Dynamic analysis and motion control of a fish robot driven by pectoral fins

VIET NAM NATIONAL UNIVERSITY HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY PHAM VAN ANH DYNAMIC ANALYSIS AND MOTION CONTROL OF A FISH ROBOT DRIVEN BY PECTORAL FINS DOCTOR OF PHILOSOPHY D

VIET NAM NATIONAL UNIVERSITY HO CHI MINH CITY

UNIVERSITY OF TECHNOLOGY

PHAM VAN ANH

DYNAMIC ANALYSIS AND MOTION CONTROL OF A FISH

ROBOT DRIVEN BY PECTORAL FINS

DOCTOR OF PHILOSOPHY DISSERTATION

HO CHI MINH CITY - 2020

VIET NAM NATIONAL UNIVERSITY HO CHI MINH CITY

UNIVERSITY OF TECHNOLOGY

PHAM VAN ANH

DYNAMIC ANALYSIS AND MOTION CONTROL OF A FISH

ROBOT DRIVEN BY PECTORAL FINS

Major: Mechanical Engineering

Major code: 62520103

Independent reviewer 1: Assoc Prof Dr Nguyen Quoc Hung

Independent reviewer 2: Assoc Prof Dr Nguyen Truong Thinh

Reviewer 1: Assoc Prof Dr Pham Huy Tuan

Reviewer 2: Assoc Prof Dr Nguyen Thanh Phuong

Reviewer 3: Assoc Prof Dr Ngo Quang Hieu

ADVISORS:

1 Assoc Prof Dr Vo Tuong Quan

2 Assoc Prof Dr Nguyen Tan Tien

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COMMITMENT

I pledge that this is the own work of myself The research results and conclusions in this dissertation are honest and not copied from any sources and under any form The references to the documentary sources had been cited as prescribed

Dissertation author

Signature

Pham Van Anh

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ABSTRACT

Demand for a novel propulsion system, which is not only more efficient than the traditional impetus structure but also more friendly to the environment, is a reason for study on robots thrust by fish-inspired fins Meanwhile, pectoral fins of biological fish play a crucial role in locomotion mechanism, in particular, only a small ratio of natural fish use the pectoral fins as the principal propelling component Nevertheless, most of the rest ratio use these fins for maneuverability and stability of swimming movements Accelerating, braking, stabling the position, and cruising in short distances are the behaviors of fish while employing pectoral fins On the other hand, the dynamics model

of pectoral fins with flexibility and diversity of shape is a significant factor, which has not mentioned in previous work In an attempt to generate a counterpart of biological fish, this dissertation recommends several novel approaches in designing, analyzing, and establishing the mathematical model for a fish-like robot with pectoral fins

Inspired by natural fish fin, the dissertation concentrates on flexible structures that allow generating smooth motion, low energy expenditure, and efficient thrust The fact proves that compliant fins of natural fish own high propulsive efficiency Three variation types

of pectoral fins comprising uniform ones, non-uniform ones, and folding ones were investigated First, the modeling issue of the robot with uniform fins was conducted The fins were considered as cantilever beams An appended simplistic controller was then designed to track the referent trajectories of direction and surge velocity Second,

to imitate the biological fish fin, the shape of snakehead fish was adopted Its mathematical model was established with the assistant of the Rayleigh-Ritz method in deflection modeling Finally, to improve the fish robot's swimming speed as well as energy consumption efficiency, artificial folding pectoral fin-type, which is inspired by the change of drag/thrust area ratio of a natural fish fin, was proposed The computation model of the above types is established on the base of body rigid dynamics and Morison's force Wherein the fluid influences on the fin movements are described as separated elements of added mass and damping For two last fin types, the Lagrange approach was applied to build dynamic equations of motion Moreover, experimental works are carried out to validate and evaluate the recommended models The achieved

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results confirmed that the proposals are feasible and able to predict the behavior of the robot relatively well Remarkably, the robotic fish with folding pectoral fins can attain faster movement speed and better maneuverability compared with previous designs using the same pectoral fins In detail, the robot can reach an average velocity of 0.58 BL/s (0.231 m/s ) and a turning radius of 0.63 BL (0.25m) in correspondence to forward swimming motion and turning motion Furthermore, the peak of velocity performance obtains 0.78 BL/s (0.308 m/s) On the other hand, it is revealed that the folding pectoral fins with reasonably flexible joints provide better speed performance than the high stiffness ones

As an obtained achievement, the outcome of the dissertation can be promoted to design practical control algorithms, which track following the desired trajectory or interact with the surrounding environment Furthermore, it can be expanded on the optimization issues of motion responses Some future trends can be addressed to tackle challenges for improving swimming efficiency as well as building a more complex dynamic model of three-dimensional motion

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TÓM TẮT

Nhu cầu về một hệ thống đẩy mới, không chỉ hiệu quả hơn cấu trúc đẩy truyền thống

mà còn thân thiện hơn với môi trường, là một lý do cho việc nghiên cứu về các robot với các vây được lấy cảm hứng từ cá Trong khi đó, vây hông của cá sinh học đóng một vai trò quan trọng trong cơ chế vận động, đặc biệt, chỉ có một tỷ lệ nhỏ cá tự nhiên sử dụng vây hông làm thành phần đẩy chính Tuy nhiên, hầu hết các tỷ lệ còn lại sử dụng các vây này cho khả năng cơ động và ổn định của chuyển động bơi Khả năng tăng tốc, giữ thăng bằng cũng như lướt đi trong khoảng cách ngắn là đặc điểm của cá sử dụng kiểu vây này Mặt khác, mô hình động lực học của các vây với sự khác nhau của hình dạng và độ linh hoạt là một vấn đề quan trọng, tuy vậy, nó chưa được đề cập trong các nghiên cứu trước đây Trong nỗ lực tạo ra một bản sao của cá tự nhiên, luận án này đề xuất một số cách tiếp cận mới trong việc thiết kế, phân tích và thiết lập mô hình toán học cho một robot giống như cá sử dụng các vây hông

Lấy cảm hứng từ vây cá tự nhiên, luận án tập trung vào các cấu trúc linh hoạt cho phép tạo ra chuyển động trơn tru, chi phí năng lượng thấp và lực đẩy hiệu quả Các khảo sát cho thấy rằng, các dạng vây mềm của loài cá tự nhiên sở hữu hiệu quả đẩy cao Trong luận án này, ba dạng vây riêng biệt bao gồm kiểu đồng dạng, kiểu không đồng dạng và kiểu vây gấp đã được nghiên cứu Đặc biệt, để bắt chước vây cá sinh học, hình dáng hình học của vây hông cá lóc đã được thông qua Mô hình toán học của nó được thiết lập với sự trợ giúp của phương pháp Rayleigh-Ritz trong mô hình hóa biến dạng Hơn nữa, để cải thiện tốc độ bơi của robot cá cũng như hiệu quả tiêu thụ năng lượng, kiểu vây hông gấp nhân tạo, được lấy cảm hứng từ sự thay đổi tỷ lệ diện tích cản/đẩy của vây

cá tự nhiên, đã được đề xuất Mô hình tính toán của robot và các loại vây trên được thiết lập dựa trên cơ sở động lực học thân cứng và mô hình lực Morison Ở đây, các ảnh hưởng của chất lỏng lên các chuyển động của vây được mô tả như là các phần tử riêng biệt với khối lượng thêm vào và độ cản chất lỏng Đối với hai kiểu vây cuối, phương pháp Lagrange được sử dụng để thiết lập các phương trình động lực học chuyển động Hơn nữa, các thử nghiệm cũng được thực hiện để kiểm tra và đánh giá các mô hình đã

