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 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: Assoc Prof Dr Vo Tuong Quan Assoc Prof Dr Nguyen Tan Tien 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 i 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 ii 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 iii TÓM TẮT Nhu cầu hệ thống đẩy mới, không hiệu cấu trúc đẩy truyền thống mà thân thiện với môi trường, lý cho việc nghiên cứu robot với vây lấy cảm hứng từ cá Trong đó, vây hơng cá sinh học đóng vai trị quan trọng chế vận động, đặc biệt, có tỷ lệ nhỏ cá tự nhiên sử dụng vây hông làm thành phần đẩy Tuy nhiên, hầu hết tỷ lệ cịn lại sử dụng vây cho khả động ổn định chuyển động bơi Khả tăng tốc, giữ thăng lướt khoảng cách ngắn đặc điểm cá sử dụng kiểu vây Mặt khác, mơ hình động lực học vây với khác hình dạng độ linh hoạt vấn đề quan trọng, vậy, chưa đề cập nghiên cứu trước Trong nỗ lực tạo cá tự nhiên, luận án đề xuất số cách tiếp cận việc thiết kế, phân tích thiết lập mơ hình tốn học cho robot giống cá sử dụng vây hông Lấy cảm hứng từ vây cá tự nhiên, luận án tập trung vào cấu trúc linh hoạt cho phép tạo chuyển động trơn tru, chi phí lượng thấp lực đẩy hiệu Các khảo sát cho thấy rằng, dạng vây mềm loài cá tự nhiên sở hữu hiệu đẩy cao Trong luận án này, ba dạng vây riêng biệt bao gồm kiểu đồng dạng, kiểu không đồng dạng kiểu vây gấp nghiên cứu Đặc biệt, để bắt chước vây cá sinh học, hình dáng hình học vây hơng cá lóc thơng qua Mơ hình tốn học thiết lập với trợ giúp phương pháp Rayleigh-Ritz mơ hình hóa biến dạng Hơn nữa, để cải thiện tốc độ bơi robot cá hiệu tiêu thụ lượng, kiểu vây hông gấp nhân tạo, lấy cảm hứng từ thay đổi tỷ lệ diện tích cản/đẩy vây cá tự nhiên, đề xuất Mơ hình tính tốn robot loại vây thiết lập dựa sở động lực học thân cứng mô hình lực Morison Ở đây, ảnh hưởng chất lỏng lên chuyển động vây mô tả phần tử riêng biệt với khối lượng thêm vào độ cản chất lỏng Đối với hai kiểu vây cuối, phương pháp Lagrange sử dụng để thiết lập phương trình động lực học chuyển động Hơn nữa, thử nghiệm thực để kiểm tra đánh giá mơ hình đề xuất Các kết đạt khẳng định đề xuất khả thi dự đoán hành vi robot tương đối tốt Đáng ý, cá robot có vây hơng gấp iv đạt tốc độ di chuyển nhanh khả động tốt so với thiết kế trước sử dụng kiểu vây Cụ thể, robot đạt vận tốc trung bình 0.58 BL/s (0.231 m/s) chuyển động bơi thẳng bán kính chuyển hướng 0.63 BL (0.25m) chuyển hướng Vận tốc cao đạt tới 0.78 BL/s (0.308 m/s) Mặt khác, tiết lộ vây hơng gấp với khớp linh hoạt vừa phải có đáp ứng tốc độ tốt so với kiểu vây có độ cứng khớp cao Kết luận án sử dụng thiết kế thuật toán điều khiển bám quỹ đạo mong muốn tương tác với môi trường xung quanh Hơn nữa, mở rộng vấn đề tối ưu hóa chuyển động Một vài hướng phát triển tương lai đề cập để giải thách thức cải thiện hiệu bơi xây dựng mô hình động lực học phức tạp cho chuyển động robot không gian ba chiều v 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) vi CONTENTS LIST OF FIGURES x LIST OF ABBREVIATIONS xv CHAPTER INTRODUCTION 1.1 General information 1.2 Motivation 1.3 Aim and scope 10 1.4 Methods and results 10 1.5 Organization of dissertation 13 CHAPTER 2.1 BACKGROUND 15 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 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 vii 3.2.3 3.3 Motion control of the non-uniform pectoral fins 53 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 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 nonuniform fins 67 4.1.3 Estimation