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This paper proposes a miniature biomimetic robotic fish based on a single joint, with a compact structure, high manoeuvrability and multiple sensors, and a model of freely swimming situation is built based on Lagrangian function. The robotic fish mimics the motion of Thunniform fish, and methods of propelling, turning and C-sharp turning are given. To model the motion of robotic fish, the fluid force acting on the robotic fish is divided into three parts. By solving Lagrange';s equation of the s
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International Journal of Robotics and Automation, Vol. 25, No. 3, 2010
THE DESIGN, MODELLING AND
IMPLEMENTATION OF A MINIATURE
BIOMIMETIC ROBOTIC FISH
C. Zhou,
∗
Z. Cao,
∗
S. Wang,
∗
and M. Tan
∗
Abstract
This paper proposes a miniature biomimetic robotic fish based on
a single joint with a compact structure, high manoeuvrability and
multiple sensors, and a model of freely swimming situation is built
based on Lagrangian function. The robotic fish mimics the motion
of Thunniform fish, and methods of propelling, turning and C-sharp
turning are given. To model the motion of robotic fish, the fluid
force acting on the robotic fish is divided into three parts. By
solving Lagrange’s equation of the second kind, the movement and
motion parameters of robotic fish are obtained. Simulated results
of motions are given, and experiments are carried out to verify the
model.
Key Words
Miniature robotic fish, biomimetic motion, kinematic modelling,
parameter optimization
1. Introduction
There are more and more productive underwater activi-
ties and research works, which make the existing under-
water equipments cannot satisfy changing requests, and
autonomous underwater vehicle (AUV) has received much
attentions. Attracted by fish with high efficiency, high
manoeuvrability and low noise, roboticists explore fish-like
underwater robots or robotic fish to develop small size,
efficient, manoeuvrable and low noise AUVs [1]. The
development of miniature robotic fish offers great advan-
tages for specialist underwater requirements associated
with pipelines and gaps, such as exploration, mining, ecol-
ogy etc. Additionally, miniature robotic fish can poten-
tially be manufactured cheap enough to be mass-produced,
which may enhance the quality of the solution by coop-
eration among them. A biomimetic robotic fish can be
defined as an aquatic vehicle propelled by bionic undu-
latory fins, usually with the undulatory/oscillatory body
∗
Laboratory of Complex Systems and Intelligence Science, In-
stitute of Automation, Chinese Academy of Sciences, No. 95,
Zhongguancun East Road, Beijing 100190, China; e-mail:
{zhouchao, zqcao, swang, tan}@compsys.ia.ac.cn
Recommended by Dr. Paolo Remagnino
(10.2316/Journal.206.2010.3.206-3316)
and fins motions. Investigations of biomimetic robotic fish
have provided significant insights into both theory and ap-
plication in recent years [2, 3]. These advantages are of
great benefit to applications in marine and military fields.
Many theories are proposed to explore the secrets of fish
swimming mechanisms and summarize driving modes of
fish motions. Based on these theories, many prototypes
of biomimetic robotic fish have been developed. Some
works are done on the motion model [4–6] and control of
robotic fish [7, 8]. McIsaac and Ostrowski [4] and Cort´es
et al. [5] gave a Lagrangian model, reduced by Lie group
symmetries, for a symmetrical structure robot eel. Boyer
et al. [6] present the dynamic modelling of a continu-
ous 3-D swimming eel-like robot. In previous project in
our lab, a series of multi-link robotic fish prototype are
finished, and the control, information procession, co-
operation and 3D locomotion of them are studied
[9, 10].
In this paper, the design of a miniature biomimetic
robotic fish is given based on single joint undulating.
The prototype is 15-cm long and integrates the control
system, wireless communication module, battery power,
servo, infrared and light intensity sensors. The robotic
fish may execute tasks independently and autonomously
by the control law. To deal with the model problem
of our fish, a model is given in this paper for freely
swimming without the assumption of non-oscillatory fish
head. The model is based on Lagrangian function and
a simplified hydrodynamic model, the two of which are
connected by the Lagrange’s equation of the second kind.
The kinematics–dynamics model is got in the form of a set
of partial differential equations.