đề xuất Các kết quả đạt được đã khẳng định rằng các đề xuất là khả thi và có thể dự đoán các hành vi của robot tương đối tốt Đáng chú ý, cá robot có vây hông gấp có thể

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đạt tốc độ di chuyển nhanh hơn và khả năng cơ động tốt hơn so với các thiết kế trước

đó sử dụng cùng kiểu vây Cụ thể, robot có thể đạt vận tốc trung bình 0.58 BL/s (0.231 m/s) đối với chuyển động bơi thẳng và bán kính chuyển hướng 0.63 BL (0.25m) khi chuyển hướng Vận tốc cao nhất cũng đạt tới 0.78 BL/s (0.308 m/s) Mặt khác, nó được tiết lộ rằng vây hông gấp với khớp linh hoạt vừa phải có đáp ứng tốc độ tốt hơn so với kiểu vây có độ cứng khớp cao

Kết quả của luận án có thể được sử dụng trong thiết kế các thuật toán điều khiển bám quỹ đạo mong muốn hoặc tương tác với môi trường xung quanh Hơn nữa, nó có thể được mở rộng trong các vấn đề tối ưu hóa chuyển động Một vài hướng phát triển trong tương lai có thể được đề cập để giải quyết các thách thức trong cải thiện hiệu quả bơi cũng như xây dựng một mô hình động lực học phức tạp hơn cho chuyển động robot trong không gian ba chiều

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ACKNOWLEDGMENTS

I want to express my sincere appreciation to my academic advisors, Associate Professor Tuong Quan Vo and Associate Professor Tan Tien Nguyen, for their patient guidance, constructive recommendations, and enthusiastic encouragement Special thanks should

be given to the first advisor throughout my research journey My dissertation would not

be completed without his invaluable support

I would also like to thank Associate Professor Le Dinh Tuan, for his advice and assistance in using the measurement sensors My thanks are also extended to Associate Professor Nguyen Quoc Chi, Associate Professor Nguyen Duy Anh, and Associate Professor Bui Trong Hieu for valuable critiques, positive feedback, and warm encouragement Additionally, I want to send my sincere thanks to Dr Do Xuan Phu and anonymous reviewers for their suggestions to complete this dissertation

Furthermore, I wish to thank my wife and my parents for their generous patience, unwavering assistance, and encouragement throughout my study tenure

Finally, I would also like to extend my thanks to Pham Van Dong University for permission to attend this research program The grateful appreciation should be given to the Ho Chi Minh City University of Technology and project 911-the Ministry of Education and Training, Vietnam, for providing financial support (TNCS-CK-2015-13)

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CONTENTS

LIST OF FIGURES x

LIST OF ABBREVIATIONS xv

CHAPTER 1 INTRODUCTION 1

1.1 General information 1

1.2 Motivation 8

1.3 Aim and scope 10

1.4 Methods and results 10

1.5 Organization of dissertation 13

CHAPTER 2 BACKGROUND 15

2.1 Literature review 15

2.1.1 Morphology and anatomy in the bio-inspired design of pectoral fin 16

2.1.2 Kinematic and experiment 17

2.1.3 Fish robot with pectoral fin ray 20

2.1.4 Modeling based numerical simulation 23

2.1.5 Application of smart materials in the design of pectoral fin 24

2.1.6 Experiment technique and data capturing 27

2.1.7 Control issue of fish robot driven by pectoral fins 28

2.1.8 Dynamic modeling 29

2.1.9 Transformation fin 33

2.2 Summary 33

2.3 Theoretical Foundations 35

CHAPTER 3 DYNAMIC ANALYSIS AND MOTION CONTROL 36

3.1 Fish robot with uniform fin flexible pectoral fins 36

3.1.1 The proposed model of fish robot with uniform flexible pectoral fin 36

3.1.2 Dynamic model of uniform flexible fins 39

3.1.3 Hydrodynamics of the robot body 42

3.1.4 Trajectory tracking control for robot motion 43

3.2 Fish robot propelled non-uniform pectoral fins 46

3.2.1 Geometric design of non-uniform pectoral fin 46

3.2.2 Dynamic model of the robotic fish with non-uniform pectoral fins 47

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3.2.3 Motion control of the non-uniform pectoral fins 53

3.3 Fish robot with folding pectoral fins 54

3.3.1 Mechanical design of folding fins 55

3.3.2 Dynamic model fish robot with folding fins 56

3.3.3 Motion control of the folding pectoral fins 63

CHAPTER 4 EXPERIMENTS 66

4.1 Experimental works concerning the fish robot with the non-uniform pectoral fins 66 4.1.1 Experimental measurement of robot motion 66

4.1.2 Estimation of natural frequencies and mode shape functions of non-uniform fins 67

4.1.3 Estimation of the internal damping of flexible non-uniform fins 69

4.1.4 Measurement of thrust coefficient C T 70

4.1.5 Other dynamic coefficients of the robot with non-uniform fins 72

4.2 Experimental setup and the parameters determination of the fish robot with folding fin 77

4.2.1 Experimental setup of the motion measurement of the robotic fish 77

4.2.2 Estimation of stiffness and damping coefficients of flexible joint 78

4.2.3 Determination of stroke ratio and amplitude ratio of stimulating moment 80 4.2.4 Determination of other coefficients 81

CHAPTER 5 RESULTS AND DISCUSSION 83

5.1 Performance of fish robot with uniform pectoral fin 83

5.2 Performance of fish robot with non-uniform fins 85

5.3 Performance of fish robot with folding pectoral fins 92

5.3.1 Influence of the fin joint flexibility on the swimming behavior of the robot 93 5.3.2 Swimming performance of the robot in the transient state 94

5.3.3 Swimming performance of the robot in the steady-state 98

5.3.4 Expenditure power, cost of transport, propulsive efficiency and Strouhal number 101 CHAPTER 6 CONCLUSION 105

6.1 Dissertation contributions 106

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6.2 Future works 107

LIST OF PUBLICATIONS 108

REFERENCES 111

APPENDIX A 126

APPENDIX B 130

APPENDIX C 132

APPENDIX D 134

APPENDIX E 135

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LIST OF FIGURES

Figure 1.1 Classification of fish species based on locomotion mechanism: (a) BCF

propulsion, (b) MPF propulsion [7] 2

Figure 1.2 A classification of fish-inspired robot [6] 2

Figure 1.3 Some prototypes of the fabricated fish robots: (a) BCA [8], (b) MPA [9], (c) JET [10] 2

Figure 1.4 Fish robot with two links and a complaint tail (a) [17], autonomous robotic fish with a soft tail part embedded fluidic actuator (b) [18] 3

