3D Locomotion Biomimetic Robot Fish with Haptic Feedback
by
Zhenying Guan (B. Eng)
Submitted in fulfilment of the requirements for the degree of
Doctor of Philosophy
Deakin University
July, 2012
1
Acknowledgments The work in this thesis is a culmination of my efforts strongly
backed by the support of many people to whom I am deeply grateful.
I owe a great deal to my supervisor, Prof. Saeid Nahavandi for
guiding and training me through my entire tenure as a student at the
Centre for Intelligent Systems Research, Deakin University. I also
appreciate my associate supervisor, Weimin Gao, who gave me
elaborative direction on my robot fish research project, especially on
the Computational Fluid Dynamics (CFD) simulation of the robot fish.
I deeply admire my advisors’ patience in putting up with my research
inexperience and helping me understand the technical concepts
involved in my work.
I would like to thank the students and staff at the Institute for
Technology Research and Innovation, Deakin University, for providing
me with all the technical, administrative and emotional support that I
asked for.
I am deeply grateful to my husband and parents for providing me
with the moral support to complete postgraduate studies. Without their
encouragement and love I would not have been able to finish my PhD
study with so many achievements.
I would like to thank everyone who helped to make this possible.
It has been an incredible journey of self-discovery, and I love every
2
last one of you.
3
Abstract Underwater exploration is becoming the focus of many scientific
research projects. The superior swimming ability of fish, and the great
tactile ability of human beings bring an idea of developing haptic robot
fish systems, which would help expand human competence to discover
the mystery of the underwater world. The primary goal of this thesis is
to develop a biomimetic robot fish and to build a novel haptic robot
fish system based on the kinematic modeling and CFD hydrodynamic
analysis of the robot fish.
The biomimetic robot fish was built based on the prototype of a
carangiform fish, which has a good balance of velocity, acceleration
and controllable properties. This robot fish cannot only get abundant
information, especially visually, but also transfer the massive amount
of information to the upper console by an information relay system
floating on water. An innovative biomimetic motion library was also
established to help users make the control scheme more efficient.
A haptic robot fish system was innovated with a new interactive
force feedback, which comes from two kinds of simulation results, the
kinematic modeling (using Lagrangian method) and CFD
hydrodynamic analysis (simulated by Fluent® 6.3.26). It supports
users in understanding the hydrodynamic properties around the robot
fish more deeply than in other common visualization systems based
4
only on graphical visualization of hydrodynamic analysis. One can feel
the force imposed on the robot fish in water and also can observe the
field distribution maps, such as velocity and pressure on need for
hydrodynamic analysis.
The most important contribution of this thesis is the successful
three-dimensional (3D) computational fluid dynamic simulation of the
biomimetic robot fish by Fluent® 6.3.26, where User-Defined Function
(UDF) was used to define the movement of the robot fish; Dynamic
Mesh was used to mimic the fish swimming in water. Hydrodynamic
analysis has been done to get comparative data about the
hydrodynamic properties of those guidelines and to improve the design,
remote control and flexibility of the underwater robot fish.
5
Vita Publications arising from this thesis include:
Z. Guan, C. Zhou, Z. Cao, N. Gu, M. Tan and S. Nahavandi, “A 3-D
locomotion biomimetic robot fish with information relay”,
Lecture Notes in Computer Science, Springer Berlin / Heidelberg,
Vol. 5314/2008, pp 1135-1144
Z. Guan, W. Gao, N. Gu and S. Nahavandi, "3D Hydrodynamic
Analysis of Biomimetic Robot Fish", 11th International
Conference on Control, Automation, Robotics and Vision
(ICARCV), Singapore, Dec. 2010, pp 793 – 798
"3D Dynamic Computational Fluid Dynamics (CFD) modeling and
Hydrodynamic Analysis of Biomimetic Robot Fish" is going for
the journal of Robotica. This paper will probe deeply into the
hydrodynamic properties of the robot fish, and the mathematic
method of describing the robot fish tail movements will be
improved.
"A Novel Robot Fish System with Haptic Interaction" is going for
Journal of Field Robotics. This paper will demonstrate the novel
haptic robot fish system design. Force sensors are going to be
applied to measure force in real-time; this will help the robot fish
perceive the fluent force around it and make instantaneous
swimming strategies to avoid vortexes or to save energy by
6
complying with currents liking similar to real fish movements.
The haptic interactions will be set up according to these force
measurements as well. For example, the users can feel the force
on the robot fish and send control commands to the robot fish via
a PHANTOM Omni Haptic Device.
7
Contents Acknowledgments.......................................................................................................... 1
Abstract .......................................................................................................................... 3
Vita ................................................................................................................................. 5
Contents ......................................................................................................................... 7
Figure List .................................................................................................................... 10
Table List ..................................................................................................................... 12
Abbreviations: .............................................................................................................. 13
1. Introduction ............................................................................................................. 15
1.1. Motivation ................................................................................................... 15
1.2. Goal and Methods ....................................................................................... 17
1.3. Outline of the Thesis ................................................................................... 19
1.4. Contributions ............................................................................................... 20
2. Literature Review .................................................................................................... 23
2.1. Background to Underwater Robot and Haptic Development ...................... 23
2.1.1. Underwater Robot Development ......................................................... 23 2.1.1.1. Background of Autonomous Underwater Vehicle ................... 24
2.1.1.2. Development of Remotely Operated Underwater Vehicles ..... 26
2.1.1.3. Hybrid Remotely Operated Underwater Vehicle ..................... 29
2.1.1.4. Shortcomings of Remotely Operated Underwater Vehicles and Autonomous Underwater Vehicles........................................... 30
2.1.2. Biomimetic Robot Fish Design ........................................................... 31 2.1.3. Haptics and Application ...................................................................... 35
2.2. Fish Propulsion Theory ............................................................................... 42
2.3. Research into Underwater Biomimetic Robots ........................................... 47
2.4. Kinematics and Locomotion Control of robot fishes .................................. 49
2.5. Hydrodynamic Analysis of Underwater Robot ........................................... 55
2.6. Haptics for Underwater Applications .......................................................... 57
2.7. Summary ..................................................................................................... 59
3. Design of a Biomimetic Robot Fish ........................................................................ 61
3.1. Problem Formulation ................................................................................... 61
3.2. The Biomimetic Robot Fish ........................................................................ 62
3.3. Mechanical Structure ................................................................................... 65
8
3.3.1. Support Frame ..................................................................................... 65 3.3.2. Actuation Unit ..................................................................................... 69 3.3.3. Communication Unit ........................................................................... 71 3.3.4. Control and Sensing Units and Accessories ........................................ 71
3.4. Control system ............................................................................................. 73
3.5. Biomimetic motion library .......................................................................... 74
3.5.1. Realisation of Propulsion..................................................................... 76 3.5.2. Swimming Direction Control .............................................................. 77 3.5.3. Diving Control ..................................................................................... 79
3.6. Prototype of the Robot Fish ......................................................................... 80
3.7. Conclusions ................................................................................................. 81
4. Kinematic Modeling of Biomimetic Underwater Robot Locomotion .................... 82
4.1. Introduction ................................................................................................. 82
4.2. Problem Formulation ................................................................................... 83
4.3. Outline of the Lagrangian Method .............................................................. 84
4.4. Kinematic Modeling of the Robot fish ........................................................ 87
4.4.1. Geometry Simplification of the Robot Fish ........................................ 87 4.4.2. The Lagrangean Equation of the Robot Fish ....................................... 90
4.5. Fluid Modeling the Robot Fish ................................................................... 93
4.6. Kinematic Modeling Results ....................................................................... 95
4.7. Conclusion ................................................................................................... 97
5. Hydrodynamic Analysis of the Biomimetic Robot Fish & Application on the Haptic Robot Fish System ....................................................................................... 99
5.1. Introduction ................................................................................................. 99
5.2. Problem formulation .................................................................................. 100
5.3. 3D Hydrodynamic Model .......................................................................... 100
5.3.1. Biomimetic Robot Fish and Pool Geometries ................................... 100 5.3.2. Mesh Scheme ..................................................................................... 101
5.3.2.1. Requirements and Conditions of Mesh Scheme ..................... 101
5.3.2.2. Logical Division of Fluid Domain ......................................... 102
5.3.2.3. Mesh Scheme Specific Implementation ................................. 103
5.3.3. Mathematic Description of the Robot Fish Locomotion ................... 104 5.3.3.1. Conditions of 3D Mathematic Description............................. 105
5.3.3.2. Robot Fish Tail Waving Description ...................................... 107
5.3.3.3. Implement of the Robot Fish Tail Movement with Fluent® ... 108
5.4. Hydrodynamic Analysis ............................................................................ 110
5.4.1. Design Properties of the Robot Fish .................................................. 110
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5.4.2. Pressure Distribution around the Swimming Robot Fish .................. 113 5.4.3. Velocity Distribution around the Swimming Robot Fish .................. 116 5.4.4. Forces of the Swimming Robot Fish ................................................. 118
5.5. Haptic Application on the Robot Fish ....................................................... 119
5.5.1. Issues to Be Solved ............................................................................ 120 5.5.2. Haptic Robot Fish System Framework .............................................. 121 5.5.3. 3D Virtual Display Design ................................................................ 124 5.5.4. Haptic Robot Fish System Force Feedback Method ......................... 125
5.5.4.1. Preset Database Based on Computational Fluid Dynamics (CFD) Simulation Results .................................................................. 126
5.5.4.2. Possibility of Real-time Calculation Based on Kinematic Modeling ................................................................................ 126
5.5.4.3. Further Haptic Robot Fish System Design ............................. 127
5.6. Underwater Experiments ........................................................................... 127
5.7. Conclusion ................................................................................................. 129
6. Analysis and Discussion on Kinematic Modeling and Computational Fluid Dynamics (CFD) Hydrodynamic Simulation ........................................................ 131
6.1. Introduction ............................................................................................... 131
6.2. Distinguishing Features of Kinematic Modeling ...................................... 131
6.3. Distinguishing Feature of Computational Fluid Dynamics (CFD) Analysis ..................................................................................................... 132
6.4. Comparison between Kinematic Modeling and Computational Fluid Dynamics (CFD) Hydrodynamic Analysis ............................................... 133
6.5. Conclusion ................................................................................................. 136
7. Conclusions and Future Works ............................................................................. 138
7.1. Conclusions ............................................................................................... 138
7.2. Future Works ............................................................................................. 140
References .................................................................................................................. 143
Appendix (published papers) ..................................................................................... 162
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Figure List Chapter 2 Figure 2:1: First Torpedo, 1866 [3] ............................................................................. 24 Figure 2:2: Cutlet, Rov, 1950s [13] ............................................................................. 27 Figure 2:3: Nereus Can Switch Between Free-Swimming And Tethered
Configurations, 2007 [15] ............................................................................... 30 Figure 2:4: Robotuna, Mit [21] Figure 2:5: Robopike, Mit [22] .................... 32 Figure 2:6: Northeastern University’s Undulatory Underwater Robot [26] ................ 34 Figure 2:7: Underwater Robot Experiment Platform, The Harbin Institute Of
Technology [40] ................................................................................................. 34 Figure 2:8: Biomimetic Dolphin, Peking University [41] ........................................... 34 Figure 2:9: Two Robot Fish Playing Ball, Institute Of Automation Chinese Academy
Of Sciences [42] ................................................................................................. 34 Figure 2:10: Professor Massimo Bergamasco Of The Scuola Superiore Di Studi
Universitari In Pisa, Italy, Demonstrating The Results Of His Early Exoskeletal System, Funded By The European Commission As Part Of An Esprit Ii Project Known As Glad-In-Art (Glove-Like Advanced Devices In Artificial Reality) [45] ..................................................................................................................... 39
Figure 2:11: The Teletact Ii Pneumatic Tactile Feedback Glove Developed By The Uk’s National Advanced Robotics Research Centre And Airmuscle Limited, Showing An Early Palmar Feedback Concept [45] ........................................... 40
Figure 2:12: The Surgical Procedures Definition And Task Analyses Conducted By The Ent Department Of Manchester’s Royal Infirmary [45] ............................. 41
Figure 2:13: Four Fish Swimming Propulsive Models [54] ........................................ 44 Figure 2:14: A: Distributed Autonomous Swimming Robot (3 Agents); .................... 52 Figure 2:15: Princeton 3d Multi-Vehicle Experimental Test-Bed (Left); ................... 53 Figure 2:16: Photograph And Schematic Of Side View Of Fish Design (Left); ......... 54 Chapter 3 Figure 3:1: Biomimetic Robot Fish System................................................................. 64 Figure 3:2: The Head Of The Biomimetic Robot Fish ................................................ 66 Figure 3:3: Internal Connection ................................................................................... 67 Figure 3:4: External Connection. The Left One Is Used For The Connection Of The
First 3 Links; The Right One Is Used For Connecting The Last Link And Caudal Fin. ......................................................................................................... 68
Figure 3:5: Support Board ........................................................................................... 68 Figure 3:6: Caudal Vertebra ......................................................................................... 69 Figure 3:7: Sanwa Servo Rs-995 [112] ........................................................................ 70 Figure 3:8: The Block Diagram Of The Control System ............................................. 73 Figure 3:9: Links Fitting Fish’s Body-Wave ............................................................... 76 Figure 3:10: The Corrected Fish Body Wave Curve ................................................... 78 Figure 3:11: The Moment Analysis Of Barycenter-Adjustor ...................................... 79 Figure 3:12: The Functional Prototype Of The Biomimetic Robot Fish ..................... 80
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Chapter 4 Figure 4:1: Robot Fish Joint-Link Structure ................................................................ 88 Figure 4:2: Simplified Coordinates Of The Robot Rish And Its Parameters Definition
............................................................................................................................ 89 Figure 4:3: The Five Links Robot Fish And Some Parameters Definition .................. 90 Figure 4:4: Simulation Results Of Forces Acting On The Robot Fish In Forward
Motion ................................................................................................................ 97 Chapter 5 Figure 5:1: Mesh Of The Biomimetic Robot Fish ..................................................... 104 Figure 5:2: Mesh Scheme For The Region Close To Robot Fish .............................. 104 Figure 5:3: The Outline Of The Robot Fish ............................................................... 105 Figure 5:4: Parameters Of The Robot Fish Tail (Unit: Mm) ..................................... 106 Figure 5:5: Node Movement ...................................................................................... 107 Figure 5:6: Meshes On Robot Fish Body .................................................................. 108 Figure 5:7: M-View ................................................................................................... 110 Figure 5:8: Velocity Vectors On The Robot Fish Surface ......................................... 111 Figure 5:9: The Pathlines Of The Robot Fish ............................................................ 112 Figure 5:10: Hydrodynamic Analysis – Pressure ...................................................... 112 Figure 5:11: Pressure Contours Of The M-View At 4 Locomotion Times (N×M–2) (A)
Approaching The Left Maximal Rotation Position (T = 0.1 S); (B) Intermedial Position During Oscillating Motion (T = 0.25 S); (C) Going On Intermedial Position During Oscillating Motion (T = 0.4 S); (D) Approaching Right Maximal Rotation Position (T =0.55 S). (It Is Supposed That A Robot Fish Locomotion Period Begin From The Position T=0 According The Equation 1) .......................................................................................................................... 113
Figure 5:12: Velocity Distribution ............................................................................. 117 Figure 5:13: Forces In X And Z Directions ............................................................... 119 Figure 5:14: The Framework Of Haptic Robot Fish System ..................................... 122 Figure 5:15: Virtual Display And Haptic Operating .................................................. 123 Figure 5:16: Command In Virtual Interface .............................................................. 124 Figure 5:17: The Image Sequence Of The Robot Fish Turning ................................ 128
12
Table List Chapter 5 Table 5.1: Parameters For Dynamic Mesh ................................................................ 109 Table 5.2: Oscillating Frequency (Hz) Versus Speed (M/S) Of Straight Swimming 128
Chapter 6 Table 6.1: Comparison Between The Kinematic Modeling And Cfd Analysis ........ 134 Table 6.2: Comparison In Special Properties Between The Kinematic Modeling And
Cfd Analysis ..................................................................................................... 135
13
Abbreviations:
3D: three-dimensional
ABE: Autonomous Benthic Explorer
AUSS: Advanced Unmanned Search System
AUV: Autonomous Underwater Vehicle
BCF: Body and/or Caudal Fin
CCD: charge-coupled device
CFD: Computational Fluid Dynamics
CMOS: Complementary Metal Oxide Semiconductor
CURV: Cable-Controlled Underwater Recovery Vehicle
DPIV: Digital Particle Image Velocimetry
EPFL: The Swiss Federal Institute of Technology Lausanne
FRP: Fiberglass-Reinforced Plastics
GLAD-IN-ART: Glove-like Advanced Devices in Artificial
Reality
IERAPSI: Integrated Environment for Rehearsal and Planning of
Surgical Interventions
MCU: Micro Control Unit
MIPS: Million Instructions Per Second
MIT: The Massachusetts Institute of Technology
MPF: Median and/or Paired Fin
MSMs: Master-Slave Manipulators
14
NMRI: National Maritime Research Institute
NSF: National Science Foundation
REMUS: Remote Environmental Measuring UnitS
POD: Proper Orthogonal Decomposition
RISC: Reduced Instruction Set Computing
ROV: Remotely Operated Underwater Vehicle
SPURV: Self Propelled Underwater Research Vehicles
UDF: User-Defined Function (in software Fluent®)
WHOI: Woods Hole Oceanographic Institution
WRCS: the world rectangular coordinate system
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1. Introduction
1.1. Motivation
Water covers 71% surface of the Earth, totaling 1,400M cubic
kilometers in volume[1]. Biotic and mineral resources in oceans and on
the bottom of seas are so abundant that the scientists are deeply
attracted to this area. There has been a growing interest in exploring
underwater objects in areas such as oceanographical observation,
underwater archaeological exploration, leak detection in pipelines, the
search for mines as well as toxic wastes, for environmental issues,
scientific study, commercial exploitation of the ocean and security
reasons. It is important to engage in this research area and establish key
enabling technologies to protect and exploit underwater resources more
efficiently. The need for the use of underwater robotic systems has
become more apparent. As a matter of fact, underwater robotics
represents a fast growing research area and there are promising
industry opportunities that will benefit from the developments of
advanced technologies in various subsystems and explorations of the
potential application areas such as computer technology,
microelectronic techniques, network techniques, new materials, sensors
and algorithms. Tremendous progress in robotics technology has
16
unleashed new opportunities for developing underwater robots to
overcome the challenging scientific and engineering problems caused
by the unstructured and hazardous underwater environment. From the
Autonomous Underwater Vehicle (AUV) to the Remotely Operated
underwater Vehicle (ROV), and even hybrid ROVs, many kinds of
underwater robots have come into the world. But in comparison with
real fish, they are so awkward that they cannot reach and handle
complex underwater circumstances.
In nature, the great and secret biological world gives scientists
some inspirations. Biomimetic robots are the grand products of this
development; their abilities are copied from the Earth's greatest
examples of success, living organisms. They tend to function better in
the unpredictable real world than in the controlled artifice of a
laboratory. Researchers also introduce biomimetics into the design of
underwater vehicles such as biomimetic robot fishes. These have
significant advantages, for example, their silence in moving, high
energy efficiency, and great maneuverability when compared to
conventional propeller-oriented propulsive underwater mechanisms.
