Camera above the robot base: eye-to-hand calibration setup

You mounted the camera high behind the robot base, lens pointing down at the work surface, and the standard hand-eye recipes look like they were written for some other geometry. They were not. This setup solves as an ordinary eye-to-hand calibration. This guide gives you the standoff that holds near-0.2 mm pixels, the field-of-view arithmetic that keeps the board in frame through every pose, the mount that keeps the camera still, and the checks that confirm the camera-to-base transform before you trust a pick to it.

Is a camera above and behind the base still an eye-to-hand setup?

Yes — the solver only asks that the camera stays fixed relative to the robot base and the target stays fixed to the flange. A high, set-back mount solves as an ordinary eye-to-hand case with an offset viewpoint. The mounting direction never enters the math; only the two rigidity conditions do. That is why your earlier camera-on-base run and this look-down run use the same solver mode.

Eye-to-hand means the camera lives in the world frame and the target rides the flange; eye-in-hand flips that. The eye-in-hand vs eye-to-hand mounting comparison shows what changes when the camera rides the wrist. The capture format is identical either way: one flange pose plus one board pose per position.

Both sides of that identity equal the board's pose in the base frame. Two constants are unknown: the camera-to-base transform X on the right and the board-to-flange mount on the left. The solver collects a set of captures and returns both. The hand–eye calibration problem encyclopedia entry summarizes the AX = XB formulation most solvers implement.

How high above the workspace should the camera sit?

For a bench arm with 300-400 mm of travel, put the lens 700-900 mm above the board plane. That holds the pixel footprint near 0.2 mm and leaves frame margin for every pose. Two demands set that band. Resolution: the pixel footprint grows in direct proportion to distance, and checker-corner detection wants at least 15-20 px per square. Focus: your tilted viewpoint changes the board's distance across the workspace, and the focal depth must swallow that spread.

Worked example, with a typical bench camera of 2592 × 1948 px on a 7.2 × 5.4 mm sensor and a 12 mm lens at 800 mm standoff:

• FOV: 7.2 mm × 800 mm / 12 mm = 480 mm wide, 360 mm high.
• Pixel footprint: 480 mm / 2592 px = 0.185 mm, so a 20 mm checker square spans 108 px.
• Distance spread: at 15° behind vertical over a 300 mm-deep workspace, 300 mm × sin 15° = 78 mm, so the board plane sits between 761 and 839 mm.
• Focal depth at f/8, with the 2.8 µm pixel pitch as focus tolerance: H = 12² / (8 × 0.0028) + 12 = 6441 mm, near limit 713 mm, far limit 912 mm — a 200 mm span.

The span covers the spread with margin at both ends, so 800 mm at f/8 carries the 15° tilt. Level the mount to 10° and f/5.6 covers the reduced 52 mm spread instead. Set focus at the middle distance and lock it. The depth-of-field calculator reruns these limits for your lens, and target and standoff at short range covers mounts closer than half a metre.

How much field of view do the calibration poses need?

Size the frame for the worst calibration pose, not the whole workspace. The board's projected width at full yaw plus its pose sweep must fit with 5% spare on each edge — a 370 mm demand inside the 480 mm frame of the worked example. Yaw swings its corners out to the diagonal, so a 140 × 100 mm board at 45° projects (140 + 100) × sin 45° = 170 mm. Add a 200 mm sweep of the board center and the demand is 370 mm against a 480 mm frame: 55 mm clear on each edge, 11% of the width. Keep at least 5% per edge so corners always have clean backdrop.

Size your own frame with the calculator below.

The other half of the sizing is the board itself: enough squares to give 20 or more inner corners, small enough that the yawed width plus sweep fits. How big a board your poses need walks that choice.

Which poses keep the target in frame and the solve stable?

