Field-focused reconfigurable magnetic metamaterial for wireless power transfer and propulsion of an untethered microrobot

Journal Pre-proofs Research articles Field-focused reconfigurable magnetic metamaterial for wireless power transfer and propulsion of an untethered microrobot Huu Nguyen Bui, Thanh Son Pham, Ji-Seok Kim, Jong-Wook Lee PII: DOI: Reference:

S0304-8853(19)31634-8 https://doi.org/10.1016/j.jmmm.2019.165778 MAGMA 165778

To appear in:

Journal of Magnetism and Magnetic Materials

Received Date: Revised Date: Accepted Date:

9 May 2019 29 July 2019 30 August 2019

Please cite this article as: H. Nguyen Bui, T. Son Pham, J-S. Kim, J-W. Lee, Field-focused reconfigurable magnetic metamaterial for wireless power transfer and propulsion of an untethered microrobot, Journal of Magnetism and Magnetic Materials (2019), doi: https://doi.org/10.1016/j.jmmm.2019.165778

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© 2019 Published by Elsevier B.V.

Field-focused reconfigurable magnetic metamaterial for wireless power transfer and propulsion of an untethered microrobot Huu Nguyen Bui, Thanh Son Pham, Ji-Seok Kim, and Jong-Wook Lee* Department of Electronics Engineering, Information and Communication System-on-chip (SoC) Research Center, Kyung Hee University, Yongin, 17104, Republic of Korea * Corresponding author: [email protected]

Abstract: Magnetic metamaterials have great potential for various future research and commercial applications. In this work, we investigate field-focused magnetic metamaterial for wireless power transfer (WPT) and propulsion of an untethered microrobot. With small dimensions, the operating time of an untethered microrobot is limited by the battery capacity. To perform critical missions for a long time, realizing stable power for the microrobot is a major challenge. We propose a new method of generating both wireless power and propulsion for a tiny untethered microrobot. The method is realized using the cavity mode created on a dynamically reconfigurable metasurface. The cavity effectively enhances the efficiency of the WPT by focusing the fields into the small regions where the receiver is located. Instead of a time-varying magnetic field, which requires shielding to generate a net force, we use a static field for propulsion. We propose a simple method to break the symmetry needed for generating a net force. Experiments are performed using a prototype microrobot having a size of 4 cm × 4 cm and a weight of 5.5 g floating on a water surface. The proposed approach achieves a velocity of 0.85 mm/s under a magnetic field of 0.815 mT and an input power of 1 W. Using the propulsion control, we demonstrate a microrobot navigating to multiple goal locations. Keywords: magnetic metamaterial, wireless power transfer, field focusing, microrobot propulsion, cavity. PACS: 41.20.Jb Electromagnetic wave propagation 78.67.Pt Metamaterials; photonic structures 85.70.Ay Magnetic devices characterization, design, and modeling 88.80.ht Wireless power transmission I. Introduction

chemical reactions [10], mechanical methods [11], magnetic force [12-17], and wireless power [18,19]. Jinxing et al. [10] present a method of generating propulsion by using a flow of oxygen gas, which is produced by the chemical reaction between the loaded fuels with the surrounding liquid. Using this approach, the dimension of the microrobot can be reduced to the micro or nanoscale. When the chemical reaction is exhausted, however, propulsion is terminated. Thus, the operation time is limited by fuel capacity. Furthermore, this approach demands special fluids for the chemical reaction. Magnetic interaction has been utilized to remotely control the microrobot for minimally invasive surgical treatment. Kummer et al. demonstrated five degree of freedom (DOF) wireless position and orientation control using stationary electromagnets with high permeability (4500 H/m) [7]. To increase the operational workspace and achieve three-dimension (3D) steering, a prototype system using six mobile coils is presented [12]. Floyd et al. use Helmholtz coils to generate a magnetic torque for multiple microrobots made of a magnetic material (neodymium-iron-boron, NdFeB) [13]. Pawashe et al. use a two-dimensional (2D) array of electrostatic anchoring combined with a Helmholtz coil for motion control [14]. A microrobot made of NdFeB interacts with the magnetic field to generate a Lorentz force. Chen et al. use a compound magnetic field generating a

Capsule endoscope has drawn increasing attention with its noninvasive and untethered operation [1, 2]. Compared to traditional wired endoscopy, it reduces both discomfort and sedation related issues, providing a promising diagnostic solution. Lack of active locomotion function in the conventional capsule, however, limits the access to complex real-life and hard-to-reach regions. The stopping mechanism is needed for prolonged diagnosis of a certain organ, for example, the esophagus to prevent fall in the stomach. To inspect a relatively large bowel, steerable propulsion is needed [3]. There are a variety of promising and challenging applications for an untethered miniaturized microrobot having active propulsion capabilities, such as targeted drug delivery [4], diagnostic imaging [5], and minimally invasive surgery [6]. Various methods have been investigated for achieving closed-loop motion control [7], a small size [8], and multi-function missions [9]. Because of the tiny dimensions, however, untethered microrobots have limited space for an onboard battery. To perform a critical mission, prolonged operating time is required; creating a method to provide stable power for the microrobot is a major challenge. Various methods have been investigated to provide propulsion for the untethered microrobot, which includes 1

