A comprehensive review on fish-inspired robots

Abstract

Recently, the increasing interest in underwater exploration motivates the development of aquatic unmanned vehicles. To execute hazardous tasks in an unknown or even hostile environment, researchers have directed on developing biomimetic robots inspired by the extraordinary maneuverability, cruising speed, and propulsion efficiency of fish. Nevertheless, the performance of current prototypes still has gaps compared with that of real fishes. In this review, recent approaches in structure designs, actuators, and sensors are presented. In addition, the theoretical methods for modeling the robotic fishes are consolidated, and the control strategies are offered. Finally, the current challenges are summarized, and possible future directions are deeply discussed. It is expected that the emergence of new engineering and biological technologies will enhance the field of robotic fish for further advancement.

Full text

Review Article
A comprehensive review
on fish-inspired robots
Yi Li
1,2
, Yuteng Xu
1,2
, Zhenguo Wu
1,2
, Lei Ma
1,2
, Mingfei Guo
1,2
,
Zhixin Li
1,2
and Yanbiao Li
1,2
Abstract
Recently, the increasing interest in underwater exploration motivates the development of aquatic unmanned vehicles. To
execute hazardous tasks in an unknown or even hostile environment, researchers have directed on developing biomimetic
robots inspired by the extraordinary maneuverability, cruising speed, and propulsion efficiency of fish. Nevertheless, the
performance of current prototypes still has gaps compared with that of real fishes. In this review, recent approaches in
structure designs, actuators, and sensors are presented. In addition, the theoretical methods for modeling the robotic
fishes are consolidated, and the control strategies are offered. Finally, the current challenges are summarized, and possible
future directions are deeply discussed. It is expected that the emergence of new engineering and biological technologies
will enhance the field of robotic fish for further advancement.
Keywords
Underwater robot, bionic robotic fish, locomotion, actuators, modeling, control
Date received: 20 December 2021; accepted: 09 May 2022
Topic: Bioinspired Robotics
Topic Editor: Chin-Hsing Kuo
Associate Editor: Hoon Cheol Park
Introduction
Under the thousands of years of natural selection, the fishes
in nature have been endowed with great locomotion cap-
abilities, such as high swimming speed and remarkable
maneuverability, prompting researchers to develop various
types of fish-inspired underwater robots.
1
Compared with
conventional underwater vehicles powered by screw pro-
pellors, robotic fish can overcome their shortcomings, such
as large scale, low energy efficiency, and disturbance to the
environment, and it has great superiority in propulsive effi-
ciency, maneuverability, and stealth.
2,3
With the develop-
ment of mechatronic technologies and computer science,
robotic fish plays a huge role in underwater exploration,
4–6
samplings,
7,8
rescues,
9
and water quality monitoring.
10
The earliest research on fish can be traced back to 1926;
Breder
11
categorized the swimming modes of fishes into
the body and/or caudal fin (BCF) propulsion and median
and/or paired fin (MPF) propulsion according to the body
1
Key Laboratory of Special Purpose Equipment and Advanced Processing
Technology of Ministry of Education, Zhejiang University of Technology,
Hangzhou, China
2
Zhejiang Provincial Key Laboratory of Special Purpose Equipment and
Advanced Processing Technology, Zhejiang University of Technology,
Hangzhou, China
Corresponding author:
Yi Li, Key Laboratory of Special Purpose Equipment and Advanced
Processing Technology of Ministry of Education, Zhejiang University of
Technology, Hangzhou 310023, China; Zhejiang Provincial Key
Laboratory of Special Purpose Equipment and Advanced Processing
Technology, Zhejiang University of Technology, Hangzhou 310023, China.
Email: ly17@zjut.edu.cn
Yanbiao Li, Key Laboratory of Special Purpose Equipment and Advanced
Processing Technology of Ministry of Education, Zhejiang University of
Technology, Hangzhou 310023, China; Zhejiang Provincial Key
Laboratory of Special Purpose Equipment and Advanced Processing
Technology, Zhejiang University of Technology, Hangzhou 310023, China.
Email: lybrory@zjut.edu.cn
International Journal of Advanced
Robotic Systems
May-June 2022: 1–20
ªThe Author(s) 2022
Article reuse guidelines:
sagepub.com/journals-permissions
DOI: 10.1177/17298806221103707
journals.sagepub.com/home/arx
Creative Commons CC BY: This article is distributed under the terms of the Creative Commons Attribution 4.0 License
(https://creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without
further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/
open-access-at-sage).

part utilized for propulsion. In 1936, through the observa-
tion of dolphins, Gary
12
calculated that dolphins need only
one-seventh of the external force generated by their mus-
cles to maintain a high swimming speed. This finding moti-
vated researchers to study the mechanism of fish
swimming. In the 1960s, some progress had been made
in the theoretical study of fish propulsion. The theories
could be categorized into resistive force theory
13
and reac-
tive force theory.
14–18
The former emphasizes the viscous
force, while the latter emphasizes the more accurate inertia
force. There are three kinds of reactive force theories that
are relatively wildly used in fish dynamic modeling:
elongated body theory (EBT),
14,18
wave plate theory
(WPT),
15,16
and actuator-disc theory.
17
In 1995, based on
previous studies, the first complete robotic fish system
named RoboTuna
19
was developed by Massachusetts Insti-
tute of Technology (MIT). Since then, many related studies
have been carried out, and the latest research results have
been applied to the design of robotic fish.
20
Various types
of fish-like robots have sprung up endlessly.
21–24
To meet the increasing requirements of underwater mis-
sions, new approaches have been constantly proposed in
design aspects. Recent advances in smart materials and
actuators and compliant mechanisms have boosted the
research studies on the mechanical design of robotic
fishes.
25
Many smart control strategies are applied to
improve the robotic performance, and closed-loop control
based on onboard sensors is used to realize the precise
control.
26
These approaches have been reviewed in recent
articles,
26–31
but few of them give an overall description.
Salazar et al.
27
reviewed the modeling, materials, and
actuators, but there is no mention of sensors and control.
Xie et al.
31
reviewed the robotic fishes with different
mechanisms in detail, but the control strategy is not deeply
discussed. Yu et al.
26
offered a detailed review of control
strategies, but the other aspects are not declared. Differ-
ently, this article focuses on the recent studies and gives a
relatively overall review. The motivation is to provide a
relevant and useful introduction to the state-of-the-art
robotic fish and to inspire researchers to explore the oppor-
tunities for further improvement and novel designs in
robotic fish from existing studies.
The remainder of this article is organized as follows:
The movement characteristics of different types of fishes
are summarized, and recent typical designs are given in the
second section. Smart soft actuators with properties and
limitations for propulsion are detailed in the third section.
The applications of sensors in robotic fish are provided in
the fourth section. Typical modeling and control methods
are proposed, and related theoretical research studies are
sorted out in the fifth section. In addition, possible future
challenges and directions are discussed in the sixth section.
Finally, conclusions are given in the seventh section.
Robotic fish designs based on different
locomotion modes
As stated in the previous section, the swimming modes of
fish can be categorized into BCF propulsion and MPF pro-
pulsion. The BCF mode is suitable for long-term swimming
(a)
(b)
Anguilliform Subcarangiform Carangiform Thunniform Ostraciiform
Rajiform Diodontiform
Labriform
Amiiform Gymnotiform Balistiform
Tetraodontiform
OscillatoryUndulatory
Undulatory
fin motions
Oscillatory
fin motions
Figure 1. Classification of swimming modes: (a) BCF and (b) MPF. Blue areas contribute to swim. Adapted and redrawn from Ref.
32
BCF: body and/or caudal fin; MPF: median and/or paired fin.
2International Journal of Advanced Robotic Systems

using the caudal fin to produce large thrust, whereas the
MPF mode uses paired pectoral fins, dorsal fins, or anal
fins to obtain sufficient maneuverability. As shown in
Figure 1,
32
based on the difference between undulatory
and oscillatory motion, BCF mode could be further
classified into anguilliform, subcarangiform, carangiform,
thunniform, and ostraciiform. MPF mode could be further
classified into rajiform, diodontiform, labriform, amiiform,
gymnotiform, balistiform, and tetraodontiform. Typical
prototypes based on each category (as presented in Tables 1
and 2) are deeply discussed in this section.
BCF mode-based robotic fishes
Swimming in anguilliform mode is based on axial waves
propagating along the body from head to tail, and the wave
number is about one body length.
49
Hyper-redundant
design is usually used in robots inspired by anguilliform
to obtain high maneuverability. Envirobot developed by
Bayat et al.
33
is composed of six active modules, a passive
flexible tail, and an un-actuated head module (see
Figure 2(b)). Struebig et al.
34
developed a new anguilliform
swimming robot—named Marine Anguilliform Robot
Table 1. Performance and characteristics of the BCF mode-based robotic fishes.
Fish type Prototypes Speed (BL/s) Characteristics
Anguilliform Envirobot
33
1.0 Six active modules, a passive flexible tail
Each module is powered by a dc motor
MAR
34
0.44 The core component is a helix actuated by a single dc
motor
15 rectangular elements to hold the helix
Subcarangiform or
carangiform
Isplash-II
35
11.6 A single motor and three passive links
Cruise straight only
Compliant robot
36
2.15 Wire-driven active body and compliant tail
The multi-pseudo-link model
Thunniform SPC-III
5
0.77 A parallel four-bar linkage mechanism
Actuated by two dc servomotors
Robot by Algarin-
Pinto
37
Not
available
A 3ucu-1 s parallel mechanism
Oscillatory motion only
Ostraciiform Robot by Costa
38
0.42 A cylindrical rigid fore body and a tail section
A cam-like mechanism powered by a DC brushed motor
Robot by Zhang
39
2.0 A two-segment caudal actuated by electromagnetic
actuator
BCF: body and/or caudal fin; MAR: marine anguilliform robot.
Table 2. Performance and characteristics of the MPF mode-based robotic fishes.
Fish type Prototypes Speed (BL/s) Characteristics
Rajiform Roman-II
40
0.8 Three parallel and compliant fin rays
Cownose ray inspired robot
41
0.7 Slider-rocker mechanisms of fin rays
Tissue-engineered robotic
ray
42
0.20 Tiny and soft
Four layers assembled
Steering upon optical stimulation
Amiiform Robognilos
43
0.87 Nine fin rays directly attached to the servo motors
An asymmetrical sinusoidal profile of propulsion waveform
Gymnotiform Robotic knifefish
44
0.55 32 fin rays actuated by 32 motors
A cylindrical and rigid body
Knifebot
45
0.37 (forward)
0.25 (backward)
0.20 (vertical)
16 fin rays actuated by 32 motor units
Oval-shaped cross-section rigid body
Fin-rayless robot
46
0.21 The fin membrane is passively undulated by crank–slider
mechanisms
A caudal fin to aid with forward thrust
Labriform Flexible feathering fin robot
47
0.17 Rigid rectangular fins
Flexible feathering joints
Flexible folding fin robot
48
0.58 Trapezoidal folding fins
Flexible joints on hinge base
MPF: median and/or paired fin.
Li et al. 3

