Magnetic fish-robot based on multi-motion control of a flexible magnetic actuator

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IOP PUBLISHING BIOINSPIRATION & BIOMIMETICS

Bioinspir. Biomim. 7 (2012) 036007 (13pp) doi:10.1088/1748-3182/7/3/036007

Magnetic fish-robot based onmulti-motion control of a flexiblemagnetic actuatorSung Hoon Kim1, Kyoosik Shin2, Shuichiro Hashi1

and Kazushi Ishiyama1

1 Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba-ku,Sendai 980-8577, Japan2 Department of Mechanical Engineering, Eric Campus, Hanyang University, 1271 Sa 3-dong,Sangnok-gu, Ansan-si, Gyeonggi-do, 426-791, Korea

E-mail: kshoon@riec.tohoku.ac.jp

Received 2 October 2011Accepted for publication 7 March 2012Published 1 May 2012Online at stacks.iop.org/BB/7/036007

AbstractThis paper presents a biologically inspired fish-robot driven by a single flexible magneticactuator with a rotating magnetic field in a three-axis Helmholtz coil. Generally, magneticfish-robots are powered by alternating and gradient magnetic fields, which provide a singlemotion such as bending the fish-robot’s fins. On the other hand, a flexible magnetic actuatordriven by an external rotating magnetic field can create several gaits such as the bendingvibration, the twisting vibration, and their combination. Most magnetic fish-like micro-robotsdo not have pectoral fins on the side and are simply propelled by the tail fin. The proposedrobot can swim and perform a variety of maneuvers with the addition of pectoral fins andcontrol of the magnetic torque direction. In this paper, we find that the robot’s dynamicactuation correlates with the magnetic actuator and the rotating magnetic field. The proposedrobot is also equipped with new features, such as a total of six degrees of freedom, a newcontrol method that stabilizes posture, three-dimensional swimming, a new velocity control,and new turning abilities.

(Some figures may appear in colour only in the online journal)

1. Introduction

There have been a number of studies on biomimetic micro-robots and magnetic actuators. The external magnetic field,which is useful in biomedical applications, controls themagnetic actuator, as well as the limited space, motion,and locomotion of a micro-robot. Abbot et al comparedthe performance of magnetic micro-robots according tothe movement methods [1]. In particular, biomimeticflagellar propulsion method-based magnetic micro-robotshave been developed for use in an environment witha low Reynolds number, such as biological organs [2–6]. In addition, using the dc gradient magnetic field andmagnetic resonance imaging, the control method (magneticforce) and system were suggested [7–11]. It is the bestcontrol method for medical micro-robots (MMRs), particularlybecause locomotion control of a rotating magnetic field

(RMF) can describe dynamic movements, such as spiral,earthworm, and 3D rotational motions. Spiral motion andits application were demonstrated by Sendoh and Ishiyama[12, 13], whereas oscillatory or undulatory motions ofmagnetic micro-robots were suggested based on an alternatingmagnetic field [14, 15].

When using an alternating magnetic field, the robot canonly perform an oscillatory or undulatory motion dependingon the driving frequency. Saotome devised a novel magneticactuator using two small NdFeB magnets as a flapping motionwithin the alternating magnetic field [16]. All of the studiesabove have the same goal: to develop and apply micro-robotics to biomedicine. There are several studies on fish-like micro-robots, especially on the materials to be used fortheir construction. Most of the materials for fish-robots arebased on shape memory alloys [17] and piezoelectric materials(PZT) by Fukuda et al and Kosa et al [18, 19], whose studies

1748-3182/12/036007+13$33.00 1 © 2012 IOP Publishing Ltd Printed in the UK & the USA

Bioinspir. Biomim. 7 (2012) 036007 S H Kim et al

Figure 1. Box-fish model and fin motion.

revealed the mechanisms and principles of propulsion usingcomputer simulation and swimming experiments. Later, Gueet al introduced a new micro-robot using ionic conductingpolymer film, a novel material as the servo actuator with threedegrees of freedom (DoFs) [20]. These materials, however,have their disadvantages: they use a wire-controlled, inserted-battery system, which is unsuitable for medical applications. Anumber of studies have suggested that the propelling velocitybe dependent on the driving frequency, which cannot bechanged into other motions [21–23].