system for guiding magnetotactic bacteria microrobots [15]. Targeted steering of the magnetotactic microrobots is demonstrated by focusing magnetic field [16]. Chowdhury et al. proposed closed-loop 2D actuation control for microrobots made of neodymium [17]. They use the static magnetic field generated by the current in a small coil to produce a Lorentz force. One disadvantage of using a magnet is that power delivery to the microrobot is difficult, which is needed to perform various complex missions, such as sensing and actuation, by using onboard active electronic devices. Magnets can be replaced with a magnetically-coupled coil. This approach allows for the adoption of the wireless power transfer (WPT) technique, which has attracted great attention for its potential of solving various power source issues. Karpelson et al. used magnetic resonance at 6.78 MHz to generate propulsion and power for a microrobot [18]. Kim et al. investigate WPT technology to generate a propulsion force and torque for the microrobot [19]. To create a Lorentz force, they used the phase difference between the time-varying magnetic field and induced current. One drawback of the previous approach is that it cannot directly control the direction of movement, which limits the ability of the microrobot to explore complex paths. To meet the requirement of challenging missions for future healthcare and biomedical applications, a tiny microrobot having onboard electronics is demanded. When the conventional WPT is used to deliver energy, however, the efficiency achievable using a small receiver is limited, constraining the dimension reduction. To overcome this limitation, several works recently propose the use of a magnetic metamaterial. In the magnetic metamaterials, negative permeability is achieved in a certain frequency range. The permeability distribution of a magnetic metamaterial has been investigated [20]. Magnetic metamaterials have been studied for magneto-inductive waveguides [21]. When the magnetic metamaterial is used for coupling to the near fields, enhanced coupling increases the power transfer efficiency [22]. D. Huang et al. show that inductive coupling can be enhanced by using a 3D metamaterial superlens [23]. Ranaweera et al. show that similar enhancement is possible by using a low loss 2D metamaterial [24]. In this paper, we propose a new approach to provide a stable power source for an untethered tiny microrobot. The approach is realized using field-focused WPT enabled by the cavity mode created on magnetic metamaterials. Instead of a time-varying magnetic field, we use a static field generated from selectively activated electromagnets to generate propulsion. By reconfiguring the cavity and the activated electromagnets, we are able to successfully control the velocity and the direction of the microrobot. Experiments are performed using an up-scaled prototype microrobot having a size of 4 cm × 4 cm and a weight of 5.5 g floating on a water surface. Using the propulsion control, we demonstrate a microrobot navigating to multiple goal locations by video imaging. To the author’s knowledge, this is the first demonstration of the propulsion and direction control of a microrobot using field-focused reconfigurable magnetic metamaterials.

2. Cavity for field focusing In the case of a photonic bandgap (PBG), the physical properties are based on interference governed by Bragg’s law, which usually requires a well-defined periodic structure. In the case of a metamaterial, which is realized using resonant unit cells, the physical characteristics originate from the overall material properties. Therefore, positional disorder does not significantly change its properties [25]. This provides a unique opportunity to realize a non-uniform metamaterial on which we create the cavity mode by inserting a unit cell having different properties from the other cells. 4T-SR

(a)

Ca

Cb

La

CV

VTUNE

Cc (b)

Ra

Lb

1.0

Reflec tio n

0.8

V TUNE 0V 0.1 V 0.4 V 0.6 V 0.8 V 1.5 V 3V 5V

0.6 0.4 0.2 0.0 12

13

14

15

Frequency (MHz)

Fig. 1. (a) Schematic of the tunable spiral resonator, (b) measured reflection as a function of frequency for different VTUNE.

To dynamically reconfigure the location of the cavity region, we use a tunable resonator. Figure 1(a) shows the schematic of the four-turn spiral resonator (4T-SR), which forms the unit cells. The dimension of the 4T-SR is similar to the one used in the previous work [26]. It has an inner radius of 1 cm, an outer radius of 2.8 cm, an inter-strip spacing of 2 mm, and a strip width of 3 mm. The 4T-SR is fabricated using 0.03 mm thick copper, which is supported on an FR-4 dielectric layer having a dimension of 6 cm × 6 cm and a thickness of 1 mm. The capacitor Ca = 200 pF is used to achieve resonance at low MHz frequency and Cb = Cc = 1 nF is used to prevent a short-circuit. We insert a resistor Ra = 1 MΩ to limit the current and two inductors La = Lb = 100 μH to provide isolation from other unit cells. A varactor diode CV (Skyworks SMV1255) provides a variable capacitance. The value of the CV is 81.2 pF and 4.7 pF at the tuning voltage VTUNE = 0 V and 5 V, respectively. The total capacitance Ctotal = Ca + (1/ Cb + 1/ Cc + 1/ CV)-1 can be varied by controlling VTUNE, which is 270 pF and 205 pF at VTUNE = 0 V and 5 V, respectively. With the inductance L = 585 nH of the 4T-SR, Ctotal determines the resonant frequency. Figure 1(b) shows the measured reflection for various VTUNE. The resonant frequency at VTUNE = 0 V is 12.8 MHz. By selecting 2

VTUNE = 0.4 V, 1.5 V, and 5 V, the resonance frequency of the 4T-SR is increased to 13 MHz, 13.5 MHz, and 14 MHz, respectively. To investigate the field focusing realized using the cavity mode created on the non-uniform metamaterial, we consider the configurations shown in Fig. 2 (for more detail, See Fig. 6). Figure 2(a) shows the configuration of the free space. Figures 2(b)-(d) show the case when one, two, and three cavities are created on metasurface. The fields emitted by the transmit (Tx) resonator are collected by the receive (Rx) resonator. The Rx resonator is closely coupled to a load coil for efficient power extraction. The size of the Rx resonator is much smaller than that of the Tx resonator; the area ratio is 1:64. The distance between the Tx resonator and the metasurface (or metamaterial slab) is approximately 15 cm. The distance between the metasurface and the Rx resonator is 3.5 cm. The metasurface is realized by assembling a 9 × 9 array of the unit cells of the 4T-SR. The unit cells in the cavity region resonate at f0 = 14 MHz, while the cells outside the cavity region, which form the bandgap for the cavity, resonate at f1 = 0.91f0. In the proposed metasurface, the dominant response is governed by the magnetic field. In our previous work [24], we show the measured negative permeability of the metamaterial with the related retrieving procedure. When the cavity mode is created, the single-cell modification does not significantly change its overall property [25]. Therefore, the non-uniform metamaterial shows similar permeability characteristics to the uniform metamaterial.