Biomimetic robot fish has been given a certain of properties
currently, such as 3D controllable free swimming, the automatic
avoidance of obstacles, the ability to obtain visual information,
communicate with an upper sole and network with other robot fish.
17
However, to imitate all genuine fish behaviors with robotized systems
is a huge challenge, especially being able to design a kind of robot fish
with a haptic function that realizes fluent force perception and makes
real-time swimming strategies to avoid vortexes or save energy by
complying with currents. Although considerable progress has been
achieved by many researchers in both biomimetic robot fish and
haptics, the joining of both of these technologies in underwater
exploration still remains due to the impenetrable nature of the
underwater environment. Underwater robot fish with touch sensation
will bring an innovative expansion in underwater explorations, for
example, remote texture analysis and sample collection especially in
muddy water, which are hardly realized by other technologies except
haptics. This thesis would join haptics in underwater robot fish to bring
an innovation in this field.
1.2. Goal and Methods
Underwater exploration is becoming the focus of many scientific
investigations. The superior swimming ability of natural fish and the
great tactile ability of human being bring an idea of developing a kind
of haptic robot fish system, which would help expand human
competence in uncovering underwater world mysteries. Both of the
technologies of biomimetic robot fish and haptics have arisen in past
18
twenty years. Researchers started to develop haptic interaction with
biomimetic robot fish, an emerging field of investigation. The primary
goal of this thesis is to develop a biomimetic robot fish, from which a
novel haptic biomimetic robot fish system will be built up.
The biomimetic robot fish was built based on the prototype of a
carangiform fish, which has a good balance of velocity, acceleration
and controllable properties. It has a barycenter-adjustor for
descending/ascending motion and multiple sensors for obtaining
environmental information from around the robot fish. It may
communicate with the outside by an information relay system on water.
Combining the movements of the tail, and the structure for descending
and ascending, the robot fish can simulate the 3D controllable free
swimming of real fish in water. This robot fish cannot only get
abundant information, especially visually, but also transfer the massive
amount of information to the upper console via wire/wireless
communication. An innovative biomimetic motion library was also
established to help users make the control scheme more efficient.
In order to make haptic biomimetic robot fish, force feedback is
quite important and currently comes from two kinds of simulation
results, the kinematic modeling (using Lagrangian method) and CFD
hydrodynamic analysis (simulated by Fluent® 6.3.26). The former is
suitable for real-time force feedback calculation and produces a good
19
solution for online mechanical analysis. The latter studies the
hydrodynamic properties of the robot fish which can meet the detailed
information requirements of operators. The added tactile sensation
function makes it possible for an operator to have interaction with the
fish and for robot fish to have the ability to feel currents, an innovation
in the biomimetic robot fish field.
1.3. Outline of the Thesis
The thesis is organised into 7 chapters:
Chapter 1 is a brief introduction to the thesis project, which will
reveal the importance of setting the haptic biomimetic robot fish
system.
Chapter 2 reviews the research in underwater robotics, biomimetic
robot fish and haptics development which helps indentify the ideas in
the growth of the relative fields.
Chapter 3 introduces the biomimetic robot fish mechanics, the
hardware and software design in detail which is the basis of the haptic
biomimetic robot fish system.
Chapter 4 presents the kinematic modeling of the robot fish
locomotion and the simulation results, which is a form of simplified
modeling and can be used online to provide force feedback for the
haptic biomimetic robot fish system.
20
Chapter 5 elaborates the 3D hydrodynamic analysis of the robot
fish in CFD and the modeling consequences; and describes the haptic
application on the robot fish. This is the essential part of the thesis.
Chapter 6 compares the advantages and disadvantages of the
kinematic modeling & CFD hydrodynamic analysis which will help
readers choose the right simulation method to support their studies.
Chapter 7 contains the conclusions and some outlook on possible
further research activities in the area of this thesis.
1.4. Contributions
The requirement of developing technologies of biomimetic robot
fish and the flourishing of haptics, provides an infinite possibility of
research into a new product, a haptics robot fish system, which will
gather the advantages of biomimetic robot fish and haptics together.
This thesis’ main contributions are in the following areas:
The first contribution of the thesis is that a functional biomimetic
robot fish based on the prototype of a carangiform fish was built up. It
has a biomimetic tail to simulate the carangiform tail, a
barycenter-adjustor for descending/ascending motions, multiple
sensors, and it may communicate with the outside by a wire connected
information relay system floating on the water. Combining the
movements of the tail and the structure for descending and ascending,
21
the robot fish can simulate the swimming of real fish in water. An
innovative biomimetic motion library is established which helps users
make the control scheme more efficient.
The second contribution is that the kinematic modeling for the
robot fish using Mathematics® software was developed. It was built up
according to the relationship between the generalized force in
Lagrange's equation of the second kind, and the fluid force. The
modeling provides a simple and time-efficient way to calculate the
force on the swimming robot fish.
The third contribution is that the thesis represents a 3D
computational fluid dynamic simulation of the biomimetic robot fish
by Fluent® 6.3.26. The UDF is used to define the movement of the
robot fish and Dynamic Mesh is used to mimic the fish swimming in
water. Hydrodynamic analysis has been done, aimed at getting
comparative data about the hydrodynamic properties of those
guidelines to improve the design, remote control, and flexibility of the
underwater robot fish.
The last but not the least contribution of this thesis, is that a novel
haptic robot fish system is established using the data of CFD
hydrodynamic analysis and kinematic modeling as the force feedback.
Users can feel the force on the robot fish via a PHANTOM Omni
Haptic Device. The velocity, pressure field distribution and any other
22
further information of the robot fish hydrodynamic properties will be
provided according the need of users.
23
2. Literature Review
The aim of this chapter is to provide a systematic overview of the
robot fish development process, including fish propulsion theory,
underwater robot research status, kinematics and locomotion control of
robot fish, hydrodynamic analysis of underwater robot and haptic
development.
2.1. Background to Underwater Robot and Haptic
Development
2.1.1. Underwater Robot Development
The underwater robot research field has emerged quickly in recent
years. There are two main categories of underwater robots:
Autonomous Underwater Vehicle (AUV) and Remotely Operated
underwater Vehicle (ROV). The former is a robotic device that is
driven through the water by a propulsion system, controlled and piloted
by an onboard computer and maneuvered in three dimensions. The
latter is controlled or remotely controlled by a human operator via a
cable or wireless communication on a ship or on the ground.
24
2.1.1.1. Background of Autonomous Underwater Vehicle
The history of underwater robot technology can date back to the
first torpedo (Figure 2:1) designed in 1866, which was driven by
compressed air carrying an explosive charge. A simple hydrostatic
valve acted directly on the elevator to hold the torpedo at a
pre-determined depth. If one ignores the fact that it carried an
explosive charge, it might be considered the first AUV [2].
Figure 2:1: First Torpedo, 1866 [3]
The first “true” underwater vehicle was developed in the late
1950s by Stan Murphy, Bob Francois and Terry Ewart of the Applied
Physics Laboratory at the University of Washington to help them
obtain oceanographic data along precise trajectories and under ice [4].
This work led to the development and operation of the Self Propelled
Underwater Research Vehicle (SPURV) in the early 60’s [5].
25
Following the development of SPURV I, which was acoustically
controlled from the surface and could autonomously run at a constant
pressure, sea saw between two depths, or climb and dive up to 50
degrees, over 400 SPURVs were researched and developed.
In 1983 an Advanced Unmanned Search System (AUSS) [6] was
developed by SPAWAR (its predecessor was the Naval Ocean System
Center) in response to the sinking of the USS Thresher, the USS
Scorpion and the H bomb loss of Palomares. It had an acoustic
communication system that transmitted video images through the water.
This system brought about the concept of using multiple controllable
freely swimming vehicles to improve system performance.
In 1990s the underwater robot technology developed rapidly and
operated world-wide. There were some leading underwater projects:
Odyssey (1992, The Massachusetts Institute of Technology,
MIT), was operated under ice and used in support of
experiments demonstrating the Autonomous Ocean Sampling
Network [7, 8]
Autonomous Benthic Explorer (ABE, in the mid 1990’s,
Woods Hole Oceanographic Institution, WHOI) carried six
thrusters which made it a highly maneuverable vehicle in all
three dimensions. ABE is an excellent platform to perform
near bottom surveys in rough terrain [8, 9].
26
Theseus (1996, International Submarines Engineering, Ltd.)
was designed for laying optical fiber cables in ice-covered
waters [10]. It operated in either depth-keeping mode or
bottom-following mode.
Remote Environmental Measuring Units—REMUS (1994,
WHOI) [11], were made up of a number of small, low cost,
controllable freely swimming vehicles operated jointly or
independently, which could offer an appropriate technology
for gathering data in the coastal and open ocean.
After 2000, more and more underwater projects are in research or
commercial use, covering a large area of exploration, wrecking,
military, and fishery. But the actions of AUVs are limited by the
onboard computer operation and AUVs are generally designed for
surveys. ROV is made for direct multipurpose interaction.
2.1.1.2. Development of Remotely Operated Underwater
Vehicles
ROVs are unoccupied, highly maneuverable and operated by a
person aboard a vessel. They are linked to a ship by a tether
(sometimes referred to as an umbilical cable), a group of cables that
carry electrical power, video and data signals back and forth between
the operator and the vehicle. High power applications often use
27
hydraulics and electrical cabling. Most ROVs are equipped with at
least a video camera and lights. Additional equipment is commonly
added to expand the vehicle’s capabilities. These may include sonars,
magnetometers, a still camera, a manipulator or cutting arm, water
samplers, and instruments that measure water clarity, light penetration
and temperature.
In the 1950s the Royal Navy used "Cutlet"(Figure 2:2), which
might be the first ROV, a remotely operated submersible, to recover
practice torpedoes. The US Navy funded most early ROV technology
in the 1960s, named the " Cable-Controlled Underwater Recovery
Vehicle" (CURV) [12], to perform deep-sea rescue operations and
recover objects from the ocean floor. Building on this technology base
the offshore oil & gas industry created the work class ROVs to assist in
the development of offshore oil fields.
Figure 2:2: Cutlet, ROV, 1950s [13]
28
More than a decade after ROVs were first introduced, they
became essential in the 1980s when much of the new offshore
development exceeded the reach of human divers. During the mid
1980s the marine ROV industry suffered from serious stagnation in
technological development caused, in part, by a drop in the price of oil
and a global economic recession. Since then, technological
development in the ROV industry has accelerated and today ROVs
perform numerous tasks in many fields. Their tasks range from the
simple inspection of sub-sea structures, pipeline and platforms to
connecting pipelines and placing underwater manifolds. They are
extensively used both in the initial construction of a sub-sea
development and the subsequent repair and maintenance.
ROV are widely used for underwater tasks as they have several
characteristics:
(1) There is no limited operation time as the cable associating the
ROV with the over water controller provides the ROV with
continuous energy.
(2) The operator directly controls and operates the ROV on the
water surface making many complex control problems easily.
(3) ROVs can be used for underwater operations which are not
achieved at this stage by AUV. For example, ROVs can
collaborate with manned submersibles to complete salvage
29
missions of crashed aircraft or submarines.
2.1.1.3. Hybrid Remotely Operated Underwater Vehicle
Recently, a new type of deep-sea robotic vehicle called Nereus,
hybrid ROV, (Figure 2:3) made by WHOI has successfully reached the
deepest part of the world's ocean. The dive to 10,902 meters (6.8 miles)
occurred on 31st May, 2009, at the Challenger Deep in the Mariana
Trench in the western Pacific Ocean [14]. The Nereus underwater
vehicle was designed to perform scientific survey and sampling to the
full depth of the ocean. Its depth capability is significantly deeper than
that of other present operational vehicles; the second deepest
underwater vehicle can dive to 7,000 m maximum depth. Nereus is a
hybrid ROV that means it can be operated in the modes of both AUV
and ROV. AUV mode was used for broad-area survey and has the
capabilities of exploring and mapping the sea floor with sonars and
cameras, while ROV enables close-up imaging and sampling. The
ROV configuration incorporated a lightweight fiber-optic tether for
high-bandwidth, real-time video and data telemetry to the surface,
enabling high quality teleoperation. A manipulator, lightweight
hydraulic power unit, and sampling instruments were added to provide
sampling capabilities.
30
Figure 2:3: Nereus can Switch Between Free-swimming and Tethered
Configurations, 2007 [15]
2.1.1.4. Shortcomings of Remotely Operated Underwater
Vehicles and Autonomous Underwater Vehicles
Previous research into underwater vehicles focused on Remotely
Operated Vehicles (ROVs), Autonomous Underwater Vehicles (AUVs)
and underwater manipulators (Hybrid ROV). Rapid development on
ROVs and AUVs boosted underwater robot technology. But ROVs and
AUVs still cannot travel as efficiently and quietly as a real fish can.
The key technology in the design of underwater vehicles is the
propulsion system. Traditional propellers employ screw propellers,
rotary jets or impellers. They have the following shortcomings:
(1) Low efficiency in energy utilization, which is the reason why
31
an underwater robot is often designed in an unwieldy shape
carrying huge energy supply units.
(2) Big structure size and large weight which makes it difficult to
control due to the lack of flexibility and mobility.
(3) Large disturbance on the environment which would make it
hard to achieve data for its worsening the visibility of water
and disturbing the biological environment.
(4) Poor hidden performance makes it almost impossible to obtain
biological data by close observation or perform some specific
tasks.
(5) Inflexible movement, which creates a big problem when it
works in a small space or needs to response quickly and
flexibly.
To meet the needs of the development of marine science,
scientists are looking for other high-efficient and flexible underwater
propulsion modes [16].
2.1.2. Biomimetic Robot Fish Design
In recent years, with bionics and robotics research, underwater
biomimetic propulsion technology became a hot spot in AUV study. It
provides new ideas for developing high-efficient, high maneuverability,
low noise and easily concealed underwater propulsion [17-19].
32
Therefore, biomimetic robot fish, a new type of underwater biomimetic
robot, has attracted great attention because of its silence in moving and
its energy efficiency when compared to conventional
propeller-oriented propulsive mechanisms.
MIT successfully developed an eight-link, fish-like
machine-RoboTuna (Figure 2:4), which was the first biomimetic tuna.
RoboTuna and the subsequent RoboPike (Figure 2:4) [18, 20] projects
attempted to create AUVs with increased energy savings and longer
mission duration by utilizing a flexible posterior body and a flapping
foil (tail fin).
Figure 2:4: RoboTuna, MIT [21] Figure 2:5: RoboPike, MIT [22]
In Nagoya University, Guo developed a kind of underwater micro
robot by using Ionic Conducting Polymer Film (ICPF) actuator [23,
24]. Mitsubishi Heavy Industries (MHI) created a robotic replica of the
rarely-seen coelacanth which died out millions of years ago and was
known only from fossils [25]. Scientists in Northeastern University
33
developed an underwater lamprey-like robot (Figure 2:6) [26]
employing SMA and links structure to mimic an lamprey’s undulated
propulsion. The Swiss Federal Institute of Technology Lausanne
(EPFL) constructed AmphiBot I, a biologically inspired amphibious
snake-like robot capable of crawling and swimming [27, 28]. Both the
structure and the controller of the robot are inspired by elongate
vertebrates. K H Low designed a robot fish with undulating fins
[29-31]. The Harbin Institute of Technology conducted underwater
robot research that imitated the propulsion mechanical structure of fish
fins and constructed an experiment platform using elastic module
(Figure 2:7) [32]. The National University of Defense Technology, Xie
et al. investigated the Long Flexible Fin Undulation equipment, which
was based on the undulatory calisthenics of Gymnarchus niloticus’s
long flexible dorsal fin [33]. Peking University developed a
biomimetic dolphin (Figure 2:8) and built a series of experiments and a
test platform [34]. The Institute of Automation Chinese Academy of
Sciences studied the control and the coordination of robot fish (Figure
2:9) [35-39].
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34
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35
Biomimetic robot fish brought revolutionary processes to the
development of underwater robots, especially in the propulsion area.
They can mimic the movement of a fish in nature and significantly
enhance the efficiency of biomimetic robot fish propulsion. But the
flexibility of a fish and its ability to perceiving the water current is hard
to be realized in robot fish. How to give underwater robots the tactile
capacity to obtain water current information is a new research topic. In
next section, haptics development will be reviewed.
2.1.3. Haptics and Application
Haptic feedback refers to sensing and manipulation through touch,
often referred to as simply "haptics". There have been several efforts to
define terminologies for haptics[43, 44]. While there is no difference
between haptic and tactile in most dictionary definitions[45], many
researchers and developers use haptic to include all haptic sensations
and limit the use of tactile to mechanical stimulation of the skin. The
science of haptics and the creation of haptic devices depend on
knowledge of the human body, especially its capability to sense both
touch to the skin and kinaesthetic activity in the limbs and body joints
[46]. When referring to mobile phones and similar devices, this means
the use of vibrations from the device's vibration alarm to denote that a
touch screen button has been pressed. In this particular example, the
36
phone would vibrate slightly in response to the user's activation of an
on-screen control, making up for the lack of a normal tactile response
that the user would experience when pressing a physical button. The
resistive force that some "force feedback" joysticks and video game
steering wheels provide is another form of haptic feedback[47].
A haptic interface is a feedback device that generates sensation to
the skin and muscles, including a sense of touch, weight and rigidity
[48]. Compared to ordinary visual and auditory sensations, haptics is
difficult to synthesize. But the sense of touch is vital for understanding
the real world. The haptic interface to enhance computer-human
interaction has been applied in many areas including computer-assisted
and simulated surgery, autonomous exploration of hazardous or remote
environments, undersea salvage, enabling technologies, micro/nano
manipulation, education and design. It mainly went through following
transversions [49]:
(1) Early haptic interface archetype
In the mid-1990s, terms such as teleoperation, telepresence,
robotics, telerobotics and supervisory control had been used
interchangeably since researchers accepted the definitions considering
the systems aspects of controlling remote robotic vehicles and
manipulators [50, 51]. The history of the haptic interface dates back to
37
this period, when a master-slave system was proposed by Goertz
(1952)[48]. Haptic interfaces were established out of the field of
tele-operation which was then employed in the remote manipulation of
radioactive materials. The ultimate goal of the tele-operation system
was "transparency". That is, a user interacting with the master device
in a master-slave pair should not be able to distinguish between using
the master controller and manipulating the actual tool itself. Early
haptic interface systems were therefore developed purely for
telerobotic applications.
(2) Early bilateral manipulators
Bilateral Master-Slave Manipulators (MSMs) , with the same
functions as today’s desktop haptic feedback systems, permit safe,
remote handling of irradiated material under direct human control and
supported by direct (lead-window) and indirect (closed-circuit TV)
vision.[52]
(3) Servo manipulators
Servo manipulators were designed to incorporate ac-driven servos,
connected back-to-back, to provide force reflection, having the
advantages of being mobile (cable linkages) and possessing large load
carrying capacities.
(4) Exoskeletons
38
Exoskeletons originated partly as “Man Amplifiers”, capable,
through direct human slaving, of lifting and moving heavy loads.
Because of the emergence of a range of lightweight, low-cost body
systems developed under the Virtual Reality (VR) banner, the
exoskeleton received renewed interest in the early 1990s as a means of
registering body movement in a virtual environment and, importantly,
as a technique for feeding haptic data back to the immersed user [53].