(MAR) (see Figure 2(a)). Different from hyper-redundant
mechanisms, the core component of the robot is a helix.
Several rectangular elements are adopted to project the
three-dimensional rotation of the helix onto the vertical
plane, and thus, a continuous traveling wave can be created.
Since the robot is actuated by a single DC motor installed
on the head, the efficiency of the robot is improved, and the
control strategy is significantly simplified. However, the
overall scale is relatively large (108 cm, 5.5 cm, and
25 cm in length, width, and height, respectively), and
waterproof measures of each element are lacking, which
leads to a larger friction force in swimming.
In contrast to anguilliform that the whole body partici-
pating in undulation, the undulations in subcarangiform
and carangiform are confined to the posterior half and the
latter third of body length, respectively, while the nonun-
dulating parts of both remain almost rigid.
50
As a result, the
swimming speed is higher than that of the anguilliform
while the maneuverability is lower.
51
Multi-joint mechan-
ism is usually utilized to fit the movement of the counter-
part fish.
52–54
The iSplash-II developed by Clapham et al.
35
is well known for its high speed (up to 11.6 body length (BL)
per second at the frequency of 20 Hz) (see Figure 2(c)).
However, it can only realize linear locomotion but can not
maneuver in 3D space. Zhong et al.
36
developed a novel
robotic fish (see Figure 2(d)) with wire-driven active body
and compliant tail, which were driven, respectively, by two
servo motors housed in the head. The active body consists of
five joints, and it could be bent in a C-shape and the soft
compliant tail lags behind, resulting in an S-shape of the
robot.
The fish swimming in thunniform mode has a crescent-
shaped caudal fin with a high aspect ratio connected to a
narrow peduncle.
12
Significant transverse movement
occurs in the peduncle, and the tail area when swimming
while the anterior body remains rigid,
55
which leads to high
speed with high efficiency. Since only the rear 10%of the
body participates in oscillation, the torpedo-shaped SPC-III
developed by Liang et al.
5
uses a parallel four-bar linkage
mechanism actuated by two DC servomotors to oscillate
the caudal fin (see Figure 2(e)). Under the lookup-table
method control and predictive control, the swimming speed
can reach 1.36 m/s with a turning radius of 1.75 m, and the
robotic fish can be operated for up to 20 h powered by the
Figure 2. Robotic fish prototypes based on different BCF modes:(a) MAR. Reproduced with permission.
34
Copyright 2019,
IOP Publishing. (b) Envirobot. Reproduced with permission.
33
Copyright 2021, IEEE. (c) Isplash-II. Reproduced with permission.
35
Copyright 2014, IEEE. (d) Compliant robot. Reproduced with permission.
36
Copyright 2017, IEEE. (e) SPC-III. Reproduced with
permission.
5
Copyright 2011, Wiley. (f) Robot by Algarin-Pinto. Reproduced with permission.
37
Copyright 2021, MDPI. (g) Robot by
Zhang. Reproduced with permission.
39
Copyright 2018, IEEE. (h) Robot by Costa. Reproduced with permission.
38
Copyright 2014,
Springer. BCF: body and/or caudal fin; MAR: marine anguilliform robot.
4International Journal of Advanced Robotic Systems

onboard battery. Pinto et al.
37
adopted the three degrees of
freedom spherical three universal–cylindrical–universal
and one spherical joint (3UCU-1 S) parallel mechanism
as the actuation system of robotic fish (see Figure 2(f)).
The 3UCU-1 S is driven by linear actuators to mimic the
flapping thunniform locomotion, which obtains a high and
efficient thrust.
The ostraciiform locomotion is considered the most sta-
ble mode as the body parts involved in oscillation is the
least. Given to large body shape and inefficient fin actua-
tion, the speed of ostraciiform is relatively low but they can
maneuver in a narrow space (almost zero radius
56
) through
the fin actuation.
57
Recently, Costa et al.
38
have proposed
an ostraciiform robot composed of a cylindrical rigid body
and a tail section (see Figure 2(h)). The actuation system is
based on a cam-like mechanism powered by a DC brushed
motor, which converts the continuous rotation of the drive
into a harmonic oscillation. Zhang et al.
39
presented a robot
with a 2-segment caudal (see Figure 2(g)). The robot has a
large and heavy main body to gain stability, and the caudal
fin is actuated by an electromagnetic actuator to obtain
higher frequency oscillations (over 50 Hz).
MPF mode-based robotic fishes
Rajiform has a pair of wing-shaped pectoral fins attached to
the fin rays extended from the body. Swimming forward
and turning are, respectively, realized by flapping and mod-
ulating phase relations of fin rays, exhibiting relatively high
maneuverability and stability.
32
To achieve the rajiform
locomotion, the actuation mechanism of the RoMan-II
40
consists of three parallel and compliant fin rays connected
to each side of the body, as shown in Figure 3(a). The fin
rays are powered by the brushless servo motors
Figure 3. Robotic fish prototypes based on different MPF modes:(a) Roman-II. Reproduced with permission.
40
Copyright 2012, IEEE.
(b) Cownose ray inspired robot. Reproduced with permission.
41
Copyright 2019, IEEE. (c) Tissue-engineered robotic ray. Reproduced
with permission.
42
Copyright 2016, Amer Assoc Advancement Science. (d) Knifebot. Reproduced with permission.
45
Copyright 2018,
IOP publishing. (e) Robotic knifefish. Reproduced with permission.
44
Copyright 2011, Royal Soc. (f) Fin-rayless robot. Reproduced with
permission.
46
Copyright 2012, IEEE. (g) Flexible feathering fin robot. Reproduced with permission.
47
Copyright 2016, IOP publishing.
(h) Flexible folding fin robot. Reproduced with permission.
48
Copyright 2020, Cambridge Univ Press. (i) Robognilos. Reproduced with
permission.
43
Copyright 2009, Pergamon-Elsevier Science. MPF: median and/or paired fin.
Li et al. 5

independently. Hence, the fin membrane attached to them
could provide flapping motion. Differently, the fin rays of
the robot developed by Cai et al.
41
are not compliant but
adopt slider-rocker mechanism to flap in sinusoidal curves
(see Figure 3(b)). Specifically, the front fin ray uses a one-
stage slide-rocker mechanism, the middle fin ray uses a
two-stage slider-rocker mechanism, and the last fin ray uses
one linkage. Park et al.
42
developed a soft-robotic ray with
a new design (see Figure 3(c)). The body of the robot is
assembled by four layers including a three-dimensional
elastomer layer, a chemically neutral skeleton layer, a thin
interstitial elastomer layer, and a muscle layer of aligned rat
cardiomyocytes. The robot is 16.3 mm in length and about
10.18 mg in weight, which is considered to be the smallest
rajiform-inspired prototype. Upon optical stimulation, the
metal skeleton induces the bending of the muscle layer to
produce undulating locomotion. Consequently, the robot
exhibits high maneuverability (turn at 1.5 mm/s), relatively
high speed (3.2 mm/s, equal to 0.20 BL/s), and long endur-
ance (6 days).
Amiiform and gymnotiform have similarities in kine-
matics. Amiiform has a long dorsal fin extending to the
entire body length, while gymnotiform has an elongated
anal fin. They undulate their fins to swim while their bodies
remain rigid. They could smoothly change the gait of
swimming forward to backward without turning.
58,59
Furthermore, they could move vertically by sending inward
counter-propagating waves, namely, the traveling wave
from head to tail meets the traveling wave from tail to head
in the middle of the fin.
44
Thus, they could maneuver in 3D
space easily by controlling the unique long fins. Hu et al.
43
developed an amiiform-inspired robot. As shown in
Figure 3(i), nine fin rays connecting with a membrane are
directly attached to nine servo motors, and the motors are
mounted in the long base. As for the gymnotiform, Curet
et al.
44
used 32 fin rays actuated by 32 motors to emulate
the dorsal fin. The bionic fin is encased in the cylindrical
main body (see Figure 3(e)). Liu et al.
45
used 16 fin rays
independently actuated by motor units (see Figure 3(d)).
The fin rays are about 7 cm in length, longer than that of
Curet et al.’ s 3.4 cm. The robot developed by Liu et al.
46
adopted the actuation mechanism using no fin rays (see
Figure 3(f)). The fin membrane is passively undulated by
two crank-slider mechanisms located at the head and the
tail, respectively. Moreover, a propulsive caudal fin is also
equipped to aid with forward thrust.
Labriform oscillates pectoral fins to generate swimming
thrust and occasionally uses caudal fin for rapid accelera-
tion. The movement of pectoral fins is a combination of
rowing (vertical rotating axis) and flapping (longitudinal
rotating axis) motion to perform slow-speed agile
swimming.
60
Rowing motion including power and recov-
ery strokes is utilized for forward swimming while the
flapping for descending or ascending.
60
The fin mechanism
put forward by Behbahani et al.
47
is about rowing motion. It
can be seen in Figure 3(g) that the rigid rectangular fins are
mounted on flexible joints driven by servo motors. The
main components of the joint are a mechanical stopper and
a rectangular flexible piece. During the power stroke, the
mechanical stopper prevents the fin from feathering (trans-
verse rotating axis) and maintains the rowing motion pre-
scribed by the servo motors. In addition, in recovery stroke,
the flexible piece makes the fin feather passively, thus
reducing the hydrodynamic drag force. Pham et al.
48
pro-
posed a different fin mechanism in the shape of a trapezoid
(less interference drag than a rectangle) (see Figure 3(h)).
The pectoral fins are mounted to the hinge base (fin ray) in
the middle of the trapezoidal fins through flexible joints.
Under this arrangement, the power and recovery strokes
can be realized in the form of folding pectoral fins.
However, in diodontiform mode (undulatory pectoral
fins), balistiform mode (undulatory anal and dorsal fins),
and tetraodontiform mode (oscillatory dorsal and anal
fins), there are no robotic systems reported to the authors’
knowledge.
Smart soft actuators for propulsion
The traditional motor-driven robotic fish systems are com-
posed of multi-joint body and transmission mechanisms,
such as gears, bearings, and pistons, which makes the
robots heavy and bulky. In addition, the motors could
generate noises and disturb marine life, incapable of inte-
grating into the underwater ecology.
4
Conversely, the
emergence of artificial muscle-based actuators provides a
new direction for the development of robotic fish. Although
their power and accuracy cannot be compared with motors,
smart soft actuators have unique advantages in terms of
high deformability and adaptability due to their excellent
compliance.
61
Moreover, they could be used as a part of the
robot to propel without additional mechanisms. Typical
smart soft actuators, such as shape memory alloy (SMA),
electroactive polymer (EAP), piezoelectric actuators
(PZT), and fluid elastomer actuator (FEA), are reported
in robotic fish design, which is discussed in this section.
The characteristics of the mainly used smart soft actuators
in robotic fish are presented in Table 3.
SMA-based robotic fishes
The principle of SMA is the shape memory effect, namely,
the low-temperature martensite reverses into the high-
temperature parent phase when heated and returns to the
pre-deformation shape during subsequent cooling through
the release of internal elastic energy.
67
SMA can be actu-
ated under a small applied voltage (about 2 V) and gener-
ates a high output stress (up to 200 MPa).
62
SMA is suitable
for underwater robots because the surrounding water is a
benefit to cooling down the SMA, and faster frequency
could be obtained.
68
SMAs in the form of wire, spring, and
plate are found in robotic fish design. Li et al.
69
attached
two SMA wires in the form of a trapezoid (to double the
6International Journal of Advanced Robotic Systems

