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Nghiên Cứu Phân Tích Động Lực Học và Ứng Dụng Giải Thuật Di TruyềnLeo Đồi Trong Việc Tối Ưu Hóa Vận Tốc Di Chuyển Thẳng Của Robot Cá 3 Khớp Dạng CarangiformNghiên Cứu Phân Tích Động Lực Học và Ứng Dụng Giải Thuật Di TruyềnLeo Đồi Trong Việc Tối Ưu Hóa Vận Tốc Di Chuyển Thẳng Của Robot Cá 3 Khớp Dạng CarangiformNghiên Cứu Phân Tích Động Lực Học và Ứng Dụng Giải Thuật Di TruyềnLeo Đồi Trong Việc Tối Ưu Hóa Vận Tốc Di Chuyển Thẳng Của Robot Cá 3 Khớp Dạng CarangiformNghiên Cứu Phân Tích Động Lực Học và Ứng Dụng Giải Thuật Di TruyềnLeo Đồi Trong Việc Tối Ưu Hóa Vận Tốc Di Chuyển Thẳng Của Robot Cá 3 Khớp Dạng CarangiformNghiên Cứu Phân Tích Động Lực Học và Ứng Dụng Giải Thuật Di TruyềnLeo Đồi Trong Việc Tối Ưu Hóa Vận Tốc Di Chuyển Thẳng Của Robot Cá 3 Khớp Dạng CarangiformNghiên Cứu Phân Tích Động Lực Học và Ứng Dụng Giải Thuật Di TruyềnLeo Đồi Trong Việc Tối Ưu Hóa Vận Tốc Di Chuyển Thẳng Của Robot Cá 3 Khớp Dạng Carangiform
246 Tuong Quan Vo VCM2012 Nghiên Cứu Phân Tích Động Lực Học và Ứng Dụng Giải Thuật Di Truyền-Leo Đồi Trong Việc Tối Ưu Hóa Vận Tốc Di Chuyển Thẳng Của Robot Cá 3 Khớp Dạng Carangiform A Study on Dynamic Analysis and Straight Velocity Optimization of 3-Joint Carangiform Fish Robot Using Genetic-Hill Climbing Algorithm Tuong Quan Vo Ho Chi Minh City, University of Technology – Viet Nam e-Mail: vtquan@hcmut.edu.vn or quanvotuong@gmail.com Tóm tắt Robot phỏng sinh học là một dạng robot mới đã và đang được phát triển trong những năm gần đây. Một số robot phỏng sinh học đầu tiên được nghiên cứu là robot nhện, robot rắn, robot bò cạp, robot gián,…Trong thời gian gần đây, hai dạng robot phỏng sinh học hoạt động dưới nước đang được quan tâm nghiên cứu là robot rắn và robot cá. Đầu tiên bài báo này giới thiệu về robot cá có 3 khâu, 4 khớp dạng Carangiform. Sau đó, bài báo sẽ giới thiệu việc áp dụng giải thuật di truyền và giải thuật leo đồi để tối ưu hóa vận tốc di chuyển thẳng cho robot cá. Đầu tiên, giải thuật di truyền được sử dụng để tạo ra bộ thông số đầu vào tối ưu cho robot cá. Sau đó, bộ thông số đầu vào này lại được tối ưu một lần nữa bằng giải thuật leo đồi nhằm đảm bảo bộ thông số điều khiển này gần với kết quả tối ưu toàn cục của hệ thống. Cuối cùng, chúng tôi sử dụng chương trình mô phỏng để kiểm tra tính đúng đắn của giải thuật đã nêu. Abstract Biomimetic robot is a new trend of researched field which is developing quickly in recent years. Some of the first researches on this field are spider robot, snake robot, scorpion robot, cockroach robot, etc. Lately, two new types of underwater biomimetic robot called fish robot and snake robot are mostly concerned. In this paper, firstly a dynamic model of 3-joint (4 links) Carangiform fish robot type is presented. Secondly fish robot’s maximum straight velocity is optimized by using the combination of Genetic Algorithm (GA) and Hill Climbing Algorithm (HCA) with respect to its dynamic system. GA is used to create the initial optimal parameters set for the input functions of the system. Then, this set will be optimized again by using HCA to be sure that the last optimal parameters set are the global optimization result. Finally, some simulation results are presented to prove the proposed algorithm. Keywords - fish robot, dynamic, optimization, GA, HCA, maximum straight velocity, input torque functions. 1. Introduction Generally, many researches about underwater propulsion mainly depend on the use of propellers or thruster to generate the motion for object in underwater environment. Besides, most of the natural solutions use the change of object’s body shape for movement. This changing shape generates propulsion force to make the object moves forward or backward effectively. Carangiform fish robot type is also one kind of the changing body shape to create the motion for itself in the underwater environment. George V. Lauder and Eliot G. Drucker made the thorough surveys and analyses about motion mechanisms of fish fin in advance in order to develop such a successful underwater robot system [1]. M. J. Lighthill also surveyed about the hydromechanics of aquatic animal propulsion because of many kinds of underwater animal whose motion mechanisms were