oints. In this 
ised for all 
fsets in the 
m the robot 
g tolerances. 
rd transform 
o control the 
:h consist of 
coders and a 
ops do not 
e not able to 
d and actual 
ler to obtain 
an external 
> differences 
estimate the 
the inverse 
| number of 
d in order to 
mation. This 
of industrial 
ers are norm 
ration will be 
5/2 industrial 
kg and has a 
r specifies a 
obot is used 
asks. 
ositions in his 
in the inverse 
position and 
. The second 
termination of 
in x, y and z 
direction are in mm. The deviation of the orientations are 
indicated in degree. 
X Y Z © $ K 
[mm] |[mm] |[mm] |[DGR] | [DGR] | [DGR] 
1.174 | -0.284 | -1.642 | —0.008 | —0.006 | 0.003 
-0.243 | 1.989 | 0.471 | 0.126 | —0.052 | —0.165 
-0.035 | -0.189 | -0.330 | 0.002 | 0.000 | 0.000 
0.172 | -0.774 | 0.152 | 0.010 | 0.004 | 0.0019 
-0.096 | 0.618 | 0.313 | 0.008 | —0.003 | —0.011 
0.386 | 0.854 | 1.459 | -0.011 | —0.028 | 0.000 
  
Table 1: Accuracy of a industrial robot 
The experiment shows not the absolute accuracy of the robot, 
it only shows the error for the repeatability using different 
paths. The result shows that the accuracy of this robot error 
are larger than 1 mm. By changing other parameters like 
temperature, payload and acceleration the error will increase. 
In other words, the absolute accuracy for this robot will be 
even lower than the relative accuracy presented in table 1. 
4. PHOTOGRAMMETRIC SYSTEM 
4.1 Camera Model 
While the basic camera model in photogrammetry is the pin- 
hole camera, additional parameters are used for a more 
complete description of the imaging device. The following 
parameters are based on the physical model of D. C. Brown 
(Brown 1971). The parameter follows the notation for digital 
cameras presented by C. S. Fraser (Fraser 1997). Three 
parameters K1, K2 and K3 are used to describe the radial 
distortion. Two parameters P1 and P2 describe the decentring 
distortions. And two parameter Bl and B2 describe the 
difference in scale between x- and y-axis of the sensor and 
the shearing. To obtain the corrected image coordinates 
(x,y) the parameters are applied to the distorted image 
coordinates (x', y") as follows: 
x=x-»% 
v=y-n 
Ax=Xr" Kı +xr*Kı +Xr°Kz +(2x' +r)E+2B + BX + B,ÿ 
Ay 7 yr Kı + yr Ky * Ks + 2B +(2y +r)B 
x=x+Ax 
y= y + Ay 
where (Xo,ÿo) is the principal point and 7 = x" + ÿ” is the 
radial distance from the principal point. The camera 
parameters are determined in a bundle adjustment using a 
planar test field. The bundle adjustment process is carried out 
before-hand. 
—35— 
4.2 Target recognition 
For the target array, we used a combination of coded and 
non-coded retro-reflective targets. In this case, the targets 
were fixed on a portable plate. They were arranged in such a 
way that for all intended robot positions at least four coded 
targets were visible in the camera image. During the 
measurement, coded targets are identified and measured first 
and an initial approximation for the camera pose is computed. 
Then, in a second step, all remaining (non-coded) targets are 
identified and measured based on this initial approximation. 
Regarding coded target design, 
there exist several possibilities. 
We used coded targets made of a 
central disk (used for 
measurement) and a concentric 
ring, which contains the code (for 
identification). Van den Heuvel 
and Kroon (1992) or Schneider 
and  Sinnreich (1992) have 
suggested such a design for 
example. Of course, the design is invariant with respect to 
rotation, scale change and perspective distortion. 
  
Figure 3 Targets 
In order to achieve a robust target identification and precise 
image coordinate measurement, a very high contrast between 
targets and background is desirable. To achieve this, we use 
retro-reflective targets in combination with an illumination in 
the near infrared (IR) spectrum. IR light emitting diodes are 
placed in a concentric ring closely around the camera's lens. 
Additionally, the lens is covered with a daylight filter. This 
way, practically no objects are visible in the images except 
for the targets. 
4.3 Resection 
The problem of spatial resection involves the determination 
of the six parameters of the camera station's exterior 
orientation. To solve the resection problem a two-stage 
process is used. A closed-form solution using 4 points gives 
the initial values of for an iterative refinement using all 
control points. 
Several alternatives for a closed form solution to the resection 
problem were given in the literature. In this approach the 
algorithm suggested by Fischler et. a1 (1981) is used. Named 
the "Perspective 4 Point Problem" their algorithm solves the 
three unknown coordinates of the projection centre when the 
coordinates of four points lying on a common plane are 
given. In our case all signals are coplanar the mapping in- 
between image and object points is a simple plane-to-plane 
transformation. The location of the projection centre can be 
extracted from this transformation T when the principal 
distance of the camera is known. The solution of this 
algorithm is not unique. There exist two possible solutions, 
one in front the plane and one behind it. In this case the 
solution in front of the plane is used. 
For the complete solution of the spatial resection problem the 
orientation of the camera must be also computed. The 
solution is based on the algorithm Kraus (1996) which gives 
a solution for the determining of the rotation angles when the 
coordinates of the projection center are already known.