stress) of different lengths to each side of an elastic substrate
(the backbone of the fishtail) to achieve both undulatory and
oscillatory motions (see Figure 4(a)). Coral et al.
70
adopted
19 ribs and a rigid caudal fin to form the fish body instead of
a compliant one. Two groups of SMA wires actuate the fish
body and the tail, respectively (see Figure 4(b)).
Notably, the recoverable strain of SMA wires is limited
(4–8%). The strain could be substantially improved (up to
200–1000%) when turning the SMA wires to springs, while
the generated stress is significantly decreased. Thus,the SMA
spring is appropriately adopted in small-size robots. Cho
et al.
71
developed a caudal fin propulsion system actuated
Table 3. The characteristics of the mainly used smart soft actuators in robotic fish.
Actuator type Properties Limitations
SMA
62
Low voltage (2 V)
Strain (4*8%)
High stress (200 MPa)
Limited frequency (1 Hz)
High driving temperature (over 70 degrees)
IPMC
63
Low voltage (1*3V)
Strain (>40%)
Low power consumption
Low stress (0.3 MPa)
PPy
64
Fast response
Considerably high strain rate
Nonlinear hysteresis phenomenon leads to poor controllability
DE
65
Fast response (200 ms)
Large actuation strokes (>100%)
High voltage (>1 KV)
PZT
25
High stress (>110 MPa)
Fast frequency (up to 10000 Hz)
Small actuation displacement (0.2%)
High voltage (100 V)
FEA
66
Helpful to body compliance and mimicry Difficulty of power supply
SMA: shape memory alloy; IPMC: ionic polymer-metal composite; PPy: polypyrrole; DE: dielectric elastomer; PZT: piezoelectric actuators; FEA: fluid
elastomer actuator.
Figure 4. SMA-based robotic fishes: (a) Actuation structure bending to side A and side B, SMA_A1 and SMA_B1 are longer than
SMA_A2 and SMA_B2 to undulatory and oscillatory movement.
69
Copyright 2019, IEEE. (b) A robotic fish based on SMA wires. The
dashed line represents the SMA wires, the red line represents the spine, and three types of swimming modes are realized. Reproduced
with permission.
70
Copyright 2018, IOP publishing. (c) The SMAs pass the holes to drive the segments. Reproduced with permission.
71
Copyright 2008, IEEE. (d) Red areas represent deforming regions. Reproduced with permission.
72
Copyright 2019, Springer.
(e) Gestures of a robotic pectoral fin based on observations. (i) relaxation; (ii) expansion; (iii) bending; (iv) cupping; and (v) undulation.
Reproduced with permission.
73
Copyright 2012, Springer. SMA: shape memory alloy.
Li et al. 7

by SMA springs (see Figure 4(c)). The propulsion system is
composed of four segments and a caudal fin. The designed
spring passes through each joint to drive them to realize sub-
carangiform movement when heated by wired power.
SMA in the form of a plate is typically adopted to the
pectoral fin design. The fin ray developed by Zhang et al.
72
is composed of two layers of SMA plates sandwiching a
layer of the elastic pad. The deforming region is limited to
one end of the fin ray (see Figure 4(d)). Multiple fin rays
are arranged in parallel and connected by a fin membrane to
achieve rajiform locomotion. Yan et al.
73
adopted a similar
fin ray mechanism but used them in the pectoral fins of
carangiform (see Figure 4(e)). Some basic gestures of the
robotic pectoral fin, namely, relaxation, expansion, bend-
ing, cupping, and undulation, are realized by the SMA
plates heated by resistance wire.
EAPs-based robotic fishes
EAP deforms when there is an electrical stimulus, which can
be categorized into ionic EAPs and electronic EAPs. The ionic
polymer-metal composite (IPMC) and polypyrrole (PPy)
based on ionic EAPs and the dielectric elastomer (DE)
based on electronic EAPs are reported in robotic fish design.
When an electric field is applied to IPMC, it will
cause its anions and cations to redistribute. The high con-
centration of cations on the cathode side will cause expan-
sion effects, while the anode side is the opposite, and then
the deformation of bending is produced.
74
IPMC has rela-
tively small output stress (0.3 MPa) and low applied vol-
tage (1*3V),
63
which makes it suitable for small-sized
robotic fish actuation (less than 100 mm in length
75,76
). The
designs of IPMC actuation share similarities. The flexible
IPMC part is utilized as a flapper to oscillate the passive
fins.
77–79
Zheng et al.
80
developed a robotic manta ray and
used the IPMC as a part of the wing-shaped pectoral fins,
shaped like a trapezoid, and the rest remains to be passive.
Hubbard et al.
81
developed a special IPMC with a deform-
able surface, capable of realizing bending, twisting, and
flapping motions. They used the designed IPMC as the
pectoral fin and connected the IPMC to a caudal fin for
Figure 5. EAPs-based robotic fishes: (a) The deformable IPMCs lead to complex gestures of the robot: (i) Caudal fin bending “flapping”;
(ii) caudal fin bending (nonneutral axis) “yaw”; (iii) caudal fin twisting “ roll/banking”; (iv) pectoral fin bending “translation/roll/banking”;
(v) pectoral fin twisting “pitch-dive/surface”; and (vi) pectoral fin twisting “rolling”. Reproduced with permission.
81
Copyright 2014,
IEEE. (b) The structure of the robot: the DE muscle is framed in the silicone body. A silicone tail attached to the body is for steering
actuated by a magnet. Reproduced with permission.
64
Copyright 2017, Amer Assoc Advancement Science. (c) The robot composition:
the body is assembled by two DEAs and two silicone layers. The head is made of a PMMA plate and two PET films. The positive DEA
electrode is smaller and arranged inside of the body to realize insulation. Actuation structure: (i) pre-stretched state. (ii) and (iii) excited
state: flaps the caudal fin to move forward. Reproduced with permission.
84
Copyright 2021, Mary Ann Liebert. (d) The structure of
the self-powered soft robot inspired by snailfish (right). Reproduced with permission.
6
Copyright 2021, Nature Research. EAP:
electroactive polymer; IPMC: ionic polymer metal composite; DEA: dielectric elastomer actuator; PMMA: polymethyl methacrylate;
PET: polyethylene terephthalate; DE: dielectric elastomer.
8International Journal of Advanced Robotic Systems

propulsion. Maneuvering motions, such as pitching, roll-
ing, and yawing, are realized (see Figure 5(a)). Apart
from the relatively low stress, the back-relaxation phenom-
enon, that is, the bending angle of IPMC increases in a
certain time and then slowly decreases, is needed to be
considered.
82
It is verified that the peak angle value and the
time to reach the peak are related to the water salinity and
the applied voltage.
82
The reason for this phenomenon is the
entry of water from the outside to the inside of the IPMC.
83
The PPy actuator is fabricated by using electrochemical
deposition to deposit PPy conductive polymer on both
sides of polyvinylidene fluoride film to form a three-layer
structure.
85
It will cause volume expansion to produce bend-
ing displacement when a small voltage is applied. This kind
of actuator has the advantages of low cost, high conductivity,
and fast response. McGovern et al.
86
described a method for
measuring the thrust of a PPy actuator and studied the poten-
tial of the conductive polymer actuator as a robotic fish
propulsion element by comparing the generated thrust with
the synthetic speed of the robotic fish. A prototype
87
actu-
ated by a PPy actuator reaches the maximum speed of
33 mm/s (0.25 BL/s) with a diameter of 20 mm.
For the DE actuator, when voltage is applied, the Max-
well stress is generated between the two electrodes and
deforms the membrane in the thickness direction, resulting
in area expansion.
88
DE possesses a fast response (less than
200 ms) and a large actuation strain (over 100%), but the
applied voltage is relatively high (over 1 kV).
65
In order to
deal with insulation problems, Li et al.
64
found that the
conductivity of the surrounding open water is weak but
sufficient to serve as the ground electrode, while the hydro-
gel film sandwiched by two DE membranes is another
electrode. The leading edges of the fins are rigid to lead
to the undulatory motions of the entire fins when flapping
(see Figure 5(b)). Li et al.
6
developed a robot inspired by
snailfish, which lives in the deep sea (see Figure 5(d)). The
DE actuators are served as links between the fish body and
fins. To adapt to the high pressure of the deep sea, they
adopted a triblock copolymer, poly (styrene-b-butyl acry-
late-b-styrene) in the DE actuator to increase the voltage-
induced area strain. The robot succeeds in flapping for
45 min in the Mariana Trench (10900 m) and reaches a
speed of 2.76 cm/s (0.24 BL/s) in the experimental condi-
tion of 110 MPa, which is a breakthrough in deep sea
exploration. Shintake et al.
84
designed a prototype consist-
ing of silicon substrate and elastomer membrane layers.
They arranged the inside high-voltage electrodes smaller
than other layers, making that there was no electrical short-
circuit path through the water and thereby realizing the
insulation (see Figure 5(c)). The swimming speed of the
robot reaches a maximum of 37.2 mm/s (0.25 BL/s) with
wired power.
PZT-based robotic fishes
The principle of PZT is based on the inverse piezoelectric
effect, which results in structural deformation on electrical
excitation. PZT actuators exhibit relatively high driving
stress (about 110 MPa) and fast frequency, while the strain
is relatively small (0.2%).
25
Typically, the robots actuated
by PZT require a stroke magnification mechanism. Borgen
et al.
89
used two THin-layer composite UNimorph ferro-
electric DrivER and sensor (THUNDERs) (PZT actuator
developed by Mossi et al.
90
), respectively, connected to the
tail fin. Although the magnifying mechanism is eliminated,
the size of the actuator itself is large, which still makes the
robotic fish bulky. The lightweight piezocomposite actua-
tor (LIPCA), another PZT actuator, is superior to THUN-
DER in many aspects, but the driving displacement is still
very small. Heo et al.
91
adopted a rack-and-pinion system
to amplify the displacement (see Figure 6(a)). Nguyen
et al.
92
used four layers of LIPCA connecting with a mag-
nifying system to flap the fish tail (see Figure 6(b)). Zhao
et al.
93
developed a micro-robotic fish (total mass: 1.93 g)
with double caudal fins. The caudal fins are actuated by
PZT bimorph cantilevers (36 mm, 2.1 mm, and 0.8 mm in
length, width, and height, respectively) through a four-bar
linkage transmission (see Figure 6(c)). The close or open
movement is realized to improve the robotic stability and
maneuverability when flapping. The maximum speed of
the robot is about 4.5 cm/s (0.75 BL/s).
Macro fiber composite (MFC), another type of piezo-
electric material, comprises rectangular cross-sectional
piezoelectric fibers and interdigitated electrodes.
95
In addi-
tion to good flexibility and large driving force, MFC strikes
a balance between the deformation and actuation force,
which means that the additional magnifying mechanism
is not required. Govindarajan et al.
96
tested the perfor-
mance of the MFC flapping beam underwater. They
observed that the beam reached its maximum efficiency
of 55%at the frequency of 2.0 Hz and the maximum thrust
reached 45 mN. Cen et al.
97
created the first prototype
actuated by MFC. It is a conceptual model that the piezo-
electric MFC bimorph actuator (without caudal fin) is con-
nected to the main body. The robot reaches a swimming
speed of 7.5 cm/s (0.3 BL/s), which shows the feasibility of
the MFC-actuated robotic fish. In addition, Tan et al.
95
designed a modular MFC bimorph tail connected to the
body. With the actuation of the MFC actuator, the proto-
type reaches the maximum speed of 0.25 m/s (0.8 BL/s).
Hu et al.
94
attached two MFCs to the caudal fin-like sub-
strate.TheMFCis20mminwidthand29.6mmin
length (see Figure 6(d)). They carefully designed a thrust
measurement system, and the maximum mean thrust of
2.95 mN was observed.
Li et al. 9