evolved throughout many generations to adapt to the harsh of underwater environment [2]. Based on natural movement, there are some other researches about this type of motion. Junzhi Yu and Long Wang calculated the optimal link ratio of 4-link fish robot by using computer simulation and he showed the simulation results by comparing the moving speed by two cases of models. One is modeled by Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 247 Mã bài: 52 using the optimal link ratio and the other one is considered without the optimal link ratio [3]. However, most of the researches about fish robot are based on quite simplified model of fish as well as experimental approaches. In our research, we considered a 3-joint (4 links) Carangiform fish robot type. The dynamic model of the robot is derived by using Lagrange method. The influences of fluid force to the motion of fish robot are also considered which is based on M. J. Lighthill’s Carangiform propulsion [4]. Besides, the SVD (Singular Value Decomposition) algorithm is also used in our simulation program to minimize the divergence of fish robot’s links when simulating fish robot’s operation in underwater environment. The main goal of this paper is the optimization method to maximize straight velocity of a 3-joint Carangiform fish robot in x direction. The straight velocity of fish robot is considered by applying optimal input torque functions to its dynamic model. The optimal input torque functions are gotten by optimized the parameters which are used to build these functions. Our proposed method to solve this optimization problem is the combination of GA and HCA with respect to fish robot’s dynamic model and some other related constraints. This combination of GA-HCA gives better results than our previous work [5]. Another solution for optimization was proposed by Keehong Seo et al [6]. They used the numerical optimization software (NLPP – Non Linear Path Planning – Tool Box for Matlab) to optimize the control parameters for a simplified planar model of a Carangiform fish robot. 2. Dynamics Analysis and Motion Equations In our fish robot, we focus mainly on the Carangiform fish’s type because of fast swimming characteristics which resemble to tuna or mackerel. The movement of this Carngiform fish type requires powerful muscles that generate side to side motion of the posterior part (vertebral column and flexible tail) while the anterior part of the body remains relatively in motionless state as seen in Fig. 1. Increasing size of movement Pectoral fin Posterior partAnterior part Caudal fin Tail fin Main axis Transverse axis Fig. 1 Carangiform fish locomotion type. We design 3-joint (4 links) fish robot in order to get smoother and more natural motion. As expressed in Fig. 2, the total length of fish robot is about 600mm which includes 4 links. The head and body of fish robot are supposed to be one rigid part (link0) which is connected to link1 by active DC motor1 (joint1). Then, link1 and link2 are connected by active DC motor2 (joint2). Lastly, link3 (lunate shape tail fin) is jointed into link2 (joint3) by two extension flexible springs in order to imitate the smooth motion of real fish. The stiffness value of each spring is about 100Nm. Total weight of the fish robot (in air) is about 4 kg. l0 (link0) (link3) (link2) (link1) 1 T1 m1 (x1,y1) Y X a1 l1 l2 a2 l3 a3 2 3 m2 (x2,y2) m3 (x3,y3) T2 Fig. 2 Fish robot analytical model. In Fig. 2, T 1 and T 2 are the input torques at joint1 and joint2 which are generated by two active DC motors. We assume that inertial fluid force F V and lift force F J act on tail fin only (link 3) which is similar to the concept of Motomu Nakashima et al [7]. The expression of forces distribution on fish robot is presented in Fig. 3 below. F F is the thrust force component at tail fin, F C is lateral force component and F D is the drag force effecting to the motion of fish robot. The calculations of these forces are similar to Motomu Nakashima et al method for their 2-joint fish robot [7]. F C V F J F F F F D Direction of movement X Y Fig. 3 Forces distribution on fish robot. We suppose that the tail fin of fish robot is in a constant flow U m so we can derive the inertial fluid force