Figure 1.5 Transmission mechanism for the tail of a fish robot: (a) using linear hypocycloid [19] (b) combining a compliant tail and driven ropes [20] 3

Figure 1.6 An Agile robotic fish with high maneuverability [64] 4

Figure 1.7 Propulsion and turn system of a vessel using propellers [126] 8

Figure 1.8 Gomphosus varius fish [128] 9

Figure 1.9 Summary of the research approach scope 11

Figure 2.1 An illustration of three basic operation modes of pectoral fins [141] 15

Figure 2.2 Anatomy of the pectoral fins on parrotfish: (a) Position of fins, (b) Structure of skeleton, (c) Illustration of muscles (adapted from [2]) 16

Figure 2.3 Motion demonstration of pectoral fin prototype mimicking the movement of bluegill sunfish fin: (a) expansion, (b) curl, (c) relax, and (d) cupping [144] 16

Figure 2.4 Illustration of a robotic design with a pectoral fin [141] 17

Figure 2.5 Mechanical design of fish robot propelled by two DOFs pectoral fins [136] 18

Figure 2.6 Motion production structure for pectoral fins (a), the illustration of transmission principle diagram on pectoral fin (b), entire transmission mechanisms on the fish robot (c) [150] 18

Figure 2.7 Prototype of fish robot Manta [40] 20

Figure 2.8 Versions of Cownose ray robot and the pectoral fin structure of Robot-ray IV [154] 20

Figure 2.9 Freshwater stingray (Potamotrygon motoro) (a), an illustration of undulation sequence of pectoral fin in a period (b) [155] 21

Figure 2.10 Analytical scheme of the pectoral fin of manta (a), the design demonstration of bionic manta robot (b) [156] 22

Figure 2.11 Definition of sweep angle (a), illustrations of MantaDroid driven by pectoral (b) [157] 22

Figure 2.12 Illustration of artificial pectoral fin based four tensegrity beam (a) and experiment of a tensegrity structure (b) [158] 22

Figure 2.13 Model of pectoral fin types: rigid fin (a), flexible fin (b), fin with variable stiffness (c) [159] 23

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Figure 2.14 An illustration of Batoid ray fish robot using IPMC pectoral fin [162] 25

Figure 2.15 Structure of a bionic pectoral fin: (a) the design model (1-fin base, 2-fin rays, 3-soft membranes), (b) the practical model underwater [163] 25

Figure 2.16 Design and deformation state of a fin ray unit: (a) initial state (1-root plate, 2-tip plate, 3-extensive plate), (b) bending root plate, (c) bending tip plate, (d) bending of two plates in simultaneous, (e) pectoral fin prototype with flapping motion [47] 26

Figure 2.17 Illustration of the motion pectoral fin: recording method of kinematic data for Koi Carp fish (a) and four-motion mode extracts from experimental data (b) [142] 27

Figure 2.18 Demonstration of pectoral fin motion patterns in both real Koi Carp fin motion and artificial fin motion: (a) relaxation, (b) expansion, (c) bending, (d) undulation [47] 28

Figure 2.19 Illustration of Boxfish inspired robot: (a) design model [168], (b) fabricated prototype [169] 29

Figure 2.20 Robotic prototype (a), movement mechanism of pectoral fins in power stroke (b) and recover stroke (c), demonstration of flexible joint in power stroke (d) and recovery stroke (e), illustration of a fabricated pectoral fin (f) [81] 30

Figure 2.21 Illustration of rowing mode in both power stroke and recovery stroke (a), full prototype of the robot (b), the structure of joint in power stroke (c) and recovery stroke (d), fabricated model of pectoral fin (e) [82] 31

Figure 2.22 The prototype of left and right pectoral fins (a), the fabricated fish robot with flexible pectoral fins and identification markers (b) [80] 32

Figure 2.23 Area variable fin [171] 33

Figure 3.1 A fish-like robot model principally propelled by flexible pectoral fins 36

Figure 3.2 Analysis diagram of robot motion utilizing the uniform pectoral fin 37

Figure 3.3 The schematic diagram of direction and velocity controller 44

Figure 3.4 The compliant non-uniform fin profile 46

Figure 3.5 The descriptive diagram of the fish robot with non-uniform fins 47

Figure 3.6 Demonstration of movement mechanism of fin panels in one cycle 54

Figure 3.7 Design illustration of a flexible folding fin: the prototype of the pectoral fin (a), the equivalent model of fin elements (b) 55

Figure 3.8 Schematic diagram of the robotic fish motion 57

Figure 3.9 The analysis model of interaction forces on the pectoral fins (a), the geometry of a fin panel (b) 58

Figure 3.10 A torque curve demonstration with the magnitude and cycle concerning the recovery stroke and power stroke 64

Figure 4.1 The experimental apparatus: The manufactured robot model (a), the primary electronic elements (b), laboratory water tank (c) 66

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Figure 4.2 Set-up of the experimental measurement of damping factor 70 Figure 4.3 Trace of the fin tip point of a clamped pectoral fin in the air environment 70 Figure 4.4 Demonstration of experimental measurement for determination of thrust coefficient of a pectoral fin 71 Figure 4.5 Performances of the thrust and displacement of fin-tip 72 Figure 4.6 Experiments of drag coefficient identification of the robot 73 Figure 4.7 The designed fish robot model with a pair of folding fins (a), the fabricated prototype (b) 77 Figure 4.8 The relationship diagram between electrical devices concerning swimming experiments of the robot 77 Figure 4.9 The water tank and the above-hanged camera for the robot movement

tracking experiments 78 Figure 4.10 The experimental determination of joint deflections and damping

coefficients of the compliant joints 78 Figure 4.11 Four joints specimen of the pectoral fin prototypes 79 Figure 4.12 The relationship between the straight swimming speed response and the coefficients  T, P at frequency 0.5 Hz concerning of the fin-type T2 80

Figure 5.1 The performances of the direction angle (a) and the surge velocity (b) 84 Figure 5.2 The real and reference propulsive forces generated by the left pectoral fin (a) and the right one (b) 84 Figure 5.3 The magnitude of the beating amplitude corresponding to the flexible left fin (a) and the right one (b) 85 Figure 5.4 The surge velocity performance (a); the rotational angles of the left hinge (b) and the right hinge (c); the fin tip simulation displacement (d) 86 Figure 5.5 Experimental demonstration of movement and deflection of flexible

pectoral fins in one cycle 87 Figure 5.6 The velocity of the robot in the variation of the frequency and amplitude of stimulating moment 88 Figure 5.7 Responses of the turning swimming speed (a) and the turning swimming radius (b) 89 Figure 5.8 The responses of the robot: Mechanical efficiency (a); Strouhal number (b) 91 Figure 5.9 The empirical responses of the straight swimming speed in correspondence with the fabricated fin types 93 Figure 5.10 The relationships between the turning swimming speed and the frequency

in correspondence with the fin prototypes 93 Figure 5.11 The experimental turning radius response via the frequency 94 Figure 5.12 The response of the surge swimming speed 95 Figure 5.13 The position of the hinge bases: The right hinge (a), the left hinge (b) 95

