Device and method for calibration of a multi-axis industrial robot

TECHNICAL FIELD

The present invention relates to a method for calibration of an industrial robot.

The invention also relates to equipment for calibration of the above-mentioned robot.

BACKGROUND OF THE INVENTION

An industrial robot may be viewed as a chain consisting of stiff links. Two links are joined to each other in such a way that they are rotatable in relation to each other around an axis of rotation, or displaceable in relation to each other along a linear movement path. An industrial robot usually has six axes of rotation. The last link in the chain may consist of a tool which, depending on the field of application, may be a gripper, a glue gun or a welding gun. In the following, the links in a robot will be referred to as arms, and their lengths will be referred to as arm's lengths.

For each of the axes of rotation or linear movement paths, servo equipment with a driving motor and a position transducer is provided, the transducer delivering a signal which is a measure of the angle of rotation of the actual axis in relation to a reference position. The servo system of each axis is supplied with a reference value of the angle of rotation or linear movement of the axis, and the driving motor of the axis causes the robot to move until the axis position indicated by the position transducer of the axis corresponds to the reference value supplied to the servo system. In order for the position and orientation of the tool to correspond to the desired values, the mechanical structure of the robot and the parameters, so-called kinematic parameters, which describe it must be known with a high accuracy. Since the kinematic parameters are not exactly the same for each robot, the individual deviations from an ideal robot, that is, the kinematic error parameters of the robot, must be known if a high accuracy is to be attained.

Examples of kinematic error parameters are variations in the lengths of the arms, so-called arm's length errors, obliquities in the axes of rotation in relation to each other, so-called axis-attitude errors, and lateral displacements of the axes in relation to each other, so-called axis-offset errors. These deviations arise during manufacture of the different mechanical components and during the assembly thereof. To this it is to be added the fact that the angle indicated by the position transducer of an axis must with great accuracy correspond to the actual angle of rotation of the arm which is controlled with the aid of the axis in question, so-called synchronizing errors.

For determining the deviation of an individual robot from an ideal robot, various forms of calibration methods are used. A large number of calibration methods are known. A disadvantage with certain of these methods is that they do not manage to make a complete calibration, that is, determine both arm's length errors, axis-attitude errors, axis-offset errors, synchronizing errors, transmission errors, and deflection errors for all of the axes of the robot. A disadvantage with the known methods which do manage to make a complete calibration is that they require expensive and delicate calibration equipment, for example theodolites.

SUMMARY OF THE INVENTION

The object of the invention is to provide a calibration method which

manages to calibrate all the axes of a six-axis robot, as well as the mounting of the tool and the mounting of the robot foot,

manages to calibrate arm's length errors, axis-attitude errors, axis-offset errors, synchronizing errors, transmission errors,

does not require expensive equipment,

provides high accuracy,

can be used under active-service conditions, for example in a production line for cars,

can be used without the robot-carried tool having to be dismantled,

can be used for fully-automatic calibration, for example during final testing of robots, and

is fast and can be performed without complicated adjustments of robot positions.

The invention also aims to provide calibration equipment to be used with the above-mentioned calibration method, wherein the equipment

is inexpensive,

is robust enough to endure a workshop environment,

is portable and hence easy to transport, and

does not need to be calibrated.

The configuration of the robot is defined by the angles of the axes of rotation thereof, and one configuration distinguishes from another if at least some of the angles of axes are changed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1

schematically shows an industrial robot which can be calibrated with a method according to the invention.

FIG. 2

shows the different coordinate systems of the robot.

FIG. 3

schematically shows a simple embodiment of measuring equipment according to the invention which is suitable for use under active-service conditions.

FIGS. 4

a

and

4

b

show the principle of how an axis of rotation is determined with a high precision by a gravity sensor.

FIGS. 5

a

-

5

d

schematically show an embodiment of measuring equipment according to the invention, which is suitable for use in an automatic calibration method.

FIG. 5

b

shows a section A—A in

FIG. 5

a.

FIG. 5

e

shows an embodiment of a calibration tool according to the invention.

FIGS. 6

a

and

6

b

show alternative embodiments of means for connection to a reference point.

FIG. 7

a

shows an embodiment of a member adapted to be in contact with the robot during the calibration method.

FIG. 7

b

shows a further embodiment of a calibration tool according to the invention.

FIGS. 8 and 8

a

and

8

b

show an embodiment of measuring equipment according to the invention, which comprises an optical measuring system.