and the lift force act on the tail fin of fish robot. Then we can calculate their thrust component F F and lateral component F C from the inertial fluid force and lift force. We also suppose that the experiment condition of testing our fish robot is in tank so that the value of U m is chosen as 0.08m/s. F v is a force proportional to an acceleration acting in the opposite direction of the 248 Tuong Quan Vo VCM2012 acceleration [7]. The calculation of F V is expressed in Eq. (1). The lift force F J acts in the perpendicular direction to the flow and its calculation as in Eq. (2). In these two equations, chord length is 2C, the span of the tail fin is L and is water’s density. 2 2 sin cos V F LC U LC U pr a pr a a (1) 2 2 sin cos J F LCU pr a a (2) These fluid force and lift force are divided into thrust component F F in x direction and lateral force component F C in y direction as presented in Fig. 4. UU Y X F FV V F CV F J F Y X F CJ FJ F Fig. 4 Model of inertial fluid force and lift force. In Fig. 4, U is the relative velocity at the center of the tail fin, is the attack angle. Based on Fig. 4, the value of F F and F C can be calculated by these two Eqs. (3)-(4): 0 1 2 3 0 1 2 3 sin 360 sin 360 F FV FJ V J F F F F F q q q q q q (3) 0 1 2 3 0 1 2 3 cos 360 cos 360 C CV CJ V J F F F F F q q q q q q (4) The above two equation can be simplified as follows: 1 2 3 1 2 3 sin sin F V J F F F q q q q q q (5) 1 2 3 1 2 3 cos cos C V J F F F q q q q q q (6) If we just consider the movement of fish robot in x direction, so the relative velocity in y direction at the center of tail fin is calculated by Eq. (7). 1 1 1 1 2 2 1 2 1 2 3 3 1 2 3 cos cos cos u l l a q q q q q q q q q q q q (7) Since U m and u are perpendicular as in Fig. 5(a), so the value of U can be calculated by Eq. (8): 2 2 2 m U U u (8) u Um U U (b)(a) Fig. 5 (a) Relationship between U and U m . (b) Diagram of attack angle calculation. By using Lagrange’s method, the dynamic model of fish robot is described briefly as in Eq. (9). 11 12 13 1 1 21 22 23 2 2 31 32 33 3 3 M M M N M M M N M M M N q q q (9) By solving Eq. (9) above, we can get the value of i q , i q (i = 1 3). However, based on the dynamic model in Eq. (9), SVD (Singular Value Decomposition) algorithm is also used in our simulation program to minimize the divergence of the oscillation of fish robot’s links when simulating the operation of fish robot in underwater environment. This divergence also cause the velocity of fish robot be diverged too. The motion equation of fish robot is expressed in Eq. (10). G x is the acceleration of fish robot’s centroid position. m is the total weight of fish robot in water ( 11.45 m kg). F F is the propulsion force to push fish robot forward and F D is drag force caused by the friction between fish robot and the surround environment when fish robot swims. G F D mx F F (10) The calculation of F D is presented in Eq. (11) 2 1 2 D D F V C S r (11) Where r is the mass density of water. V is the velocity of fish robot relative to the water flow. D C is the drag coefficient which is assumed to be 0.5 in the simulation program. S is the area of the main body of fish robot which is projected on the perpendicular plane of the flow 2 0.021 S m . 3. Velocity Optimization Method 3.1 Genetic Algorithm (GA) and Hill Climbing Algorithm (HCA) Genetic Algorithm [8] [9] is based on the process of Darwin’s theory of evolution by starting with a set of potential population with some or many individuals and then changing them during several iterations. The first potential population is generated or selected randomly or arbitrary. The individual in the population is called chromosome. The entire set of these chromosomes is called population. The chromosomes evolve during several iterations called generations. GA uses the concept of survival of the fitness by randomly initializing a population of individual in which each individual contains the parameters to reach to Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 249 Mã bài: 52 a possible solution of an optimization problem. Each individual in the population is assigned a fitness value that is used to indicate the quality of the individual as an optimal solution for the problem or