FEA-based robotic fishes
FEA is integrated within and distributed throughout the
body, which makes the robot soft and compliant.
66
FEA
is made of super-elastic materials inside with several cham-
bers expanded by pressurized gas or liquid, resulting in
bending or stretching motion. Pneumatic and hydraulic
actuators are two categories in underwater applications.
Marchese et al.
98
developed a robotic fish that comprises
two pairs of pneumatic layers longitudinally attached to an
inextensible constraint layer (see Figure 7(a)). With an
onboard gas regulation mechanism, the robot achieves
escape maneuvers of a maximum heading angle of
100 degrees. However, the insufficient power supply
resulting in limited endurance and the uncontrollable buoy-
ancy center due to the release of gas are unignorable prob-
lems. In contrast, hydraulic actuators are capable of using
surrounding water in a cycle, providing faster frequency
response and larger force. Katzschmann et al.
4
adopted a
similar actuator structure but used an onboard gear bump to
pressure the fluid (see Figure 7(b)). The robot could dive up
to 18 m and swim at the speed of 0.5 BL/s and show good
integration into the marine environment.
Furthermore, Chen et al.
99
studied the relationship
between the bending angle and the pressure of the fluid.
They developed a flexible water hydraulic soft bending
actuator (FWBA) for a fishtail as shown in Figure 7(c). The
bending angle of FWBA is approximately 79.8 degrees
with the water pressure of 18 KPa, and the bending angle
drops to 56.5 degrees with the water pressure of 20 KPa
when paired FWBAs are adopted to flap a caudal fin.
Sensors for robotic fishes
Sensing technology is an essential part of the robotic fish. It
can sense changes in the surrounding environment to
provide feedback control. Generally, in terms of realizing
autonomous navigation, infrared sensors are mainly used in
the detection of obstacles, effectively in planning routes,
and avoiding obstacles. Pressure sensors are used for depth
Figure 6. PZT-based robotic fishes: (a) The movement of LIPCA is transformed into the rotation of gears, which drives the rotation of the
four-bar mechanism, thereby flapping the caudal fin. Reproduced with permission.
91
Copyright 2021, Springer. (b) When LIPCAs bend up,
the flapping tail motion is realized through the long link and vice versa. Reproduced with permission.
92
Copyright 2010, IOP publishing.
(c) Schematic of the micro-robotic fish and the movements of four-bar linkage transmission. Reproduced with permission.
93
Copyright
2021, Elsevier. (d) Structure diagram of the MFC-actuated bionic robotic fish. Reproduced with permission.
94
Copyright 2021, Academic
Press-Elsevier Science. PZT: piezoelectric actuators; LIPCA: lightweight piezocomposite actuator; MFC: macro fiber composite.
10 International Journal of Advanced Robotic Systems

perception to prevent excessive pressure from damaging
components. Accelerometer and gyroscope are used to
maintain the stable swimming of the robotic fish. Compass
realizes the direction recognition. The current sensor pre-
dicts battery life and provides variable current to the robot.
Force/torque sensor measures thrust. More details are pre-
sented in Table 4.
As an important part of underwater perception, artificial
lateral line (ALL) has received more and more attention.
The lateral line system is a unique skin sensory organ of
aquatic vertebrates.
119
The basic sensory unit of the lateral
line is the neuroma, which is a receptor organ that consists
of sensory hair cells and support cells covered by a gelati-
nous cupula.
120
The ALL system inspired by it uses pres-
sure sensors as the main sensing components. Multiple
pressure sensors are distributed on the surface of the fuse-
lage. Specifically, Wang et al.
121
distributed nine pressure
sensors around the body to perceive the state of adjacent
robotic fish by sensing the reverse Carmen vortex street.
Zheng et al.
122
distributed eleven pressure sensors on the
fuselage: four at each side of the shell, one at the tip of the
head, and two at the top and bottom of the head. The state
of adjacent fish was obtained by collecting hydrodynamic
pressure variations data. Furthermore, piezoresistive,
piezoelectric, capacitive, optical, and hot-wire sensors can
be used to build ALL systems as well. See literature
123
for
more details.
Modeling and control of robotic fishes
Modeling and control are considered to be the core parts of
the robotic fish design. In this section, the methods of
dynamic modeling are first presented. Then, two main con-
trol approaches: (1) trajectory approximation method and
(2) central pattern generators (CPGs) are reviewed.
Dynamic modeling
Due to the complexity of the morphology and hydrody-
namics of fish, it is very difficult to establish an accurate
dynamic model. The numerical method and analytical
method are typically adopted. The former often requires
the establishment of N–S equations. Computational Fluid
Dynamics (CFD) is applied to numerical simulations.
Figure 7. FEA-based robotic fishes: (a) (i) antagonistic actuator, (ii) flexible and inextensible layer, and (iii) agonistic actuator.
Reproduced with permission.
98
Copyright 2014, Mary Ann Liebert. (b) Overview of Soft robotic fish (top right). The elastomer tail (cut
view) is driven by a gear pump, and the two inlets at the tail form a liquid circulation. Dive planes are driven by servos to ascend or
descend. The buoyancy control unit, control electronics including an acoustic receiver, and fisheye camera are the subcomponents of
the system. Reproduced with permission.
4
Copyright 2018, Amer Assoc Advancement Science. (c) Pre-stretched state (left) and the
bending state of the FWBA (right). Reproduced with permission.
99
Copyright 2021, Elsevier Sci. FEA: fluid elastomer actuator; FWBA:
flexible water hydraulic soft bending actuator.
Li et al. 11

Using the CFD method based on the N–S equations, the
viscous force can be fully considered, and the unsteady and
nonlinear effects caused by the tail swing can be analyzed,
which makes the hydrodynamic prediction more reli-
able.
124
However, this method is very time-consuming due
to the huge amounts of calculations, and it lacks the support
of classified and fined experimental data. The latter, based
on certain simplifications, is more feasible but less accu-
rate. For instance, the Resistive Force Theory
13
is only
suitable in the low Reynolds number condition for neglect-
ing the inertia force. The WPT
15
simplifies the fish body as
a flexible thin plate for wave motion, thereby being more
suitable for the flatfish swimming. The EBT
14
is suitable
for slender fish with small lateral deformation. It presents
that the thrust of the fish is generated by the additional
momentum corresponding to the motion of the fish body
wave propagating backward. Based on the momentum bal-
ance in the hemisphere control volume containing the fish
body, the effect of wake dynamics is also approximated.
The large-amplitude elongated-body theory
18
proposed
later extends its applications to larger lateral deformation,
which makes it the most acceptable theory. In addition, Yu
et al.
125
proposed a data-driven approach. In their method,
the dynamic model is first derived with the Morrison
equation and the strip method, and the parameters are
directly identified from experimental data and integrated
into the dynamic model to reshape it. Therefore, it is appli-
cable to model swimming robots with complex and irregu-
lar geometric profiles and numerous heterogeneous
hydrodynamic parameters.
Trajectory approximation
To approximate the trajectories of the fishes, it is important
to get a deep understanding of the principles of their loco-
motion, which is characterized by the deforming bodies. A
widely adopted function of the traveling body wave is pro-
posed by Lighthill
14
ybody ðx;tÞ¼½ðc1xþc2x2Þ½sinðkx þwtÞ (1)
where ybody denotes the lateral displacement of the fish, x
denotes the displacement along the fish axis, k¼2p=l,
ldenotes the wavelength, wdenotes the body wave fre-
quency, c
1
denotes linear wave amplitude envelope, and
c
2
denotes quadratic wave amplitude envelope. To elimi-
nate the head swing of fish for stable swimming, the new
function is obtained by subtracting the function of the
head from the traveling wave function above.
126
The
Table 4. Different types of sensors used in robotic fishes.
Sensor type Sensor model Applications
Camera
CMOS camera
100, 101
CCD camera
102
Positioning and tracking
100
Infrared sensor
Sharp GP2Y0A21YK0F
103
GP2Y0A02YK(0 to 15 psi)
104
Detect obstacles
103, 105, 106
Remote control receiver
75
Pressure sensor
CYY4
107
CP131
108
MS5803-01BA
109
40PC001
110
40PC015
104
Depth control
101, 104, 105, 107, 110
Remote control
111
Estimate the speed of the underwater robot
108
Control the orientation of the robot
109
Compass
Dinsmore 1490 sensor
112
Navigation
112
Accelerometer
ADXL330(6.78 mg)
113
Measure the static gravity acceleration
113
Gyroscope
LPR503AL, LPY503AL
100
MPU9150
107
IDG300(2.44 /s)
113
Improve positioning accuracy
100
3D motion control
107
Provide the angular rate
113
Servo angle sensor
MAE-3 US-Digital
113
Measure exact angular displacement
113
Current sensor
ACS712
114
Measure torque
114
Soft eGaIn sensor
Not available
Curvature estimation
115
Strain sensing
116
Force/torque sensor
Nano 17
117
Measure thrust
117
Temperature sensor
TC1047A
41
Detect water temperature
118
12 International Journal of Advanced Robotic Systems

head is typically considered to be rigid, thus the function
is linear
yheadðx;tÞ¼c3x¼@ybody ðx;tÞ
@xjx¼0¼c1xsinðwtÞ(2)
where yheadðx;tÞdenotes the lateral displacement of the
head and c
3
denotes the coefficient of the linear equation
of the head. The redefined lateral displacement of the fish,
yBODYðx;tÞ, is obtained
yBODYðx;tÞ¼ybody ðx;tÞyheadðx;tÞ
¼ðc1xþc2x2Þsinðkx þwtÞc1xsinðwtÞ(3)
Then, the function is discretized to fitting the body wave
yBODYðx;tÞ¼ðc1xþc2x2Þsin kx 2p
Mi