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Figure 5.14 The response of angular positions of the fin panels in the comparison between simulations and experiments: under right fin panel (a), upper right fin panel (b), under left fin panel (c), upper left fin panel (d) 96 Figure 5.15 The response of the surge swimming speed 97 Figure 5.16 The hinge position: the right hinge (a), the left hinge (b) 97 Figure 5.17 The responses comparison of rotational angles of the fin panels between simulations and experiments: under right fin panel (a), upper right fin panel (b), under left fin panel (c), upper left fin panel (d) 98 Figure 5.18 Straight swimming speed responses in the comparison between simulation and experiment 99 Figure 5.19 The turning swimming speed response in the comparison between

simulation and experiment 99 Figure 5.20 The responses of turning swimming radius in the correspondence between simulation and experiment 100

Figure 5.21 The expenditure power and COT in the forward swimming form 101

Figure 5.22 The responses, in the straight movement form, of the total thrust

efficiency, mechanical efficiency, and Strouhal number 102 Figure A.1 Structure of the Hammerstein-Wiener model 128

Figure B.1 Mode shapes of the non-uniform fin corresponding to the lowest five

estimated natural frequencies 131

Figure E.1 Motion trace demonstration of the experimental fish robot propelled by non-uniform flexible pectoral fins in straight swimming (a) and turning modes (b) 135 Figure E.2 Motion trace demonstration of the experimental fish robot with folding pectoral fins in straight swimming (a) and turning modes (b) 135

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LIST OF TABLES

Table 4.1 Comparison of estimating approaches to natural frequencies 68

Table 4.2 The robot parameter values 72

Table 4.3 Results from identification of turning swimming mode 75

Table 4.4 Coefficient of C d 76

Table 4.5 Coefficient of C a 76

Table 4.6 The equivalent magnitudes of stiffness coefficient and damping coefficient 80

Table 4.7 The parameter values of the body part and fins 81

Table 5.1 The parameters of the robot with uniform fins in simulation 83

Table 5.2 Average values of absolute straight velocity errors 89

Table 5.3 The nRMSE indexes of the investigated parameters 99

Table 5.4 A response comparison of swimming velocity and turning radius with previous searches 103

Table D.1 Apparatus for experimental work 134

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LIST OF ABBREVIATIONS

AI Artificial Intelligent

ANN Artificial Neural Network

AoA Angle of Attack

AUV Autonomous Underwater Vehicle

BCA Body/Caudal Actuator

BCF Body, and/or Caudal Fin

BET Blade Element Theory

BL Body Length

CFD Computational Fluid Dynamics

COT Cost Of Transport

CPG Central Pattern Generator

DBM Drag Based Mode

DOF Degree of Freedom

EBT Elongate Body Theory

FLC Fuzzy Logic Control

FPS Frames Per Second

FSI Fluid-Structure Interaction

GIM General Internal Model

ILC Iterative Learning Control

IPMC Ionic Polymer-Metal Composite

LAEBT Large Amplitude Elongated Body Theory

LBM Lift Based Mode

MIT Massachusetts Institute of Technology

MPA Median/Paired Actuator

MPF Median/Paired Fin

nRMSE normalized Root Mean Squared Error

PFC Piezoelectric Fiber Composite

PPy Polypyrrole

SBT Slender Body Theory

SISO Single Input Single Output

SMA Shape Memory Alloys

SMC Sliding Mode Control

UUV Unmanned Underwater Vehicles

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Fish-inspired robots have grown as a new research branch of the biomimetic robot field

in recent years In this dissertation, a novel view of the bio-inspired robotic fish propelled by pectoral fins is introduced From the finding of research gaps in the applications and theories, contributions were proposed The contents of this chapter introduce the general information concerning morphology, the anatomy of biological fish; the division of fish robot groups; material and actuation; modeling, and control issue The next components are the motivation and objective of the study The final is the proposed method and the expected outcomes

1.1 General information

The first approach to the fish robot's research is an attempt to investigate structure, morphology, anatomy involving in locomotion of natural fish These are vital information for underwater robot designs in concern with the transmission, self-propulsive mechanisms, turning swimming mechanisms, efficient propulsion, and maneuverability The discovery of biological fins has also revealed many crucial data For example, understanding includes 3D kinematics, morphology, electromyography of muscles, anatomy structure of fin blade, muscles, and skeleton, and swimming modes were investigated in detail [1, 2] In another additional example, morphology, and hydrodynamic of natural fin-type as the tail fin, pectoral fins, dorsal fin, and anal fin also aided in the improvement of AUV design [3] Based on the biological features, live fish was divided into the following groups

Figure 1.1 presents the division of fish firstly proposed by Lindsey [4] There are two dominant locomotion groups, named by BCF and MPF Additionally, fish have been divided the swimming modes into undulation or oscillatory The distribution of fish robots use an analogous model based on propulsive structures and swimming modes Detailed demonstrations of corresponding fish robot classification can be found in [5] However, with this arrangement, the number of groups increases significantly while the

2

mechanical structure and shape of the robots have just a little difference Won-Shik Chu

et al [6] proposed a modified model, shown in Figure 1.2, from Lindsey’s one [4]

Figure 1.1 Classification of fish species based on locomotion mechanism: (a) BCF

3

Corresponding to BCF and MPF, robot fish also consist of BCA [8, 11-13] and MPA Each group was further subdivided into U-undulation and O-oscillatory Additionally, jet propulsion was considered as an extension [10, 14-16] For example, several robotic fish prototypes representing for distinguishing robot groups are described in Figure 1.3 Fish robot researches are quite diverse However, they mostly focus on some directions

as follows

(a) (b)

Figure 1.4 Fish robot with two links and a complaint tail (a) [17], autonomous robotic

fish with a soft tail part embedded fluidic actuator (b) [18]

(a) (b)

Figure 1.5 Transmission mechanism for the tail of a fish robot: (a) using linear hypocycloid [19] (b) combining a compliant tail and driven ropes [20]

The first versions of the fish robot developed by MIT are RoboTuna and RoboPike, using a combination of motor, rope, and pulley to generate wave motion to caudal links This structure is suggested popularly in many designs for large size and multilink form [8, 21-29] Some others concentrate on the propulsive mechanism using a rigid tail [24]

or flexible tail fin [17, 30-33] In reference [30], V Kopman et al modeled a fish robot

owning a complaint tail (shown in Figure 1.4(a)), where tail fin considered as an elastic

4

beam and its deformation is due to surrounding fluid force Propulsive mechanism using

a motor also appear in the design of high-speed robot [34] With this structure, the robot fish can reach to a straight swimming speed 1.14 m/s (3.07 BL/s) and an angular speed

of turning of 90 degrees/s Another design employing hypocycloid to control tail trajectory also proved efficiency [19, 35] (Figure 1.5(b)) Additionally, wire-driven structures referred to the BCA group developed and improved high efficiency [20, 36, 37] (Figure 1.5(b)) Despite employing traditional mechanisms with servo motor, designs of robotic fish still have their advantages

On the other hand, fin ray or undulating fin with a kinematical design optimized has attracted more attention [38-44] Besides, many researchers have been engrossed in smart materials by smaller size than other actuators enabling to mimic the complex motions of real fish, for example, SMA [45-47], [48-50], IPMC [51-56], PPy [57], PFC [58] Additionally, the improved electromagnetic structure has been used to replaced traditional actuators using motors [59-63] New materials help designers easier to reduce the size of the actuators However, their cost is still an obstacle