Figure 2:10 shows the GLAD-IN-ART (Glove-like Advanced Devices
in Artificial Reality) project. The system was designed to record both
the pose and configuration of angles of the user's hand. Then the
manipulation performed by the human hand was replicated in 3D
computer world model.
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42
2.2. Fish Propulsion Theory
In nature, a fish adjusts itself to its hydrodynamic environment
and becomes a perfect swimming expert through years of evolution.
Fish can achieve tremendous propulsive efficiency and excellent
maneuverability with little loss of stability by coordinating its body,
fins and tail. Researchers believe that these remarkable abilities can
inspire innovative designs to improve the performance, especially
maneuverability and stabilization, of underwater robots. It also could
bring forward a revolutionary change in future navigation propulsion.
Many researchers studied fish body structures and swimming
characteristics and fruitful results have been achieved through
long-term research activities.
In 1926, Breder classified fish swimming locomotion into two
generic categories on the basis of the movement of temporal features
[17, 55]:
(1) Periodic (or steady or sustained) swimming, characterized by
a cyclic repetition of the propulsive movements. Periodic
swimming is employed by fish to cover relatively large
distances at a more or less constant speed.
(2) Transient (or unsteady) movement that includes rapid starts,
escaping maneuvers and turns. Transient movement lasts
milliseconds and is typically used for catching prey or
43
avoiding predators.
In 1984 P. Webb put forward a detailed method of classifying fish
swimming propulsive models according to the different part of the
body which a fish uses to swim [56-58]. Fish propulsive models can be
categorized into:
(1) Body and/or caudal fin (BCF) model. It can achieve greater
thrust and acceleration
(2) Using median and/or paired fin (MPF) propulsion. It is
generally employed at slow speeds, offering greater
maneuverability and better propulsive efficiency
The BCF model can be subdivided into the eel model (Figure 2:13
(a)), the sub-caranginae model (Figure 2:13 (b)), the caranginae model
(Figure 2:13 (c)) and the caranginae plus crescent shape caudal fin
model (Figure 2:13 (d)) based on the ratio of the locomotion part
length to the whole length of the fish body.
44
(a) (b) (c) (d)
Figure 2:13: Four Fish Swimming Propulsive Models [58]
In 2000, M. Triantafyllow research group of MIT pointed out in
the overview of fish propulsive mechanism study [59, 60]:
(1) The three-dimensional (3D) unsteady flow mechanics model
describing the fish tail trace is incomplete.
(2) Vorticity control is one of the most important key factors for
fish swimming highly efficiently and at a high velocity. In
1991 Tokomaru et al. found that fish can use unsteady body
motion and unsteady forcing in the flow for efficient vorticity
control [61]. This was confirmed theoretically [62] and
experimentally [63] in 1994. As to a high-aspect ratio flapping
foil, five prime parameters affect its propulsion capability: (a)
the amplitude of heave motion compared with the chord length;
(b) the feathering parameter (ratio of pitching angle compared
with the maximum angle of attack induced by the heave
45
motion); (c) the phase angle between heave and pitch; (d) the
reduced frequency; and (e) the relative position of the pitching
axis. The Strouhal number and the nominal angle of attack
may be used instead of the reduced frequency and feathering
parameter.
The Strouhal number is a nondimensionalized frequency,
defined in analogy with bluff body flows as S = / (2- 1)
where f is the frequency of oscillation, A is the width of the
wake (often approximated by the lateral total excursion of the
foil), and U is the velocity of motion. Because the width of the
wake is not a priori known, the lateral excursion of the foil is
often used to determine the Strouhal number. The optimum
range of Strouhal number—between 0.25 and 0.35—is found
for certain specific profiles used in the research of
Triantafyllou et al. [63]; in other cases, different values may be
obtained.
(3) The flow about the fish body and the tail and the formation of
a reverse Kármán Street in the wake have been observed by
using experimental Digital Particle Image Velocimetry (DPIV)
[64, 65]or calculated by an inviscid numerical formulation[66].
(4) The rapidity and efficiency of the fishes’ swimming are
46
relative to the “C” shape movement of the fish body[67, 68],
where the fish is bent into a “C” shape at the end of the first
contraction of the lateral musculature.
Based on the steady flow theory, Taylor calculated the fluid
dynamics of a swimming fish, which is the early resistance model[69].
Afterwards, kinematic models were built up close to the actual fish
movement. Lighthill developed the mathematic model analyzing
carangiform fish propulsion movement according to the
small-amplitude potential theory for the first time [70]. Wu
investigated two-dimensional (2D) waving plate theory by using
potential flow theory and linearized boundary conditions [71]. This
theory treats fish as elastic plates so as to analyse the hydrodynamic
features of the carangiform fish. Lighthill built a model based on
elongated-body theory (an extended version of inviscid slender-body
theory) to study the carangiform propulsion mechanism [72]. Later, the
large-amplitude elongated-body theory [73] was propounded to analyse
the irregular amplitude of the tail. Chopra et al. brought forward
two-dimensional theory [74] to evaluate the propulsion of the lunate
tail of large aspect ratio. this is a complement to the large-amplitude
elongated-body theory of Lighthill.
Considering the biomechanical properties of swimming fishes and
the dynamic characteristics of its structure, Videler et al. put forward
47
the thin body theory being specific to fish with a small ratio of its body
length to its lateral amplitude[75]. With the assumption that the
stiffness of the fish longitudinally bending is a constant, Cheng et al.
lodged the waving plate theory and dynamic beam theory [76].
Triantfyllou [18, 59, 77] found that the jet formed behind the fish body
played an important part in propulsion. Tong developed the 3-D
waving plate theory (3DWDP) based on the 2-D waving plate theory
and a semi-analytic semi-numeric method was adopted to obtain the
3-D nonstationary linear solutions [78].
These seminal works provided a firm theoretical basis for
studying the swimming of fish and gave insight into the basic
swimming propulsive mechanisms. It made the development of
underwater biomimetic robots possible.
2.3. Research into Underwater Biomimetic Robots
With the development of propulsive theories and robotic
technologies, the research into a biomimetic robot fish with high
velocity, high efficiency and high maneuverability is a hotspot. It may
provide significant insights into both the theory and application of
underwater robotics. Observations show that a fish in nature can
achieve great propulsive efficiency and excellent maneuverability
through the coordinated motion of the body, fins, and tail. In 1994,
48
RoboTuna (Figure 2:4), the first robotic fish in the world was
successfully developed, demonstrated that the power required to propel
the swimming fish-like body was significantly smaller than that
required to drag the body straightforward with the same speed [18, 20].
McIsaac et al. developed an underwater eel robot [79, 80] and analysed
its kinematics and kinetics. National Maritime Research Institute
(NMRI) developed a high-performance and multi-purpose fish robot,
UPF-2001 [81], whose length is 0.97m made up of 2 links. It can
swing maximum at 12Hz and swim at 0.97m/s. UPF-2001 already has
had the ability of 3D locomotion with pectoral fins and rubber,
realizing diving, turning and so on. Xiao et al. designed an arithmetic
of point-to-point fuzzy control based on a control response table with
Max-Min inference in Matlab. This met the needs of research into
real-time cooperation and coordination of multiple Biomimetic
Robot-fish. [82]. Wang et al. developed the biomimetic dolphin and
built a series of experiments on a test platform to explore the
coordination method for multiple robot fish in underwater transport
tasks[83].
Previous underwater biomimetic robots mimicked many of the
good properties of real fish, but an important function, apperceiving
currents, cannot be enforced without haptic functions. In this thesis,
haptic function for underwater biomimetic robots will be explored
49
based on a fully functional biomimetic robot fish. It was designed
according to the prototype of the carangiform fish with a carangiform
tail for propulsion, a barycenter-adjustor for diving, an information
relay system on water for information transmission with an upper
console and sensors for detecting information. The locomotion control
of a robot fish is a major factor for investigation in robot fish. In the
following section, the Kinematics and Locomotion Control of robot
fish will be reviewed.
2.4. Kinematics and Locomotion Control of robot fishes
Based on the research of fish movement mechanism and the
prototypes, researchers carried out much investigation work into a
variety of dynamics, kinematics and motion control of the robot fish
prototypes. Triantafyllou et al. [18, 77] and Barrett et al. [20] measured
the force distribution on the swimming 8-joints, swing-wing-propelled
Robotuna. The experimental results demonstrated that the power
required to propel an actively swimming, streamlined, fish-like body is
significantly smaller than the power needed to tow the body straight
and rigid at the same speed. The drag reduction was caused exclusively
by the actively controlled transverse motion when the phase speed of
the body wave was greater than the forward speed. In the same period,
Barrett et al. [84] developed a self-optimizing motion controller based
50
on a genetic algorithm, which effectively used evolutionary principles
to search for the main seven parameters of the robot fish movement
mechanical model and that exponentially optimized swimming
performance.
Kato et al. [85] studied the control of the pectoral fins propulsive
mechanical model applied on Black Bass. Harper et al. [86] developed
a model for the dynamics of oscillating foil propulsion when springs
are used in series, with actuators to reduce energy costs. Explicit
expressions were derived for spring constants which are optimal in this
sense. Kelly et al. [87] proposed a planar model for the swimming of
the carangiform fish based on reduced Euler-Lagrange equations for
the interaction of a rigid body and an incompressible fluid. Hirata et al.
[88] designed a form of three-link robotic fish to analyse the
carangiform-like swimming. They also experimentally verified a
sample quasi-steady fluid flow model for predicting the thrust
generated by the flapping tail.
Morgansen et al. [89] realized trajectory tracking for an
experimental planar carangiform-like robotic fish system by applying
the nonlinear control methods to generate the system input. Saimek at
el [90] proposed a practical maneuvering control strategy for an
aquatic vehicle using an oscillating foil as a propulsor, where the
control task was decomposed into the off-line step of motion planning
51
and the on-line step of feedback tracking.
In order to achieve an autonomous system which could adaptively
behave through learning in the real world, Iilima et al. [19] constructed
a distributed autonomous swimming robot (Figure 2:14). This
consisted of a mechanically linked multi-agent and an adopted adaptive
oscillator method, called a general decision making for distributed
autonomous systems (DASs). This robot could complete a target
approach including obstacle avoidance via a modified Q-learning,
where plural Q-tables were used alternately according to dead-lock
situations. As shown in Figure 2:14-A and Figure 2:14-B, each round
float (diameter: 15 cm) was taken as one agent, and a three-agent
version was demonstrated here. Each agent had four solar panels that
functioned as light sensors, a CPU, and an angular controlling servo
motor that were located at the pivot of each joint between neighboring
agents. Two-channel serial ports were used for communication
between agents. Moving force was generated by pushing water aside
with fins. Additionally, for structural necessity, the robot had a dummy
agent at one end of the chain carrying battery cells for driving the
robot.
52
Figure 2:14: A: Distributed Autonomous Swimming Robot (3 agents);B:
Structure of an Agent [19]
Supported by the National Science Foundation (NSF) from 2000,
Princeton University began to study the dynamics of the coordinated
movements among several Underwater Gliders[91]. They aimed to
establish an autonomous, cooperative multi-glider system to achieve
the monitoring of the Monterey Bay ecosystem. Figure 2:15 shows the
Princeton 3D multi-vehicle experimental test-bed. The
multi-underwater-glider system, Princeton Grouper, could be
teleoperated. Leonard et al. proposed a framework for coordinated and
distributed control of multiple autonomous vehicles using artificial
potentials and virtual leaders [92, 93]. Artificial potentials defined the
interaction control forces between neighboring vehicles and were
designed to enforce a desired inter-vehicle spacing. A virtual leader
was a moving reference point that influenced vehicles in its
neighborhood by means of additional artificial potentials which were
used to manipulated group geometry and direct the motion of the group.
Based on artificial potentials and virtual leaders, Ogren et al. put
forward a stable coordination strategy for vehicle formation missions
53
involving group translation, rotation, expansion and contraction [94].
Symmetry in the framework was exploited to partially decouple the
mission control task into a formation management subtask and a
manoeuver management subtask. The designed dynamics of the virtual
leaders played a key role in satisfying the mission and ensuring the
stability and convergence properties of the formation.
Figure 2:15: Princeton 3D Multi-Vehicle Experimental Test-bed (left);
Experimental Pool (right) [95]
McIsaac et al. [79, 96] built up a symmetrical structure eel-like
robot based on the Lagrangian model to verify a simplified dynamic
model and open-loop control routines. Lie group method was
employed to simplify the model and a series of motion results was
obtained. Boyer et al. [97] set up the dynamic model of a continuous
three-dimensional swimming eel-like robot based on the
“geometrically exact beam theory”. It allowed the computation of the
motion of the eel and the control torque distribution from the
knowledge of the desired internal deformation imposed on its body.
54
The Nonlinear Dynamics and Control Lab of University of Washington
[98] realized the depth control on their fin-actuated untethered
autonomous vehicles. Morgansen et al. [89, 99] at Control and
Dynamical Systems Lab of California Institute of Technology designed
oscillatory controls for mechanical systems (Figure 2:16), which could
measure the data of the system in real-time. They also made use of
employing the nonlinear control methods to control the complex fluid
in the fluctuating propulsion. The use of this type of feedback was
shown to work quite well in simulation. A slightly modified version of
the controller demonstrated convergence with a simple forward
swimming trajectory in experiments.
Figure 2:16: Photograph and Schematic of Side View of Fish Design (left);
Photograph from Rear and Schematic of Top View of Fish Design (right) [89]
Every modeling above had their own distinguishing feature. But
55
for the special requirements of the simulation of the haptic biomimetic
robot fish, another suitable modeling method had to be found. In this
thesis, the kinematic modeling for the biomimetic robot fish will be set
up using Lagrangian method based on a simplified link structure of the
machine, a typical series structure. The kinematic modeling provided a
real-time motion analysis result for the robot fish.
2.5. Hydrodynamic Analysis of Underwater Robot
It should be noted that most existing control algorithms of robot
fish are based on a simplified propulsive model that only provides a
rough prediction of the effect of hydrodynamics on robot fish. To
obtain an accurate prediction of the hydrodynamic force on robotic fish,
it is necessary to conduct dynamic analysis of the surrounding fluid by
computational fluid dynamics (CFD) [100].
CFD analysis has been widely used in many areas, including
vehicle design, aircraft design and ground robot developments due to
the following reasons [101]:
(1) CFD simulations can be a useful tool for designers to
understand the complex physics of the flow phenomena
involved in the fluid dynamics.
(2) CFD simulations require less time than field tests.
Moreover, different models can be tested with CFD
56
simulation before actual prototype models are created for
tests.
(3) CFD also provides detailed visualization of the flow field,
which is difficult to be obtained by experimental facilities.
CFD simulations and analyses of robot fish have been studied in
the past years. Zhang et al. [102] investigated fluid dynamics, pressure
and velocity distribution, and the production of forces associated with
an undulatory mechanical fin. Tangorra et al. [103] also employed
CFD simulation, together with stereo DPIV and Proper Orthogonal
Decomposition (POD), to estimate the hydrodynamic force generated
by the complex component motions of their biorobotic pectoral fin and
to analyse its hydrodynamics. The fins studied by Zhang et al. and
Tangorra et al. were important factors in the development of propulsive
devices that would make an underwater robot fish have the ability to
produce and control thrust like highly maneuverable fish.
Mohammadshahi et al. [104] evaluated hydrodynamic forces of a
fish-like swimming robot by using a two-dimensional (2D) CFD model;
this provided important results in optimizing performance parameters
in the process of design and fabrication. However, 2D model of robot
fish cannot offer abundant tri-dimensional information when compared
to 3D simulation. Anton et al. [105] adopted CFD modeling and
examined the flow field, the produced thrust, and the bending moments
57
at the joints of two-link tails of a robot fish. However, the two-link tail
fins were assumed to be rigid, thin and light. In reality, popular
biomimetic robot fish bodies are soft and quite flexible. Listak et al.
[106] created a 3D computer model for a biomimetic robot and
simulated the ideal ellipsoid with Gerris which helped them find an
ideal robot fish body with low drag and improved the design, although
without detailed analysis of the simulation results.
In this thesis, to produce significant information on flow pattern,
velocity and pressure fields, and to provide an insight into both the
design and the application of robot fishes, a 3D CFD simulation was
investigated for the robot fish prototype [107] using Fluent® 6.3.26.
2.6. Haptics for Underwater Applications
The idea of using touch as a means of communication was
popularized by Craig et al. [108] and Sherrick [109]: “Our
understanding of how simple patterns combine to yield the complexity
needed to increase channel capacity for continuous information
streams is still primitive”. Haptic feedback technology development
went from telepresence to virtual reality (referring to section 2.1.3).
New technologies from the area of virtual reality (VR) now allow
computer users to use their sense of touch to feel virtual objects.
Unlike traditional interfaces that provide visual and auditory
58
information, haptic interfaces not only generate mechanical signals that
stimulate human kinesthetic and touch channels, but also provide
humans with the means to act on their environment. This is defined as
the association of gesture to touch and kinesthesia to provide for
communication between the humans and machines[110].
Researchers recently began to use haptic devices to study physical
interaction with virtual environments and enhance the ability of
performing a variety of complex computer interaction tasks [111-113].
Underwater haptic application is necessary when visual
information is difficult to obtain due to unclear water or poor light
especially in manned underwater machines. Taketsugu et al. presented
a teleoperation of construction machines with haptic information
substituting for visual information in underwater applications [114]. It
was applied to manned underwater backhoes using electric control
valves, articulation angle sensors and a reaction force sensor. The
components control technologies included the visualization of haptic
images, force feedback and similar figure controllers. They obtained
good results in both 2D and 3D level experiments on land. Further
research on its underwater application is expected to be done.
It is common that people apply force sensors in an underwater
machine to test the force for haptic force feedback. Yoshinori D. et al.
presented a method for very rapidly estimating and displaying forces in
59
haptic interaction with water[115]. They simulated the dynamics of
water which was decomposed into two parts. One was a linear flow
expressed by a wave equation used to compute water waves. The other
was a more complex nonlinear flow around the object precomputed by
solving Navier-Stokes equations and stored in a database. The
precomputed non-linear flow and the linear flow were combined to
compute the forces due to water. Their method provided the real-time
display of the forces acting on rigid objects due to water. But they still
have limitations, such as their inability to take into account for
randomness due to turbulent flow, cannot correctly compute the forces
for a rotating pointer object, and cannot accurately reproduce the forces
for the pointer object with other near objects.
There are few published techniques for haptic interaction and
rendering with fluids. In this thesis, two kinds of simulation methods
for calculating the force on the robot fish when it swims in water are
presented. The results were used for the haptic interaction with the
haptic robot fish system.
2.7. Summary
In this chapter, a systematic review on the development of
underwater robot fish, haptic technology and their extensions were
provided. Both the expertise of underwater robot fish and haptics have
60
achieved great growth. However, combining these together to obtain a
new haptic robot fish system is an innovation. It would bring
underwater research many benefits, for example, the tactile interaction
for users feeling the force the robot fish gets in water; easier control of
the robot fish via the direct haptic feedback and the detection of data of
the current surrounding the robot fish to help it autonomously evade
dangerous currents.
In the remainder of the thesis, the hardware and software design
of the biomimetic robot fish, its CFD simulation results and the
framework of the haptic robot fish system will be demonstrated.
