METHOD OF DETECTING AN INTER-AXIS OFFSET OF 6-AXIS ROBOT

• US 20120239194A1
• Filed: 03/19/2012
• Published: 09/20/2012
• Est. Priority Date: 03/18/2011
• Status: Active Grant

• Current Assignee: Denso PS Corporation (DENSO Corporation)
• Original Assignee: Denso PS Corporation (DENSO Corporation)
• Inventors: KAGAWA, Naoya
• Granted Patent: US 8,918,210 B2
• Time in Patent Office: Days
• US Class Current: 700/254
• CPC Class Codes: B25J 9/1692 Calibration of manipulator
• CPC Class Codes: G05B 2219/40588 Three laser scanners project beam on photodiodes on end effector

Abstract

In a 6-axis robot, as an example, an inter-axis offset can be measured and calibrated. A light emitting diode is installed on an end effector, and the end effector is located on a plurality of target positions of movement on the axis X (Xb) of a robot coordinate. Then, the position of the light emitting diode is measured by a three-dimensional gauge, and an inter-axis offset F is detected based on an error between the target positions of movement and actually moved positions. For the inter-axis offset F, DH parameters are calibrated.

Claims

1. A method of detecting an inter-axis offset of a robot, which is a 6-axis robot including a base link fixed to an installation surface and a robot arm opposed to the base link, and the robot arm is configured by sequentially interconnecting a first link, a second link, a third link, a fourth link, a fifth link, and a sixth link of a robot arm through a first rotation joint, a second rotation joint, a third rotation joint, a fourth rotation joint, a fifth rotation joint, and a sixth rotation joint, wherein a rotation center line of a rotation shaft of the second rotation joint connecting the second link to the first link extends in parallel to a direction perpendicular to a rotation center line of a rotation shaft of the first rotation joint connecting the first link to the base link, a rotation center line of a rotation shaft of the third rotation joint connecting the third link to the second link extends in parallel to the rotation center line of the rotation shaft of the second rotation joint, a rotation center line of a rotation shaft of the fourth rotation joint connecting the fourth link to the third link extends in parallel to a direction perpendicular to the rotation center line of the rotation shaft of the third rotation joint, a rotation center line of a rotation shaft of the fifth rotation joint connecting the fifth link to the fourth link extends in parallel to a direction perpendicular to the rotation center line of the rotation shaft of the fourth rotation joint, a rotation center line of a rotation shaft of the sixth rotation joint connecting the sixth link to the fifth link extends in parallel to a direction perpendicular to the rotation center line of the rotation shaft of the fifth rotation joint, coordinates of the first to sixth links are set on the rotation center lines of the rotation shafts of the first to sixth rotation joints, and a coordinate of an end effector of the robot arm is set at a position of a rotation center of a distal end surface of the sixth link, the distal end surface corresponding to a most distal end of the robot arm, the position of the rotation center of the distal end corresponding to a position of the end effector, the method comprising:

arranging a measurement point on the end effector and arranging a three-dimensional measurement means capable of measuring a three-dimensional position of the measurement point;

rotating the robot arm around the rotation shaft of the first rotation joint while maintaining a posture in which the rotation center line of the fifth rotation joint is in parallel to the rotation center lines of the second rotation joint and the third rotation joint, and measuring three or more different positions of the measurement point, which moves along a circular rotation trajectory by the rotation of the robot arm, by a three-dimensional measurement means;

from the three or more different positions of the measurement point on the circular rotation trajectory, obtaining a normal line of a plane including a center position of the rotation trajectory and the three or more different positions of the measurement point, and determining a reference coordinate in which a center of the rotation trajectory of the measurement point serves as an origin of the reference coordinate, a linear lines extending through the origin in parallel to the normal line serves as a Z-axis thereof, a linear lines extending through the origin and perpendicular to the Z-axis serves as an X-axis thereof, and a linear lines extending through the origin and perpendicular to both the Z-axis and the X-axis as a Y-axis thereof;

determining a plurality of positions on one plane including the Z-axis of the reference coordinate and extending from the Z-axis as target positions of movement, and moving the end effector to the target positions of movement;

performing a correction in order to prevent occurrence of position error of the end effector due to a motor origin error of a motor operating the first to sixth links through first to sixth driving systems including the rotation shafts of the first to sixth rotation joints, a deflection of the first to sixth rotation driving systems, the position errors by the length errors of the first to sixth links, and angle errors between rotations shafts of a rotation joint and a next rotation joint;

rotating the rotation shaft of the first rotation joint to a position, which enables the end effector to be moved to the target positions of movement by rotating at least one rotation joint among the second, third, and fifth rotation joints while maintaining a state in which the rotation center line of the fifth rotation joint is parallel to the rotation center lines of the rotation shafts of the second and third rotation joints, moving the end effector to each of the target positions of movement by rotating at least one rotation joint among the second, third, and fifth rotation joints, while fixing the rotation shaft of the first rotation joint, and measuring the position of the measurement point by the three-dimensional measurement means at the respective target positions of movement;

obtaining X and Y coordinate values of the measurement point on the reference coordinate by performing a coordinate transformation of the positions of the measurement point measured at the target positions of movement into positions on the reference coordinate, plotting the obtained X and Y coordinate values of the measurement point on the X-Y plane of the reference coordinate, putting segments interconnecting the plotted points as measurement dependence segments, obtaining a length of a perpendicular line from the origin of the reference coordinate onto a linear lines obtained by extending the measurement dependence segments, and determining the obtained length of the perpendicular line as an amount of deviation; and

determining the determined amount of deviation as a sum of inter-axis offsets of the second, third, and fifth rotation joints.