By considering the coupling of the kinematic law in
continuous motions and the force acted on robotic fish,
both of which cannot be calculated respectively, the La-
grangian function of the freely swimming robotic fish is
built. In this model, the robotic fish is simplified to jointed
plates. The kinematic model of this robotic fish is given to
discuss the propulsion, which is based on the Lagrange’s
equation and the hydrodynamic force. Then, the move-
ment is calculated by solving the Lagrange’s equation of
the second kind. Based on this model, the kinematic pa-
rameters are calculated, and the amplitude and frequency
210
of the tail oscillating are optimized based on the power
of the motor.
The rest of the paper is organized as follows. The
structure design and the biomimetic motion of the robotic
fish are introduced in Section 2. Section 3 approaches the
robotic fish’s dynamic model and the fluid force model. Re-
sults of simulations and experiments are given in Section 4,
and Section 5 concludes the paper.
2. The Design of the Robotic Fish and Motion Con-
trol
2.1 The Structure of the Robotic Fish
Fish swimming motion of BCF (body/caudal fin propul-
sion) modes can be divided into five different modes ac-
cording to the wavelength and the amplitude envelope of
the propulsive wave underlying the fish’s behaviour. They
are
Anguilliform mode, Subcarangiform mode, Carangi-
form mode, Thunniform mode and Ostraciiform mode
[11]. Among them, Thunniform mode is one of the
most efficient, where thrust is generated with a lift-based
method, allowing high cruising speeds to be maintained for
long periods, and it is one of the popular bionic targets.
Significant lateral movements occur only at the caudal fin.
In addition, the reduction of the length of the undulating
part simplifies the structure, and reduces the volume on
the whole. In this paper, a novel Thunniform-mode-based
miniature robotic fish is designed (Fig. 1). A servo motor
is adopted to drive a lunate caudal fin as the propeller of
the robotic fish, according to fish outline and its motion
characteristics. The servo is agile and controllable with-
out additional driver, and more energy is saved than the
driving units which adopt the new materials such as SMA
(shape memory alloys).
Figure 1. The schematic structure of the robotic fish.
All assembly units are highly cost-effective ones be-
cause of the volume restriction. The forebody is fish-
shaped, thin and hard plastic with the servo fixed on it.
The controller integrates the functions of information ac-
quisition and processing, communication, control and mo-
tion decision. The tail is covered by thin flexible rubber
film as waterproofer, which has little affection on the un-
dulating. The wireless signal is sent by an antenna out
of the water. Li-Polymer Batteries are chosen because of
the high energy density. In addition, infrared sensors are
selected, instead of the sonar sensors to minimize volume.
Photosensitive sensors are mounted on the robot for de-
tecting the light source. The average density of the robotic
fish except the buoyage is made a little higher than water.
The robotic fish will float on water with the buoyage, so
that all the body is under the water, which is favourable
to the stable propelling.
2.2 The Bionic Motion
Thunniform mode motion involves the undulation of the
entire body, whose large amplitude undulation is mainly
confined to the last 1/3 part of the body. A Thunniform
propulsive model is given to describe the motion in the
frame as shown in Fig. 2. It is a polar coordinate system
with the pole O at the joint and the polar axis pointing
to the tail’s initial direction. The other one XO
1
Y is the
world rectangular coordinate system (WRCS):
Figure 2. Coordinates of the robotic fish.
Equation (1) provides a method to design the robotic
fish: choose parameters
Amp and f to determine the
proper body wave and then develop a mechanical structure
to fit the curve, so that the fish’s locomotion may be
emulated. Discretize (1), and we have (2):
A
body
(t)=Amp · sin(2πft) (1)
where A
body
is the real-time angle of the tail, Amp is the
undulation amplitude and f is the frequency of the wave:
A
body
(i)=Amp · sin(2πi/M) (2)
where i is the variable of spline curve sequence, M is the
body-wave resolution that represents the discrete degree of
the overall travelling wave.
The turn of the fish is implemented by changing the
axis of the body undulation. Based on it, the direction
of the robotic fish may be controlled. A certain angle is
superposed on the caudal fin. It is necessary to ensure that
the undulating rule marches (2) when turning. Rewriting
(2), we have:
A
body
(i)=Amp · sin(2πi/M)+A
turn
(3)
where A
turn
is the deflection angle of the caudal fin. This
turning method is used in continuing and stable turning
movement.
There is another fish motion called C-sharp turning,
in which the fish bend to the shape of the letter “C”, and
211
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