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3. Design of a Biomimetic Robot Fish
A novel medium size biomimetic robot fish (62 centimetres in
length) with a carangiform tail for propulsion and barycenter-adjustor
for diving were designed based on the analysis of propulsion and
maneuvering mechanisms for carangiform swimming. It integrated an
information relay system on water for information transmitting and
kinds of sensors, infrared sensors, press sensor and CCD camera, for
information processing. It has the most functions in this dimension of
robot fish. This chapter presents the detailed design of the biomimetic
robot fish including the mechanical structure diagram, the control
system design and the biomimetic motion library conception [107]. It
is the basis of the development of the novel haptic biomimetic robot
fish.
3.1. Problem Formulation
The carangiform fish was chosen as the prototype of the
biomimetic robot fish. There were several difficult tasks in the design
of the fish:
(1) The following properties were required for the design of the
support frame (aluminum exoskeleton + head):
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good water proof qualities to let the robot fish swim under
water; the ability to carry and protect a variety of inside units,
keeping the same volume when the robot fish changes
swimming depth, and with a function to mimic the tail shape
transformation of a real fish.
(2) The realization of real-time communication between the robot
fish and the upper console was an important issue in this
project. Abundant data, especially from the camera, should be
transferred to the upper console in a real time way. But general
wireless signals cannot transfer far because of bad underwater
signal attenuation.
(3) The ability to control the free swimming of the robot fish,
especially the descending and ascending motions. Realizing an
up-down motion in a 3-D workspace is quite hard for a small
robot fish prototype because of the limited volume of the robot
fish body. In future applications, autonomous motion control is
surely necessary for robot fish. All motions that a real fish has
should be considered to be implemented on robot fish.
3.2. The Biomimetic Robot Fish
The biomimetic robot fish actualizes the carangiform swimming
method via the coordinated movement of the four links driven by
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motors. Four links are used in this robot fish for the mean between the
maneuverability and redundancy of the mechanism and the control and
construction of the robot. As shown in Figure 3:1, the biomimetic robot
fish was made up of the following parts:
A sensing unit including 3 infrared sensors, an underwater
press sensor, and a charge-coupled device (CCD) camera)
A control unit composed of the Micro Control Unit (MCU)
and peripherals
A communication unit involving an optical transmitter, an
optical receiver, wireless modules, optical fiber cable and
other cables
An actuation unit which consisted of a pitch motor and 4 tail
motors
A support frame containing an aluminum exoskeleton and a
head
Accessories ranging from Li-polymer batteries, waterproofed
skin and a caudal fin
64
Figure 3:1: Biomimetic Robot Fish System
The robot fish has a clipper-built head, a flexible body and a
caudal fin. The rigid head is made from FRP (Fiberglass-Reinforced
Plastics). Inside, MCU, batteries, sensors and peripherals are installed.
The flexible body is built by four links jointed together by an
aluminum exoskeleton which is driven by four tail motors and
airproofed by a waterproofed skin. The flexible body cooperates with
the caudal fin which simulates the movement of the carangiform fish
tail causing the robot fish to swim forward. At the same time, in order
to maintain balance when the robot fish is swimming in water, some
weights are fitted into the robot fish’s body.
65
3.3. Mechanical Structure
3.3.1. Support Frame
Each part of the robot fish has quite different properties, as
following:
(1) The robot fish head:
The head, made of 5 mm thick FRP, is composed by two parts
joggled together and sealed by glue. The structure makes it easy to
install the MCU, batteries, sensors and peripherals into the space inside
the robot fish head. (Figure 3:2. Please note: In all mechanical
drawings of this chapter, the surface roughness is 12.5 and the
tolerance is ±0.1 without any special indication.)
66
Figure 3:2: the Head of the Biomimetic Robot Fish
67
(2) The flexible body:
The flexible body is built of four motor driving links. Every motor
is mounted in two pieces of aluminum exoskeleton including an
internal connection (Figure 3:3) and an external connection (Figure
3:4), which are called one link. Every two adjacent links are connected
together by a 2 mm thick aluminum support board (Figure 3:5), which
doubles for propping up the outside waterproofed skin and shaping the
fish tail.
Figure 3:3: Internal Connection
68
Figure 3:4: External Connection. The left one is used for the connection of the
first 3 links; the right one is used for connecting the last link and caudal fin.
Figure 3:5: Support Board
(3) The caudal fin:
The shape of the caudal fin is similar in shape to a swordfish’s tail,
which looks like a crescent as show in Figure 3:1. It is made of a tough,
thin plastic plate and fixed to the last external connection by a caudal
vertebra (Figure 3:6).
69
Figure 3:6: Caudal Vertebra
3.3.2. Actuation Unit
To realize a controllable freely swimming robot, Sanwa Servo
RS-995 (Figure 3:7) was chosen for the robot fish motor as it has
excellent performance when compared to other types of motors. The
actuation unit of the robot fish is made up of one pitch motor and four
tail motors (refer to Figure 3:1)
70
Figure 3:7: Sanwa Servo RS-995 [116]
The four tail motors drive the four links and the caudal fin to
mimic the swing of the tail of carangiform fish which causes the robot
fish to swim forward. Section 3.5.1 will expound the method as to how
the motors are controlled.
There are several methods to implement a descending or
ascending motion such as changing gravitation (Buoyancy), pectoral
fins, changing body shape and changing the barycenter[117].
Considering the features of these methods and the difficulties of their
realization, changing the gravity center was chosen to realize the robot
fish’s 3-D movement. A barycenter-adjustor was then designed and
implemented. It is driven by a motor and can swing to different angles
to change the gravity center of the whole robot fish. The robot fish can
pitch to swim upwards or downwards with this shift in the gravity
center. This will be discussed in detail in section 3.5.3.
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3.3.3. Communication Unit
Due to the limitation of the information processing capability of
the robot fish, it was necessary to design a communication system
between the robot fish and the outside. There are several methods of
the information transmission in the robot fish. One is to utilize wireless
equipment, which only works above the water surface because of
severe attenuation of the electromagnetic wave in water. The robot fish
has to swim only on water or ascend to the water surface to exchange
the data with the upper console. Another is to connect the robot fish
with the upper console by a cable directly; this can assure transfer
speed and accuracy. However, this method will limit the robot fish. In
this project, a buoyage information relay is presented. It is used as a
communication relay that connects the robot fish by cables on one
hand and communicates with the upper console by wireless on the
other.
3.3.4. Control and Sensing Units and Accessories
The processor of the robot fish MCU is ATmega128, a low-power
Complementary Metal Oxide Semiconductor (CMOS) 8-bit
microcontroller based on the Atmel AVR enhanced Reduced
Instruction Set Computing (RISC) architecture. By executing powerful
72
instructions in a single clock cycle, the ATmega128 achieves
throughputs approaching 1 Million Instructions Per Second (MIPS) per
1 MHz, allowing the power consumption versus processing speed to be
optimized.
Several kinds of sensors equip the robot fish for autonomic
control and environmental monitoring. Firstly, three infrared sensors
mounted on the left, front and right side of the robot fish head are used
to detect obstacles. This is processed by MCU directly and keeps the
fish swimming safely. Secondly, the water depth information can be
gained by a pressure sensor set on the body; the robot fish can get
feedback about depth data for diving depth control. Thirdly, a camera
is installed on the fish head to provide abundant information in front of
the fish.
Some accessories, such as Li-polymer batteries (7.4V), and a
waterproofed skin are necessary for the normal work of the robot fish.
It is obvious that the capacity of the batteries should be as big as
possible but the volume and the mass should be as low as possible.
Two groups of batteries supplied power to the robot fish: one group for
the motors and the other one for the electro circuits. A rubber skin was
applied to protect the robot fish tail and satisfy the flexibility
requirement.
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3.4. Control system
The control system is shown in Figure 3:8. The MCU, using the
uCOS-II real-time operating system based on the minimal system of
Mega128, sends task-related PWM signals to the tail motors to control
its motion and to pitch the motor to change the fish’s center of gravity.
It exchanges the information with the outside via the buoyage
information relay.
Figure 3:8: The block diagram of the control system
There are two kinds of data: One is the mass visual record from
CCD camera, the other is the digital signal including the information
provided by other sensors and commands from the upper console. They
are transmitted separately. The digital signals are sent to the buoyage
information relay via normal cable after being converted into RS232
74
Serial signal and then sent out by low frequency wireless module and
received by the upper console later. Vice versa, the digital signals may
be sent to the robot fish by the upper console via this information relay
system. At the same time, the visual signals are converted into light
signals and sent to the buoyage information relay via optical fiber cable,
where the light signals are resumed into electronic signals and then
sent out by high frequency wireless module. The upper console
receives the information and extracts it to make decisions for remote
control. The result of vision processing and the target identification
reflects the information of the environment and goals.
With the information from sensing units, the robot fish may make
decisions independently or execute a task after combining with the
commands from the upper console.
3.5. Biomimetic motion library
According to the behaviors of real fish and the specifics of
biomimetic robot fish, a biomimetic motion library was designed based
on the mechanical structure and the control system. The robot fish
adjusts its poses in water by controlling the oscillatory frequency of the
tail and the position of the gravity center. Accordingly, the motion
library includes acceleration, deceleration, uniform motion, turn, dive,
and even includes swimming backwards. Different combinations of
75
these motions may be chosen according to the task required to be
executed.
The biomimetic motion library was established on the different
effects of the robot fish tail motion. Researchers point out that there is
an implied travelling wave in the body of swimming fish which runs
from its neck to tail [85, 118]. The wave amplitude increases gradually,
appears as the curvature of the fish’s spine and muscle and travels
faster than the fish’s forward movement. The robotic fish is devised
according to carangiform propulsion model whose propulsive wave
curve starts from the fish’s inertia center to its caudal link. It is
assumed that this kind of curve can be described by Eq. 3.1 [70, 84].
)])][sin([(),( 221 tkxxcxctxybody ω++= 3.1
where bodyy is the transverse displacement of fish body, x is the
displacement along main axis, k is the body wave number and
λπ2=k ,λ is the body wave length, 1c is the linear wave amplitude
envelope, 2c is the quadratic wave amplitude envelope, ω is the
body wave frequency, T/2πω = . A sample of the fish body wave
curve is shown in Figure 3:9.
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Figure 3:9: Links fitting fish’s body-wave
The parameters ( )ωλ,,, 21 cc are chosen to determine the proper
body wave. Four hinge links were adopted to simulate the locomotion
of fish tails Figure 3:1, the robot fish’s oscillatory part can be modeled
as a planar serial chain of links at an interval of 0 to π2×R along the
axial body displacement, where R is defined as the length ratio of the
fish's oscillating part to the whole sine wave. Let the length of each
link be )4,3,2,1( =jI j , the ratio of them be 4321 ::: llll , and the link
angle between 1−jl and jl be jϕ [119]. With the jϕ changing,
the fish's oscillatory part undulates along the travelling wave as Eq. 3.1
expressed. Impetus is produced when the speed of body wave
propagation exceeds the speed of the fish swimming forward [85, 118].
3.5.1. Realisation of Propulsion
The acceleration, deceleration and uniform motion are realized by
77
changing the swing frequency of the robot fish tail. This is realized by
sending different signals to the motors driving the links of the tail.
Increasing the duty ratio of the PWM signal to the tail motors results in
the increase of the tail's swing frequency which increases the fish’s
swimming speed. On the contrary, reducing the duty ratio of the PWM
signal will result in the deceleration of the speed. If the tail motor
rotates uniformly, the robot fish will swim at uniform velocity [5].
In addition, the robot fish can be considered to realize swimming
backwards according to the study on kinematics and kinetics of the
Europe eel [120].
3.5.2. Swimming Direction Control
The orientation control is realized by superimposing different
link’s deflection. It is necessary to ensure that the oscillating rule
matches Eq. 3.1 in turning, so the arc is chosen as the oscillating axis
of the links. Correcting Eq. 3.1 gets Eq. 3.2 [121, 122]:
2 2 21 2( , ) [( )][sin( )]bodyy x t c x c x kx t R x Rω= + + + − − 3.2
where R is the radius of the tail axis, which is connected with the
turning radius. A sample of the corrected fish body wave curve is
shown in
78
1l
2l3l
4l
( )dm
( )dm
Figure 3:10.
1l
2l3l
4l
( )dm
( )dm
Figure 3:10: The Corrected Fish Body Wave Curve
79
3.5.3. Diving Control
As described above, the robot fish pitch uses the
barycenter-adjustor to change its posture [120]. As shown in Figure
3:11, O0 and O1 are respectively the initial position of buoyancy (FB)
centre and the gravity centre. m is the weight of the adjustor. M is the
fish weight without m. r is the length of the turning arm. When the
pitch motor turns θ (clockwise, assumed to be “+”), the
barycenter-adjustor moves forward. As a result, the robot fish’s gravity
centre moves forward to O1' and the robot fish gets a pitch angle α,
together with the tail’s swinging movement, it will swim downwards.
Figure 3:11: The Moment Analysis of barycenter-adjustor
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3.6. Prototype of the Robot Fish
Figure 3:12 gives a functional prototype of the biomimetic robot
fish with a flexible tail for propulsion, a barycenter-adjustor for diving
control and an information relay system for communicating to the
upper console. The hard head made of FRP contains and protects the
important MCU, batteries, sensors and peripherals. Three infrared
sensors are mounted on the left, front and right side of the robot fish
head for the detecting of obstacles, a pressure sensor is set on the body
for depth data feedback and a camera is installed on the fish head for
the obtaining of visual information. Jtag and recharge interface are also
mounted on the head for the convenience of software updating and
battery recharging. The whole robot fish size is about 620×160×80
mm3.
Figure 3:12: The functional prototype of the biomimetic robot fish
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3.7. Conclusions
In this chapter, a fully functional biomimetic robot fish with a
carangiform tail for propulsion and barycenter-adjustor for diving was
designed based on the analysis of propulsion and maneuvering
mechanisms for carangiform swimming. An information relay system
on water was designed for information transmission with the upper
console. The sensor information processing of the fish were studied.
The following two chapters will respectively demonstrate the
kinematic modeling and CFD simulation of the robot fish and a new
idea of adding haptics into the robot fish system will be described. This
will let the operator feel the force that the robot fish get when it is
swimming in water.
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4. Kinematic Modeling of Biomimetic Underwater Robot Locomotion
This chapter proposes a kinematic modeling method for the
biomimetic underwater robot locomotion in order to develop a simple
model to quickly analyse the swimming robot fish.
4.1. Introduction
The kinematic performance of underwater robot fish has been
studied, including the analysis of thrust forces and frictional forces, the
control the movement of robot fishes and to develop useful
applications [79, 97, 123]. McIsaac K. A., et al. [79] gave a Lagrangian
model, reduced by Lie group symmetries, for a symmetrical structured
robot eel. Boyer F., et al. [97] presented a dynamic modeling of a
continuous three-dimensional swimming eel-like robot. Morgansen K.
A., et al. [89] studied nonlinear control methods of robot fish
locomotion.
A kinematic modeling of biomimetic underwater robot
locomotion is offered. In this kinematic modeling method, a
Lagrangian function is built for free swimming robot fish based on a
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simplified geometric model as coupling the kinematic law of
continuous motion and the forces acted on the robot fish cannot be
calculated respectively. The fluid force acting on the robot fish is
divided into three components: the pressure on links, the approach
stream pressure and the frictional force. The movement of the robot
fish can be obtained by solving the second kind Lagrangian equation
and the fluid force. The forward motion of the swimming robot fish is
simulated and verified by experiment.
4.2. Problem Formulation
As the robot fish swimming action involves the kinematics of its
body and the hydrodynamic interaction with the surrounding fluid, it is
difficult to formulate a precise mathematical model by purely
analytical approaches. Kinematics and hydrodynamics modeling is one
of the most difficult tasks in robot fish research. Researchers have
focused on studying the mechanical movement of fishes. Most of the
obtained results are described by complex differential equations on the
theoretical analysis, but not on the kinematics, which cannot be used
conveniently for robot fish motion analysis and control.
On the other hand, the locomotion of fish in nature is continuous
and smooth due to the movements of a large number of spinal joints
smoothed by fish muscles. But in most robot fish, the machines are
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applied to simulate a small number of joints in the spine of fish and the
motors are used to simulate the muscle motion of fish. Four joints are
used in this case so the robot fish cannot be regarded as a smooth form,
but a cascade of multi-joint movement.
The basic theory for modeling the biomimetic robot fish is to
build the Lagrangian function unrelated with the internal force based
on the structure of four cascaded joints. The generalized forces from
the second kind Lagrange's equation are equal to the fluid forces
calculated according to the hydrodynamics. Then a series of partial
differential equations can be built to solve the movement of the robot
fish.
4.3. Outline of the Lagrangian Method
Robot dynamics is concerned with the relationship between the
forces and torque acting on a robot mechanism and the accelerations
they produce. To make the robot accelerate, the drive must provide
sufficient force and torque to drive the robot movement. Establishing
dynamic equations for the robot to determine the force, mass and
acceleration, and their relationship with the torque, moment of inertia
and angular acceleration, will be useful for the calculation of the
required force to complete a specific motion. Kinematic analysis of the
robot will help designers determine the external maximum load and
85
select the appropriate drives.
As the mechanical structure of the robot fish is quite similar to the
multi-joint series structure of industrial robots, the dynamics analysis
and modeling will be mainly based on Lagrange mechanics and
Newton's mechanics. For industrial robots with multi-degrees of
freedom and three-dimensional mass distribution, using Lagrangian
mechanics can create a well-structured robot dynamic equation.
Lagrangian mechanics is a method that describes a time derivative and
system variables derivative based on the energy item. The Lagrangian
for classical mechanics is taken to be the difference between the kinetic
energy and the potential energy, as Eq. 4.1:
PKL −= 4.1
where, L is the Lagrangian function, K is the system kinetic energy, P
is the potential energy.
For an industrial robot, in Eq. 4.1, K is the total kinetic energy of
the motion arm, P is the total potential energy of the motion arm. So
the Lagrangian-Euler function is obtained:
ii i
d L Ldt q q
τ⎡ ⎤∂ ∂= −⎢ ⎥∂ ∂⎣ ⎦&
4.2
in which, L is the Lagrangian function, iτ is the system generalized
force or torque, iq is the system variables, iq& is the first derivative of
the system variables, 1, 2, , i n= K .
86
For industrial robots, iτ is the generalized force or torque which
works on the ith joint in the system to drive the ith member bar, iq is
the generalized coordinates for the operating arm, iq& is the first
derivative of the generalized coordinates for the operating arm. Known
from Eq. 4.2, a group of generalized coordinates should be selected
which can easily and accurately describe the system. Because the angle
of the rotating joint and the displacement of the moving joint of the
industrial robot can be measured by potentiometers, encoders and other
kinds of sensors, the industrial robot generalized coordinates are
usually defined by the angle and the displacement of the joints.
As the robot fish keeps a continuous locomotion in water and gets
coupled fluid forces, which cannot be calculated independently, the
Lagrange function was established for free moving robot fish
according to the mechanical characteristics of the joint structure. The
fluid forces that the robot fish suffers in water were also simplified into
the side pressure, the facing flow resistance, and the friction resistance.
According to the above second Lagrange equation, I solved the robot
fish real-time motion, calculated the kinematic parameters and then
offered the simulation results of its various movement strategies. The
optimal parameters of the robot fish locomotion were obtained
according to this simulation calculation. Finally, the simulation results
were verified by experiments made on a global test platform with
87
visual positioning of the robot fish.
