Braking Performance of a Biomimetic Squid-Like Underwater Robot

Journal of Bionic Engineering 10 (2013) 265–273

Braking Performance of a Biomimetic Squid-Like Underwater Robot Md. Mahbubar Rahman, Sinpei Sugimori, Hiroshi Miki, Risa Yamamoto, Yugo Sanada, Yasuyuki Toda Laboratory of Hull Form Design, Department of Naval Architecture and Ocean Engineering, Graduate School of Engineering, Osaka University, Osaka 565-0871, Japan

Abstract In this study, the braking performance of the undulating fin propulsion system of a biomimetic squid-like underwater robot was investigated through free run experiment and simulation of the quasi-steady mathematical model. The quasi-steady equations of motion were solved using the measured and calculated hydrodynamic forces and compared with free-run test results. Various braking strategies were tested and discussed in terms of stopping ability and the forces acting on the stopping stage. The stopping performance of the undulating fin propulsion system turned out to be excellent considering the short stopping time and short stopping distance. This is because of the large negative thrust produced by progressive wave in opposite direction. It was confirmed that the undulating fin propulsion system can effectively perform braking even in complex underwater explorations. Keywords: biomimetics, squid-like underwater robot, undulating fin propulsion system, braking performance, motion simulation Copyright © 2013, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved. doi: 10.1016/S1672-6529(13)60222-X

1 Introduction Underwater robots can explore the unknown resources or sunken ships in the complicated seabed topology of the coastal area and oceans, both from the scientific and industrial perspectives. The increasing demand for high-performance underwater vehicle has attracted many researchers in studying this challenging but intellectually satisfying field. A lot of studies have been conducted theoretically, numerically and experimentally on the swimming motion of fishes for understanding the mechanism of the propulsion of fish and applying the mechanism to the artificial underwater vehicles. Arrays of new concepts have emerged in the field of biologically inspired underwater propulsion systems[1–4] including several undulating-finned robots[5–7]. The braking of the translational and rotational motions is very important performance as well as the cruising speed, because the short term and short distance stopping after discovering the target is very important in the disturbed flow for exploration. So, the braking performance of the squid-like underwater robot with undulating side fins was investigated in this paper. Corresponding author: Md. Mahbubar Rahman E-mail: [email protected]

A squid-like underwater robot with two undulating side fins which mimics stingrays or cuttlefishes has been studied for many years by the authors’ group. The present model is the fifth generation of the squid-like underwater robot. Our investigation towards the development of an efficient and environmentally friendly underwater vehicle was initiated in 2002 with the construction of Model-1[8,9]. In accordance with our continued development efforts we improved it to Model-2 in 2004[10] and to Model-3 in 2006[11] and subsequently to the Model-4 in 2009. The present study is based on the Model-4; the outline of this model is shown in Fig. 1. The brief description of the Model-4 along with the force calculations and free-run tests were presented through towing tank experiments in our previous study[12]. The study on the performance of the undulating side fins with various aspect ratios using computed flow, pressure field and hydrodynamic forces has been reported in Refs. [13,14]. A numerical computation was also conducted using the finite analytic method, Euler implicit scheme and PISO algorithm[15]. In that study, the features of the flow field and hydrodynamic forces acting on the body and fin were discussed and a simple relationship among