of the internal damping of flexible non-uniform fins 69 4.1.4 Measurement of thrust coefficient CT 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 RESULTS AND DISCUSSION 83 5.1 Performance of fish robot with uniform pectoral 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Triantafyllou, and D K P Yue, "Efficiency of fish propulsion," Bioinspiration & Biomimetics, vol 10, no 4, p 046013, 2015 [215] A Krishnadas, S Ravichandran, and P Rajagopal, "Analysis of biomimetic caudal fin shapes for optimal propulsive efficiency," Ocean Engineering, vol 153, pp 132-142, 2018 [216] C Eloy, "Optimal Strouhal number for swimming animals," Journal of Fluids and Structures, vol 30, pp 205-218, 2012 125 APPENDIX A (A-i) The Morison force exerting on a cylinder is described as a superposition of the inertia and drag forces per length of unit as follows: 1 dU F  Cd  D U U  Ca D , dt (A1) where Cd and Ca denotes the drag and inertial coefficients, respectively;  , D , and U are the density of water, the diameter of the cylinder, and the ambient flow velocity, respectively (A-ii) To discover the natural frequencies and the mode shapes of a non-uniform beam that is fixed at one end and free at another, the Rayleigh-Ritz method is employed According to this approach, the assumption of a harmonic excitation with frequency  and magnitude   x  is assigned A quantity  is calculated as follows:   Tmax  Vmax , (A2) where Tmax and Vmax denote the maximum kinetic energy and the maximum potential energy, respectively And, their descriptions are given by: Tmax  2  L  A  x    x  dx, (A3) Vmax  d 2  L   EI  x    dx  dx  (A4) By substituting equations (A3) and (A4) into equation (A2), the description of  is rewritten as:  2  d 2  x   L  A  x    x  dx   EI  x    dx 2  dx   L (A5) Assume that the magnitude of fin vibration can be expressed by: N   x    cnn  x , (A6) n 1 where n  x  and cn are the trial function and the undetermined coefficient, respectively 126 The Rayleigh-Ritz declares that the requirement for the stationery value of  is satisfied by the following expression:   , n  1, 2, , N cn (A7) By substituting equations of (A5) and (A6) into equation (A7), the outcome obtained as the following expression: N N l 1 l 1   cl I1,nl   cl I 2,nl  0, where: (A8) I1, pl    A  x  l  x   p  x  dx ; I 2, pl   EI  x  l x   p  x  dx L L 0 The prime indicates the derivative concerning x In matrix form, the equation of (A8) can be rewritten as follows:  I c    I1 c  0, (A9) where  I k ,11 I  I k    k ,21   Ik ,N1 I k ,11 I k ,22 Ik ,N I k ,1N   c1   c  I k ,2 N    , k  1, ; c        cN  I k , NN  It should be noted that the equation of (A9) is an eigenvalue equation from  and, thus, the mode shapes   x  , in correspondence, can be decided as soon as I1,nl , and I 2,nl are determined By arranging the eigenvalues in ascending order and then normalizing   x  to the unitary displacement of fin tip, that satisfies the condition:   L   The mode shape functions of the beam-like fins can obtain (A-iii) Equations, expressing the motion of the robot body in the six-DOFs body-fixed frame, is present as follows:      CM   ,      CM    VCM   127 (A10) T T where, the symbol "  " is a cross product VCM  vx , v y , vz  and CM  x ,  y , z  are the linear velocity vector and the angular velocity vector of the body in the body-fixed frame vx , v y , and v z refer to components of surge velocity, sway velocity and heave velocity, respectively x ,  y , and z are the velocities of roll motion, pitch