JP2000055664A - Articulated robot system with function of measuring attitude, method and system for certifying measuring precision of gyro by use of turntable for calibration reference, and device and method for calibrating turntable formed of n-axes - Google Patents

Abstract

PROBLEM TO BE SOLVED: To realize a real-time, non-contact, and highly precise attitude measurement free from limitation of measuring range by arranging a piezoelectric rotary gyro at the fingertip of a robot. SOLUTION: An articulated robot system 100 is provided with a piezoelectric element rotary gyro 50 which consists of, for example, two gyro units each consisting of two sets of piezoelectric element-made benders and detects the angular velocity around three axes and acceleration in three axial directions of the fingertip of a robot 10. The detected angle speed is arithmetically processed by a signal processing box 55, whereby the attitude change from the initial attitude can be determined. The static and dynamic precision certification with the assumption of the natural movement of the robot with respect to the gyro 50 is performed, for example, by use of a turntable with three degrees of freedom as calibration reference, and a laser tracking system, for example, is used for the calibration of dimensional error or mounting error of the turntable itself.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an articulated robot system comprising an articulated robot having two or more arms and a shaft rotatably supporting each arm. The present invention relates to an articulated robot system having a measuring function.

[0002] The present invention also relates to a method and a system for verifying the measurement accuracy of a gyro using a turntable as a calibration standard. In particular, the present invention considers a dimensional error of the turntable itself and a mounting error to the table. The present invention relates to a method and a system for verifying measurement accuracy of a gyro.

[0003] The present invention also relates to an apparatus and a method for calibrating a turntable composed of N axes, and more particularly, to an apparatus for verifying measurement accuracy of a gyro.
An apparatus and method for calibrating an axis turntable.

[0004]

2. Description of the Related Art In recent years, automation of production work in a factory
Various types of industrial robots (indust
Research and development of real robots are being actively conducted.

[0005] The basic structure of a robot is a link mechanism connected in series with many degrees of freedom. That is, this is an articulated and multi-degree-of-freedom arm type robot in which a plurality of arms are connected by axes and each axis is driven by a motor. Usually, one end of the arm type robot is fixed to define a base position, and the other end means the tip of the arm. Each joint is provided with an encoder for measuring the rotation angle of the shaft, and the position of the hand can be obtained from the length of each arm and the rotation angle of each shaft by using well-known geometric calculations. it can. A sensor built into the robot, such as an encoder, is called an “internal sensor”. Further, the robot constitutes one system integrally with a control unit “robot controller” for controlling the driving of the motor of each axis.

The following equation (1) is provided between the hand position X (x ₁ , x ₂ , x ₃ ) and the rotation angle Θ (θ ₁ , θ ₂ ,..., Θ _n ) of each axis.
Holds (known). Here, f in the equation is a coordinate conversion matrix.

[0007]

(Equation 1)

A robot controller for controlling the operation of the robot receives a three-dimensional position X (x ₁ ,
x ₂ , x ₃ ), the inverse matrix f ^-1 of the coordinate transformation matrix f
The rotation angle 式 (θ ₁ , θ ₂ ,
.., Θ _n ) are obtained, and each motor is driven in accordance with this.

[0009]

(Equation 2)

However, the above equations (1) and (2) are merely theoretical equations in which the arm and the axis are captured by lines and points, and include errors in the arm length, deflection of the arm and each axis in the reducer, and The mechanism parameters such as assembly accuracy are completely ignored. The mechanism parameter P is usually presented as a nominal value by the device vendor, and the above equation (1) is replaced by, for example, the following equation (3).

[0011]

(Equation 3)

However, the mechanism parameter P is only a nominal value and has a property including an error ΔP. This error ΔP
Naturally leads to an absolute positioning error ΔX with respect to the command value X to the robot system. The following equation (4) is established between the error ΔP of the mechanism parameter and the positioning error ΔX. Here, the matrix J in the following equation is a Jacobian matrix, which is obtained from the coordinate transformation matrix f.

[0013]

(Equation 4)

In general, as a robot becomes more articulated and larger, the absolute positioning accuracy decreases. In order to improve the accuracy, it is essential to evaluate the current position / posture accuracy and accurately measure the error of the mechanism.

Conventionally, it has been general to evaluate the position / posture accuracy of a robot using an "external sensor" placed outside the mechanism of the robot. In this method, markers are provided at several places of the robot, and the movement position of each marker is determined by CCD.
The position is measured by tracking with an external sensor such as a camera or a laser. However, complicated coordinate calculation processing based on the measurement position is required, and depending on the posture of the robot, measurement cannot be performed if the marker is hidden behind or facing the back (that is, the measurement range is limited). With the disadvantages of

In order to evaluate the absolute accuracy of a multi-degree-of-freedom robot, it is essential to measure the position and orientation of the robot's hand in a three-dimensional space in real time, in a non-contact manner, and with high accuracy. There are few examples of satisfactory measurement methods and devices, and it is extremely difficult in practice.

For example, an ISO (Internationa)
l Organization for Standa
9283 includes the characteristics and characteristics of the robot.
Although items for measuring functions are specified,
No actual measurement method or measurement means is disclosed.

As a method of teaching an operation to an industrial robot, an alternative from a teaching / playback method, which requires much time and labor for manual teaching, to an offline teaching method is expected. However, this off-line teaching method is based on the premise that the robot has high absolute position accuracy and posture accuracy. In this sense, it can be said that a method and a method for evaluating the absolute accuracy of the robot are important.