Figure 1.6 An Agile robotic fish with high maneuverability [64]

Especially, mechanical designs for agile fish robots also developed that help to reach a high swimming speed of 1.21 BL/s [64] or 3.7 BL/s [34] Figure 1.6 illustrates a maneuverable fish robot using four fins that simulate wings of flying insects and fish fins This design keeps robot better stability by suppressing the effect of yaw motion Additionally, soft structures regarded by the capability to mimic movement behavior of fish is also an engaging challenge for many robot designers [14, 18, 65, 66] In summary, each mechanical structure has advantages and disadvantages, and choices depend on each application as well as its cost

5

The next challenge in studies on the fish-inspired robot is the establishment of the mathematical model of robot motion in fluid flow There are two used conventional approaches composing of the numerical method obtained by the solution of Navier-Stokes (a) and analytical method (b) At first method (a), the suggestions include CFD [67-71], FSI [15, 72-75] This approach can attain great accuracy but much time consumption and high computational cost Meanwhile, the second approach (b) owns lower accuracy without time expenditure and low calculation cost Therefore, this method gratifies to controller design or low-cost modeling

Some theories applied to the analytical method are classified as follows: resistive force theory [76], SBT [77], EBT and LAEBT [8, 78, 79], BET [80-82] SBT and EBT adapt

to model Anguilliform, Subcarangiform, and Carangiform while BET is more suitable

to gain the solution of Labriform Detailed comparisons between the above methods can

be found in [83]

Besides the mathematical modeling for fish inspired robots, the determination of parameters concerning these models is also very crucial There are some popular methods mentioned in [83], for example, the approximate model of shape [84, 85], simulation using CFD, direct measurement of experiments, or identification from operative data of robot [79, 80] At the first method, the commonly approximated shape

is a prolate spheroid due to simplification in estimating added mass and added inertia However, this approach is inappropriate for complicated architectures The numerical method adopting CFD can be employed to the intricate shape of the robot but calculated time consumption In some particular cases, parameters involving in kinematic or dynamic modeling can be directly measured or identified through combine between the gray box model and experimental data [13, 86]

Next to motion modeling for fish robots, designing controllers is one of the challenges because of the complicated impact of fluid flow on the behavior and performance of the robot Some previous research focuses on planning motion trajectory [87], controlling motion using traditional law such as SMC [8, 86], Back-stepping algorithm [88], ILC [38, 89] or intelligent control law as FLC [88, 90-92], CPG [93-99], ANN [100], Petri

network [101] In [102], N Xuelei et al proposed a control design, combined CPG and

6

neural network, enable the fish robot to mimic the swimming movement of live fish such as forward swimming or backward swimming It supports that the robot learns fast new gait from the extracted swimming pattern of real fish Several intelligent controllers are employed in the fish robots, for instance, to track to desired deep via ANN [100] or SMC-FLC [103] Controllers proposed to fish robots have attained remarkable advancement However, natural swimming ability is still a challenge Additionally, the adaptation of autonomously robotic fish to variation of the environmental condition has not yet been recognized

To find the solution to design issues or motion control for robotic fish, optimal algorithms have been applied broadly [24, 104, 105] In reference [105], the swimming speed of a fish robot was optimized by using the Taguchi method with the constraint of motor power limitation Input parameters include the aspect ratio of tail fin (AR), stiffness of spring transmitting force to foil, stiffness of tail fin, and oscillating

frequency In [106], Licheng Zheng et al concentrated on the mechanical design of fin

ray of cow-nosed robot fish, where key geometrical parameters optimized for the stage rocker-slide mechanism As a result, design problems with many parameters became more efficient with optimization algorithms

two-Furthermore, some researches concerning and supporting applications on robotic fish have been implemented For example, the image quality enhancement from a fish robot camera [107], the effect of the head swing angle on the performance of fish robot [108], , the pressure sensory system on lateral line [109], information remembrance skin [110] These researches can complement the capability of a fish robot to converge on biological counterpart one

There is a spread of studies on fish robots However, this area has still been very potential The trends of researches on robotic fish, in the next time, can be enumerated

as follows [5, 12, 83, 111, 112]:

(a) Researches on actuators of fish robot aim to improve swimming efficiency

- Speed and maneuverability: Electrical-mechanical mechanisms as electrical motors consume much energy and limit maneuverability Hence, it is necessary to replace or

- Enhance the efficiency of energy expenditure It can obtain from increasing locomotion efficiency of the propulsive actuator On the other hand, the motion trajectory of the robot should be not only optimized while avoiding collision, obstacle , and unexpected turbulence from the surrounding environment [117] but also taken advantage of Kármán vortex street to economize energy [118]

(b) Improve the gait of the robotic fish through compliant structures: The robot's body part and caudal using multi-link mechanisms [22, 23, 119] have generated movements quite similar to live fish However, in the above designs, real motion is discontinuous and redundant for control due to a large number of DOF of actuators Therefore, using flexible and continuous mechanisms is being a constructive approach It can also be combined with the electrical-mechanical structure or smart material [120]

(c) Enhance the autonomous ability of fish robots: Autonomous operation is a challenging issue in the complexity condition of the environment that requires new algorithms in planning the trajectory of motion, handling navigation system, or controlling swimming adaptively

(d) Study new sensors on robotic fish: These are also a different approach to advance the autonomous capability under the distinctively environmental condition

(e) Study on fabrication and manufacture: Fish robot consists of components of the electric and mechanic, compliant structure, smart material Thus it requires that production need to obtain accuracy reliability under durably working condition New designs need to be feasible to fabricate and endure under the influence of environmental conditions

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(f) Apply AI in control the operation of the fish robots: With the fast development

of AI, application capability is positive, for instance, in planning trajectory, controlling motion, making decisions on interaction with the surrounding environment

1.2 Motivation

Firstly born from 1957s, autonomous underwater systems were developed for a wide range of fields such as exploring and exploiting the ocean environment, marine geoscience, archeology, commercial, and military [121-125] However, traditional propulsion systems almost reached the limits of performances For demonstration, a versatile propulsion system using propellers is depicted in Figure 1.7 Meanwhile, natural selection gave aquatic animals the ability to swim amazingly As a result, this produces chances for the appearance of new propulsive mechanisms inspired by underwater creatures

Figure 1.7 Propulsion and turn system of a vessel using propellers [126]

Since the first version published in 1989 from MIT, robotic fish have attained a more rapid progression Application researches inspired by fish are diverse such as the studies

on the behavior of fish, education, cooperation in transportation, incorporation in voiding obstacle, environmental exploration, monitoring water quality, investigating coral reefs, seeking marine debris In the military field, fish robots were researched early, especially from the US and China For example, a fish robot from China named bionic machine shark, with a real shark size, was introduced in a military expo in Beijing

in 2019 [127] It is reported that the robot has high swimming speed, large load, and low

9

oceanic noise It can also perform missions of reconnaissance, surveillance, and intelligence Therefore, the potential for future applications of robotic fish is still enormous