various cavity patterns. Figures 3(b)-(d) show the field distributions when one, two, and three cavities are created on the metasurface. The results show strong field confinement realized on the metasurface. Furthermore, the regions where the field is focused on are controlled by the number of cavities. Comparison of field enhancement achieved by the uniform and non-uniform metamaterials can be found in our previous work [26, 27].

y

(c)

(c)

(d)

The field focusing is experimentally characterized using the magnitude of the transmission coefficient S21 (or transmission) similar to the previous work [22]. The transmission is measured using a network analyzer Keysight 5063A. Figure 4(a) shows the field intensity distribution of the free space. Figures 4(b)-(d) show the results when different numbers of cavities are created on the metasurface. Compared to the case of free space, the result shows that a significant enhancement in the transmission is achieved when cavities are created. The case of a single cavity shows the highest transmission among the other cases. When the number of cavities is increased, the peak transmission is reduced and the field spreads over the entire cavity region. The results show that the cavity mode allows the field to be focused at the subwavelength scale. The physical mechanism of the field focusing on the cavity on the metamaterial can be explained using a hybridization bandgap (HBG). The HBG is formed by the completely destructive Fano interference between incoming and emitted waves from the locally resonant cells [28]. When the resonant frequency of a unit cell is blue-shifted, its frequency falls into the HBG dip. Through the bandgap formed outside the cavity, the waves are not allowed to propagate. Consequently, the fields are confined within that cavity region. Thus, the proposed approach is different from a spoof surface plasmon [29], photonic bandgap [30], and plasmonic metamaterial [31]. Furthermore, this is different

Unit cell

x

(b)

Fig. 3. Field intensity distributions. (a) free space, (b) one cavity, (c) two cavities, (d) three cavities created on the metasurface.

(b)

(a)

(a)

Cavity

(d) Tx resonator

Rx resonator & load coil

Fig. 2. Various configurations investigated in this work. (a) free space, (b) one cavity, (c) two cavities, (d) three cavities created on the metasurface.

Using an electromagnetic (EM) simulator Ansoft HFSS, we obtain field intensity distributions. Similar to the previous work [22], we show the comparison of field intensity between free space and the metamaterials. The case of free space presented in Fig. 3(a) shows a relatively uniform distribution. The intensity in the center region is slightly higher than that of the edge, which is attributed to the incident field from the Tx resonator. Using tunable unit cells, the metasurface is dynamically reconfigurable to create 3

from the previous approach using the macroscopic average material property of the metamaterial [32].

three cavities are used, which correspond to 16.5, 13.8, and 12.4 times improvements compared to the case of the free space, respectively. By closely matching the cavity region with a power-demanding area, field focusing reduces the unnecessary leakage power more than the conventional method. Thus, power can be transferred efficiently when a small receiver is used.

25

(a) y/ (10-3)

20 15 10

0.6

5

0.5

0

5

10

15

-3

20

25

x/ (10 )

Transmission

0

25

(b) y/ (10-3)

20 15

0

0.4 0.3 0.2 0.1

10 5

0.0 12

0

5

10

15

20

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25

x/ (10-3)

14

Frequency (MHz)

15

25

20

Efficiency (%)

y/ (10-3)

20 15 10 5 0

5

10

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10

25

20

x/ (10-3)

0 12

13

S21

0.5 0.4 0.3 0.2 0.1 0.0

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y/ (10-3)

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5

0

25

(d)

16

Free-space Uniform 1-cavity 2-cavity 3-cavity

(b)

25

(c)

Free space Uniform 1-cavity 2-cavity 3-cavity

(a)

15 10

14

Frequency (MHz)

15

16

Fig. 5. (a) Measured transmission and (b) efficiency as a function of frequency.

3. WPT system

5 0

0

5

10

15

20

x/ (10-3)

The average Lorentz force FL generated on a wire segment of length l over a time period T can be expressed as [34] T n (1) FL   i  Bl , T0 where n is the number of turns, B is the magnetic flux density, and i is the current of the wire. When sinusoidal signals are considered for B = |B| cos(ωt) and i = |I| cos(ωt + α), we obtain T n FL   | B | cos(t ) | I | cos(t   ) sin( )ldt T0 , (2)

25

Fig. 4. Measured transmission for the case of (a) free space, (b) one cavity, (c) two cavities, (d) three cavities. The dimension is normalized to wavelength.

Figure 5(a) shows the transmission as a function of frequency. In the case of the free space, peak transmission is 0.12. When the uniform metasurface is used, it increases to 0.26. In the cases when one, two, and three cavities are used, the transmission is increased to 0.48, 0.44, and 0.41, respectively. Figure 5(b) shows the WPT efficiencies obtained using the method [33]. The peak efficiency is 1.4% for the case of the free space. The efficiency is low because most of the magnetic flux is not captured by the small Rx resonator. When the uniform metasurface is used, it increases to 7.2%. When the cavity mode is created, results show significant efficiency improvement; the efficiencies are 23.1%, 19.4%, and 17.3% (at 14 MHz) when one, two, and

nI l | B | cos( ) sin( ) 2 where θ is the angle between the two vectors, B and i. The result (2) shows that FL depends on the phase difference α. At the resonant frequency where the maximum current occurs, α is 90° and the net FL becomes zero. 