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the fin’s principal dimensions was established. Recently, a real time simulation system of the Model-4 has been developed based on the analysis of 6-Degree of Freedom (DOF) motion and by using the Open Dynamic Engine (ODE)[16,17]. The simulator can be used in the operation training to improve the skill of operators. The swimming performance of Model-4 was demonstrated at Suma Aqualife Park (Kobe, Japan) with the real fishes (Fig. 2) and in some Underwater Robot Festivals. Our robot swam freely in the environment similar to real coastal water with tidal current. It was quite interesting to note that the robot did not annoy the fishes – fishes were not scared swimming together with the robot and they did not attack it. This proved the environment friendliness of the robot. The robot also showed excellent maneuverability in swimming and it could move in any direction in the 3D space. However, for precise maneuverability, the robot should have highly efficient braking capacity. The ability of moving along any prescribed route in calm water has already been proved by different experiments. However, the fine braking ability becomes more important in case of underwater robotic applications, since during the operation the robot has to move around an unknown geometry in the underwater region to find an untraced item or for installation or repairing activities. In the previous study[12], it was found that the robot can change the direction for translational and rotational motions very easily due to the large negative thrust in the early stage of the change of direction. It could be predicted by equation of motion under the quasi-steady assumption. The open characteristics of side fins found in the previous study are shown in Fig. 3. Here the thrust coefficient (Kx) and advanced coefficient (Jx) are defined as Kx = Tx / (N |N| L4) and Jx = U/(NL), where Tx is thrust,  is density of water, U is advanced velocity of the robot, N is frequency of the fin (negative N means that the wave direction of fin is opposite, i.e. forward direction), and L is length of the fin. From Fig. 3, it is observed that the undulating side fin propulsion system of the robot can produce large thrust in the negative Jx region (the forward velocity of the robot and negative frequency of the fin or backward velocity of the robot and positive frequency of the fin lead to negative Jx). In the present study, the characteristics for forward and backward motions are same due to symmetric geometry. In Fig. 3, the characteristics in two quadrants are shown.

Parameters of the body

Value

Parameters of the fin

Value

Length

1400 mm

Length (outside)

874 mm

Width

714 mm

Length (inside)

833 mm

Thickness

100 mm

Width

Model weight

62.8 kg

Thickness

75 mm 0.5 mm

Fig. 1 The outline of the squid-like robot (Model-4).

Fig. 2 Squid-like robot is swimming with real fish. N = 1.0 Hz N = 1.5 Hz N = 2.0 Hz

0.003

0.002

0.001

0.000 0.8

0.4

0.0 Jx

0.4

0.8

Fig. 3 Fin open characteristics (Kx, Jx).

The braking performance has not been investigated because the short term operation of negative direction is required. In this study, the model operation was first investigated by manual handling. In the tests, the operator could stop the model at desired point after a few times of training. The time for braking operation was measured and the motion was predicted by solving the quasi-steady equation of motion. Although the unsteady or transient effect seems to be required, because the time for negative direction operation is very short, the braking motion was predicted well for translational and rotational motion. After those tests, various stopping

Rahman et al.: Braking Performance of a Biomimetic Squid-Like Underwater Robot

maneuver strategies were tested by simulation. Considering the time and distance from the start of stopping motion to full stop position, it was confirmed that the braking performance of this robot is sufficient enough for exploring the underwater region.

frequency) were applied to right and left fins, respectively for steady turning at one point. After the steady motion, the opposite wave direction motions for both sides were applied and then N = 0 was applied for both fins.

T 4 (s)sin(2Ks  2Nt ),

2 Materials and methods 2.1 Experimental setup The experiment was conducted in a towing tank (width 8 m, depth 4.5 m, length 100 m) in Osaka University. The picture of the towing tank and the sketch of the experimental setup are shown in Fig. 4. As shown in the illustration, the range of movement of the model was 2.5 m in width and 1.5 m in depth. Two cameras were set at the upper side and in the underwater to take the videos of the upper view and side view of the robot motion respectively. Eight ping-pong balls were put with the rope at four sides to know the real position from the image. Though this method lacks high level of accuracy, it is simple and the results can be used for understanding the basic performance and the validation of mathematical model to a certain extent. From the videos, the positions were estimated by tracking the same marks on the body of the robot. The details of various fin motions were discussed in the previous studies[12,15]. In this study, the following fin motion was adopted in experiments. In Eq. (1), we considered the sign of frequency N. The frequency is usually positive, if we substitute negative N, the phase velocity of progressive wave is negative, that means the wave direction is opposite. At N = 0, it is considered that the fin is flat and hydrodynamic force produced by fin is zero. It is noted that, the hydrodynamic force produced by fin is the difference between the force acting when the fin is moving and the force acting on the flat fin. The braking operation means that the negative N is applied for short period and then N = 0 is applied after the steady motion using positive N for translational motion. For the rotational motion, the positive and negative N (same