The purpose of this paper is to present a fish-like magneticmicro-robot based on the dynamic actuation of a flexiblemagnetic actuator within an RMF [24]. As mentioned above,the RMF has been used for generating rotating motionssuch as spiral and flagellar motions, whereas the oscillatoryor undulatory motions have been driven by the alternatingmagnetic field [2, 4, 5, 12–15]. Therefore, using the RMF forthe magnetic fish-robot aside from the rotating motion hasnot yet been reported from other research groups. Directionalcontrol of the magnetic torque causes various oscillatorymotions in a single actuator within the RMF, based onthe three-axis Helmholtz coil system. In addition, this basicmechanism and control method can be used for various typesof biomimetic locomotion, such as insect walking and snake-like locomotion. Their mechanism and active locomotion aresuitable for diagnostic robots.

The proposed magnetic fish-robot has six DoFs—two sidefins (a single side fin with pitch and roll motion) and one tail fin(with roll and yaw motion)—a very unique feature in fish-likemicro-robots. The robot can swim straight, turn, dive, and rise

Table 1. The specifications of the prototype magnetic fish-robot(mm).

Body 26 (length) × 12 (width) × 11 (height)Weight 2.15 gTail fin 10 × 7 × 0.0025Pectoral fin 7 × 5 × 0.0025Magnet Tail fin: 7 (length) × 0.7 (diameter)

Pectoral fin: 3 × 0.7Head: 2 × 0.7

using the RMF and the resultant multi-motion control of eachfin (see figure 1). These fin motions are similar to the rotatingmotions of roll, pitch, and yaw. To improve the movementvelocity without increasing the frequency, we adjusted the tail-fin actuation to the swimming performance of a real box-fish[25–27]. Although their external appearances are dissimilar,the swimming method of the robot is the same as that of thebox-fish. This paper mainly discusses the dynamic motions ofswimming. The results show that the robot can perform variousswimming movements through the new control method and thedynamic motions of the flexible magnetic actuator in the RMF.

2. Magnetic fish-robot

2.1. The structure of the magnetic fish-robot

The proposed magnetic fish-robot is composed of a body, twopectoral fins, and a tail fin; as such, it has three actuatorsas shown in figure 2. Table 1 lists the specifications of theprototype magnetic fish-robot, including its shape as well asthe sizes of its tail and pectoral fins, respectively. In particular,each joint (2 mm × 1mm) on the fins is designed to improveall actuations. Actuation of the pectoral fin can bring about anunstable swimming posture. To maintain a stable posture, ahead magnet was added. Its direction of magnetic moment isopposite to that on the pectoral fin. The swimming performanceof the robot depends on the actuation of the fins, as in a real box-fish. The main function of the tail fin is to provide propulsionfor swimming whereas its sub-function is steering (turningperformance). The pectoral fin provides steering functions(turning and underwater swimming) based on the roll andpitch motion of the fin.

(a) (b)

Figure 2. The structure of the magnetic fish-robot. (a) The totally assembled magnetic fish-robot and each direction of magnetic moment.(b) The structure of the pectoral and tail fins: M denotes the direction of the magnetic moment.

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Bioinspir. Biomim. 7 (2012) 036007 S H Kim et al

(a) (b) (c)

Figure 3. The transition of the fin’s motion according to the changes in the plane of an RMF. (a) The control of the plane of the RMF usingthe both a zenith angle (α) and an azimuth angle (ζ ). (b) The three types motion of the pectoral fin by changes in the field plane. (c) The threetypes of motion of the tail fin by changes in the field plane. The red arrows represent variation of the torque direction (trajectory of the fins).

2.2. The driving method and multi-motion of fins

In general, magnetic fish-robots are controlled by analternating magnetic field, which can only drive a singlemotion (e.g. bending) based on the constant oscillation orundulation of the fin. To create dynamic and varying motionsusing a single actuator, we control the direction of the magnetictorque using an RMF in a three-axis Helmholtz coil. Themagnetic torque (T) is expressed as

T = MH sin θ (Nm), (1)

where M is the vector of the magnetic moment of the magnet,H is the vector of the amplitude of the magnetic field, and θ

is the angle between M and H. To change the magnetic torquedirection, we change the plane and rotating direction of themagnetic field. Figure 3(a) shows the changes in the planeof the RMF, in which the position of the axis of rotation ofthe plane of the RMF is determined by angles α and ζ . Theranges of α and ζ are from 0◦ to 360◦. The changing intervalof angles α and ζ is 90◦ and their time-interval is 60 ms per90◦ which can change the fin motion without changing themoving direction. In addition, the rotation of the magneticfield is divided into clockwise (CW) and counter-clockwise(CCW) directions. Therefore, the changed field plane causesmulti-motion in a single fin because of the changed torquedirection. Each fin on the fish-robot produces an oscillatorymotion based on roll, pitch, yaw, and their combination (mixedmotion). The maximum of the single dynamic rotation (roll,pitch, and yaw motion) is generated when the direction of themagnetic moment on the fin is parallel to the plane of theRMF, whereas the maximum mixed-motion is produced whenthe direction of the magnetic moment is perpendicular to theplane of the RMF. Figures 3(b) and (c) show all the maximumactuations with the trajectories of the pectoral fins and the tailfin according to the changes in the plane of the RMF.