4

Diodes Microrobot

Rx resonator & load coil

Water surface

BMagn

FL

i

Electromagnet Metasurface

CL Load coil

CR A -A

’

Rx resonator

BU

Electromagnet

A-A’

Coil Carrie

Wa ter

r

IMagn

BU

z

Moving direction

Cavity

4T-SR

Coil

y Tx resonator

x

DC power source Soure coil

Carrier Water

z = 1.5 cm RS VS

Control panel

RF power source

Electromagnet

Fig. 6. Schematic of the metamaterial-enhanced WPT system. The microrobot and the electromagnet array are also shown. Two power sources, an RF power for the source coil and a DC power for the electromagnet, are used for the system.

To create non-zero FL, Kim et al. use the non-resonant region where the available current is smaller than the maximum value [19]. Another issue is that the overall FL acting on a loop of wire becomes zero. This is because the two same FL acting on the opposite segment of the wire is cancelled out. To handle this issue, the previous work applies shielding to one segment of the wire, which breaks the symmetry and generates a non-zero FL needed for propulsion [35]. Different from the previous works, we propose a new approach using metamaterial-enhanced WPT to deliver power to the microrobot. Figure 6 shows the proposed WPT system. The system includes a source coil, a Tx resonator, a reconfigurable metasurface, an array of electromagnets, an Rx resonator, and a load coil. The Rx resonator and the load coil are part of the up-scaled prototype for the microrobot. To minimize the effect of friction, we place the microrobot on a small carrier (or ship), which is floating on water. The source coil is connected to a radio-frequency (RF) power source for providing the source voltage VS. When VS is applied, the induced current IU on the unit cell (4T-SR) generates the magnetic flux density BU. The electromagnets array is connected to a DC power source to generate BMagn using the current IMagn . The source coil, which is added to couple VS to the Tx resonator, is a single loop having a diameter of 32 cm. The Tx resonator is a five-turn spiral coil, which has an outer diameter of 36 cm and a spacing of 0.5 cm. It is fabricated with a hollow copper pipe having a thickness of 0.6 mm and a diameter of 5 mm. The Rx resonator (nine turns) and the load coil (one turn) for the microrobot have the same size of 4 cm × 4 cm for overlaying together. Fabrication is realized using a polyurethane-enameled copper wire having a diameter of 0.5 mm. Capacitors are used to tune the resonant frequency of the resonators to 14 MHz. Instead of the time-varying magnetic fields used in the previous work [35], we propose the use of static fields BMagn from the electromagnet. The electromagnet is fabricated by

winding coils around a carbon steel core. Thus, the field strength can be controlled by varying the current. The static magnetic field from the electromagnet, however, cannot generate net FL under the sinusoidal current which is induced by the cavity formed on the metasurface. To generate the propulsion using static fields, we convert the alternating current (AC) to direct current (DC) during WPT. For this purpose, we embed four diodes (DIOFIT Tech. 1N4001) in the load coil and realize a full-bridge rectifier. The cavity created on the metasurface realizes the field-focusing on the corresponding unit cell, which generates the current IL in the load coil. Then, the rectifier converts the load current IL = |IL| cos(ωt + α) to direct current IDC = 2|IL| /π (See Appendix A). Figure 7(a) shows the method to control the direction of the microrobot by activating one of four electromagnets. When the electromagnet eME (east) or eMS (south) is activated, the microrobot moves in the +x- or –y-direction, respectively. Figure 7(b) shows the configuration of electromagnets eMi and unit cells uj for location control (i, j ≧1). The eMi provides the magnetic field and uj provides the current for the microrobot. The time setting for eMi and uj is determined by detecting the location of the microrobot using video imaging. When the microrobot is moving, the control signals are generated to sequentially activate electromagnets eM2i and eM2i+1. During this time, unit cells uj and uj+1 are kept activated. For example, when the microrobot moves past u1, the control signals for eM2 and eM3 are sequentially activated while that for eM1 is deactivated. In addition, two unit cells, u1 and u2, are kept activated during the time when either eM2 or eM3 is activated. By the generated FL, the microrobot starts moving from the initial location to the +x-direction. The sequence is repeated until the microrobot reaches the goal location. Using the proposed approach, we note that propulsion and power are delivered to the microrobot simultaneously. The delivered power to the microrobot allows it to perform various complex missions, such as sensing and actuation, using onboard electronic devices. Currently, the size of the 5

cavity region is similar to the size of the microrobot. Further dimension scaling can be easily achieved using the subwavelength property of the metamaterial. (a)

eMN

+y

microrobot. For pathfinding on the map, we use a heuristic graph search algorithm called A*, which is a method used in pathfinding and graph traversal [36]. This method efficiently optimizes the path for the microrobot. By using the heuristics to guide the path search, A* solves problems by searching among all possible paths and generates an optimal solution having the smallest cost (or the shortest path).