2. The method of claim 1, wherein an operation of determining a plurality of positions on a plane including the Z-axis of the reference coordinate and extending from the Z-axis as target positions of movement and moving the end effector to the target positions of movement on the plane is performed with respect to two planes extending in opposite directions from the Z-axis of the reference coordinate, and a movement of the end effector from a plane extending in one direction from the Z-axis to a plane extending in the opposite direction is performed by inverting the robot arm by rotating a rotation shaft of at least one rotation joint among the second, third, and fifth rotation joints in a state in which the rotation shaft of the first rotation joint is fixed.

3. The method of claim 1, comprising, in place of an operation up to when the inter-axis offset is obtained, after the reference coordinate is determined:

when the end effector is moved to a plurality of target positions of movement on the reference coordinate,

performing a correction in order to prevent occurrence of position error of the end effector due to a motor origin error of a motor operating the first to sixth links through first to sixth driving systems including the rotation shafts of the first to sixth rotation joints, a deflection of the first to sixth rotation driving systems, the position errors by the length errors of the first to sixth links, and angle errors between rotations shafts of a rotation joint and a next rotation joint;

moving the end effector to each of the target positions of movement by rotating at least one rotation joint among the second, third, and fifth rotation joints, while maintaining a state in which the rotation center line of the fifth rotation joint is parallel to the rotation center lines of the rotation shafts of the second and third rotation joints, and measuring the position of the measurement point by the three-dimensional measurement means at the respective target positions of movement;

obtaining coordinate values of the measurement point on the so reference coordinate by performing a coordinate transformation of the positions of the measurement point measured at the target positions of movement into positions on the reference coordinate;

for each of the target positions of movement, plotting X and Y coordinate values of the target position of movement and X and Y coordinate values of the measurement point on the X-Y plane of the reference coordinate, putting a length of a segment from the origin of the reference coordinate to the target position of movement as a target position radius, and putting a length of a perpendicular line from the measurement point to a linear lines extending through the origin and the target position of movement as an offset error component;

for each of the target positions of movement, drawing a graph having two orthogonal axes indicating the target position radius and the offset error component, respectively, plotting dots reflecting a relation between the target position radius and the offset error component for the target position of movement, putting a linear lines passing through the plotted dots as an error linear lines, drawing a perpendicular line from an origin of the graph to the error linear lines, and obtaining a length of the perpendicular line as an amount of deviation; and

determining the obtained amount of deviation as a sum of inter-axis offsets of the second, third, and fifth rotation joints.

4. The method of claim 3, wherein an operation of moving the end effector to a plurality of target positions of movement on the reference coordinate is performed in both a forward fallen-down posture in which the robot arm is fallen down in one direction from the first link and a backward fallen-down posture in which the robot arm is fallen down in an opposite direction from the first link, by rotating the rotation shafts of at least the second and third rotation joints among the second, third, and fifth rotation joints in one direction and an opposite direction in a state in which the rotation shaft of the first rotation joint is fixed.

5. A method of detecting an inter-axis offset of a robot, which is a 6-axis robot including a base link fixed to an installation surface and a robot arm opposed to the base link, and the robot arm is configured by sequentially interconnecting a first link, a second link, a third link, a fourth link, a fifth link, and a sixth link of a robot arm through a first rotation joint, a second rotation joint, a third rotation joint, a fourth rotation joint, a fifth rotation joint, and a sixth rotation joint, wherein a rotation center line of a rotation shaft of the second rotation joint connecting the second link to the first link extends in parallel to a direction perpendicular to a rotation center line of a rotation shaft of the first rotation joint connecting the first link to the base link, a rotation center line of a rotation shaft of the third rotation joint connecting the third link to the second link extends in parallel to the rotation center line of the rotation shaft of the second rotation joint, a rotation center line of a rotation shaft of the fourth rotation joint connecting the fourth link to the third link extends in parallel to a direction perpendicular to the rotation center line of the rotation shaft of the third rotation joint, a rotation center line of a rotation shaft of the fifth rotation joint connecting the fifth link to the fourth link extends in parallel to a direction perpendicular to the rotation center line of the rotation shaft of the fourth rotation joint, a rotation center line of a rotation shaft of the sixth rotation joint connecting the sixth link to the fifth link extends in parallel to a direction perpendicular to the rotation center line of the rotation shaft of the fifth rotation joint, coordinates of the first to sixth links are set on the rotation center lines of the rotation shafts of the first to sixth rotation joints, and a coordinate of an end effector of the robot arm is set at a given position on the rotation center line of the rotation shaft of the sixth rotation joint of the sixth link, the given position corresponding to a position of the end effector, the method comprising:

arranging a measurement point integrally operating with the sixth link at a position spaced apart from the rotation center line of the sixth link, and arranging a three-dimensional measurement means capable of measuring a three-dimensional position of the measurement point;

rotating the first link to three or more different angle positions while maintaining the robot arm in a posture in which the rotation center line of the fifth rotation joint is in parallel to the rotation center lines of the second rotation joint and the third rotation joint, and measuring three or more different positions of the measurement point on a rotation trajectory, which rotates integrally with the sixth link, by a three-dimensional measurement means during a rotation of the sixth link at each of the angle positions of the first link;