not. Then, the selected individuals become parents based on their fitness value and then continue to create the next generation of the potential solution to the optimal problem. The new potential generations are generated using the methods of crossover and mutation. Sometimes, the result of GA is just the local optimum. It is not the global optimal solution for the whole problem. In this case, we use HCA to optimize the result of GA again to make this result better. Besides, the optimization by HCA will also find the global optimal solution for the problem. Y X Global maximum Local m axim um Flat local maxim um Beginning Position Fig. 6 Hill climbing demonstration. However, there are two popular combinations between these two algorithms such as: HCA-GA, GA-HCA. The first type of combination (HCA- GA) was used in our previous work [5] which gave worse result than the second combination (GA-HCA) as introduced in this paper. HCA [10] [11] is one of the effective methods to find the global optimum of a problem. The conceptual diagram of HCA can be seen in Fig. 6. The process of HCA can be expressed by the following steps: Step 1: Pick a random point in the search space. Step 2: Consider all the neighbors of the current state. Step 3: Choose the neighbor with the best quality and move to that state. Step 4: Repeat Step 2 to Step 4 until all the neighboring states are of lower quality. Step 5: Return the current state as the solution of the problem. 3.2 Using GA-HCA to maximize the straight velocity of fish robot The general algorithm diagram of the optimal problem is introduced in Fig. 7. Fish robot has two active joints that are joint1 and joint2 to generate the movement for whole robot. Two input torque functions equations which support for joint1 and joint2 as T1 and T2 in Fig. 2 are calculated as in Eqs. (12)-(13): 1 1 1 sin 2 T A f t p (12) 2 2 2 sin 2T A f t p b (13) 1 2 , A A : Amplitude of input torques for motor 1, 2 . 1 2 , f f : Frequency of input torques for motor 1, 2. b : Phase angle between input torques of two motors. From two Eqs. (12)-(13), there are five parameters 1 2 1 2 , , , , A A f f b need to be optimized to build two input functions 1 T and 2 T for the system. Fig. 7 General algorithm of the optimization problem. The propulsive speed of fish robot in steady state is presented by Eq. (14): F P F h u (14) h : Propulsive efficiency 0.4 h . P : Average consumed power. 1 1 2 2 2 T T P q q In GA and HCA, fitness function is used to evaluate the suitable parameters’ value for the system. The main ideas of fitness function for GA and HCA is: maximum propulsive speed gives maximum velocity of fish robot. Besides, the 250 Tuong Quan Vo VCM2012 algorithm of this fitness function is also based on the dynamic model of fish robot in order to check the suitability of these parameters to the fish robot or not. The algorithm of fitness function is expressed in Fig. 8. 21 , F F P F ig. 8 Fitness function of GA-HCA. In order to use the optimization method by GA- HCA, it requires 6 constraints criteria of the optimized parameters as expressed in Eq. (15) below: 1 2 1 2 0 0 1. 0 5 2. 0 5 3. 0 2 4. 0 2 5. 0 60 6. Dynamic model of fish robot A A f f b (15) The role of HCA is used to find the global optimal values of parameters set which is based on the population of parameters set generated by GA and fitness function. HCA algorithm is expressed by Fig. 9 below. Fig. 9 HCA By using GA, if the result is the real optimal one, it will keep in similar values in many next generations. We can depend on this characteristic of GA to make the stop condition for the optimized process. 