FIG. 8

shows a measuring device and

FIGS. 8

a

and

8

b

show alternative locations and embodiments of a calibration tool for optical measurement.

FIG. 8

c

shows an embodiment of measuring equipment with a non-contacting, non-optical sensor.

FIG. 9

shows how the measuring device and the calibration tool in

FIG. 5

a

are arranged for measuring the synchronizing error of axis A

5

, and the attitude and offset errors of axis A

6

in relation to axis A

4

.

FIG. 10

a

shows how the attitude error of the calibration tool in the y-direction is calculated.

FIG. 10

b

shows how the attitude error of axis A

6

in the y-direction is calculated.

FIG. 10

c

shows how the synchronizing error of axis A

5

is calculated.

FIG. 10

d

shows how the offset error of axis A

6

in relation to axis A

4

in the z-direction is calculated.

FIGS. 11

a

and

11

b

show a measurement arrangement for measuring the attitude error of axis A

1

in relation to the gravitational direction and the synchronizing error of axes A

3

-A

6

.

FIGS. 12

a

and

12

b

show a measurement arrangement for measuring the attitude error and offset error of axis A

1

in relation to the workshop floor and the synchronizing error of axes A

1

, A

2

and A

3

.

FIGS. 13 and 14

show a measurement arrangement for measuring attitude errors in axis A

3

.

FIG. 15

shows a measuring arrangement for measuring attitude errors in axis A

2

.

FIG. 16

shows a measurement arrangement for measuring arm's length errors.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1

shows an example of a known industrial robot which may advantageously be calibrated with the method and the device according to the invention. On a base

1

, the foot

2

of the robot is mounted. The robot has a first arm

3

, which is rotatable in relation to the foot

2

around a vertical axis A

1

. At the upper end of the first arm, a second robot arm

4

is journalled and rotatable in relation to the first arm around a second axis A

2

. In the outer end of the second arm, a third arm

5

is journalled and rotatable in relation to the second arm around an axis A

3

. The third robot arm

5

comprises two parts

5

a

and

5

b

, the outer part

5

b

being rotatable in relation to the inner part

5

b

around an axis of rotation A

4

coinciding with the longitudinal axis of the arm. At its outer end, the third arm

5

supports a fourth arm

6

, which is rotatable around an axis of rotation A

5

perpendicular to the longitudinal axis of the third arm. The outer part of the fourth arm consists of a tool attachment

6

a

which is rotatable in relation to the inner part of the fourth arm around an axis of rotation A

6

. The angles of rotation in the six axes of rotation A

1

. . . A

6

are designated θ

1

. . . θ

6

in the figure. On the tool attachment, a calibration tool

7

is mounted. The fourth arm and the tool attachment are referred to as the hand of the robot.

FIG. 2

shows in the form of a simple sketch the kinematics of the six-axis robot in FIG.

1

and its associated coordinate systems. The robot has four current arm's lengths referred to as L

1

, L

2

, L

3

, L

4

, which means that there may be four arm's-length errors designated ΔL

1

, ΔL

2

, ΔL

3

, ΔL

4

. The nominal arm∝s lengths are designated L

1

nom

, L

2

nom

, L

3

nom

, L

4

nom

. The current arm's length constitutes the sum of the nominal arm's length and the arm's-length error. The first arm's length L

1

is the distance between the origin of coordinates in the so-called base coordinate system (see below) and the axis A

2

. The second arm's length L

2

is the distance between the axis A

2

and the axis A

3

. The third arm's length L

3

is the distance between the axis A

3

and the axis A

5

. The fourth arm's length L

4

is the distance between the axis A

5

and the tool attachment

6

a.

The robot foot comprises a base coordinate system (x

1

, y

1

, z

1

), which is an orthogonal coordinate system with the z

1

axis coinciding with the axis of rotation A

1

and with the x

1

axis in a predetermined direction in relation to the robot foot (normally pointing straight ahead). Axis A

1

has a synchronizing error Δθ

1

, two offset errors O

1

x1

, O

1

y1

, and two attitude errors φ

1

x1

, φ

1

y1

. Axis A

2

is parallel to the y

1

axis in the base coordinate system and has a synchronizing error Δθ

2

and two attitude errors φ

2

x1

, φ

2

z1

. The attitude errors φ

2

x1

and φ

2

z1

are defined as those directional errors the axis A

2

has in the x

1

and z

1

directions, respectively. The attitude error φ

2

y1

is the same error as the synchronizing error Δθ

2

.