c1xsin 2p
Mi

;iE½0;M1(4)
where iis a serial number in an undulation circle and M
represents the resolution of the discrete travelling wave.
Therefore, a MNlook-up table of the joints is obtained
(Ndenotes the number of joints).
Similarly, other swimming patterns could be realized by
establishing corresponding kinematic functions.
127
In con-
clusion, this method is easy to implement but could not
realize smooth gait transition, and the instantaneous torque
changes and jerky movements have the risk of damaging
the motors and gearboxes. Moreover, the online parameter
tuning is difficult since each joint involves many values to
promise accuracy.
Central pattern generator
Another control method is to use CPG, which is a neural
network that exists in both invertebrates and vertebrates. It
can generate rhythmic neural activity patterns, such as
respiration, chewing, and sucking, in the absence of exter-
nal signal input like sensory feedback or higher control
centers.
128
In biology, CPG is turned out to be a distributed
network composed of several coupled oscillators, which is
suitable for multi-link mechanisms.
129
In particular, the
oscillators are coupled in a certain topology, and each of
the oscillators is in charge of a specific joint. Simple or
low-dimensional input signals are sufficient to propose the
coordinated wave motion of the robot. CPG-based control-
ler exhibits superiorities: (1) provides stable rhythmic pat-
terns, (2) realizes diverse motion modes of the robot
through a variety of stable phase relationships, (3) presents
smooth transition online between different gaits with sim-
ple control parameters, and (4) although CPG does not
require sensory feedback, they are crucial to shaping the
CPG control to improve adaptability and robustness.
CPG models. The first step to construct a CPG controller is to
choose an appropriate CPG control model. The most
widely used CPG model in a robotic fish domain is the
oscillator model, of which the most common are the Hopf
oscillator and the Ijspeert phase oscillator.
Hopf oscillator possesses a stable limit cycle.
130
It is
able to produce sinusoidal oscillation independently. The
dynamics of the Hopf oscillator could be described by the
following differential equations
_
x¼m2ðx2þy2Þxþ!y
_
y¼m2ðx2þy2Þy!x(5)
where xand yare the states of the oscillator, !is the
intrinsic oscillation frequency, and mdetermines the
steady-state amplitude of oscillation, that is, the state vari-
ables xand ywill eventually converge to a stable limit cycle
with mas the radius. It should be noted that there are no
parameters to control the phase lags. Actually, the phase
lags are determined by the coupling weight between the
joints and added as an extra term to the equations.
Ijspeert et al.
131
developed a phase oscillator to control a
salamander robot. The oscillator could be described as
follows
qi
_
¼2pviþX
j
rjwij sinðqjqiijÞ
ri
€¼ai
ai
4ðRiriÞri
_

xi¼ri1þcosðqiÞ(6)
where qiand r
i
are the state variables representing the phase
and the amplitude of oscillator i,v
i
and R
i
determine its
intrinsic frequency and amplitude, and a
i
denotes the
amplitude convergence speed. Couplings between oscilla-
tors are defined by the weights wij and phase biases ij.A
positive oscillatory signal, x
i
, represents the output of oscil-
lator i. The phase model is an abstract simulation of the
biological movement process. The system also exhibits
limit cycle behavior, and the analytical solution clearly
expresses the parameters controlling amplitude, frequency,
and phase lag.
Parameter tuning. Parameter tuning is the key problem in
CPG modulation, as the CPGs involve many uncertain
parameters in the equations while a well-established design
methodology for CPGs to achieve the desired motion beha-
vior is still missing. Lately, some intelligent learning meth-
ods are being proposed. Yu et al.
132
searched the optimized
parameters by integrating particle swarm optimization
(PSO) and a dynamic model. In PSO, each particle has the
ability to perceive the best position of itself and the swarm
and then adjust its actions based on this information by
iteration. Specifically, the dynamic model is first devel-
oped as a guide to search the control parameters and the
Li et al. 13

swimming patterns, and then, the PSO refines the searched
parameters of the CPGs. Zhou et al.
133
adopted the genetic
algorithm (GA) to optimize the parameters of the CPGs as
GA possesses high-dimensional global searching capabil-
ity. The speed and the instantaneous swimming power con-
sumption are used as feedback to improve the controlling
parameters by GA. Hu et al.
134
proposed a learning method
to acquire fishlike swimming. First, they used the trajectory
approximation method to obtain the joint angles as the
teaching signals. By converting the parameters of fre-
quency, phase difference, and amplitude into new state
variables with their own dynamics, the teaching signals and
their phase relations could be learned by the CPG network,
thus the instructed locomotor pattern can be reproduced by
the robotic fish. The learning is embedded into the
dynamics of the oscillator, thereby external optimization
or preprocessing of the teaching signal is not required. Ren
et al.
135
proposed a general internal model (GIM)-based
learning method. The GIM is composed of three compo-
nents, namely the inner Hopf oscillator, the artificial
neural network (ANN), and the outer signal modulator.
The Hopf oscillator generates periodic input signals. The
ANN is trained to yield the desired motion patterns when
receiving the input signals from the inner Hopf oscillator,
and the outer signal modulator adjusts the amplitude of the
generated motion pattern according to task specifications
since the output of the ANN cannot be resized by the input
as the ANN is a nonlinear mapping. The GIM exhibits
excellent function approximation ability, and the speed
and direction control are realized by monotonically tuning
parameters.
Close-loop CPG system. The close-loop CPG system plays a
very significant role in the generation of diverse and stable
movements. The framework of closed-loop control is sche-
matically shown in Figure 8. Specifically, the sensory sig-
nal generated by them could directly act on the CPG, like a
reflex action, which is an involuntary and nearly instanta-
neous movement in response to a stimulus, or received by
the high-level center as feedback. Due to the nonlinear
environment, the fuzzy or (proportional–integral–deriva-
tive) controller is adopted as the high-level center to decide
the swimming mode based on the feedback. The gait tran-
sition could be realized by a finite state machine (FSM)
since each gait corresponds to a set of control parameters.
The combination of the CPGs and the FSM provides an
effective way to switch locomotor patterns. Under this
frame, Bal et al.
136
realized excellent autonomous swim-
ming performance through precise yaw control. Yan
et al.
137
achieved stable motion mode switching between
swimming and crawling.
Challenges and future directions
With the unique driving characteristics and application
diversity, robotic fish will certainly become one of the
major development trends in performing underwater tasks.
However, there is a gap between the robotic fish and the
real fish regarding the performance. The maximum speed
of the robotic fish is 3.7 m/s, which is far more outstanding
than others, while the swordfish reaches about 27 m/s. The
maximum turning speed of the robotic fish is 670 /s, while
the archerfish is 4500 /s. Moreover, fishes exhibit flexible
and freely maneuvering, such as escape, rapid acceleration,
and braking, while the robotic fish only execute simple
turning or diving. The possible directions of robotic fish
might focus on the following aspects.
First, one possible direction is drag reduction, which
might contribute to the high speed of real fish inspired by
Gray’s paradox.
12
The micron-scale caves distributed on
the fish surface play an important role in drag reduction.
138
The concave shape creates a negative pressure area, suck-
ing oil out of the hole to lubricate the surface to minimize
frictional resistance. Dou et al.
139
developed a coating tech-
nology that autonomously forms the micron-scale caves
when swimming. The gas-phase develops in the solid–
liquid interface in low-pressure conditions due to flow
separation and vortex and partially replaces the solid–liquid
shear force with gas–liquid shear force, resulting in drag
reduction. It is noteworthy that the drag reduction effi-
ciency of the bionic surface becomes more significant as
theflowrateincreases(over10%at the flow speed of
13.1 m/s). In the future, the drag reduction mechanism
needs to be clarified, and more remarkable performance
and simple fabrication of drag reduction technology are
needed to be adopted in the robotic fish system.
Second, the question of improving the actuation system
is another direction. On the one hand, the prototypes based
Fuzzy/PID
controller
Feedback Reflex
FSM CPG Robotic fish
Sensory
information
Figure 8. The schematic of the close-loop CPG system. CPG: central pattern generator.
14 International Journal of Advanced Robotic Systems

on the multi-link mechanism actuated by the traditional DC
and servo motors still represent the state-of-the-art swim-
ming speed. However, it cannot perfectly fit the flexible
movement of real fish, and the friction loss caused by addi-
tional transmission mechanisms cannot be ignored.
Furthermore, it requires multiple motors to independently
drive the fin rib to reproduce the undulation of ribbon fins,
which is bulky and difficult to control. The design of MAR,
using a single helix to realize undulation, shows a new
direction of actuation system simplification.
34
On the other
hand, the smart materials and soft actuators can be well
integrated into the body of the robot fish with a smaller
size and higher maneuverability, but most of the robotic
fish with such actuators have a maximum speed of no more
than 3 BL/s.
31
The FEA shows high compliance and the
best “biomimicry”. This actuator is essentially powered by
motors but uses fluid as the energy conversion medium,
which gives it the advantages of high speed and flexible
movement, especially the form of hydraulic exhibits great
promise in terms of stability and energy recyclability. In the
future, it is expected to be applied to undulation and
muscle-like movements.
Third, the underwater perception is still not well-
developed. Powerful perception offers detailed feedback
in control and improves the adaptability of the robotic fish.
However, current sensors, such as cameras, IMU, and GPS,
have difficulty performing well in the harsh underwater
environment. Moreover, they could only provide a single
sensing signal and had blind areas, where they unable to
sense objects or creatures’ subtle movements.
140
Lateral
line is an important modality to sense the subtle changes
in the water flow, which is composed of a row of neuro-
masts distributed throughout the fish body.
120
Based on it,
the ALL is typically constructed by an array of distributed
pressure sensors to sense the fluid velocity or reverse car-
men vortex street, which is crucial to the perception among
groups of underwater robots.
141
However, it is still worth
exploring how to realize real-world perception. Recently,
the increasing interest in proprioceptive sensing provides a
new direction for underwater perception, which utilizes the
kinematics or parts of the body to extract useful informa-
tion inflow.
142
Since related research studies are just begin-
ning, future directions might include determining the type
of proprioceptive signal perceived and clarifying the neu-
rotransmission mechanisms between proprioceptive and
motor control.
143
From a long-term perspective, it is excit-
ing to combine proprioceptive sensing with an ALL to
realize powerful underwater perception.
Fourth, the control methods are needed to be improved.
The close-loop CPG system has strong adaptability and
robustness. However, how exactly the properties of sensory
information affect the characteristics of the CPG output has
not been fully investigated. Recent studies have shown that
sensory feedback topology has a significant impact on the
way that the neural oscillator setting affects the entrainment
characteristics of the coupled system.
144
In general, a
systematic design method for sensory feedback control is
needed to be developed in the future. Alternatively, con-
sidering the complexity of nonlinear hydrodynamics, the
iterative learning control could be regarded as a potential
candidate.
145
The accurate model is not required when an
appropriate learning gain is chosen. The learning formu-
lates the input signal based on previous experimental data,
and good speed tracking performance is achieved with con-
stant iteration during the entire operation interval. In the
future, it is expected to be applied in tracking maneuvering
movements, such as turning, yawing, or pitching motions.
Conclusions
In this article, we have reviewed the characteristics of dif-
ferent fish locomotion and the robot designs based on it.
We also have outlined features of smart soft actuators and
sensors. Then, we have summarized modeling and control
methods for efficient and stable swimming. Fish have many
complex structural features, most of which are not yet
known clearly for their potential impact on swimming per-
formance. However, it is certain that the use of mechanical
devices for imitation is a sure way to help us understand the
hydrodynamic principles of fish movement and thus
achieve the transcendence of the real fish. The robotic fish
is still in the preliminary prototype development stage, and
there is still a certain distance from the practical applica-
tion, but with its excellent potential performance, it will
certainly expand a wide range of applications in military
and civil applications.
Acknowledgments
This work was supported by the Zhejiang Provincial Natural Sci-
ence Foundation of China (Grant Nos. LY22E050019 and
GG21E050044) and the National Natural Science Foundation of
China (Grant Nos. 51805482 and 51975523).
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with
respect to the research, authorship, and/or publication of this
article.
Funding
The author(s) disclosed receipt of the following financial support
for the research, authorship, and/or publication of this article: This
research is funded by natural science foundation of zhejiang prov-
ince (GG21E050044 and LY22E050019) and national natural sci-
ence foundation of china (51805482 and 51975523).
ORCID iD
Yi Li https://orcid.org/0000-0001-8485-2937
References
1. Lauder GV. Fish locomotion: recent advances and new
directions. Ann Rev Mar Sci 2015; 7: 521–545. 2014/09/25.
DOI: 10.1146/annurev-marine-010814-015614.
Li et al. 15