Capture 10-15 flange poses that sweep the board across roughly three quarters of the frame and rotate it through at least ±45° of yaw and ±20° of pitch. Pose diversity, not pose count, is what pins all six unknowns of the transform. Work the set against four rules:

• Sweep the board's full extent through 70-80% of the frame width; the remaining margin is your detector backdrop.
• Include pitches that turn the board 10-30° off the camera axis; those tilted pairs make the rotation of X observable.
• Skip translation-only sets: without board rotation the rotational part of X stays undetermined. If the wrist cannot pitch, fix the board at a permanent angle to the flange so flange yaw tilts it.
• Inspect every capture before saving; a corner hidden under the flange or clipped at the frame edge poisons the whole solve.

If a planned pose turns out unreachable at your standoff, scaling the calibration grid to the robot's reach shows how to shrink the sweep without losing diversity.

What holds the camera still while the arm moves?

Bolt the camera to its own rigid stand outside the arm's swept volume. The solver reads any stand motion between captures as noise, and a 1 mm camera shift becomes roughly a 1 mm pick error at the workspace. The failure is quiet: nothing tips over, but a lean on the column or a taut cable moves the camera a millimetre, and every pick afterwards misses by that millimetre. Calibrate, then re-image the scene an hour later; if the board's camera-frame pose moved, the mount moved.

A machine-vision camera stand holds stiller than a photo tripod because the column locks with a clamp, not a friction head; the accessories finder filters by column height and base size. The LS-MNT-0040 has a 700 mm column height and a 400 × 450 mm base. Sized for a bench, it puts the lens close to the 800 mm worked standoff.

A manual tilt stage under the camera holds the set-back angle through a whole session, and a small XY-plus-rotation stage lets you aim laterally without touching the column clamp.

How do you run the solve and check the result?

Run it as five steps — lock the intrinsics, capture flange-and-image pairs, solve in eye-to-hand mode, demand residuals under 1 mm, then verify on a pose the solver never saw.

1. Solve the lens intrinsics once, at the same focus and aperture you will calibrate with; the camera intrinsics for hand-eye calibration guide covers the order of operations.
2. At each pose, let the arm settle for about a second, then save the flange pose (position and quaternion in the base frame) and the image together — one pair per pose, 10-15 pairs.
3. Feed the pairs to your hand-eye tool in its camera-on-base, eye-to-hand mode, using the same tool frame you will pick with; the nine-point alignment walkthrough shows what such a solve consumes, and the planar variant is covered in configuring XY tablet mapping for eye-to-hand calibration.
4. Read the residuals before accepting the result: on a bench rig expect corner reprojection below 0.5 px and pose-to-pose translation error below 1 mm. A single pose above 2 mm usually means a clipped corner or an early save — drop it and re-solve.
5. Verify on a pose the solver never saw: park the flange over a marked point, read it in the camera, push it through X into the base frame and compare with the controller's own position. Agreement within 1-2 mm is a working calibration; verifying the camera-to-base result gives the full test.

With X verified, using the result to compute robot-base picks turns the matrix into grasp targets; the same pixel-to-base chain is walked through in this pixel-to-robot-base transform walkthrough.

When does the set-back mount fail?

The set-back geometry fails for three reasons — the flange hides the board at steep tool angles, the tilt pushes corners out of focus, or the stand moves between captures — and re-running the solver fixes none of them.

• Occlusion: when the flange pitches toward the camera it can shadow board corners. Reduce the pitch of those poses or raise the standoff until every corner is visible in every capture.
• Focus: if the distance spread outgrows the focal depth computed above, stop down one f-stop or level the mount, then recompute the near and far limits for the new numbers.
• Stand drift: any bump invalidates the whole transform, so keep the unseen-pose check from the last section as a 30-second daily test.
• Frame-edge distortion: very wide lenses bend corners near the frame edge, so calibrate with the lens you pick with and keep the board out of the outer 10% of the frame.

If the camera is one of the structured-light 3D sensors rather than a 2D camera, run the same solve: it consumes board poses in the camera frame either way. For your own bench, size standoff and frame with the calculators above, choose a stand that clamps rather than leans — the stand configurator pairs stand, tilt stage and camera in one pass — and if you want a second opinion on the pose plan, contact the team.