from the three or more different positions of the measurement point on the rotation trajectory by the rotation of the sixth link measured at the respective angle positions of the first link, obtaining a position of a rotation center of the measurement point at each of the angle positions, determining a center of the rotation center of the measurement point as a virtual end effector position for setting a reference coordinate, obtaining a normal line of a plane, which includes a center position of a circle passing through the virtual end effector position for setting a reference coordinate and three or more virtual end effector positions for setting the reference coordinate, from the obtained virtual end effector position for setting the reference coordinate, and determining a reference coordinate in which a center of the obtained circle of the measurement point serves as an origin of the reference coordinate, a linear lines extending through the origin in parallel to the normal line serves as a Z-axis thereof, a linear lines extending through the origin and perpendicular to the Z-axis serves as an X-axis thereof, and a linear lines extending through the origin and perpendicular to both the Z-axis and the X-axis as a Y-axis thereof;

determining a plurality of positions on one plane extending from the Z-axis of the reference coordinate as target positions of movement, and moving the end effector to the target positions of movement;

performing a correction in order to prevent occurrence of position error of the end effector due to a motor origin error of a motor operating the first to sixth links through first to sixth driving systems including the rotation shafts of the first to sixth rotation joints, a deflection of the first to sixth rotation driving systems, the position errors by the length errors of the first to sixth links, and angle errors between rotations shafts of a rotation joint and a next rotation joint;

rotating the rotation shaft of the first rotation joint to a position, which enables the end effector to be moved to the target positions of movement by rotating at least one rotation joint among the second, third, and fifth rotation joints while maintaining a state in which the rotation center line of the fifth rotation joint is parallel to the rotation center lines of the rotation shafts of the second and third rotation joints, moving the end effector to each of the target positions of movement by rotating at least one rotation joint among the second, third, and fifth rotation joints, while fixing the rotation shaft of the first rotation joint, and measuring three or more different positions on a rotation trajectory of the measurement point, which rotates integrally with the sixth link, by a three-dimensional measurement means during a rotation of the sixth link at the respective target positions of movement;

obtaining a rotation center position of the measurement point from the three or more positions on the rotation trajectory of the measurement point measured at the respective target positions of movement, and obtaining X and Y coordinate values of the virtual end effector position for setting the reference coordinate on the reference coordinate by performing a coordinate transformation of the virtual end effector position for setting the reference coordinate into positions on the reference coordinate;

plotting the obtained X and Y coordinate values of the virtual end effector position for setting the reference coordinate on the X-Y plane of the reference coordinate, putting segments interconnecting the plotted points as measurement dependence segments, obtaining a length of a perpendicular line from the origin of the reference coordinate onto a linear lines obtained by extending the measurement dependence segments, and determining the obtained length of the perpendicular line as an amount of deviation; and

determining the determined amount of deviation as a sum of inter-axis offsets of the second, third, and fifth rotation joints.

6. The method of claim 5, wherein an operation of determining a plurality of positions on a plane extending from the Z-axis of the reference coordinate as target positions of movement and moving the end effector to the target positions of movement on the plane is performed with respect to two planes extending in opposite directions from the Z-axis of the reference coordinate, and a movement of the end effector from a plane extending in one direction from the Z-axis to a plane extending in the opposite direction is performed by inverting the robot arm by rotating a rotation shaft of at least one is rotation joint among the second, third, and fifth rotation joints in a state in which the rotation shaft of the first rotation joint is fixed.

7. The method of claim 5, comprising, in place of an operation up to when the inter-axis offset is obtained, after the reference coordinate is determined:

when the end effector is moved to a plurality of target positions of movement on the reference coordinate,

performing a correction in order to prevent occurrence of position error of the end effector due to a motor origin error of a motor operating the first to sixth links through first to sixth driving systems including the rotation shafts of the first to sixth rotation joints, a deflection of the first to sixth rotation driving systems, the position errors by the length errors of the first to sixth links, and angle errors between rotations shafts of a rotation joint and a next rotation joint;

moving the end effector to each of the target positions of movement in a state, in which the rotation center line of the rotation shaft of the sixth rotation joint is parallel to the rotation center line of the rotation shaft of the first rotation joint, by rotating at least one rotation joint among the second, third, and fifth rotation joints, while maintaining a state in which the rotation center line of the fifth rotation joint is parallel to the rotation center lines of the rotation shafts of the second and third rotation joints, and measuring three or more different positions on a rotation trajectory of the measurement point, which rotates integrally with the sixth link, by a three-dimensional measurement means during a rotation of the sixth link at the respective target positions of movement;

obtaining a rotation center position of the measurement point from a plurality of positions on the rotation trajectory of the measurement point measured at the respective target positions of movement, performing a coordinate transformation of the virtual end effector position for setting the reference coordinate into positions on the reference coordinate, and obtaining X and Y coordinate values of the virtual end effector position for setting the reference coordinate on the reference coordinate;

for each of the target positions of movement, plotting X and coordinate values of the target position of movement and X and Y coordinate values of the measurement point on the X-Y plane of the reference coordinate, putting a length of a segment from the origin of the reference coordinate to the target position of movement as a target position radius, and putting a length of a perpendicular line from the virtual end effector position for setting the reference coordinate to a linear lines extending through the origin of the reference coordinate and the target position of movement on the X-Y plane as an offset error component;

for each of the target positions of movement, drawing a graph having two orthogonal axes indicating the target position radius and the offset error component, respectively, plotting dots reflecting a relation between the target position radius and the offset error component for the target position of movement, putting a linear lines passing through the plotted dots as an error linear lines, drawing a perpendicular line from an origin of the graph to the error linear lines, and obtaining a length of the perpendicular line as an amount of deviation; and

determining the obtained amount of deviation as a sum of inter-axis offsets of the second, third, and fifth rotation joints.