267

2 ª­ § s · 4 ( s) sin ®1  0.905 ¨  0.5 ¸ «° © fL ¹ ¬¯ 1 « °

º ½° ¾ sinT max » , (2) » ¿° ¼

where fL is fin length (m) which is divided into sixteen units, s = (i1)·fL/16 (i = 1, 2, …, 17) is the distance from the fin leading edge (m) to unit i,  is the deflection angle (degree) of each unit, (s) is the amplitude of the deflection angle, N is frequency (Hz), K is wave number (1/m), and K·fL = 1.0 in this study; t is time (s), and max is the maximum fin’s ray angle from the flat position (degree). 2.2 Simulation The simulation study based on the equations of motion was conducted under the similar condition as that of the experiment for comparing the results. The coordinate system is sketched in Fig. 5, where the space fixed coordinate system (X, Y, Z) and body fixed coordinate system (x, y, z) are shown. Here u, v, w are the advanced velocities of the model in x, y, z directions respectively and p, q, r are the angular velocities around x, y, and z axes, respectively. The simulation was carried out for the translational motion and rotational motion. The results were found by solving the equations of motion and the hydrodynamic coefficients were obtained based on quasi-steady assumption from the towing tank captive test and the CFD computations of fluid force around the side fins. Eqs. (3) to (5) present the translational motion. Space-fixed coordinate system Z Body fixed coordinate system z w X

O

Y

r

o p u

Fig. 4 Brief description of the experiment. (a) Picture of the towing tank; (b) sketch of experimental setup.

(1)

q v y

x

Fig. 5 Sketch of coordinate system of the simulation.

Journal of Bionic Engineering (2013) Vol.10 No.3

268

dx dt

u,

(M  M x )

(3)

du dt

Fx ,

(4)

( f xpr  f xpl )  Cx ˜ u ˜ u ,

Fx

(5)

where M is the mass of the model (62.8 kg); Mx is the added mass in x-direction (5.975 kg); Cx is the constant for drag force in x-direction (47.70 kg·m1); Fx is the total hydrodynamic force in x-direction (N); and fxpr and fxpl are the thrust forces produced by the right and left fins respectively (N). Eqs. (6) to (8) describe the rotational motion. d\ dt ( I zz  J zz )

Tz

dr dt

r,

(6)

Tz ,

(7)

§ bB fB · ( f xpr  f xpl ) ˜ ¨  ¸  C\ ˜ r ˜ r , 2 ¹ © 2

(8)

where, is heading angle (degree); Tz is hydrodynamic moment around z-axis (N·m); Izz is moment of inertia along z-axis (10.133 kg·m2); Jzz is the added moment of inertia along z-axis (1.438 kg·m2); C is constant for drag moment (6.0 kg); bB is the width of the model (0.714 m); and fB is the width of the fin (0.12 m). The advance coefficients (Jxr, Jxl), the thrust coefficients (Kxr, Kxl), and the thrust forces (fxpr, fxpl) produced by fins were calculated as follows.

d\ dt , J xl N r ˜ fL

u  l0 J xr

d\ dt , Nl ˜ fL

u  l0

(9)

and fL is fin length (0.87 m). From Eqs. (12) to (13), it is seen that positive frequency of the fins produces positive thrust and negative frequency (i.e. opposite wave direction of fin) produces negative thrust. The initial frequency of 1 Hz was applied to the fins in both of translational motion and rotational motion. The rotational motion was created by applying the same but opposite (positive or negative) frequency to the right and left fins. In both cases the maximum oscillation angle of the fins was considered as 45.

