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nowns two 
or more robot displacements needed to obtain a unique 
solution under certain condition. 
Figure 5 shows the accuracy for solving the above equation 
by using 2 or more robot movements. It illustrates that the 
increase of the measured robot poses has no influence on the 
accuracy of the hand-eye-calibration. The reason is the low 
precision of the robot control in absolute positioning the tool 
centre point. 
Hand-Eye-Calibration 
2,00000 , 
1,60000 | 
1,20000 | 
0,80000 | 
0,40000 | 
Deviations [mm] 
0,00000 
3 5 6 7 8 9 10 11 15: 30 
Number of robot movements 
Figure 6 Hand-Eye-Calibration 
6. RESULTS 
For the experimental results a Basler A113 camera with a 
Sony CCD chip and a resolution of 1300 x 1030 pixels is 
used. The camera provides a digital output according to IEEE 
standard RS 644. A frame-grabber is integrated into a 
standard PC. With this combination Schneider-Kreuznach 
lenses with 12 mm focal length are mounted onto the camera. 
To maximize the signal intensity we use retro-reflective 
targets and a ring light on the camera described in 4.2. 
The set-up for our experiments consisted of a Kuka KR15 
robot. It is a six-axis robot with a maximum payload of 15 kg 
at a maximum range of 1570 mm. The robot is specified with 
a repeatability of * 0.1mm. The absolute accuracy is not 
specified. 
The sensor delivers a frame rate of about 12 frames per 
second. The implemented system is capable to process a 
single image in 420 ms. A typical image will contain 30 
coded and about 200 un-coded targets. This gives a 
processing speed of 500 targets per second including all 
image processing steps and the resection process. 
6.1 Simulation 
The following tables shows the result of absolute accuracy 
obtained by a simulation. View angle describes the angle 
between the optical axis and the plane of the targets. The 
assumed value of the precision of measurement of the targets 
is in this case 1/10 Pixel. 
  
  
  
  
  
  
  
  
  
Spatial-Resection | Forward-Intersection 
View Angle |60 90 60 90 
[Degree] | [Degree] | [Degree] [Degree] 
Resection in x | 0.03 mm | 0.5 mm | 0.23 1.05 
Resection in y | 0.04 mm | 0.6mm 025 1.10 
Resection in z | 0.08 mm |0.05 mm |0.32 0.28 
  
  
  
Table 2 Absolute accuracy of the camera position 
-37-— 
The next table shows the interior accuracy of the resection 
process dependent on the accuracy of the image 
measurement. The Testrun column shows real obtained 
accuracy of the implemented system. 
  
Simulation Test-run 
Image 1/5 Pixel | 1/10 Pixel 1/10 — 1/20 Pixel 
measurement 
Resection in x | 0.06 mm | 0.03 mm 0.05 — 0.14 mm 
Resection in y | 0.06 mm | 0.03 mm 0.05 — 0.14 mm 
Resection in z | 0.02 mm | 0.009 mm 0.05 — 0.07 mm 
  
  
  
  
  
  
  
  
  
  
Table 3 Standard deviation of resection 
6.2 Circular Test 
ISO 230-4 (ISO 1996) describes the “Circular test for 
numerical controlled machine tools”. While tests were 
originally designed for the simultaneous movement for only 
two axes, they also have valid implications for other 
machines. When the test is carried out the robot performs a 
circular motion and measurement system detects any 
deviation from the ideal path. 
  
  
  
  
  
Figure 7 Circular test 
Figure 6 shows the result of the circular test. The robot 
moves 10 times on a circle path with a radius of 300 mm. The 
dark line shows the path computed in the robot base system, 
the light line computed in the camera system. The distance 
from the ideal path (inner circle) is 100 times excessive. 
The figure gives a rough estimate of the exterior accuracy of 
0,1 mm. The distance between true and required value is due 
to the uncertainty of the robot control. 
7. SUMMARY 
The implemented system is an improvement of our offline 
system published earlier (Hefele 2000). It has proven to be 
quite flexible and we believe it can be easily integrated into 
many applications in robotics, especially applications in 
optical measurement. The simulation showed, that by use the 
forward incision instead of the resection no increase of the 
precision is to be reached.