Figure 1.8 Gomphosus varius fish [128]

However, fish robots are still far from swimming speed, maneuverability, energy consumption, and efficiency compared to biological counterparts For example, experimentally forward swimming speed of a robot can reach 3.07 BL/s [34] or 11.6 BL/s (3.7 m/s) [129] while natural fish's one achieves 25 BL/s [130] (Gomphosus varius fish– Figure 1.8) In consideration of maneuverability, Nibble fish can perform a turning radius from 10% to 30% its body length, 10-times lower than corresponding to ship one [12] The maximum turning swimming speed of fish robot that can reach 670 deg/s [131]

is lower than compared to 2600 deg/s of natural fish (Esox masquinongy) [132] Additionally, the propulsive efficiency of mullet can attain 97% in continuous swimming mode These are challenging gaps for future researches

Unlike fish robots driven by caudal, fish robots propelled by the pectoral fins have high stability due to the elimination of head swing phenomena that exist on BCA swimming Furthermore, they can generate powerful acceleration thrust For example, living fish using pectoral fins can also perform a speed range of 1-6 BL/s [133] For Labriform movement mode, fish obtain higher efficiency in a low-speed range [7], especially in drag-based swimming However, knowledge of swimming structures employing robotic pectoral fins is very humble Recently, an increase in pectoral fin researches has been mentioned Some investigations have been realized on rigid pectoral fins [134-136] and uniform ones [80-82] In particular, studies into robot fish, thrust by compliant structures with natural bionic shape, have not yet been regarded Meanwhile, these structures own movement efficiency better than rigid robotic ones

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From all of the above-analyzed factors, a concentration on novel pliant structures, inspired by natural pectoral fins, is necessary to implement further understand to underwater robot designs using fin pairs These are an excellent chance to fill the research gap by dissertation contributions

1.3 Aim and scope

This dissertation aims to build analysis models of a fish robot employing pectoral fins

to explore the influence of pectoral fin structures at different swimming modes on the robot's locomotion behavior from analyzed research intentions The propulsive methods

of fin include lift based one and drag based one

Some objectives are addressed to achieve the mentioned aim as follows: Firstly, new designs based on bio-inspired pectoral fin types are constructed Secondly, to describe fin deformation and body part movement, novel dynamically mathematical models are developed Thirdly, experimental data are also collected and measured to complete the evaluation model, including unknown coefficients and relationships between parameters Finally, the author compares between simulation and practical responses to examine the precision of prediction models Additionally, it should be noted that some results are vital to assess the effectiveness of recommended fin types and identify the critical parameters on the swimming performances of robotic fish

The dissertation provides an in-depth understanding of the pectoral fin parameters on robot locomotion behavior through the mentioned aspects However, in the dissertation's scope, the propulsion of the robot is due to pectoral fins The influence of tail fin motion

is ignored Additionally, since time and financial sources restrict, this dissertation is only limited to the fish robot's movement near the water surface and static inviscid freshwater environment These are also the current constraint in this research

1.4 Methods and results

Based on the presented objectives, research issues were deployed accordingly Figure 1.9 summarizes a diagram that facilitates following the study contents and used methods Wherein three groups of robotic fish with different pectoral fin types, including uniform pectoral fins, non-uniform pectoral fins, and folding pectoral fins,

11

were mentioned For more details, dynamic models and motion control issues were established to all of the fin structures However, after attaining theory approaches, experimental works to validate simulation models were only applied to the fish robot with two last fin types due to the complication of their designs

Euler-Bernoulli beam theory, Morison s equation

Numerical simulation

Fish robot propelled by the flexible pectoral fins

The fish robot with non-uniform pectoral

model of body

motion

Lagrange method, Morison equation

Rigid body dynamics Rigid body dynamics Rigid body dynamics

Control design

Direction and surge velocity controller based on feedback linearization

Fin motion control with different strokes based

on the amplitude modulation method

Fin motion control based on the amplitude modulation method

Validation

Numerical simulation and evaluation experiment

Numerical simulation and evaluation experiment

Figure 1.9 Summary of the research approach scope

On the other hand, because of the difficulties in establishing mathematical modeling, a series of methods were combined Firstly, to describe the impact of fluid flow on surfaces of fins or panels, there are several feasible approaches to fluid forces Generally, they depend on the Reynolds number With low Reynolds number case, resistance force theory is appropriate because the effect of drag is dominant (i.e [78])

In contrast, the reactive force model mainly concerning the inertial effect is proper for the high Reynolds number one (i.e., Lighthill's SBT) For average Reynolds number, models as Jordan' model [137] or Morison' one [138] are more suitable However, in another case, the viscous force effect of fluid was taken into account in modeling's eel robot next to drag force and inertial ones [139] In this dissertation, force interactions of

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inertia and drag, in the general form of Morison's model, were considered trade-off of complexity and calculation capacity It should also be noted that the viscous force was neglected due to the average Reynolds number in the study realm

Secondly, the dissertation focused on the uniform pectoral fin type with the assumption that only exist bending displacement in a small magnitude region Thus, the Euler-Bernoulli beam theory is suitable for fin motion modeling Moreover, this theory enables earlier to achieve the mathematical model of uniform fin motion

Thirdly, in the dissertation, the Lagrange method was employed due to simplicity and clarity in describing dynamics relations between input control torque from motors to the robot's output performances This approach has been mentioned in previous research on

a compliant caudal structure [120]

Fourthly, to determine natural frequencies and mode shape functions of a beam-like non-uniform fin, in deformation modeling, Rayleigh-Ritz approximate method was applied It was noted that fins were assumed which only exist a bending deflection along the fin length Compared to others, for example, an exact solution from the analysis method has been a challenge to obtain For this issue, the Rayleigh-Ritz method is a brilliant choice that can produce excellent results However, it also requires a suitable trial function which has to satisfy boundary conditions as merely geometric boundary conditions It is not easy to choose a trial function, which has decisive influences on the rate of convergence of results [140] A set of trial function candidates can be considered

as admissible functions, comparison functions Details of this choice were presented in Chapter 4

Finally, in efforts to reduce the mathematical model complexity of body motion, the dissertation applied equations taken from rigid body dynamics to describe swimming motions in a horizontal plane Additionally, the dissertation implemented an amplitude modulation method to stabilize the oscillating direction of fins under the complex influence of vortex wake disturbance from flow interaction surrounding fins

Based on research objectives, the dissertation also deployed and obtained outcomes in some aspects as follows:

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(i) Establishing a hydrodynamic model for the fish robot propelled by uniform pectoral fins A simple control structure was designed to track the following reference swimming direction and desired surge velocity Simulation responses revealed that achieved results are relatively feasible

(ii) Proposing a dynamic model for the fish robot with non-uniform pectoral fins inspired from the natural shape of a live fish Simulation results and experimental validations showed that the suggested model predicts the behavior of the robot's real motion relatively precisely

(iii) Recommending a type of folding pectoral fins aim to improve the speed and locomotion efficiency of the robot