The structure of the pectoral fin is such that it is oriented ina direction horizontal to the robot’s body. Therefore, its motiondepends on the roll (bending vibration) and pitch (twisting

Figure 4. Coordinate system for torque calculation.

vibration) motions. The direction of the magnetic moment isperpendicular to the XZ plane, in which the head direction isfacing the XY plane, and the plane of the RMF is located inthe XY plane (the blue area). Under this condition, positiveand negative bending (roll) motions are generated duringthe different periods of the magnetic torque, respectively(θ ∈ {0, 180◦} and θ ∈ {180◦, 360◦}) (see equation (1)), asshown in figure 3(b). When the plane of the RMF changesfrom the XY plane to the YZ plane, the direction of the magnetictorque is represented at the YZ plane. Therefore, the pectoralfin generates the twisting (pitching) motion by the magnetictorque and fin structure, as shown in figure 3(b). In addition,when the plane of the RMF is the XZ plane and the directionof the magnetic moment is perpendicular to this plane, thepectoral fin generates the mixed (roll–sway–pitch) motion inorder to return to the parallel state. The form of the tail fin isperpendicular to the robot body. Therefore, its motion dependson yaw (bending), roll (twisting), and mixed (roll–sway–yaw)motions, as shown in figure 3(c). These motions are generatedby magnetic torque. Figure 4 shows a coordinate system forcalculating the torque. We considered one case where the plane

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Bioinspir. Biomim. 7 (2012) 036007 S H Kim et al

of the RMF is the YZ plane and a magnetic moment vector mis in the YZ plane:

m = (0, m0 cos θ, m0 sin θ ), (2)

H = (H0 sin ζ cos α sin ωt, H0 cos α cos ωt, H0 cos ζ sin ωt),

(3)

where m0 is the magnitude of the magnetic moment, and thereis an RMF H with strength H0 and angular velocity ω ofcurrent source. Therefore, magnetic torque can be expressedas follows:

T = m × H = (Tx,Ty,Tz),⎡⎣Tx

Ty

Tz

⎤⎦ =

⎡⎣cos α cos θ sin ωt − cos ζ sin θ cos ωt

sin ζ cos α sin θ sin ωtsin ζ cos α cos θ sin ωt

⎤⎦

⎡⎣ m0H0

m0H0

−m0H0

⎤⎦ ,

(4)

where α and ζ represent a zenith and an azimuth angle,respectively. To generate an RMF in the XZ plane, anglesα and ζ are α < 90◦ and ζ > 0◦, respectively, and the zterm becomes H0 cos ζ sin

(ωt − π

2

)by control software. The

changes in the plane of an RMF manipulate both the typesof actuation and the turning performance (direction control),as shown in figure 4. Equation (4) represents the direction ofthe magnetic torque. When angles α and ζ are 0◦, the rotatingaxis of the magnet becomes the X-axis. Thus, the directionof magnetic torque becomes Tx = m0H0(cos α cos θ sin ωt −cos ζ sin θ cos ωt). The expressed magnetic torque matrix canbe changed according to a magnetic moment vector m rotatingin the field plane. The direction of the magnetic torquedetermines the fin actuations, as shown in figure 3.

For multiple motions and direction control, three fieldplanes (YZ, XY, XZ) are expressed as follows.

(1) YZ plane:

HY Z = (0, H0 cos ζ cos 90, H0 cos α sin 90)(∴ θ = ωt = 90◦)= (0, H0 cos 90, H0 sin 90) (∴ α = ζ = 0◦). (5)

(2) XY plane:

HXY = (H0 sin α cos ζ sin ωt, H0 cos ζ cos ωt, 0)

(∴ θ = ωt = 90◦)= (H0 sin 90, H0 cos 90, 0), (6)

where α = 0◦, ζ = 90◦ and Ax is the offset for uniform field.

(3) XZ plane:

HXZ=(

H0 sin ζ cos α sin ωt, 0, H0 cos ζ sin(ωt − π

2

))= (H0Ax sin ζ cos α sin 90, 0, H0Az cos ζ cos 90), (7)

where α < 90◦, ζ > 0◦ and Ax and Az are the offset for uniformfield.

For directional control of the robot, control of the anglesof α and ζ is required; the changing interval of �α and �ζ is200 ms per 5◦.