[0019]

An object of the present invention is to provide an articulated robot system comprising an articulated robot comprising at least two arms and a shaft rotatably supporting each arm. An object of the present invention is to provide an excellent articulated robot system having a posture measuring function.

It is a further object of the present invention to provide a method and a system for verifying the measurement accuracy of a gyro using a turntable as a calibration standard, taking into account dimensional errors of the turntable itself and mounting errors to the table. An object of the present invention is to provide an excellent method and system for verifying the measurement accuracy of a gyro.

A further object of the present invention is to provide an apparatus and a method for calibrating a turntable composed of N axes, which can be applied to verification of the measurement accuracy of a gyro.

[0022]

SUMMARY OF THE INVENTION The present invention has been made in consideration of the above problems, and a first aspect of the present invention is to provide an articulated robot system having a function of measuring a posture, comprising: An articulated robot comprising at least two arms and a shaft rotatably supporting between the arms; (b) at least two driving units for rotationally driving the respective axes of the robot; (c)
A piezoelectric element rotary gyro disposed substantially at the tip of the robot, (d) a drive control unit for controlling the drive of each of the drive units according to a command value, and (e) the drive unit driving the robot A measuring unit that measures the posture of the robot according to the output of the piezoelectric element rotating gyro between
This is a multi-joint robot system comprising:

According to a second aspect of the present invention, there is provided a method for verifying the measurement accuracy of a gyro using a turntable as a calibration standard, wherein (a) a dimensional error of the turntable itself and a gyro error. A first stage of calibrating the mounting error, and (b) a forward motion for calculating a theoretical attitude angle (roll, pitch, yaw angle) taken by the gyro from the rotation angle of each axis of the turntable. And (c) comparing each attitude angle obtained from the forward kinematics model with an actual output value from the gyro, to verify the measurement accuracy of the gyro. And a method of verifying the measurement accuracy of the gyro by using a turntable as a calibration standard.

Here, in the first stage, calibration may be performed using a measuring device provided outside the turntable.

According to a third aspect of the present invention, there is provided a system for verifying measurement accuracy of a gyro, wherein (a) a turn table used as a calibration reference, and (b) a dimensional error of the turn table itself. And first means for calibrating the mounting error of the gyro, and (c) a theoretical attitude angle (roll, pitch, and pitch) taken by the gyro from the rotation angle of each axis of the turntable.
(D) comparing each attitude angle obtained from the forward kinematics model with an actual output value from the gyro, and A third means for verifying the measurement accuracy, and a system for verifying the measurement accuracy of the gyro.

Here, the first means is provided by the turn
The calibration may be performed using a measuring device provided outside the table.

[0027] The turntable may have three or more degrees of freedom.

According to a fourth aspect of the present invention, there is provided an apparatus for calibrating a turntable composed of N axes, comprising: (a) a test object disposed substantially at an outer peripheral edge of the turntable; (B) means for tracking the test object while driving each axis of the turntable to measure the positions of multiple points on its trajectory; and (c) based on the measured positions of the multiple points. And a means for identifying a rotating axis. A device for calibrating a turntable composed of N axes.

Here, a jig having a long shape may be installed in the radial direction of the turntable, and the test object may be installed at a substantially leading edge of the jig. By increasing the radial position of the test object, the measurement accuracy will be further improved.

A second jig having substantially the same shape and weight is installed at a rotation position on the turntable opposite to the jig, and a counterweight having substantially the same shape and weight as the test object is provided. May be installed at a substantially leading edge of the second jig. With the second jig and the counter weight, the weight imbalance during rotation of the turntable could be corrected.

According to a fifth aspect of the present invention, there is provided a method for calibrating a turntable composed of N axes, comprising the steps of: (a) arranging a test object on a substantially outer peripheral edge of the turntable; And (b) one of the axes of the turntable
(C) tracking the object while driving the axis of the turntable to determine the position of multiple points on its trajectory; and (d) measuring the multiple points. And a step of identifying a rotating axis based on the position of the turntable. 3. A method of calibrating a turntable including N axes, comprising the steps of:

Here, in the step (a), a longitudinal jig is set in the radial direction of the turntable, and
The method may include placing the test object at a substantially leading edge of the jig. By increasing the radial position of the test object, the measurement accuracy will be further improved.

Further, the step (a) further includes the step of substantially isomorphing the rotary position on the turntable facing the jig.
The method may further include installing a second jig having the same weight, and installing a counterweight having substantially the same shape and weight as the test object at a substantially leading edge of the second jig. With the second jig and the counter weight, the weight imbalance during rotation of the turntable could be corrected.

[0034]

The robot system according to the first aspect of the present invention is characterized in that a piezoelectric element rotating gyro is disposed at the hand of the robot for posture measurement. Gyro attitude measurement can be performed in real time, non-contact, and with high accuracy. In addition, there is an advantage that the sensor unit is simply attached to the hand of the robot, no measurement device is required outside the robot, and the measurement range is not limited (measurement can be performed behind a shadow or facing the back).