Unit cell eME

-x

+x

4. Analysis

eMW eMS (b) u1

Microrobot u2 u3 u4

eM1 eM3 eM5 eM2 eM4

-y

u5

When the cavity is created on the metasurface, the current IU induced on the unit cell generates the magnetic field BU. Using the field strength generated from four concentric loops of the 4T-SR, we approximate the magnitude of BU at a distance z as 4 2 rk2  (3) I , BU ( z)   0 r 3/2 U 2 2 4  k 1 z r

Microrobot Unit cell: (uj) u6 u7 u7

u9



. . . . . . . . . . . . . . . . . . . . eM17 Electromagnet: (eMi)

Image feedback

Algorithm for path finding (Using graph search algorithm)

Compute actuation sequence 1) Elecrtomagnet eMi={eM1, eM2, …,eMi} 2) Unit cell uj={u1,u2, …, uj}

Generate control signals Electromagnet

Microrobot

Metasurface

Power driver



where µ0 is the permeability of the free space, μr is the relative permeability, and rk = 1.15 + 0.5(k - 1) cm is the radius of the wire loop of the 4T-SR (k = [1,4]). IU is obtained from the WPT system model (See Appendix A). Using IU = 0.85 A and the parameters in (3), the calculated BU at z = 1.5 cm is 50.6 μT. BU reaches the load coil through a thin (~5 mm) layer of water and an array of electromagnets. The conductivity of water increases with saline concentration [37]. When the EM waves propagate through the water, electric fields couple to the lossy medium, causing power loss. The loss can be characterized using the imaginary part of the mutual inductance [38]. For the magnetic fields, however, the thin layer of water does not significantly reduce the transmission. In addition, the activation and deactivation of the electromagnets do not significantly change IU. This is because the diameter (0.7 cm) and spacing (3 cm) of the electromagnet are relatively small compared to the size of the unit cell. We confirm the result by measurements performed using an array of electromagnets and a thin layer of water, which shows a negligible change in the transmission. The magnitude of BMagn generated by the electromagnet at a distance z can be expressed as [39]

Fig. 7. (a) Method to control the direction of the microrobot. (b) The configuration of the electromagnets and unit cells. Robot location detection using camera (Using C++, Opencv)

k

Generate output pulses 1) Voltage signal to activate the unit cells 2) Current signal to activate electromagnets

Fig. 8. The proposed method of propulsion control.

Figure 8 shows the proposed method of closed-loop propulsion control for accurate microrobot positioning. Using images from a camera, we are able to identify the microrobot and detect its location. Image processing is implemented using the OpenCV library in the C++ language. When different colors are used for each microrobot, multiple robots can be detected. By reconfiguring the regions activated by the cavity and the electromagnet array, we are able to achieve navigation control of the microrobot. The actuation sequences for the electromagnets and unit cells are determined after calculating the optimal path from the start to the goal locations. Two control signals are generated and sent to the WPT system. One signal activates the unit cells of the metasurface so that the cavity regions follow the selected path from the start to the goal locations. The other one is sent to the electromagnet array to create the magnetic field. These pulse signals are sent through the power driver. By the interaction between the magnetic field and the induced current, propulsion for the microrobot is generated. In this work, we use a grid-based map (9 × 5) to detect the location of the

0 r nMagn (2rMagn )2

IMagn , (4) 3 K   lcarbon   1  2  z      2     r,s ratio  where nMagn = 200 is the number of turns, IMagn is the DC current in the wire of the electromagnet, rMagn = 0.35 cm is the radius of the electromagnet, lcarbon = 1.5 cm is the length of the carbon core, σratio = 2.14 is the ratio of the length to the diameter of the carbon core, K = 1.32[ln(2σratio)-1] is a factor depending on σratio, and μr,s = 100 is the relative permeability of the carbon core [40]. The calculated BMagn is 815 μT using IMagn = 0.85 A at z = 1.5 cm. Because BMagn is more than 16 times larger than the root-mean-square (RMS) value of BU, the overall magnetic flux is dominated by BMagn. When the ship carrying the microrobot moves on the water surface, the resistance force FR appears near the area contacting the water [41]. FR depends on the velocity, the shape of the carrier, and the viscosity of the medium. In the BMagn ( z)  12.5

6

case when the ship has the dimension of lShip (length) >> hShip (wetted height), FR can be estimated using 1 (5) F  C v2S , R

m

ln(

e

2 FL m

2

t m

1

2 FL . t

)

(11)

m

W

D

2

x(t ) 

2m

Figure 9(a) shows the calculated FL using (8) as a function of source power PS and current IMagn. FL depends on IMagn and IL. IL increases with the square root of PS. FL increases linearly with IMagn. Figure 9(b) shows a contour plot of FL. FL as a function of PS for IMagn = 0.85 A is shown (dashed line). FL as a function of IMagn for PS = 2 W is also shown (dotted line). In this case, a peak FL up to 8.4 μN is available with IMagn = 2 A.

where ρ is the density of the medium (water), CD is the drag (resistance) coefficient of the ship, and v is the velocity [42]. SW ≅ 4 (hShip × lShip) + l2Ship is the wetted area of the ship, which can be obtained using the sum of the side area and bottom area contacting the water [43]. The net propulsion force, which is the sum of FL and FR, generates acceleration a(t). The one-dimensional kinetic equation can be written as (6) m a  FL ( t )  FR . Using (5) and (6), we obtain the second-order differential equation for the distance x(t) as

(a)

2

d 2x 1  dx  (7)   CD S W    FL (t )  0 . 2 dt 2  dt  The periodic activation of electromagnets indicates time-dependent dynamics for the microrobot, which is varied by the instantaneous value of FL(t). We note that the dynamics are relatively slow; considering its dimension, the velocity of the microrobot is relatively small. To simplify the analysis and obtain a closed-form expression for x(t), we use the time-average value of fields and current as T 2n n FL  L  (i  Bl)dt  nL B i l  L BMagn IL lEff,side , (8) T 0  where nL is the number of turns, IL is the current in the load coil, and lEff,side is the effective length, which is the half of the side length l of the load coil. The effective length is used because the dimension of the electromagnet is relatively small. The vector sum of force is used to obtain propulsion in the direction of movement (see Appendix B). Different from the previous works [7, 12], which used both force and torque, the proposed method does not use torque for positional control. In this experiment, the microrobot is floating on the water surface; the distance z between the transmitter and receiver is fixed to 1.5 cm. And the receiver in the microrobot is aligned for the maximum field transmission. In a real application, however, the fixed condition can be hardly met for the microrobot. In the cases when z is increased to 3 cm and 4.5 cm, the measured transmission is reduced from 0.44 to 0.37 and 0.25, respectively. In this case, the magnitude of IL and BMagn will be dependent on z, thus affecting the generated FL. To simplify the calculation, we neglect the effect of angular alignment. After substituting (8) into (7) and solving the equation, we obtain the velocity v(t) as m