We used 25 μm flexible thin film for the fins (tail andpectoral fins) and fixed them to the robot’s body. Therefore,the flexible fins produce a regular fin actuation (oscillation).At this time, the motion of the fin is analyzed by the flexible

(a)

(b)

Figure 5. (a) Coordinate system of a flexible multi-body [28].(b) Coordinate systems for a fin motion.

multi-body system of the Lim et al model. The flexible finsproduce bending that can be expressed by a deformed positionin the coordinate system. In addition, the flexible multi-bodysystem is the generalized form. Thus, we applied the modelto analyze the motion. Their motions can be analyzed by aflexible multi-body system [28]. Figures 5(a) and (b) show thecoordinates on a planar rotating body and on a non-planar finmodel, respectively. The local frame (X–Y–Z) is fixed at thefin body α. The location of point P′

a on the deformed fin canbe expressed by Rα vector:

Rα = Rαo + Aαrα

d (uαd = Sαζ α

d ),

Rα = Rαo + Aα(uα

o + Sαζ αd ),

(8)

where ζ αd is the vector of elastic generalized coordinates of the

deformable body α and Sα is the normal vector of the space-dependent shape function. Differentiating equation (2) can bewritten in a matrix form:

Rα = [I Aα

θ rαd AαSα

] ⎡⎣Rα

o

θα

ζα

d

⎤⎦ . (9)

The kinetic energy (Tα) of the flexible body α can beexpressed as follows:

Tα =N∑ 1

2

∫vα

ραRαTRαdvα

= 1

2ζ

αT

Mα ζα, (10)

where ρα , vα , and Mα are the mass density, volume, andmass matrix of the flexible body (α), respectively. In addition,

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Bioinspir. Biomim. 7 (2012) 036007 S H Kim et al

(a)

(b)

(c )

(d )

Figure 6. The simulation results of the tail fin: (a), (b) the displacement and distribution of the elastic strain intensity of the roll motion(twisting) on the tail fin. The displacement is 0.94 mm, and the elastic strain intensities are 0.006 45 (maximum) and0.782 × 10–5 (minimum), respectively. (c), (d) The displacement and strain intensities of the yaw motion (bending). The force is1.98 × 10–4 (N), and the distributions of the elastic strain intensity are from 0.135 × 10–6 to 0.010 151. The maximum displacement is 6.232mm (bending–yaw motion).

the strain energy (δwαs ) of the fin’s motion can be written as

follows:

δwαs = −

N∑ζαT

[ ∫vα

(DαSα )T EαDαSαdvα

]δζα

= −ζαTKα

ddδζα

= −[RαTθαT

ζαT]

⎛⎝0 0 0

0 0 00 0 Kα

dd

⎞⎠

⎡⎣ δRα

δθα

δζα

⎤⎦ , (11)

5

Bioinspir. Biomim. 7 (2012) 036007 S H Kim et al

Figure 7. The experimental setup and drive system.

where Dα is the differential operator between the strains andthe displacement. Eα denotes the symmetric matrix of elasticcoefficients. Kα

dd represents the positive definite stiffnessmatrix of the flexible fin α. Using equations (2)–(5), theequation of motion of the fins can be derived from Lagrange’sequation as follows:⎡⎣mα

rr mαrθ mα

rdmα

θθ mαθd

Symmetric mαdd

⎤⎦

⎧⎨⎩

Rα

θα

ζα

⎫⎬⎭ +

⎡⎣0 0 0

0 0 00 0 Kα

dd

⎤⎦

⎧⎨⎩

Rα

θα

ζα

⎫⎬⎭

=⎧⎨⎩

QαR

Qαθ

Qαζ

⎫⎬⎭ , (12)

where the mass and stiffness matrices and displacement andforce vectors are partitioned according to the translation,rotation, and the elastic generalized coordinates of the flexiblefin body α. Qα

R and Qαθ are the generalized force vectors relative

to the translational and the rotational coordinates, respectively.Qα

ζ is the vector of the generalized force relative to the elasticgeneralized coordinates of the flexible fin body α.

Figure 6 shows the simulation results of the tail finbased on roll (twisting vibration) and yaw motion (bendingvibration). We investigated the force, the distribution of theelastic strain intensity on the tail fin and the deformedposition. The roll motion (twisting) of the tail fin producesthe displacement of 0.94 mm and an elastic strain intensityof 0.006 45 (maximum) and 0.782 × 10–5 (minimum),respectively, as shown in figures 6(a) and (b). A yaw motion(bending) of the tail fin produces the displacement of 6.23 mmand the maximum and minimum values of elastic strainintensity are 0.0101 and 0.135 × 10–6, respectively, and thebending force is 1.98 × 10–4 N, as shown in figures 6(c) and(d). In the case of the pectoral fins, they generate the pitch androll motions. Table 2 shows the parameters for the simulation.