8. The method of claim 7, wherein an operation of moving the end effector to a plurality of target positions of movement on the reference coordinate is performed in both a forward fallen-down posture in which the robot arm is fallen down in one direction from the first link and a backward fallen-down posture in which the robot arm is fallen down in an opposite direction from the first link, by rotating the rotation shafts of at least the second and third rotation joints among the second, third, and fifth rotation joints in one direction and an opposite direction in a state in which the rotation shaft of the first rotation joint is fixed.

9. A method of detecting an inter-axis offset of a robot, which is a 6-axis robot including a base link fixed to an installation surface and a robot arm opposed to the base link, and the robot arm is configured by sequentially interconnecting a first link, a second link, a third link, a fourth link, a fifth link, and a sixth link of a robot arm through a first rotation joint, a second rotation joint, a third rotation joint, a fourth rotation joint, a fifth rotation joint, and a sixth rotation joint, wherein a rotation center line of a rotation shaft of the second rotation joint connecting the second link to the first link extends in parallel to a direction perpendicular to a rotation center line of a rotation shaft of the first rotation joint connecting the first link to the base link, a rotation center line of a rotation shaft of the third rotation joint connecting the third link to the second link extends in parallel to the rotation center line of the rotation shaft of the second rotation joint, a rotation center line of a rotation shaft of the fourth rotation joint connecting the fourth link to the third link extends in parallel to a direction perpendicular to the rotation center line of the rotation shaft of the third rotation joint, a rotation center line of a rotation shaft of the fifth rotation joint connecting the fifth link to the fourth link extends in parallel to a direction perpendicular to the rotation center line of the rotation shaft of the fourth rotation joint, a rotation center line of a rotation shaft of the sixth rotation joint connecting the sixth link to the fifth link extends in parallel to a direction perpendicular to the rotation centerline of the rotation shaft of the fifth rotation joint, a coordinate of the robot is set on the rotation center line of the rotation shaft of the rotation shaft of the first ration joint, coordinates of the first to sixth links are set on the rotation center lines of the rotation shafts of the first to sixth rotation joints, and a coordinate of an end effector of the robot arm is set at a given position on the rotation center line of the rotation shaft of the sixth rotation joint of the sixth link, the given position corresponding to a position of the end effector, the method comprising:

arranging a measurement point integrally operating with the sixth link at a position spaced apart from the rotation center line of the sixth link, and arranging a three-dimensional measurement means capable of measuring a three-dimensional position of the measurement point;

setting an initial rotation position of the first link corresponding to a proper rotation position of the first link and setting an initial rotation position of the sixth link corresponding to a proper rotation position of the sixth link gained when the first link is at the initial rotation position;

rotating the first link to three or more different rotation positions while maintaining the robot arm in a posture in which the rotation center line of the fifth rotation joint is in parallel to the rotation center lines of the second and third rotation joints and the rotation center line of the sixth rotation joint is in parallel to the rotation center line of the rotation shaft of the first rotation joint, and measuring, at each of the rotation positions of the first link, the position of the measurement point using the three-dimensional measurement means in a state where the sixth link is rotated from the initial rotation position thereof by an angle corresponding to a rotation angle of the first link obtained when the first link is rotated from the initial rotation position thereof to each of the respective rotation positions of the first link in a direction oppositely to a rotation direction of the first link;

obtaining, from the three or more positions of the measurement point measured at each of the rotation positions of the first link, a center position of a circle passing through the three or more positions and a normal line to a plane including the three or more positions, and setting a reference coordinate whose origin is the center position of the circle, whose Z-axis is a line parallel with the normal line passing through the origin, whose X-axis is a line being normal to the Z-axis and passing through the origin, and whose Y-axis is a line being normal to both the Z- and X-axes and passing through the origin;

setting, as target positions of movement, plural positions on a plane including the rotation center line of the rotation shaft of the first rotation joint, the plane being extended from the rotation center line of the rotation shaft of the first rotation joint;

performing a correction in order to prevent occurrence of position error of the end effector due to a motor origin error of a motor operating the first to sixth links through first to sixth driving systems including the rotation shafts of the first to sixth rotation joints, a deflection of the first to sixth rotation driving systems, the position errors by the length errors of the first to sixth links, and angle errors between rotations shafts of a rotation joint and a next rotation joint;

moving the end effector to the plural target positions of movement by rotating the rotation shafts of at least two of the second, third and fifth rotation joints in a state where i) the rotation center line of the rotation shaft of the fifth rotation joint is parallel with the rotation center lines of the rotation shafts of the second and third rotation joints and ii) a target-position reached posture is maintained, the target-position reached posture providing a state where the rotation center lines of the rotation shafts of the sixth and first rotation joints are parallel with each other;

obtaining offset-calculating measurement positions which are the positions of the target positions of movement measured by the three-dimensional measurement means, the measurement being made at each of the target positions of movement in the state where the sixth link is rotated from the initial rotation position thereof by the angle corresponding to the rotation angle of the first link obtained when the first link is rotated from the initial rotation position thereof to each of the respective rotation positions of the first link in the direction oppositely to the rotation direction of the first link;

calculating X and Y coordinate values of the offset-calculating measurement positions in the reference coordinate by coordinate-converting the offset-calculating measurement positions to positions in the reference coordinate;

plotting the calculated X and Y coordinate values of the offset-calculating measurement positions on the X-Y plane of the reference coordinate, putting segments interconnecting the plotted points as measurement dependence segments, obtaining a length of a perpendicular line from the origin of the reference coordinate onto a linear lines obtained by extending the measurement dependence segments, the length being an amount of deviation; and

determining the obtained amount of deviation as a sum of inter-axis offsets of the second, third, and fifth rotation joints.