3 Results and discussion 3.1 Comparison The experimental and simulation studies were conducted on the Model-4 of the squid-robot with the aim of investigating the braking performance. The performance was analyzed based on the braking capacity in translational motion and rotational motion. In both motions, the starting frequency of the undulating side fins of the robot was kept at 1 Hz while the maximum oscillation angles were 45. When the robot reached the stable stage, the frequency of the fin was abruptly changed to zero; that is, no thrust condition was imposed. The robot slowed down due to the resistance of water and finally stopped after travelling some distance. However, when the braking force was applied by adopting the same but opposite frequency to the side fins, it stopped very quickly and within very short distance. In both cases (translational motion and rotational motion), the robot showed excellent stopping capability. Fig. 6 shows video snap shots of the experiment of rotational motion. Here, the braking was imposed at around 14 s. It is seen from the figure that the model almost instantly stopped just

where l0 = bB/2 + fB/2, = 0 for translational motion, and u = 0 for rotational motion. K xr K xl



2

T 0.0312 J xr 2  0.015 J xr  0.005 ˜ §¨ mr ·¸ , (10) 30 ¹ ©



 0.0312 J

2 xl

2s

4s

6s

8s

10 s

12 s

13 s

14 s

15 s

16 s

17 s

2

T  0.015 J xl  0.005 ˜ §¨ ml ·¸ , (11) 30 ¹ ©



0s

f xpr

K xr ˜ U ˜ N r ˜ N r ˜ fL4 ,

(12)

f xpl

K xl ˜ U ˜ N l ˜ N l ˜ fL4 ,

(13)

where, Nr and Nl are the frequencies of right and left fins respectively (Hz); Jxr and Jxl are advance coefficients; Kxr and Kxl are thrust coefficients; mr and ml are the maximum oscillation angles of the side fins (degree);

Fig. 6 Images of the experimental video at different times of the rotational motion before and after braking stage.

Rahman et al.: Braking Performance of a Biomimetic Squid-Like Underwater Robot

around 14 s. The simulation study based on the equations of motion discussed in section 2.2 was conducted under the similar condition as that of the experiment. Fig. 7 shows the comparison of experimental and simulation results in the case of translational motion in terms of the x-direction movement with respect to time before braking, under no braking condition and after braking state. The solid line represents the usual graph of frequency (Nr = 1 Hz, Nl = 1 Hz) in translational motion. The no braking condition (Nr = 0 Hz, Nl = 0 Hz) and the braking condition (Nr = 1 Hz, Nl = 1 Hz) were applied on the 20 s. Though the data of the simulation and experiment were minimally edited for maintaining the similar condition, the results showed nice consistency in all cases. Similar study was also conducted for rotational motion; however in this case the change in frequency was done on the 10 s. Fig. 8 shows the comparison of experimental and simulation results of changing in heading angle of the robot for frequency 1 Hz (Nr = 1 Hz, Nl = 1 Hz), under no braking condition (Nr = 0 Hz, Nl = 0 Hz) and after braking condition (Nr = 1 Hz, Nl = 1 Hz).

Distance traveled (m)

6

4

Simulation 2 Experiment 0

0

10

20

^

^

30 Time (s)

Translational motion No braking Braking Braking No braking 40

50

60

Fig. 7 Comparison of experimental and simulation results in case of translational motion with and without braking.

400

300

200 Simulation 100 Experiment 0

0

10

^ ^

20 Time (s)

Rotation Braking No braking Braking No braking 30

40

Fig. 8 The experimental and simulation results of heading angle in case of rotational motion with and without braking.

269

In this case also, the simulation and experiment results show good conformity. So, it is confirmed that the simulation result agrees well with the experimental observations for both motions. From the above discussion, it can be concluded that the program could simulate the braking motion accurately for translational motion as well as rotational motion. For more investigation on the braking performance of the undulating fin propulsion system of the robot, the simulation study was extended for different braking frequencies which will be discussed in the next two sections. 3.2 Braking in translational motion The braking of the translational motion is discussed based on the simulation results for different frequencies. For all the cases, the thrusting frequency of 1 Hz was applied in the starting stage. After certain time (about 30 s in this case), the motion reached steady state (constant velocity), the braking frequencies, 0.5 Hz, 1.0 Hz, 1.25 Hz, 1.5 Hz and 2.0 Hz, were applied, respectively. When the velocity approached zero the braking frequency was switched off. Braking force was produced by imposing the braking frequency to the undulating side fins. The travelled distance of the model in x-direction with respect to time is shown in Fig. 9a. The black solid line represents that no braking frequency was applied at t = 30 s. The other curves show that different braking frequencies were applied at t = 30 s. The changes of the trajectory in the x-direction due to brakes are clearly shown in the enlarged view near the stopping point (Fig. 9b). From this figure, it is observed that the higher braking frequency can stop the model more quickly. For quantitative analysis, the data of the stopping time and the travelled distance during the stopping motion were measured and shown in Table 1. The non-dimensional distance with respect to the body length (140 cm) of the robot is also given. The higher frequency needed less time and the robot travelled shorter distance to stop. For example, with braking frequency of 0.5 Hz the model needed 5.17 s and travelled 40.2 cm before stopping; while in the case of braking frequency of 2 Hz the model took only 0.55 s and travelled only 5.34 cm before stopping. The braking performance of the squid-like robot can be easily understood if its body length is considered. The actual length of the model is 140 cm; so it travelled only 1/26 body length to stop when the

