IEEE Systems, Man and Cybernetics Magazine - July 2022 - 62

Introduction
Traditionally, robots have been used to achieve actions that
are impossible for humans. Their characteristics, such as
strength, accuracy, speed, and robustness, have contributed
greatly to the development of industry. However, robots are
now required to replace humanlike movements; for example,
handling food and parts of various shapes and assisting with
movements of the human body. Sometimes, robots are
expected to serve as replacements for organs. In these cases,
they need to be flexible in their structure and behavior. Actuators
made of malleable materials have been attracting
attention as a technology to realize devices that meet these
requirements. These actuators, called soft actuators, have
been proposed in a wide range of materials, inputs, and
shapes to satisfy different requirements. In addition, methods
used to control those actions are being studied [1]-[3].
A McKibben artificial muscle is a type of pneumatic
soft actuator that is composed of a rubber tube and the
mesh fibers covering it [4]. The expansion of the tube due
to input is suppressed by fibers, and the artificial muscle
3-DOF Soft Actuator
produces an axial contraction force. Its simple structure
and high output per size make it suitable for a variety of
applications [7], [8]. In general, this artificial muscle is
proposed to be applied using the antagonism of contraction
forces between artificial muscles [5], [6]. In these
cases, the deformation of each artificial muscle is linear.
The 3-DOF soft actuator consists of three McKibben artificial
muscles, and each artificial muscle itself is curved.
The contractile forces produced in each artificial muscle
deform the actuator. Depending on the combination of the
input patterns to the three artificial muscles, the actuator
bends in any direction or contracts axially. Thus, more complex
motions are possible compared to conventional soft
actuators. In addition, because of its small size and flatness,
this actuator is expected to be used as a support robot to
support human joints and as a manipulator to search small
spaces. However, it is a multiple-input, multiple-output system
and has nonlinear characteristics. These characteristics
make modeling and control system design difficult [9].
In this article, a method used to control the tip position
of this actuator is proposed. The suggested control system
is based on a model derived from mathematical models
and machine learning techniques. In addition, the control
system has been compensated for stability by operator theory
[10]-[12]. Finally, the effectiveness of the proposed
approach is confirmed by experiments.
Overview of the Actuator
Figure 1. The 3-DOF soft actuator.
Tip of the Actuator
y
x
z
3-DOF Soft Actuator
Figure 1 presents the structure of the 3-DOF soft actuator.
The three McKibben artificial muscles are placed in parallel
and bonded together by silicone rubber. Figure 2 shows
its structure. However, as displayed in the figure, the center
artificial muscle is displaced from the artificial muscles at
both sides. This gap allows for a variety of curvatures.
Each artificial muscle is deformed by air pressure input, as
depicted in Figure 3, to produce a contraction force and
bend the actuator. Depending on the pattern of input to
each artificial muscle, the actuator bends in various directions
[13]. Figure 4 shows a curved deformation of the actuator.
However, it contracts axially only when the same size
air pressure is input to all the artificial muscles.
Artificial
Muscle
Gap
12 3
Input Side
Figure 2. The structure of the actuator.
62 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE July 2022
Deformation and Position of the Tip
Figure 5 gives an analytical model of the 3-DOF soft actuator.
In this article, the actuator is assumed to be curved in
the shape of an arc. The center of gravity of the actuator is
the center of gravity of the triangle formed by the three
artificial muscle centers
Oi ( ,,).123i
=
L ti=
The length of the
actuator at the center of gravity, L, is represented by (1).
,
(1)
where t is the radius of curvature and i is the bending
angle. In addition, L is expressed as (2) by the initial length L0
and contraction ratio .f
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