2. Wen L, Wang TM, Wu GH, et al. Quantitative thrust effi-
ciency of a self-propulsive robotic fish: experimental method
and hydrodynamic investigation. IEEE-ASME Transact
Mechatron 2013; 18: 1027–1038. Article. DOI: 10.1109/
tmech.2012.2194719.
3. Reddy NS, Sen S, Shome SN, et al. An investigation on the
performance of an oscillating flat plate fin with compliant
joint for underwater robotic actuation. In: 1st IEEE interna-
tional conference on control, measurement and instrumenta-
tion (CMI), Jadavpur Univ, Kolkata, INDIA, 08–10 January
2016, pp. 201–205. New York: IEEE.
4. Katzschmann RK, DelPreto J, MacCurdy R, et al. Explora-
tion of underwater life with an acoustically controlled soft
robotic fish. Sci Robot 2018; 3. 2018/03/21. DOI: 10.1126/
scirobotics.aar3449.
5. Liang J, Wang T, and Wen L. Development of a two-joint
robotic fish for real-world exploration. J Field Robot 2011;
28: 70–79. DOI: 10.1002/rob.20363.
6. Li GR, Chen XP, Zhou FH, et al. Self-powered soft robot in
the Mariana Trench. Nature 2021; 591: 66–71. DOI: 10.1038/
s41586-020-03153-z.
7. Zhang F, Ennasr O, Litchman E, et al. Autonomous sampling
of water columns using gliding robotic fish: algorithms and
harmful-algae-sampling experiments. IEEE Syst J 2016; 10:
1271–1281. DOI: 10.1109/jsyst.2015.2458173.
8. Zhang FT, Wang JX, Thon J, et al. Gliding robotic fish for
mobile sampling of aquatic environments. In: IEEE 11th
international conference on networking, sensing and control
(ICNSC), Miami, FL, 07–09 April 2014, pp.167–172.
New York: IEEE.
9. Fattah SA, Abedin F, Ansary MN, et al. R3Diver: remote
robotic rescue diver for rapid underwater search and rescue
operation. In: IEEE region 10 conference (TENCON), Singa-
pore, 22–25 November 2016, pp. 3280–3283. New York:
IEEE.
10. Wu Z, Liu J, Yu J, et al. Development of a novel robotic
dolphin and its application to water quality monitoring.
IEEE/ASME Transact Mechatron 2017; 22: 2130–2140.
DOI: 10.1109/tmech.2017.2722009.
11. Breder CM. The locomotion of fishes. Zoologica 1926; 4:
159–256.
12. Gray J.Studies in animal locomotion, VI. The propulsive
powers of the dolphin. J Exp Biol 1936; 13: 192–199.
13. Taylor G. Analysis of the swimming of long and narrow
animals. Proceed Royal Soc London 1952; 214: 158–183.
14. Lighthill MJ. Note on the swimming of slender fish. J Fluid
Mechan 1960; 9: 305–317. DOI: 10.1017/s00221120600
01110.
15. Wu YT. Swimming of a waving plate. J Fluid Mechan 1961;
10: 321–344. Article. DOI: 10.1017/S0022112061000949.
16. Cheng JY, Zhuang LX, and Tong BG. Analysis of swimming
three-dimensional waving plates. J Fluid Mechan 1991; 232:
341–355. Article. DOI: 10.1017/S0022112091003713.
17. Horlock JH. Actuator disk theory. McGraw-Hill Interna-
tional Book Company 1978; 85: 29.
18. Lighthill M J. Large-amplitude elongated-body theory of fish
locomotion. Proceed Royal Soci London 1971; 179: 125–138.
19. Triantafyllou MS and Triantafyllou GS. An efficient swim-
ming machine. Sci Am 1995; 272: 64–70. DOI: 10.1038/
scientificamerican0395-64.
20. Laschi C, Mazzolai B, and Cianchetti M. Soft robotics: tech-
nologies and systems pushing the boundaries of robot abil-
ities. Sci Robot 2016; 1. 2016/12/06. DOI: 10.1126/
scirobotics.aah3690.
21. Jin-Dong L and Huosheng H. Biologically inspired behaviour
design for autonomous robotic fish. Int J Automat Comput
2006; 04: 16–27.
22. Zhou C and Low KH. Design and locomotion control of a
biomimetic underwater vehicle with fin propulsion. IEEE/
ASME Transact Mechatron 2012; 17: 25–35.
23. Zhang S, Qian Y, Liao P, et al. Design and control of an agile
robotic fish with integrative biomimetic mechanisms. IEEE/
ASME Transact Mechatron 2016; 21: 1846–1857.
24. Yu J, Ding R, Yang Q, et al. On a bio-inspired amphibious
robot capable of multimodal motion. IEEE-ASME Transact
Mechatron 2012; 17: 847–856.
25. Chu W-S, Lee K-T, Song S-H, et al. Review of biomimetic
underwater robots using smart actuators. Int J Precis Eng
Manufact 2012; 13: 1281–1292. DOI: 10.1007/s12541-012-
0171-7.
26. Yu J, Ming W, Dong H, et al. Motion control and motion
coordination of bionic robotic fish: a review. J Bionic Eng
2018; 15: 579–598.
27. Salazar R, Campos A, Fuentes V, et al. A review on the
modeling, materials, and actuators of aquatic unmanned vehi-
cles. Ocean Eng 2019; 172: 257–285.
28. Junzhi YU, Wen L, and Ren ZY. A survey on fabrication,
control, and hydrodynamic function of biomimetic robotic
fish. Sci China Technol Sci 2017; 60: 1–16.
29. Scaradozzi D, Palmieri G, Costa D, et al. BCF swimming
locomotion for autonomous underwater robots: a review and
a novel solution to improve control and efficiency. Ocean
Eng 2017; 130: 437–453.
30. Raj A and Thakur A. Fish-inspired robots: design, sensing,
actuation, and autonomy—a review of research. Bioinsp Bio-
mimet 2016; 11: 031001.
31. Xie F, Zuo Q, Chen Q, et al. Designs of the biomimetic
robotic fishes performing body and/or caudal fin (BCF)
swimming locomotion: A review. J Intell Robot Syst 2021;
102: 1–19.
32. Sfakiotakis M, Lane DM, and Davies JBC. Review of fish
swimming modes for aquatic locomotion. IEEE J Oceanic
Eng 1999; 24: 237–252. DOI: 10.1109/48.757275.
33. Bayat B, Crespi A, Ijspeert A, et al. Envirobot: a bio-inspired
environmental monitoring platform. In: IEEE OES joint sym-
posium/workshop on autonomous underwater vehicles
(AUV), Univ Tokyo, Inst Ind Sci, Tokyo, Japan, 06–09
November 2016, pp. 381–386. New York: IEEE.
34. Struebig K, Bayat B, Eckert P, et al. Design and development
of the efficient anguilliform swimming robot- MAR.
16 International Journal of Advanced Robotic Systems

Bioinspir Biomim 2020; 15: 035001. 2020/01/16. DOI: 10.
1088/1748-3190/ab6be0.
35. Clapham RJ and Hu H.iSplash-II: Realizing fast carangiform
swimming to outperform a real fish. Berlin: Springer Berlin
Heidelberg 2015.
36. Zhong Y, Li Z, and Du RX. A novel robot fish with wire-
driven active body and compliant tail. IEEE-ASME Transact
Mechatron 2017; 22: 1633–1643. Article. DOI: 10.1109/
tmech.2017.2712820.
37. Algarin-Pinto JA, Garza-Castanon LE, Vargas-Martinez A,
et al. Dynamic modeling and control of a parallel mechanism
used in the propulsion system of a biomimetic underwater
vehicle. Appl Sci-Basel 2021; 11. DOI: 10.3390/app111
14909.
38. Costa D, Palmieri G, Palpacelli MC, et al. Design of a
bio-inspired autonomous underwater robot. JIntellRobot
Syst 2018; 91: 181–192. Article. DOI: 10.1007/s10846-017-
0678-3.
39. Zhang R, Shen Z, and Wang Z. Ostraciiform underwater
robot with segmented caudal fin. IEEE Robot Autom Lett
2018; 3: 2902–2909. DOI: 10.1109/lra.2018.2847198.
40. Zhou CL and Low KH. Design and locomotion control of a
biomimetic underwater vehicle with fin propulsion. IEEE-
ASME Transact Mechatron 2012; 17: 25–35. DOI: 10.1109/
tmech.2011.2175004.
41. Cai Y, Bi S, Li G, et al. From natural complexity to biomi-
metic simplification the realization of bionic fish inspired by
the cownose ray. IEEE Robot Automat Magaz 2019; 26:
27–38. DOI: 10.1109/mra.2018.2861985.
42. Park S-J, Gazzola M, Park KS, et al. Phototactic guidance of a
tissue-engineered soft-robotic ray. Science 2016; 353:
158–162. DOI: 10.1126/science.aaf4292.
43. Hu T, Shen L, Lin L, et al. Biological inspirations, kinematics
modeling, mechanism design and experiments on an undulat-
ing robotic fin inspired by Gymnarchus niloticus. Mechan
Mach Theory 2009; 44: 633–645. DOI: 10.1016/j.mech-
machtheory.2008.08.013.
44. Curet OM, Patankar NA, Lauder GV, et al. Aquatic manoeuver-
ing with counter-propagating waves: a novel locomotive strat-
egy. J Royal Soc Inter 2011; 8: 1041–1050. DOI: 10.1098/rsif.
2010.0493.
45. Liu H and Curet O. Swimming performance of a bio-inspired
robotic vessel with undulating fin propulsion. Bioinspirat
Biomimet 2018; 13. DOI: 10.1088/1748-3190/aacd26.
46. Liu F, Lee K-M, and Yang C-J. Hydrodynamics of an undu-
lating fin for a wave-like locomotion system design. IEEE-
ASME Transact Mechatr 2012; 17: 554–562. DOI: 10.1109/
tmech.2011.2107747.
47. Behbahani SB and Tan X. Bio-inspired flexible joints with
passive feathering for robotic fish pectoral fins. Bioinspirat
Biomimet 2016; 11. DOI: 10.1088/1748-3190/11/3/036009.
48. Pham VA, Nguyen TT, Lee BR, et al. Dynamic analysis of a
robotic fish propelled by flexible folding pectoral fins.
Robotica 2020; 38: 699–718. DOI: 10.1017/s02635747190
00997.
49. Gray J. Studies in animal locomotion. J Exp Biol 1933; 10:
88–104. DOI: 10.1242/jeb.10.1.88.
50. Duraisamy P, Sidharthan RK, and Santhanakrishnan MN.
Design, modeling, and control of biomimetic fish robot: a
review. JBionicEng2019; 16: 967–993. DOI: 10.1007/
s42235-019-0111-7.
51. Raj A and Thakur A. Fish-inspired robots: design, sensing,
actuation, and autonomy—a review of research. Bioinsp Bio-
mimet 2016; 11. DOI: 10.1088/1748-3190/11/3/031001.
52. Yu JZ, Tan M, Wang S, et al. Development of a biomimetic
robotic fish and its control algorithm. IEEE Transact Syst
Man Cybernet Part B-Cybernet 2004; 34: 1798–1810.
DOI: 10.1109/tsmcb.2004.831151.
53. Yu J, Ding R, Yang Q, et al. Amphibious pattern design of a
robotic fish with wheel-propeller-fin mechanisms. JField
Robot 2013; 30: 702–716.
54. Yu J, Kai W, Min T, et al. Design and control of an embedded
vision guided robotic fish with multiple control surfaces.
Scient World J 2014; 2014: 631296.
55. Hu Y, Liang J, and Wang T. Mechatronic design and loco-
motion control of a robotic thunniform swimmer for fast
cruising. Bioinspir Biomim 2015; 10: 026006. 2015/03/31.
DOI: 10.1088/1748-3190/10/2/026006.
56. Kodati P, Hinkle J, Winn A, et al. Microautonomous robotic
ostraciiform (MARCO): hydrodynamics, design, and fabrica-
tion. IEEE Transact Robot 2008; 24: 105–117. DOI: 10.1109/
tro.2008.915446.
57. Salazar R, Fuentes V, and Abdelkefi A.Classification of bio-
logical and bioinspired aquatic systems: a review. Ocean Eng
2018; 148: 75–114. DOI: 10.1016/j.oceaneng.2017.11.012.
58. Jagnandan K and Sanford CP. Kinematics of ribbon-fin loco-
motion in the bowfin, amia calva. J Exper Zool Part A-Ecol
Integrat Phys 2013; 319: 569–583. DOI: 10.1002/jez.1819.
59. Oufiero CE, Kraskura K, Bennington R, et al. Individual
repeatability of locomotor kinematics and swimming perfor-
mance in a gymnotiform swimmer. Physiolog Biochem Zool
2021; 94: 22–34. DOI: 10.1086/712058.
60. Sitorus PE, Nazaruddin YY, Leksono E, et al. Design and
implementation of paired pectoral fins locomotion of labri-
form fish applied to a fish robot. J Bionic Eng 2009; 6: 37–45.
DOI: 10.1016/s1672-6529(08)60100-6.
61. Josie H, Utku C, Fabio G, et al. Soft manipulators and grip-
pers: a review. Front Robot AI 2016; 3: 69.
62. Hunter IW and Lafontaine S. A comparison of muscle with
artificial actuators. Technical Digest IEEE Solid-State Sensor
and Actuator Workshop (Cat No92TH0403-X) 1992:
178–185. Conference Paper. DOI: 10.1109/solsen.1992.
228297.
63. Bhandari B, Lee G-Y, and Ahn S-H. A review on IPMC
material as actuators and sensors: fabrications, characteristics
and applications. Int J Precis Eng Manuf 2012; 13: 141–163.
DOI: 10.1007/s12541-012-0020-8.
64. Li T, Li G, Liang Y, et al. Fast-moving soft electronic fish.
Sci Adv 2017; 3. DOI: 10.1126/sciadv.1602045.
65. O’Halloran A, O’Malley F, and McHugh P. A review on
dielectric elastomer actuators, technology, applications, and
Li et al. 17

