# US 12,194,642 B2 · Kinematics calibration method and calibration system for robot with multiple degrees of freedom

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- Number: US 12,194,642 B2
- Document ID: US12194642B2
- Status: Granted
- Kind: B2
- Application number: 17/617,677
- Filed: 2021-11-05
- Published: 2024-01-11
- Granted: 2025-01-14
- Earliest claimed: 2021-11-05
- Assignees: Foshan Flexiv Robotics Technology Co, . Ltd.; Flexiv Ltd.
- Applicants: Foshan Flexiv Robotics Technology Co, . Ltd.; Flexiv Ltd.
- Inventors: Xuesen Li; Kenneth Chao; Yakun Ma; Hao Jiang; Peizhang Zhu; Mengshen Wu; Maozhi Liu; Shuyun Chung; Xiyang Yeh; Shiquan Wang
- Web page: https://patentgrep.com/patent/US12194642B2

## CPC

- B25J 9/1692: {Calibration of manipulator}
- B25J 9/1653: {parameters identification, estimation, stiffness, accuracy, error analysis}
- B25J 9/1664: {characterised by motion, path, trajectory planning}
- G05B 2219/39027: Calibrate only some links, part of dofs, lock some links, ref pins on links
- B25J: MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES ({manipulators specially adapted for use in surgery A61B34/70; manipulators used in cleaning hollow articles B08B9/04}; manipulators associated with rolling mills B21B39/20; manipulators associated with forging machines B21J13/10; {manipulators associated with picking-up and placing mechanisms B23P19/007}; means for holding wheels or parts thereof B60B30/00; {vehicles with ground-engaging propulsion means, e.g. walking members B62D57/02, B62D57/032; devices for picking-up and depositing articles or materials between conveyors B65G47/90, B65G47/91; manipulators with gripping or holding means for transferring packages B65H67/065}; cranes B66C; {manipulators used in the protection or supervision of pipe-line installations F17D5/00; walking equipment adapted for nuclear steam-generators F22B37/006}; manipulators specially adapted for, or associated with, nuclear reactors G21C; {apparatus used for handling wafers during manufacture or treatment of semiconductor H10P72/50})
- G05B: CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS (systems for controlling or regulating non-electric variables G05D; systems for regulating electric or magnetic variables G05F; control devices or systems insofar as characterised by mechanical features only G05G)

## Abstract

The present disclosure relates to a kinematics calibration method for a robot with multiple degrees of freedom. The robot includes a base, an end effector, and a plurality of links connected by joints. The method includes locking part of the multiple degrees of freedom by limiting the base and the end effector impose a limitation of degree of freedom; moving the robot to perform a first movement and accordingly obtaining a first set of data associated with joint angles and a first actual motion of the end effector; calculating a first theoretical motion of the end effector based on the first set of data and initial kinematics parameters; and updating the initial kinematics parameters of the robot to obtain a first set of updated kinematics parameters based on the first theoretical motion and the first actual motion.

## Claims

### Claim 1

A kinematics calibration method for a robot with multiple degrees of freedom, the robot comprising a base, an end effector, and a plurality of links connected by joints, the kinematics calibration method comprising:
locking part of the multiple degrees of freedom by limiting the base and the end effector to impose a limitation of degree of freedom;
moving the robot to perform a first movement and accordingly obtaining a first set of data associated with joint angles and a first actual motion of the end effector;
calculating a first theoretical motion of the end effector based on the first set of data and initial kinematics parameters; and
updating the initial kinematics parameters of the robot to obtain a first set of updated kinematics parameters based on the first theoretical motion and the first actual motion;
wherein the robot comprises an n-axis robot with n degrees of freedom, where n is a natural number greater than or equal to 2; and
wherein locking part of the multiple degrees of freedom comprises locking n−1 degrees of freedom by fixing the base and the end effector simultaneously, such that the robot is configured to move in its null space, and moving the robot to perform the first movement comprises moving the robot to perform a first null-space motion.

### Claim 2 (depends on 1)

The kinematics calibration method of claim 1, wherein the moving the robot to perform the first movement comprises controlling the joint to move the robot to perform the first movement, or moving the robot to perform the first movement by an external force.

### Claim 3 (depends on 1)

The kinematics calibration method of claim 1, further comprising:
moving the robot to perform a second movement in the same null-space as the first movement and accordingly obtaining a second set of data associated with the joint angles and a second actual motion of the end effector, the second movement being different from the first movement;
calculating a second theoretical motion of the end effector based on the second set of data and the initial kinematics parameters; and
updating the initial kinematics parameters to obtain a second set of updated kinematics parameters based on the second theoretical motion and the second actual motion, and determining calibrated kinematics parameters based on the first set of updated kinematics parameters and the second set of updated kinematics parameters.

### Claim 4 (depends on 1)

The kinematics calibration method of claim 1, further comprising:
moving the robot to perform a second movement and accordingly obtaining a second set of data associated with the joint angles and a second actual motion of the end effector, the second movement being different from the first movement;
calculating a second theoretical motion of the end effector based on the second set of data and the first set of updated kinematics parameters; and
updating the first set of updated kinematics parameters to obtain a second set of updated kinematics parameters based on the second theoretical motion and the second actual motion, the second set of updated kinematics parameters being taken as calibrated kinematics parameters.

### Claim 5 (depends on 1)

The kinematics calibration method of claim 1, wherein the moving the robot to perform the first movement comprises changing the angles of all the joints of the robot to perform the first movement.

