Lab 2 · Hand-eye calibration

Goal#

Solve for T_World_Cam — and deliberately produce the illusion of "wrong configuration, small residual".

Steps#

1. Confirm C1 pixel size is done and still valid (Calibration → Overview).
2. Calibration → Hand-eye, configuration eye-to-hand, nine points, 60 mm span.
3. Record residual RMS and verify deviation.
4. Get it wrong on purpose: switch the configuration to eye-in-hand and re-solve on the same data. Record the residual — it may still be small.
5. Use the verify deviation to decide which one is right.
6. Close the loop: click a point in the image, let the stage move there, measure how far off it lands.

Pass criteria#

Item	Criterion
Step 3 residual RMS	< 0.03 mm
Step 3 deviation	< 0.05 mm
Step 4 residual	possibly just as small — that is the point of this lab
Step 4 deviation	far outside tolerance
Step 6 closed-loop error	< 0.08 mm

Common mistakes#

• Wrong configuration. No error is raised; you get a small residual and a wrong answer.
• Nine points in a line. The matrix is near singular and the solve is unstable. Spread them into a grid.
• Touching the camera mid-run. The extrinsics change and every earlier pose is invalid.
• Solving and verifying on the same data. The residual is guaranteed to look good and proves nothing.

Review questions#

1. Why can the residual stay small when the configuration is wrong? What does that say about "self-consistent" versus "correct"?
2. What happens if the nine points form a 3×3 grid with only 2 mm spacing? Sketch how the condition number changes with span.
3. In the closed-loop error, how much comes from hand-eye, how much from pixel size, how much from motion? Decompose it with the error budget method.