Design and Implementation of a Magnetically Actuated Miniature Robotic Fish*

Proceedings of the 20th World The International Federation of Congress Automatic Control The International Federation of Congress Automatic Control Proceedings of the 20th9-14, World Toulouse, France, July 2017 Available online at www.sciencedirect.com Toulouse, France,Federation July 9-14, 2017 The International of Automatic Control Toulouse, France, July 9-14, 2017

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IFAC PapersOnLine 50-1 (2017) 6851–6856 Design and Implementation of a Design and Implementation of a Magnetically Actuated MiniatureofRobotic Design and Implementation a Magnetically Actuated⋆Miniature Robotic Fish ⋆Miniature Robotic Magnetically Actuated Fish ⋆ Fish ∗,∗∗ Xingyu Chen, Zhengxing Wu, ∗∗ Chao Zhou, ∗∗ ∗∗ ∗,∗∗ Zhengxing Wu, ∗∗ Xingyu Chen, ∗,∗∗ Chao Zhou, ∗∗ and Junzhi Yu ∗∗ ∗∗ ∗,∗∗ ∗∗ ∗∗ ∗∗ Xingyu Chen, and Zhengxing Wu, Chao Zhou, ∗∗ Junzhi Yu and Junzhi Yu ∗∗ Bejing, 100049, China ∗ University of Chinese Academy of Sciences, ∗ ∗ University of Chinese Academy of Sciences, Bejing, 100049, China (e-mail:[email protected]) ∗ ∗∗ University Chinese Academy of Sciences, China (e-mail:[email protected]) State KeyofLaboratory of Management and Bejing, Control100049, for Complex ∗∗ ∗∗ State Key Laboratory (e-mail:[email protected]) of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, ∗∗ State Key Laboratory of Management andAcademy Control for Complex Systems, Institute of Automation, Chinese of Sciences, Beijing, 100190, China (e-mail: [email protected], Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China (e-mail: [email protected], [email protected], [email protected]) Beijing,[email protected], 100190, China (e-mail: [email protected], [email protected]) [email protected], [email protected]) Abstract: At present, most of bio-inspired robotic fish are designed with large sizes and Abstract: present, mostInofthis bio-inspired fish are designed large and sizesbuilt, and actuated by At electric motors. paper, an robotic 89-mm-long robotic fish iswith designed Abstract: present, mostInfast ofthis bio-inspired fish designed large sizes and actuated by At electric motors. paper, an robotic 89-mm-long robotic fishrobotic iswith designed built, which is capable of swimming and turning flexibly. Thisare miniature fish isand intended actuated byaselectric motors. this paper, an flexibly. 89-mm-long fishrobotic is missions. designed and built, which is capable of swimming and turning Thisrobotic miniature fish isCompared intended to be used a tool for animalInfast behavioral research and special underwater which is capable of swimming fast andsystem turning This miniature robotic fish intended to betraditional used as a tool for animal behavioral research and special underwater missions. with design, the propulsion isflexibly. characterized by no motor, which is is aCompared magnetic to be used as a tool for animal behavioral research and special underwater missions. Compared with traditional design, the propulsion system is characterized by no motor, which is a magnetic actuator. Bluetooth low energy is utilized for remote control, allowing convenient operation via with design, system is characterized by motor, which is a magnetic actuator. Bluetooth lowthe energy for remote control, allowing convenient operation via smarttraditional devices. By means of propulsion law isofutilized electromagnetic induction, theno relationship between current actuator. Bluetooth low energy for remote control, allowing convenient operation via smart devices. By means of law isofutilized induction, thetail-beat relationship between current and magnetic induction intensity iselectromagnetic explored. Further, a novel rhythm for magnetic smart devices. By means of law of electromagnetic induction, the relationship between current and magnetic induction intensity is explored. Further, a novel tail-beat rhythm for magnetic actuator is proposed. Meanwhile, a dynamic modeling of fishlike swimming is constructed based and induction intensity explored. Further, novel swimming tail-beat for magnetic actuator is proposed. Meanwhile, aisdynamic modeling of afishlike is constructed based on amagnetic Lagrange approach to analyze its propulsive performance. Finally, rhythm aquatic experiments actuator proposed. Meanwhile, a dynamic modeling ofactuated fishlike swimming is constructed based on a Lagrange approach its propulsive performance. Finally, aquatic experiments verify theiseffectiveness of to theanalyze formulated magnetically design scheme along with the on a Lagrange approach its propulsive performance. Finally, aquatic experiments verify the effectiveness of to theanalyze formulated magnetically actuated design scheme along with the conducted theoretical analyses. verify the effectiveness of the formulated magnetically actuated design scheme along with the conducted theoretical analyses. © 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. conducted theoretical analyses. Keywords: Underwater robot, Robotic fish, Magnetic actuator, Dynamic modeling. Keywords: Underwater robot, Robotic fish, Magnetic actuator, Dynamic modeling. Keywords: Underwater robot, Robotic fish, Magnetic actuator, Dynamic modeling. 