IEEE Robotics & Automation Magazine - December 2020 - 60

where (output max - output min) local is calculated when one
input value varies and others are assumed to be constant in
particular geometry and (output max - output min) global is
quantified when all of the inputs vary. Figure 5(b) presents
the local sensitivity analysis of each design parameter in percentages. As can be observed, the chamber diameter (D 3)
and actuation pressure (P1) are estimated to be the most
important elements with direct relation to the bending angle;
in other words, compared to other variables, increasing these
two elements results in more intense positive changes in the
final bending angle. The joint diameter (D 1) and chamberto-wall distance (H 1) stand next in the ranks of the most
influential parameters but in reverse relation to the main
objective, which means that reducing the values of these
parameters causes the final bending angle to increase. On the
other hand, variations of the hole-to-wall distance (H 2) and
the pressure inside the link (P2) are estimated to be almost
ineffective for the main objectives of the optimization and,
hence, can be neglected. Nevertheless, it should be noted that
P2 is an important parameter for changing the finger stiffness and thus the applied fingertip force. The effect of this

parameter is discussed in the following section. As for H 2 ,
the value is determined according to manufacturing considerations and is set to 2 mm. The low value of this parameter
would result in aligning the surfaces of the joint and the link
in the bending direction. This would eventually lead to a uniform smooth surface in that area, which can be beneficial in
future possible grasping applications.

Optimization Process
After identifying the influential design parameters with local
sensitivity review, an optimization analysis must be conducted.
The goal is to maximize the bending angle up to 90° and simultaneously minimize the length and diameter of the joint (miniaturizing the dimension of the finger to be more like a
human's) under the applied pressure [(P1) around 14 kPa]. The
optimization process and perquisites are shown in the flowchart in Figure 6. Due to the multiple numbers of the design
parameters, objectives, and constraints, the adaptive multipleobjective optimization method is selected to find the global
optimum parameters. This method is a variation of the
NSGA-II based on controlled elitism concepts [16]. This average value is selected through trial and
error so that the finger with the specified ranges of geometrical dimensions
can bend up to 90° and not burst. The
Start
calculation converged by generating 400
samples with 50 samples per iteration
and finding the best candidate in eight
Modeling the Proposed Finger in CAD Software (Figure 3)
iterations. Furthermore, during the process, if the FEM simulation of a sample
Finding the Design Parameters (Seven Parameters: Figure 4)
failed (for example, bursting), it was
eliminated and replaced by a new sample. In total, 146 new samples have been
Finding a Reasonable and Manufacturable Range of Design
Parameters by FEM Analysis [Figure 5(a) and Table 1]
generated to replace the failed ones.
The optimization charts are shown in
Building the Design Parameters of the
FEM
Figure 7(a)-(e), where the empty circles
Experiment (DOE) Table
show the samples and the blue lines
illustrate the moving average, i.e., the
Changing Mesh Quality, Step Times,
No
Solved?
best-fitted line that represents the conand Design Parameters Range
vergence trend of the samples to the
Yes
optimized values. Table 2 summarizes
the eventual optimized values. These
Local Sensitivity Analysis (Figure 5(b))
dimensions will be used to manufacture
the prototype of the finger. The molds
Rebuilding the DOE Table With Effective Parameters
are printed with the Ultimaker3 3D
printer. Thanks to recent advances in
Adaptive Multiple Objective Optimization Method (NSGA-II)
3D printing technology, the fabrication
process of soft components has been
Changing the Range of
No
facilitated significantly, which leads to
Converged?
Parameters
producing more complex parts with
higher precision. For each silicone, two
Optimal Design Values
Yes
liquid parts should be mixed with the
(Figure 7 and Table 2)
same ratio, followed by a 2-3-min
vacuum degassing to eliminate any
Figure 6. A flowchart of the proposed optimization methodology. The trapezoid shapes
entrapped air bubbles. This is done by
represent a manual operation, and the other rectangular shapes are the automated process.
DOE: design of experiment.
placing the molds in a vacuum chamber.

IEEE ROBOTICS & AUTOMATION MAGAZINE

DECEMBER 2020

IEEE Robotics & Automation Magazine - December 2020

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - December 2020