What methods exist for hand–eye calibration?

• A. Methods include Tsai, Dania or dual-quaternions; practitioners collect correspondences between known robot poses and camera observations to solve for the transform
• B. Only manual alignment
• C. Using only magnetometers
• D. Hand–eye calibration is not possible

Answer: (A)

Finding the fixed spatial relationship between the robot’s end-effector and the camera is done by estimating a single rigid transform that links the two frames. In practice you record a sequence of robot motions and, for the same movements, observe how the camera frame changes relative to the world. Those paired motions are used to solve for the transform X in the relation A_i X = X B_i (where A_i is the robot motion and B_i is the camera motion between poses). Using multiple motion pairs provides enough information to determine X accurately. Classical methods like Tsai–Lenz give a closed-form solution, while dual-quaternion approaches offer an efficient and robust way to handle rotations and translations together; some formulations explicitly include Daniilidis’s dual-quaternion approach as another effective path. This is why the described approach is correct: it uses known robot poses and camera observations to compute the fixed hand–eye transform.

Manual alignment alone lacks the data redundancy needed for a reliable 6-DoF calibration. Relying only on magnetometers doesn’t capture the full spatial relationship between the camera and the robot, and hand–eye calibration is indeed possible and routinely performed in practice.