1. INTRODUCTION underwater environments, like exploration in some narrow 1. INTRODUCTION underwater environments, like exploration in some narrow and cluttered underwater areas. Up to now, even though 1. INTRODUCTION environments, like exploration inattention some narrow and cluttered underwater Upgreater to now, even though miniature robotic fish has areas. received (Yu Recently, underwater robot has been increasingly applied underwater and cluttered underwater areas. Up to now, even though miniature robotic fish has received greater attention Recently, underwater robotsuch has as been increasingly al. to a variety of situations, data collection, applied under- et al. (2016), Wang and Tan (2015) and Kopman et(Yu robotic fishand hashave received greater attention et al. (2016), Wang Tan (2015) and their Kopman et(Yu al. Recently, underwater has as been increasingly to a variety of situations, such data collection, under(2015)), few researchers conducted works on water monitoring androbot underwater exploration forapplied rescue miniature et al. (2016), Wang and Tan (2015) and Kopman et al. to a variety of situations, such as data collection, under(2015)), few researchers have conducted their works on water monitoring and underwater exploration for rescue extremely tiny robotic fish with body length less than or salvage, e.g., Bluefin 21 was applied in the search for few researchers havewith conducted their works on extremely tiny robotic fish body length less than water monitoring and underwater exploration for rescue or salvage, e.g., Bluefin 21 was applied search for (2015)), 10 cm. On the other hand, most existing robotic fish Malaysia Airlines Flight 370. Along with in thethe improvement extremely tiny robotic fish with body length less than 10 cm. On the other hand, most existing robotic fish or salvage, e.g., Bluefin 21 was applied in the search for Malaysia Airlines Flight Along with the improvement of bionic methods, many370. researches on fish-inspired robot adopted a servomotor-based driven system (Liu and Hu cm. Shao On the other hand, most robotic fish Malaysia Airlines Flight 370. Along not with thethe improvement adopted a servomotor-based system (Liu and Hu of bionic many researches on only fish-inspired robot 10 (2010), et al. (2008) anddriven Malec existing et al. (2010)), which have beenmethods, conducted which involve kinematic adopted a servomotor-based driven system (Liu and Hu (2010), Shao et al. (2008) and Malec et al. (2010)), which of bionic methods, many researches on fish-inspired robot have been conducted which involve not only the kinematic could generate a fish-like motion style through mimicking mechanism and hydrodynamic analyses of the natural Shao etaof al. (2008)fin. andNamely, Malec al. (2010)), which could generate fish-like motion styleet through have been conducted involve not onlyofof the mechanism and hydrodynamic analyses the natural (2010), the undulation caudal there is atmimicking least one fish by biologists, butwhich also the exploration a kinematic practical, generate fish-like motion stylethere through mechanism hydrodynamic analyses ofofby the natural could the undulation caudal fin. Namely, atmimicking least one fish by biologists, butpropulsive also the exploration a practical, motor used in aof common design (Wang andis Tan (2015), effective andand flexible mechanism engineers the undulation of caudal fin. Namely, there is at least one motor used in common design (Wang and Tan (2015), fish by biologists, but also the exploration of a practical, effective and flexible propulsive mechanism by engineers (Aureli et al. (2010) and Yu et al. (2004)). Crespi et al. Kopman et al. (2015) and Kopman and Porfiri (2013)) and motor used in common design (Wang and Tan (2015), Kopman et al. (2015) and Kopman and Porfiri (2013)) and effective and flexible propulsive mechanism by engineers (Aureli et al. (2010) and Yu et al. (2004)). Crespi et al. some high-performance robotic fish need more than eight (2008) developed a robotic box fish to explore the control et al.