The intersection point between axis A

1

and axis A

2

constitutes the origin of coordinates in a second coordinate system (x

2

, y

2

, z

2

). The Z

2

axis in the second coordinate system is parallel to the second robot arm, and the y

2

axis coincides with the axis A

2

. The axis A

3

has a synchronizing error Δθ

3

and two attitude errors φ

3

x2

, φ

3

z2

. The axis A

3

has an offset error in the x

2

direction, but it is part of the synchronizing error of axis A

2

, that is Δθ

2

.

The intersection point between axis A

3

and axis A

4

constitutes the origin of coordinates in a third coordinate system (x

3

, y

3

, z

3

). The x

3

axis in the third coordinate coincides with the axis A

4

, and the y

3

axis coincides with the axis A

3

. The axis A

4

has a synchronizing error Δθ

4

, two offset errors O

4

y1

and O

4

z3

in relation to the axes A

1

and A

3

, respectively, and two attitude errors φ

4

y3

, φ

4

z3

. The axis A

5

has a synchronizing error Δθ

5

, two attitude errors φ

5

x3

, φ

5

z3

. The axis A

5

has an offset error in the z

3

direction, but it is part of the synchronizing error of axis A

3

, that is Δθ

3

.

The origin of coordinates in the fifth coordinate system (x

5

, y

5

, z

5

) consists of the intersection point between the axis A

5

and the axis A

6

. The x

5

axis in the third coordinate system coincides with the axis A

6

, and the y

5

axis coincides with the axis A

5

. The axis A

6

has a synchronizing error Δθ

6

, two offset errors O

6

y5

, O

6

z5

, and two attitude errors φ

6

y5

, φ

6

z5

. The attitude error φ

6

z5

is part of the synchronizing error Δθ

5

. All the parameters are defined when the robot in

FIG. 2

is in its so-called synchronizing position, that is, when the second arm is vertical and the third and fourth arms are horizontal.

FIG. 3

shows a simple embodiment of calibration equipment according to the invention. The calibration equipment comprises a measuring device

10

which in turn comprises a measuring rod

11

, one end of which is formed as a tip

12

for connection to a reference point (x

0

,

0

, z

0

) in a first precision hole

13

in the robot foot or in the floor or the device

14

on which the robot foot is mounted. The other end of the measuring rod comprises a resilient measuring tip

15

for connection to a predetermined measuring point on the robot (x

r

, y

r

, z

r

) in a second precision hole

16

, which is arranged in a robot arm or in a robot-carried calibration tool

17

. The resilient measuring tip may alternatively include a position sensor for distance measurement in the z-direction. The measuring rod

11

has an axis of rotation

11

a

which intersects the reference point (x

0

, y

0

, z

0

) and the measuring point (x

r

, y

r

, z

r

). The measuring device

10

further comprises a gravity sensor

18

arranged on a sensor shelf

19

, which is arranged on the measuring probe

11

and substantially perpendicularly and outwardly therefrom. The gravity sensor measures the angle between the gravity vector and a reference axis

20

which intersects the reference point (x

0

, y

0

, z

0

) and the measuring point (x

r

, y

r

, z

r

). The gravity sensor may, for example, be an electronic spirit level.

FIGS. 4

a

and

4

b

show the principle of how an axis of rotation

21

is determined with high precision by means of a gravity sensor

18

. The angle α which is to be determined is the average direction

22

of the axis of rotation in relation to the direction

23

of the gravity force. This means that the axis of rotation

21

in

FIG. 4

a

has the direction α−ξ/2, where ξ/2 is the spin amplitude when the sensor is rotated around the axis of rotation, and that the axis of rotation

21

in

FIG. 4

b

has the direction α+ξ/2. A gravity sensor

18

, with an offset error ∂ and with a mounting error β, is mounted so that the axis

25

of the gravity sensor, that is, its zero direction, is to be substantially parallel to the axis of rotation

21

. Angles are indicated relative to the gravity vector with a positive clockwise angle. The angle of deflection

24

of the sensor is dependent, among other things, on the offset error ∂ and the mounting error β. The output signal of the sensor in

FIG. 4

a

is given by the difference between the direction of deflection

24

and the zero direction

25

:

u

s1

=K

s

(−α+ξ/2−β−∂) (1)

K

s

is the sensitivity of the sensor.