Table 2. The simulation parameters.

Torque 13.45 × 10−7 N mYoung’s modulus 400 kPaPoisson ratio 0.5Thickness 25 μmDimension 17 mm2

Material PDMS elastomer

2.3. Experimental analysis

The experimental apparatus consists of a three-axis Helmholtzcoil, the control software, a function generator, a power supply,and an external joystick. Changes in the plane of the uniformlyRMF in a regular hexahedron space (25 cm × 25 cm × 25 cm)of the three-axis Helmholtz coil, as well as in the direction ofits rotation, are controlled by the external joystick, as shownin figure 7.

The angles (α and ζ ) for changing the field plane arecontrolled at 0◦ up to 90◦ and their time-interval can becontrolled at 40 ms up to 4000 ms in the control software.In addition, the bandwidth of the actuators is 10 Hz. The RMFis created as a vector sum of the supplied current signals.The equipment can rotate, as well as change the plane of,the RMF. The commands from the joystick are transmittedto the control software of the PC, which in turn controls thefunction generator and power supply. Our control system hasvarious adjustable parameters. For instance, we can adjustthe strength of the magnetic field up to 13.528 kA m−1, theposition of the RMF, and the frequency of rotation, amongothers. For experiments, we used a control system with thefollowing setup: a fixed magnetic field of 7.957 kA m−1 andfrequency adjusted in the range of 1–10 Hz. To change theswimming direction, the time-interval of the angle (α and ζ ) isadjusted over 200 ms, whereas the control of the fin’s motionsis adjusted to below 60 ms.

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Bioinspir. Biomim. 7 (2012) 036007 S H Kim et al

(a) (b)

Figure 8. (a) A mixed motion composed of the bending and twisting motions in the RMF (frequency = 1 Hz and H = 4.774 kA m−1).(b) The embodiment of the mixed motion for bending and twisting (simulation result).

Figure 9. The twist angle on the mixed motion and displacement ofthe bending motion.

The proposed control method and fin structure, in whichthe fin’s motion is similar to that of a real box-fish, create botha single (bending or twisting) and mixed (their combination)oscillatory motions. Figure 8 illustrates the mixed oscillatorymotion of the actuator based on the experiment and simulationin the unstable state: the plane of an RMF is the XY planeand the direction of the magnetic moment is the XY plane.The motion of the actuator creates the mixed (yaw and roll)motion. Using the silicone-type actuator, the twisting vibrationrevealed a maximum angle of ± 45◦ and the bending vibrationyielded a maximum angle of ± 50◦. In contrast, the polyimidebeam showed a maximum angle of ± 28◦ on the yaw motionand a maximum angle of ± 40◦ on the roll motion, as shown infigure 9. These differences in angle are due to differences in the

flexibility (Young’s modulus) of the material. As mentionedearlier, the direction of the magnetic torque determines thetype of fin motion.

As mentioned above, the general one DoF fin structuregenerates a single motion of either an undulatory or anoscillatory nature, according to the transition of the drivingsource (current, frequency, voltage, etc). The proposed fin isbased on a single actuator and the control method produces thevarious oscillatory motions using the directional control of themagnetic torque. Figure 10 shows the three kinds of oscillatorymotion of the tail fin: the bending (yaw), the twisting (roll), andmixed (e.g. roll–sway–yaw) motions. The red arrows indicatethe basic direction of the magnetic moment on the tail fin. Inaddition, the direction of the robot’s head is fixed to the XYplane.

First, a bending motion is generated when the plane of theRMF is located in the XY plane. Here, the trace of the tail-finmotion represents the straight line in figure 10(a-1). Second, atwisting motion is generated within the XY plane of the RMF.Third, a mixed motion (bending and twisting vibrations) iscreated within the XY plane of the RMF. In this case, the trace ofthe motion represents the roll–sway–yaw motion, as shown infigure 10(a-3). Figure 10(b) shows the experimental resultsof the relationship between the displacement of each finand the magnetic torque in a single oscillatory motion. Tocalculate the magnetic torque of the fins, we measured theangle (θ ) in equation (1) through the video analysis: we usedtwo high-speed cameras (CASIO EX-F1, 1200 fps) placed atthe top and front; the position of the RMF was measured bythe magnetic rotator. Therefore, the two high-speed camerasrecorded the fin’s motion and the position of the magneticfield. The maximum magnetic torques of the pectoral fin andthe tail fin are 4.21×10−7 and 13.45×10−7 N m, respectively.In addition, the maximum displacement of the pectoral fin

