Hand-Eye Calibration

Key Insight

A camera bolted to a robot arm is useless until you know the exact transform between the camera's frame and the arm's frame, and you cannot measure that offset with a ruler. Hand-eye calibration recovers it by moving the arm to many poses, recording how a fixed tag appears to shift in the camera, and solving the resulting AX = XB equation, where the unknown X is the rigid camera-to-hand offset. Get it right and the arm can grasp whatever the camera sees; get it wrong by even a degree and every grasp drifts, which is why reporting the residual error is part of finishing the project.