(Wu (2015) and Kopman and Porfiri (2013)) and some high-performance robotic fish need moreto than (Aureli et al. and Yu al. to (2004)). Crespi et al. Kopman (2008) developed a robotic boxetgenerators fish explore the control servomotors et al. (2014)), which leads largeeight size mechanism of (2010) central pattern (CPGs). Curet some high-performance robotic fish need more than eight (2008) developed a robotic box fish to explore the control servomotors (Wu et al. (2014)), which leads to large size mechanism central generators (CPGs). et al. (2011) of focused onpattern the mechanical properties of Curet a bio- and huge cost. Besides, these motor-based driven systems servomotors (Wu et al. (2014)), which leads to large size and huge cost. Besides, these motor-based driven systems mechanism of central pattern generators (CPGs). Curet et al. (2011) focused on the mechanical properties of a bioalso cause massive energy consumption, which severely inspired robotic knifefish with an undulatory propulsor. huge cost. Besides, these motor-based driven systems also cause massive energy consumption, severely et al. (2011) on the mechanical properties of a bio- and inspired robotic with an an undulatory propulsor. impacts the endurance of the robot. For which this reason, it Phamduy etfocused al. knifefish (2015) employed interactive idevicecause massive energy consumption, which severely inspired with an an undulatory propulsor. impacts the endurance of the robot. For thisstyle reason, Phamduy et al. knifefish (2015) interactive idevice- also is worth creating another motor-free driven for ita controlledrobotic robotic fish foremployed education. the endurance of athe robot. For thisstyle reason, is worthfish, creating another motor-free driven for ita Phamduy et al. (2015) an interactive idevice- impacts controlled robotic fish foremployed education. robotic especially for miniature one. Most researchers on long and large robotic fish in ex- is worthfish, creating another driven style for a robotic especially for a motor-free miniature one. controlled roboticfocus fish for education. Most long and large robotic fish in ex- robotic In this paper, we focus for on aanminiature extremelyone. miniature robotic isting researchers researches, focus due toon the sufficient space for mechanical fish, especially Most researchers long and about large robotic fish in ex- In this paper, wetofocus on an extremely miniature robotic isting researches, due toon the sufficient space for mechanical fish. According the law of electromagnetic induction, a design. In general,focus robotic fish with 40-cm-long body In this paper, we focus on an extremely miniature robotic fish. According to the law of electromagnetic induction, a isting researches, due to the sufficient space for mechanical design. In general, robotic fish with about 40-cm-long body magnetic actuator consisting of a solenoid and two small are more common (Yu et al. (2004)). Miniature robotic According to the electromagnetic induction, a magnetic consisting of a solenoid and two small design. In general, about 40-cm-long body fish. are common (Yu an etfish al. with (2004)). Miniature magnets isactuator designed forlaw the of robotic fish. Through modulatfish,more however, will robotic play important role in many robotic special magnetic actuator consisting of a solenoid and two small are more common (Yu et al. (2004)). Miniature robotic magnets is designed for the robotic fish. Through modulatfish, however, will play an important role in many special ing the frequency and pulse width of the electric current in ⋆ This work was supported by the National Natural Science Foundais designed forpulse thecaudal robotic modulating frequency width fin, offish. the electric in fish, however, will play an important role in many special magnets the the solenoid fixed and with the anThrough alteringcurrent magnetic ⋆ This work was supported by61603388, the National Natural Science Foundation of China (nos. 61633020, 61633004 and 61421004), by ing the frequency and pulse width of the electric current in the solenoid fixed with the caudal fin, an altering magnetic field is periodically generated. Coupled with a constant ⋆ This tion of China (nos. 61633020, 61603388, 61633004 and 61421004), by workNatural was supported the National Natural Science Foundathe Beijing Science by Foundation (nos. 4161002 and 4164103), the solenoid fixed with the caudal fin,aan altering magnetic field is periodically generated. Coupled with a constant magnetic field from the two magnets, periodical magnetic the Science Foundation (nos. 4161002 4164103), tion of China (nos.Career 61633020, 61603388,Award 61633004 and and 61421004), by and Beijing by the Natural Early Development of SKLMCCS. field is periodically generated. Coupled with a magnetic constant magnetic field from the two magnets, a periodical and Beijing by the Natural Early Career Development of SKLMCCS. the Science FoundationAward (nos. 4161002 and 4164103), magnetic field from the two magnets, a periodical magnetic and by the Early Career Development Award of SKLMCCS.

