VIET NAM NATIONAL UNIVERSITY HO CHI MINH CITY
UNIVERSITY OF TECHNOLOGY
NGUYEN VAN DONG
SWIMMING GAIT CONTROL OF ELONGATED UNDULATING FINS BASED ON THE CENTRAL PATTERN GENERATOR
DOCTOR OF SCIENCE DISSERTATION
Trang 2VIET NAM NATIONAL UNIVERSITY HO CHI MINH CITY
UNIVERSITY OF TECHNOLOGY
NGUYEN VAN DONG
SWIMMING GAIT CONTROL OF ELONGATED UNDULATING FINS BASED ON THE CENTRAL PATTERN GENERATOR
Major: Mechanical EngineeringMajor code: 62520103
Independent reviewer 1:
Independent reviewer 2: Assoc Prof Ngo Quang Hieu, PhD Assoc Prof Nguyen Hung, PhDReviewer 1: Assoc Prof Truong Nguyen Luan Vu, PhD
Reviewer 2: Assoc Prof Nguyen Truong Thinh, PhDReviewer 3: Assoc Prof Nguyen Tan Luy, PhDSCIENCE ADVISOR:
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COMMITMENT
I pledge that this is my work of myself This dissertation's research results and conclusions are honest and not copied from any sources or under any form The references to the documentary sources had been cited as prescribed
Dissertation author
Signature
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ABSTRACT
One of the inevitable consequences of modern warfare is the presence of explosive remnants scattered throughout various areas, causing long-term adverse effects on the quality of life for individuals In the coastal regions of Vietnam, fishermen constantly face the potential risk posed by undetonated mines still embedded in the seabed, often covered by layers of moss and mud Consequently, employing human clones to undertake detection and disposal tasks not only demands substantial labor but also entails significant risks Recognizing this limitation, several units within the Vietnamese Navy have turned to underwater robots for conducting mine clearance surveys However, a new challenge arises from the specific characteristics of the mine environment, which typically features mossy surroundings and accumulations of oceanic debris As a consequence, propeller-based robots encounter obstruction and inefficiency, necessitating the exploration of solutions to address these pressing issues The objective of this thesis is to address the aforementioned pressing issue by investigating the optimal configuration of parameters for the propulsion system of an underwater robot, utilizing the swimming mechanism of the Gymnotiform fish class This involves analyzing, selecting, and constructing the motor controller structure for the underwater robot, inspired by the design of the South American black knifefish and employing the central pattern generator (CPG) motor mechanism To achieve this, advanced optimization algorithms are employed to determine the specific parameters of the CPG motor controller Through the utilization of reinforcement learning
algorithms, the coefficient K, which governs the transition speed of the swimming pattern, is
determined Additionally, stroke adjustments are made to minimize the time required for swimming shape transformation while ensuring minimal output error compared to the desired stroke Furthermore, maintaining a consistent swimming frequency (The time required to complete one cycle of coordination between the fins to generate a propulsion waveform), avoiding fluctuations in underwater sound frequency to prevent the detonation of non-contact fuse torpedoes (sonar turbulence), while still ensuring maximum thrust to rapidly navigate the robot out of hazardous areas regardless of energy consumption, is crucial To achieve this, the thesis proposes the application of the swarm optimization algorithm to determine the set of amplitude parameters A1, A2 ., and A16, optimizing thrust output at a fixed frequency Following 4251 thrust simulations, a maximum thrust of 3.60N was obtained from the module
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TÓM TẮT LUẬN ÁN
Một trong những hệ quả tất yếu của chiến tranh hiện đại là tàn tích vật liệu nổ cịn sót lại, gây ảnh hưởng lâu dài đến sự an toàn của người dân Đối với ngư dân vùng ven biển Việt Nam, họ phải đối mặt với những nguy cơ tiềm ẩn từ thủy lơi cịn nằm dưới đáy biển, phủ đầy rong rêu và bùn lầy Việc sử dụng người nhái để thực hiện công việc tìm kiếm và phá hủy khơng chỉ tốn nhân lực mà cịn mang đến nhiều rủi ro đến tính mạng của những người lính đặc cơng này Gần đây, một số đơn vị công binh Hải Quân Nhân Dân Việt Nam đã nhận thấy nhược điểm trên và đã áp dụng robot dưới nước để thực hiện nhiệm vụ khảo sát và phá huỷ thủy lôi Tuy nhiên, một vấn đề mới đã xuất hiện do đặc điểm của môi trường nơi thủy lơi cịn sót lại, thường có nhiều rong rêu và rác thải đại dương Các robot sử dụng chân vịt thường bị mắc kẹt và hoạt động khơng hiệu quả, vì vậy cần có một giải pháp để giải quyết vấn đề này Luận án này đóng góp vào việc giải quyết vấn đề cấp bách trên bằng cách nghiên cứu tối ưu hóa một số thơng số của hệ thống tạo lực đẩy cho robot dưới nước, theo cơ chế bơi của lớp cá Gymnotiform Bằng cách phân tích và lựa chọn cấu trúc bộ điều khiển vận động cho hệ thống tạo lực đẩy của robot dưới nước, được lấy cảm hứng từ cấu trúc của cá dao đen ở Nam Mỹ và sử dụng cơ chế vận động bộ thần kinh trung tâm (CPG), luận án này áp dụng các thuật toán tối ưu hiện đại để lựa chọn các thông số của bộ điều khiển vận động CPG
Cụ thể, thông qua sử dụng giải thuật học tăng cường, luận án lựa chọn các hệ số K đặc trưng cho tốc độ chuyển đổi dáng bơi Mục tiêu là đảm bảo thời gian chuyển đổi dáng bơi là thấp nhất, đồng thời đáp ứng sai số đầu ra so với dáng bơi mong muốn là tối thiểu
Ngoài ra, để đảm bảo tần số bơi nhất quán và tránh tạo ra biến động trong tần số âm thanh dưới nước, nhằm tránh kích nổ hoặc gây nhiễu động sonar không mong muốn từ ngịi nổ khơng tiếp xúc của thủy lơi, luận án đề xuất áp dụng giải thuật tối ưu bầy đàn Giải thuật này được sử dụng để tìm ra bộ thông số biên độ A1, A2, , A16 cho lực đẩy tối đa tại cùng một tần số Kết quả mô phỏng cho thấy sau 4251 lần lặp, luận án đã tìm được giá trị cực đại của lực đẩy là 3.60N Kết quả này cũng được chứng minh bằng thực nghiệm
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Tối ưu hóa các thơng số CPG cho các module đẩy có thể giúp tăng cường hiệu suất và khả năng di chuyển của robot cá Bằng cách điều chỉnh các thông số, như biên độ và tần số của mỗi module đẩy, ta có thể tạo ra các mẫu chuyển động phù hợp với mục đích và yêu cầu cụ thể của robot Điều này cung cấp sự linh hoạt trong cách điều khiển và chuyển động của robot cá, đồng thời cải thiện hiệu suất và khả năng thích ứng của nó trong mơi trường nước