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Bioinspir. Biomim. 7 (2012) 036007 S H Kim et al

(a)

(b)

Figure 10. Three kinds of motion and trajectory of the tail fin: M is the basic direction of the magnetic moment. M is parallel to the plane ofthe RMF in the yaw and the roll motions, and is perpendicular to the plane of the RMF in the mixed motion.

reaches 4.25 (bending) and 1.43 mm (twisting), and thoseof the tail fin reach 6.89 (bending) and 2.1 mm (twisting)at a 1 Hz driving frequency and an applied magnetic field of7.957 kA m−1. Therefore, the propulsion in swimming dependson the tail fin because it has the largest bending motion. Whenwe compared the simulation with the experiment of the tail-fin’s motion (bending and twisting), the error was 0.66 mm(bending) and 1.059 mm (twisting), respectively.

Typically, the swimming speed depends on the drivingfrequency or the magnetic field strength. The proposed fish-robot provides both frequency control and motion-basedcontrol for the swimming speed. Figure 11(a) shows theexperimental results of the motion-based velocity control,

when the magnetic field is fixed at 7.957 kA m−1 and thefrequency ranges from 1–5 Hz. The twisting motion producesthe smallest displacement in the tail fin, which results in theslowest swimming speed. Although the bending motion of thetail fin produces a large displacement, the resulting swim speedis slower than that of the mixed motion, because the twist angleof the mixed motion reduces the propulsive frictionat drivingfrequency of below 5 Hz. Motion-based velocity control issuitable for low driving frequencies because high drivingfrequencies (5–10 Hz) cause fast actuation and decrease thetwist angle of the mixed motion. As a result, the magneticfish-robot provides two control modes for swimming speed: afrequency control mode and a motion-based control mode.

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Bioinspir. Biomim. 7 (2012) 036007 S H Kim et al

(a)

(b)

Figure 11. The experimental results of the swimming speed.(a) Motion-based control at 1–5 Hz driving frequency and a fixedmagnetic field of 7.957 kA m−1 in the three-axis Helmholtz coil: thered line is the swimming speed with the bending motion, the blackline is that with the mixed motion, and the blue line is the result withthe twisting motion. (b) The swimming speed with the bendingmotion of the tail fin at 6 Hz fixed driving frequency, as a function ofthe magnetic field between 4.774 and 8.753 kA m−1.

(1) Motion-based control mode (at driving frequencies of 1to 5 Hz):

Twisting motion � Bending motion < Mixed motion.

(2) Frequency-based control (at driving frequencies of 5 to10 Hz):

Twisting motion � Mixed motion � Bending motion.

However, the driving frequency is limited in the frequencycontrol mode because high frequencies over 10 Hz producesmall displacements of the tail fin and saturate the magnet onthe fin.

Figure 11(b) shows changes in the swimming speed asthe magnetic field strength is increased at a fixed drivingfrequency of 6 Hz. In this case, the velocity decreases above7.957 kA m−1 because the tail fin has reached a step-outregion. Therefore, the propulsive range is limited by the drivingconditions.

Directional control of the magnetic torque gives rise tomotion-based control of the swimming speed. In addition, itprovides other swimming capabilities to the fish-robot. Shortcurvature turning controls the angle of bending displacementon the tail fin, as shown in figure 12(a). Here, both right-and left-based motions of the tail fin generate right and leftturning, respectively, at an angle α of 45◦ inclination of theRMF in the YZ plane. This is because the magnet has thecharacteristic of a correspondence between the angle of theRMF and the magnetic torque. In this case, an RMF (H)is H = (0, H0 cos ζ cos 90, H0 cos α sin 90) at ζ = α =45◦ and ωt = 90◦. Therefore, the inclination of the RMFcauses a variation in the magnetic torque and motion of thetail fin, as shown in figure 12(b).

Figure 12(b) shows the right-based motion of the tail finat a driving frequency of 1 Hz, a magnetic field of 7.957 kAm−1, a CW rotating of the magnetic field, and an inclination(angle α) of 45◦ in the YZ plane. In the case of the sameangle (ϕ1 = ϕ2) of tail-fin displacement, the duty ratio of themagnetic torque is equal (the black line in figure 9). However,the real duty ratio of the tail fin is different (the red line infigure 13), because only the magnetic torque causes a linearvariation of the bending motion (step 1), whereas the limitedbending motion (see figure 12(b-5)) brings about an elasticreaction force with the magnetic torque. Therefore, the rapidvariation in the magnetic torque causes step 2. These motionmechanisms can enhance turning performance.