3.3 GA-HCA implementation The simulation results of the algorithms in this paper are carried out by using Matlab program with the toolbox of GA [12]. The GA simulation program runs with the population of 500 and the generation of 500. During the heredity process, we use the selection method as normalized geometry select, the multi-non-uniform mutations as the mutation method and the arithmetic crossover as the crossover method. Then, the optimal population generated by GA will be optimized by HCA to be sure that the last optimal parameters set is the global optimal set for the system. Besides, in order to prove the effective of this proposed optimization method we also carried out the survey about the behavior of fish robot velocity which input torque functions’ parameters set are chosen arbitrary (arbitrary case). Normally, there is no method to choose the suitable values of Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 251 Mã bài: 52 a five parameters set of 1 2 1 2 , , , , A A f f b to build two input torque functions for the system. Besides, the range value of each parameter in the set also does not know exactly. By surveying the relationship between velocity and each parameter in the set, we know the divergent range of velocity value. So, base on this result we can choose suitable the range value of each parameter for the optimal case as expressed in Eq. (15). Actually in arbitrary case, we can also base on this survey to choose the parameters’ value for the system which relies on their range. However, this is not an optimal method because if one of the values in the set is chosen unsuitable, these input functions will make the system halt or divergence. Or we can choose the most maximum parameters for the input functions to create the maximum velocity for fish robot. This method is also not good because the maximum value of parameters set can also be harmful to the mechanism structure of fish robot. Therefore, by using the optimal algorithm by GA- HCA, the combination values of these five parameters 1 2 1 2 , , , , A A f f b are chosen and evaluated suitably to be sure that those values will make fish robot swim at the maximum velocity. Moreover, by comparison our optimal results done by simulation method with other results carried out by experiment method of other researchers, the advantage of our proposed methods can be proved. 4. Simulation Results 4.1 Survey the influence of input torque functions’ parameters to the velocity of fish robot The influences of those parameters to fish robot velocity are considered by observing the relation graphs between velocity and those parameters. In these cases, we consider the behavior and velocity value of fish robot with respect to amplitudes (A 1 , A 2 ), frequencies (f 1 , f 2 ), or phase angle . 4.1.1 The relationship between fish robot velocity and amplitudes In order to survey this relation, the values of amplitude A 1 , A 2 are changed while the value of frequencies and phase angle are kept as constants. Then we input some different input functions pairs which are built by this rule to the dynamic model of fish robot to consider the behavior of its velocity as presented in Fig. 10. In Fig. 10 the value of f 1 = f 2 = 0.2Hz and = 30 0 are kept as constants. 0 1 2 3 4 5 6 7 8 9 10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 The relationship between amplitude and velocity - Beta = 30 Degree, f1 = f2 = 0.2 Hz Time (s) Velocity of fish robot(m/s) A1 = A2 = 1 Nm A1 = A2 = 2.5 Nm A1 = A2 = 3.5 Nm A1 = A2 = 4.5 Nm A1 = A2 = 5 Nm (a) 0 1 2 3 4 5 6 7 8 9 10 0 2 4 6 8 10 12 14 16 18 The relationship between amplitude and velocity - Beta = 30 Degree, f1 = f2 = 0.2 Hz Time (s) Velocity of fish robot(m/s) A1 = A2 = 5.5 Nm (b) Fig. 10 (a) The relationship between amplitudes and velocity with f 1 = f 2 = 0.2Hz, = 30 0 . (b) Divergence case. In Fig. 10(a), when A 1 = A 2 = 5Nm (the topmost continuous line), velocity of fish robot has the trend to be diverged. So, if the amplitudes A 1 and A 2 are increased to over 5Nm (for example 5.5 Nm), the velocity will be diverged as expressed in Fig. 10(b). Besides, in Fig. 10(a), the performance of velocity has big oscillation when amplitude values reach to 5Nm. Therefore, we can choose the value of amplitudes be smaller or equal than 5Nm. And the value of amplitudes equal to 5Nm can be called the limited amplitude of divergence in this case. 