Các giải thuật điều khiển lớp cao hơn có thể được phát triển dựa trên kết quả tối ưu hóa từ luận án này Bằng cách tích hợp các thơng số tối ưu của CPG vào hệ thống điều khiển lớp cao, ta có thể đạt được sự tương thích và tương đồng giữa các module đẩy và các khả năng di chuyển của robot cá có nhiều module đẩy Điều này mở ra cánh cửa cho việc phát triển các giải thuật điều khiển phức tạp hơn, giúp robot cá đạt được hiệu quả và độ linh hoạt cao hơn trong các nhiệm vụ khác nhau
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ACKNOWLEDGMENTS
I sincerely appreciate my academic advisor, Associate Professor Tan Tien Nguyen, for their patient guidance, constructive recommendations, and enthusiastic encouragement Special thanks to Associate Professor Tan Tien Nguyen throughout my research journey, both financially and academically My dissertation would not have been completed without his invaluable support
Also, special thanks to my family, including my parents and wife, for their patience and sacrifice so that I can focus on my research
In addition, Dr Huy Hung Nguyen and Dr Van Tu Duong are advisors who help me publish scientific works in international scientific journals
Trang 9ix CONTENTS INTRODUCTION 11.1 Background 1 1.2 Motivation .2 1.3 Literature review 3
1.3.1Aquatic Locomotion Modes of Fish 3
MPF propulsion 8
1.3.2The swimming mechanism of fishes 9
1.3.3The Development of Vertebrate Locomotion 10
1.3.4Locomotion control for elongated undulating fin 11
1.4 Discussion & Objective of the Disertation 23
1.5 Outline of the Dissertation 24
DESIGN SWIMMING GAIT CONTROLLER AND THRUST MODELING252.1 Elongated undulating fin description 25
2.2 Swimming gait controller for elongated undulating fin base on CPGs 27
2.2.1Oscillating neuron models 27
2.2.2Coupling Schemes 30
2.2.3Configurations of Oscillators 36
2.2.4Swimming gait using Multiple Coupled CPG Oscillators 39
2.3 Modeling of elongated undulating fin .40
2.4 Simulate the thrust of the fin ray when changing the waveform 44
2.5 Conclusions: 48
OPTIMIZING CONVERGENCE SPEED OF SWIMMING GAIT CONTROLLER BASE ON CPG BY REINFORCEMENT LEARNING 49
3.1 Problem statement 49
3.2 Theoretical foundations of reinforcement learning 52
3.2.1Introduction to Reinforcement Learning 52
3.2.2Markov decision processes 52
3.2.3Canonical RL algorithm 55
3.2.4Evaluation in RL 56
3.2.5Q-Learning 56
3.3 Reinforcement learning based optimization convergence speed 57
3.4 Simulation and discussion 60
3.5 Conclusions 64
FORCE OPTIMIZATION OF ELONGATED UNDULATING FIN ROBOT USING IMPROVED PSO BASED CPG 66
4.1 Problem statement 66
4.2 Theory of Particle Swarm Optimization (PSO) .68
4.2.1Introduction 68
4.2.2The concept of intelligent swarm 69
4.2.3Classical PSO algorithm 70
4.3 Developed PSO-based CPG Optimization 72
4.3.1D-PSO 72
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4.4 Test Results and Discussion .76
4.4.1Testing the D-PSO algorithm on the basic math function 79
4.4.2Testing the D-PSO algorithm on the modified CPG network 80
4.5 Conclusions 82
EXPERIMENT 83
5.1 Introducing experimental models and measuring devices 83
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LIST OF FIGURES
Figure 1-1 Mine underwater (source internet) 3
Figure 1-2 Diagram of swimming propulsors and swimming functions 5
Figure 1-3 Swimming mode (a): BCF , (b): MPF [17] 6
Figure 1-4 Gradation of BCF from (a) Anguilliform through, (b) Subcarangiform, (c) Crangiform (d) thunniform [18] 6
Figure 1-5 Growth of the undulatory MPF modes [3] 8
Figure 1-6 CPG with a loop connection to control the movement of four legs turtle-like underwater robot [24] 14
Figure 1-7 Configuration of the formulated CPG model (a) simplefied structure (b) CPG network configuration [25] 14
Figure 1-8 The proposed three- layers CPG model [26] 16
Figure 1-9 An FSM-based pattern transition diagram [27] 17
Figure 1-10 CPG model based on Hoft oscillator with input transformation [28] 18
Figure 1-11 Close loop CPG network [29] 18
Figure 1-12 Structure of ANN - CPG network [30] 19
Figure 1-13 Neuromorphic VLSI device[31] 20
Figure 1-14 Structure of CPG network and behavior - based hierarchical architecture for coordination control [32] 20
Figure 1-15 Illustration of the CPG network utilized to control the robotic fish [33] 21
Figure 2-1 Waveform commonly used by undulatory swimming machines [35] 26
Figure 2-2 Parallel linkage mechanisms are used to make the fish robots move 26
Figure 2-3 Changed amplitude and frequency 27
Figure 2-4 Typical structure of Hopf oscillator 28
Figure 2-5 Output of Hopf oscillator in abrupt change of amplitude and frequency 29
Figure 2-6 Convergence to limit cycle of Hopf oscillator 30
Figure 2-7 Single –directional coupling between two oscillators 31
Figure 2-8 Illustration of perturbation in the direction of phase angle φ 32
Figure 2-9 Mutual coupling between two oscillators 34
Figure 2-10 Couplings among three oscillators 34
Figure 2-11 Output u of two oscillators CPG1 and CPG3 for two types of coupling 36
Figure 2-12 Radial type CPG coupling 37
Figure 2-13 Ring coupling 37
Figure 2-14 Fully connected coupling Chain coupling: 38
Figure 2-15 One-way chain coupling 38
Figure 2-16 Two-way chain coupling 38
Figure 2-17 Chain coupling structure CPGs model for Elongated Undulating Fin 39
Figure 2-18 Fin Discrete Model 40
Figure 2-19 Representation of coordinate systems 41
Figure 2-20 Transition from Static to Elliptic waveform 45
Figure 2-21 The thrust of the fin-ray module is generated relative to the Elliptic waveform 46 Figure 2-22 Transition from Static to Quadratic waveform 46
Figure 2-23 The thrust of the fin-ray module is generated relative to the Quadratic waveform 47
Figure 2-24 Transition from Static to Linear waveform 48
Figure 2-25 The thrust of the fin-ray module is generated relative to the Linear waveform 48
Figure 3-1 Diagram for the Markov process [83] 55
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Figure 3-3 a) Impact of transient-state time and oscillatory error on the convergence speed b)
Distribution of Q-value on state variable and action variable 60
Figure 3-4 Swimming patterns of elongated undulating fin propulsion 61
Figure 3-5 The relative convergence rate concerning transient-state time and oscillatory error 61
Figure 3-6 The output of a single oscillator with 𝑘 = 86, 𝑘 = 96, 𝑘 = 106 62
Figure 3-7 Output of sixteen oscillators with changes of swimming pattern, oscillatory frequency, and waveform number 63
Figure 3-8 Output of sixteen oscillators with changes of phase lag angle enabling for reverse swimming direction 64
Figure 3-9 Relation of transient-state time with respect to convergence rate 64
Figure 4-1 Four locomotion patterns 66