2.4. Swimming capability

Figure 14 illustrates successive turning and forward swimmingmovements in water, in which the range of Reynolds number(Re) is approximately 350. The physical properties (density,viscosity, and kinematic viscosity) of water are 998.2 kg m−3,1.0 × 10−3 Pa s, and 1.0 × 10−6 m2 s−1, respectively. Thedirection of the robot’s head and the plane of the RMF arein the YZ plane and XY plane, respectively.

The pectoral fins perform the twisting (pitching) motionand the tail fin performs the mixed motion at an operatingfrequency of 6 Hz. To perform turning movements, theplane of the RMF is changed from XY plane-CCW (CCWand CW: rotating direction) to YZ plane-CCW, as shown infigures 11(a)–(d). Second, forward movements appear throughchanges in the field plane (YZ plane to XY plane-CW).In particular, turning requires an adjustable time-interval ofchanges in the field plane because this determines the strengthof the fin’s motion. In this case, �ζ is 5◦ and the time-intervalis 200 ms per 5◦ (see figure 3(a)). In other words, controlof angle ζ causes the change of the field plane with turningperformance as shown by equations (3)–(7).

Table 2 lists each motion of the magnet on the fish-robot’sdepending on the relationship between the direction of therobot’s head and the plane of the RMF.

Figure 15 shows the short-turning performance using theinclination of the field plane in a roll motion of the robot’sbody, generated by the pectoral fin. The reason for the rollmotion of the robot’s body is that the magnetic moment on thetwo pectoral fins, at low driving frequencies at 0.5–1 Hz, is in

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Bioinspir. Biomim. 7 (2012) 036007 S H Kim et al

(a)

(b)

Figure 12. Tail-fin control of turning by changing the direction of the RMF: (a) an inclination of 45◦ of RMF and the tail-fin motion,(b) CW RMF and its motion (right-based tail-fin actuation). The red arrows denote the position of the magnetic moment.

Figure 13. The magnetic torque of the tail-fin motion: the red line isthe real motion of the tail fin (right-based tail-fin actuation).Numbers 4 and 6 show the maximum torque. The black line is themagnetic torque of same duty ratio of the displacement.

the same direction. Subsequently, the left-based motion of thetail fin accelerates the short turning performance. Its rotationalradius is 50 mm.

To perform a diving motion, the state of the pectoral finsmust change to a twisting (pitching) motion and the drivingfrequency must be converted from high to low in order toincrease the amplitude of the pitching motion. The robot’s headmust then move with the pitching motion at the low frequencyrange (0.1–0.5 Hz) which causes the pitching motion of therobot’s body. Under these conditions, the robot’s head entersthe water: the head in the direction of the YZ plane and the field

in the XY plane (see table 3). It is then necessary to increasethe driving frequency to increase the propulsion of the tail fin(10 Hz), as shown in figures 16(a)–(d).

After diving, the robot begins to turn because of changesin the field plane from the XY plane (CW) to the YZ plane(CW) and from the YZ plane (CW) to the XY plane (CCW).Subsequently, the direction of the robot’s head changes asshown in figures 16(a)–(h). In this case, the rate of changein the angle �ζ is 20◦ every 100 ms, in order to increasethe variation in the magnetic torque within a short time ata driving frequency of 6 Hz. For the final turning and risingmotion, the driving frequency is reduced to increase buoyancy.At this time, the field plane is then changed into the YZ plane(CCW) in the XZ plane (CCW). In this state, the robot’shead is in the direction of the XZ plane. Hence, the pectoralfin generates a twisting vibration (pitch) which supports thebuoyancy. Therefore, general swimming performance dependson the frequency control mode (propulsion of the tail fin).However, the motion control mode enables three-dimensionalswimming performances because its motions are based ondynamic rotation. As a result, the combination of the twocontrol modes created various swimming performances, asshown in figure 16.

3. Discussion

This study introduced a new control method for a flexiblemagnetic actuator within the RMF applied to a magneticfish-robot. In general, a single actuator of a fish-robot’s finproduces a single undulatory or oscillatory motion, dependingon the driving frequency. To produce each motion, at least twoactuators are required. This complex structure is unsuitablefor the compact sizes of miniature or micro-robots. Therefore,

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Bioinspir. Biomim. 7 (2012) 036007 S H Kim et al

Table 3. The relationship between the direction of the robot’s head and the plane of the RMF.