motion, T and yaw motion, respectively    Fx , Fy , Fz  ,    M x , M y , M z  respectively denote external force vector and external moment vector exerting on the mass center of the robot concerning corresponding axes in the body-fixed frame  and  denote linear momentum and angular momentum concerning six-DOFs body fixed frame, respectively Their expressions are written as: T    VCM   CM ,     V     CM CM  (A11) where,  and  are the mass matrix and inertial one, the  denotes the Coriolis and centripetal one (relevant to the body-fixed frame), respectively (including both actual and added components) (A-iv) A structure of Hammerstein Wiener model is presented in Figure A.1 uHW(t) Input nonlinearity function f(.) wHW(t) Linear function xHW(t) Input nonlinearity function h(.) yHW(t) Figure A.1 Structure of the Hammerstein-Wiener model Input/output nonlinear block: Piecewise linear function (pwlinear) is defined as a nonlinear function with n breakpoints, where f . and h . are linearly interpolated between points Linear block: Structure of linear block is shown as below equation: with xHW  t   [ BHW  q  / FHW  q ]wHW  t  nk   e  t  , (A12)  BHW (q )  b1  b2 q 1   bnb q  nb 1 ,  nf 1 F q  f  f q   f q    HW nf (A13) 128 where nb and n f are the numbers of zeros, poles, respectively nk is the delay from inputs to output in terms of the sample number q and e  t  denote time-shift operation and the error signal, respectively It should be noted that the coefficient number in numerator polynomial BHW (q ) is equal to the zeros number ( nb ) plus one and the coefficient number in denominator FHW  q  is equal to poles number ( n f ) 129 APPENDIX B (B-i) The equations of five mode shape functions of the non-uniform pectoral fins obtained from the Rayleigh-Ritz technique: 1  x   (4652567012015251 sin ((4975976255517187 x )/140737488355328))/3242344524523616 - (2251799813685248 sin ((4441609944083711 x )/35184372088832))/101323266391363 + (8325148586440473 sin ((4469965519475467 x )/35184372088832))/405293065565452 + (4722319833964537 sin ((3715844511367963 x )/35184372088832))/810586131130904 - (7023908659131179 sin ((3498674146857787 x )/35184372088832))/1621172262261808; 2  x   (133565388363600544 sin ((4469965519475467 x )/35184372088832))/3789133972601957 - (144115188075855872 sin ((4441609944083711 x )/35184372088832))/3789133972601957 - (44421643238607 sin ((4975976255517187 x )/140737488355328))/541304853228851 + (34896936879001804 sin ((3715844511367963 x )/35184372088832))/3789133972601957 - (25183627839894728 sin ((3498674146857787 x )/35184372088832))/3789133972601957; 3  x   (6134998300011545 sin ((4975976255517187 x )/140737488355328))/46833027674504008 - (144115188075855872 sin ((4441609944083711 x )/35184372088832))/5854128459313001 + (136054532366090848 sin ((4469965519475467 x )/35184372088832))/5854128459313001 + (14868130867079312 sin ((3715844511367963 x )/35184372088832))/5854128459313001 - (5083617886275337 sin ((3498674146857787 x )/35184372088832))/5854128459313001; 4  x   (568994218219518 sin ((4975976255517187 x )/140737488355328))/1411660933423651 + (576460752303423488 sin ((4441609944083711 x )/35184372088832))/1411660933423651 - (551497570972094080 sin ((4469965519475467 x )/35184372088832))/1411660933423651 - (53761381193989496 sin ((3715844511367963 x )/35184372088832))/1411660933423651 + (34483083200623424 sin ((3498674146857787 x )/35184372088832))/1411660933423651; 5  x   (67334080953327976 sin ((4441609944083711 