### Claim 6 (depends on 1)

The kinematics calibration method of claim 1, wherein the robot comprises a redundant robot with seven degrees of freedom, the locking n−1 degrees of freedom comprising locking the base and locking the end effector to a first position, thereby locking six degrees of freedom.

### Claim 7 (depends on 6)

The kinematics calibration method of claim 6, further comprising:
moving and locking the end effector to a second position different from the first position;
moving the robot to perform a third null-space motion and accordingly obtaining a third set of data associated with the joint angles and a third actual motion of the end effector;
calculating a third theoretical motion of the end effector based on the third set of data and the initial kinematics parameters; and
updating the initial kinematics parameters to obtain a third set of updated kinematics parameters based on the third theoretical motion and the third actual motion, and determining calibrated kinematics parameters based on the first set of updated kinematics parameters and the third set of updated kinematics parameters.

### Claim 8 (depends on 1)

The kinematics calibration method of claim 1, wherein the updating the initial kinematics parameters of the robot to obtain a first set of updated kinematics parameters based on the first theoretical motion and the first actual motion comprises updating the initial kinematics parameters by performing pair-wise distance measurements.

### Claim 9 (depends on 1)

The kinematics calibration method of claim 1, wherein the locking part of the multiple degrees of freedom comprises locking the base while allowing movement of the end effector in a plurality of directions, a number of the plurality of directions being less than that of the multiple degrees of freedom.

### Claim 10 (depends on 9)

The kinematics calibration method of claim 9, wherein the end effector is configured to move in a fixed linear direction along a linear track.

### Claim 11 (depends on 9)

The kinematics calibration method of claim 9, wherein the end effector is configured to rotate about an axis of a bearing.

### Claim 12 (depends on 9)

The kinematics calibration method of claim 9, wherein the end effector is configured to move in a plane.

### Claim 13 (depends on 9)

The kinematics calibration method of claim 9, wherein the end effector is configured to rotate about a center of the ball joint.

### Claim 14

A kinematics calibration system for a robot with multiple degrees of freedom, the robot comprising a base, an end effector, and a plurality of links connected by joints, part of the multiple degrees of freedom of the robot being locked by limiting the base and the end effector, wherein the kinematics calibration system comprises a control system for kinematically calibrating the robot, and the control system is configured to:
calculate a first theoretical motion of the end effector based on a first set of data associated with joint angles due to a first movement of the robot and initial kinematics parameters; and
update the initial kinematics parameters of the robot to obtain a first set of updated kinematics parameters based on the first theoretical motion and a first actual motion due to the first movement of the robot;
wherein the robot comprises an n-axis robot with n degrees of freedom, where n is a natural number greater than or equal to 2, and n−1 degrees of freedom are locked by fixing the base and the end effector simultaneously, such that the robot is configured to move in its null space, the first movement of robot comprising a first null-space motion.

### Claim 15 (depends on 14)

The kinematics calibration system of claim 14, wherein the control system is further configured to perform the first movement.

### Claim 16 (depends on 14)

The kinematics calibration system of claim 14, wherein the control system is further configured to:
calculate a second theoretical motion of the end effector based on a second set of data associated with the joint angles due to a second movement in the same mill-space as the first movement of the robot and the initial kinematics parameters, the second movement being different from the first movement; and
update the initial kinematics parameters to obtain a second set of updated kinematics parameters based on the second theoretical motion and a second actual motion due to the second movement of the robot, and determining calibrated kinematics parameters based on the first set of updated kinematics parameters and the second set of updated kinematics parameters.

### Claim 17 (depends on 14)

The kinematics calibration system of claim 14, wherein the control system is further configured to:
calculate a second theoretical motion of the end effector based on a second set of data associated with the joint angles due to a second movement of the robot and the first set of updated kinematics parameters, the second movement being different from the first movement; and
update the first set of updated kinematics parameters to obtain a second set of updated kinematics parameters based on the second theoretical motion and a second actual motion due to the second movement of the robot, the second set of updated kinematics parameters being taken as calibrated kinematics parameters.

### Claim 18 (depends on 14)

The kinematics calibration system of claim 14, wherein the robot comprises a redundant robot with seven degrees of freedom, six of which are locked by locking the base and locking the end effector to a first position.

### Claim 19 (depends on 18)

The kinematics calibration system of claim 18, the control system is further configured to:
calculate a third theoretical motion of the end effector based on a third set of data associated with the joint angles due to a third null-space motion of the robot and the initial kinematics parameters, the third null-space motion of the robot is performed when the end effector has been moved to a second position different from the first position; and
update the initial kinematics parameters to obtain a third set of updated kinematics parameters based on the third theoretical motion and a third actual motion due to the third null-space motion of the robot, and determining calibrated kinematics parameters based on the first set of updated kinematics parameters and the third set of updated kinematics parameters.

### Claim 20 (depends on 14)

The kinematics calibration system of claim 14, wherein the control system is configured to update the initial kinematics parameters based on the first theoretical motion and a first actual motion by performing pair-wise distance measurements.

### Claim 21 (depends on 14)

The kinematics calibration system of claim 14, wherein the base of the robot is locked while the end effector is allowed to move in a number of directions less than that of the multiple degrees of freedom, and
wherein the end effector is configured to move in a fixed linear direction along a linear track, rotate about an axis of a bearing, move in a plane, or rotate about a center of the ball joint.