10. The method of claim 9, wherein setting the target positions of movement and moving the end effector to the plural target positions of movement are performed for two planes extended from the rotation center line of the rotation shaft of the first rotation joint in mutually opposite directions,

the method comprising transferring one of the planes to the other plane by inverting the robot arm, wherein the rotation shafts of at least two of the second, three and fifth rotation joints are rotated with the first link fixed.

11. A method of detecting an inter-axis offset of a robot, which is a 6-axis robot including a base link fixed to an installation surface and a robot arm opposed to the base link, and the robot arm is configured by sequentially interconnecting a first link, a second link, a third link, a fourth link, a fifth link, and a sixth link of a robot arm through a first rotation joint, a second rotation joint, a third rotation joint, a fourth rotation joint, a fifth rotation joint, and a sixth rotation joint, wherein a rotation center line of a rotation shaft of the second rotation joint connecting the second link to the first link extends in parallel to a direction perpendicular to a rotation center line of a rotation shaft of the first rotation joint connecting the first link to the base link, a rotation center line of a rotation shaft of the third rotation joint connecting the third link to the second link extends in parallel to the rotation center line of the rotation shaft of the second rotation joint, a rotation center line of a rotation shaft of the fourth rotation joint connecting the fourth link to the third link extends in parallel to a direction perpendicular to the rotation center line of the rotation shaft of the third rotation joint, a rotation center line of a rotation shaft of the fifth rotation joint connecting the fifth link to the fourth link extends in parallel to a direction perpendicular to the rotation center line of the rotation shaft of the fourth rotation joint, a rotation center line of a rotation shaft of the sixth rotation joint connecting the sixth link to the fifth link extends in parallel to a direction perpendicular to the rotation center line of the rotation shaft of the fifth rotation joint, a coordinate of the robot is set on the rotation center line of the rotation shaft of the rotation shaft of the first ration joint, coordinates of the first to sixth links are set on the rotation center lines of the rotation shafts of the first to sixth rotation joints, and a coordinate of an end effector of the robot arm is set at a given position on the rotation center line of the rotation shaft of the sixth rotation joint of the sixth link, the given position corresponding to a position of the end effector, the method comprising:

arranging a measurement point integrally operating with the sixth link at a position spaced apart from the rotation center line of the sixth link, and arranging a three-dimensional measurement means capable of measuring a three-dimensional position of the measurement point;

setting an initial rotation position of the first link corresponding to a proper rotation position of the first link and setting an initial rotation position of the sixth link corresponding to a proper rotation position of the sixth link gained when the first link is at the initial rotation position;

rotating the first link to three or more different rotation positions while maintaining the robot arm in a posture in which the rotation center line of the fifth rotation joint is in parallel to the rotation center lines of the second and third rotation joints and the rotation center line of the sixth rotation joint is in parallel to the rotation center line of the rotation shaft of the first rotation joint, and measuring, at each of the rotation positions, of the first link, the position of the measurement point using the three-dimensional measurement means in a state where the sixth link is rotated from the initial rotation position thereof by an angle corresponding to a rotation angle of the first link obtained when the first link is rotated from the initial rotation position thereof to each of the respective rotation positions of the first link in a direction oppositely to a rotation direction of the first link;

obtaining, from the three or more positions of the measurement point measured at each of the rotation positions of the first link, a center position of a circle passing through the three or more positions and a normal line to a plane including the three or more positions, and setting a reference coordinate whose origin is the center position of the circle, whose Z-axis is a line parallel with the normal line passing through the origin, whose X-axis is a line being normal to the Z-axis and passing through the origin, and whose Y-axis is a line being normal to both the Z- and X-axes and passing through the origin;

setting, as target positions of movement, plural positions on a plane including the rotation center line of the rotation shaft of the first rotation joint, the plane being extended from the rotation center line of the rotation shaft of the first rotation joint;

performing a correction in order to prevent occurrence of position error of the end effector due to a motor origin error of a motor operating the first to sixth links through first to sixth driving systems including the rotation shafts of the first to sixth rotation joints, a deflection of the first to sixth rotation driving systems, the position errors by the length errors of the first to sixth links, and angle errors between rotations shafts of a rotation joint and a next rotation joint;

moving the end effector to the plural target positions of movement by rotating the rotation shaft of the first joint and the rotation shafts of at least two of the second, third and fifth rotation joints in a state where i) the rotation center line of the rotation shaft of the fifth rotation joint is parallel with the rotation center lines of the rotation shafts of the second and third rotation joints and ii) a target-position reached posture is maintained, the target-position reached posture providing a state where the rotation center lines of the rotation shafts of the sixth and first rotation joints are parallel with each other;

obtaining offset-calculating measurement positions which are the positions of the target positions of movement measured by the three-dimensional measurement means, the measurement being made at each of the target positions of movement in the state where the sixth link is rotated from the initial rotation position thereof by the angle corresponding to the rotation angle of the first link obtained when the first link is rotated from the initial rotation position thereof to each of the respective rotation positions of the first link in the direction oppositely to the rotation direction of the first link;

calculating X and Y coordinate values of the offset-calculating measurement positions in the reference coordinate by coordinate-converting the offset-calculating measurement positions to positions in the reference coordinate, and calculating target positions of movement in the reference coordinate by coordinate-converting the X and Y coordinate values of the target positions of movement to X and positions in the reference coordinate;