Copyright © 2017 IFAC 7055 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2017, 2017 IFAC 7055Hosting by Elsevier Ltd. All rights reserved. Peer review©under of International Federation of Automatic Copyright 2017 responsibility IFAC 7055Control. 10.1016/j.ifacol.2017.08.1206

Proceedings of the 20th IFAC World Congress 6852 Xingyu Chen et al. / IFAC PapersOnLine 50-1 (2017) 6851–6856 Toulouse, France, July 9-14, 2017

force is produced and the robotic fish can be rhythmically driven to oscillation. Considering the requirement of shortrange control and low power, we adopt Bluetooth Low Energy (BLE) as a communication tool for the miniature robotic fish, which can also strengthen the interactive experiences if a phone or pad is applied as controllers. To explore the driven mechanism, the theoretical analyses in magnetic induction intensity and magnetic force are executed. Further, a dynamic model of fishlike swimming based on the Lagrange method is constructed, and a more practical regulation rule of tail beat, called Magnetic Induction Pulse Width Modulation (MIPWM), is proposed to enhance the effectiveness of the developed model. Finally, the miniature robotic fish successfully realizes fast swimming and flexible turning motions. The experimental results verify the effectiveness of the formulated magnetically actuated design scheme and the conducted theoretical analyses. Because of the small size and convenience of control, the robotic fish is envisaged as a tool for animal behavioral research, social behavioral study and mimicking complex swimming pattern of comparable live fish. The remainder of the paper is organized as follows: the mechatronic design of the miniature robotic fish is overviewed in Section 2. Section 3 provides the magnetic actuator and motion model analyses. Experimental results are elaborated in Section 4. Finally, Section 5 concludes the paper with an outline of future work. 2. MECHATRONIC DESIGN THE ROBOTIC FISH Fig. 1 presents the physical dimensions of the miniature robotic fish developed in this paper. Modeled after a scup fish, the robotic fish is 88.75 mm in length, 62.40 mm in width, and 47.48 mm in height. Generally, the robotic fish consists of a rigid body and a flexible caudal fin, as shown in Fig. 2. The anterior body part divided into electric compartment and actuator compartment contains the main mechatronic components. The electric compartment primarily includes a control board, a mini Li-Po battery and other facilitation designs. Regarding to the actuator compartment, a novel magnetic actuator is designed. Generally, the actuator consists of a solenoid, two magnets, a peduncle and an O-ring. As a alternating field generator, the solenoid yields directionvariable driven forces in a constant magnetic field from two 88.75

Solenoid

Peduncle Caudal Fin

Battery Hole for water awareness

O-ring

Control board ard Permanent magnet

(a)

(b)

Fig. 2. Mechanical design of the robotic fish. (a) Concept design; (b) Robotic prototype. magnets, which can vibrate as desired mode. As for the O-ring, it has two functions, one is protecting the internal electronics from water while the caudal fin is oscillating flexibly; the other is to facilitate the caudal fin to return to its initial position, when the magnetic field disappears. The whole control system can be divided into four parts, separately termed as BLE Client, BLE Server, Driver and Actuator. As a control terminal, the BLE client plays an important role in data exchange and an Android device is employed. Obviously, the robotic fish works as the BLE server. Notice that nRF51822 which combines a control unit and a communication module is selected as the MCU to minimize the size of the control board. When in BLE mode, the nRF51822-based MCU works as a 2.4 GHz transceiver. Besides, it also produces the Pulse Width Modulation (PWM) signals for the driver. For the purpose of excellent capacities of the current amplification, L9110s is adopted as the driver for the magnetic field generator. With the powerful driven current, the actuator can generate a strong altering magnetic field for the caudal fin. As a result, the caudal fin could oscillate following the given signals.

47.48

31.63

26.50

Hole for antenna

3. MAGNETIC ACTUATOR AND MOTION ANALYSIS

62.40

50

23.29

3.1 Magnetic Induction Intensity Analysis According to Biot-Savart Law (Haddon (1972)), the magnetic induction intensity at a point beside a ring current can be expressed below,

Fig. 1. Physical dimensions of the designed miniature robotic fish (unit: mm) 7056

µ0 B= 4π



L

Idl × R R2

(1)

Relative magnetic induction intensity and force

Proceedings of the 20th IFAC World Congress Xingyu Chen et al. / IFAC PapersOnLine 50-1 (2017) 6851–6856 Toulouse, France, July 9-14, 2017

h

H N

N

β1 β2

X

d

O

r x

6853

2.5

2

1.5

Bs Bml Bmr

1

F

0.5

0

-6

-4

-2

Fig. 3. Model and analysis of the magnetic actuator where B is the magnetic induction intensity; µ0 is the vacuum permeability; and I is the magnitude of current while dl stands for the element of length; Finally, R is the corresponding distance vector. Thus, the axial magnetic induction intensity coming from a circular wire can be calculated below and the direction is determined by right-hand rule, where r is the radius of the circular wire and θ stands for the angle between the axis and the direction of magnetic field.