Figure 4-2 Undulating fin in water tank 66
Figure 4-3 The flowchart of the PSO algorithm 72
Figure 4-4 Proposed DPSO search mechanism of pth particle at kth iteration in a multi dimensional search space [94]………………………………………………………… ……73
Figure 4-5.Flowchart of the proposed DPSO 74
Figure 4-6 Flowchart of the proposed approach 75
Figure 4-7 The output of the real CPG model 77
Figure 4-8.Simulation results with the random values of amplitude - 05 CPG outputs 78
Figure 4-9 Simulation results with the random values of amplitude - The characteristic curve of average thrust 78
Figure 4-10 Simulation results with the D-PSO-based CPG -05 CPG outputs 80
Figure 4-11 Simulation results with the D-PSO-based CPG - The average thrust force 81
Figure 4-12 The convergence characteristic of some CPG optimization techniques 82
Figure 5-1 Overview of elongated undulating fin 83
Figure 5-2 Fin ray drive mechanism 84
Figure 5-3 Control system structure 85
Figure 5-4 Block diagram of the control Fin module board 85
Figure 5-5 Module elongated undulating fin 86
Figure 5-6 Instrument for measuring the true angle of rotation of the fin ray 87
Figure 5-7 Experiment tank and equipment setup 88
Figure 5-8 Software and automatic parameter recording tool 88
Figure 5-9 CPG-based motion controller when changing frequency, amplitude 89
Figure 5-10 Experimental arrangement to determine the optimal K factor 90
Figure 5-11 The signal of all 16 CPGs in turn when k=86 91
Figure 5-12 The signal of all 16 CPGs in turn when k=96 91
Figure 5-13 The signal of all 16 CPGs in turn when k=106 92
Figure 5-14 Liner waveform 94
Figure 5-15 Quadratic waveform 94
Figure 5-16 Elliptic waveform 95
Figure 5-17 Random waveform 96
Figure 5-18 GA CPG waveform 96
Figure 5-19 Straight CPG waveform 97
Figure 5-20 PSO CPG waveform 97
Figure 5-21 DPSO waveform 98
Figure 5-22 Force of liner waveform 99
Figure 5-23 Force of liner waverform 99
Figure 5-24 Force of elliptic waverform 100
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Figure 5-26 Force of GA waveform 101
Figure 5-27 Force of straight CPG waveform 101
Figure 5-28 Force of D-PSO CPG waveform 102
Figure 5-29 Force of PSO CPG waveform 102
Figure 5-30 Average force of strokes from CPG 103
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LIST OF TABLE
Table 3-1 Pseudo-code of the Q-learning optimization 59
Table 4-1.Morphology parameter of the undulating robotic fin 67
Table 4-2 Parameters of CPG network 77
Table 4-3 The tested five math functions 79
Table 4-4 Optimization results of CPG model with/without D-PSO algorithm 80
Table 4-5 Optimization results of CPG model using different meta-heuristic algorithms 81
Table 5-1 Specific parameters of elongated undulating fin 83
Table 5-2 Servo RC specific 84
Table 5-3 Experimental module parameters 85
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Central Nervous System Central Pattern Gait
Differential Particle Swarm Optimization Body And/Or Caudal Fins
Median And/Or Paired Fins Feedback Sensor Modulation Body Length
Artificial Neural Network Very Large Scale Integration Micro Controller Unit
Spiking Central Pattern Generator Pulse Width Modulation
Radio Control
Reinforcement Learning Markov Decision Process Value Iteration
Temporal Difference
Genetic Algorithm
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INTRODUCTION
This dissertation describes the research work done in determining the scientific basis for modeling and selecting the appropriate number of fin rays per wavelength for the propulsion module using a biomimetic swimming mechanism; the use of a reinforcement learning algorithm in determining the optimal coefficient for the time to change swimming posture while minimizing swimming form error At the same time, research to find the optimal swimming shape for maximum thrust at a specific frequency to create the best moving dynamics while keeping a fixed undulating frequency to minimize the risk of detonation Underwater sound mines In addition, research motivation and outline are discussed in this chapter
1.1 Background
With the development of new biology, materials, and robotics technologies, it may be possible to make robots that move like animals and swim like a fish[1]–[3] This kind of robot is a particular biologically-inspired underwater vehicle (BIUV) that moves by mimicking the actions of aquatic animals [4] Instead of screw propellers, BIUVs are powered by biomimetic fins, flippers, or bodies The BIUV systems are similar to traditional Autonomous Underwater Vehicles (AUVs) in that they can be used in many different ways, such as marine sourcing, seabed charting, military surveillance, environmental assessments, sea exploration, finding mines, and doing scientific research, among other things[5], [6] Also, BIUVs have unique features that make them better than traditional AUVs, especially regarding how well they move Regarding how animals move underwater, fish swimming is a popular topic of study [7] Over millions of years of evolution and natural selection, fish have perfected how their bodies work and swim to move around underwater It has been said that most fish can swim more efficiently than 80% of the time[8] Some Thunniform fish can swim with more than 90% efficiency, while the average efficiency of screw propellers today is between 40% and 50%[8] Fish can also turn with a turning radius of less than 10% to 30% of their body length and still move at high speed This fantastic skill is way beyond the abilities of any current ship, which usually has a turning radius much more significant than its hull length and a turning speed less than half of its average cruising speed[8]
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marine life has been getting worse because of how often propellers, which make loud noises in the wake, have been used Fish move without making noise because of the way they swim Because of this, engineers are also forced to develop new ways to make vehicles that haven't rotary propellers[11]
Biomimetic propulsion systems for swimming machines can learn a lot from how fish move[12]–[14] People have become increasingly interested in robotic fish in the last 20 years The goal of the research on fish robots in robotics is simple: to turn the idea behind biomimetic fish into new underwater vehicles that can help people To achieve this goal, researchers need to study many things, such as the mechanical design of fish robots, the materials of biomimetic propellers, the methods of actuation and actuators for underwater environments, the sensors and electronic systems for underwater measurements, the control of swimming for highly efficient locomotion, intelligent control strategies for autonomous manipulations, etc.[2], [3], [15], [16]