The gyro is a device for outputting an angular velocity (known in the art), and can measure an angle by integrating the angular velocity with time. In order to measure the attitude of the articulated robot, it is necessary to detect the rotational angular velocities around three axes, and to attach the robot to the hand of the robot, the sensor must be small and lightweight. Furthermore, it is necessary to have high drift stability. Currently, fiber optic gyros and tuned
The dry gyro has a high drift stability of about 0.1 mm / h. However, at present, one unit is relatively large and it is difficult to attach it to the robot's hand if three units are combined. turn into. On the other hand, since the piezoelectric element rotating gyro is small and lightweight, it can be attached to the hand of a robot, and it is also possible to simultaneously obtain angle data about three axes. The drift stability of the piezoelectric element rotary gyro is about 3 mm / h, but considering that the posture accuracy other than the posture drift accuracy is defined by ISO 9283 that a measurement time of about 10 seconds is sufficient, the robot becomes It can be expected that the method can be adapted to the use of the posture accuracy verification of the robot.

In the future, small, lightweight and high-precision optical fibers and gyros may appear, but at the time of the present application, it is best to select a piezoelectric element rotating type gyro for the posture accuracy verification of the robot. Please understand that there is.

Further, the second and third aspects of the present invention are a method and a system for verifying the measurement accuracy of a gyro, and a piezoelectric element rotating type gyro mainly has a performance useful for posture accuracy verification of a robot. Applied to determine if

The static performance of each gyro for each single axis is usually inspected at the time of shipment using a turntable having one degree of freedom as a calibration standard. However, since the hands of an actual robot dynamically perform complex rotational movements with three degrees of freedom, before applying the gyro to the posture accuracy verification of the robot, accurately grasp the gyro measurement accuracy under similar conditions in advance. It is necessary to keep. For this reason, it is important to verify the static and dynamic measurement accuracy of the gyro using a turn table having three degrees of freedom, that is, a turn table including three motors, as a calibration standard. However, the multi-degree-of-freedom turntable itself constitutes a multi-degree-of-freedom, multi-joint type robot, and inevitably, the mounting error of each axis due to machining and assembly accuracy (three motor axes are mutually It includes dimensional errors of the mechanism such as horizontal / vertical) and encoder offset errors (deviation between mechanical origin and electrical origin).

Therefore, in the method and system for verifying the measurement accuracy of the gyro according to the second and third aspects of the present invention, first, calibration is performed for the dimensional error of the turntable itself and the gyro mounting error. , A forward kinematics model that calculates the theoretical attitude angles (roll, pitch, yaw angle) taken by the gyro from the rotation angles of each axis of the turntable is created, and each attitude angle and the gyro obtained from the forward kinematics model The accuracy of the gyro measurement is verified by comparing the actual output value from the gyro.

Further, the fourth and fifth aspects of the present invention
An apparatus and method for calibrating a turntable composed of axes, which is mainly used to measure a dimensional error and a mounting error of a three-degree-of-freedom turntable applied to verify the measurement accuracy of a gyro. Can be

More specifically, a test object is disposed substantially on the outer peripheral edge of the turntable, and one of the shafts of the turntable is driven to track the rotating test object. The position of the multiple points on the trajectory is measured, and the axis of rotation is identified based on the measured positions of the multiple points. In this specification, such a method of calibrating a turntable is referred to as a “pair-even axis identification method”.

A long jig may be installed in the radial direction of the turntable, and the test object may be installed at a substantially leading edge of the jig. By increasing the radial position of the test object, the measurement accuracy will be further improved.

Further, a second jig having substantially the same shape and weight is installed at a rotational position on the turntable opposite to the jig, and a counter having substantially the same shape and weight as the test object is provided. -A weight may be installed at a substantially leading edge of the second jig. With the second jig and the counter weight, the weight imbalance during rotation of the turntable could be corrected.

Still other objects, features and advantages of the present invention are:
It will become apparent from the following more detailed description based on the embodiments of the present invention and the accompanying drawings.

[0045]

Embodiments of the present invention will be described below in detail with reference to the drawings.

A. Robot System FIG. 1 shows a robot system 10 capable of realizing the present invention.
0 is schematically shown. The system 100
It includes a robot body 10, a robot controller 20 for controlling the driving of the robot 10, and a computer system 30 provided for measuring the position and orientation of the robot 10.

The basic structure of the robot 10 is a link mechanism connected in series with many degrees of freedom. That is, this is an articulated and multi-degree-of-freedom arm type robot in which a plurality of arms are connected by axes and each axis is driven by a motor. One end of the robot 10 is fixed on the base 11 to define the base position of the robot 10 and the other end is
Means minions. Each joint is provided with an encoder (inner sensor) for measuring the rotation angle of the shaft, and the position of the hand can be obtained from the length of each arm and the rotation angle of each shaft.

The robot controller 20 is a unit for controlling the operation of the robot 10, and more specifically, the three-dimensional position X (x ₁ , x ₂ ,
x ₃ ), the rotation angle of each axis Θ (θ ₁ , θ ₂ ,.
θ _n ), and each motor is driven in accordance with this.

The robot system 100 according to the present embodiment
Is characterized in that the piezoelectric element rotating type gyro 50 is disposed at the hand of the robot 10 for measuring the posture of the robot 10. Gyro attitude measurement can be performed in real time, non-contact, and with high accuracy. In addition, there is an advantage that the sensor unit is simply attached to the hand of the robot, no measurement device is required outside the robot, and the measurement range is not limited (measurement can be performed behind a shadow or facing the back).