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 The relationship between amplitude and velocity - Beta = 30 Degree, f1 = f2 = 0.6 Hz Time (s) Velocity of fish robot (m/s) A1 = A2 = 0.5 Nm A1 = A2 = 1 Nm A1 = A2 = 2 Nm A1 = A2 = 3 Nm A1 = A2 = 4 Nm Fig. 11 The relationship between amplitudes and velocity, f 1 = f 2 = 0.6Hz, = 30 0 . In next example, we increase the value of frequencies to 0.6Hz and keep phase angle’s value does not change to consider the behavior of this relationship. In Fig. 11 above, with the value of f 1 252 Tuong Quan Vo VCM2012 = f 2 = 0.6Hz and = 30 0 , if amplitude values are greater than 4Nm (the topmost dash line) the velocity will have the trend to be diverged. So, the amplitudes value equal to 4Nm can also be called the limited amplitude of divergence in this case. Generally, from two Figs. 10-11, if frequencies are increased, the amplitudes need to be decreased to keep the velocity of fish robot not diverges. Moreover, bigger amplitude also makes bigger velocity of fish robot. 4.1.2 The relationship between fish robot velocity and frequency Similar to previous case, to survey about the relationship between frequency and velocity, we keep the values of amplitudes and phase angle are constants while changing the value of frequencies to consider the performance of fish robot velocity as expressed in Fig. 12. In Fig. 12(a), the velocity has trend to be diverged when f 1 = f 2 = 0.7Hz (the top dash dot line) or f 1 = f 2 = 0.9Hz (the topmost dash line). So, if frequencies’ value are greater than 0.9Hz (for example 0.98Hz), the velocity will be diverged as expressed in Fig. 12(b). Therefore, 0.98Hz can be said to be the limited frequency of divergence in this case. 0 1 2 3 4 5 6 7 8 9 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 The relationship between frequency and velocity - A1 = A2 = 3 Nm, Beta = 30 Degree Time (s) Velocity of fish robot (m/s) f1 = f2 = 0.1 Hz f1 = f2 = 0.3 Hz f1 = f2 = 0.5 Hz f1 = f2 = 0.7 Hz f1 = f2 = 0.9 Hz (a) 0 1 2 3 4 5 6 7 8 9 10 0 5 10 15 20 25 The relationship between frequency and velocity - A1 = A2 = 3 Nm, Beta = 30 Degree Time (s) Velocity of fish robot (m/s) f1 = f2 = 0.98 Hz (b) Fig. 12 (a) The relationship between frequencies and velocity with A 1 = A 2 = 3Nm, = 30 0 . (b) Divergence case. By reducing the amplitudes value, the divergent frequency value will be increased as expressed in Fig. 13. So, with smaller amplitudes value A 1 = A 2 = 1Nm, the velocity of fish robot will be diverged when frequencies’ value are greater than or equal 1.6Hz (the topmost dash line). Similarly, the value of 1.6Hz is also called limited frequency of divergence in this case. Therefore, in the relationship between frequency and velocity, the bigger frequency will make the bigger velocity of fish robot. Besides, frequency range will be extended when amplitude range is shrunk. 0 1 2 3 4 5 6 7 8 9 10 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 The relationship between frequency and velocity - A1 = A2 = 1 Nm, Beta = 30 Degree Time (s) Velocity of fish robot (m/s) f1 = f2 = 0.3 Hz f1 = f2 = 0.7 Hz f1 = f2 = 1 Hz f1 = f2 = 1.4 Hz f1 = f2 = 1.6 Hz Fig. 13 The relationship between frequencies and velocity with A 1 = A 2 = 1Nm, = 30 0 . 4.1.3 The relationship between fish robot velocity and phase angle The phase angle between two input torque functions also has big influence to the velocity of fish robot. The relationship between velocity of fish robot and phase angle is carried out by keeping in constant the values of amplitudes (A 1 , A 2 ) and frequencies (f 1 , f 2 ). The performance of velocity based on this relation is expressed by Figs. 14 below. Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 253 Mã bài: 52 0 1 2 3 4 5 6 7 8 9 10 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 The relationship between phase angle and velocity - A1 = A2 = 1.5 Nm, f1 = f2 = 0.3 Hz Time (s) Velocity of fish robot (m/s) Beta = 1 Degree Beta = 10 Degree Beta = 30 Degree Beta = 50 Degree Beta = 60 Degree 0 1 2 3 4 5 6 7 8 9 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 The relationship between phase angle and velocity - A1 = A2 = 3 Nm, f1 = f2 = 0.7 Hz Time (s) Velocity of fish robot (m/s) Beta = 1 Degree Beta = 10 Degree Beta = 30 Degree Beta = 50 Degree Beta = 60 Degree Fig. 14 The relationship between phase angle and velocity 4.2 Optimal results created by GA-HCA In this optimization method, the optimal value of five parameters 1 2 1 2 , , , , A A f f b will be generated by GA-HCA simultaneously base on each parameter’s range values as in Eq. (15). The input torque functions built by these optimal parameters will make fish robot