In

FIG. 4

b

the sensor is rotated 180° around the axis of rotation

22

. The output signal of the sensor is then:

u

s2

=K

s

(α+ξ/2−β−∂) (2)

(

u

s2

−u

s1

)/2=

K

s

·α (3)

The difference between the deflections of the sensor for the two measurements is thus proportional to the average direction α of the axis of rotation in relation to the direction of the force of gravity. Thus, neither the mounting error β nor the offset angle ∂ of the sensor will influence the measurement result, and therefore the sensor may be mounted in a simple way and a sensor without absolute calibration can be used. In addition, any centering errors ξ which give rise to spin of the axis of rotation will be compensated for.

The measuring device in

FIG. 3

may, for example, be used to determine the coordinates for the measuring point (x

r

, y

r

, y

r

). The measuring device is connected to the two precision holes

13

and

16

and are then rotated three times one-fourth of a revolution, whereby the gravity sensor is read at the angles 0, π/2, π and 3π/2. The corresponding sensor deflections are u

s0

, u

sπ/2

, u

sπ

and u

s3π/2

, and with the aid of these values, the inclination of the measuring rod in the x- and y-directions can be calculated according to:

α

x

=(

u

s0

−u

sπ

)/2

Ks

(4)

α

y

=(

u

sπ/2

−u

s3π/2

)/2

Ks

(5)

If the length of the measuring probe is L

s

the coordinates of the measuring point, (x

r

, y

r

), can be calculated according to:

x

r

=x

0

+L

s

·sin(α

x

) (6)

y

r

=y

0

+L

s

·sin(α

y

) (7)

This simple embodiment of the measuring device is suitable for calibration under active-service conditions, whereby the measuring device is rotated around manually or by the axis A

6

of the robot driving it around. To use the measuring device in

FIG. 3

in an automatic calibration method, a simple motor may be used to rotate the sensor to the four different angles. The robot must also be able to release the measuring probe to measure the position at different z coordinates along the measuring device and against different measuring points of the robot.

FIG. 5

a

shows an example of how a separate measuring device

30

, with an associated calibration tool

41

suitable for automatic calibration, may be designed.

FIG. 5

b

shows the measuring device and the calibration tool in a section A—A in

FIG. 5

a

. The measuring device

30

comprises a cylindrical measuring rod

31

, one end of which is designed as a point

32

for connection to a reference point (x

0

, y

0

, z

0

) in the robot foot or on the workshop floor

40

, and the other end of which comprises a position sensor

33

for measuring the distance to the reference point in the z-direction. In that end of the measuring rod which is connected to the reference point, a balance weight

38

, in the form of a circular disc, is arranged for balancing the measuring rod. To give the measuring device a vertical position of rest, a number of springs

43

a

,

43

b

are mounted between the balance weight and the base

40

. The angle α

xmax

determines the limit of the working range for α

x

.

The measuring device

30

further comprises a gravity sensor

34

and a motor

35

a

, for example a stepping motor, adapted to rotate the gravity sensor around its axis

36

and a counterweight

35

b

to the motor

35

a

. The axis of rotation

36

of the gravity sensor is measured in relation to the axis of rotation

37

of the measuring rod by rotating the measuring rod. It is sufficient to do this once. The gravity sensor

34

, the motor

35

a

and its counterweight

35

b

are arranged on the balance weight

38

. To define the x-axis direction, a guide pin

39

is arranged in the robot foot or on the workshop floor

40

. During the calibration, the robot is in contact with the measuring rod via a calibration tool

41

.

FIG. 5

c

shows the calibration tool viewed from the side. The calibration tool comprises a cylindrical rod

41

on which two cylindrical branches

46

a

and

46

b

are arranged perpendicular to the rod

41

. The two branches make possible measurement with the measuring device

30

in two different positions, POS A and POS B. The measuring device

30

is provided with a hook

47

which may be hooked onto a slotted holder

48

which is arranged on the calibration tool. By hooking the measuring device onto the calibration tool, the measuring device may be lifted out of the precision hole

13

. The measuring device may need to be lifted out both when moving between different precision holes, and when measuring directions of axes of the robot.

If the distance L

s

between the reference point (x

0

,

0

, z

0

) and a measuring point (x

r

, y

r

, z

r

) on the calibration tool is known, see

FIG. 5

a

, x

r

and y

r

for the measuring point may be determined with the following method:

running the measuring device and the calibration tool into contact with each other,

rotating the gravity sensor three-fourths of a revolution and reading it at the angles

0

, π/

2

, π,

3

π/

2

. The corresponding sensor deflections are u

s0

, u

sπ/2

, u

sπ

and u

s3π/2

,

calculating the inclination of the measuring rod in the x-and y-directions (α

x

, α

y

) according to equations 4 and 5,

calculating the coordinates (x

r

, y

r

) of the measuring point according to equations 6 and 7.