challenges. J Appl Phys 2008; 104: 9. DOI: 10.1063/1.29
81642.
66. Katzschmann RK, Marchese AD, and Rus D. Hydraulic
autonomous soft robotic fish for 3D swimming. In: 14th
International symposium on experimental robotics (ISER)
Morocco, 15–18 June 2014, pp. 405–420. Cham: Springer
International Publishing Ag.
67. Huang XN, Michael F, Patterson ZJ, et al. Shape memory
materials for electrically-powered soft machines. J Mat Chem
B2020; 8: 4539–4551. Review. DOI: 10.1039/d0tb00392a.
68. Huang XN, Kumar K, Jawed MK, et al. Highly dynamic
shape memory alloy actuator for fast moving soft robots. Adv
Mater Technol 2019; 4: 9. Article. DOI: 10.1002/admt.
201800540.
69. Li J, He JM, Wang YW, et al. A biomimetic flexible fishtail
embedded with shape memory alloy wires. IEEE Access
2019; 7: 166906–166916. Article. DOI: 10.1109/access.
2019.2953546.
70. Coral W, Rossi C, Curet OM, et al. Design and assessment of
a flexible fish robot actuated by shape memory alloys. Bioin-
spir Biomim 2018; 13: 056009. 2018/07/04. DOI: 10.1088/
1748-3190/aad0ae.
71. Cho KJ, Hawkes E, Quinn C, et al. Design, fabrication and
analysis of a body-caudal fin propulsion system for a micro-
robotic fish. In: IEEE international conference on robotics
and automation, Pasadena, CA, 19–23 May 2008, vols 1–9,
pp. 706–711. New York: IEEE.
72. Zhang YH, He JH, and Low K. Design and motion testing of a
multiple SMA fin driven BIUV. J Hydrodyn 2019; 31:
124–136. Article. DOI: 10.1007/s42241-018-0148-9.
73. Yan Q, Wang L, Liu B, et al. A novel implementation
of a flexible robotic fin actuated by shape memory alloy.
J Bionic Eng 2012; 9: 156–165. DOI: 10.1016/s1672-6529
(11)60111-x.
74. Chen Z. A review on robotic fish enabled by ionic polymer-
metal composite artificial muscles. Robotics Biomim 2017; 4:
24. 2017/12/22. DOI: 10.1186/s40638-017-0081-3.
75. Ye XF, Su YD, Guo SX, et al. A centimeter-scale autono-
mous robotic fish actuated by IPMC actuator. In: IEEE inter-
national conference on robotics and biomimetics (ROBIO
2007), Sanya, Peoples R China, 15–18 December 2007, vols
1–5, pp. 262–267. New York: IEEE.
76. Shen Q, Wang TM, Liang JH, et al. Hydrodynamic perfor-
mance of a biomimetic robotic swimmer actuated by ionic
polymer-metal composite. Smart Mater Struct 2013; 22: 13.
Article. DOI: 10.1088/0964-1726/22/7/075035.
77. Aureli M, Kopman V, and Porfiri M. Free-locomotion of
underwater vehicles actuated by ionic polymer metal compo-
sites. IEEE/ASME Transact Mechatron 2010; 15: 603–614.
DOI: 10.1109/tmech.2009.2030887.
78. Zheng C, Shatara S, and Xiaobo T. Modeling of biomimetic
robotic fish propelled by an ionic polymer–metal composite
caudal fin. IEEE/ASME Transact Mechatron 2010; 15:
448–459. DOI: 10.1109/tmech.2009.2027812.
79. Yang T and Chen Z. Development of 2D maneuverable
robotic fish propelled by multiple ionic polymer-metal
composite artificial fins. IEEE International Conference on
Robotics and Biomimetics (ROBIO), 2015, pp. 255–260.
DOI: 10.1109/ROBIO.2015.7418776.
80. Zheng C, Um TI, and Bart-smith H. Bio-inspired robotic
manta ray powered by ionic polymer-metal composite artifi-
cial muscles. Int J Smart Nano Mat (UK) 2012; 3: 296–308.
DOI: 10.1080/19475411.2012.686458.
81. Hubbard JJ, Fleming M, Palmre V, et al. Monolithic IPMC
fins for propulsion and maneuvering in bioinspired under-
water robotics. IEEE J Oceanic Eng 2014; 39: 540–551. Arti-
cle. DOI: 10.1109/joe.2013.2259318.
82. Yi XF, Chakarvarthy A, and Chen Z. Cooperative collision
avoidance control of servo/IPMC driven robotic fish with
back-relaxation effect. IEEE Robot Autom Lett 2021; 6:
1816–1823. Article. DOI: 10.1109/lra.2021.3060717.
83. Chen Z and Tan XB. A control-oriented and physics-
based model for ionic polymer-metal composite actuators.
IEEE-ASME Transact Mechatonr 2008; 13: 519–529. Arti-
cle. DOI: 10.1109/tmech.2008.920021.
84. Shintake J, Cacucciolo V, Shea H, et al. Soft biomimetic fish
robot made of dielectric elastomer actuators. Soft Robot 2018;
5: 466–474. Article. DOI: 10.1089/soro.2017.0062.
85. Wu Y, Alici G, Spinks GM, et al. Fast trilayer polypyrrole
bending actuators for high speed applications. Synthetic
Metals 2006; 156: 1017–1022. DOI: 10.1016/j.synthmet.
2006.06.022.
86. McGovern ST, Abbot M, Emery R, et al. Evaluation of thrust
force generated for a robotic fish propelled with polypyrrole
actuators. Polym Int 2010; 59: 357–364. DOI: 10.1002/pi.
2777.
87. McGovern S, Alici G, Truong V-T, et al. Finding NEMO
(novel Electromaterial muscle oscillator): a polypyrrole pow-
ered robotic fish with real-time wireless speed and directional
control. Smart Mater Struct 2009; 18. DOI: 10.1088/0964-
1726/18/9/095009.
88. Brochu P and Pei QB. Advances in dielectric elastomers for
actuators and artificial muscles. Macromol Rapid Commun
2010; 31: 10–36. DOI: 10.1002/marc.200900425.
89. Borgen MG, Washington GN, and Kinzel GL. Design and
evolution of a piezoelectrically actuated miniature swimming
vehicle. IEEE/ASME Transact Mechatron 2003; 8: 66–76.
DOI: 10.1109/tmech.2003.809131.
90. Mossi KM, Selby GV, and Bryant RG. Thin-layer composite
unimorph ferroelectric driver and sensor properties. Mater
Lett 1998; 35: 39–49. DOI: 10.1016/s0167-577x(97)00214-0.
91. Heo S, Wiguna T, Park HC, et al. Effect of an artificial caudal
fin on the performance of a biomimetic fish robot propelled
by piezoelectric actuators. J Bionic Eng 2007; 4: 151–158.
DOI: 10.1016/s1672-6529(07)60027-4.
92. Nguyen QS, Heo S, Park HC, et al. Performance evaluation of
an improved fish robot actuated by piezoceramic actuators.
Smart Mater Struct 2010; 19. DOI: 10.1088/0964-1726/19/3/
035030.
93. Zhao QL, Liu SQ, Chen JH, et al. Fast-moving piezoelectric
micro-robotic fish with double caudal fins. Robot Auton Syst
2021; 140: 9. Article. DOI: 10.1016/j.robot.2021.103733.
18 International Journal of Advanced Robotic Systems