This dissertation focuses on exploiting the motion controller aspect of the propulsion module using the swimming mechanism of the Gymnotiform fish class The very important factor that characterizes the flexibility of this propulsion system lies in the time of changeover, which has not been mentioned in any previous studies In addition, with the characteristics of robot application orientation in underwater mine removal, it is necessary to find a swimming posture for maximum thrust without causing changes in underwater sound frequencies caused by them when swimming out of position With the thesis as a framework, the following are some specific limitations and research limitations:
1- It is impossible to simulate the effects of disturbance on the marine environment
2- in the analytical calculation to focus on the thrust in the translational direction, the thesis temporarily ignores the horizontal, oblique force analysis
3- The effect of vortices and the experimental tank's narrowness is considered negligible and will develop in future studies
1.2 Motivation
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survey work However, a new inadequacy arises from the characteristics of the environment where the mines are located, which is often a mossy environment with a lot of ocean garbage Figure 1‑1 The robots using propellers are all stuck and not working effectively, so a solution is needed Solutions to these problems
Figure 1-1 Mine underwater (source internet)
The above situation, concerning the operating mechanism of fish robots in the world, has motivated me to conduct a research-oriented approach to underwater robots with high stability and a rigid body to install and place the devices The contributions in the thesis are the foundation for the orientation of building a complete underwater robot for surveying and clearing mines left on the seabed
1.3 Literature review
1.3.1 Aquatic Locomotion Modes of Fish
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Swimming locomotion has been broken down into two general types based on how quickly the movements happen[1]:
• Periodic Swimming (or steady or sustained), in which propulsive movements are repeated cyclically Periodic Swimming enables fish to cover relatively large distances at a relatively constant rate
• Voluntary (or transient) movements such as rapid acceleration, escape maneuvers, and turns Typically, millisecond-long movements are used to capture prey or evade predators
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increase in the undulation wavelength In addition, the propulsor's smaller parts move together to make both types of movement Generally, fish that use the same propulsion method regularly exhibit similar morphology However, form differences exist and are related to each species' unique mode of life Three basic optimal designs for fish morphology are derived from specializations for accelerating, cruising, and maneuvering [4], and they are intimately related to the locomotion method used (Figure 1‑2) Additionally, because they are primarily mutually exclusive, no single fish performs optimally in all three functions However, none of these fish are specialists in a single activity; instead, they are locomotor generalists incorporating design elements from all three specialists to varying degrees [4] and [5] give more information about how function and morphology work together in swimming fish
Figure 1-2 Diagram of swimming propulsors and swimming functions
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Figure 1-3 Swimming mode (a): BCF , (b): MPF [17]
BCF propulsion
In undulatory BCF modes, the propulsive wave moves through the fish's body in a different direction than the overall movement and at a faster rate than the overall speed of the fish when it swims Figure 1‑3 shows four undulatory BCF locomotion modes that move in different ways, such as the one shown in the figure Each method has a unique wavelength and amplitude envelope that makes it special In addition, other modes have different ways of making thrust This can be done with a lift-based (vorticity) method and a method that adds more mass to it Two main ways to do this: As you can see, this is where the added-mass method has been used the most It has been linked to the added-mass process for a long time, but now They know why Carangiform and Subcarangiform fish are found in the sea and have vorticity mechanisms that help them move
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Anguilliform mode is characterized by large-amplitude undulations that involve the entire body Figure 1-4(a) A wave that moves your body is at least one full wavelength long, which means that lateral forces are enough to cancel each other out This reduces the body's tendency to recoil when the wave is applied By shifting the propagation direction of the propulsive wave, many anguilliform swimmers can swim both backward and forward Backward swimming necessitates greater lateral forces and body flexibility [7] The eel and the lamprey [8] are well-known examples of this widespread movement style The sub-carangiform mode (for example, trout) exhibits similar motions, but the amplitude of the undulations is limited to the front of the body and only increases in the back of the body Figure 1-4(b)
Carangiform swimming makes this much clearer because the body undulations are
limited to the last third of the body length Figure 1‑4(c), and a relatively stiff caudal fin gives propulsion In general, Carangiform swimmers are faster than their Anguilliform or Subcarangiform counterparts However, because of the relative rigidity of their bodies, their turning and accelerating skills are severely limited Furthermore, because the lateral forces are focused on the posterior, there is a greater tendency for the body to rebound
