Calibration Principles

This topic describes the working principles of calibrations in different scenarios.

Hand-Eye Calibration in the ETH Setup (Multiple Random Calibration Board Poses)

calibration reference eth 1

The coordinates of the robot flange in the robot base reference frame, denoted by A, are known. By capturing images of the calibration board, the coordinates of the camera’s optical center relative to each calibration circle, denoted by B, can be obtained. The transformation relationship between the reference frames of the camera’s optical center and the robot base, denoted by X, is the unknown variable. Thus, A, B, C, and X form a closed loop (C is a constant), and the value of X can be calculated through the equations generated from the loop. By moving the robot, multiple poses of the calibration board can form a set of equations, which give an optimal value of X by numerical fitting and optimization algorithm. This is shown in the following figure.

calibration reference eth explanation

Equations for calculating the transformation relationship between the camera and robot reference frames are shown in the following figure.

calibration reference random eth math

Hand-Eye Calibration in the EIH Setup (Multiple Random Calibration Board Poses)

calibration reference eih 1

In this scenario, the camera is mounted on a flange that is fixed at the end of the robot. The spatial relationship between the center of the flange and the camera’s optical center, denoted by X, is an unknown constant. The pose of the flange in the robot base reference frame denoted by B, is a known variable. The spatial relationship between the camera’s optical center and each circle on the calibration board, denoted by C, can be calculated by capturing images of the calibration board with the camera. The calibration board is placed within the camera’s field of view. The pose of the calibration board in the robot base reference frame, denoted by A, is a measurable constant. Thus, A, B, C, and X form a closed loop. In the equations, since A is a constant, when the first two equations are combined, X will be the only unknown variable. As the robot moves to different poses, the camera will capture images from different angles and produce multiple sets of A, B, and C. Then, these values can be used to perform numerical fitting and obtain an optimal solution of X.

calibration reference eih explanation

Equations for calculating the transformation relationship between the camera and robot flange reference frames are shown in the following figure.

calibration reference random eih math

Hand-Eye Calibration in the ETH Setup (TCP Touch)

calibration reference eth 2

When the TCP touch method is used, the calibration board is placed on the object plane and a sharp-tipped tool with known dimensions is installed on the robot flange. Then, the robot will be moved to let the center point of the tool touch the cross center points of the calibration circles. As shown in the following figure, the values of A and B are known, and the value of X can be obtained. When the calibration board is not fixed on the flange, the value of A can be calculated by touching the cross center points of the calibration circles on the calibration board using a sharp-tipped tool with known TCP coordinates.

calibration reference eth tcptouch

Hand-Eye Calibration in the EIH Setup (TCP Touch)

calibration reference eih 2

When the TCP touch method is used, the calibration board is placed on the object plane and a sharp-tipped tool with known dimensions is installed on the robot flange. Then, the robot will be moved to let the center point of the tool touch the cross center points of the calibration circles. As shown in the following figure, since the values of A, B and C are known, the value of X can also be obtained.

calibration reference eih tcptouch

Hand-Eye Calibration in the ETE Setup

Using double cameras can expand the camera field of view and improve the point cloud quality of the two cameras’ overlapping part, as shown in the following figure.

calibration reference ete fov

In the eye-to-eye (ETE) setup, two cameras, one as main camera and the other as sub-camera, are mounted on a stand independent of the robot. Eye to Eye calibration will not only calibrate the extrinsic parameters for the two cameras, but also calibrate the pose relationship between the two cameras. For the ETE setup, Mech-Vision provides a standard ETE calibration procedure.

Please pay attention to the following issues when calibrating with two cameras.

  • The two cameras used should have the same resolution and the overlapping area of their field of view (2D&3D) should cover the entire working area.

  • Mounting the two cameras in the EIH setup is not supported. If the cameras have to be mounted in the EIH setup, you can view the fusion effect for dual camera calibration through the Mech-Vision project.

  • The parameter group of dual camera calibration can be directly calculated based on the calibrated camera parameter groups in the ETH or EIH setup.

  • Once the parameter group of dual camera calibration is calculated directly from the calibrated camera parameter group in the EIH setup, the point cloud cannot be viewed by loading the existing calibration parameters.

We Value Your Privacy

We use cookies to provide you with the best possible experience on our website. By continuing to use the site, you acknowledge that you agree to the use of cookies. If you decline, a single cookie will be used to ensure you're not tracked or remembered when you visit this website.