94. Hu D, Lou J, Chen T, et al. Micro thrust measurement experi-
ment and pressure field evolution of bionic robotic fish with
harmonic actuation of macro fiber composites. Mechan Syst
Signal Process 2021; 153. DOI: 10.1016/j.ymssp.2020.
107538.
95. Tan D, Wang Y-C, Kohtanen E, et al. Trout-like multifunc-
tional piezoelectric robotic fish and energy harvester. Bioin-
spirat Biomimet 2021; 16: 046024. DOI: 10.1088/1748-3190/
ac011e.
96. Govindarajan G and Sharma R. Experimental investigation
on a flapping beam with smart material actuation for under-
water application. Mechan Adv Mater Struct 2021; 28:
1020–1034. DOI: 10.1080/15376494.2019.1629047.
97. Cen L and Erturk A. Bio-inspired aquatic robotics by unteth-
ered piezohydroelastic actuation. Bioinspirat Biomimet 2013;
8: 13. Article. DOI: 10.1088/1748-3182/8/1/016006.
98. Marchese AD, Onal CD, and Rus D. Autonomous soft robotic
fish capableof escape maneuvers using fluidic elastomer actua-
tors. Soft Robot 2014; 1: 75–87. 2014/03/01. DOI: 10.1089/
soro.2013.0009.
99. Chen G, Yang X, Zhang X, et al. Water hydraulic soft actua-
tors for underwater autonomous robotic systems. Appl Ocean
Res 2021; 109. DOI: 10.1016/j.apor.2021.102551.
100. Takada Y, Koyama K, and Usami T. Position estimation of
small robotic fish based on camera information and Gyro
sensors. Robotics 2014; 3: 149–162. DOI: 10.3390/robotics
3020149.
101. Yu J, Sun F, Xu D, et al. Embedded vision-guided 3-D
tracking control for robotic fish. IEEE Transact Industr
Electr 2016; 63: 355–363. DOI: 10.1109/tie.2015.2466555.
102. Ichikizaki T and Yamamoto IIEEE. Development of robotic
fish with various swimming functions. In: 5th international
symposium on underwater technology/5th workshop on sci-
entific use of submarine cables and related technologies,
Tokyo, Japan, 17–20 April 2007, Vols 1 and 2, pp. 378–383.
103. Phamduy P, LeGrand R, and Porfiri M.Robotic fish: design
and characterization of an interactive iDevice-controlled
robotic fish for informal science education. IEEE Robot
Automat Magaz 2015; 22: 86–96. DOI: 10.1109/mra.2014.
2381367.
104. Chuanmeng N, Lige Z, Shusheng B, et al. Development and
depth control of a robotic fish mimicking cownose ray.
2012, p.814–818.
105. Yu J, Ding R, Yang Q, et al. Amphibious pattern design of a
robotic fish with wheel-propeller-fin mechanisms. J Field
Robot 2013; 30: 702–716. DOI: 10.1002/rob.21470.
106. Yan Q, Han Z, Zhang S-W, et al. Parametric research of
experiments on a carangiform robotic fish. J Bionic Eng
2008; 5: 95–101. DOI: 10.1016/s1672-6529(08)60012-8.
107. Yu J, Chen S, Wu Z, et al. On a miniature free-swimming
robotic fish with multiple sensors. Int J Adv Robot Syst
2017; 13: 62. DOI: 10.5772/62887.
108. Wang W, Gu D, and Xie G. Autonomous optimization of
swimming gait in a fish robot with multiple onboard sensors.
IEEE Transact Syst Man Cybernet Syst 2019; 49: 891–903.
DOI: 10.1109/tsmc.2017.2683524.
109. Yen W-K, Sierra DM, and Guo J.Controlling a robotic fish to
swim along a wall using hydrodynamic pressure feedback.
IEEE J Oceanic Eng 2018; 43: 369–380. DOI: 10.1109/joe.
2017.2785698.
110. Zhang L, Zhao W, Hu Y, et al. Development and depth
control of biomimetic robotic fish. 2007, p.3566–3571.
111. Ye X, Su Y, Guo S, et al. Design and realization of a remote
control centimeter-scale robotic fish. 2008 IEEE/ASME
international conference on advanced intelligent mechatro-
nics, Vols 1-3. 2008, pp.25–30.
112. Tan XB, Kim D, Usher N, et al. An autonomous robotic fish
for mobile sensing. In: IEEE/RSJ international conference
on intelligent robots and systems, Beijing, Peoples R China,
09–13 October 2006, vols 1–12, pp. 5424–5429.
113. Barbera G, Lijuan P, and Xinyan D. Attitude control for a
pectoral fin actuated bio-inspired robotic fish. In: IEEE
international conference on robotics and automation,
2011, pp.526–531.
114. Wen L, Wang T, Wu G, et al. Quantitative thrust efficiency
of a self-propulsive robotic fish: experimental method and
hydrodynamic investigation. IEEE/ASME Transact Mecha-
tron 2013; 18: 1027–1038. DOI: 10.1109/tmech.2012.
2194719.
115. Wright B, Vogt DM, Wood RJ, et al. Soft Sensors for Cur-
vature Estimation under Water in a Soft Robotic Fish.
Piscataway, NJ: IEEE, 2019, pp. 367–371.
116. Lin Y-H, Siddall R, Schwab F, et al. Modeling and control
of a soft robotic fish with integrated soft sensing. Adv Intel-
lig Syst 2021. DOI: 10.1002/aisy.202000244.
117. Jusufi A, Vogt DM, Wood RJ, et al. Undulatory swimming
performance and body stiffness modulation in a soft robotic
fish-inspired physical model. Soft Robot 2017; 4: 202–210.
2017/11/29. DOI: 10.1089/soro.2016.0053.
118. Liu B, Hao L, Deng J, et al. A remote operated robotic fish
with temperature sensor based on IPMC Actuator. In: 21st
Chinese control and decision conference, Guilin, Peoples R
China, 17–19 June 2009 2009, vols 1–6, pp .5730–5734.
119. Dijkgraaf S. The functioning and significance of the lateral-
line organs. Biol Rev Camb Philos Soc 1963; 38: 51–105.
1963/02/01. DOI: 10.1111/j.1469-185x.1963.tb00654.x.
120. Mogdans J and Bleckmann H. Coping with flow: behavior,
neurophysiology and modeling of the fish lateral line sys-
tem. Biol Cybern 2012; 106: 627–642. 2012/10/27. DOI: 10.
1007/s00422-012-0525-3.
121. Wang W, Zhang XX, Zhao JW, et al. Sensing the neighbor-
ing robot by the artificial lateral line of a bio-inspired
robotic fish. In: IEEE/RSJ international conference on intel-
ligent robots and systems (IROS), Hamburg, Germany, 28
September– 02 October 2015, pp. 1565–1570. New York:
IEEE.
122. Zheng XW, Xiong ML, Xie GM, et al. Data-driven model-
ing for superficial hydrodynamic pressure variations of
two swimming robotic fish with leader-follower formation.
In: IEEE international conference on systems, man
and cybernetics (SMC) Bari, Italy, 06–09 October 2019,
pp. 4331–4336. New York: IEEE.
Li et al. 19

123. Liu G, Wang A, Wang X, et al. A review of artificial lateral
line in sensor fabrication and bionic applications for robot
fish. Appl Bionics Biomech 2016; 2016: 4732703. 2017/01/
25. DOI: 10.1155/2016/4732703.
124. Wei X, Shen H, and Chen W. Review on the research of bio-
hydrodynamics. J Ship Mech 2020; 24: 962–970.
125. Yu J, Yuan J, Wu Z, et al. Data-driven dynamic modeling
for a swimming robotic fish. IEEE Transact Industr Electr
2016; 63: 5632–5640. DOI: 10.1109/tie.2016.2564338.
126. Liu JD and Hu HS. Biological inspiration: from carangiform
fish to multi-joint robotic fish. J Bionic Eng 2010; 7: 35–48.
DOI: 10.1016/s1672-6529(09)60184-0.
127. Liu J and Hu H. Mimicry of sharp turning behaviors in a
robotic fish. Proceedings of the 2005 IEEE International Con-
ference on Robotics and Automation, 2005, pp. 3318–3323.
DOI: 10.1109/ROBOT.2005.1570622.
128. Ijspeert AJ. Central pattern generators for locomotion con-
trol in animals and robots: a review. Neural Netw 2008; 21:
642–653. 2008/06/17. DOI: 10.1016/j.neunet.2008.03.014.
129. Cheng JG, Stein RB, Jovanovic K, et al. Identification, loca-
lization, and modulation of neural networks for walking in
the mudpuppy (Necturus maculatus) spinal cord. J Neurosci
1998; 18: 4295–4304.
130. Shun-ichi A. Characteristics of random nets of analog
neuron-like elements. IEEE Trans Syst Man Cybern (USA)
1972; SMC-2: 643–657. DOI: 10.1109/tsmc.1972.4309193.
131. Ijspeert AJ, Crespi A, Ryczko D, et al. From swimming to
walking with a salamander robot driven by a spinal cord
model. Science 2007; 315: 1416–1420. Article. DOI: 10.
1126/science.1138353.
132. Yu J, Wu Z, Wang M, et al. CPG network optimization for a
biomimetic robotic fish via PSO. IEEE Transact Neural
Networks Learn Syst 2016; 27: 1962–1968. DOI: 10.1109/
tnnls.2015.2459913.
133. Zhou C and Low KH. On-line optimization of biomimetic
undulatory swimming by an experiment-based approach.
J Bionic Eng 2014; 11: 213–225. DOI: 10.1016/s1672-
6529(14)60042 -1.
134. Hu YH, Liang JH, and Wang TM. Parameter synthesis of
coupled nonlinear oscillators for CPG-based robotic
locomotion. IEEE Transact Industr Electron 2014; 61:
6183–6191. DOI: 10.1109/tie.2014.2308150.
135. Ren Q, Xu J, Fan L, et al. A GIM-based biomimetic learning
approach for motion generation of a multi-joint robotic fish.
J Bionic Eng 2013; 10: 423–433. DOI: 10.1016/s1672-
6529(13)60237 -1.
136. Bal C, Koca GO, Korkmaz D, et al. CPG-based autonomous
swimming control for multi-tasks of a biomimetic robotic
fish. Ocean Eng 2019; 189. DOI: 10.1016/j.oceaneng.2019.
106334.
137. Yan Z, Yang H, Zhang W, et al. Research on motion mode
switching method based on CPG network reconstruction.
IEEE Access 2020; 8: 224871–224883. DOI: 10.1109/
access.2020.3045227.
138. Videler JJ. Body surface adaptations to boundary-layer
dynamics. Symposia Soci Exp Biol 1995; 49: 1–20.
139. Dou Z, Wang J, and Chen D. Bionic research on fish scales
for drag reduction. J Bionic Eng 2012; 9: 457–464. DOI: 10.
1016/s1672-6529(11)60140-6.
140. Zhang X, Wang W, Chen S, et al. Study on perception of
neighbor bionic fish based on artificial lateral line system.
Measurem Control Technol 2016; 35: 33–37.
141. Zheng XW, Wang C, Fan RF, et al. Artificial lateral line
based local sensing between two adjacent robotic fish. Bioin-
spirat Biomimet 2018; 13. DOI: 10.1088/1748-3190/aa8f2e.
142. Pollard B and Tallapragada P. Learning hydrodynamic sig-
natures through proprioceptive sensing by bioinspired
swimmers. Bioinspirat Biomimet 2021; 16. DOI: 10.1088/
1748-3190/abd044.
143. Li L, Liu D, Deng J, et al. Fish can save energy via proprio-
ceptive sensing. Bioinspirat Biomimet 2021; 16. DOI: 10.
1088/1748-3190/ac165e.
144. Carryon GN and Tangorra JL. The effect of sensory feed-
back topology on the entrainment of a neural oscillator with
a compliant foil for swimming systems. Bioinspirat Biomi-
met 2020; 15. DOI: 10.1088/1748-3190/ab76a0.
145. Li XF, Ren QY, and Xu JX. Precise speed tracking control
of a robotic fish via iterative learning control. IEEE Trans-
act Industr Electron 2016; 63: 2221–2228. DOI: 10.1109/
tie.2015.2499719.
20 International Journal of Advanced Robotic Systems