The difference in the position of the measuring point between two different measurements is obtained at small angular differences Δα

x

, Δα

y

:

Δx

m

=L

s

·Δα

x

(8)

Δ

y

m

=L

s

·Δα

y

(9)

Δx

m

: The movement of the measuring rod in the x direction, (see

FIG. 5

d

)

Δy

m

: The movement of the measuring rod in the y direction.

This embodiment of the calibration equipment can be directly used in order to automatically calibrate, in one sequence, the axes of rotation A

1

-A

6

with respect to the synchronizing error, and to measure most of the kinematic error parameters of the robot.

Instead of using one rotating gravity sensor, two gravity sensors may be arranged perpendicular to each other. These are calibrated by rotation of the measuring rod. Whether one rotating or two perpendicular gravity sensors are used is determined by the sensor price and by the long-term stability of the offset error ∂.

To obtain a reliable contact between the measuring rod and the calibration tool, the calibration tool may be provided with magnets, preferably electromagnets.

FIG. 5

e

shows a calibration tool

44

provided with two magnets

45

a

and

45

b.

FIGS. 6

a

and

6

b

show alternative embodiments of means for connection to the reference point (x

0

, y

0

, z

0

).

FIG. 6

a

shows a connection means in the form of a sphere

50

which is inserted into a conically shaped precision hole

51

in the workshop floor

14

. An advantage with a sphere compared with a point is that the sphere gives the measuring device a larger working range. Instead of a balance weight and springs, the measuring device shown in

FIG. 6

b

is provided with two supporting legs

52

a

,

52

b

to balance the measuring device. Each of the supporting legs terminates with a spherical body which is inserted into respective conical holes in the floor.

FIG. 7

a

shows an embodiment of a means adapted to be in contact with the robot during the calibration process, wherein the means is formed as a sphere

55

which will be referred to in the following as a measuring ball. During the calibration process, the measuring ball is in contact with a conically shaped hole

56

in the robot or a calibration tool

57

. For distance measurements in the z-direction, a position sensor

58

is arranged below the measuring ball.

FIG. 7

b

shows an example of a calibration tool

57

adapted to be used in combination with the measuring ball

55

. The calibration tool comprises a rod

58

with a plurality of conical holes,

56

a

,

56

b

,

56

c

,

56

d

, arranged in spaced relationship to each other.

To reduce the number of necessary measurements when determining the kinematic error parameters of the robot, the calibration tool may be provided with a gravity sensor

59

, whereby both the working point (TCP) of the tool and the inclination in the xz-plane may be measured with high accuracy.

If the measuring device comprises more than one measuring ball with an associated position sensor, a large working range may be obtained for measuring the error parameters of the robot.

By making the measuring device in telescopic design and measuring the compression of the telescope with, for example, a resolver arrangement, the measuring range in the z-direction may be greatly extended.

A further extension of the measuring range is obtained with a measuring device

77

comprising an optical measuring system, whereby either the measuring device is provided with a light source and the robot-carried tool is provided with light detectors or vice versa.

FIG. 8

shows the case where a light source

60

, suitably a laser diode, is mounted in a cylindrical and hollow measuring rod

61

. The measuring rod

61

may be rotated by a motor

62

, which is arranged on a platform

63

, balanced by springs, with guide pins

64

and a precision ball

65

in a conical precision hole

66

in the workshop floor. On the measuring rod

61

, a gravity sensor

67

is mounted, and when the motor

62

rotates around the measuring rod

61

, the gravity sensor measures the direction

60

a

of the axis of rotation relative to the direction of gravity. At the same time the axis of rotation

60

a

is the axis around which the light beam from the laser diode will move. If the light beam hits a lateral photodetector, for example a lateral photodiode or photomatrix, the illuminated spot on the detector will move in a circular path on the surface of the detector. The center of this path will thus be the point of intersection of the axis of rotation with the surface of the detector.