The gyro is a device for outputting an angular velocity (well-known), and can measure an angle by integrating the angular velocity with time. In order to measure the attitude of the articulated robot, it is necessary to detect the rotational angular velocities around three axes, and the gyro must be small and lightweight in order to attach it to the hand of the robot. Furthermore, it is necessary to have high drift stability. Currently, optical fiber gyros and tuned dry gyros used for space and military applications have a high drift stability of about 0.1 mm / h, but at present one unit is relatively large and has three axes. Combining the minutes makes the robot too heavy to attach to the robot's hands. On the other hand, a piezoelectric element rotating gyro is generally small and lightweight, so that it can be attached to the hand of a robot, and angle data about three axes can be obtained at the same time.
Although the drift stability of the piezoelectric element rotary gyro 50 used in the present embodiment is about 3 ° / h, all of the posture accuracy other than the posture drift accuracy requires a measurement time of about 10 seconds.
O (International Organizat)
ion for Standardization) 9
Considering the definition in 283, it is expected that the piezoelectric element rotating gyro 50 can be adapted for use in verifying the posture accuracy of a robot.

In the future, small-sized, light-weight, and high-precision optical fibers and gyros may appear, but at the time of the present application, it is most suitable to select a piezoelectric element rotating type gyro for robot posture accuracy verification. Please understand that there is. However, the configuration and operation characteristics of the piezoelectric element rotary gyro 50 will be described in detail in section B.

The output voltage of the rotary gyro 50 is input to a signal processing box 55. The signal processing box 55 calculates an attitude angle such as a roll, a pitch, and a yaw angle by performing digital signal processing and arithmetic processing on the input value. The signal processing box 55
These calculation results are supplied to the computer system 30.

The computer system 30 includes consoles such as a keyboard and a display in addition to a system main body including various arithmetic and control units. The computer system 30 processes the attitude angles such as roll, pitch, and yaw angle input from the signal processing box 55. For example, the attitude angle is output to the display as a console or passed to the robot controller 20 via an output port to form a closed-loop attitude control system. As the computer system 30, a general-purpose personal computer can be applied. One example is PC / AT compatibles and successors marketed by IBM Corporation. Further, in FIG. 1, the robot controller 20 and the computer system 30 are configured as separate units, but both may be configured as a single unit.

B. Configuration Figure 2 of the piezoelectric element rotating gyro is a structure of the piezoelectric element rotating gyro 50 used in this embodiment shows schematically. As shown in the figure, the gyro 50 is composed of two cylindrical gyro units 51 and 52 which are vertically assembled as shown.

FIG. 3 illustrates the structure of a gyro unit 51 which is a component of the rotary gyro 50 of the piezoelectric element.

As shown, one unit is composed of two sets of piezoelectric element benders 51a and 51b. Each of the benders 51a and 51b rotates at a high speed of 12,000 rpm, and one bender 51a detects Coriolis force, and the other bender 51b detects acceleration by a piezoelectric effect. The output voltage of each of the benders 51a and 51b is a sinusoidal waveform having a cycle of one rotation. The output voltage is subjected to phase discrimination based on a signal from a rotational position detector (not shown), and separated into X and Y components. It has become.
Each of the units 51a and 51b can detect an angular velocity around two axes and an acceleration in two directions. Therefore, the rotary gyro 50 having a two-unit configuration shown in FIG. 2 can detect all six-axis components (that is, angular velocities around three axes and acceleration in three axes).

As shown in FIG. 4, the gyro coordinate systems α, β, and γ are set with reference to the bottom and side surfaces of the casing of the piezoelectric element rotating gyro 50. Furthermore, if the world coordinate system is XYZ, each of the roll, pitch, and yaw angles is defined as φ, θ, and の in FIG. 5 according to the relative positional relationship between the two coordinate systems. Α by the piezoelectric element rotating gyro 50
Detects the angular velocity around each axis of βγ. Further, the signal processing box 55 (described above) performs digital signal processing and arithmetic processing on these angular velocities, so that changes Δφ, φ,
Δθ, Δψ can be calculated at a predetermined cycle (for example, 60 Hz). It should be understood that the posture change from the initial posture can be obtained by sequentially integrating each of Δφ, Δθ, and Δψ.

An example of a product applicable as the rotary piezoelectric element gyro 50 is a “multi-sensor” (model: MSE-3302) manufactured and marketed by Mitsubishi Precision Corporation. Table 1 below shows performance test results for each single axis of the piezoelectric element rotating gyro 50 shown by the bender.

[0059]

[Table 1]

The drift stability of the piezoelectric element rotary gyro 50 applied to this embodiment is 3 ° / h or less, and the linearity is about 0.1%. For example, using the gyro 50
When a relative angle change of 0 ° is measured in a measurement time of 10 seconds, an error of about 0.04 ° obtained by adding 0.008 ° of drift and 0.03 ° due to non-linearity in the measurement result. Will be included. These errors mainly depend on the asymmetry, temperature characteristics, hysteresis and the like of the piezoelectric element.

In order to improve the absolute positioning accuracy of the robot system 100, the piezoelectric element rotating gyro 5
It is necessary to confirm to what extent 0 is useful for verifying the posture accuracy of the robot defined in ISO 9283. However,
Details are given in section C.