B=



µ0 Ir µ0 Idl r = 4πR2 R 4πR3



dB cos θ =



dl =

µ0 Ir2 2R3 (2)

Furthermore, the solenoid can be treated as a plenty of circular wires. As shown in Fig. 3, there are four important shape-related parameters (marked in blue) in the model of the magnetic actuator. The green line illustrates one of circular currents and the origin point locates at the central of solenoid. Magnetic induction intensity generated by the solenoid is denoted by Bs and its magnitude can be formalized by the following equation, −h 2



D

µ0 IN n = 2h(D − d)



Bs =



−h 2

µ0 Ir2 2(x2

d

−h 2

−h 2

+



d

D

3 r2 ) 2

N n drdx h D−d r2 3

(x2 + r2 ) 2

0

2

4

6

x (mm)

(3)

Fig. 4. Magnetic induction intensity and force along X -axis In general, if β1 and β2 are regarded as variables, the magnetic induction intensity produced by the solenoid at each point along X-axis can be expressed by (4). Concisely, Bs is constant at any points with the same x in the narrow space. Obviously, Bs is linear correlated to I, N and n, which is inversely proportional to h. Fig. 4 shows relative intensity curve of magnetic induction in interval between two magnets along X-axis. The red curve describes the magnetic induction intensity Bs , when the solenoid locates in the middle of two magnets. Obviously, the red curve will move along X-axis with the solenoid moving. The other curves named as Bml and Bmr denote the magnetic induction intensity generated by the left and right magnets. The green curve depicts the generated magnetic force when the solenoid moving. 3.2 Magnetic Force Analysis The element of magnetic force acting on circular current can be calculated by dF = Idl × B. Owing to the consistency of the direction of the force from two magnets, we treat B = |Bml |+|Bmr |+|Bs | concisely. Because of symmetry, the orientation of resultant force is horizontal. Thus, its magnitude can be expressed as follows,  Fs = IB sin α cos σdl = 2πrIB cos σ (5) L

drdx

where α = 90◦ at any dl.

where x and r are indeed discrete variables. N/h and n/(D − d) are used to convert them into continuous variables. N and n represents the total number of wire layers and the amount of wire rings in each layer, respectively. Owing to the narrow variable range of r, the integral midvalue theorem can be used to solve the integral. Thus, an assumption is proposed: Hypothesis 1. The magnetic induction intensity produced by r-varied circular current is constant and it is equal to that generated by the one with rd = (D + d)/2. Therefore, if x/rd = tan β, (3) can be simplified as follows:  h µ0 IN nrd2 2 1 dx Bs = 2 3 2 h 2h − 2 (x + rd ) 2  µ0 IN n µ0 IN n β2 d tan β (sin β2 − sin β1 ) = = 2 2h 2h β1 1 + tan β (4)

According to the coordinate system shown in Fig. 3, we find that the variables σ and B are functions of |x|. They may be denoted by σ(|x|) and B(|x|), which are governed by the property of the magnet. Considering Hypothesis1 as well as the thickness and angle from vibration with negligible effect, the total magnetic force acting on the solenoid can be expressed below approximatively, F = 2πrd IB(|x|)nN (cos σ(|x|) + cos σ(2H − |x|)) (6) Owing to the contrary variation of cos σ(|x|) and cos σ(2H− |x|)), the term cos σ(|x|) + cos σ(2H − |x|) can be treated as a constant. The green curve in Fig. 4 describes the magnetic force, when the solenoid, or the center of red curve, locates at corresponding coordinate. Thereby, F is strong when the solenoid closes each magnet, and it is weakest when the solenoid locates at the center of interval. 3.3 Motion Analysis Tail-Beat Rhythm Firstly, define φ as the tail deflection angle with respect to the initial position of the caudal fin.