4.4. Kinematic Modeling of the Robot fish
4.4.1. Geometry Simplification of the Robot Fish
The propeller of the robot fish developed in this study is
essentially different from the traditional AUV, and there is not any
existing model for the movement. To analyse, control and optimize the
motion of the robot fish, a motion model is needed. This robot fish is a
typical serial link robot, in which the relationship between its
movement and energy can be represented by the Lagrange equations.
The robot fish has a significant difference to general robots in
kinematics. It has neither any fixed base (such as the fixed point of a
robot arm), nor any fixed reference system (such as the ground
reference system of a mobile robot) in its motion. The robot fish
swimming in water is completely free and the locomotion of each joint
interacts with water which determines the magnitude and direction of
the fluid forces. The forces also determine the robot fish’s movement.
In another word, the kinematics and dynamic properties are
interdependent and a combined solution is required.
Some assumptions are made to simplify the simulation:
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(1) The body of the robot fish can be treated as five plates jointed
together [79, 123].
(2) The robot fish swims in still water, and it is not affected by the
reflection wave from the environment.
(3) The deformation of the robot fish can be ignored except for
the motion of the joints.
The robot fish can be treated as being made up of three simple
parts: a hard head, a flexible tail and a crescent-shaped caudal fin. The
head moves passively to some extent, and the tail in the mechanical
point of view is designed to be a multi-joint series-connected structure.
The robot fish joints are redefined. The head and the tail are no longer
distinguished so that all parts are considered as links [79, 89, 96, 99],
as shown in Figure 4:1:
Figure 4:1: Robot Fish Joint-link Structure
Two coordinates, a world rectangular coordinate system (WRCS)
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and a polar coordinate system, are given to describe the robot fish
motion, shown in Figure 4:2. XOY is the WRCS. Another coordinate
is the polar coordinate system with the pole O at the first joint and the
polar axis pointing in the tail’s initial direction when the fish is in a
naturally laxative status.
Axial Body Displacement 1l 2l 4l
3l
1φ
2φ3φ
4φ
5l
Figure 4:2: Simplified Coordinates of the Robot Rish and its Parameters
Definition
The traveling body-wave is decomposed into two parts: the
time-independent spline curve sequences in an oscillation period,
which is described by Eq. 4.3, and the time-dependent oscillating
frequency, which is described as Eq. 4.4
)])][sin([(),( 221 tkxxcxctxybody ω++= 4.3
21 2
2( , ) [( )][sin( )]bodyy x i c x c x kx iMπ= + ±
4.4
But it is too difficult to calculate above equations, the joint angles
are defined as Eq. 4.5:
( ) sin( )i i it A tφ ω ψ= + 4.5
90
where iA is ith link’s amplitude, iψ is ith link’s phase, 1, ..., 1i N= − ,
N is the number of links. Both of them can be calculated from Eq. 4.3
as Eq. 4.6:
1 12
1 22 2 2
1 22 2
1
2
( ( ) )( )
i i
i j jN Nn n
j jn ni
i jj
AmpA c l c lc l c l
k lψ
+ +
= =
= =
+
=
= ++
=
∑ ∑∑ ∑
∑4.6
Where, Amp is adjustable caudal swinging amplitude,and
21 2
2 2
( )N N
j jn n
c l c l= =
+∑ ∑ is normalization coefficient.
4.4.2. The Lagrangean Equation of the Robot Fish
rr1ϕ
2θ
1θ
3θ4θ
2ϕ 3ϕ
1 1( , )g gx y
1 1( , )f fx y2 2( , )f fx y
5θ4ϕ
Figure 4:3: The Five Links Robot Fish and Some Parameters Definition
Figure 4:3 shows the links at a moment under the coordinate
systems. XOY is the WRCS. In the figure, li is the length of ith link of
the robot fish. θi is the angle between ith link and the polar coordinate,
φi is the angle between the ith link and the extension line of the (i-1)th
91
link. Both of them are anti-clockwise positive. ( ,f fi ix y ), ( ,g g
i ix y ) and
( ,i ix y ) are the center of form,the center of gravity and the extreme
point near fish head of the ith link, respectively. Fi is the force the ith
link suffers, which will be decomposed into several component forces
in the following analysis. The joint angle φi is pre-given according to
the fish swimming mechanism.
The potential energy is a constant, E, while the robot fish swims
in water. The kinetic energy of each link is the sum of the kinetic
energy of translation under WRCS and the kinetic energy of rotation
under the centre-of-mass system, so the Lagrange’s function is defined
as Eq. 4.7:
( ) ( )( ) ( )
2 2
1 1
22 2
1 1
1 12 21 12 2
N N
i i i ii iN N
g gi i i i i
i i
L m v I E
m x y I E
ω
θ
= =
= =
= + +
= + + +
∑ ∑
∑ ∑ && &
4.7
where,mi is the mass of the ith link,Ii is the moment of inertia of the ith
link under the centre-of-mass system. 1 1 2, , x y θ are selected as the
generalized coordinate, let 1 1 2, , X x Y y θ= = Θ= . gil is the distance
between ( 1 1,i ix y− − ) and ( ,g gi ix y ). They can be written into:
92
1 1 1 1
1 1 1 1
2 2 2
2 2 2
1 1 21
2
1
2
1
2
( ) cos
( )sin
cos
sin,
cos cos 3
sin sin 3
3
g g
g g
g g
g g
ig gi j j i i
j
ig gi j j i i
j
i
i jj
x X l l
y Y l l
x X l
y Y l
x X l l i
y Y l l i
i
θθ
θθ
θ ϕ θ
θ θ
θ θ
θ ϕ
−
=
−
=
−
=
⎧ = − −
= − −
= +
= += Θ − = Θ
⎨= + + ≥
= + + ≥
= Θ + ≥
∑
∑
∑
⎪⎪⎪⎪⎪⎪⎪⎪
⎪⎪⎪⎪⎪⎪⎪⎪⎩
4.8
Rewrite the Lagrange’s function into ( , , )L L X Y= Θ :
( ) ( )( )( ) ( )
( ) ( ) ( )( )( )
2
1 1 1
2 2
2 2 1
2
1 1 1
2 22 2 2
1 ( - ) - sin -21 1sin -2 21 - - - cos -21 1- cos2 2
g
g
g
g
L m X l l
m X l I
m Y l l
m Y l I
ϕ ϕ
ϕ
ϕ ϕ
= + Θ Θ
+ + Θ Θ + Θ
+ Θ Θ
+ Θ Θ + Θ
&& &
& && &
&& &
& &
2
-1
3 2
2-1
3 2
2-1
3 2
1 cos cos2
1 sin sin2
12
N ig
i j j i ii j
N ig
i j j i ii j
N N
i i ji j
dm X l ldt
dm Y l ldt
dI Edt
θ θ
θ θ
ϕ
= =
= =
= =
⎡ ⎤⎛ ⎞+ + +⎢ ⎥⎜ ⎟
⎢ ⎥⎝ ⎠⎣ ⎦
⎡ ⎤⎛ ⎞+ + +⎢ ⎥⎜ ⎟
⎢ ⎥⎝ ⎠⎣ ⎦
⎡ ⎤⎛ ⎞+ Θ + +⎢ ⎥⎜ ⎟
⎢ ⎥⎝ ⎠⎣ ⎦
∑ ∑
∑ ∑
∑ ∑
4.9
thus the Lagrange's equations of the second kind are:
X
Y
d L LFdt X Xd L LFdt Y Y
d L LMdtΘ
∂ ∂⎧ = −⎪ ∂ ∂⎪ ∂ ∂⎪ = −⎨ ∂ ∂⎪
∂ ∂⎪ = −⎪ ∂Θ ∂Θ⎩
&
&
&
4.10
93
where, XF , YF and MΘ are the components on X-axis and Y-axis of
the resultant of forces and the resultant moment on ( 1 1,x y ) respectively.
4.5. Fluid Modeling the Robot Fish
The fluid forces acting on the robot fish are decided by its
instantaneous movement. A fluid drag model is employed to analyse
the forces perpendicular to the surface of the swimming robot fish,
which has been used extensively in the case of the large Reynolds
number in the literature [79, 89, 96, 124, 125]. That is:
2sgn( )( )F v vμ ⊥ ⊥= − 4.11
where, 12
CSμ ρ= is the drag coefficient, ρ is the density of water, C is
shape coefficient and S is effective area. v ⊥ is the projection of the
velocity along the direction perpendicular to the surface.
The forces acting on the robot fish are divided to three
components: pressure on links, approach stream pressure and friction:
(1) The pressure on links: the fluid force on the robot fish’s ith link
when it swings:
2
sgn( )i i i i iF v v v vμ μ⊥ ⊥ ⊥ ⊥ ⊥ ⊥ ⊥= − = − 4.12
where, iF ⊥
is the pressure on ith link, iv⊥
is the projection of the
velocity of ith link along the perpendicular direction, and u⊥ is the
drag coefficient with C of flat plate type [9], and:
94
sin cosf f
i ii i i
dx dyvdt dt
θ θ⊥ = − 4.13
where,
1 1 1 1
1 1 1 1
2 2 2
2 2 21
2
( )cos
( )sin
cos
sin
cos cos 3
f f
f f
f f
f f
if f
i j j i ij
x X l l
y Y l l
x X l
y Y l
x X l l i
θθ
θθ
θ θ−
=
⎧ = − −⎪
= − −⎪⎪ = +⎪⎨
= +⎪⎪⎪ = + + ≥⎪⎩
∑
1
2
1
2
sin sin 3
3
if f
i j j i ij
N
i jj
y Y l l i
i
θ θ
θ ϕ
−
=
−
=
⎧ = + + ≥⎪⎪⎨⎪ = Θ + ≥⎪⎩
∑
∑
4.14
where, f
il is the length from ( 1 1,i ix y− − ) to ( ,f fi ix y ).
(2) The approach stream pressure: It is introduced because the
water pushes on the cross section of the robot fish when the robot fish
swims forward.
1 1 1F u v v= = = == − 4.15
where, 1 1 1cos sinv X Yθ θ= = +& & is the projection of the velocity of the first
link along the parallel direction, and u = is drag coefficient with the
type of bullet[110]. Considering the cross-sectional area of the second
link is much smaller than the first, the flow’s effect is reduced and 2F=
is ignored.
(3) The friction drag: There is friction drag acting on the surface
of the robot fish which is parallel to the body. It is often evaluated
empirically (30%-50% of the approach stream pressure). 50% is
selected because of the unsmooth surface of the robot fish.
95
1 1 150%2f
uF F v v=
= = == = − 4.16
The composition of forces on the X-axis and Y-axis are:
( )1 11
cosN
xx i f
i
F F F F θ=
=
= + +∑
4.17
( )1 11
sinN
yy i f
i
F F F F θ=
=
= + +∑
4.18
The composition of moment act on the joint is:
1 1
( ) ( )N N
x f y fi i i i
i i
M F y Y F x XΘ= =
⎡ ⎤= − − + −⎣ ⎦∑ ∑
4.19
From Eq. 4.16-4.18 and 4.10 the differential equation group of
, , ,X Y tΘ can be obtained:
( )
( )
1 11
1 11
1 1
cos
sin
( ) ( )
Nx
X i fiN
yY i f
iN N
x f y fi i i i
i i
d L LF F F Fdt X Xd L LF F F Fdt Y Yd L LM F y Y F x Xdt
θ
θ
=
=
=
=
Θ= =
∂ ∂⎧ = − = + +⎪ ∂ ∂⎪∂ ∂⎪ = − = + +⎨ ∂ ∂⎪
⎪ ∂ ∂ ⎡ ⎤= − = − − + −⎪ ⎣ ⎦∂Θ ∂Θ⎩
∑
∑
∑ ∑
&
&
&
4.20
The equations can be solved by numerical method with boundary
conditions at initial time. The action of the robot fish depends on the
cooperation among all of the joint angles.
4.6. Kinematic Modeling Results
The experiments were implemented according to Eq. 3.1where
c1=0.05, c2=0.09 and k=0.5, in the pool of 4.0m×3.0m×0.75m. Figure
4:4 gives the simulation results of forces acting on the robot fish in
96
forward motion with Amp =π / 4, Aturn =0, f = 10/7 Hz. The simulation
scalar velocity was stabilized on 0.179531 m/s (similar to the
experiment velocity of 0.18 m/s). Its direction deflected a little from
the original one because the component force in the X-axis direction
was asymmetric.
In next chapter, the force will be compared with the CFD
simualtion results.
5 10 15tHsL
-2
2
4
6
8FxHNL
97
Figure 4:4: Simulation results of forces acting on the robot fish in forward
motion
4.7. Conclusion
In this chapter, the Kinematic Modeling of the robot fish was
5 10 15tHsL
-4
-2
2
FyHNL
5 10 15tHsL1
2
3
4
5
6
FHNL
98
presented. The multi-joint robot fish was simplified as the link
structure. Basing on this typical series structure, the Lagrangian
method was introduced for analysis. On one hand, the Lagrangian
energy function for the robot fish in the freedom movement was
written according to the robot fish functional principle and the
geometry. On the other hand, the fluid forces of the robot fish were
simplified into three components: the link positive pressure, incident
flow resistance and friction resistance, which were calculated
according to the principles of hydromechanics. Finally, a kinematics -
mechanics combined equation for the robot fish was obtained by
uniting the generalized force and fluid force according to their
relationship in the Lagrange equation on which the real-time motion
can be solved.
The kinematic modeling simulation provided the real-time forces
for the forward swimming robot fish and was verified by experiment.
99
5. Hydrodynamic Analysis of the Biomimetic Robot Fish & Application on the Haptic Robot Fish System
5.1. Introduction
Most existing control algorithms for robot fish are based on a
simplified propulsive model, which only provides a rough prediction of
the effect of hydrodynamics on robot fish. To obtain an accurate
prediction, it is necessary to conduct dynamic analysis of the
surrounding fluid by CFD [100].
This chapter presents a 3D CFD simulation for the biomimetic
robot fish. Fluent® and UDF are used to define the movement of the
robot fish. The Dynamic Mesh is used to mimic the fish swimming in
water. Hydrodynamic analysis produces significant information on
flow pattern, velocity and pressure fields to help readers understand the
internal information on the hydrodynamic properties of the robot fish.
This is also used to improve the design, remote control and flexibility
of the underwater robot fish. The 3D CFD simulation is investigated
for the robot fish prototype using Fluent® 6.3.26.
100
5.2. Problem formulation
CFD simulation processing large amount data is time consuming.
The first target is the method of reducing the number of the mesh
nodes and elements created for the geometries. Another important
issue to be resolved is how to mimic the body motion of the robot fish.
The irregular profile of the robot fish brings difficulties into
generating the geometries and the mesh for its 3D CFD simulation.
The type and the number of the elements used in the simulation will
directly affect computation efficiency and accuracy.
The 3D flexible body deformation of the fish swimming in water
is so complex that all nodes need be controlled exactly to describe the
motion of the robot fish. The law of the robot fish motion should be
found to help researchers redefine and program in order to control
every node on the robot fish to mimic its real swimming motion.
5.3. 3D Hydrodynamic Model
5.3.1. Biomimetic Robot Fish and Pool Geometries
The 3D geometry and the meshes of the robot fish were generated
by Gambit (V2.3.16). In the current study, the effect of the connection
cable between the robot fish and the buoyage information relay was
101
ignored to simplify the robot fish model.
The dimension of the robot fish is 0.62m×0.16m×0.08m (length ×
max high × max width). To allocate enough space for approach
accurate hydrodynamic properties, a pool was designed to be
9m×9m×4m. The pool walls were defined as moving walls and their
local velocities depend on the fluid velocity. The main currents were
backward flow generated by the locomotion of the fish tail so that the
robot fish was located at the centre of the vertical cross section of the
pool, while the distance between the fish head and the pool inlet was
1.53m.
5.3.2. Mesh Scheme
5.3.2.1. Requirements and Conditions of Mesh Scheme
In the last 30 years, CFD has achieved significant progress and is
considered to be very close to its maturing stage in the computation of
flows around airplanes at designed conditions. It also can solve the
simulation problems for geometrically complex and largely moving
and deforming bodies. The Dynamic-Mesh Method is an automatic
mesh generation method that controls the grid moves accompanied
with body movement and deformation. This method will be used to
control the nodes on the robot fish surface in the simulation which will
102
conduct the effect of the robot fish motion. When the water around the
robot fish is squeezed and stretched, the hydrodynamic force can be
calculated.
However, the Dynamic Mesh method was used for the processing
of the couple between the robot fish changing shape and the water.
Tetrahedron mesh elements must be chosen in the concerned area. This
kind of element has more elements and less accurate calculation than
any other kinds of mesh elements. An elaborate planned mesh scheme
is needed made up of tetrahedron, and other kinds, of mesh elements. It
will be expatiated later.
5.3.2.2. Logical Division of Fluid Domain
As discussed above, tetrahedron mesh elements were only used
for the cube area (0.91m×0.7m×0.4m) close to the robot fish, while
Quant mesh elements as big as possible were used for other areas to
reduce the number of elements. The distance between the small cube
with tetrahedron elements and the inlet was 1.42 m. This meshing
scheme, with high qualified tetrahedron around the robot fish, would
give enough space to process meshing and approach a lower number of
meshes to reduce computational time.
On the other hand, hexahedral elements were selected to fill the
rest of the volume of the water, which could produce highly accurate
103
calculation with smaller numbers of mesh elements than that of the
tetrahedron elements. The mesh grew at the rate of 1.5 ratio from the
cube around the robot fish to the walls of the pool.
5.3.2.3. Mesh Scheme Specific Implementation
The mesh sizes are determined based on the characteristics of
fluid dynamics of the water close to the fish:
Reynolds number,
5Re 1.1 10ULv
= = × 5.1
The thickness of the boundary,
14.64 0.00865( )Re
L mσ = × × =
5.2
where U=0.18 m/s (it is the experimental velocity of the robot fish)
L=0.62 m (the length of the robot fish)
v=1.01×10-6 m·kg·s (water viscosity)
To reach an accurate calculation of the forces acting on the fish
surface and to reduce the number of meshes, a boundary schema with a
growing rate of 1.4 ratio and 4 layers was applied for mashing the
hydrodynamic boundary of the robot fish. According to Eq. 5.2, the
size of the minimum grids adhered to the robot fish is 2 mm.
An effective mesh schedule was produced with the above settings,
which proved that logical division of the fluid domain works
104
excellently in this project.
Finally, this simulation contained a total of 189683 nodes and
837773 elements for the fluid domain. Figure 5:1 & Figure 5:2 show
the mesh distribution in the fluid area and a close view around the fish.
Figure 5:1: Mesh of the Biomimetic Robot Fish
Figure 5:2: Mesh scheme for the region close to Robot Fish
5.3.3. Mathematic Description of the Robot Fish Locomotion
In this section, how to mimic the robot fish locomotion in CFD
simulation will be introduced.
105
5.3.3.1. Conditions of 3D Mathematic Description
Figure 5:3 and Figure 5:4 respectively describe the 3D geometric
outline of the robot fish and the parameters of its tail.
Figure 5:3: The outline of the Robot Fish
106
Figure 5:4: Parameters of the Robot Fish Tail (Unit: mm)
Every point on the robot fish tail can be defined by mathematical
equations easily when it is in a natural relaxed status which will be the
initial status of the robot fish. The motion law of the robot fish tail
centerline is described by Eq. 3.1. But the 3D fish tail is quite flexible,
which creates a problem in controlling the movement of every point on
the surface of robot fish tail to mimic the action of the robot fish. If the
mathematical description of the robot locomotion can be found, UDF
can be used to realize this aim and the DEFINE macro of
DEFINE_GRID_MOTION[126] will work well in the control of every
slight motion of the robot fish tail.