2 FL e

m

t m

t 2 FL m m

1 ,

PS(W) 0

e [e

2 FL m

2 FL m

t m

t m

,

4

6

8

FL(N)

1.2 0.85

0.8

IMagn(A)

1.6

0.4 0.0

2 force FL depending on PS and IMagn. (b) Contour Fig. 9. (a) Lorentz plot of FL. The Lorentz force at PS = 2 W (dotted-line) and IMagn = 0.85 A (dashed line) are also shown. TABLE I. Experimental parameters for the microrobot

Parameter Mass m (g) Drag coefficient CD Wetted area SW (cm2) Liquid mass density ρ (kg/m3) Carrier (or ship) dimensions (cm3)

(9)

1 e where λm = ρCDSW. Using (9), we obtain a(t) and x(t) as

4F a (t )  L m

2

10 8 6 4 2 0 10 2.0

10 8 6 4 2 0

v (t ) 

2 FL m

(b)

(10)

Value 5.5 3.2 21 1000 4 × 4 ×1

Using (9)-(10) and the experimental parameters of Table I, we obtain v(t) and a(t) as a function of time for different PS. When PS is varied from 1 W to 4 W with a 1 W step, the corresponding IL is 0.24 A, 0.35 A, 0.42 A, and 0.49 A,

 1]

2

7

Velocity (mm/s)

1.4

value of v(t) is 0.71 mm/s, 0.86 mm/s, 1.0 mm/s, and 1.12 mm/s, respectively. The corresponding peak value of a(t) is 0.31 mm/s2, 0.45 mm/s2, 0.62 mm/s2, and 0.76 mm/s2, respectively. In the results shown in Fig. 10 and Fig. 11, the current drawn by electronic components (such as sensors and actuators) attached to the microrobot is not considered. In the case when the additional components are added to the microrobot, IDC is reduced by the current IElec = VDC / RElec. Here, VDC is the DC output voltage from the rectifier and RElec is the resistance representing the loading of the electronic components. To investigate the loading effect on the propulsion, we obtain v(t) when RElec is increased from 5 Ω to 110 Ω as shown in Fig. 12. For a given IDC, the result shows that v(t) is reduced when IElec increases (or RElec decreases). To obtain a certain level of propulsion, IElec cannot exceed IDC.

(a)

1.2 1.0 0.8 0.6

PS = 1 W

0.4

PS = 2 W PS = 3 W

0.2 0.0

PS = 4 W 0

1

2

3

4

5

Time (s)

(b)

PS = 1 W PS = 3 W

0.6

0.2

0

1

2

3

4

5

Fig. 10. Calculated (a) velocity and (b) acceleration as a function of time for different PS. IMagn = 0.85 A.

Velocity (mm/s)

0.00

0.4 0.2

0

20

40

60

80

100

0.0 120

Fig. 12. Calculated velocity of the microrobot as a function of RElec. PS = 2 W, IMagn = 0.85 A, IDC = 0.24 A, and VDC = 1.2 V.

0.8 0.6

IMagn = 0.4 A

0.4

IMagn = 0.6 A

0.2

IMagn = 0.8 A

5. Results We demonstrate a microrobot moving to multiple goal locations with direction control. Figure 13 shows the images of the microrobot towards goal locations (See supplementary material for the recorded video result). We set two start locations (S1 and S2) and two different goal locations (G1 and G2). Figures 13(a)-(c) show the images captured from the camera when we select S1 and G1. After the pathfinding algorithm calculates the optimal path, the power driver generates the pulse signals for the electromagnet and the metasurface. In this case, the electromagnet in the x-direction (indicated with a red dotted line) is controlled for propulsion. After initial attitude change shown in Fig. 13(b), which is caused by the asymmetric forces from the electromagnets (See Appendix B), the result shows that the microrobot successfully arrives at G1. In addition, we demonstrate the capability of the microrobot to change direction. Figures 13(d)-(e) show the captured images when we select a new path from S2 to G2. When the microrobot moves along the new path, it changes the path from the -y-direction to the -x-direction towards G2.

IMagn = 1 A 0

1

2

3

4

5

Time (s) 1.0

Acceleration (mm/s2)

Velocity

0.6

RElec ()

1.0

0.0

IElec

0.10

(a)

1.2

0.8

0.15

0.05

Time (s)

1.4

1.0

0.20

PS = 4 W

0.4

0.0

1.2

0.25

PS = 2 W

0.8

IElec (A)

Acceleration (mm/s2)

1.0

Velocity (mm/s)

respectively. With a constant PS, v(t) increases with time and saturated as shown in Fig. 10. The maximum value of v(t) is 0.87 mm/s, 1.04 mm/s, 1.15 mm/s, and 1.24 mm/s when PS is increased from 1 W to 4 W, respectively. The peak value of a(t) is 0.47 mm/s2, 0.65 mm/s2, 0.8 mm/s2, and 0.93 mm/s2.