FIGS. 8

a

and

8

b

show how the robot-carried calibration tool

68

is provided with two lateral photodetectors

69

and

70

, which are mounted perpendicular to each other to capture the two light beams

72

and

73

from a beamsplitter

71

. When the calibration tool is placed straight above the measuring rod

61

, as shown in

FIG. 8

a

, the detector

70

will read the position of the tool in the x- and z-directions whereas the detector

69

reads the orientation of the tool in the xz plane. If a beamsplitter

74

is mounted at the orifice of the measuring rod

61

, possibilities of making measurements perpendicular to the axis of rotation of the measuring rod are obtained. Thus, according to

FIG. 8

b

, the two detectors

69

and

70

measure the position in the z-direction, whereas the detector

70

may also be used for measuring the tool orientation in the xz plane.

FIG. 8

c

shows how an electromagnetic sensor

75

, which may be capacitive or inductive, measures the position of the measuring point (x

r

, y

r

) in the xy-plane relative to the cylindrical surface of the measuring rod

61

. The cylindrical surface may, where necessary, consist of plane grinding surfaces. By placing collars

76

on the measuring rod, the sensor can also measure the position of the measuring point in the z-direction, that is, z

r

. In addition to electromagnetic sensors, mechanical or ultrasonic sensors can be used.

FIG. 9

shows how the measuring device and the calibration tool in

FIG. 5

a

are arranged for measuring the synchronizing error Δθ

5

of the axis A

5

as well as the attitude error φ

6

y5

and the offset errors O

6

y5

of axis A

6

relative to axis A

4

. The configuration of the robot is chosen so that axis A

4

and axis A

6

are horizontal. The calibration tool

41

is mounted on the tool attachment

6

a

of the robot in such a way that the calibration tool

41

becomes centered in the average direction of rotation of the axis A

6

. The robot is run so that the calibration tool

41

makes mechanical contact with the measuring rod

31

. The measurements are carried out with the calibration tool or the robot axis A

2

in two positions, POS A and POS B. In POS A, contact is achieved between the measuring rod and that part of the calibration tool which is nearest the tool attachment, and in POS B contact is achieved between the measuring rod and the outer part of the calibration tool. The distance between the measuring rod in position A and in position B is L

AB

. The following measurement sequence is carried out:

a) With the calibration tool (or robot) in position according to POS A, axis A

6

is rotated three-fourths of a revolution and the gravity sensor is read at the angles θ6=0, π/2, π, 3π/2 for axis A

6

. The robot thus assumes four different configurations at which the gravity sensor is read.

b) With the calibration tool in position according to POS A, axis A

4

is rotated at least three-fourths of a revolution and the gravity sensor is read at the angles θ4=0, π/2, π, 3π/2 for axis A

4

. The robot thus assumes an additional four different configurations at which the gravity sensor is read.

c) Repeat point a above with the calibration tool in position according to POS B.

d) Repeat point b above with the calibration tool in position according to POS B.

From the readings from point a and point c, the offset errors, OT

y

, OT

z

, and the attitude errors AT

y

, AT

z

, of the calibration tool relative to axis A

6

are calculated, both in the y- and z-directions.

FIG. 10

a

shows how the attitude errors of the calibration tool in the y-direction are calculated. The average movement in the y-direction in positions A and B is calculated according to the following:

Δ

y

m

A

=(

y

m

A

(θ6=0)−

y

m

A

(θ6=π)/2 (10)

Δ

y

m

B

=(

y

m

B

(θ6=0)−

y

m

B

(θ6=π)/2 (11)

y

m

B=The position of the measuring rod in the y-direction when measuring in POS B.

y

m

A=The position of the measuring rod in the y-direction when measuring in POS A.

AT

y

=(Δ

y

m

B−Δy

m

A

)/

L

AB

(12)

From the readings from point b and point d, the offset errors for axis A

6

relative to axis A

4

, and the attitude errors for axis A

6

relative to axis A

4

are calculated.

FIG. 10

b

shows how the attitude error φ

6

y5

for axis A

6

in the y-direction is calculated. The distance between the center point of the tool, TCP (Tool Center Point), and position B is designated L

TCP

. The movement of the measuring rod in the y-direction when measuring in position B, Δy

m

B, is calculated according to the following:

Δ

y

m

B

=(

y

m

B

(θ

4

=0)−

y

m

B

(θ

4

=π)/2 (13)

The attitude error of axis A

6

in the y-direction relative to axis A

4

, φ

6

y5

, is calculated according to the following equation:

φ6

y5

=Δy

m

B/L

TCP

(14)

FIG. 10

c

shows how the synchronizing error Δθ

5

of axis A

5

may be calculated. The synchronizing error Δθ

5

of axis A

5

is identical with the attitude error in the z-direction for axis A

6

, φ

5

z5

.

