# US 12,109,714 B1 · Kinematics parameter calibration method and system of multi-axis motion platform

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- Number: US 12,109,714 B1
- Document ID: US12109714B1
- Status: Granted
- Kind: B1
- Application number: 18/483,499
- Filed: 2023-10-09
- Published: 2024-10-10
- Granted: 2024-10-08
- Earliest claimed: 2023-04-06
- Assignees: Guangdong University of Technology
- Applicants: Guangdong University of Technology
- Inventors: Jian Gao; Guoqing Wu; Yuheng Luo; Lanyu Zhang; Zhuojun Zheng; Disai Chen; Xin Chen
- Web page: https://patentgrep.com/patent/US12109714B1

## CPC

- B25J 9/1692: {Calibration of manipulator}
- B25J 9/1697: {Vision controlled systems}
- Y02T 10/40: Engine management systems
- 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})
- Y02T: CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION

## Abstract

Disclosed are a kinematics parameter calibration method and system of a multi-axis motion platform. The method comprises the following steps of: collecting calibration board images in different spatial positions according to a position relation between the platform and a camera, recording a corresponding motor motion amount, solving a hand-eye pose relation matrix and a pose matrix of a calibration board coordinate system in a platform tail end coordinate system, further solving a coordinate measured value of an angular point on the calibration board in a platform base coordinate system and a coordinate theoretical value of a position matrix of the tail end of the motion platform, determining a residual error matrix according to the measured value and the theoretical value, and identifying an error parameter by the residual error matrix to complete kinematics parameter calibration of the platform.

## Claims

### Claim 1

A kinematics parameter calibration method of a multi-axis motion platform, comprising the following steps of:
calibrating intrinsic parameters of a camera;
establishing a theoretical kinematics model of the multi-axis motion platform, establishing a kinematics error model of the multi-axis motion platform according to the theoretical kinematics model, and determining an error parameter;
based on photos of a calibration board taken by the camera at different spatial positions, solving for a first homogeneous coordinate pose matrix of a calibration board coordinate system in a camera coordinate system using a PnP (Perspective-n-Point) algorithm and recording a first motor motion amount corresponding to the multi-axis motion platform at each spatial position;
substituting the first motor motion amount into the theoretical kinematics model to obtain a platform pose matrix; based on a one-to-one relationship between the first homogeneous coordinate pose matrix and the platform pose matrix, and using a hand-eye calibration method corresponding to a type of hand-eye position relationship, calculating a hand-eye pose relation matrix and a pose matrix of the calibration board coordinate system in an end coordinate system of the multi-axis motion platform; wherein the types of the hand-eye position relation include an eye outside hand and an eye on hand;
controlling the multi-axis motion platform to move to different poses, capturing images of the calibration board through the camera; based on the images of the calibration board, solving for a second homogeneous coordinate pose matrix of the calibration board coordinate system in the camera coordinate system using the PnP algorithm; obtaining a corner point coordinate matrix formed by at least three coplanar calibration board corner points in the calibration board coordinate system; and based on the hand-eye pose relationship matrix, the corner point coordinate matrix, and the second homogeneous coordinate pose matrix, determining coordinate measurement values of the calibration board corner points in a platform base coordinate system;
based on second motor motion amounts in different poses, the theoretical kinematic model, the pose matrix and the corner point coordinate matrix of the calibration board in the end coordinate system of the multi-axis motion platform, determining coordinates theoretical values of an end position matrix of the multi-axis motion platform; and based on multiple sets of coordinate measurement values and coordinates theoretical values, determining a residual error matrix, and identifying error parameters to obtain a calibration result of the kinematic parameters of the multi-axis motion platform.

### Claim 2 (depends on 1)

The kinematics parameter calibration method of the multi-axis motion platform according to claim 1, wherein the step of determining a residual error matrix and identifying error parameters to obtain a calibration result of the kinematic parameters of the multi-axis motion platform comprises the following step of:
determining the residual error matrix according to the multiple sets of the coordinate measurement values of the end of the multi-axis motion platform and coordinate theoretical values of the end of the multi-axis motion platform, and identifying the error parameters by an LM (Levenberg-Marquardt) algorithm or a Trust Region algorithm according to the residual error matrix to obtain the kinematics parameter calibration result of the multi-axis motion platform.

### Claim 3 (depends on 1)

The kinematics parameter calibration method of the multi-axis motion platform according to claim 1, wherein the step of calibrating intrinsic parameters of the camera comprises the following step of:
collecting the photos of the calibration board taken by the camera at different spatial positions, and calibrating the intrinsic parameters of the camera by Zhang Zhengyou's Calibration Method.

### Claim 4 (depends on 1)

The kinematics parameter calibration method of the multi-axis motion platform according to claim 1, wherein a calculation formula for the pose matrix of the calibration board coordinate system in the end coordinate system of the multi-axis motion platform is:
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wherein, boardendM is the pose matrix of the calibration board coordinate system in the end coordinate system of the multi-axis motion platform, endbaseM is the platform pose matrix, camerabaseM is the hand-eye pose relationship matrix, and boardcameraM1 is the first homogeneous coordinate pose matrix.

### Claim 5 (depends on 4)

The kinematics parameter calibration method of the multi-axis motion platform according to claim 4, wherein a calculation formula for determining the coordinate measurement values of the calibration board corner points on the calibration board in the multi-axis motion platform base coordinate system is:
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wherein, PHO are coordinate measurement values of the calibration board corner points in the platform base coordinate system, T is the corner point coordinate matrix in the calibration board coordinate system, and boardcameraM2 is the second homogeneous coordinate pose matrix.

### Claim 6 (depends on 5)

The kinematics parameter calibration method of the multi-axis motion platform according to claim 5, wherein a calculation formula for determining the coordinate theoretical values of the position matrix of the end of the multi-axis motion platform is:
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wherein, PHT are the coordinate theoretical values of the position matrix of the end of the multi-axis motion platform.