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yellow. Since only the planar swimming considered, we define {X, Z, Θ} to express the status of mass center of the robot. Meanwhile, define ri = (Xif , 0, Zif )T to denote the centroid of two links and lif be a half of the link length, both expressed in O − XY Z. So we can get,   r1 = [X, 0, Z]T (8)  W f W f [l2 , 0, 0]T [l1 , 0, 0]T + RC r2 = r1 + RB

400

0 −0.2 0

1

10

2

αφ (rad/s )

ωφ (rad/s)

φ (rad)

0.2

0 −10

2

0

1

200 0 −200 −400 0

2

1

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1

2

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0 −0.2 0

1

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αφ (rad/s )

ωφ (rad/s)

φ (rad)

0.2

0 −10

2

0

1

200 0 −200 −400 0

2

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0 −0.2 0

1 t (s)

10

2

αφ (rad/s )

ωφ (rad/s)

φ (rad)

0.2

0 −10

2

0

1 t (s)

2

200 0 −200 −400 0

1 t (s)

2

Fig. 5. The curve of φ and its differential. The coefficients formed by (frequency, duty ratio) of each row is (1 Hz, 50%), (3 Hz, 30%), (4 Hz, 70%).

where θ2 = Θ + φ.

Z O

W W where RB and RC denote the transformation matrix from body reference frames to the global one, which have the following expressions,  � � cos Θ 0 − sin Θ   W   RB 0 1 0 =    sin Θ 0 cos Θ (9) � �  cos θ2 0 − sin θ2    RW =  0 1 0   C sin θ2 0 cos θ2

Ф

X

θ2

Y

Next, the translative velocities vi and angular velocities ωi of the CM (center of mass) of the i−th link with respect to the global reference frame O − XY Z can be obtained by vi = r˙i and ωi = θ˙i .

((Xf2,Yf2,0)

ϴ

(X, 0, Z)

Therefore, we can write the Lagrangian equal to the sum of potential energy(E), and kinetic energy which contains both the translational and the rotational kinetic energy,

Ob

L=

2 � 1 i=1

Fig. 6. Coordinate system and link model of robotic fish According to the analyses above, the traditional approach (φ(t) = A sin(ωt)) is unsuitable for the magnetic actuator. Through fitting by a polynomial, we establish a novel function to describe the regulation rule of the caudal fin, namely MIPWM, which is formed as follows, φ = φ(d, f, A, t) = MIPWM(d, f, A, t), (7) where d, f , and A are coefficients of duty ratio, frequency, and amplitude (fixed as π/12 in this paper). Fig. 5 shows the curve of MIPWM and the differential. As observed from the second and the third rows of Fig. 5, the different duty ratio in magnetic actuator works similarly to the bias in servo motor system. Dynamic Modelling In order to analyze the propulsive performance, a dynamic modeling of fishlike swimming is constructed based on a Lagrange approach (Zhou et al. (2013)). For the convenience of the theoretical analysis, some suppositions are proposed as follows: 1) The robotic fish is regard as a two-rigid-body system. 2) The impact from water ripple is ignored. 3) The joint-irrelevant deformation is negligible. The coordinate systems are illustrated in Fig. 6, including a global inertial reference frame denoted by O − XY Z, and two body-fixed moving reference frames denoted by Ob − Xb Yb Zb and Oc − Xc Yc Zc , respectively. According to the suppositions above, the fish body and caudal fin have been separately simplified as two links in blue and

2

mi vi2 +

2 � 1 i=1

2

Ii ωi2 + E,

(10)

where mi and Ii represent the mass and angular inertia of each link, including the added mass and inertia. Thus, the Lagrange’s equations can be given by,  d ∂L ∂L   −  FX =  ˙ dt ∂X  ∂ X     d ∂L ∂L FZ = − ˙  dt ∂ Z ∂Z       d ∂L ∂L   MΘ = − ˙ dt ∂ Θ ∂Θ

(11)

Hydrodynamic Model The hydrodynamic forces acting on the robotic fish are decided by the instantaneous movement. Here, we employ a hydrodynamic drag model to analyze the forces perpendicular to the surface of the robotic fish, which has been adopted in the case of large Reynolds number (Zhou et al. (2013)). Before these calculation, we need firstly obtain the velocities expressed in body-fixed reference frames. � B W T v1 = (RB ) v1 (12) W T v2C = (RC ) v2

Thus, the hydrodynamic force on each link could be divided into lift force (F L ) and drag force (F D ), which can be calculated by,

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180

0.4

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Speed (mm/s)