Δ

z

m

B

=(

z

m

B

(θ

4

=π/2)−

y

m

B

(θ

4

=3π/2)/2 (15)

Δθ5=φ6

z5

=Δz

m

B/L

TCP

(16)

FIG. 10

d

shows how the offset error O

6

z5

of axis A

6

relative to axis A

4

in the z-direction can be calculated. The following relationship may be set up:

φ6

z5

=(Δ

z

m

A−O

6

z5

)/(

L

TCP

−L

AB

)=(Δ

z

m

B−O

6

z5

) /

L

TCP

(17)

From this equation, the offset error O

6

z5

may be solved:

O

6

z5

=Δz

m

A·L

TCP

/L

AB

−Δz

m

B

·(

L

TCP

−L

AB

)/

L

AB

(18)

In the above-mentioned calculations, the errors of the calibration tool have already been compensated for. The same principle may be used for measuring the offset errors between axis A

1

and axis A

4

.

FIGS. 11

a

and

11

b

show how the attitude errors φ

1

x1

, φ

1

y1

of axis A

1

relative to the direction of gravitation are measured. φ

1

x1

=α

x

and φ

1

y1

=α

y

, see

FIGS. 4

a

and

4

b

, and is calculated according to equations

4

and

5

. In this embodiment, the robot holds the measuring rod

31

by hooking the rod onto the calibration tool

41

with the aid of the hook

47

which is placed across the holder

48

on the calibration tool. The measuring device, which is fixed to the calibration tool, is suspended somewhat above the shop floor.

FIG. 11

b

shows a simplified sketch of

FIG. 11

a

viewed from above. The robot is then run to four different configurations (A, B, C, D according to

FIG. 11

b

) at which the gravity sensor is read. The four configurations differ only in that the angle of axis A

1

is different. The measured values thus obtained from the gravity sensor then provide the attitude errors of axis A

1

relative to the direction of gravity. The measured values in positions A and B give φ

1

x1

, and the measured values in positions B and D give φ

1

y1

. The same principle may be used for determining the synchronizing error of axes A

3

-A

6

.

In

FIG. 12

a

the measuring rod

31

has been placed in the hole

13

and a hole

56

in the calibration tool has been positioned across the measuring ball

55

which is mounted on the position sensor

33

. For a given robot configuration, that is, for given angles of the axes of rotation A

1

-A

6

, the position (x

r

, y

r

, z

r

) of the measuring point is determined. In the z-direction the position is measured by means of the position sensor

33

. In the x- and y-directions, the position is calculated by means of the equations 4, 5, 6 and 7 using output signals read from the gravity sensor

34

. If the attitude errors and the offset errors of axis A

1

relative to the workshop floor are desired, three precision holes

13

,

13

b

and

13

c

with separate reference points (x

0

, y

0

, z

0

), (x

1

, y

1

, z

1

) and (x

2

, y

2

, z

2

) may be arranged in the floor according to

FIG. 12

b

. The robot then inserts the measuring rod

31

into these recision holes and at each precision hole, measurements of the position of the measuring point are performed according to the above. During the measurements in the holes

13

,

13

b

and

13

c

, the robot is to have the same axial angles for axes A

2

-A

6

, that is, only axis A

1

has different values of the axial angles. From the differences between the measured values in the z-direction for holes

13

,

13

b

and

13

c

, the attitude errors in the x- and y-directions for axis A

1

relative to the floor shop are calculated. From the position determinations in the x- and y-directions for holes

13

,

13

b

and

13

c

, the offsets in the x-direction (

01

x1

) and in the y-direction (

01

y1

) of axis A

1

relative to the nominal position (P

1

) for axis A

1

are calculated.

The synchronizing errors of axes A

1

, A

2

and A

3

are measured with the same arrangement as in

FIG. 12

a

. The hole

13

is measured so as to constitute the zero position for the position sensors of axis A

1

and axis A

2

. The length of the measuring rod corresponds to the zero position of the position sensor of axis A

3

. The synchronizing error of axis A

1

, Δθ

1

is given by the inclination of the measuring rod in the y-direction. In order to directly separate the synchronizing errors of axis A

2

, Δθ

2

from the synchronizing error in axis A

3

, Δθ

3

, axes A

2

and A

3

should be in synchronizing position during the measurement (the second arm

4

vertical and the third arm

5

horizontal). If this is the case, the inclination of the measuring rod in the x-direction will provide the synchronizing error of axis A

2

whereas the value in the z-direction read by the sensor

34

gives the synchronizing error of axis A

3

.

