International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
The servo calibration data consists of pairs of recorded servo
coordinates and corresponding, photogrammetrically measured
3-D points obtained from the laser cross in the object surface.
The units and scales of the servo coordinates are chosen and
fixed before the calibration using a separate control program
for the servo system.
The mathematical model between the servo coordinates and the
corresponding 3-D laser point can be put in form:
X4v-f'(X)s A(QX 4 V). (1)
where x is the 2x1 vector of the servo coordinates, v contains
their residuals, £"(x) is the polynomial function of degree p
for the servo coordinates, À is a 2x4 parallel projection matrix
for the 3-D laser cross coordinates, X is the homogeneous 4x1
vector containing the 3-D coordinates of the laser cross in the
object surface, V is their residual vector. Currently, up to a
fourth degree polynomial can be used. The adjustment model
corresponds to the generalized least squares model. Either of
the residual vectors can also be ignored to simplify
computations.
Due to the underlying parallel projection, the 3-D points used
in the calibration cannot lie on a plane. They have to come
from at least two different 3-D planes, to avoid a singular
system.
The laser crosses are measured from an object surface using a
grid covering the entire movement area. To get all non-linear
effects calibrated, the grid is measured several times, each time
placing the object at different height level. After the servo
calibration, the laser cross can be driven accurately to a desired
3-D point on a known surface. Similarly, the required servo
coordinates, and the predicted 3-D coordinates of the satellite
cover targets can be computed for a given 3-D object point.
4. MEASUREMENT ALGORITHM
A robot always puts the object to be measured in a certain
position and orientation in the measurement table. The
accuracy of this positioning is typically about one millimetre.
A CAD file controls the measurement. The CAD file contains
the nominal geometry of the object, the features to be
measured, and their tolerances. There can also be additional
information about the object type or colour, which may be used
to adjust certain measurement parameters. Only the features
marked in the CAD file are measured and reported. Each
different object type requires its own CAD file, and the system
has to be told which CAD file to be used when a new
measurement task begins.
At first, the system checks the position of the object and
determines the similarity transformation between the
measurement coordinate system and the CAD system. Further
measurements can then be made directly in the predicted CAD
nominal positions.
The satellite can see only a certain fraction ofthe object area in
one measurement position. Measurement of larger features,
like long sides of a rectangular object, has to be measured in
several satellite positions, and join the results only later.
The measurement time depend mostly on the number of
satellite positions needed and the total length of the satellite
movements. It can take several minutes to measure a complex
object. To save time consumed in the satellite movements, the
satellite positions should be optimised, and their number
should be minimized. A simple algorithm is developed for that
purpose. It decides optimal satellite positions, the number of
needed satellite positions, and the parts of features measured
in each position.
First, the entire object area is divided into areas, sizes of which
correspond to the area seen by the satellite. The features are
then converted into 2-D points, and it is checked which
features or parts of them fall into which areas. Empty areas can
then be ignored. If possible, the remaining areas are centred
with respect to the desired data in their area. Finally the
optimal path between the areas is determined.
For most geometric features, like edges and holes, the image
measurements can be made using edge search in a window
whose direction is normal to the edge of the feature. The sub-
pixel position corresponding to the largest gradient is searched
using interpolation. The image data is first verified or filtered
in the image domain, by fitting it robustly to a line or ellipse.
Only the filtered data is stored for later, final 3-D fit which is
made only after all satellite positions are measured. Certain
geometric features, like angles, parallelity of lines, side
lengths, etc., can be computed only after the final 3-D data is
first computed and possibly rectified to a plane.
The curvature of the object surface can be determined coarsely,
by measuring the laser cross on several positions on the object
surface, and fit the data to a cylinder surface, for example. This
way, the influence of the curvature on the predicted positions
of the features can be taken into account. After all features
have been measured, a better estimate for the curvature can be
computed using all gathered 3-D data.
5. CONCLUSIONS
This article describes a new photogrammetric 3-D
measurement system designed to measure flat objects, like
plywood boards, in an industrial production line. The system
consists of two nested four-camera systems, the inner system
being a moving satellite. The inner system measures the details
in the object space, while the outer system measures the
position of the satellite. The accuracy of the outer system
describes also the final accuracy of the system. The
functionality of the system relies entirely on photogrammetry,
not on high precision machinery.
The moving satellite makes the system slow compared to the
fastest real-time systems. It is therefore best suited for on-line
quality control and measurement purposes where a few
minutes wait per a measured object can be tolerated.
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