Journal of Bionic Engineering (2013) Vol.10 No.3

270

0.25 No braking 0.50 Hz 1.00 Hz 1.25 Hz 1.50 Hz 2.00 Hz

Distance (m)

Velocity (m·s1)

0.20 0.15 0.10 0.05 0.00 0 7.0

10

20

30

40

50 60 Time (s)

70

80

90

100

Fig. 10 Velocity with respect to time in translational motion. (b)

Distance (m)

6.5

0

6.0

10

20

30

40

50 60 Time (s)

70

80

90

100

10 No braking 0.50 Hz 1.00 Hz 1.25 Hz 1.50 Hz 2.00 Hz

5.5

5.0

0

26

28

30

32 34 Time (s)

36

38

No braking 0.50 Hz 1.00 Hz 1.25 Hz 1.50 Hz 2.00 Hz

20

30 40

Fig. 9 (a) Travelled distance in translational motion with respect to time; (b) enlarged view near the braking point.

40

Fig. 11 The time series of thrust for various braking frequencies in translational motion.

Table 1 Stopping time and travelled distance with different 2.5

stopping frequency in translational motion Frequency (Hz)

Stopping time (s)

Travelled distance (cm)

Distance (non-dimensional*)

2.0

0.50 1.00

5.1699810 1.7948360

40.21835 16.20572

0.287274 0.115730

1.5

1.25

1.2391410

11.55574

0.082541

1.50

0.9073238

8.642387

0.061731

2.00

0.5460224

5.343938

0.038171

No braking 0.50 Hz 1.00 Hz 1.25 Hz 1.50 Hz 2.00 Hz

1.0

*Distance was non-dimensionalized by the body length of the robot (140 cm).

0.5

braking frequency was 2 Hz; while when the braking frequency was 1 Hz, the model travelled 1/8.5 body length to stop. It was also confirmed that these data were consistent with the experimental results. The x-direction velocity with respect to time is shown in Fig. 10. When no braking was applied, the model slowed down unhurriedly because of water resistance to the model. When a braking frequency was applied the velocity decreased to zero quickly; higher braking frequency stopped the model more quickly. The graphs of thrust and drag of the model are shown in Fig. 11 and Fig. 12, respectively, the trends of which moved along the expected way. From these figures it is seen that the value of thrust and drag is same in the steady state region, which is obvious.

0.0

0

20

40

60

80

100

Time (s)

Fig. 12 The time series of drag for various braking frequencies in translational motion.

3.3 Braking in rotational motion Alike the translational motion, the ability of braking of the robot in rotational motion was also studied. The braking frequencies of 0.5 Hz, 1.0 Hz, 1.25 Hz, 1.5 Hz and 2.0 Hz were checked based on the theoretical discussion in section 2.2. To make the rotational motion with respect to z-axis the frequency of +1 Hz and 1 Hz were given in the right and left fins respectively. For braking, the reversed frequencies were applied in the corresponding fins. In the rotational motion the model rotated with respect to z-axis without moving in x or y