Δθ1

=Δy

m

/(

L

TCP

+L

3) (19)

Δθ2=Δ

x

m

/L

2 (20)

Δθ3=Δ

z

m

/(

L

TCP

+L

3) (21)

When the direction of axis A

1

is known in relation to the direction of gravity (FIG.

11

), the attitude error φ

2

z1

and φ

3

z2

of axes A

2

and A

3

may be determined as the deviation from 90° between axis A

2

and axis A

1

and between axis A

3

and axis A

1

, respectively.

In

FIG. 13

, the attitude error φ

3

z2

of axis A

3

is measured by recording the inclination of the measuring rod in the y-direction at two different robot configurations, Kon A and Kon B, which have the same axial angles for axes A

1

, A

2

, A

4

-A

6

, that is, only axis A

3

has different values of the axial angles. To measure the attitude error in the x-direction, φ

3

x2

, the axis A

2

is rotated so that also the attitude error in the x-direction gives rise to detectable differences in inclination of the measuring rod (see FIG.

14

). The attitude error φ

3

x2

is calculated from the difference in measured attitude error between the measurements in FIG.

14

and FIG.

13

. The measured attitude errors apply relative to the direction of gravity and are therefore re-calculated to apply relative to the direction of axis A

1

with knowledge of the direction of axis A

1

relative to the direction of gravity, which is measured according to FIG.

11

.

The attitude error of axis A

2

in the z-direction, φ

2

z1

, is measured in a corresponding way (see FIG.

15

). Measurements are carried out for two different robot configurations, Kon E and Kon F, which have the same axial angles for axes A

1

, A

3

-A

6

, that is, only axis A

2

has different values of the axial angles. The attitude errors of axis A

2

in the x-direction are normally compensated for during the synchronization of axis A

1

, unless the robot has a design with a large offset between axis A

1

and axis A

2

.

Transmission errors caused by errors in the parallelogram transmission between the motor of axis A

3

and the second robot arm

4

are measured in the simplest way when the measuring rod

31

is hooked onto the calibration tool according to

FIG. 11

a

. The inclination of the measuring rod in the x-direction for different angles of axis A

2

and axis A

3

is then measured with the sensor

34

. From these measurements, a table is then calculated which denotes the transmission error for different angular values of axis A

2

and axis A

3

.

FIG. 16

shows a method of measuring and identifying the arm's length error of the second robot arm

4

. The measurements are carried out in two different robot configurations, Kon G and Kon H. The configurations are chosen such that axis A

4

and axis A

6

are horizontal. Axis A

2

is then run to two positions in which the calibration tool and the measuring rod are in contact with each other. In Kon G, axis A

2

is in the zero position, which means that the second robot arm is vertical. In Kon H, axis A

2

has an angle φ

2

which is known. In both configurations, the measuring rod

31

is rotated, and x

m

G and x

m

H are calculated by means of equations 4 and 6. From

FIG. 16

the following relationship may be set up

x

m

G

=(

L

3

+L

54

+L

c

+L

GH

) (22)

x

m

H

=(

L

2

·sinφ

2

+L

3

+L

4

+L

c

) (23)

x

m

H

−x

m

G

=L

2

·sinφ

2

−L

GH

(24)

L

2

=(

x

m

H=x

m

G+L

GH

)/sinφ

2

(25)

Δ

L

2

=L

2

nom

−L

2

(26)

The other arm's length errors may be measured in the same way.

Number	Name	Date
4435905	Bryan	Mar 1984
4804897	Gordon et al.	Feb 1989
4883938	Sarugaku	Nov 1989
5151007	Maruo	Sep 1992
5239855	Schleifer et al.	Aug 1993
5343397	Yoshino et al.	Aug 1994
5404086	Takenaka et al.	Apr 1995
5448146	Erlbacher	Sep 1995
5668453	Muto et al.	Sep 1997

Number	Date	Country
44 19 909 A1	Dec 1997	DE
69911	Mar 1989	JP

Device and method for calibration of a multi-axis industrial robot

Information

Patent Number

Date Filed

Date Issued

Inventors

Original Assignees

Examiners

Agents

CPC

US Classifications

Field of Search

US

International Classifications

Abstract

Description

Claims

Priority Claims (1)

PCT Information

US Referenced Citations (9)

Foreign Referenced Citations (2)