140

Y (m)

0.2 0.1 50%

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120

20 0 0

0.45

1

2

3

4

5

6

7

8

9

10

Tail-beat frequency (Hz)

X (m)

Fig. 7. Simulation results in 10 seconds with tail-beat frequency of 2 Hz and different duty ratios of MIPWM.  1   FiL = − ρCiL SiL |viQ (3)|viQ (3)   2   1 (13) D Fi = − ρCiD SiD |viQ (1)|viQ (1)   2     Fi = [FiD , 0, FiL ]T

Fig. 8. Plot of speed versus tail-beat frequency

where the coefficients C L , C D , ρ, and S represent lift force coefficient, drag force coefficient, water density and wetted area, respectively. The symbol viQ (q) denotes the qth dimension of velocities viQ . If i = 1, then Q = B; Otherwise, Q = C. Then, the hydrodynamic forces need to be transformed into the global inertial reference frame,  W W F1 = RB F1    W (14) F2W = RC F2    M W = (r1 − r0 ) × F2W Thus, we can get the generalized forces and moments expressed in the global inertial frame as follows,  FX = F1W (1) + F2W (1)     (15) FZ = F1W (3) + F2W (3)     MΘ = M W According to the derived equations above, we get the propulsive performance of the robotic fish. Fig. 7 demonstrates simulation results about the swimming trajectories, where the employed duty ratio of MIPWM is clarified. 4. EXPERIMENTS AND RESULTS

0s

9.67s

15.34s

21.12s

26.76s

32.53s

38.24s

43.86s

49.52s

Fig. 9. Snapshot sequence of circular motion mode (drawn with KCF tracking algorithm). The circles with radius of 653 mm and 403 mm describe the motion trajectory under coefficients of (8 Hz, 60%) and (8 Hz, 20%). the relationship between the propulsive speed and oscillation frequency, we measured the propulsive speed with the tail-beat frequency changing from 1 Hz to 10 Hz. As illustrated in Fig. 8, the propulsive speed increases following the tail-beat frequency. When the tail-beat frequency reaches to 10 Hz, the miniature robotic fish obtained a highest propulsive speed up to 171.05 mm/s, about 1.9 body lengths per second. When the fish swims over the high tail-beat frequency area, the speed is simultaneously influenced by the the tail-beat amplitude. 4.2 Turning Maneuver

In order to evaluate the presented analysis and the performance of the miniature robotic fish, extensive experiments were carried out. Particularly, how the tail-beat frequency and duty ratio affect the swimming speed and turning radius were explored and discussed. The experiments were executed in a 4 × 5-m-size tank and a global camera was installed 1.9 m above the water for video data collection. 4.1 Straight Swimming The first experiment focused on the straight swimming. Thanks to the well-streamlined body shape and flexible caudal fin driven by a magnetic actuator, the robotic fish realized a very fast straight swimming. In order to explore

The second experiment focused on the turning maneuvers. Through adjusting the duty ratio of the MIPWM, the robotic fish can perform a flexible turning motion, as shown in Fig. 9. Unlike the traditional turning control for the motor-driven robotic fish, the applied magnetic actuator can easily realize a flexible turning motion relaying on the duty ratio of MIPWM. Fig. 10 illustrates the relationship among the turning radius, tail-beat frequency and duty ratio of MIPWM from massive experiment data (red points). In these experiments, the tail-beat frequency ranged from 1 Hz to 10 Hz, and the duty ratio of MIPWM varied from 10% to 40%. Finally, the robotic fish obtained a wide

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formance based on the shape, material, as well as flexibility of caudal fin in the future. REFERENCES