In the aquatic environment, the Thunniform style has evolved as the most efficient mode of locomotion Thrust is generated by the lift-based approach, which allows high cruising speeds to be maintained for extended periods It is regarded as a climax in the evolution of swimming patterns because it is found in a diverse range of vertebrates (teleost fish, sharks, and marine mammals), all of which have developed in distinct environments The thunniform mode is seen in scombrids, which include tuna and mackerel, among other teleost fish Only the caudal fin generates more than 90% of the thrust, and the area near the narrow peduncle is subjected to significant lateral motion The body is well streamlined to reduce pressure drag, and the caudal fin is rigid and high, with a crescent-moon shape known as the lunate Figure 1-4(d) Because of the caudal thrust strength, the body shape and mass distribution ensure that recoil forces are efficiently minimized and that very little sideslipping is caused by the thrusts The primary function of Thunniform swimmers is to swim quickly in calm water; however, other activities such as slow swimming, turning maneuvers, and quick acceleration from immobile or turbulent water are not well-suited to their design
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used as an auxiliary locomotion method, caudal oscillations can aid in the creation of thrust at higher speeds, the maintenance of appropriate rigidity of the body, and prey tracking [6] The hydrodynamic adaptations and refinements found in Thunniform swimmers don't show up in Ostraciiform movement, which has low hydrodynamic efficiency even though it looks similar
MPF propulsion
Many fish employ undulating fins as alternate propulsors, as well as for maneuvering and stabilization, regularly These propulsion systems can also provide sufficient thrust to be included in the sole means of locomotion at generally low speeds Certain fish can actively bend their median fins rays because they have a muscle group (usually six) for each fin ray that allows them to move with two degrees of freedom The muscular system of paired fins is even more complex, allowing them to perform movements like rotations of individual fin rays Several reviews of the literature on teleost fin’s structure and properties are provided in [6],[3] Figure 1‑5 illustrates how their adaptability has played a crucial role in the growth of the undulatory MPF modes
Figure 1-5 Growth of the undulatory MPF modes [3]
Some experts say that many fish, like rays, skates, and manta rays, move in the same way as birds do when they fly Rajiform mode is found in fish like this To generate thrust, vertical undulations must be passed along the extremely large, triangular-shaped pectorals and flexible Increasing the amplitude of the undulations from the anterior portion to the apex of the fin and then decreasing it again toward the posterior part, It is also possible to flap the fins up and down
Diodontiform mode moves the animal forward by skipping down the wide pectoral fins and not causing them to move As a result, light waves can spread across the fins in two full wavelengths, and the waves and flapping movements of the fin are often seen together
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The African freshwater electric eels are the best examples of this characteristic, and they can be found in large numbers in Africa It lacks the anal and caudal fins but has many fin rays and extends along most of the body length before tapering to a posterior point (up to 200)
Because a long-based anal fin moves, Gymnotiform mode can be thought of as the upside-down version of amiiform mode because it moves to move forward Gymnotiform mode is one of the types of amiiform modes that can be used to play games The dorsal fin isn't usually there during swimming, and the body is held straight again, like before Electric eels tend to keep their bodies rigid while swimming, which has long been thought necessary because they have a system detecting electricity On the other hand, the fact that undulatory movements don't make friction drag go up might also be a factor
In Balistiform locomotion, both the anal and dorsal fins move to make the animal move
forward This is mainly observed in the Balistidae family Their distinguishing characteristics are that their median fins are typically inclined toward one another, whereas their bodies are generally flat and compressed laterally These design features have been linked to increased propulsion efficiency in various studies
1.3.2 The swimming mechanism of fishes
Studies related to the swimming mechanism of fishes have been ongoing for many years Researchers have been interested in understanding how fish are able to swim efficiently through water, and how this knowledge can be applied to the design of underwater vehicles and robots
One area of research has focused on the undulating motion of fish fins In a study, the authors investigated the factors contributing to the propulsive thrust and efficiency of undulating fins for various swimming modes They noted that tissue fibers in the fin of cuttlefish may store elastic energy during fin bending, allowing the fin to function as a harmonic oscillator and increasing the efficiency of the fins during locomotion[125]
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Researchers have also developed mathematical models to describe the effect of sinusoidal inputs over a cycle of fish locomotion Leonard’s research derived an average-formula approach to describe this effect, which is appealing because fish locomotion often involves oscillatory motions of the fins and body[127] Li and Saimek developed a Kalman filter-based estimation scheme that recovers the hydrodynamic potential from a set of pressure measurements along a fish’s body[128]
Overall, studies related to the swimming mechanism of fishes have provided valuable insights into the design of underwater vehicles and robots By understanding how fish are able to swim efficiently through water, researchers can develop more effective and efficient underwater technologies
1.3.3 The Development of Vertebrate Locomotion
An organism, like a vertebrate, is a dynamic system that has changed since it was first created However, even though the parts change, the organism works similarly Self-organization is the process by which the organism grows and changes in a way that makes sense This process is based on genetic, chemical, mechanical, and activity-dependent mechanisms
All vertebrate brains go through the same stages as they grow Researchers have found that synaptogenesis depends on what the animal is doing This process happens both before and after the animal is born So, the adult pattern of brain connections is made possible by processes that depend on how the brain is used The function also determines structure
It is well known that all embryos of vertebrates move around before they are born[19], [20] But the effects of the pattern of prenatal behavior have only been fully understood in the last few years[19], [21]–[23] It has been suggested that these movements during pregnancy could be how the nervous system connects sensory inputs to specific patterns of muscle activity Prenatal movements can be broken down into the following stages[19], [20], [23]:
Pre-Motile Stage: In species like Xenopus Laevis, when fine hair is touched on the head during the pre-motile stage, right before the animal moves on its own, it bends away from the stimulus Roberts[23] says that a reflex pathway is to blame for this bending
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animal starts to move While the spinal cord is still being built, the movement begins Over time, the animal's whole body starts to bend this way
C-Bending: The forward bending of the head gives way to a bend The shape is made when the animal bends very far in one direction and then very far in the other The sides of the animal work together, which is different from early head flexion This shows that the two parts of the animal work together
S-Bending: The bending replaces the bending The letter says a lot As in the letter "S", two bend points become apparent During the "C" bending phase, both sides of the spinal cord work simultaneously During the "S" bending phase, They see the first signs that the spinal cord is starting to separate into different parts that work together
S-Wave Traveling and Swimming: Eventually, the "S" bend gives way to a moving "S" wave and a "swimming" motion In the traveling "S" wave, an "S"-shaped wave moves from the top to the bottom In short, They can infer from this that development is made up of separate events that happen in a strict order How the nervous system is set up anatomically also depends on how the body moves
1.3.4 Locomotion control for elongated undulating fin
Many approaches studied bio-fish robots concerned with the diversity of fish species These studies pointed out that many significant factors affect the hydrodynamics of bio-fish robots One such factor is the swimming pattern that enables bio-fish robots to perform complex operations such as turning, swaying, twisting, and curving Research on robotic fish locomotion control undulating fins is divided into two groups: offline swimming gait control and online swimming gait control
1.3.4.1 Offline swimming gait controller
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tuning the fin ray parameter set to get better thrust [10]–[14] Mohsen Siahmansouri et al extend the concepts of phase difference angle and thrust direction to further develop the motion controller for fish robots with a sine wave oscillator [15] Our group is also working on propulsion systems that use undulating fins Almost all use sine wave oscillators to control servo motors, and they all work together [16]–[18] However, in general, locomotion control is not only a fixed control of a swimming posture for a biomimetic robot, so adapting to the water environment and having flexibility requires a better solution for control Swimming shape can adjust parameters such as frequency and amplitude, smoothly
1.3.4.2 Online swimming gait controller used central paten generator
Orjan Ekeberg et al have laid the foundation for applying a central pattern generator (CPG) to control fish locomotion According to biologists who study fish, the fin rays are coordinated by the spinal nervous system, which is not directly related to the brain The model proposed by Orjan Ekeberg et al is a model that realizes that thinking With only a few inputs changing, like those emitted by the central nervous system, the swimming postures were flexibly switched without interfering too profoundly with the control details placed under the fin motion control [19] However, the application of CPG in motion control was made early in the motion simulation of humanoid robots, salamanders, etc., with different oscillators In 2006, Dai-bing Zhang et al applied controlled CPG to a fish robot with the model foundation that Orjan Ekeberg built Zhang proposed a sine-cosine oscillator In this study, he et al thinks it is reasonable and flexible for fish movement and superior to traditional oscillators such as Matsuoka and Hofp [20] In the same year (2006), a study on CPG for motion control of boxfish was published Daisy Lachat et al do not use classical oscillators but create a separate oscillator for each movement joint of the boxfish The research objective is only to prove the flexibility of movements such as turning the head and waving the fish body according to different amplitude and frequency signals In this study, they do not present the details of the CPG controller nor the required parameters that make up the quality of the locomotion controller [21] From the synthesis and evaluation of research on CPG application in robotics, in 2008, Auke Jan Ijspeert and colleagues presented specific steps as a principle to design the locomotion control CPG The main steps include [22]:
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(2)- The type and topology of couplings are essential considerations These will determine the conditions for synchronization between oscillators and the resulting gaits, i.e., the stable phase relationships between oscillators, among other things
(3)- The waveforms themselves During a cycle, these will determine which trajectories will be performed by each joint angle and which ones will not However, the waveforms depend on the shape of the limit cycle produced by the chosen (neural) oscillator, and the addition of filters can transform them into the mix
(4) - Input signals affect control parameters, which means that control parameters can modulate essential quantities such as frequency, amplitude, phase lags, or waveforms, among other things The influence of feedback signals is how feedback from the body will affect the activity of the CPG (for instance, accelerating or decelerating it, depending on environmental conditions)
(5) - The fact that these five design axes are all highly interconnected presents a significant challenge when developing CPGs.These steps later become the standard procedure for developing locomotion control
To control the movement of a fish with a combined swimming style of pectoral, body, and caudal fins, Yonghui Hu and his colleagues built a CPG network with a Mastsuka oscillator The results show that the controller produces smooth motion when changing the frequency or amplitude The author considers this necessary for protecting the servo motor to avoid damage In addition, the article also mentions the genetic algorithm to find the optimal swimming posture to achieve the highest speed [23]