107
5.3.3.2. Robot Fish Tail Waving Description
In describing the position of every node on the robot fish surface,
the most important thing is the relationship between it and its
neighboring nodes. The node motion rules are specified as follows
according to the characteristics of the swimming robot fish (refer to
Figure 5:5):
(1) A node always tries to keep the same projection position on
the centerline and the same distance to the centerline.
(2) A node cannot change the location sequence and will keep a
certain distance with its neighbor nodes.
(3) Every node always keeps its original horizontal position.
(4) The centerline of the robot fish is flexible but not elastic. The
surface of the robot fish tail is unlimitedly flexible.
Figure 5:5: Node Movement
According the above assumptions for node movement, one can
108
program and control the position of every node on the robot fish tail
using UDF.
5.3.3.3. Implement of the Robot Fish Tail Movement with
Fluent®
As discussed above, the oscillation of the fish tail (moving part-1)
and the caudal fin (moving part-2) as shown in Figure 5:6, are complex
and flexible, and the DEFINE macro DEFINE_GRID_MOTION was
chosen to describe the movement of the fish tail and the caudal fin. A
program was developed based on Eq. 3.1 and c1=0.05, c2=0.09 and
k=0.5.
Figure 5:6: Meshes on Robot Fish Body
To couple accurately the posture of the fish body in time, the
109
performance of the dynamic mesh is quite important in the simulation.
Smoothing and Remeshing mesh method was used here. The relative
parameters used are listed in Table 5.1.
A commercial CFD code, Fluent® 6.3.26 with a standard k–
epsilon turbulent model, and standard wall functions, were used in all
simulations. Table 5.1: Parameters for dynamic mesh
Mesh Methods
Parameters Setting
Items Setting
Smoothing
Spring Constant Factor 0.05
Boundary Node Relaxation 0.8
Convergence Tolerance 1e-05
Number of Iterations 100
Remeshing
Minimum Length Scale (m) 0.00072372
Maximum Length Scale (m) 0.0008
Maximum Cell Skewness 0.8
Maximum Face Skewness 0.79
Size Rmesh Interval 1
Size Function Resolution 1
Size Function Variation 48.94077
Size Function Rate 0.7
In this section, the 3D body swing of the robot fish was
successfully imitated using UDF, which is the solid foundation of the
fluent simulation. The rules of the nodes motion on the robot fish tail
were prompted. This is simple and can be used in any kind of model of
110
robot fish movement.
5.4. Hydrodynamic Analysis
In the simulations, the robot fish oscillates its tail and caudal fin at
T = 0.7s (swinging period). The pressure distribution will be analysed
on the horizontal cross section of the pool at the middle position
(M-view), as in Figure 5:7
Figure 5:7: M-View
5.4.1. Design Properties of the Robot Fish
1. Velocity effect on the robot fish. Figure 5:8 shows the velocity
vectors on the robot fish surface when it stops in steady flow,
111
coming from its head to tail at velocity of 0.1 m/s. The
conclusion can be drawn easily that the robot fish’s shape is
excellent with no disorder flow on the fish surface and that it
is suitable for swimming in water.
Figure 5:8: Velocity Vectors on the Robot Fish Surface
2. The Pathline of the Robot Fish. Figure 5:9 (the same condition
with item 1) shows flow velocity profiles along the robot fish
surface. It indicates that the surface of the robot fish is
clipper-built and will get high performance in water.
112
Figure 5:9: The Pathlines of the Robot Fish
3. Hydrodynamic analysis – pressure. Figure 5:10 (the same
condition with the above item 1) manifests that there are two
kinds of point: one is stagnation point, a normal point, where
the robot fish meets the coming flow; and the other is shoulder
point need to be enhanced in next outline design.
Figure 5:10: Hydrodynamic analysis – pressure
The above results illustrate that the outline design of the robot fish
113
is quite good. In the next step, we will enter the hydrodynamic analysis
of the robot fish.
5.4.2. Pressure Distribution around the Swimming Robot
Fish
Figure 5:11: Pressure Contours of the M-view at 4 Locomotion Times (N×m–2) (a) approaching the left maximal rotation position (t = 0.1 s); (b) intermedial position
during oscillating motion (t = 0.25 s); (c) going on intermedial position during oscillating motion (t = 0.4 s); (d) approaching right maximal rotation position (t =0.55
s). (It is supposed that a robot fish locomotion period begin from the position t=0 according the Equation 1)
Figure 5:11 shows the pressure contours at four locomotion times
(“The right” / “the left” means the side of the right / left hand when one
(a) 0.1s (b) 0.25s
(c) 0.4s (d) 0.55s
114
stands on the point of the robot fish’s inertia centre and faces to the
fish head. ):
At t = 0.1s (Figure 5:11(a)), the fish tail and the caudal fin are
swinging from the right to the left and almost reach the
maximal displacement. On the left side of the fish tail and the
caudal fin, a bigger positive pressure is generated and a wider
distribution than the right side can be found. Especially, the
positive pressure focuses mostly on the rear of the tail, which
generates forces pointing to the right-front of the fish. These
positive pressures are generated as the water is extruded by the
movement of the fish tail and the caudal fin. Also, they grow
bigger along the direction from the fish tail to the caudal fin
due to the growing up amplitudes of the fish tail and the
caudal fin oscillating. This also implies that a tip vortex can be
generated near the edge of the robot fish caudal fin and
considerable fluid is pushed into the downstream region on the
left side of the caudal fin.
At t = 0.25s (Figure 5:11(b)), the robot fish body and the
caudal fin are already swinging back from the left to right.
This action pushes the water away, so a positive pressure is
exerted and widely distributes on the right side of the fish tail
and the caudal fin. Immediately after the anticlockwise stroke
115
began, which is a change of the fish tail swinging direction,
one observes a small positive pressure distribution on the right
side of the caudal fin and a negative pressure distribution on
its left side. This shows the generation of the thrust. The
direction of the thrust is left-front according the angle of the
robot fish body posture.
At t = 0.4s (Figure 5:11(c)), the fish tail and the caudal fin
keep swinging from the left to the right. The positive pressure
grows and turns to the left side of the robot fish. On the other
side of the robot fish body, the negative pressure decreased.
This demonstrates that the robot fish achieves a larger
right-front direction thrust.
At t = 0.55s (Figure 5:11(d)), the fish tail and the caudal fin
keep on swinging from the left to the right and its body
reaches almost the most flexible position. The positive
pressure grows up quickly and distributes on both the left side
of the middle tail and the right side of the caudal fin. On the
contrary, a negative pressure distributes on the right side of the
tail. At this point, the robot fish achieves the largest forward
direction thrust during the whole period.
After the period described above, the fish tail and the caudal
fin continue to swing for the next half period.
116
According to the above analysis, the resulting forces that the robot
fish acquired by periodically oscillating its tail and caudal fin can be
divided into two types, the fluctuant thrust at forward direction and the
drag at left-right direction.
5.4.3. Velocity Distribution around the Swimming Robot
Fish
The velocity contours of the robot fish at critical instants are
shown in Figure 5:12 during the oscillation, using the same instants
and views as the ones for pressure contours analysis.
At t = 0.1s (Figure 5:12(a)), a counter-rotating vortex is
observed. This vortex is shed from the distal edge (especially
the tip edge of the tail fin) on the robot fish. The shedding of
vortex may be one of the main effects on the pressure
distribution at the robot fish surface mentioned in the pressure
analysis.
At t = 0.25s (Figure 5:12(b)), a thin clockwise vortex sheds
from the tip of the caudal fin at the beginning of the fish tail
and the caudal fin reverse motion.
At t = 0.4s (Figure 5:12(c)), one observes a clockwise vortex
at the right middle side of the fish tail. The shedding of this
vortex into the wake leads to a momentary increase in the
117
thrust.
At t = 0.55s (Figure 5:12(d)), a large anticlockwise vortex
sheds at the left middle side of the fish tail. Two clockwise
vortexes are shed at the right side of the upper tail and the
caudal fin. The shedding of these vortexes into the wake leads
to larger increase in the thrust than the one at t = 0.4s.
After the periods described above, the robot fish will endure the
next similar half period.
Figure 5:12: Velocity Distribution
(a) 0.1s (b) 0.25s
(b) 0.4s (d) 0.55s
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5.4.4. Forces of the Swimming Robot Fish
The robot fish oscillates its tail and caudal fin at T = 0.7s
(swinging period). After ten swinging periods, the inlet velocity
becomes stable and is about 0.18m/s, which is the same as the
experiments. This says the simulation is valid. Figure 5:13 shows the
forces exerted on the robot fish along with X and Z axis directions. In
the X-axis direction, the fish suffers a much bigger force than in the
Z-axis direction. The composite of the forces in the X axis direction are
almost zero generated by the swing movement of the fish tail and the
caudal fin. It will be counteracted by the force arisen from the
movement of inside motors. The force in the Z-axis direction is always
positive. This is caused by the movement of the fish tail and the tail fin.
The robot fish will be driven by the force in the Z-axis direction.
Moreover, the force in the Z-axis direction is about 3N, which is
coincident with the results from the Kinematic Modeling simulation
(referring Figure 4:4. Please note: Z-axis is equivalent to X-axis in the
Kinematic Modeling simulation. X-axis is equivalent to Y-axis in the
Kinematic Modeling simulation)
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Figure 5:13: Forces in X and Z Directions
5.5. Haptic Application on the Robot Fish
Haptic application has been a popular development in kinds of
areas in the field of robotics. To easily control the robot fish movement,
let operators feel the force and study the hydrodynamic properties of
the robot fish when it is swimming in water, a 3D interactive
visualization haptic robot fish system with haptic feedback was
designed in this section. The model was manipulated to visualize the
effects of force feedback using the most advanced industry haptic
device – a SensAble Technologies PHANTOM Omni – to provide
continual force feedback for studying and controlling the movements
of the robot fish.
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5.5.1. Issues to Be Solved
Several problems in designing the haptic robot fish system are
considered.
(1) Haptic interfaces are used to provide touch feedback to a user
from a virtual (or remote) environment. The haptic device
needs to be driven in real-time to let the user feel the force the
robot fish gets in water. Applying force sensors to the robot
fish is definitely the most direct method to reach this aim.
However, any force sensors are not used in current haptic
robot fish system. The haptic framework of the robot fish will
be set up using a preset database. It even will calculate the
force in real-time instead of force data from sensors. These
will help the setting up of the virtual force feedback quickly
and easily for the haptic robot fish system in the initially
period of this research project. It will also guide on designing
the real force sensors applied on the robot fish.
(2) How to get the position of the robot fish and display it on the
PC display port? A good choice is to employ a camera and use
the digital image processing to get the position and posture of
the robot fish. Another choice is using the pre-calculated
results from simulations to estimate the position which will
also help on controlling the robot fish.
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(3) How to use the haptic controller (Omni phantom) to send
control commands to the robot fish? One method is using
pre-designed commands. Another method is to use the haptic
device to measure the intention of the operator, driving the
robot fish to go forward, turn or dive at some level speed, then
translate it into commands and send to the robot fish.
5.5.2. Haptic Robot Fish System Framework
The proposed haptic robot fish system includes two main steps:
First, the position and posture of the robot fish is achieved for the
virtual display, and the force the robot fish gets in water has been
obtained for the haptic device force feedback; Second, the control
commands of the operator can be defined according to the real-time
status of the current task implementation and transferred to the robot
fish.
The haptic robot fish system employs three parts to achieve the
two procedures: First is a display used to show 3D virtual robot fish;
the second is a computer to fetch the information from the robot fish
from pre-set database or calculate it in real time and communicate with
both the robot fish and the haptic device; thirdly is a haptic interface
transferring the information of the control commands and force
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feedback.
Figure 5:14: The Framework of Haptic Robot Fish System
As shown in Figure 5:14, the haptic robot fish system integrates
visual and haptic information to give assistive force feedback through a
haptic controller (Omni Phantom) to the user. A pre-set database
provides force feedback to help the user feel the force that the robot
fish gets in water and the estimated position and posture information of
the robot fish to help display the robot fish in the 3D virtual vision. A
camera is mounted to monitor the whole pool to provide information of
the position. With on-line visual feedback, the fishes’ position and
orientation, the speed of straight swimming and turning performance
can be measured, posture of the robot fish for the 3D virtual display
can be shown, and also help the user to decide the intended path to the
selected target. Furthermore, this real-time system is versatile. The
haptic component can be used for rehabilitation purposes in cases
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where hydrodynamic property analysis can be shown to give the
operator professional information about the robot fish, for example,
pressure distribution at specified cross sections. It can also be used for
teleoperation with force feedback in either the supervisory or automatic
modes. The former one provides a very indirect method of interaction
with the preset hydrodynamic analysis database.
Figure 5:15: Virtual Display and Haptic Operating
124
Figure 5:16: Command in Virtual Interface
The proposed haptic robot fish system (refer to Figure 5:15 &
Figure 5:16, the fish model used for the virtual interface is a fungible
one) employed Omni Phantom haptic device as the hardware platform.
The system was coded by Visual C++ in Windows XP. The display
design was developed by OpenGL. Force interaction was designed by
calling the Omega 3DOF own modules to communicate with the haptic
robot fish and upper console.
5.5.3. 3D Virtual Display Design
A 3D virtual graphic user interface used in the haptic robot fish
system brings the following advantages:
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(1) The interface enables the user to create the special virtual
robot fish world. For example, the user can decorate the
aquatic environment with static objects and seaweeds, and can
specify the number, type, size, initial positions as well as
individual habits (i.e. innate behavioral characteristics) of the
robot fish.
(2) It allows the user to do experiments with the physical
properties of the robot fish, the hydrodynamic medium and the
mental parameters of the robot fish.
(3) It controls the display of a binocular fish-view from the “eyes”
of the robot fish.
In this thesis, the simulation was made in a simple “environment”,
quiet water area without any obstacle in order to simplify the current
study.
5.5.4. Haptic Robot Fish System Force Feedback Method
The simulation results were used to build up the database for the
haptic robot fish system. The upper console obtains the real-time
movement status of the robot fish and looks up the database to fetch
the information about the simulation results for the haptic interaction
with the operator.
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5.5.4.1. Preset Database Based on Computational Fluid
Dynamics (CFD) Simulation Results
The preset database of the haptic robot fish system includes two
kinds of data:
(1) Composite and component forces along different axes or
based on different effects can be provided according to the
initial conditions, swimming speed, direction and swinging
frequency of the robot fish. They were mapped to the haptic
space using direct force mapping. These force data can be set
up according to the haptic display rendering requirement and
can be rendered stably.
(2) The velocity, pressure field distribution and any other further
information of the robot fish’s hydrodynamic properties can be
provided by CFD simulation.
5.5.4.2. Possibility of Real-time Calculation Based on
Kinematic Modeling
The force rendering frequency of haptic display is required to be
over 1 KHz. Kinematic modeling is performed for different swimming
postures of the robot fish and analytic solutions were calculated by
software Mathematics®, which has strong ability in symbolic
127
computation. As soon as the robot fish’s movement parameters are set,
the calculated force feedback for haptic interacting is satisfies the
haptic rendering requirement.
5.5.4.3. Further Haptic Robot Fish System Design
Further improvement is to apply force sensors into this haptic
robot fish system to implement multi-dimensional force measurement
and hopefully provide a more precise sensation of reality, a step
forward toward the development of a haptic virtual environment. The
force sensors can be applied on the robot fish surface to provide the
force feedback to the haptic robot fish system to let the operator feel
the force of the robot fish directly.
5.6. Underwater Experiments
Experiments are conducted in a pool of 4.0m×3.0m×0.75m.
Figure 5:17 describes a turning process implemented by adding a
deflection to the tail in the experiment pool. This shows the feasibility
of the biomimetic robot fish designed in the present work.
128
(a) (b)
(c) (d)
Figure 5:17: The Image Sequence of the Robot Fish Turning
Table 5.2: Oscillating frequency (Hz) versus Speed (m/s) of straight swimming Frequency 0.5 0.67 0.8 1 1.43 2
Speed 0.09 0.12 0.13 0.15 0.18 0.26
Table 5.2 contains the test results of the oscillating frequency and
the straight swimming speed. It shows a general tendency that the
swimming speed increases with the oscillating frequency. The speed
cannot be infinitely expanded since the servomotors can hardly follow
sufficiently high speeds under high oscillating frequency condition.
It should be noticed, when the robot fish’s tail swinging frequency
is 10/7 Hz (1.43 Hz), its swimming forward velocity was about 0.18
129
m/s. This experimental result is consistent with the simulation results:
• The Kinematic Modeling indicates that the simulation
scalar velocity was stabilized on 0.179531 m/s (similar to
0.18 m/s ) when the robot fish is in forward motion with
Amp =π / 4, Aturn =0, f = 10/7 Hz, (refer to sections 4.6).
• In the CFD simulation, the robot fish oscillates its tail and
caudal fin at T = 0.7s (swinging period). After ten swinging
periods, the inlet velocity becomes stable and is about
0.18m/s too, which illustrates the simulation is valid (refer
to section 5.4.4).
5.7. Conclusion
In this chapter, a computational fluid dynamic model was built for
a biomimetic robot fish. The hydrodynamic properties, such as the
exerted pressure and the force on the fish, have been obtained. They
explained how the fish oscillated the tail and the caudal fin to push
water away behind it and get the thrust pushing it forward.
The CFD simulations provided the information of the flow of
water around the robot fish and the pressure distribution. This will be
used for the optimization and improvement of the design and
fabrication of robot fish. It also provided more complex fluid flow
characteristics for the research and development of robot fish used in
130
different external situations.
A new interactive haptic robot fish system with force feedback for
3D hydrodynamic analysis of the robot fish was also proposed in this
chapter. The haptic robot fish system supports users to understand the
hydrodynamic properties around the robot fish more deeply than other
common visualization systems based only on the graphic visualization
of hydrodynamic analysis. By attaching a haptic interface to the system,
a fully interactive haptic robot fish system in 3D space was developed
for interactive visualization of moving objects inside the display
domain. Hence, one cannot only observe the field distribution maps,
such as velocity and pressure field distributions, but also interactively
perceive the forces at the same time, interactively, in real time. This
system would be applicable for educational and design purposes in
robot fish research.
Some experiments were carried out upon the biomimetic robot
fish, and the results demonstrated the performance of the mechanical
structure and control system of the biomimetic robot fish. The
experiments also verified the simulation results.
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6. Analysis and Discussion on Kinematic Modeling and Computational Fluid Dynamics (CFD) Hydrodynamic Simulation
6.1. Introduction
Kinematic modeling and computational fluid dynamics analysis
have their own significant features. This section will compare their
features and identify their contribution to the haptic robot fish systems.
6.2. Distinguishing Features of Kinematic Modeling
The kinematic modeling used a typical series structure for the
robot fish simulation. On one hand, the Lagrangian energy function for
simplified multi-links structures in free movement was written
according to the robot fish functional principle and the geometry. On
the other hand, the fluid forces on the robot fish were calculated
according to the principles of hydromechanics. Then, the kinematic
equations, combined with mechanics for the robot fish, were obtained
by uniting the generalized forces and fluid forces according their
132
relationship in the Lagrange equation. The components of the resultant
forces in X-axis and Y-axis and the resultant moment of the robot fish
can be calculated according Eq. 4.10. When the boundary conditions at
initial time are set, instantaneous robot fish motion data can be
obtained by solving the equations using numerical method.