Rahman et al.: Braking Performance of a Biomimetic Squid-Like Underwater Robot

Heading angle (degree)

direction. After certain time (30 s) when the model reached steady state, different braking frequencies were applied. The change in heading angle with respect to time is shown Fig. 13a. When no braking was applied, i.e. the frequency of zero was maintained at 30 s, the rotation of the model became slower and stopped after long time. However when the brake frequencies were applied, the model stopped instantly. The enlarged view (Fig. 13b) near the braking point shows the clear change in angular position due to different frequencies. The data of the stopping frequency, stopping time and the change in heading angle during the brake are shown in Table 2. The non-dimensional values by 360

271

of the heading angle are also listed. From this table it is also observed that the higher braking frequencies stopped the robot more quickly for rotational motion also. The experiment was conducted for the braking frequency of 1 Hz; in that case the model rotated about 13 to stop after brake, which agrees well with the simulation result shown in the table. From these observations, it can be concluded that the braking efficiency of the robot is very high in case of rotation as well. In most of the cases, the robot took less than 1 s to stop and it travelled at best, less than 10. Another point should be noted that the robot took less time to stop in rotational motion than in translational motion; this might be due to the difference in shape of the robot at front-tail and sides direction. The change in angular velocity (r) with respect to time due to different braking frequency is shown in Fig. 14. The zero velocity indicates the stopping of the model after applying brake. The turning moment produced by undulating side fins and the drag moment acting on the body during the rotation in the water of the corresponding cases are shown in Fig. 15 and Fig. 16 respectively. In this case also, it is ensured that the turning moment and the drag moment is equal in the steady state region. 30

800 (b)

No braking 0.50 Hz 1.00 Hz 1.25 Hz 1.50 Hz 2.00 Hz

25

780 20 760

15 No braking 0.50 Hz 1.00 Hz 1.25 Hz 1.50 Hz 2.00 Hz

740

720

10 5 0

700

26

28

30

32 34 Time (s)

36

38

26

40

28

30

32 34 Time (s)

36

38

40

Fig. 14 The angular velocity with respect to time (enlarged view).

Table 2 The braking frequency, the stopping time and change in heading angle due to brake in case of the rotational motion Braking frequency (Hz)

Stopping time (s)

Change in heading angle (degree)

Change in heading angle (non-dimensional*)

0.50

3.3767760

32.79260

0.0910905

1.00

1.1708840

12.66049

0.0351680

1.25

0.8077374

8.851536

0.0245876

1.50

0.5906496

6.997125

0.0194364

2.00

0.3555546

3.501827

0.0097272

*Angle was non-dimensionalized by 360.

Turning moment (N·m)

Fig. 13 (a) Heading angle in rotational motion with respect to time; (b) enlarged view near the braking point.

Fig. 15 The time series of turning moment for various braking frequencies in rotational motion (enlarged view).

Journal of Bionic Engineering (2013) Vol.10 No.3

Drag moment (N·m)

272

(stopping) thrust to stop itself instantly and within a very short distance. The braking performance proves the applicability of this underwater propulsion system in the exploration of complicated areas of oceans with unprecedented control and minimal disturbances to the underwater environment.

References [1]

Sfakiotakis M, Lane D M, Davies J B C. Review of fish swimming modes for aquatic locomotion. IEEE Journal of Oceanic Engineering, 1999, 24, 237–252.

Fig. 16 The time series of drag moment for various braking frequencies in rotational motion (enlarged view).

[2]

and Flying, Springer-Verlag, Tokyo, Japan, 2004. [3]

In Figs. 14 to 16, only the enlarged views are drawn for clear observation of the changes near the stopping point. From the above discussion it is confirmed that the braking ability of the robot is outstanding in rotational motion also. Braking performance is very important issue in case of moving in an untraced topology and searching a submersed item in underwater area. From this study it is clear that the squid-like robot is able to move in any direction on a 2D plane by combining the 1-DOF translational motion and rotational motion with the help of its highly efficient braking process. If the braking ability is not so efficient then this work becomes difficult or somehow impossible. It should be noted that the robot can change the depth using caudal fins and also side fins[17].

Riggs P, Bowyer A, Vincent J J. Advantages of a biomimetic stiffness profile in pitching flexible fin propulsion. Journal of Bionic Engineering, 2007, 4, 151–158.