obtaining offset error components, wherein, for each of the target positions of movement, the X and Y coordinate values of the target positions of movement and the X and Y positions of the offset-calculating measurement positions are plotted on an X-Y plane of the reference coordinate, a length of a segment from an origin of the reference coordinate to the target position of movement on the X-Y plane is set as a target position radius, and a length of a normal line from the offset-calculating measurement position on the X-Y plane to a linear line passing through the origin of the reference coordinate and the target position of movement on the X-Y plane is set as the offset error component;

obtaining an amount of deviation, wherein, for each of the target positions of movement, a relationship between the target position radius and the offset error component is plotted on a graph with mutually orthogonal two axes such that the target position radius is assigned to one of the axes and the offset error component is assigned to the other axis, plotted points in the graph is connected by a liner line, and a normal line is drawn from an origin of the graph to the liner line, the normal line presenting the amount of deviation; and

determining the obtained amount of deviation as a sum of inter-axis offsets of the second, third, and fifth rotation joints.

12. The method of claim 11, wherein setting the target positions of movement and moving the end effector to the plural target positions of movement are performed for forward-bending and rearward-bending postures of the robot arm which are realized by rotating, in two mutually-opposite directions, the rotation shafts of at least the second and third rotation joints among the second, third and fifth rotation joints with the rotation shaft of the first rotation joint fixed, rotating the robot arm in the two directions providing the robot arm with the forward-bending and rearward-bending postures, respectively.

13. A method of detecting an inter-axis offset of a robot, which is a 6-axis robot including a base link fixed to an installation surface and a robot arm opposed to the base link, and the robot arm is configured by sequentially interconnecting a first link, a second link, a third link, a fourth link, a fifth link, and a sixth link of a robot arm through a first rotation joint, a second rotation joint, a third rotation joint, a fourth rotation joint, a fifth rotation joint, and a sixth rotation joint, wherein a rotation center line of a rotation shaft of the second rotation joint connecting the second link to the first link extends in parallel to a direction perpendicular to a rotation center line of a rotation shaft of the first rotation joint connecting the first link to the base link, a rotation center line of a rotation shaft of the third rotation joint connecting the third link to the second link extends in parallel to the rotation center line of the rotation shaft of the second rotation joint, a rotation center line of a rotation shaft of the fourth rotation joint connecting the fourth link to the third link extends in parallel to a direction perpendicular to the rotation center line of the rotation shaft of the third rotation joint, a rotation center line of a rotation shaft of the fifth rotation joint connecting the fifth link to the fourth link extends in parallel to a direction perpendicular to the rotation center line of the rotation shaft of the fourth rotation joint, a rotation center line of a rotation shaft of the sixth rotation joint connecting the sixth link to the fifth link extends in parallel to a direction perpendicular to the rotation center line of the rotation shaft of the fifth rotation joint, a coordinate of the robot is set on the rotation center line of the rotation shaft of the rotation shaft of the first ration joint, coordinates of the first to sixth links are set on the rotation center lines of the rotation shafts of the first to sixth rotation joints, and a coordinate of an end effector of the robot arm is set at a given position on the rotation center line of the rotation shaft of the sixth rotation joint of the sixth link, the given position corresponding to a position of the end effector, the method comprising:

locating a measurement point integrally operating with the six axis and arranging a three-dimensional measurement means capable of measuring a three-dimensional position of the measurement point;

first measuring, using the three-dimensional measurement means, three or more positions of the measurement point which moves on a circular rotary trajectory produced by rotating the robot arm about the rotation shaft of the first rotation joint with the robot arm maintained in an arbitrary posture thereof during the rotation;

first obtaining, from the measured three or more positions of the measurement point, a normal line to a plane including a center position of the rotation trajectory of the measurement point and the measured three or more positions of the measurement point, and setting a reference coordinate whose origin is provided as the center position of the rotation trajectory, whose Z-axis is provided by a linear line being parallel with the normal line and passing the origin, and whose X-axis is provided by an arbitrary linear line passing the origin and being perpendicular to the Z-axis, and whose Y-axis provided as a linear line being perpendicular to the Z- and X-axes and passing the origin;

setting a plurality of positions, as target positions of movement, on a plane including the rotation center line of the rotation shaft the first rotation joint;

performing a correction in order to prevent occurrence a positional error of a two-axis orthogonal intersection due to errors of origin positions of motors driving the first to fourth links via first to fourth rotation drive systems including the first to fourth rotation joints respectively, deflection of the first to fourth rotation drive systems, errors of lengths of the first to fourth links, and an error of an angle between rotation shafts of a rotation joint and a next rotation joint, the two-axis orthogonal intersection being a point at which the rotation center lines of the rotation shafts of both the fifth and sixth rotation joints intersect orthogonally to each other;

rotating the rotation shaft of the first rotation joint to a position which allows the two-axis orthogonal intersection to travel to the target positions of movement by rotating the rotation shafts of the second and third rotation joints;

moving the orthogonal intersection to each of the target positions of movement by rotating the rotation shafts of the second and third rotation joints with the rotation shaft of the first rotation joint positionally fixed;

second measuring three or more positions of the measurement point moving on a circular rotation trajectory produced by rotating the rotation shaft of the sixth rotation joint at each of the target positions of movement, by using the three-dimensional measurement means;

second obtaining, from the measured three or more points on the rotation trajectory, a center position of the rotation trajectory, a normal line normal to a plane including the center position and the measured three or more positions, and a first linear line being parallel with the normal line and passing the center position of the rotation trajectory;

