value, that is, the first derivative value is non-continuous.

(83) FIGS. 10A and 10B illustrate the result of control when the moving average filter illustrated in FIGS. 9A and 9B is applied to the filter unit 302 and third-degree interpolation is applied to the interpolating unit 301.

(84) As illustrated in FIG. 10B, by using such a first dynamic characteristic computing unit 300, the amplitude of vibration in the Z direction can be decreased to a value less than or equal to 110.sup.5 m.

(85) In addition, FIGS. 11A to 11D illustrate an example of a moving average filter corresponding to the second order. A derivative value up to the (N1 (=1))th derivative value of a step response is continuous, and the N (=2)th derivative value is non-continuous. By applying the moving average filter illustrated in FIGS. 11A to 11D to the filter unit 302 and applying second-degree interpolation to the interpolating unit 301, vibration can be prevented as in FIGS. 10A and 10B.

(86) FIG. 12A to FIG. 12E illustrate an example of a moving average filter corresponding to the third order. A derivative value up to the (N1 (=2))th derivative value of a step response is continuous, and the N (=3)th derivative value is non-continuous. By applying the moving average filter illustrated in FIGS. 12A to 12E to the filter unit 302 and applying first-degree interpolation to the interpolating unit 301, vibration can be prevented as in FIGS. 10A and 10B.

(87) Similarly, even when control is performed by using only the filter unit 302 having the moving average filter corresponding to the fourth order applied thereto after zeroth-order hold, the effect of control that is the same as in FIGS. 10A and 10B can be provided.

(88) Note that in the case of a moving average filter, the weight coincides with an impulse response, and the derivative value of a step response coincides with an impulse response. Accordingly, the (N1)th derivative value of the step response is equivalent to the (N2)th derivative value of the impulse response.

Third Embodiment

(89) The present inventors further studied the elastic deformation compensation control device 10 of the first embodiment (refer to FIG. 13) and discovered the following results.

(90) That is, in the elastic deformation compensation control device 10 illustrated in FIG. 13, if Gda=0, vibration of the top end of the welding torch can be reliably prevented even when the first dynamic characteristic computing unit 300 is configured from the interpolating unit 301 configured by the Nth-degree curve interpolation, where (N+M) is 3 or more, and the filter unit 302 configured by an Mth-order filter. In addition, the adverse effect of the elastic deformation of each of the shafts can be compensated for, and an operation such as weaving can be performed with high accuracy of trajectory.

(91) In particular, the present inventors also discovered that if Gda=Gdv=0, the first dynamic characteristic computing unit 300 can be configured from the interpolating unit 301 configured by the Nth-degree curve interpolation and the filter unit 302 configured by the Mth-order filter, where (N+M) is 2 or more.

(92) That is, if Gda0, (N+M) needs to be greater than or equal to 4. However, if Gda=0, it is only required that (N+M) is 3 or more. If Gda=Gdv=0, it is only required that (N+M) is 2 or more. At that time, the high-frequency cutoff characteristic of the dynamic characteristics (2) needs to be higher than or equal to the high-frequency cutoff characteristic of the dynamic characteristics (1).

(93) As described above, according to the elastic deformation compensation control device 10 of the present invention, the first dynamic characteristic computing unit 300 is configured from the interpolating unit 301 configured by Nth-degree curve interpolation and the filter unit 302 configured by an Mth-order filter, and (N+M) is set to a value greater than 4 or more. In this manner, vibration of the top end of the welding torch can be reliably prevented, and the adverse effect of the elastic deformation of each of the shafts can be compensated for. Thus, an operation such as weaving can be performed with high accuracy of trajectory.

(94) The presently disclosed embodiments should in all respects be considered to be illustrative and not limiting. The scope of the present invention is set forth not by the foregoing description but by the scope of the appended claims, and is intended to include meanings equivalent to the scope of the patent claims and all modifications within the scope of the invention.

(95) For example, the technique of the present invention is applicable to an elastic deformation compensation control device 20 illustrated in FIG. 15 as well. In the elastic deformation compensation control device 20, the motor angle control unit 510 that constitutes the device 20 does not include the speed feedforward control and/or the acceleration feedforward control. By applying the technique of the present invention to the device 20, the operations and effects that are substantially the same as those described in the first to third embodiments can be provided.

(96) This application claims the benefit of Japanese Patent Application No. 2013-027947 filed Feb. 15, 2013, which is hereby incorporated by reference herein in its entirety.

REFERENCE SIGNS LIST

(97) 1 articulated robot 10, 20 elastic deformation compensation control device 100 joint angle command value calculation unit 200 axial force torque calculation unit (axial force FF) 300 first dynamic characteristic computing unit (dynamic characteristics (1)) 400 second dynamic characteristic computing unit (dynamic characteristics (2)) 500 feedback control unit (servo control FB characteristics) 600 motor angle command value calculation unit (elastic deformation compensation) 510 motor angle control unit 520 motor current control unit (current control)