swim at the maximum velocity with respect to its dynamic model. In this optimization program, we will consider the two frequencies of two motors are similar 1 2 f f f and it is called same frequencies case. Therefore, the optimization method will optimize four parameters 1 2 , , , A A f b . Table 1: Optimal value of parameters set by GA- HCA A1 A2 f1 = f2 Beta Fitness 1.36 1.38 1.24 14.62 7.46 The two input torque functions for the system are introduced as Eq. (17) 1 2 1.36sin 2 *1.24 1.38sin 2 *1.24 14.62 T t T t p p (17) By applying two input torque functions in Eq. (17) to the dynamic model of fish robot, the average velocity value of fish robot is about 0.59 (m/s) during the concerning time of 20 seconds. Fig. 15 simulates the operation of fish robot’s mechanism system during concerning time in same frequencies case. The relationship graph between velocity-time and moving distance-time of fish robot by inputting Eq. (17) to the dynamic system are expressed in Fig. 16 below. In this case, fish robot swims at distance at about 11.69m after 20 seconds. After about 14 seconds, velocity of fish robot will be kept stable at the average value of 0.62 (m/s). 0 5 10 15 20 -20 -10 0 10 20 Link 1 Displacement link1 (theta1) (Degree) Time (s) 0 5 10 15 20 -4 -2 0 2 4 Link 1 Angular velocity theta1 (rad/s) Time (s) 0 5 10 15 20 -10 -5 0 5 10 Link 2 Displacement link2 (theta2) (Degree) Time (s) 0 5 10 15 20 -2 -1 0 1 2 Link 2 Angular velocity theta2 (rad/s) Time (s) 0 5 10 15 20 -2 -1 0 1 2 Link 3 Displacement link3 (theta3) (Degree) Time (s) 0 5 10 15 20 -0.2 -0.1 0 0.1 0.2 Link 3 Angular velocity theta3 (rad/s) Time (s) Fig. 15 Fish robot links ‘oscillation and their angular velocities created by using Eq. (17). 0 2 4 6 8 10 12 14 16 18 20 0 5 10 15 The relation between moving distance and time Time (s) Moving distance (m) 0 2 4 6 8 10 12 14 16 18 20 0 0.2 0.4 0.6 0.8 The relationship between real velocity and time Time (s) Velocity of fish robot (m/s) Fig. 16 Fish robot velocity and moving distance with respect to time by using Eq. (17). In Fig. 16, the velocity of fish robot takes about 12 seconds to reach to the stable state. Or, it can be said that there is no big change in velocity’s value after the steady state as in Fig. 16. Generally, in our proposed method, the optimal result is generated by GA-HCA. The results of this method are just the simulations. Our next step is to carry out some experiment which is based on these simulation results. Besides, some researchers as Motomu Nakashima et al [7] and Koichi Hirata et al [13] used experiment method to find the optimal velocity for their fish robot. The maximum velocity of fish robot done by Motomu Nakashima is about 0.5 (m/s) and Koichi Hirata’s fish robot velocity is around 0.2 (m/s). By comparison our proposed method and these two experiment method of two researchers above, our simulation results are nearly similar. This means; by using optimization algorithm by GA-HCA, we know that 254 Tuong Quan Vo VCM2012 our fish robot will swim at the maximum velocity at about 0.62 (m/s) in optimal cases. 5. Conclusion In this paper, a model of 3-joint Carangiform fish robot type is presented. From this type of fish robot, its dynamic model is derived by using Lagrange’s method. Besides, the influence of fluid force which exerts on the motion of fish robot in underwater environment is also considered in robot’s dynamic model by using the concept of M. J. Lighthill’s Carangiform propulsion. Besides, SVD algorithm is also used in our simulation program as an effective method to reduce the divergence of fish robot links when solving the matrix of its dynamic model. By inputting different arbitrary values of input torque functions T 1 , T 2 to fish robot’s dynamic system, we made a survey on the relationship between fish robot velocity and other parameters of two input functions. For example, some of the relationships are amplitude-velocity, frequency- velocity and phase angle-velocity. The results of this survey are used to define the range value of each parameter in the input function. Besides, these ranges of parameters’ value are also the constraints criteria for the optimization program of GA-HCA. Then, by using the combination of GA- HCA simulation program, the optimal parameters set which are built two input torque functions for two active motors at joint1 and joint2 are gotten. These two optimal input torque functions can make fish robot swim at the maximum velocity at about 0.62 (m/s) with respect to its dynamic model. 