Touch Test Unsafe to perform due to Bad Hand-Eye Calibration (Meters instead of Millimeters)

Problem

The hand-eye calibration results are bad, and it is unsafe to perform the touch test.

Hand-Eye Transform	Hand-Eye Residuals	Projection Verification	Touch Test
Bad	Bad	Bad	Unsafe

Example of bad hand-eye calibration results

The Hand-Eye Transformation Matrix does not look correct because several of its values differ from the physical measurements by extremely large amounts that are not reasonable for this setup.

Hand-Eye Transformation Matrix

0.971	-0.214	-0.108	-1.683
-0.019	0.380	-0.925	375.305
0.239	0.900	0.365	457.970
0	0	0	1

The value 457.970 should be approximately 130 mm, and the value 375.305 should be roughly 90 mm. At this stage we ignore the sign (+/-), because it depends on the coordinate-system definitions; we focus only on the distances.

The calibration residuals are also significantly larger than expected, a couple of orders of magnitude higher.

Residuals

N (Poses)	Rot. avg (°)	Rot. max (°)	Trans. avg (mm)	Trans. max (mm)
14	5.247	12.851	135.333	760.322

For smaller robots, we expect the residuals to in the sub-millimeter range, while for larger robots, the residuals can be in the millimeter range. As for the rotational component of the residuals, we expect them to be in the sub-degree range.

Complete Residuals

Residuals

Pose	Rotation (°)	Translation (mm)
1	0.948	760.322
2	0.746	92.317
3	2.557	177.495
4	9.364	167.930
5	10.202	174.986
6	0.951	55.776
7	10.514	65.690
8	12.851	69.575
9	2.470	70.544
10	2.625	81.236
11	0.927	43.069
12	2.134	32.829
13	10.851	44.558
14	6.316	58.329

Verification by Projection fails, which suggest that the hand-eye calibration is not correct, and that the touch test will fail badly.

Potential Cause

The robot poses (translation component) for the Hand-Eye Calibration are provided in meters.

Most industrial robots use meters as the default unit for the robot poses. However, Zivid point clouds are given in millimeters. To have a correct hand-eye calibration, the robot input poses for hand-eye calibration and point clouds must expressed in the same units. Having the robot poses in meters and the point clouds in millimeters is destined to lead to a bad hand-eye calibration with completely incorrect hand-eye transformation matrix.

Potential Solution

1. Ensure the robot input poses are in millimeters.

   Note: You can just divide the translation component of the robot poses by 1000 if they are in meters, to convert them to millimeters.

2. Repeat the hand-eye calibration using the same dataset (with robot poses in millimeters).

3. Verify the hand-eye calibration results (transform, residuals, projection).

4. Run the touch test (if the hand-eye calibration results are good).

Reproducing the Issue (Robot Pose in Meters instead of Millimeters)

Good Dataset

A hand-eye calibration was successfully performed using the dataset shown in the images below.

The calibration resulted in the following results:

Hand-Eye Transformation Matrix

0.999	-0.004	0.043	-55.476
0.004	1.000	0.013	-91.613
-0.043	-0.013	0.999	128.667
0	0	0	1

Residuals

N (Poses)	Rot. avg (°)	Rot. max (°)	Trans. avg (mm)	Trans. max (mm)
14	0.019	0.029	0.144	0.222

Complete Residuals

Residuals

Pose	Rotation (°)	Translation (mm)
1	0.026	0.071
2	0.013	0.218
3	0.020	0.146
4	0.026	0.222
5	0.026	0.181
6	0.007	0.114
7	0.007	0.128
8	0.015	0.066
9	0.023	0.110
10	0.010	0.113
11	0.024	0.149
12	0.023	0.175
13	0.029	0.184
14	0.022	0.132

The Hand-Eye calibration was verified with a touch test.

The touch test was successful, which confirms that the hand-eye calibration is correct and accurate.

Bad Dataset (robot poses in meters instead of millimeters)

To simulate the problem, translation vectors from the input robot poses in the hand-eye calibration dataset were converted from millimeters to meters. Hand-Eye calibration was performed again on the same dataset with modified robot poses.

The calibration resulted in the following results:

Hand-Eye Transformation Matrix

0.971	-0.214	-0.108	-1.683
-0.019	0.380	-0.925	375.305
0.239	0.900	0.365	457.970
0	0	0	1

Residuals

N (Poses)	Rot. avg (°)	Rot. max (°)	Trans. avg (mm)	Trans. max (mm)
14	5.247	12.851	135.333	760.322

Complete Residuals

Residuals

Pose	Rotation (°)	Translation (mm)
1	0.948	760.322
2	0.746	92.317
3	2.557	177.495
4	9.364	167.930
5	10.202	174.986
6	0.951	55.776
7	10.514	65.690
8	12.851	69.575
9	2.470	70.544
10	2.625	81.236
11	0.927	43.069
12	2.134	32.829
13	10.851	44.558
14	6.316	58.329

Verification by Projection failed, which suggests that the hand-eye calibration is not correct, and that the touch test will fail badly. Therefore, the touch test was skipped for safety reasons.

Comparisons

The results between hand-eye transformation matrices (translation values) and hand-eye calibration residuals are compared in the tables below.

Translation Values in Hand-Eye Transformation Matrix

Dataset	X (mm)	Y (mm)	Z (mm)
Good (Poses in mm)	-55.476	-91.613	128.667
Bad (Poses in m)	-1.683	375.305	457.970
Δ (Good - Bad)	-53.793	-466.918	-329.303

Residuals

Dataset	N	Rot. avg (°)	Rot. max (°)	Trans. avg (mm)	Trans. max (mm)
Good (Poses in mm)	14	0.019	0.029	0.144	0.222
Bad (Poses in m)	14	5.247	12.851	135.333	760.322