C. Measurement accuracy of the piezoelectric gyro
In the previous and previous sections, it has been proposed to use the piezoelectric element rotating gyro 50 for posture measurement of the robot.

It is customary in the art that, at the time of shipment, a static performance test for each single axis is performed using a turntable having one degree of freedom as a calibration standard at the time of shipment of the piezoelectric element rotary gyro 50. However, in order to measure the posture of a robot with higher absolute accuracy, not only the static measurement accuracy of the gyro but also the dynamic measurement accuracy that assumes the robot's unique motion such as multi-degree-of-freedom rotational motion is verified in advance. It is necessary to keep. Therefore, in this section, a method and a method for verifying the measurement accuracy of the piezoelectric element rotating gyro 50 will be described.

The present inventors have conducted a three-degree-of-freedom turntable (described later) composed of three DD motors in order to perform static and dynamic accuracy verification assuming a motion unique to a robot. Is used as a calibration standard.

C-1.3 Freedom Turntable Cap
The three-degree-of-freedom turntable itself has many degrees of freedom.
It constitutes an articulated robot, which inevitably
The dimensional errors of the mechanism such as the mounting error of each axis due to the assembly accuracy (the three motor axes are not horizontal and vertical to each other) and the offset error of the encoder (the deviation between the mechanical origin and the electrical origin) Includes.

Therefore, in this embodiment, first, calibration is performed for the dimensional error and the mounting error of the turntable itself, and the theoretical attitude angles (roll, pitch) taken by the gyro from the rotation angles of the respective axes of the turntable. ,
A forward kinematics model for calculating the yaw angle is created, and the accuracy of the gyro measurement is verified by comparing each posture angle obtained from the forward kinematics model with the actual output value from the gyro (however, Verification of the measurement accuracy of the gyro will be described in the next section C-3).

In this embodiment, a calibration method of a turntable, which the present inventors call "an even-axis identification method", is adopted. Here, the even-axis identification method is
The basic principle is to rotate only one pair even axis in the multi-degree-of-freedom turntable at a constant angle and to identify the position of the pair even axis from the locus of a circle drawn during the rotation. All the even-numbered axes are identified, and the parameters can be obtained from between the adjacent joint coordinates using the identified even-numbered axes. Hereinafter, the paired-axis calibration method will be described in detail.

FIG. 6 shows a three-degree-of-freedom turntable 20.
0 is shown. As shown in the figure, the turntable 200 includes a first motor 211 and a second motor 2.
12 and a third motor 213, and the table 210 is given three degrees of freedom by driving the axes of the motors that are substantially orthogonal. A DD motor is employed for each of the motors 201..., And a high-resolution (655, 360 pulses / rotation) encoder is additionally provided for each of the motors 201. Hereinafter, the axes of the motors 201 are simply referred to as first to third axes. The specifications of the turntable 200 applied in this embodiment are shown in Table 2 below.

[0069]

[Table 2]

In order to implement paired-axis calibration, it is necessary to measure a circular orbit. In the present embodiment, this measurement is performed using the laser tracking system 300. Laser tracking system 3
An example of 00 is a model SMART310 manufactured by Leica Corporation, whose outline is shown in FIG. The SMART 310 measures a circular orbit of the turntable 200 by placing a reflective target called a cat's eye on the turntable 200 and following the reflected light of the irradiation laser. Since the cat's eye always returns reflected light in the same direction as the irradiation light, SMART31
A value of 0 can favorably follow the cat's eye reflected light.

Laser tracking system 300
Are a laser interferometer 301 and a tracking mirror 302
Is used to obtain the position of the target cat's eye in polar coordinate format. By converting this polar coordinate position into the rectangular coordinate XYZ format, it is possible to determine a cat's eye, that is, a measurement position on a circular orbit.
The repetition measurement accuracy of each XYZ coordinate of this embodiment is ± 5 pp
m (μm / m), the absolute measurement accuracy is ± 10 ppm (μm / m
m).

In this embodiment, the mechanism of the turntable is modeled using the so-called DH notation. FIG. 8 schematically shows DH modeling, and FIG. 9 schematically shows modified DH modeling.

In the DH notation, the direction of the joint axis is defined as the Z axis,
A common perpendicular line is drawn between adjacent Z _i−1 and Z _i axes and Z _i and Z _{i + 1} axes. 1) d _i : distance between two common perpendicular lines, 2) θ _i : common perpendicular line 3) α _i : twist angle around X _{i + 1} between Z _i axis and Z _{i + 1} axis, 4) a _i : length of common perpendicular line between Z _i and Z _{i + 1} axes These four variables define the position and orientation between the links. However, when adjacent paired axes are completely parallel (that is, when α _i = 0), the common perpendicular is not uniquely determined, and is generally defined as d _i = 0.

In the case where adjacent pairs even slightly deviate from parallel, the rotation angles intersect at infinity. In the DH notation, a _i changes from a finite value to 0 and d _i changes from 0 to ± ∞. Change. That is, in the vicinity of α _i = 0, a relative change in alpha _i
i, the sensitivity of the change in d _i increases, the estimated value of a _i, d _i becomes unstable during calibration. Therefore, the measurement coordinate system of the laser tracking system 300 and the first
With respect to the axis coordinate systems, since the adjacent paired axes are almost parallel, the modified DH notation as shown in FIG. 9 is used. In the modified DH notation, d _i = 0, and instead of the common perpendicular in the DH notation, Z _{i + 1} passes through O _i in the X _i Y _i plane.
Use a straight line that intersects the axis. Other rotation angles alpha _i around the straight line as a twist angle between the Z _i axis and Z _{i + 1} axis, newly introduce beta _i around the Y _{i + 1} as shown in FIG. This β
_i indicates the deviation of the adjacent axis from the parallel state, and the instability of the estimated value is resolved.