(iv) Introducing a dynamic description for fish robot propelled by the folding pectoral fins, where swimming performances, energy expenditure efficiency, propulsive efficiency, Strouhal number were investigated Results of both simulation and experimental evaluation claimed that the achieved model forecasts the swimming responses of the robot relatively comprehensively

Generally, in a combination of the mentioned approaches, above hydrodynamic models own less complication Thus, they allow expanding to swimming performance analysis, optimization issues, or control design Moreover, the suggested design analyses facilitate to enhance movement speed, maneuverability, and swimming efficiency for fish robot actuated by bio-inspired pectoral fins

1.5 Organization of dissertation

The remainder of the dissertation is organized in the following structure:

In chapter 2, a literature review of recent researches involving fish robots using pectoral fin is principally focused Then, the proposals to fill the research gap are explored and complemented by my contribution Furthermore, theoretical knowledge regarding the proposed approaches of the dissertation is addressed

Chapter 3 mentions to approaches of modeling and control issues of the fish robot Three types of flexible pectoral fins consisting of cantilever-beam-like uniform fins, non-

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uniform fins, and folding fins are considered It is worth noting that the corresponding dynamic models are established Moreover, the control issue of direction and surge velocity of fish robot propelled uniform fins is recommended The results were examined by simulation However, this dissertation's principal contributions were focused on the fish robot with types of non-uniform fins and folding fins Instead of adopting the approach of exact computation via CFD or FSI, the combinations among standard Lagrange method, the Morison's force model, and dynamics of a rigid body were conducted to establish the approximate dynamic model with less complexity Chapter 4 presents the experimental works concerning the validation of proposed models of self-propelled robot fish with non-uniform fins and folding fins The identification is included in the parameters corresponding to the case of non-uniform fins: natural frequency, mode shape, internal damping, thrust coefficient of fin actuator, and dynamic coefficient of the robot body For the case of folding fins, the estimated parameters comprise of coefficients of spring and damping of the equivalent flexible joint, the time ratio of the power stroke and the recovery stroke, and the moment ratio amplitude between strokes

In chapter 5, results and discussion are exhibited and assessed Some aspects are regarded as follows: (1) the simulation performances of dynamic model and controller

in both swimming velocity and motion direction; (2) behavior of fish robot adopting the non-uniform pectoral fins; (3) performances of the fish robot with flexible folding pectoral fins

Chapter 6 summarizes my novel contributions forward fish robot area Some proposals are recommended to the robot employing flexible pectoral fin Moreover, the limitations and challenges are presented Finally, the trend of future works is also addressed to improve the performance and behavior of fish robot with the pectoral fins

Publications, references, and concerned appendix of chapters are presented in the final part of this dissertation

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This work mentions study reports on both biology fish and robotic counterparts It reveals that researches on the pectoral fins of fish-like robots are not much Implemented investigations include the following aspects: morphology and anatomy in the bio-inspired design of pectoral fin, kinematic and experiment, fish robots with pectoral fin ray, modeling based numerical simulation, application of smart materials in the design

of pectoral fin, experiment technique and data capturing, control issue of fish robot driven by pectoral fins, dynamic modeling, and transformation fin Several trends and critical discussions were presented to clarify the proposed methods for undertaking challenges and the dissertation's contributions then Lastly, the fundamental theories concerning the Morison equation, the Rayleigh-Ritz method, Kirchhoff’s equation, and the Hammerstein Wiener model are introduced

2.1 Literature review

Pectoral fins have an imperative position in fish locomotion A range of 15%-20% of biological fish employs pectoral fins as the dominant source of thrust in particular of MPF group [1] Furthermore, BCF fish uses pectoral fins to keep balance, turning, backward swimming, or braking swimming Therefore, they generate movement gaits, which have high flexibility and maneuverability Recently, studies on bio-inspired pectoral fins have obtained significant achievements Review and discussion of studies concerning pectoral fin on BCA and MPA have presented as follows:

Figure 2.1 An illustration of three basic operation modes of pectoral fins [141] The actual motion of the biological pectoral fin is immensely complicated For example, the movement of a pectoral fin of Koi Carp fish has included different forms such as cupping-expansion, expansion-cupping, undulation, bending-cupping [142] However, according to [141], it has been divided into three principal motion depicted in Figure

16

2.1: rowing, feathering, and flapping Moreover, the operations of the pectoral fin have been arranged into two modes, including the drag based mode (DBM) and the lift based mode (LBM) [143] Researches have based on this division to design their fish robots Considerations for approaches of studies on the pectoral fin were conducted in some directions mentioned follows

2.1.1 Morphology and anatomy in the bio-inspired design of pectoral fin

To solve the challenges of designing the biomimetic fish robot, knowledge about the morphology and anatomy of aquatic animals is hugely crucial It allows utilizing advantages obtained from evolution and adaptation of fish into the design of bionic pectoral fin

In reference [2], M W Westneat et al have concentrated on structures, the motion of

pectoral fins, and the neural control of Labriform fish (demonstrated in Figure 2.2) Three discussed areas included as follows: (1) structures of muscle, skeleton, fin blade; (2) movement modes of flapping and rowing; (3) electrical muscle motion and neuroanatomy Recommends have been then implemented to the design of fin shape, motion patterns that are essential information for studying underwater vehicles propelled the bio-inspired pectoral fins

Figure 2.3 Motion demonstration of pectoral fin prototype mimicking the movement of bluegill sunfish fin: (a) expansion, (b) curl, (c) relax, and (d) cupping [144]

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Another study mentioned in [144] focused on anatomy, kinematic, and hydrodynamic

of bluegill sunfish CFD simulation has been employed to estimate the propulsive force Authors have discovered that the complex motion of pectoral fins enables to generate force vector in 3D efficiently in both strokes of abduction and adduction while only producing a small value of lateral and lift forces These results have been used to guide experimental studies of pectoral fin mimicking the complex and maneuverable motions

of sunfish fin Furthermore, this research has heavily concentrated on the anatomy of real fish to prepare forward equipment pectoral fins to UUVs with the capacity of high maneuverability (illustrated in Figure 2.3) However, because a high number of DOFs

is high, therefore, the control issue of actuators is quite complicated Additionally, several studies on the morphology of MPA pectoral fin in undulation form have been investigated in references [145, 146]

Above mentioned results are not only useful for biologists in finding functions of aquatic creatures but also significant for developers to improve the swimming efficiency of robots with artificial propulsive fins

2.1.2 Kinematic and experiment

Figure 2.4 Illustration of a robotic design with a pectoral fin [141]

As initial studies mentioned fish robot using pectoral fins, some research groups have carried out preliminary works in the pectoral fin designs regarding kinematic and experiment [134-136, 141, 147-149] For example, a model of three DOFs pectoral fin has been suggested in reference [141], where fin motions driven by servo motor include: rowing, feathering, and flapping (see Figure 2.4) Movement modes have been based on

18

drag and lift forces in detail Specifically, fluid forces exerted on the fin surface and obtained propulsive efficiency has been analyzed through experimental data However, this study has not yet provided the shape of the fin or optimal trajectory corresponding

to operation modes In other research, from the investigation of morphology and anatomy of live fish pectoral fins [136], a design of two DOFs fin mechanism for Labriform robotic fish has been implemented (illustrated in Figure 2.5) Experimental results have proved the feasibility of the proposed method It is noted that the robot operates in rowing mode However, the movement speed of the robot is quite low and obtained Strouhal number also lies far efficient swimming range Moreover, this study only focuses on the kinematic solution of the robot