third measuring three or more positions of the measurement point moved on a circular trajectory produced by rotating the rotation shaft of the fifth joint, by using the three-dimensional measurement means;

third obtaining, from the measured three or more points on the rotation trajectory, a center position of the rotation trajectory, a normal line normal to a plane including the center position and the measured three or more positions, and a second linear line being parallel with the normal line and passing the center position of the rotation trajectory;

fourth obtaining an intersection of both the first and second liner lines as the two-axis orthogonal intersection, and obtaining X- and Y-coordinate values of the intersection in the reference coordinate by coordinate-converting a position of the intersection into the reference coordinate;

fifth obtaining an amount of deviation by plotting the obtained X- and Y-coordinate values on the X-Y plane of the reference coordinate, and putting a segment interconnecting the plotted points as a measurement dependence segment, and obtaining a length of a perpendicular line from the origin of the reference coordinate onto a linear line obtained by extending the measurement dependence segment, the length being the amount of deviation; and

determining the obtained amount of deviation as a sum of inter-axis offsets of the second, third, and fifth rotation joints.

14. The method of claim 13, wherein

the first measuring step is a measuring step in which, with the rotation shafts of, at least, the second to fourth rotation joints among the first to sixth rotation joints fixed, and the first link is rotated to any three or more angular positions, and the rotation shaft of the sixth rotation joint is rotated at each of the three or more angular positions of the first link to produce the three or more positions of the measurement point on the rotation trajectory for the measurement using the three-dimensional measurement means;

and

the first obtaining step includes

a step of obtaining, from the measured three or more positions of the measurement point on the rotation trajectory, a center position of the rotation trajectory, a normal line normal to a plane including the center position and the three or more positions on the rotation trajectory, and a first linear line being parallel with the normal line and passing the center position of the rotation trajectory,

a step of making the rotation shaft of the fifth rotation joint rotate to produce a circular rotation trajectory, three or more positions of the measurement point being provided on the rotation trajectory, the three or more positions being measured by the three-dimensional measurement means,

a step of obtaining, from the measured three or more positions, a center position of the rotation trajectory and a normal line normal to a plane including the center position and the measured three or more positions, and obtaining a second linear line being parallel with the normal line and passing the center position of the rotation trajectory,

a step of designating an intersection of the obtained first and second liner lines as a measurement position of the two-axis orthogonal intersection, and

a step of defining the reference coordinate by obtaining, from the three or more two-axis orthogonal lines obtained at the respective angular positions, a center position of an arch passing the measurement positions of the three or more two-axis orthogonal intersections and a normal line to a plane including the measurement positions of the three or more two-axis orthogonal lines, the reference coordinate having an origin which is the center of the arc, the Z-axis which passes the origin and is parallel with the normal line, and the X-axis which passes the origin and is orthogonal to the Z-axis, and the Y-axis which passes the origin and is orthogonal to both the Z- and X-axes.

15. The method of claim 13, wherein, in place of the step of setting the target positions of movement, the step of performing the correction, the step of rotating the rotation shaft of the first rotation joint, the step of moving the orthogonal intersection, the second measuring step, the second obtaining step, the third measuring step, the third obtaining step, the fourth obtaining step, and the fifth obtaining step,

defining, as target positions of movement, a plurality of positions within a movable range of the two-axis orthogonal intersection;

moving the two-axis orthogonal intersection to each of the plurality of target positions of movement by rotating the rotation shafts of the first to third rotation joints, wherein a correction is made to prevent occurrence a positional error of the two-axis orthogonal intersection due to errors of origin positions of motors driving the first to fourth links via first to fourth rotation drive systems including the first to fourth rotation joints respectively, deflection of the first to fourth rotation drive systems, errors of lengths of the first to fourth links, and an error of an angle between rotation shafts of a rotation joint and a next rotation joint;

measuring, by using the three-dimensional measuring means, three or more positions on a circular rotation trajectory of the measurement point produced by rotating the rotation shaft of the six rotation joint at each of the target positions of movement;

obtaining, from the measured three or more positions of the measurement point, a center position of the rotation trajectory and a normal line to a plane including the measured three or more positions to obtain a first linear line being parallel with a normal line and passing the center position;

measuring, using the three-dimensional measuring means, three or more positions on a rotation trajectory of the measurement point produced by rotating the rotation shaft of the fifth rotation joint;

obtaining, from the measured three or more positions of the measurement point, a center position of the rotation trajectory and a normal line to a plane including the measured three or more positions to obtain a second liner line being parallel with the normal line and passing the center position;

obtaining a target position of movement in the reference coordinate by obtaining a measured position of a two-axis orthogonal intersection defined as an intersection of the first and second linear lines, coordinate-converging the measured position of the two-axis orthogonal intersection into X- and Y-coordinate values in the reference coordinate, and coordinate-converting X- and Y-coordinate values of each of the target positions of movement in the robot coordinate into X- and Y-coordinate values in the reference coordinate;

plotting the X- and Y-coordinate values of each of the target positions of movement and the X- and Y-coordinate values of the measured position of the two-axis orthogonal intersection into an X-Y plane of the reference coordinate, obtaining, as a target position radius, as a length of a segment from an origin of the reference coordinate to each of the target positions of movement in the X-Y plane, and obtaining, as an offset error component, a length of a normal line extending from the measured position of the two-axis orthogonal intersection in the X-Y plane to a liner line passing the origin of the reference coordinate and each of the target positions of movement; and

plotting, in a graph having mutually orthogonal two axes, for each of the target positions of movement, a relationship between the target position radius and the offset error component and the target position radius, the relationship being assigned to one of the axes and the target position radius being assigned to the other of the axes, obtaining an error liner line passing plotted points in the graph, and obtaining, as an amount of deviation, a length of a normal line from an origin of the graph to the error linear line.