Returning to FIG. 6, the paired-axis calibration will be described. As shown in the figure, a 500 mm long 2
The main arms 201 and 202 are installed in the radial direction at opposed rotation positions. At a position of 547.5 mm from the center of the table 210 surface on each arm 201, 202,
Cat's eye 203 and counter weight 204, respectively
Is attached. Since the cat's eye 203 is placed on the arm 201 whose radius is larger than the outer circumference of the table 210, the measurement accuracy is improved. Also, the arm 20
Arms 20 of substantially the same shape and weight are located at the rotational position opposite to 1.
2 and the same shape as Cat's Eye 203
Since the counterweight 204 having the same weight is installed on the arm 202, it is possible to correct the weight imbalance when the table 210 rotates.

Since the position measurement error of the laser tracking system 300 is about 10 μm (described above), the angle measurement error is tan ⁻¹ (10 × 10 ⁻⁶ /547.5)=
1.05 × 10 ⁻³゜.

In the calibration, first, each axis of the turntable 200 is set to an initial state (that is, each axis is set to 0).
゜), and then rotating one axis at fixed angle intervals while the other axis is fixed. While rotating the shaft by a certain angle, the turntable 200
The laser tracing system 300 measures a circular trajectory drawn by the tip of the arm 201 attached to the camera. The position of the rotation axis can be identified from the normal line of the plane on which the circular orbit is placed and the center position of the circular orbit. By performing the above operation for each axis, the positions of the three axes in the initial state are obtained. Based on each identified axis, a link parameter between the third axis coordinate system can be calculated from the measurement coordinate system as shown in FIG. However, the coordinate system x ₀ y ₀ z in FIG.
₀ is a measurement coordinate system formed by the laser tracking system 300.

Next, an error when the piezoelectric element rotating gyro 50 is mounted on the table 210 will be considered.

The γ-axis direction of the piezoelectric element rotary gyro 50 coincides with the normal direction of the table 210 surface. Therefore,
The cat's eye 203 is installed at various positions on the surface of the table 210, and each position is measured to obtain the equation of the surface constituting the table 210, and the direction of the γ-axis is obtained.

As shown in FIG. 11, the α-axis direction of the rotary gyro 50 corresponds to the longitudinal direction of the jig in FIG. Therefore, the cat's eye 203 is installed at several positions along the jig, and each position is measured to obtain an equation of a straight line formed by the jig, thereby obtaining the α-axis direction.

The gyro coordinate system αβ obtained as described above
From the relative positional relationship between γ and the third axis coordinate system X ₃ Y ₃ Z ₃ , link parameters θ ₃ and α ₃ corresponding to the mounting error of the gyro 50 can be obtained.

Table 3 below shows the calibration results of α, β, and θ regarding the attitude among the DH parameters of the turntable and the mounting errors of the gyro.

[0083]

[Table 3]

Since θ ₀ depends on the installation of the turntable 200 with respect to the measurement coordinate system, there is no nominal value. Other parameters are small values of 1 ° or less, but it can be seen that there is a deviation between the nominal value and the estimated value, and there is a dimensional error of the mechanism.

In this embodiment, the turntable 2
To measure the circular orbit around each axis of 00
Although the tracking system 300 is used, any other device that can measure a circular orbit may be used. For example, calibration may be possible using a large three-dimensional measuring machine.

C-2. Calculation of theoretical value An attitude conversion matrix for converting the gyro coordinate system to the measurement coordinate system is P (3 × 3). When each axis of the turntable 200 is rotated by Φ = (Φ ₁ , Φ ₂ , Φ ₃ ), the attitude conversion matrix P obtained by the DH parameter is given by the following equation (5).
It is represented as

[0087]

(Equation 5)

Here, the matrices C ₀ and C _i (i = 1 to 3)
Is defined as in the following equations (6) and (7). However, in each equation, Cθ = cosθ and Sθ = sinθ.

[0089]

(Equation 6)

[0090]

(Equation 7)

In the accuracy verification experiment, the turntable 20
Gyro 50 in initial state Φ = (0,0,0) of 0
Are reset to 0, and this is set as the initial posture. If the attitude conversion matrix from the gyro coordinate system after the turn table 200 rotation to the gyro coordinate system in the initial attitude is G (3 × 3), the attitude conversion matrix P is
It is expressed as the following equation (8).

[0092]

(Equation 8)

FIG. 12 schematically shows the state of the above-mentioned posture conversion. Assuming that the right sides of the above equations (5) and (8) are equal, solving for G yields the following equation (9).

[0094]

(Equation 9)

On the other hand, the matrix G is expressed by the following equation (10) using the attitude angles φ, θ, and の of the gyro 50.

[0096]

(Equation 10)

By comparing the elements of the above equations (9) and (10), the theoretical attitude angles φ, θ, ψ after the turntable 200 has been rotated as functions of Φ ₁ , Φ ₂ , Φ ₃ can be obtained. Desired.

