Two-camera sheet alignment with coordinated gripper moves

When one gripper reaches its reference but moves the opposite target away, the correction is treating a coupled mechanism as independent image positions. For a sheet that behaves approximately as a rigid body, both cameras should contribute to one pose estimate, and both grippers should follow one coordinated motion. This procedure shows how to establish shared coordinates, calculate that motion, and separate measurement errors from slip or mechanical constraints. It assumes fixed cameras viewing targets on a nominally flat sheet.

1. Define the pose your mechanism can control

Start with the machine, not the camera origins. A rigid sheet moving in its plane has three pose variables: X translation, Y translation and rotation. Two grippers moving only along Y generally provide two independent controls, not three.

1. Identify which axes each gripper can move and which directions permit passive movement.
2. Define the machine X and Y directions, positive rotation and engineering units.
3. Record the desired target coordinates in that frame.
4. Establish how the machine locates X if the grippers only correct Y and angle.
5. Confirm that the clamps and support arrangement permit the intended sheet motion without stretching it.

A camera's upper-left pixel is not a mechanical datum. Equal pixel coordinates from different cameras do not necessarily represent equal machine positions.

Also distinguish fiducial locations from clamp contact locations. A target near a corner may sit well inside the gripper span. Its required displacement is therefore not automatically the displacement required at the clamp.

2. Select imaging around target repeatability

Use area scan cameras when a central processor will combine both measurements. The camera finder helps narrow the imaging hardware, but the control architecture must also support paired results and calibrated coordinates.

The LS-MV-133GM-GE is a mono camera with a global shutter and C-mount lens interface.

Choose machine vision lenses around the target size, permitted sheet displacement and mounting distance. The lens finder and lens selection guide help establish a suitable field of view.

The LS-SMV2528P-6M is a C-mount machine vision lens. Check sensor coverage and required working distance before treating any camera and lens as a matched setup.

For an illustrative image spanning 80 mm across 1600 pixels:

An observed localization repeatability of 0.2 pixel would correspond to 0.01 mm at that sampling. This is a conversion, not an accuracy guarantee; verify it with repeated images.

Keep illumination, exposure, focus and target definition stable. Measure a circle center or a defined corner consistently, rather than switching between bounding-box edges.

Smart cameras and vision sensors are another architecture, provided their documented software can export the required coordinates and result identifiers. Do not assume that an inspection pass/fail output supplies everything needed for coordinated motion.

3. Calibrate both cameras into one machine frame

Each camera needs a mapping from image coordinates to the same physical plane. Correct lens distortion where necessary, then establish the planar mapping using known machine-coordinate points.

Here, H represents the calibrated mapping, including the chosen distortion-correction workflow. Its outputs are machine X and Y, not pixels.

For a tilted camera viewing a flat plane, a projective mapping may be appropriate. A simple scale-and-offset conversion only works when its geometric assumptions hold. Fit and validate the model over the complete operating region, not just near the reference position.

The camera views do not need to overlap. A surveyed fixture or calibration plate can establish known locations in both views. Alternatively, a qualified stage can transfer a target between known positions. Its positioning uncertainty then becomes part of the calibration uncertainty.

Use more calibration observations than the mathematical minimum. A practical commissioning pattern is a grid covering the center and edges of each operating region, followed by separate validation positions excluded from fitting.

Check three things explicitly:

• A positive machine Y displacement produces the expected coordinate change in both views.
• Known point spacing agrees across the two calibrated regions.
• Independent validation errors remain within the allocated calibration budget.

Calibrate at the sheet's measurement height. Height changes can create apparent lateral motion with conventional perspective optics. The telecentric gauging guide explains when different optics may help; neither optics nor calibration makes a buckled sheet rigid.

4. Calculate one rigid-body correction

Let the measured target centers be pL and pR. Let their desired coordinates be qL and qR. Preserve left/right target identity throughout the calculation.

This mapping aligns the target midpoints and baseline directions. It aligns both target coordinates exactly only when their measured and desired separations agree within measurement uncertainty.

Do not add scale correction to hide disagreement. A rigid sheet correction cannot change the distance between two material points. Compare the measured baseline length with its expected value before commanding motion.

Use both X and Y coordinates where available. Two Y measurements alone do not observe arbitrary X translation. They support a reduced Y-and-angle calculation only when the baseline geometry and remaining machine constraints are known.