Figure 2.5 Mechanical design of fish robot propelled by two DOFs pectoral fins [136]

Figure 2.6 Motion production structure for pectoral fins (a), the illustration of transmission principle diagram on pectoral fin (b), entire transmission mechanisms on

the fish robot (c) [150]

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A design of robotic fish consisting of a couple of pectoral fins and a tail fin has been introduced in [150] The tail part has been constructed by several discontinuous segments and mechanisms of wires and motor Meanwhile, each pectoral fin possesses

an actuator with two DOFs of flapping and feathering motions (see Figure 2.6) In the incorporation of the pectoral and caudal fins, the robotic fish has reached a speed of 0.66 BL/s or 0.26 BL/s for using only the pectoral fins For turning radius, the fish robot has taken a value of 0.6 BL without applying the pectoral fins or reduced to 0.25 BL with these fins On the other hand, this work has employed Lighthill's EBT to estimate thrust produced by the tail fin, while forces from the pectoral fins have been calculated on the drag model The research has pointed out that a combination of caudal and pectoral fins improves performances significantly, including straight swimming speed, turning speed, and turning swimming radius These results are positive, which are bases to enhance the operating range of bio-inspired robots

Another research based on the kinematic design of robotic fish has been reported in [151] The authors have proposed a control law to the multilink robot with the assistance

of pectoral fins Based on the GIM, the robot has generated undulating gait of the body and tail parts while pectoral fins have aided to adjust movement direction Moreover, several swimming control strategies employed FLC have supported to conduct cruise and C sharp turning modes Experimental results have claimed the feasibility of proposals However, the principal weakness of this approach is the hydrodynamic relationship between the body part, fins, and surrounding fluid flow has not been established explicitly yet With a combination of tail and pectoral fins, the swimming and turning performances of a robotic fish have also been completed in studies [20, 152] Wherein the robots have a design inspired by Carangiform fish, and its pectoral fins work at mode flapping or feathering to intensify maneuverability and motion speed

In general, the pectoral fins play an assistant role in swimming modes in the above researches Use of high DOFs pectoral actuators in combination with the tail part, robots can increase maneuverability However, with individual usage of pectoral fins, the robot's locomotion efficiency reduces appreciably

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2.1.3 Fish robot with pectoral fin ray

Figure 2.7 Prototype of fish robot Manta [40]

In the form of Rajiform, robotic fish, as a counterpart of Manta ray, attracted the attention of researchers by silent motion and fast speedup compared with underwater vehicles using traditional propellers For example, an illustration of design with fin rays and the artificial membranes is presented in Figure 2.7 In [40, 153], authors have developed a version that mimics the behavior of a live Manta ray To simulate motions

of fin ray units, the CPG controller has been employed Nevertheless, the main limitation

of the above researches is that proposals have been only verified through simulation and on-ground experiments

Figure 2.8 Versions of Cownose ray robot and the pectoral fin structure of Robot-ray

IV [154]

In [154], Lige Zhang et al have developed some fish robot versions inspired by

Cownose Result illustrations are shown in Figure 2.8 The authors have the flapping kinematic model of pectoral fins on the base of motion and characteristics of the Cownose rays It is noted that a two-DOFs parallel mechanism is utilized in the current version of a pectoral fin skeleton to mimic heaving and pitching motion Moreover, the

21

optimization issue of the design has analyzed through simulation Experimental results have claimed that the new pectoral fin model owns better swimming performance while maintaining high maneuverability of previous versions However, the primary limitation

of these work shows that their approach only mentions to kinematic design and mechanism optimization-based kinematics

(a) (b)

Figure 2.9 Freshwater stingray (Potamotrygon motoro) (a), an illustration of

undulation sequence of pectoral fin in a period (b) [155]

Also inspired by maneuverability and high propulsive efficiency at the low-speed range,

a study that simulates the motion of Freshwater Stringer has been explored in [155] (depicted in Figure 2.9) First, the authors reviewed the morphology and motion patterns

of a live stingray On the base of some assumptions, the kinematic model of fins has been established Then, authors have designed disc-like pectoral fins to mimic the cruising or maneuvering undulation motions It is noted that the influences of the parameters, including oscillating frequency, angular deformation, the wavenumber of fin rays in the production of thrust force, and swimming speed, have been explored through experiments However, the swimming speed of 0.18 BL/s, the robot reaches, is quite low compared to some previous research Additionally, the design of the robot is only on the base of kinematics analyses

In the other study [156], a bionic design based on motion observation of manta ray has also been proposed Its structure has consisted of an integration of a flexible mechanism and rigid elements in the same design (see Figure 2.10) The simulation results reveal that performances show the real deflection of pectoral fins well This research has also utilized a CPG controller to achieve rhythmic swimming gait Moreover, through some experimental works, the feasibility of proposals has been verified The authors present

an interesting approach with a compliant structure to imitate the movement of real

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manta However, the research still focuses mainly on the kinematic challenge Additionally, experiments are insufficient in confirmation of the advantage of designs Generally, researches on the fish robot using pectoral fin ray have still existed several challenges, for example, dynamically analytical model, swimming efficiency, and energy expenditure

(a) (b)

Figure 2.10 Analytical scheme of the pectoral fin of manta (a), the design

demonstration of bionic manta robot (b) [156]

(a) (b) Figure 2.11 Definition of sweep angle (a), illustrations of MantaDroid driven by

pectoral (b) [157]

(a) (b)

Figure 2.12 Illustration of artificial pectoral fin based four tensegrity beam (a) and

experiment of a tensegrity structure (b) [158]

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The influence of the kinematic factors on the swimming response of a Manta robot was regarded in [157] (demonstrated in Figure 2.11) Based on experimental data on a variety of fin patterns with different sweep angles under the condition of free water and still one, this study has revealed that sweep angle has no effects significantly on thrust generation This result can support in the design of a fish robot using flapping pectoral fins Additionally, another research on the optimal design of artificial pectoral fin has been carried out in [158] (see Figure 2.12) Inspired by manta ray with deformation and large thrust production of pectoral fin while using low energy expenditure, a variety of mechanical structures based on tensegrity mechanism have been analyzed Optimal kinematic solutions have revealed that tensegrity based designs can provide high performance to pectoral fins With this mechanism, the pectoral fin can become lighter and more durable while maintaining flexibility

Diversity in the mechanical structures of developed MPF fish robots assists to chose designs easier in imitating the pectoral fin motion of real fish in both flapping and undulation modes However, in most of the approaches, authors have concentrated on analysis, design, and optimization issues based on kinematics

2.1.4 Modeling based numerical simulation

Numerical simulation tools that emulate the fluid environment has remarkably attracted attention of researchers Simulation approaches based on the solution of the Navier-Stokes equation attain reliability and high accuracy but high computation cost and extremely time consumption

Figure 2.13 Model of pectoral fin types: rigid fin (a), flexible fin (b), fin with variable

stiffness (c) [159]