6. Future works In continuing to this problem, some experiments are going to be carried out to check the agreement between simulation results and the experiment results. Besides, another control problems will also considered in the next steps. References [1] Lauder, G.V. and Drucker, E.G., Morphology And Experimental Hydrodynamics Of Fish Fin Control Surfaces, IEEE Journal of Oceanic Engineering, Vol. 29, No. 3, pp. 556-571, July 2004. [2] M. J. Lighthill, Hydromechanics Of Aquatic Animal Propulsion, Annual Review of Fluid Mechanics, January 1969, Vol. 1, pp. 413-446 [3] Junzhi Yu and Long Wang, Parameter Optimization Of Simplified Propulsive Model For Biomimetic Robot Fish, Proceeding of the 2005 IEEE, International Conference on Robotics and Automation, Barcelona, Spain, pp. 3306-3311, April 2005. [4] M. J. Lighthill, Note On The Swimming of Slender Fish, Journal of fluid mechanics, Vol 9, pp 305-317, 1960. [5] Tuong Quan Vo, Byung Ryong Lee, Hyoung Seok Kim and Hyo Seung Cho, Optimizing Maximum Velocity of Fish Robot Using Hill Climbing Algorithm and Genetic Algorithm, The 10 th International Conference on Control, Automation, Robotics & Vision, 17-20 December 2008, Hanoi, Vietnam. [6] Keehong Seo, Richard Murray, Jin S. Lee, Exploring Optimal Gaits For Planar Carangiform Robot Fish Locomotion, 16 th IFAC World Congress in Prague, 2005. [7] Motomu NAKASHIMA, Norifumi OHGISHI and Kyosuke ONO, A Study On The Propulsive Mechanism Of A Double Jointed Fish Robot Utilizing Self-Excitation Control, JSME International Journal, Series C, Vol. 46, No. 3, pp. 982-990, 2003. [8] Colin R. Reeves, Jonathan E. Rowe, Genetic Algorithms – Principles And Perspectives, A Guide to GA Theory, Kluwer Academic Publishers, 2003. [9] Randy L.Haupt, Sue Ellen Haupt, Practical Genetic Algorithms – Second Edition, A John Willey & Son, Inc., Publication, May 2004. [10] Andrew W. Moore, Iterative Improvement Search Hill Climbing, Simulated Annealing, WALKSAT, and Genetic Algorithms, School of Computer Science Carnegie Mellon University. [11] Masafumi Hagiwara, Pseudo Hill Climbing Genetic Algorithm (PHGA) for Function Optimization, Proceeding of 1993 International Joint Conference on Neural Networks. [12] Christopher R. Houck, Jeffery A. Joines, Michael G. Kay, A Genetic Algorithm for Function Optimization: A Matlab Implementation, North Carolina State University. [13] Koichi HIRATA*, Tadanori TAKIMOTO** and Kenkichi TAMURA***, Study on Turning Performance of a Fish Robot, *Power and Energy Engineering Division, Ship Research Institute, Shinkawa 6-38-1, Mitaka, Tokyo 181- 0004, Japan, **Arctic Vessel and Low Temperature Engineering Division, Ship Research Institute, *** Japan Marine Science and Technology Center. Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 255 Mã bài: 52 Vo Tuong Quan was born in 1979, Ho Chi Minh City, Viet Nam. In 2005, he received his MSE in Ho Chi Minh City University of Technology, Viet Nam about Machine Building Engineering. And, in 2010, he received his PhD in University of Ulsan, Ulsan, Korea about Mechanical and Automotive Engineering. He has been a Lecturer in the Department of Mechatronics, Faculty of Mechanical Engineering, Ho Chi Minh City University of Technology from 2002 until present. His currently researches are about the underwater robots, biomimetic robots, bio-mechatronics systems and automatic control systems in industry. . 246 Tuong Quan Vo VCM2 012 Nghiên Cứu Phân Tích Động Lực Học và Ứng Dụng Giải Thuật Di Truyền-Leo Đồi Trong Việc Tối Ưu Hóa Vận Tốc Di Chuyển. thiệu việc áp dụng giải thuật di truyền và giải thuật leo đồi để tối ưu hóa vận tốc di chuyển thẳng cho robot cá. Đầu tiên, giải thuật di truyền được sử dụng để tạo ra bộ thông số đầu vào tối ưu. robot gián,…Trong thời gian gần đây, hai dạng robot phỏng sinh học hoạt động dưới nước đang được quan tâm nghiên cứu là robot rắn và robot cá. Đầu tiên bài báo này giới thiệu về robot cá có 3