XY plane (magnetic field) YZ plane XZ plane

(Head direction) Pectoral fin Bending (roll) Twisting (pitch) Mixed (pitch–yaw)XY plane Tail fin Twisting (roll) Mixed (roll–yaw) Bending (yaw)

Head Roll Pitch Mixed (pitch–yaw)YZ plane Pectoral fin Twisting (pitch) Bending (roll) Mixed (pitch–yaw)

Tail fin Mixed (roll–yaw) Twisting (roll) Bending (yaw)Head Pitch Roll Mixed (pitch–yaw)

XZ plane Pectoral fin Twisting (pitch) Mixed (roll–pitch) Bending (roll)Tail fin Mixed (roll–yaw) Bending (yaw) Twisting (roll)Head Pitch Unstable (roll–pitch–yaw) Roll

(a)

(b)

Figure 14. Surface swimming performance: (a) the relationshipbetween the plane of an RMF and position of the robot (b) turningand forward movements using the mixed motion.

the proposed control method provided a single actuator,which was capable of producing the various motions neededin order to achieve a compact size for the fish-robot. Inparticular, the way in which the various fin’s motions wereused in the robot’s swimming behavior was similar to the realbehavior of the box-fish. Finally, the proposed actuator andcontrol methods of the magnetic fish-robot are satisfied by

(a) (b) (c)

(d ) (e) (f )

(g) (h) (i )

Figure 15. Short-turning performance using the inclination of theRMF plane with the tilted motion of the robot’s body: 0.5–1 Hz,7.957 kA m−1 and an inclination angle of 45◦ (motion control mode).

a biomimetic approach. In particular, the two control modesfor swimming performance are very unique features becausethe swimming movements of general fish-robots (based onPZT, IMPC and magnetic materials) depend on the drivingfrequency and single harmonic vibration of a tail fin [21–23,29]. By understanding the physical phenomena of magnetictorque, we can easily manipulate the fish-robot. If the directionof magnetic moment is parallel to the plane of the RMF, thetail fin produces a roll and yaw motion for propulsion; whereasif the direction of the magnetic moment is perpendicular tothe plane of the RMF, the tail fin produces a mixed motionfor propulsion. Although skilled manipulation is required forspecial motion control, such as short curvature turning, themain focus of this research is swimming performance and anincrease of DoF of motion based on a single actuator using theRMF.

Therefore, we did not consider the Reynolds numberand skilled manipulation. However, the Reynolds numberis an important factor in swimming performance becausethe robot’s behavior depends on the viscosity of the liquidand the size of the solid object. Because a single actuatorproduces a single motion as one DoF, a minimum of twoactuators is required for two DoFs of motion. However,directional control of a magnetic torque using flexiblemagnetic actuators with an RMF, provides multi-motion witha single actuator. Therefore, the proposed fish-robot withan RMF provided various swimming methods. Furthermore,the generated fin motions are similar to the actual finmotion of a fish. In addition, the proposed fin mechanismscan be applied to the general fish-robot when the fin

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Bioinspir. Biomim. 7 (2012) 036007 S H Kim et al

(a)

(f ) (b)

(c)

(d )

(e)

Figure 16. Underwater swimming performance using both the frequency and motion control modes. A diving motion is generated by themotion control mode (pitching motion of the robot’s body and the pectoral fin) at 0.5–1 Hz and the frequency control mode (propulsion ofthe tail fin) at 10 Hz. The red color is the position of the fish-robot during swimming.

joint is a ball-magnet (ball-joint) which is controlled bycoils inside the robot’s body. Consequently, the mechanismand control method have various applications in roboticfields.

4. Conclusion

We have built a magnetic fish-robot based on multi-motioncontrol, using an RMF to explain and demonstrate howapplying such a unique actuation mechanism to roboticsis possible. We introduced a new control method andtheoretically and experimentally investigated the dynamicswimming movements of the robot. Our micro-robot can easilybe controlled in order to make it swim towards a desiredlocation. Such control and maneuvering are unique becauseother magnet-driven fish-like micro-robots can only perform asingle swimming motion in two dimensions. The RMF of thethree-axis Helmholtz coil system provides a dynamic actuationof the pectoral fins and tail fin’s allowing the micro-robot toswim straight, turn, dive, and surface. This control methodmay be useful for the dynamic actuation of magnetic robotsin general. Using the magnet-based actuator and magneticfield, the proposed micro-robot uses wireless controls and doesnot require batteries—features that are helpful in the fieldof biomedicine. Our ongoing work is focused on designingvarious biologically inspired magnetic micro-robots based onactive locomotion for use in medical fields because dynamicactuation, structural simplicity, and wires and battery-freeoperation are crucial for MMRs.

Acknowledgment

This study was supported by Grant-in-Aid for Japan Societyfor Promotion of Science (JSPS) fellows.

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