16. A method of detecting an inter-axis offset of a robot, which is a 6-axis robot including a base link fixed to an installation surface and a robot arm opposed to the base link, and the robot arm is configured by sequentially interconnecting a first link, a second link, a third link, a fourth link, a fifth link, and a sixth link of a robot arm through a first rotation joint, a second rotation joint, a third rotation joint, a fourth rotation joint, a fifth rotation joint, and a sixth rotation joint, wherein a rotation center line of a rotation shaft of the second rotation joint connecting the second link to the first link extends in parallel to a direction perpendicular to a rotation center line of a rotation shaft of the first rotation joint connecting the first link to the base link, a rotation center line of a rotation shaft of the third rotation joint connecting the third link to the second link extends in parallel to the rotation center line of the rotation shaft of the second rotation joint, a rotation center line of a rotation shaft of the fourth rotation joint connecting the fourth link to the third link extends in parallel to a direction perpendicular to the rotation center line of the rotation shaft of the third rotation joint, a rotation center line of a rotation shaft of the fifth rotation joint connecting the fifth link to the fourth link extends in parallel to a direction perpendicular to the rotation center line of the rotation shaft of the fourth rotation joint, a rotation center line of a rotation shaft of the sixth rotation joint connecting the sixth link to the fifth link extends in parallel to a direction perpendicular to the rotation center line of the rotation shaft of the fifth rotation joint, a coordinate of the robot is set on the rotation center line of the rotation shaft of the rotation shaft of the first ration joint, coordinates of the first to sixth links are set on the rotation center lines of the rotation shafts of the first to sixth rotation joints, and a coordinate of an end effector of the robot arm is set at a given position on the rotation center line of the rotation shaft of the sixth rotation joint of the sixth link, the given position corresponding to a position of the end effector, the method comprising:

locating a measurement point integrally operating with the sixth link and arranging a three-dimensional measurement means capable of measuring a three-dimensional position of the measurement point;

measuring, using the three-dimensional measuring means, three or more positions on a circular trajectory of the measurement point produced by rotating the robot arm about the rotation shaft of the first rotation joint in a state the robot arm is maintained in an arbitrary posture,

defining a reference coordinate using the measured three or more positions, wherein data of the measured three or more positions are used to obtain a center position of the rotation trajectory and a normal line to a plane including the measured three or more points, and the reference coordinate is defined to have an origin as the center position, a Z-axis being parallel with the normal line and having the origin, an X-axis being orthogonal to the Z-axis and passing the origin, and a Y-axis being orthogonal to both the Z- and X-axes and passing the origin;

measuring, using the three-dimensional measuring means, a position of the measurement point with the end effector maintained in a reference posture and three or more points on a circular trajectory of the measurement point produced by rotating the rotation shaft of the sixth rotation joint;

obtaining a first linear line, wherein the measured three or more positions of the measurement point are used to obtain a center position of the rotation trajectory and a normal line to a plane including the measured three or more positions, the first linear line being parallel with the normal line and passing the center position;

measuring, using the three-dimensional measuring means, three or more positions on a circular rotation trajectory of the measurement point by rotating the rotation shaft of the fifth rotation joint;

obtaining a second linear line, wherein the measured three or more positions of the measurement point are used to obtain a center position of the rotation trajectory and a normal line to a plane including the measured three or more positions, the second linear line being parallel with the normal line and passing the center position;

obtaining a vector directed from the measured point in the reference posture of the end effector to an intersection of the first and second linear lines and an angle made between the vector and the X-, Y- and Z-axes of the reference coordinate;

defining, as target position of movements, a plurality of positions in a single plane including the rotation center line of the rotation shaft of the first rotation joint;

performing a correction in order to prevent occurrence a positional error of a two-axis orthogonal intersection due to errors of origin positions of motors driving the first to fourth links via first to fourth rotation drive systems including the rotation shafts of the first to fourth rotation joints respectively, deflection of the first to fourth rotation drive systems, errors of lengths of the first to fourth links, and an error of an angle between rotation shafts of a rotation joint and a next rotation joint, the two-axis orthogonal intersection being a point at which the rotation center lines of the rotation shafts of both the fifth and sixth rotation joints intersect orthogonally to each other;

rotating the rotation shafts of the second and third rotation joints such that the rotation shaft of the first rotation joint is rotated to a position which allow the two-axis orthogonal intersection to be moved to the target positions of movement;

moving the two-axis orthogonal intersection to each of the plural target positions of movement by rotating the rotation shafts of both the second and third rotation joints with the rotation shaft of the first rotation joint fixed;

measuring, using the three-dimensional measuring means, a position of the measurement point at each of the target positions of movement with the end effector maintained in the reference posture;

coordinate-converting the measured positions into positions in the reference coordinate;

defining a measured point of the two-axis orthogonal intersection in the reference coordinate, the measured point being an end point of the vector produced in the reference coordinate such that the vector is made to have the angle at the measured point;

obtaining a segment produced by connecting plotted points in the X-Y plane of the reference coordinate, wherein X and Y coordinate values of the measured position of the two-axis orthogonal intersection are plotted in the X-Y plane of the reference coordinate for each of the target positions of movement;

obtaining, as an amount of deviation, a length of a normal line drawn from the origin of the reference coordinate to a line extended from the segment; and

determining the obtained amount of deviation as a sum of inter-axis offsets of the second, third, and fifth rotation joints.