[4]

Heo S, Wiguna T, Park H C, Goo N S. Effect of an artificial caudal fin on the performance of a biomimetic fish robot propelled by piezoelectric actuators. Journal of Bionic Engineering, 2010, 7, 113–119.

[5]

Zhang Y, Jia L, Zhang S, Yang J, Low K H. Computational research on modular undulating fin for biorobotic underwater propulsor. Journal of Bionic Engineering, 2007, 4, 25–32.

[6]

Low K H. Modeling and parametric study of modular undulating fin rays for fish robot. Mechanism and Machine Theory, 2009, 44, 615–632.

[7]

Zhang Y, He J, Low K H. Parametric study of an underwater finned propulsor inspired by bluespotted ray. Journal of Bionic Engineering, 2012, 9, 166–176.

[8]

4 Conclusion The braking ability of a biomimetic squid-like robot with two undulating side fins was investigated through experiment and simulation. In the experiment, the stopping time and travelling distance (or rotational angle) after the braking frequency was applied for translational and rotational motions were measured. The equation of motion was solved with the quasi-steady assumption and using the hydrodynamic forces found from previous experiment and CFD computation. The simulation for different cases was carried out to observe the stopping ability of the undulating fin propulsion system. A good agreement between the experimental and simulation results was confirmed. From the results, it is confidently concluded that the undulating fins of the robot are capable of producing very large negative

Kato N, Ayers J, Morikawa H. Bio-mechanism of Swimming

Toda Y, Hieda S, Takashi S. Laminar flow computation around a plate with two undulating side fins. Journal of Kansai Society of Naval Architects, 2002, 237, 71–77.

[9]

Toda Y, Fukui K, Sugiguchi T. Fundamental study on propulsion of a fish-like body with two undulating side fins. The Proceeding of the First Asia Pacific Workshop on Marine Hydrodynamics, Kobe, Japan, 2002, 227–232.

[10] Toda Y, Suzuki T, Uto S, Tanaka N. Fundamental study of a fishlike body with two undulating side-fins. In: Kato N, Ayers J, Morikawa H (eds). Bio-mechanism of Swimming and Flying, Springer, Berlin, 2004, 93–110. [11] Toda Y, Ikeda H, Sogihara N. The motion of a fish-like under-water vehicle with two undulating side fins. Proceedings of the Third International Symposium on Aero Aqua Biomechanisms, Ginowan, Okinawa, Japan, 2006, 27. [12] Toda Y, Danno M, Sasajima K, Miki H. Model experiments on the squid-like under-water vehicle with two undulating side fins. The 4th International Symposium on Aero Aqua

Rahman et al.: Braking Performance of a Biomimetic Squid-Like Underwater Robot Biomechanisms, Shanghai, China, 2009. [13] Rahman M M, Toda Y, Miki H. Study on the performance of

273

squid-like underwater robot with two undulating side fins. Journal of Bionic Engineering, 2011, 8, 25–32.

the undulating side fins with various aspect ratios using

[16] Rahman M M, Miki H, Sugimori S, Sanada Y, Toda Y. De-

computed flow, pressure field and hydrodynamic forces.

velopment of a real time simulator based on the analysis of

Proceedings of the 5th Asia-Pasific Workshop on Marine

6-degrees of freedom motion of a biomimatic robot with two

Hydrodynamics, Osaka, Japan, 2010, 333–338.

undulating side fins. The 5th International Symposium on

[14] Rahman M M, Toda Y, Miki H. Computational study on the

Aero Aqua Biomechanisms, Taipei, Taiwan, 2012, 234–239.

fish-like underwater robot with two undulating side fins for

[17] Rahman M M, Miki H, Sugimori S, Sanada Y, Toda Y. De-

various aspect ratios, fin angles and frequencies. The 7th

velopment of a real time simulator based on the analysis of

International Conference on Marine Technology (MARTEC),

6-degrees of freedom motion of a biomimatic robot with two

Dhaka, Bangladesh, 2010, 29–34.

undulating side fins. Journal of Aero Aqua Biomechanisms,

[15] Rahman M M, Toda Y, Miki H. Computational study on a

2013, 3, 71–78.