IEEE Robotics & Automation Magazine - June 2023 - 51

6) This projected surface point cloud is then transferred into a
closed volume, representing the solid fingertip body, and
exported to an STL file (Figure 3, Finger design A, a1, and
Finger design B, b2). This STL file can then be further processed
and printed on top of the finger bases to be finally used
by the task execution robot to manipulate the desired object
(Figure 3, Finger design A, a2 and Finger design B, b3).
BÉZIER SURFACE FITTING
Due to its character, Bézier surfaces result in more organic
rounded surfaces, which potentially simplify the object centering
during the grasping process, in the context of potential
position offsets. The counter side is a potentially less-precise
surface representation of the desired object. The surfacematching
quality depends on the number of Bézier control
points and the object geometry complexity. Bézier surfaces
represent a continuous surface interpolation based on a specified
set of control points [19]. To fit the given projected object
surface, we conducted the following optimization problem:
cDc
c
fit =argmin
N
M
Dc
bez
()
Pu vc(, ,)
==
/
/
/ /
m
x=1 y=1
n
Bu Bv c ,ij
n() () .
i
i =1 i =1
Here, the control points c are optimized
to minimize the distance D(c)
between each Bézier surface point
Pbez and object surface point Pobj to
get a sufficient shape matching (Figure
3, Finger design B, b1). The Bézier
surface points Pbez of degree n and m
are calculated via the Bernstein polynomials
()
Bui
and () and depend
Bvj
on the control points c ,ij as well as
the coordinates u and v [19]. The position
and number of the control points
define the shape of the resulting Bézier
surface. Similar to [6], we use quadratic
programming to solve this optimization
problem.
After the Bézier surface matching
was conducted, the surface was transferred
to a closed volume and corresponding
STL file, as conducted for the
projected surface approach of the first
design method.
MACHINE LEARNINGBASED
DESIGN
The described design approaches can
also be used to automatically generate a
training dataset for a potential machine
learning-based design method. Here,
Base Process
Bezier Surface Fit
m
j
(( ,,)Px yc Px y(, )) ,
2
bezobj
(),
both methods serve as a desired output reference for the
learning process. They require less data to represent the fingertip
surface compared to the given object point clouds.
This can potentially simplify and speed up the learning process
of a machine learning-based design method. For example,
the output of the projected surface-based process can
be used as a low-dimensional input, while the control
points of the fitted Bézier surfaces can serve as the desired
reference output.
We want to illustrate the potential advantages of our
described design methods (projected surface and Bézier
surface fit) for automatic training-data generation, using a
neural network-based learning approach. The final goal is
to speed up the Bézier surface generation by using a neural
network instead of the slower Bézier surface fit optimization.
The trained network should then generate the Bézier
surface for our battery manipulation object. To achieve this,
we set up a designated training and testing pipeline (Figure
4). Input for the training process is a set of 21 manually
designed reference objects, which are variations of different
cylindrical objects. To preprocess the object data for the neural
network training, the previously described base process
of the projected surface design approach (20 # 20 voxels)
as well as the following Bézier surface fit optimization (4 #
4 control points) is conducted for each object. The depth
parameter of the regular distributed fingertip surface grid
Training Objects
...
Learning Process
Base Process
y1
y2
y3 y4
Neural Network Training
y1
y2
y3
y4
CP1
CP2
CP3
CP1
CP3
Fingertip Surfaces
Neural Network
CP2
Bezier
Test Object
Surface Fit
Similarity
Check
Testing Process
FIGURE 4. Neural network-based design. The training process is conducted by applying
the base process of the projected surface design method to the designated set of training
objects. The resulting surfaces are used to generate corresponding Bézier surfaces. Both
serve as training data for a neural network, which can be used to generate Bézier surfaces
for a desired target object.
JUNE 2023 IEEE ROBOTICS & AUTOMATION MAGAZINE
51
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