(b)

IMagn = 0.4 A

0.8

IMagn = 0.6 A IMagn = 0.8 A

0.6

IMagn = 1 A

0.4 0.2 0.0

0

1

2

3

4

5

Time (s)

Fig. 11. Calculated (a) velocity and (b) acceleration as a function of time for different IMagn. PS = 2 W.

Figure 11 shows the calculated v(t) and a(t) for different IMagn. For IMagn = 0.4 A, 0.6 A, 0.8 A, and 1 A, the maximum 8

(a)

y

(d)

S1

x

G1

(b)

(c)

(e)

(f)

6 cm

G2

S2

Fig. 13. Images of the microrobot. (a) Initial scene with start (S1) and goal (G1) locations, (b) robot following a selected path, (c) robot reaching the goal location, (d) robot moving backwards to a new start (S2) location, (e) robot following a new path, (f) robot changing direction to reach the second goal (G2) location. Grid maps for pathfinding are shown in the insets. Start and goal locations are indicated with blue and green squares, respectively.

Figure 14(a) shows the measured and simulated velocities using IMagn = 0.85 A. The simulation is performed using Matlab assuming a homogeneous field strength along the path. We measure the velocity by detecting the position of the microrobot from the images captured at 25 frames per second. The result shows that the microrobot moves at a constant velocity after t = 5 sec when the applied force is equal to the total resistance force. The simulated saturated velocity is 0.87 mm/s and 1.24 mm/s for PS = 1 W and 4 W, respectively. The measured velocity is 0.85 mm/s and 1.2 mm/s, respectively. Figure 14(b) shows the measured and simulated distance. The simulated distances at t = 5 sec are 3.3 mm and 5.0 mm for PS = 1 W and 4 W, respectively. The measured distances are 3.2 mm and 4.8 mm, respectively. Figure 15(a) shows the measured and simulated velocities using PS = 2 W. The simulated saturated velocity is 0.78 mm/s and 1.12 mm/s for IMagn = 0.5 A and 1 A, respectively. The measured velocity is 0.73 mm/s and 1.07 mm/s, respectively. The difference between the measured and simulated velocities is caused by the distance between the two electromagnets being relatively large compared to the dimensions of the microrobot. When the microrobot travels for a relatively long time, the kinetic dynamics settle and the saturated velocity agrees with the simulated result. Figure 15(b) shows the measured and simulated distances. The simulated distances at t = 5 sec are 2.8 mm and 4.5 mm for IMagn = 0.5 A and 1 A, respectively. The measured distances are 2.5 mm and 4 mm. To investigate the power transmission efficiency during the experiment, we measure the rectified current IDC of the microrobot. Using PS = 2 W, the measured IDC is 244 mA at VDC = 1.2 V. Using measured rectifier efficiency of 75.6%, we obtain an output power of 0.387 W, which corresponds to an efficiency of 19.3%. The result agrees with the value (19.4%

for the case of two cavities) obtained using transmission efficiency (Fig. 5). 1.4

(a)

Velocity (mm/s)

1.2 1.0 0.8 0.6

Sim. PS = 1 W

0.4

Sim. PS = 4 W

0.2

Meas. PS = 1 W

0.0

Meas. PS = 4 W 0

1

2

3

4

5

3 Time (s)

4

5

Time (s)

Distance (mm)

6

(b)

5

Sim. PS = 1 W

4

Meas. PS = 1 W

Sim. PS = 4 W Meas. PS = 4 W

3 2 1 0

0

1

2

Fig. 14. Measured and simulated results of (a) velocity and (b) distance. IMagn = 0.85 A.

Using images from the camera, the location of the microrobot is finely controlled. Using PS = 4 W and IMagn = 0.85 A, we align the initial location of the microrobot at the 9

center of the electromagnet. The relative error between the target and the actual locations is obtained by averaging 30 measurements. The calculated distance is 5 mm at 5 sec. The difference between the calculated and measured average distance is 0.26 mm, which corresponds to 5.2% error. The result shows that the proposed closed-loop control achieves a relatively accurate positioning of the microrobot. 1.4

(a)

1.2

Velocity (mm/s)

The proposed WPT system provides a good opportunity to charge the onboard battery. The peak efficiency of 1.4% for the case of the free space is enhanced to 23.1% when a cavity mode is used, which corresponds to a 16.5 times improvement. By taking advantage of the prolonged operating time, which is enabled by the efficient WPT proposed in this work, the microrobot can perform various complex missions using sensing and actuation. The main idea of this work is demonstrating simultaneous WPT and propulsion generation using field-focused reconfigurable metamaterials. To idea is realized using a prototype system demanding several coils and an array of electromagnets. In addition, our system is based on simple 2D positional control using only force with limited DOF. Increased DOF and 3D steering using complex field control will be required for future biomedical and biological applications. In addition to microrobot propulsion, the proposed magnetic metamaterial can find applications in magnetic resonance imaging, subwavelength waveguide components, and magneto-inductive wave devices.

1.0 0.8 0.6 Sim. IMagn = 0.5 A

0.4

Sim. IMagn = 1 A Meas. IMagn = 0.5 A

0.2 0.0

Meas. IMagn = 1 A 0

1

2

3

4

5

Time (s) 6

(b)

Distance (mm)

5

Acknowledgement

Sim. IMagn = 0.5 A Sim. IMagn = 1 A

4

Meas. IMagn = 0.5 A

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF-2018R1A2A2A05018621).

Meas. IMagn = 1 A

3 2 1 0

0

1

2

3 Time (s)

4

5

Appendix A: Calculation of current using WPT system model

Fig. 15. Measured and simulated results of (a) velocity and (b) distance. PS = 2 W.