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Figure 1-6 CPG with a loop connection to control the movement of four legs turtle-like underwater robot [24]
Researchers from the Chinese Academy of Sciences have been investigating the movement mechanism for amphibious robots that have been specially designed and built for the past two years With two wheels on the ground and flexible body movement, this robot can walk on land and swim in water like a fish, just like a real fish The authors of these two publications have used a CPG-based motion controller to coordinate the movements of the body joints and the two front wheels, which is the most notable aspect of their work A serial arrangement of links at the neural nodes of the CPG network is followed by associative branching of the links As a result, the robot's movements as it transitions from underwater to land and vice versa are smooth and rely on only a few parameters from the high-level controller to function correctly A sliding controller was also added to the locomotion controller in the 2nd version, which the authors believe is an improvement over the first As a result, when walking on land, the robot's turning radius has been significantly increased by this method [24], [25]
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Following the publication of a new CPG-based locomotion control method by Chen Wang and colleagues, a robotic fish model was used to demonstrate the effectiveness of the proposed method The proposed CPG model, a coupled linear oscillator system, has several advantages over the existing models First, the CPG model has been made simpler by substituting linear differential oscillators for nonlinear ones instead of the latter This makes it easier to put the CPG model into practice [26] Another advantage is that the dynamic performance has been maintained to a satisfactory level thanks to the adaptive structural parameters
Additionally, the explicitly presented parameters of the CPG model have improved the clarity of the applications they support As a result of our experiments, they can conclude that their CPG model is well-suited for the locomotion control of a three-jointed robotic fish All biomimetic multi-joint underwater robots with link structures, they believe, can be represented by our model, and They believe their model can be represented by their model for all of them They are currently working on broadening their scope of work to include the following areas of expertise:
- First and foremost, the paper does not consider the stable performance of the locomotion because the authors have chosen the locomotion speed as the only optimization goal However, to improve the stability and transient performance of the parameters, they are currently experimenting with various optimization methods
- Second, because the robotic fish does not have a sensor, the optimization has relied on the experimental platform used to perform the optimization Several pose sensors are mounted on the robot's body, and they are being integrated into the design Once this has been accomplished, the locomotion controller can be installed onboard, and online optimization can be performed with relative ease using the resulting software
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In 2013, Wei Wang et al proposed a bio-inspired CPG model This locomotion controller allows you to control fish-like robots with multiple swimming modes, including forward, turning, and rolling, as well as different swimming gaits, with only two input drive motors An Ostraciform fish robot with two pectoral fins and one caudal fin is used to demonstrate its immediate application The robot mimics the natural counterpart in four primary locomotion characteristics: swimming gait transition, linear relationship between speed and fin beating frequency/amplitude, inherent frequency of caudal gait that is lower than that of pectoral gait, and a variety of swimming modes It works the same way a biological neural system receives external stimuli, generates rhythmic and smooth neural signals, and outputs drive movements to the actuators [27]
Figure 1-8 The proposed three- layers CPG model [26]
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dorsoventral swimming for their robotic fish did better than fish-like lateral swimming, but only by a small amount, the researchers found
Figure 1-9 An FSM-based pattern transition diagram [27]
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Figure 1-10 CPG model based on Hoft oscillator with input transformation [28]
Researchers Wei Wang and colleagues proposed two types of CPG-based controllers for a boxfish-like robot in 2014 The open-loop and closed-loop controller based on the CPG-based controller are proposed successively for the robot, which can switch between multiple 3D swimming patterns and control its attitude of yaw and roll precisely while swimming A two-layer open-loop CPG model with only four control parameters is first proposed in an explicit expression to generate all the typical swimming patterns of the robotic fish, including swimming forward and backward, turning left and right, swimming upward and down, as well as rolling in a clockwise or counterclockwise fashion This article makes a significant contribution by introducing a novel closed-loop CPG-based control method that can automatically stabilize the robot's attitude without the need for intervention from the upper control center [30]
Figure 1-11 Close loop CPG network [29]
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trained By using the outer amplitude modulator, they can change the outputs of the ANN smoothly, so They can get the amplitudes Them want This will happen after they have looked at all three parts of the CPG in detail They will then go over the qualities of the CPG and show that each one is true This means that the motion pattern that the CPG creates can be compressed and stretched along both the spatial and temporal axes It can also change the phase differences between different outputs This is only the beginning To go even further, they take the movements of a live Anguilliform fish and use them to drive the robotic fish around its environment A lot of calculations are done before anything else is done to ensure the CPG is the right size Then, a new pattern is made that, on the one hand, keeps the real fish's swimming pattern but is better for the robotic fish Experiments have shown that the CPG technique works well, and the robotic fish can move both forward and backward with the robot
.