5. Work through the gripper geometry

Consider an illustrative sheet with desired targets at:

Suppose the calibrated measurements are approximately:

The midpoint is approximately (300, 2) mm. The measured baseline angle is:

Now suppose the current clamp contact coordinates are gL = (-50, 2) mm and gR = (650, 2) mm. Apply the same rigid transformation to these contacts, not the target displacements directly.

Relative to the measured midpoint, the contacts lie at (-350, 0) mm and (350, 0) mm. Their Y corrections are:

The complete calculated displacements are:

These are rounded application values, not equipment specifications. Notice that the gripper span differs from the target span. Simply sending each target's Y error to its nearest gripper would therefore produce the wrong angular correction.

The small X movements also matter conceptually: a finite rigid rotation generally requires lateral motion, even when its magnitude is small.

6. Match the correction to the available axes

For small rotations, the Y correction at a contact has a useful approximation:

Use radians for Δθ. This shows the coordinated action directly: common motion changes Y position, while differential motion changes angle.

For larger angles, use the full transformation and the machine's actual kinematics. Coordinate the trajectories as well as the endpoints. Two clamps following unrelated motion profiles can load or distort the sheet during travel, even if their final positions appear compatible.

If both clamps rigidly constrain X, arbitrary finite rotation may be mechanically impossible without sheet strain. Depending on the machine design, the solution may require lateral freedom, rotary compliance, an additional axis or a different clamping arrangement. A smaller software correction does not remove that constraint.

When the mechanism has repeatable coupling, an experimentally identified local sensitivity matrix can help:

Measure each column through small, permitted commissioning motions, observing both targets after settling. Solve for coordinated actuator changes only if the matrix is well conditioned and the response is repeatable.

This local model is an alternative control mapping, not proof of rigid motion. Hysteresis, slip and changing tension can invalidate it. For the separate question of selecting a reliable gripping feature, see camera selection for robot handling.

7. Verify residuals before requesting another move

Acquire both results from the same settled sheet state. Exact exposure synchronization is less critical for a fully stationary sheet, but the sheet must remain still throughout both acquisitions. Use trigger or batch identifiers so the controller cannot combine a fresh result with a previous cycle's measurement.

After a coordinated move, compare the measured target positions with the predicted positions. Record axis positions, detection confidence, calibration version and clamp state with the result.

Two targets are insufficient to prove that the whole sheet remains undeformed. A third verification feature can reveal departures from the fitted rigid motion. It can also help distinguish a misplaced target from a genuine pose change.

Target spacing affects angle uncertainty. For independent, equal transverse localization uncertainty σ at each target:

This estimate excludes systematic calibration errors and correlated movement. Increasing target separation improves angular sensitivity, but only if both targets remain stable and accurately calibrated.

Use a verification image after the planned move. If residuals exceed tolerance, classify the failure before allowing another bounded correction. Repeated motion that alternates direction or fails to reduce error is a diagnostic condition, not a reason to keep chasing the targets.

8. Release the setup with a commissioning checklist

Before accepting the sequence, verify the following across the intended operating envelope:

• Coordinate convention: Both cameras and the controller agree on units, axis signs and rotation direction.
• Acquisition state: Both measurements belong to the same stationary sheet and cycle.
• Calibration coverage: Independent checks include the largest expected target excursions.
• Target identity: Left and right features cannot be swapped or confused with nearby markings.
• Mechanical freedom: The calculated trajectory is compatible with clamp constraints and sheet support.
• Motion bounds: Corrections respect documented travel, force, speed and process limits.
• Acceptance limits: Position, angle, baseline discrepancy and detection quality each have explicit thresholds.
• Fault handling: Missing features, incompatible geometry or nonconverging residuals stop the correction sequence for diagnosis.

Allocate the error budget before ordering higher-resolution hardware. For example, a worst-case budget of 0.10 mm might allocate 0.03 mm to calibration, 0.02 mm to localization and 0.05 mm to mechanics. These are planning allowances, not universal recommendations.

Start the hardware selection in the camera configurator. If the mechanism's controllable motion is uncertain, send the target coordinates, clamp geometry, axis freedoms and required tolerance through applications support before finalizing the imaging components.