C-3. Gyro Accuracy Verification Result Static Accuracy Verification Result All the axes of the turntable 200 were simultaneously driven from the initial state, and were positioned at intervals of 5 ° from −25 ° to 25 ° respectively. That is, Φ = (− 25 + 5i, −25 + 5i,
−25 + 5i) (i = 0 to 10; unit deg).

The theoretical and experimental values of the angular output of the gyro 50 at this time are shown in FIG. 13, and the deviation between them is shown in Table 4 below.

[0100]

[Table 4]

In the experiment, the turn table 200 was once returned to the initial state for each trial, and the output angle of the gyro 50 was reset there. The time required for positioning was 10 seconds or less in each trial, and the effect of drift estimated from the performance of the gyro 50 was 0.008 °.

From the experimental results, it can be seen that the theoretical value and the experimental value coincide with the precision of the roll angle of 0.02 °, the pitch angle of 0.01 °, and the yaw angle of 0.03 °. These are estimated to be 0.04 from the performance test results for one degree of freedom rotational motion.
It keeps the same order as ゜. Therefore, it can be said that the piezoelectric element rotation type gyro 50 according to the present embodiment is sufficiently effective also in posture measurement with three degrees of freedom characteristic of an articulated robot.

The reason why the yaw angle error is large is that the length of the jig shown in FIG. 11 cannot be long due to the experiment and the estimation error in the α-axis direction is large.

Dynamic Accuracy Verification Results All motors of the turntable 200 were simultaneously driven in the same angular step shape and sine wave shape, and the rotation angles were measured by the piezoelectric element rotating gyro 50.

FIG. 14 and FIG. 15 show examples of experimental results on the roll axis. The theoretical values in each figure are obtained by detecting the rotation angle of the motor of the turn table 200 and calculating from the values using a forward kinematics model (described above). The experimental value and the theoretical value coincide with each other with an accuracy of about 0.05 °.
It can be seen that it is effective for dynamic verification of the posture trajectory accuracy determined in 3.

In FIG. 15, the output value of the piezoelectric element rotary gyro 50 has a delay of 0.02 sec from the theoretical value. This is because the sampling cycle of the gyro 50 is 60 Hz, and correction by data processing is possible.

Considering that the natural frequency of a robot using a speed reducer which is currently most widely used is about several to 10 Hz, the piezoelectric element rotating gyro 50 is sufficient for application to dynamic measurement in this range. It can be said that it has sufficient performance. However, in order to apply to a high-speed robot such as a DD robot, it is necessary to further improve the sampling period, and it should be improved by speeding up the arithmetic processing.

From the above description, it can be confirmed that posture measurement using the piezoelectric element rotary gyro 50 is effective for static and dynamic posture accuracy verification of the robot specified in ISO 9283.

D. The present invention has been described in detail with reference to specific embodiments. However, it is obvious that those skilled in the art can modify or substitute the embodiment without departing from or expanding the gist of the present invention. That is, the present invention has been disclosed by way of example, and should not be construed as limiting. In order to determine the gist of the present invention, the claims described at the beginning should be considered.

[0110]

As described above in detail, according to the present invention,
An articulated robot system composed of an articulated robot composed of two or more arms and an axis rotatably supporting each arm, the articulated robot having an attitude measuring function. A system can be provided.

Further, according to the present invention, there is provided a method and a system for verifying the measurement accuracy of a gyro using a turntable as a calibration standard, taking into account dimensional errors of the turntable itself and mounting errors to the table. An excellent method and system for verifying the measurement accuracy of the gyro can be provided.

Further, according to the present invention, it is possible to provide an apparatus and a method for calibrating a turntable composed of N axes, which can be applied to verification of measurement accuracy of a gyro.

[Brief description of the drawings]

FIG. 1 is a diagram schematically showing a configuration of a robot system 100 according to the present embodiment.

FIG. 2 is a view showing a structure of a piezoelectric element rotary gyro 50;

FIG. 3 illustrates the structure of a gyro unit 51.

FIG. 4 is a diagram showing a state in which gyro coordinate systems α, β, and γ are defined with reference to a bottom surface and a side surface of a housing of a piezoelectric element rotating gyro 50;

FIG. 5 is a diagram showing a roll φ, a pitch θ, and a yaw angle 定義 defined by a relative positional relationship between a gyro coordinate system αβγ and a world coordinate system XYZ.

FIG. 6 is a diagram showing an overview of a three-degree-of-freedom turntable 200;

FIG. 7 is a diagram showing a schematic configuration of a laser tracking system (model: SMART310) manufactured by Leica Corporation.

FIG. 8 is a diagram illustrating DH modeling used in the present embodiment.

FIG. 9 is a diagram showing modified DH modeling used in the present embodiment.

FIG. 10 is a diagram showing an outline of calculating a link parameter between a measurement coordinate system and a third axis coordinate system.

FIG. 11 is a diagram showing mechanism parameters relating to a gyro mounting error.

FIG. 12 is a diagram schematically showing a state in which a posture is converted from a gyro coordinate system after rotation of the turn table 200 to a gyro coordinate system in an initial posture.

FIG. 13 is a graph showing the results of verifying the static accuracy of the gyro 50, and more specifically, a graph in which a theoretical value and an experimental value of the output angle of the gyro 50 are plotted.