Figure 1-12 Structure of ANN - CPG network [30]
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Figure 1-13 Neuromorphic VLSI device[31]
Expanding the linking role of the locomotion controller between independent individuals to control the swarm fish robot to perform a collective task In 2015 Junzhi Yu et al established four similar CPG models for four fish robots Along with building a more advanced management layer, the authors have worked to combine them Experimental results on tracking the ball off four fish robots open up the prospect of designing a swarm underwater robot that coordinates flexible and flexible movements [33]
Figure 1-14 Structure of CPG network and behavior - based hierarchical architecture for coordination control [32]
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Figure 1-15 Illustration of the CPG network utilized to control the robotic fish [33]
Research works on CPG-based motion controllers mainly interact with electric motors' actuators Christina L Hamlet et al has a new approach when changing the actuator is an artificial muscle Artificial muscle activities, when controlled by a CPG-based locomotor controller, show the advantages of this controller For example, swimming postures are performed flexibly [35]
Q Liu and colleagues published a paper in 2018 that concentrated on the existing problems of the Matsuoka CPG and developed an inherent bursting neuron model Based on this neuron model, a new locomotion control network model has been developed [36] The new locomotion control networks are distinct from the existing CPG models, primarily concerned with generating rhythmic movements in the body This model is capable of generating both rhythmic and non-rhythmic movements First, the spinal locomotion networks of the lamprey are constructed to validate the properties of this new locomotion control network model Then, to generate forward swimming, turning, and non-rhythmic movement, they simulated the properties of the spinal locomotion networks of lamprey
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prototype exhibiting a reflex The combination of these components of a hierarchical control structure behaves similarly to the Central Nervous System The robotic fish's three-dimensional motion abilities are also being improved by developing a Center of Gravity control mechanism Results from the experiments include three specific swimming modes, such as yaw and pitch and keep level These experiments were carried out in a variety of different scenarios Yaw control is achieved through the use of three references Pitch control is demonstrated for two desired up/down motions, and finally, keeping level is performed for both close to the base and the object's surface All of the results demonstrate that the proposed control structure can produce effective and robust responses when dealing with realistic fish movements
Continuing with this research topic, the proposed control structure is comprised of a biologically based CPG, a Fuzzy Logic sub-controller, and a Finite State Machine algorithm, as well as other components To construct the CPG model, a unidirectional network of coupled Lamprey oscillators and sensory neurons has been used These neurons are responsible for the acquisition of external stimuli from the environment It is intended to achieve phase-locked behavior in the CPG network by utilizing a brainstem model in conjunction with the MCU [38] The closed-loop Fuzzy Logic controller acts as a decision-making mechanism, allowing the swimmer to swim around independently Aside from that, the Finite State Machine algorithm has been modified to determine the priority of tasks and to perform multiple tasks within a single cycle of computation The entire control structure ensures that the gait transitions are stable, adaptable, and smooth regardless of the environmental changes that occur The open-loop CPG control of the robotic fish is first implemented with three cases to analyze the characteristic performance of the robotic fish In all experiments, it was demonstrated that the proposed closed-loop control structure provides effective and robust responses for real-world missions and explorations
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holding its high-level drive Simulated multiple locomotor tasks were done in the Neurorobotics Platform
1.4 Discussion & Objective of the Disertation
It can be concluded that these earlier studies related to CPG have been successfully applied to the locomotion control of biomimetic robots However, most of these researches rely on trial-and-error data fitting to adjust a control parameter of the CPG model called convergence rate Increasing the convergence rate can reduce the processing time for achieving the limit cycle; however, this can raise an oscillatory error defined as the difference between the intrinsic amplitude of CPG and the maximum amplitude envelope of the CPG’s output This issue is still a challenge for researchers with the lack of optimization for the convergence rate of CPG In terms of parameter optimization, several studies used the particle swarm optimization (PSO) algorithm to seek the CPG parameters to minimize the difference between the desired oscillatory waveform and the generated output of the CPG [47], to reduce the control parameters [48] and to refine the feature parameters of the CPG [49]
The above-aforementioned studies regarding CPG-based bio-fish robots have not conducted optimization for the convergence rate (Characteristic coefficient for the time to change swimming form) Inspired from the studies concerned with applying RL for CPG, this dissertation proposes a reinforcement learning-based optimization of locomotion controller using CPG network for an elongated undulating fin.
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swarm optimization (PSO) to find the best parameters for the Hopf oscillator-based CPG for better propulsion These metaheuristic algorithms do an excellent job of finding the CPG parameters, but they often get stuck in local optima This dissertation investigates a new ideal for differential particle swarm optimization (D-PSO) to improve optimization problems The amplitude values of the CPG network increase the average propulsive force of the undulating fin robot to make a faster movement.
1.5 Outline of the Dissertation
The dissertation is presented, including six chapters:
Chapter 1: focuses on researching scientific publications in the same field to find out the contribution orientation of the dissertation
Chapter 2: Building a Motion Controller for a Specific Fish Robot Propulsion Module Model Available on the CPG Platform Simultaneously, model the propulsion mentioned above system module
Chapter 3: Research on optimizing the specificity coefficient for the stroke switching speed of the locomotor controller built by a reinforcement learning algorithm
Chapter 4: Research on selecting the optimal set of amplitude parameters for the motion controller with the criterion of keeping the frequency unchanged and achieving the maximum thrust by the swarm optimization algorithm
Chapter 5: Testing the ability to change swimming posture flexibly, optimizing the speed
characteristic coefficient of the change of swimming form found in Chapter 3, and measuring the thrust caused by the best set of parameters found in Chapter 4.
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DESIGN SWIMMING GAIT CONTROLLER AND THRUST MODELING
This Chapter proposes a locomotion controller inspired by black Knifefish for an undulating elongated fin robot The proposed controller is built by a modified CPG network using sixteen coupled Hopf oscillators with the feedback of the angle of each fin-ray By employing the proposed controller, the undulating elongated fin robot can realize swimming pattern transformations naturally Additionally, the proposed controller enables the configuration of the swimming pattern parameters, known as the amplitude envelope and oscillatory frequency, to perform various swimming patterns
2.1 Elongated undulating fin description
The elongated undulating fin comprises sixteen oblique adjacent fin-rays interconnected with a flexible membrane Each fin-ray is driven by an RC servo motor that enables the fin-ray to sway around a rotary joint fixed to a supporting frame Accordingly, each fin-ray reacts as a shaker bar with a limited angle, and the phase difference between two adjacent fin-rays is regarded as a phase lag angle By changing one of the kinematic parameters, such as amplitude envelope, oscillatory frequency, and swimming pattern, the magnitude of the propulsive force can be adjustable To perform forwarding/reversing motion, the elongated undulating fin might change the sign of the phase lag angle Additionally, to avoid the counter-torque of the elongated undulating fin, the number of oscillation wavelengths should be an even number Traditionally Swimming Gait Based on Sine Generators is implemented as follows:
Fish move by undulating and/or oscillating their fins and/or bodies in a rhythmic way to move forward They use a kinetic method led by Lighthill's Elongated Body Concept to move forward [34] According to Lighthill's theory, thrust is generated by the formula:
𝑦 = 𝑓𝑒(𝑥) sin (2𝜋𝑓𝑡 + 2𝜋 𝑥)
(2-1)
Where:
𝑓𝑒(𝑥) : is the envelop equation (see Fig 2-1)