This is a quite easy and direct method to look for the movement
data of the whole robot fish, from which the first-hand data can be
gained in order to control robot fish locomotion. It will help the
operators to control robot fish movement on line or make a route
planning off line. The energy consumption for performing the task can
also be estimated via this simulation, so the operators can get guidance
about the implementation strategy.
In summary, the kinematic modeling is a good macroscopic tool
to help the researchers study and control robot fish.
6.3. Distinguishing Feature of Computational Fluid
Dynamics (CFD) Analysis
Compared to the macroscopic kinematic modeling, CFD analysis
can give researchers more detailed information of the robot fish on
both macroscopic and microscopic aspects.
In the macroscopic aspect:
133
(1) The forces on the whole robot fish can be calculated.
(2) The forces acting on any special parts of the robot fish can be
calculated.
(3) Different fluid forces can be calculated separately, such as
thrust, lift and drag.
(4) The pressure and velocity distribution on or around the robot
fish can be analysed.
In the microscopic aspect:
(1) The pressure and velocity on or around every point of the
robot fish can be analysed.
(2) The forces acing on every point of the robot fish can be
calculated.
6.4. Comparison between Kinematic Modeling and
Computational Fluid Dynamics (CFD) Hydrodynamic
Analysis
The kinematic modeling and CFD analysis have their own
significant advantages and disadvantages in the simulation of robot fish
swimming as listed in Table 6.1. Some special properties are compared
in Table 6.2
134
Table 6.1: Comparison between the kinematic modeling and CFD analysis
kinematic
modeling
CFD
analysis
Note
Software Mathematics® Fluent®, Gambit®
Modeling build up
Simplified the robot fish structure, then united the generalized forces and fluid forces according their relationship in the Lagrange equation
Generated 3D meshes for the robot fish; mimic the robot fish locomotion using UDF, then performed the simulation with Fluent®
Calculation accuracy
General accuracy Greater accuracy and fidelity
Duration Simulation period
After the modeling being built up, results for new parameter simulation can be produced quickly, generally within several minutes or hours.
Long period for modeling built up and debugging many parameters. The calculation is time-consuming, several days, even several weeks.
Simulation data
Provides macroscopic data of the swimming robot fish
Provide both macroscopic and microscopic data of the swimming robot fish
Refer to section 7.2 & 7.3
135
Table 6.2: Comparison in special properties between the kinematic modeling and CFD analysis
Kinematic modeling CFD analysis
Body shape analysis
No, it cannot provide body shape analysis.
Yes, kinds of parameters can bring some ideas about the Quarlity of the robot fish shape.
Force the fish gets in water
Similar to CFD simulation results, but at low accuracy.
2 4 6 8 10tHsL
-0.8
-0.6
-0.4
-0.2
0.2
0.4
0.6FxHNL
2 4 6 8 10tHsL
-2.0
-1.5
-1.0
-0.5
0.5
1.0
Fy HNL
136
Velocity Can be calculated for the whole fish and a specific section, but cannot directly displayed in graphic detail
The velocity at any surface of the robot fish can be calculated and displayed easily.
Pressure Can be calculated for the whole or and a specific section, but no directly graphic display
The pressure of every point at any surface of the robot fish can be calculated and displayed easily.
6.5. Conclusion
Both kinematic modeling and CFD analysis were used for the
haptic robot fish system in different ways to exert their respective
advantages.
The kinematic modeling results were used for the whole fish
status analysis, for example, the composite forces and moments, the
137
components of forces and moments on the swimming robot fish will
help researchers study the efficiency of the robot fish locomotion, the
relationship among velocity and amplitude, and frequency of the robot
fish swinging. All of them will provide abundant data for assigning
robot fish tasks. Another usage of this simulation is attributed to its
quick solution. It will be applied for on line calculation; this will
contribute to the real time control of robot fish in the future.
CFD analysis results were used to build up the database of the
haptic robot fish system for force feedback. It can provide abundant
information and give the operators direct tactile experience to study the
swimming robot fish. CFD hydrodynamic analysis can also help
researchers study the robot fish in detail, for example, pressure and
velocity distribution on or around the robot fish, which cannot be
obtained through physical experiences. This is quite important in the
design and improvement of the robot fish.
138
7. Conclusions and Future Works
7.1. Conclusions
This thesis demonstrated a medium size (62 centimetres in length)
biomimetic robot fish design based on the carangiform prototype
(shown in Figure 3:1). It had the most functions in this dimension of
robot fish and was made up of a sensing unit, a control unit, a
communication unit, an actuation unit, a support frame and other
accessories. A biomimetic motion library conception was brought
forward to help researchers easily control robot fish to realize 3D
controllable free swimming in water. The robot fish can detect
obstacles through the sensing unit and can swim autonomously. It also
can communicate with an upper console, send out the visual and other
information and receive operation commands. These functions make it
possible to the robot fish system complete special tasks with, or
without, real-time commands from the upper console.
Two kinds of modeling, the kinematic modeling and CFD
simulation were carried out to study the robot fish characteristics, the
foundation of the haptic robot fish system. On one side, the kinematic
modeling was built according to the relationship between the
139
generalized force in Lagrange's equation of the second kind and the
fluid force based on a simplified geometric model of the robot fish. It
provided a simple and time-efficient way to calculate the force on the
swimming robot fish. The swimming forward motion of the robot fish
was simulated, which has been verified by experiment. On the other
side, the 3D CFD simulation of the biomimetic robot fish was
investigated using Fluent® version 6.3.26. The UDF was used to define
the movement of the robot fish and the Dynamic Mesh contributed to
the simulation too. The hydrodynamic analysis produced detail
information not only the forces exerted on the robot fish, but also the
flow pattern, velocity and pressure fields, providing researchers with
an insightful view into the hydrodynamic properties of the robot fish.
This also can assist in improving the design, remote control and
flexibility of the underwater robot fish. The results of the two kinds of
simulation were respectively used for the analysis of the whole fish
status and the buildup of the haptic robot fish system database
according to their different simulation features.
A haptic robot fish system was innovated with a new interactive
force feedback using direct force mapping. It supports users in
understanding the hydrodynamic properties around the robot fish more
deeply than in other common visualization systems based only on
graphical visualization of hydrodynamic analysis. One can feel the
140
force imposed on the robot fish in water and also can observe the field
distribution maps, such as velocity and pressure on need for
hydrodynamic analysis. This system would be applicable for
educational and design purposes in robot fish research.
7.2. Future Works
The haptic robot fish system is innovative in robot fish
development and many things still need to be done. Future activities
will aim to improve and enhance its performance and also to make the
haptic feedback directly come from test results by adding force sensors.
Here are some:
(1) In the present system, the robot fish communicates with the
upper console on shore via a cable that is connected to a
Buoyage Information Relay. The relay generates drag force
which greatly reduces the efficiency of the robot fish
movement. Under water communication is difficult due to the
factors such as multi-path propagation, time variations of the
channel, small available bandwidth and strong signal
attenuation, especially over long range. In underwater
communication there are low data rates compared to terrestrial
communication, since underwater communication uses
141
acoustic waves instead of electromagnetic waves. In future,
underwater acoustic communication will be a good choice for
the robot fish communicating with the outside.
(2) The diving ability of the robot fish is limited by its diving
method and the materials of its outer shell. The robot fish must
currently dive when it is swimming. It was realized using a
barycenter-adjustor to change the robot fish posture to get a
pitch swim route. The shape of the robot fish changes in a way
when it swims in water at different depths, which brings many
difficulties in controlling its locomotion. In future, some
special mechanical structures will be added to help the robot
fish obtain an easier diving method. New materials will be
applied to the robot fish outer shell, which should be soft but
still be able to resist the unwanted deformation coming from
water pressure.
(3) To build a true haptic robot fish system, some force sensors
will be applied on the robot fish body surface in the future.
Then the force information can be obtained from the real-time
measurement of the force sensors. This will help researchers
build more intellectualized robot fish like real fish, for example,
autonomously keeping away from underwater vortexes
measured and judged by its own sensors.
142
(4) Both the kinematic modeling and CFD hydrodynamic
analysis should be improved to enhance the simulation
accuracy. More accurate and realistic numerical simulations
should be investigated for the robot fish when it is swimming
in different kinds of modes, such as turning and diving, and in
different water flows, such as downstream, in adverse currents,
turbulence or other complex stream currents. Those may
contribute to a better understanding and modeling of all the
sophisticated solutions in a near future.
(5) The simulation force data were mapped to the haptic space via
direct force mapping method. This will be improved later to
get better haptic interaction results.
There is a long way to go in building a real-fish robot and which
give operators good tactile interaction with the robot fish. But nature
gives researchers some revelation which will help them keep going
with it.
143
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Appendix
A 3-D LOCOMOTION BIOMIMETIC ROBOT FISH WITH INFORMAITON RELAY
Zhenying Guan*, Chao Zhou**, Zhiqiang Cao**, Nong Gu*,
Min Tan**, Saeid Nahavandi*
* Intelligent Systems Research Lab., Deakin University, Geelong, VIC 3217, Australia ** Laboratory of Complex Systems and Intelligence Science, Institute of Automation,
Chinese Academy of Sciences, Beijing, 100190, China *{zgua, ng, nahavand}@deakin.edu.au
**{zhouchao, zqcao, tan}@compsys.ia.ac.cn
Abstract: In this paper, a biomimetic robot fish is designed. It has a biomimetic tail to simulate the carangiform tail, a barycenter-adjustor for descending/ascending motions, multiple sensors, and it may communicate with the outside by an information relay system on water. Combining the movements of the tail and the structure for descending and ascending, the robot fish can simulate the swimming of real fish in water and a biomimetic motion library is established. Finally, the prototype and experiments are given.
Keywords: biomimetic robot fish, 3-D locomotion, information relay, biomimetic motion library
1 INTRODUCTION
In nature, the fish adjusts itself to hydrodynamics environment and becomes a perfect swimming expert during years of evolution. Many researchers study its body structure and swimming characteristics and many propulsive theories are given. Lighthill built a model based on elongated-body theory to analyze the carangiform propulsive mechanism [1][2]. The large-amplitude elongated-body theory [3] was propounded to analyze the irregular amplitude of the tail. Wu developed a two-dimensional (2-D) waving plate theory, treating fish as elastic plates to analyze the hydrodynamic feature of the carangiform fish [4]. Triantfyllou [5][6] found that the jet formed behind the fish body played an important part of propulsion. Tong developed the 3-D waving plate theory (3DWDP) based on the 2-D waving plate theory and a semi-analytic semi-numeric method was adopted to obtain the 3-D nonstationary linear solutions [7].
With the development of propulsive theories and robotic technologies, the research on a biomimetic robot fish with high velocity, high efficiency and high maneuverability has been a hotspot. MIT successfully developed an eight-link, fish-
like machine-RoboTuna. RoboTuna and subsequent RoboPike [5][8] projects attempted to create AUVs with increased energy savings and longer mission duration by utilizing a flexible posterior body and a flapping foil (tail fin). In Nagoya University, Guo developed a kind of underwater microrobot by using ICPF actuator [9][10]. Mitsubishi Heavy Industries (MHI) created a robotic replica of the rarely-seen coelacanth, which died out millions of years ago and was known only from fossils [11]. Scientists in Harvard University developed an underwater eel robot [12][13] and analyzed its kinematics and kinetics. K H Low designed a robot fish with undulating fins [14]-[16]. The Harbin Institute of Technology conducted the underwater robot research on imitating the propulsion mechanical structure of the fish fins and constructed an experiment platform using elastic module [17]. National University of Defense Technology investigated on the Long Flexible Fin Undulation equipment, which was based on the undulatory Calisthenics of Gymnarchus niloticus’s long flexible dorsal fin [18]. Peking University developed the biomimetic dolphin and built a series of experiments and a test platform [19]. Institute of Automation Chinese Academy of Sciences studied on the coordination and control of robot fishes [20].
As a new idea for developing a robot fish system under the water, we construct a biomimetic robot fish with a simulating-carangiform tail, a barycenter-adjustor and several kinds of sensors, which performs 3-D locomotion and may avoid obstacles with the help of infrared sensors. The robot fish can communicate with the upper console via a buoyage information relay, which makes it possible for the upper console to get more information under water and send instructions to the robot fish to execute complicated tasks.
In the rest of the paper, section 2 describes the design of the mechanical structure and the control system. The biomimetic motion library is given in Section 3. The robot fish prototype and experiments are introduced in Section 4 and Section 5 concludes the paper.
2 DESIGN OF THE ROBOT FISH
2.1 Design of the Mechanical Structure
The biomimetic robot fish is designed based on the Carangiform prototype as it has a good balance of velocity, acceleration and controllable properties. As shown in Fig. 1, the biomimetic robot fish is made up of the following parts:
• sensing unit (infrared sensors + press sensor + CCD camera); • control unit (MCU + peripherals); • communication unit (optical transmitter + optical receiver + wireless modules +
optical fiber cable + cable); • actuation unit (pitch motor + 4 tail motors); • support frame (aluminium exoskeleton + head); • accessories (Li-polymer batteries + waterproofed skin + caudal fin, etc.).
A 3-D LOCOMOTION BIOMIMETIC ROBOT FISH WITH INFORMAITON RELAY 3
The robot fish has a clipper-built head, flexible body and a caudal fin. The rigid head made of FRP (Fiberglass-Reinforced Plastics) has a big room inside, where MCU, batteries, sensors, peripherals etc. are installed. The flexible body is built by four links, which are jointed together by an aluminium exoskeleton, driven by four tail motors and airproofed by a waterproofed skin. The flexiblle body cooperates with the caudal fin on simulating the movement of the carangiform fish tail, which impulses the robot fish to swim forward. At the same time, in order to maintain the balance when the robot fish is swimming in water, some weights are fitted into the robot fish’s body.
Fig. 1. Biomimetic robot fish system
There are several methods to descend or ascend, such as Changing Gravitation (Buoyancy), Pectoral fins, Changing body shape, Changing the barycenter and so on[21]. Considering these methods’ features and limitations in the realization, changing the gravity center is chosen to realize the robot fish’s 3-D movement. A barycenter-adjustor mechanical structure is designed and implemented. It is driven by a motor and can swing to different angles to change the gravity center of the whole robot fish. With shifting of the gravity center, the robot fish can pitch to swim upwards or downwards.
Moreover, several kinds of sensors equip the robot fish for autonomic control and environmental monitoring. Firstly, three infrared sensors mounted on the left, middle and right side of the robot fish head are used to detect obstacles, which are processed by MCU directly and keep the fish swimming safely. Secondly, the water depth information can be gained by a pressure sensor set on the body, by which the robot fish can get feedback of depth data using for diving depth control. Thirdly, a camera is installed on the fish head to provide abundant information in front of the fish.
Limited by the information processing capability of the robot fish, it is necessary to design a communication system between the robot fish and the outside. There are several methods on the information transmission of the robot fish. One is to utilize
wireless equipment, which only works above the water surface because of severe attenuation of the electromagnetic wave in water. The robot fish has to swim only on water or ascend to the water surface to exchange the data with the upper console. Another is to connect the robot fish with the upper console by a cable directly, which can assure the transfer speed and accuracy. However, this method will limit the robot fish. In this paper, a buoyage information relay is presented. It is used as a communication relay that connects the robot fish by cables on one hand and communicates with the upper console by wireless on the other hand.
2.2 The Control System
The robot fish’s control system is shown in Fig. 2. The MCU using uCOS-II real-time operating system based on the minimal system of Mega128 sends task-related PWM signals to tail motors to control its motions and to pitch the motor to change the fish’s gravity center. It exchanges the information with the outside via the buoyage information relay.
Fig. 2. The block diagram of the control system
Two kinds of data, the mass visual data from CCD camera, the digital signals including the information provided by other sensors and commands from the upper console should be transmitted separately. The digital signals are sent to the buoyage information relay via normal cable after being converted into RS232 Serial signal and then sent out by low frequency wireless module and received by the upper console later. And vice versa, as the digital signals may be sent to robot fish by the upper console via this information relay system. At the same time, the visual signals are converted into light signals and sent to the buoyage information relay via optical fiber cable, where the light signals are resumed into electronic signals and then sent out by high frequency wireless module. The upper console receives the information and extracts it to make decisions for remote control. The result of vision processing and the target identification reflects the information of environment and goals.
In one word, with the information from sensing units, the robot fish may make decisions independently or execute a task after combining them with the commands from the upper console.
A 3-D LOCOMOTION BIOMIMETIC ROBOT FISH WITH INFORMAITON RELAY 5
3 THE BIOMIMETIC MOTION LIBRARY
According to the behaviors of real fish and the functions of biomimetic robot fish, a biomimetic motion library is designed based on the mechanical structure and the control system. The robot fish adjusts its poses in water by controlling the oscillatory frequency of the tail and the position of the gravity center. Accordingly, the motion library includes acceleration, deceleration, uniform motion, turn, dive, and even swimming backwards. Different combinations of these motions may be chosen according to the task required to be executed.
The tail’s movement is the basis of the biomimetic motion library. Researchers point out that there is an implied travelling wave in the body of swimming fish, which runs from its neck to tail. The wave whose amplitude increases gradually appears as the curvature of the fish’s spine and muscle. It travels faster than the fish’s forward movement. The robotic fish is devised according to carangiform propulsion model, whose propulsive wave curve starts from the fish’s inertia centre to its caudal link. It is assumed that this kind of curve can be described by Eq. (1) [1][22].
)])][sin([(),( 221 tkxxcxctxybody ω++= (1)
where bodyy is the transverse displacement of body, x is the displacement along
main axis, k is the body wave number, λπ2=k , λ is the body wave length, 1c is the linear wave amplitude envelope, 2c is the quadratic wave amplitude envelope, ω is the body wave frequency T/2πω = . A sample of the fish body wave curve is shown in Fig. 3.
Fig. 3. Links fitting fish’s body-wave
The parameters ( )ωλ,,, 21 cc are chosen to determine the proper body wave. We adopt four hinge links to simulate the locomotion of fish tails (see Fig. 1), the robot fish’s oscillatory part can be modeled as a planar serial chain of links at an interval of 0 to π2×R along the axial body displacement, where R is defined as the length ratio of the fish's oscillating part to the whole sine wave. Let the length of each link be )4,3,2,1( =jI j , the ratio of them be 4321 ::: llll , and the link angle between 1−jl
and jl be jϕ [23]. With the jϕ changing, the fish's oscillatory part undulate along
the travelling wave as Eq. (1) expressed. Impetus is produced when the speed of body wave propagation exceeds the speed of fish swimming forward [24][25].
Propulsion: The acceleration, deceleration and uniform motion are realized by changing the swing frequency of the robot fish tail, which is realized by sending different signals to the motors of the tail. Increasing duty ratio of the PWM signal to the tail motors results in increasing the tail's swing frequency, which increases the fish swimming speed. On the contrary, reducing duty ratio of the PWM signal may result in the deceleration of the speed. If the tail motor rotates uniformly the robot fish will swim at uniform velocity [23].
In addition, the robot fish may be considered to realize swimming backwards according to the study on kinematics and kinetics of Europe eel [26].