FIG. 14 is a graph showing the dynamic accuracy verification result of the gyro 50, and more specifically, a graph in which the roll angle detection result at the time of a step response is plotted.

FIG. 15 is a graph showing the dynamic accuracy verification result of the gyro 50, and more specifically, a graph in which the roll angle detection result at the time of frequency response is plotted.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 10 ... Robot main body 20 ... Robot controller, 30 ... Computer system, 50 ... Piezoelectric element rotary gyro, 51, 52 ... Cylindrical gyro unit, 51a, 51b ... Piezoelectric element bender, 55 ... Signal processing box, 100 ... Robot system, 200 ... 3 degree of freedom turntable, 201,202 ... Arm, 203 ... Cat eye, 204 ... Counter weight, 210 ... Table, 211 ... Turntable first motor, 212 ... Turntable second motor 213: turntable third motor 300: laser tracking system 301: laser interferometer 302: tracking mirror

 ──────────────────────────────────────────────────続 き Continued on the front page (72) Inventor Hiroshi Takagi 345 Kamimachiya, Kamakura City, Kanagawa Prefecture Inside Mitsubishi Precision Co., Ltd. (72) Inventor Hideo Kondo 345 Kamimachiya, Kamakura City, Kanagawa Prefecture, Mitsubishi Precision Corporation ( 72) Inventor Yoshiyoshi Kamiya 2-40-20 Kodano, Kanazawa-shi, Ishikawa Pref. Faculty of Engineering, Kanazawa University (72) Inventor Jun Fujioka 2-40-20 Kodano, Kanazawa-shi, Ishikawa Pref. F-term 2F069 AA83 AA93 DD15 GG07 HH11 HH30 (54) [Title of the Invention] Articulated robot system with function to measure posture, method and system for verifying gyro measurement accuracy using turntable as calibration standard, and N-axis Apparatus and method for calibrating a turntable

Claims (11)

[Claims] An articulated robot system having a function of measuring a posture, wherein (a) an articulated robot comprising two or more arms and a shaft rotatably supporting between the arms, and (b). Two or more driving units for rotating and driving each axis of the robot; (c) a piezo-electric element rotary gyro disposed substantially at the end of the robot; and (d) driving each of the driving units according to a command value. And (e) a measuring unit for measuring a posture of the robot according to an output of the piezoelectric element rotating gyro while the driving unit drives the robot. Articulated robot system. 2. A method for verifying measurement accuracy of a gyro using a turntable as a calibration reference, the method comprising: (a) calibrating a dimensional error of the turntable itself and a mounting error of the gyro. And (b) creating a forward kinematics model for calculating a theoretical attitude angle (roll, pitch, yaw angle) taken by the gyro from the rotation angle of each axis of the turntable.
And (c) a third step of verifying the measurement accuracy of the gyro by comparing each attitude angle obtained from the forward kinematics model with an actual output value from the gyro. A method for verifying the measurement accuracy of a gyro using a turntable characterized by the following as a calibration standard. 3. The method according to claim 2, wherein in the first stage, calibration is performed using a measuring device provided outside the tan table. A method to verify the measurement accuracy of a gyro. 4. A method for verifying measurement accuracy of a piezoelectric element rotary gyro having three degrees of freedom.
A method for verifying measurement accuracy of a three-degree-of-freedom piezoelectric element rotary gyro, which uses a table. 5. A system for verifying measurement accuracy of a gyro, comprising: (a) a turntable used as a calibration reference; and (b) a calibration for a dimensional error of the turntable itself and a mounting error of the gyro. And (c) creating a forward kinematics model for calculating a theoretical attitude angle (roll, pitch, yaw angle) taken by the gyro from the rotation angle of each axis of the turntable. A second means, and (d) third means for verifying measurement accuracy of the gyro by comparing each attitude angle obtained from the forward kinematics model with an actual output value from the gyro. Gyro measurement accuracy verification system. 6. The system for verifying measurement accuracy of a gyro according to claim 5, wherein the turntable has three or more degrees of freedom. 7. The method according to claim 5, wherein the first means performs the calibration using a measuring device provided outside the turn table. A system for verifying gyro measurement accuracy. 8. An apparatus for calibrating a turntable composed of an N-axis, comprising: (a) a test object arranged substantially at the outer peripheral edge of the turntable; and (b) each of the turntable. Means for tracking the object while driving the axis and measuring the positions of multiple points on the trajectory; and (c) means for identifying the rotating axis based on the measured positions of the multiple points. And a device for calibrating a turntable composed of N axes. 9. The N-axis according to claim 8, wherein a jig having a long shape is installed in a radial direction of the turntable, and the test object is installed at a substantially leading edge of the jig. A device for calibrating a turntable composed of: 10. A method for calibrating a turntable composed of N axes, comprising the steps of:
Arranging the test object on substantially the outer periphery of the table; (b)
Driving one of the axes of the turntable; (c)
Tracking the object while driving the axis of the turntable to determine the position of multiple points on its trajectory; (d)
Identifying the axis of rotation based on the measured positions of the multiple points. The method for calibrating a turntable comprising: 11. The method according to claim 11, wherein the step (a) includes setting a jig having a longitudinal shape in a radial direction of the turntable, and setting the test object at a substantially leading edge of the jig. The method for calibrating a turntable composed of N axes according to claim 10.