Fig. 10. Turning radius schema. Two pathes denote the minimum radius along respective axis. turning radius from 183.14 mm to 1261.81 mm. According to the experimental data, the minimum radius was acquired when the frequency was approximately 2.87 Hz with a 10% MIPWM duty ratio. More careful inspection shows that the turning radius along duty ratio axis changes little when the frequency is less than 3.5 Hz, and when the frequency reaches to 4.9 − 8.9 Hz, the turning radius changes in a parabola form. The main reason for these situations are that the middle value of the MIPWM duty ratio usually results in an expected centripetal forces for a circular trajectory. Besides, the turning radius could decrease when the duty ratio increases at a relative high tail-beat frequency, because the caudal fin always fails to track the desired amplitudes if the frequency is too high or the duty ratio is too large or too small, see Figs. 5. Thus, the position of minimal radius under every frequency is variable, which is shown by the yellow curve in Fig. 10. Comprehensively, the miniature robotic fish realized high maneuverability under frequency from 4.4 Hz to 5.9 Hz and duty ration limited in the range between 15% and 27%, where a better duty-based “bias” can be generated. 5. CONCLUSIONS AND FUTURE WORK In this paper, we have developed a miniature robotic fish based on the electromagnetic induction principle. Distinct from the traditional motor-driven system of the existing robotic fish, a magnetic actuator is constructed to mimic fish swimming. Based on a constant magnetic field from two small magnets, the miniature robotic fish can successfully realize oscillation through periodically changing the direction of the electric current in caudal solenoid. According to detailed analysis in the magnetic actuator and locomotion, a novel MIPWM-based control method is provided to govern the straight swimming and turning maneuvers. Meanwhile, a dynamic modeling of the developed robotic fish is built via the Lagrange method to analyze the swimming performance. Finally, the miniature robotic fish realized a fast straight swimming and a flexible turning motion. Further discussion on how the tail-beat frequency and duty ratio of MIPWM impact the propulsive speed and turning radius is also presented. The experimental results validate the effectiveness of the mechatronic design and the MIPWM-based control method for the robotic fish. The future work will focus on the optimization design of the mechatronic structure and multiple sensors integration. Meanwhile, we will explore a better swimming per-

Aureli, M., Kopman, V., and Porfiri, M. (2010). Freelocomotion of underwater vehicles actuated by ionic polymer metal composites. IEEE/ASME Transactions on Mechatronics, 15(4), 603–614. Crespi, A., Lachat, D., Pasquier, A., and Ijspeert, A. (2008). Controlling swimming and crawling in a fish robot using a central pattern generator. Autonomous Robots, 25(1), 3–13. Curet, O., Patankar, N., Lauder, G., and MacIver, M. (2011). Mechanical properties of a bio-inspired robotic knifefish with an undulatory propulsor. Bioinspiration and Biomimetics, 6(2), 026004. Haddon, R. (1972). The application of the biot-savart law to the ring current analysis of proton chemical shifts. Tetrahedron, 28(14), 3613–3633. Kopman, V., Laut, J., Acquaviva, F., Rizzo, A., and Porfiri, M. (2015). Dynamic modeling of a robotic fish propelled by a compliant tail. IEEE Journal of Oceanic Engineering, 40(1), 209–221. Kopman, V. and Porfiri, M. (2013). Design, modeling, and characterization of a miniature robotic fish for research and education in biomimetics and bioinspiration. IEEE/ASME Transactions on Mechatronics, 18(2), 471–483. Liu, J. and Hu, H. (2010). Biological inspiration: From carangiform fish to multi-joint robotic fish. Journal of Bionic Engineering, 7(1), 35–48. Malec, M., Morawski, M., and Zajac, J. (2010). Fishlike swimming prototype of mobile underwater robot. Journal of Automation Mobile Robotics and Intelligent Systems, 4(3), 25–30. Phamduy, P., LeGrand, R., and Porfiri, M. (2015). Robotic fish: Design and characterization of an interactive idevice-controlled robotic fish for informal science education. IEEE Robotics and Automation Magazine, 22(1), 86–96. Shao, J., Wang, L., and Yu, J. (2008). Development of an artificial fish-like robot and its application in cooperative transportation. Control Engineering Practice, 16(5), 569–584. Wang, J. and Tan, X. (2015). Averaging tail-actuated robotic fish dynamics through force and moment scaling. IEEE Transactions on Robotics, 31(4), 906–917. Wu, Z., Yu, J., Su, Z., and Tan, M. (2014). Implementing 3-d high maneuvers with a novel biomimetic robotic fish. IFAC Proceedings Volumes, 47(3), 4861–4866. 19th IFAC World Congress. Yu, J., Chen, S., Z.Wu, and Wang, W. (2016). On a miniature free-swimming robotic fish with multiple sensors. International Journal of Advanced Robotic Systems, 13(62). Yu, J., Tan, M., Wang, S., and Chen, E. (2004). Development of a biomimetic robotic fish and its control algorithm. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 34(4), 1798–1810. Zhou, C., Hou, Z.G., Cao, Z., Wang, S., and Tan, M. (2013). Motion modeling and neural networks based yaw control of a biomimetic robotic fish. Information Sciences, 237, 39–48.

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