Turn: The orientation control is realized by superimposing different link’s deflection. It is necessary to insure that the oscillating rule matches Eq. (1) when turning, so the arc is chosen as the oscillating axis of the links. Correcting Eq. (1), we have [27] [28]:
2 2 21 2( , ) [( )][sin( )]bodyy x t c x c x kx t R x Rω= + + + − − (2)
where R is the radius of the tail axis, which is connected with the turning radius. A sample of the corrected fish body wave curve is shown in Fig. 4.
1l
2l3l
4l
( )dm
( )dm
Fig. 4. The corrected fish body wave curve
Dive: As described above, the robot fish pitch uses the barycenter-adjustor to change its posture [26]. As shown in Fig. 5, O0, O1 are respectively the initial position of buoyancy (FB) centre and the gravity centre. m is the weight of the adjustor. M is the fish weight without m. r is the length of the turning arm. When the pitch motor turns θ (clockwise, assumed to be “+”), the barycenter-adjustor moves forward. As a result, the robot fish’s gravity centre moves forward to O1' and the robot fish gets a pitch angle α, together with the tail’s swinging movement, it will swim downwards.
A 3-D LOCOMOTION BIOMIMETIC ROBOT FISH WITH INFORMAITON RELAY 7
Fig. 5. The moment analysis of barycenter-adjustor
4 EXPERIMENTS
Fig. 6 gives a functional prototype of the biomimetic robot fish with a tail for propulsion, barycenter-adjustor and information relay system.
Fig. 6. The functional prototype of the biomimetic robot fish
The experiments are conducted in a pool of 4.0m*3.0m*0.75m. Fig. 7 describes the process of turn by adding deflection on the tail in the experiment pool, which shows the feasibility of the biomimetic robot fish design.
(a) (b)
(c) (d)
Fig. 7. The image sequence of the robot fish turning
Another experiment is related to goal recognition. The camera on the robot fish sends out the video to the upper console, which extracts the goal based on the given color decided by the operator. Fig. 8 gives the selected image from the camera of the robot fish, where the robot fish swims in the experiment pool with the goal A. B is the recognition result based on the color characteristic, which shows that the goal is successfully recognized in water, which is useful for future process.
Fig. 8. The selected image and the corresponding recognition result
A 3-D LOCOMOTION BIOMIMETIC ROBOT FISH WITH INFORMAITON RELAY 9
5 CONCLUSION
In this paper, a novel biomimetic robot fish with a carangiform tail for propulsion and barycenter-adjustor for diving are designed based on the analysis of propulsion and maneuvering mechanisms for carangiform swimming. An information relay system on water is designed for information transmitting. The sensors information processing of the fish are studied. Some experiments are carried out upon the biomimetic robot fish, and the results have initially demonstrated the performance of the mechanical structure and control system of the biomimetic robot fish.
In the future, we will endeavour to improve the performance of the robot fish and make use of the reserved interfaces and big space in its head to extend new functions.
ACKNOWLEDGEMENT This work is funded by research grants from National Natural Science Foundation of China under Grants 60725309, 60635010. The authors would also like to thank Intelligent Systems Research Lab., Deakin University, Australia for the support to this work.
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305-317 (1960) 2 Lighthill M. J.: Aquatic animal propulsion of high hydromechanical efficiency. Journal of
Fluid Mechanics, vol.44, 265-301 (1970) 3 Lighthill M. J.: Large-amplitude elongated-body theory of fish locomotion. Proceedings of
the Royal Society of London. Series B, Biological Sciences, vol. 179, Issue 1055, 125-138 (1971)
4 Wu T. Y.: Swimming of a waving plate. J. Fluid Mech, vol.10, 321-344 (1961) 5 Triantafyllou M. S., and Triantafyllou G. S.: An efficient swimming machine. Scientific
American, 272(3): 64-70 (1995) 6 Triantafyllou M. S., Barrett D. S., and Yue D. K. P.: A new paradigm of propulsion and
maneuvering for marine vehicles. Trans. Soc. Naval Architects Marine Eng, vol.104, 81-100 (1996)
7 Tong B.: Propulsive mechanism of fish's undulatory motion. Mechanics In Engineering, 22: 69-74 (2000) (in Chinese)
8 Barrett D. S., Triantafyllou M. S., Yue D. K. P., et al: Drag reduction in fish-like locomotion. J. Fluid Mech, vol.392, 183-212 (1999)
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978-1-4244-7815-6/10/$26.00 ©2010 IEEE ICARCV2010
3D Hydrodynamic Analysis of a Biomimetic Robot Fish
Zhenying Guan Centre for Intelligent Systems Research
Deakin University Geelong, Australia
Nong Gu Centre for Intelligent Systems Research
Deakin University Geelong, Australia
Weimin Gao Institute for Technology Research and Innovation
Deakin University Geelong, Australia
Saeid Nahavandi Centre for Intelligent Systems Research
Deakin University Geelong, Australia
Abstract— This paper presents a three-dimensional (3D) computational fluid dynamic simulation of a biomimetic robot fish. Fluent and user-defined function (UDF) is used to define the movement of the robot fish and the Dynamic Mesh is used to mimic the fish swimming in water. Hydrodynamic analysis is done in this paper too. The aim of this study is to get comparative data about hydrodynamic properties of those guidelines to improve the design, remote control and flexibility of the underwater robot fish.
Keywords—robot fish, computational fluid dynamics (CFD), user-defined function (UDF), Dynamic mesh, hydrodynamic analysis
I. INTRODUCTION Recently, there has been a growing interest in studying
biomimetic robot fish as it can provide significant insights into both theory and application of underwater robotics. Observations show that a fish in nature can achieve great propulsive efficiency and excellent maneuverability through coordinated motion of the body, fins, and tail. In 1994, RoboTuna, a first robotic fish in the world was successfully developed, which demonstrated that the power required to propel the swimming fish-like body was significantly smaller than that required to drag the body straight forward at the same speed [1][2]. McIsaac et al. developed an underwater eel robot [3][4] and analysed its kinematics and kinetics. Liu et al. conducted the underwater robot research to imitate the propulsion mechanical structure of the fish fins and constructed an experiment platform using an elastic module [5]. Xie et al. investigated the Long Flexible Fin Undulation equipment, which was based on the undulatory calisthenics of the long flexible dorsal fin of the gymnarchus niloticus[6]. Wang et al. developed a biomimetic dolphin, built a test platform and performed a series of experiments to explore a coordination method for multiply robot fishes to conduct an underwater
transport task [7]. Yu et al. studied the coordination and control of robot fishes [8].
It should be noted that most existing control algorithms of robot fishes are based on a simplified propulsive model that only provides a rough prediction of the effect of hydrodynamics on robot fishes. To obtain an accurate prediction to the hydrodynamic force on robotic fish, it is necessary to conduct dynamic analysis of the surrounding fluid by computational fluid dynamics (CFD) [9].
CFD analysis has been widely used in many areas, including vehicle design, aircraft design and ground robot development due to the following reasons [10].
• CFD simulations can be a useful tool for designers to understand the complex physics of the flow phenomena involved in the fluid dynamics.
• CFD simulations require less time than field test. Moreover, different models can be tested with CFD simulation before accrual prototype models are created for tests.
• CFD also provides detailed visualization of flow field, which is difficult to be obtained by experimental facilities.
CFD simulations and analyses for robot fishes have been carried out. Zhang et al. [11] investigated the fluid dynamics, pressure and velocity distribution, and the production of forces associated with an undulatory mechanical fin. Tangorra et al. [12] also employed CFD simulation, together with using stereo digital particle image velocimetry (DPIV) and proper orthogonal decomposition (POD), to estimate the hydrodynamic force generated by the complex component motions of their biorobotic pectoral fin and to analyse its hydrodynamics. The fins studied by Zhang et al. and Tangorra et al. are important factors towards developing propulsive
devices that will make an underwater robot fish having the ability to produce and control thrust like highly maneuverable fish. Mohammadshahi et al. [13] evaluated hydrodynamic forces of a fish-like swimming robot by using a two-dimensional (2D) CFD model, which provided impactful results to optimize performance parameters in the process of design and fabrication, but 2D model of robt fish cannot offer abundant tridimensional information compared to 3D simulating. Anton et al. [14] adopted CFD modeling and examined the flow field, the produced thrust, and the bending moments at the joints of two-link tails of a robot fish, but the two-link tail fins were assumed to be rigid, thin and light. Actually, popular biomimetic robot fish bodies are soft and quite flexible. Listak et al. [15] created a 3D computer model for a biomimetic robot and simulated the ideal ellipsoid with Gerris, which helped them find an ideal robot fish body with low drag and improved the design, although without detail analysis on the simulation results. In this paper, to produce significant information on flow pattern, velocity and pressure fields and to prvide an insight into both the design and the application of robot fishes, a 3D CFD simulation was investigated for our robot fish propoto type [16] by using Fluent 6.3.26.
II. BIOMIMETIC ROBOT FISH We developed a biomimetic robot fish (Fig. 1) with 3D
locomotion capability. It consists of a simulating-carangiform tail, a barycenter-adjustor, a CCD camera and several infrared and pressure sensors. With these sensors, it is able to avoid running into obstacles automatically. Moreover, the robot fish can communicate with a remote computer via a buoyage information relay. The information relay enables operators to obtain the information of underwater situations in real time and send commands to the robot fish to execute complex tasks.
Figure 1. Biomimetic Robot Fish
The movement of the robotic fish is based on a carangiform propulsion model where the propulsive wave curve starts from the inertia centre to the caudal link of the fish (We call this part of the fish body as “fish tail”). The curve can be described by the following Equation.
21 2( , ) ( )sin( )bodyy x t c x c x kx tω= + + (1)
where bodyy is the transverse displacement of the fish body, x is the intergeted distance along the backbone of the fish from its inertia centre, k is the wave number, λπ2=k ,
λ is the body wave length, 1c is the linear wave amplitude envelope, 2c is the quadratic wave amplitude envelope, ω is the body wave frequency, T/2πω = .
III. 3D HYDRODYNAMIC SIMULATION MODEL
A. Biomimetic Robot Fish and The pool The 3D geometry and the mesh of the robot fish is
generated by Gambit (V2.3.16). To simplify the robot fish model, we ignore the effect of the connection cable between the robot fish and the buoyage information relay.
The dimension of the robot fish is 0.62m×0.16m×0.08m (length × max high × max width). To allocate enough space for dynamic current stretching, a pool is designed to be 9m×9m×4m. The pool walls are defined as moving walls and their local velocities depend on the fluid velocity. The main currents are backward flow generated by the locomotion of the fish tail so that the robot fish is located at the centre of the vertical cross section of the pool, while the distance between the fish head and the pool inlet is 1.53m.
B. Mesh Scheme To achieve a much quicker and more accurate calculation,
tetrahedronal mesh elements are only used for the cube area (0.91m×0.7m×0.4m) close to the robot fish, while Quant mesh elements as big as possible are used for other areas to reduce the number of elements. The distance between the small cube with tetrahedronal elements and the inlet is 1.42 m. This meshing scheme will give enough space to process meshing with high qualified tetrahedron around the robot fish and approach a lower number of meshes to reduce computational time. The key parameters for determining the mesh size are.
Reynolds number,
(2)
The thickness of the boundary,
(3)
where U=0.18 m/s (it is the experimental velocity of the robot fish)
L=0.62 m (the length of the robot fish)
v=1.01*10-6 (water viscosity)
To reach an accurate calculation of the forces acting on the fish surface and reduce the number of meshes, a boundary schema with a growing rate of 1.4 ratio and 4 layers is applied for the mashing the hydrodynamic boundary of the robot fish. According to Eq. (3), the size of the minimum grids adhered to the robot fish is 2 mm.
With the above settings, for the fluid domain, the total number of nodes is 189683 and the total number of elements is
5Re 1.1 10ULv
= = ×
14.64 0.00865( )Re
L mσ = × × =
837773. Figs. 2 & 3 show the mesh distribution in the fluid regain and a close view around the fish.
Figure 2. Mesh of the Biomimetic Robot Fish
Figure 3. Robot Fish
C. Defination of the Locamotion of the Robot Fish User-defined function (UDF) is used to define the
movement of the robot fish and the dynamic mesh is used to simulate the fish swimming in water. As the oscillation of the fish tail (moving part-1, shown in fig. 4) and the caudal fin (moving part-2, shown in fig. 4) is complex and flexible, we choose the DEFINE macro DEFINE_GRID_MOTION to describe the movement of the fish tail and the caudal fin. DEFINE_GRID_MOTION is implemented according to Eq. (1) where c1=0.05, c2=0.09, k=0.5 and R=0.6
To couple the posture of the fish body accurately and timely, the performance of the dynamic mesh is quite important in the simulation. We used Smoothing and Remeshing mesh method here. The relative parameters used are listed in table I.
A commercial CFD code, Fluent 6.3.26 with a standard k–epsilon turbulent model and standard wall functions, are used in all simulations.
Figure 4. Mesh on Robot Fish body
TABLE I. PARAMETERS FOR DYNAMIC MESH
Mesh Methods
Parameters Setting Items setting
Smoothing
Spring Constant Factor 0.05
Boundary Node Relaxation 0.8
Convergence Tolerance 1e-05
Number of Iterations 100
Remeshing
Minimum Length Scale (m) 0.00072372
Maximum Length Scale (m) 0.0008
Maximum Cell Skewness 0.8
Maximum Face Skewness 0.79
Size Rmesh Interval 1
Size Function Resolution 1
Size Function Variation 48.94077
Size Function Rate 0.7
IV HYDRODYNAMIC ANALYSIS
A. Pressure distribution In the simulations, the robot fish oscillates its tail and
caudal fin at T = 0.7s (swinging period). The pressure distribution will be analysed on the horizontal cross section of the pool at the middle position (M-view), like Fig. 5.
Figure 5. M-view
Figure 6. Pressure contours of the M-view at 4 locomotion times (N*m–2) ( a)
approaching the left maximal rotation position (t = 0.1 s); (b) intermedial position during oscillating motion (t = 0.25 s); (c) going on intermedial
position during oscillating motion (t = 0.4 s); (d) approaching right maximal rotation position (t =0.55 s). (It is supposed that a robot fish locomotion period
begin from the position t=0 according the Equation 1)
Fig. 6 shows the M-view of the pressure contours at four locomotion times (“The right” / “the left” means the side of the right / left hand when one stands on the point of the robot fish inertia centre and face to the fish head. ):
• At t = 0.1s (Fig. 6 (a)), the fish tail and the caudal fin are swinging from the right to the left and almost reach the maximal displacement. On the left side of the fish tail and the caudal fin, a bigger positive pressure is generated and a wider distribution than the right side can be found. Especially, the positive pressure focuses most on the rear of the tail, which generates forces pointing to the right-front of the fish. These positive pressures are generated as the water is extruded by the movement of the fish tail and the caudal fin. Also, they grow bigger along the direction from the fish tail to the caudal fin due to the growing up amplitudes of the fish tail and the caudal fin oscillating. This also implies that a tip vortex can be generated near the edge of the robot
fish caudal fin and considerable fluid is pushed into the downstream region on the left side of the caudal fin.
• At t = 0.25s (Fig. 6 (b)), the robot fish body and the caudal fin are already on the way of swinging back from the left to the right. This action pushes the water away, so a positive pressure is exerted and widely distributes on the right side of the fish tail and the caudal fin. Actually, immediately after the anticlockwise stroke began, which is a change of the fish tail swinging direction, one observes a small positive pressure distribution on the right side of the caudal fin and a negative pressure distribution on its left side. This shows the generation of the thrust. The direction of the thrust is left-front according the angle of the robot fish body posture.
• At t = 0.4s (Fig. 6 (c)), the fish tail and the caudal fin keep on swinging from the left to the right. The positive pressure grows up and turns to the left side of the robot fish. On the other side of the robot fish body, the negative pressure seems to be decreased. This demonstrates that the robot fish achieves a larger right-front direction thrust.
• At t = 0.55s (Fig. 6 (d)), the fish tail and the caudal fin keep on swinging from the left to the right and its body reach almost the most flexuous position. The positive pressure grows up quickly and distributes on both of the left side of the middle tail and the right side of the caudal fin. On the contrary, a negative pressure distributes on the right side of the tail. At this point, the robot fish achieves the largest forward direction thrust during the whole period.
• After the period described above, the fish tail and the caudal fin continue to swing for the next half period.
According to the above analysis, the resulting force that the robot fish acquires by periodically oscillating its tail and caudal fin can be divided into two types, the fluctuant thrust at forward direction and the drag at left-right direction.
B. velocity The velocity contours of the robot fish at critical instants
are shown in Figure 7 during the oscillation, the same instants and views with the ones for pressure contours analysis.
• At t = 0.1s (Fig. 7 (a)), a counter-rotating vortex is observed. This vortex is shed from the distal edge (especially the tip edge of the tail fin) on the robot fish. The shedding of vortex may be one of the main effects on the pressure distribution at the robot fish surface mentioned in the pressure analysis.
• At t = 0.25s (Fig. 7 (b)), a thin clockwise vortex sheds from the tip of the caudal fin at the beginning of the fish tail and the caudal fin reverse motion.
• At t = 0.4s (Fig. 7 (c)), one observes a clockwise vortex at the right middle side of the fish tail. The shedding of this vortex into the wake leads to a momentary increase in the thrust.
(a) 0.1s (b) 0.25s
(c) 0.4s (d) 0.55s
• At t = 0.55s (Fig. 7 (d)), a large anticlockwise vortex sheds at the left middle side of the fish tail. Two clockwise vortexes shed at the right side of the upper tail and the caudal fin. The shedding of these vortexes into the wake leads to larger increase in the thrust than the one at t = 0.4s.
• After the period described above, the robot fish will endure the next similar half period.
Figure 7. Velocity distribution
C. Force After ten swinging periods, the inlet velocity becomes
stable and is about 0.18m/s, which is the same as our experiments. This says the simulation is valid. Figure 8 shows the forces exerted on the robot fish along with X and Z axes directions. In the X-axis direction, the fish suffers a much bigger force than in the Z-axis direction. The composite of the force in the X axis direction is almost zero, which is generated by the swing movement of the fish tail and the caudal fin. It will be counteracted by the force arisen from the movement of inside motors. The force in the Z-axis direction is always positive. This is caused by the movement of the fish tail and the tail fin. The robot fish will be driven by the force in the Z-axis direction.
Figure 8. Force in X and Z directions
IV. CONCLUSIONS In this paper, a computational fluid dynamic model was
built for a biomimetic robot fish. Lots of hydrodynamic properties, such as the exerted pressure and the force of the fish, have been obtained. This paper explained how the fish oscillated the tail and the caudal fin to push water away behind it and get the thrust pushing it forward.
The CFD simulations provided the information of the flow of water around the robot fish and the pressure distribution, which will be used for the optimization of robot fish and the improvement of the design and fabrication of the robot fish. It can also provide more complex fluid flow characteristics for the research and development of robot fishes used in different external situations.
For future work, we should investigate more accurate and realistic numerical simulations of the robot fish when it is swimming in kinds of modes, turning, diving or others, and in different water flow, downstream, adverse current, turbulence or other complex stream currents. Those may contribute to a better understanding and modeling of all the sophisticated solutions we need to develop in a near future.
ACKNOWLEDGMENT This research was funded by CISR, Deakin University. The
authors would also like to thank Mr. K. Khoshmanesh for his kind help on the CFD work presented in this paper.
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