Course-Eye-in-Hand Camera Calibration Guide (Using RGB + Pose Data)

🎯 Objective

The goal of this calibration is to determine the intrinsic and extrinsic parameters of an RGB camera that is mounted on a robotic arm (eye-in-hand configuration).

• Intrinsic Parameters: Describe the internal characteristics of the camera (e.g., focal length, principal point, distortion).
• Extrinsic Parameters: Describe the spatial relationship (rotation and translation) between the camera and the robot end-effector.

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🗃️ Dataset Description

• Data Format: Each calibration sample includes:
  • One RGB image
  • One 6-DOF pose of the robot end-effector
• Total Samples: 37
• Pose Representation:
  • Translation: $ (x, y, z) $, in millimeters
  • Rotation: $ (r_x, r_y, r_z) $, in radians
  • Rotation Order: XYZ (fixed angles)
  • Coordinate System: Right-hand coordinate system

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📌 Calibration Setup

• Camera Mounting: Eye-in-hand (camera is fixed on the robot end-effector)
• Target: Usually a checkerboard or AprilTag board fixed in the world coordinate frame
• Assumption: The transformation between the robot base and the calibration target is static

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🧮 Calibration Procedure

Step 1: Image and Pose Collection

• Move the robotic arm to various poses while ensuring the target is visible in the camera view.
• For each pose:
  • Record the RGB image
  • Record the 6-DOF pose of the robot end-effector

Step 2: Detect Features in Image

• Detect corner points or tag centers (e.g., checkerboard corners) in each image.
• These 2D image points correspond to known 3D points on the target.

Step 3: Estimate Intrinsic Parameters

• Use OpenCV or similar toolboxes to compute:
  • Focal lengths $ f_x, f_y $
  • Principal point $ p_x, p_y $
  • Lens distortion coefficients

Step 4: Estimate Extrinsic Parameters

• Solve the Hand-Eye Calibration problem:
  • Input: Robot poses + camera poses relative to the calibration board
  • Output: Transformation from camera to robot flange $ \mathbf{T}_{\text{camera}}^{\text{end-effector}} $
• Common method: Tsai-Lenz or Dual Quaternion-based approach

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📐 Output

• Intrinsic Matrix $ K $:

\[K = \begin{bmatrix} f_x & 0 & p_x \\ 0 & f_y & p_y \\ 0 & 0 & 1 \end{bmatrix}\]

• Distortion Coefficients: $ k_1, k_2, p_1, p_2, k_3 $

• Extrinsic Matrix $[\mathbf{R} \mid \mathbf{t}]$: Rotation and translation from robot end-effector to camera

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✅ Notes

• Accuracy improves with more diverse poses and clear feature detection
• Avoid positions with poor visibility or insufficient viewpoint change
• Double-check unit consistency (e.g., mm vs m, degrees vs radians)

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📚 Recommended Libraries

• OpenCV
• Kalibr
• ROS camera_calibration

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📎 Application

This calibration result can be used in:

• 3D vision-based grasping
• Visual servoing
• Pose estimation
• Robotic SLAM and mapping