x )/35184372088832))/4513627138401969 -(4635424265835275 sin ((4975976255517187 x )/140737488355328))/144436068428863008 -(72057594037927936 sin ((4469965519475467 x )/35184372088832))/4513627138401969 +(9237008405525938 sin ((3715844511367963 x )/35184372088832))/4513627138401969 -(3207770535994854 sin ((3498674146857787 x )/35184372088832))/1504542379467323; 130 (B-ii) Performances of the mode shape functions in the lowest five modes are described in the following figure 1 0 0.02 0.04 0.06 0.08 0.06 0.08 0.06 0.08 0.06 0.08 0.06 0.08 x (a) 2 -3 0.02 0.04 x (b) 3 -2 0.02 0.04 x (b) 4 -2 -12 0.02 0.04 x (c) 5 -2 0.02 0.04 x (d) Figure B.1 Mode shapes of the non-uniform fin corresponding to the lowest five estimated natural frequencies 131 APPENDIX C (C-i) Rotational transformation matrixes between coordinate systems: B W c    s      RB   s   c    ,  0  RHR   s  R  c  R       c  R   s  R   ,  0  HL 0  1   RL  0 s   L  c   L   , 0 c   L  s   L   HR B HL RHL  c  L  s  L        s  L  c  L   ,  0  0  1   RL1  0 c   L1   s   L1   , 0 s   L1  c   L1   HR (C1)  c   R1  s   R1     RR1   ,   s   R1  c   R1    s  R  c  R        c   R   s   R   RR (C-ii) Coordinate vector of a point of fins and hinge bases on the neutral axis     L0    W PR1  W g R1  d s d p  ds  ,    2L  2   L0        W PL1  W g L1  d s d p  ds  ;    2L  2   W  L  W W PHR  g HR     W d p  ds   ds    2L   W L0  PR  W g R  ,       L0     d p  d s  ds   W PL  W g L  2L        (C2) g Kk  W g B B g HK HK g Kk (C3)  L0   W W PHL  g HL     (C4)   ,    g HK  W g B B g HK , 132       (C5) W R where W g B   B  O B d HR  a1    b1  ,   HK W X  B dB  W  Y  , B g   RHK , d    B HK     O   g Kk  HK RKk   O d Kk  ,  HK HK B  a1  d HK  B    , d HL   b1  ,      d K    , bH  HK dK       bH  (C-iii) Inertial moment of fin hinges and fin plates: I HR I HL w  I CH     l  I CH     I l CH 0 I w CH t  I CF     , I R1   t   I CH   l  I CF     , I L1   t  e  I CF I CH   I I l CF e CF I t CF w  I CF   e e  I CF  , I R   I CF w   I CF   l e  I CF  I CF  e   , I L   I CF w   I CF   133 e I CF I l CF e I CF I w CF 0   , t  I CF     t  I CF  (C6) APPENDIX D Table D.1 Apparatus for experimental work Apparatus NI 9237 (National Instruments) NI cDAQ-9171 NI CB-37F-LP Precision electronic scale DJ600 Loadcell sensor Rotary Encoder MXE252C100UO1 Casio EXILIM EX-ZR1000 Zigbee-UART CC2530 Moog motor Maxson motor Specification/Description Strain/Bridge Input Module, channel 24 bit Half/Full Bright Analog input, +/-25mV/V NI CompactDAQ One-Slot Bus-Powered USB Chassis Screw Terminals for 37-Pin D-SUB 600g/0.001g J785202 wire, small inertia moment High speed camera, up to 1000 FPS video Wifi receiver/transmitter module AS780D-131E, DC servo motor with encoder Maxon 2332.968-56.236-200, brushed DC motor with no gear, 24VDC, 15W with encoder Tiva-TM4C123g Processor module MAXSON ESCON Module 24/2 Servo motor controller (electrical current control module) IMU sensor GY-86 Angular sensor 134 APPENDIX E (a) (b) 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) (a) (b) Figure E.2 Motion trace demonstration of the experimental fish robot with folding pectoral fins in straight swimming (a) and turning modes (b) 135 ...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... 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... crucial It allows utilizing advantages obtained from evolution and adaptation of fish into the design of bionic pectoral fin Dorsal fin Caudal (tail) fin Pectoral fins Peduncle Anal fin Pelvic fins