Seite - 15 - in Joint Austrian Computer Vision and Robotics Workshop 2020
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Object
parallel with X-axisofcameracoordinatesystem
normal
to𝑢
ଶୄ
𝑢
ଵ 𝑢
ଶ 𝑢
ଵ
Figure 2. Visualization of the correct alignment of vector
~u2
torwith the smallest eigenvalue (eg. variance).
As the formof theshape is symmetrical, themean
of thepoints in thegrabbingareaestimates theorigin
of the coordinate system shown in Figure 1. There-
fore, themeanof thePCAcanbeusedas the transla-
tional componentof the transformationmatrix.
~t=(~µx, ~µy, ~µz)
T (2)
The rotation matrix has to be assembled from
three orthonormal vectors. The first vector has al-
ready been found, which is the smallest eigenvector
ofthePCA,whichformstheZvectorpicturedinFig-
ure1. Thesecondvectorcanbeobtainedby leverag-
ing knowledge about the environment of the indus-
trialgraspingusecase. As the targetobject is located
at a target location that is parallel to the ground, the
rotation around the Z axis can be neglected. That is
whythesecondvectorcanbealignedwith theYaxis
of the camera coordinate system. But since the first
vector found with the PCA could be rotated around
the Y axis of the object coordinate system, the sec-
ond vector has to be projected orthogonally to the
first. This is done with Equation (3) and the process
isvisualized in Figure2.
~u2||=(~uT2 · ~u1) · ~u1 (3)
~u2⊥= ~u2− ~u2||
The third vector can then be calculated using the
cross product of ~u1 and ~u2. The resulting rotation
matrix is constructedusingEquation (4).
R=
u3,x u3,y
u3,zu2,x
u2,y u2,z
u1,x u1,y u1,z
(4)
Aftercalculating the rotationand translationcom-
ponentsof theobject, a transformationmatrixcanbe
formulated usingEquation (5). Camera
Optical Axis
Distance mark
Angle around camera α β
d
β
Figure3. Visualization of the test setup
Tcameraobj =[R ~t ] (5)
The transformationmatrixcan thenbeused toex-
press the grasping point in the world coordinate sys-
tem, which is used for motion planning of the robot
arm. Having calculated the transformation between
thecameracoordinatesystemandtheobjectscoordi-
natesystemonecancalculate theobjectsworldposi-
tionas follows
Tobj=T world
camera ·Tcameraobj (6)
In the following chapter, the performance of the
proposedapproach isdiscussed.
4.Results
The test setup consisted of the 3D printed model
of the target object shown in Figure 1 and an Intel
RealSense D4351. The RGB-D camera has been set
upatadefined locationona tableand the3Dprinted
modelhasbeenplaced in frontof it ascanbeseen in
Figure3.
To measure the error of the PCA-based approach,
a metric had to be defined. For this, the Euclidean
distance between the ground truth vector and the es-
timatedplanenormalvectorofthePCAisused. Usu-
1https://www.intelrealsense.com/depth-camera-d435/
15
Joint Austrian Computer Vision and Robotics Workshop 2020
- Titel
- Joint Austrian Computer Vision and Robotics Workshop 2020
- Herausgeber
- Graz University of Technology
- Ort
- Graz
- Datum
- 2020
- Sprache
- englisch
- Lizenz
- CC BY 4.0
- ISBN
- 978-3-85125-752-6
- Abmessungen
- 21.0 x 29.7 cm
- Seiten
- 188
- Kategorien
- Informatik
- Technik