A simple circuit model of a spiral resonator has been previously reported [44]. Using this method, we represent the unit cell of a metasurface using lumped elements (inductance L, capacitance C, and resistance R). Figure A1 shows an equivalent model of the proposed WPT system used for calculating IL and IU. To simplify the analysis, we divide the metasurface into two regions, cavity and non-cavity regions. The unit cell in the cavity region is coupled to the Tx and Rx resonators, of which the coupling coefficients are represented using k23 and k34, respectively. The unit cells in the non-cavity region are characterized using coupling coefficients k’um,un and k’2,um (2 ≤ m, n ≤ 81). k’2,um is a weak coupling coefficient between the Tx resonator (resonating at f0) and the unit cell (resonating at f1 = 0.91f0). k’um,un is the coupling coefficient between unit cells um and un in the non-cavity region. Because of the different resonant frequency, k’2,um is relatively small. In addition, the contribution of k’um,un on IL can be neglected. This is because strong field confinement isolates the cavity from other unit cells in the non-cavity region. This observation allows us to simplify the analysis; we consider only the unit cells in the cavity. Using Kirchhoff’s law, we solve for the currents IL and IU as

6. Conclusion In this work, we investigate a new method of generating both power and propulsion for a small untethered microrobot. The proposed method is achieved using a field-focused WPT enabled by the cavity mode created on a dynamically reconfigurable metasurface. The cavity created on the metasurface allows field focusing on the subwavelength scale, which can provide an opportunity to further reduce the dimensions of the microrobot. The electromagnet arrays used with the metasurface successfully generate propulsion for the microrobot. A simple method is proposed to break the symmetry needed for generating the net propulsion under a static field. Experiments performed using an up-scaled version of the microrobot demonstrate successful navigation control to multiple goal locations. For the experiment, the electromagnet is supplied with IMagn = 0.85 A at 2.9 V using a DC power source. For WPT, an input power PS = 1 W is supplied using an RF power source. Under the condition, we obtain a maximum velocity of 0.85 mm/s. In addition, the closed-loop navigation control achieves a relatively accurate (5.2% error) positioning of the microrobot. 10

IL 

 4 M 12 M 23 M 34 M 45 V ,  4 ( M 232 M 452 Z1  M 122 M 452 Z 3  M 122 M 342 Z 5 )   2 ( M 232 Z1 Z 4 Z 5  M 122 Z 3 Z 4 Z 5  M 342 Z1 Z 2 Z 5 )  Z1 Z 2 Z 3 Z 4 Z 5 S IU 

 2  2 M 122 M 34 Z 5  M 34 Z1Z 2 Z 5  , iL   M 12 M 23VS  M 45  

1  ( M Z1  M 122 Z 3 )  Z1Z 2 Z 3 2

2 23

where Zi characterizes the impedance of the coils and resonators using corresponding RLC values as Z1  RS  j L1 1/ CS  , Z2  RT  j L2 1/ CT  , Z3  Ru0  j L3 1/ Cu0 

Z4  RR  j L4 1/ CR  , Z5  RL  j L5 1/ CL  Mij = kij (Li Lj)1/2 is the mutual inductance between two coils i and j (i, j = 1 to 5), Li and Lj are self-inductances, kij is the coupling coefficient, VS = (PS / RS)1/2 is a root-mean-square

RS

k23

L3

Unit cell (cavity region) Ru0

(f0)

VS L1

k12

Cum L2

k’2,um

(f1) Lum

Source TX resonator coil k’2,un

Cun

CL

CR

RT

(f0)

,

k34

RR

RL

(f0)

(f0)

IL

RLoad

IU

CT

(A-2)

(RMS) value of the voltage source, PS is a source power, and RS is the resistance of the source coil. Table II shows the electrical parameters of the WPT system.

Cu0 (f0) CS

(A-1)

k45

Rum

L4

L5 VDC

k’um,un

RX resonator Load coil

(f1) Run

IDC

Rectifier

Unit cells (non-cavity region)

Lun

Fig. A1. Equivalent model of the WPT system. T

FL1 

TABLE II. Electrical parameters of the WPT system

Parameter M12 (µH) M23 (µH) M 34 (µH) M 45 (µH) RS (Ω) L1 (μH) CS (pF) RT (Ω) L2 (μH) CT (pF)

Value 0.015 0.107 0.082 0.065 0.11 1.61 80.3 0.17 20.6 6.3

Parameter Ru0 (Ω) L3 (μH) Cu0 (pF) RR (Ω) L4 (μH) CR (pF) RL (Ω) L5 (μH) CL (pF) Rload (Ω)

Value 0.27 0.59 208.7 0.22 6.12 21.1 3.25 0.68 190 5

nL 2 (i  Bl1)dt  nL B i l1  BMagn IL l1 ,  T0 

(A-3)

T

FL2 

nL 2 (i  Bl2 )dt  nL B i l2  BMagn IL l2 ,  T 0 

(A-4)

where nL=1 is the number of turns. The angle between the magnetic field and the current is 90°. FL1 can be decomposed to FL1x and FL1y in the x- and y-directions as

2 BMagn IL l1cos() ,  2 FL1y  BMagn IL l1sin() , 

FL1x 

(A-5) (A-6)

where φ is the angle between the side of the wire and x-axis. In a similar manner, FL2 can be decomposed into FL2x and FL2y as

2 BMagn I L l2 cos() ,  2 FL2y  BMagn IL l2sin() . 

Appendix B: Calculation of net force using effective length

FL2x 

Figure A2 shows the geometry used to calculate the Lorentz force acting on the load coil. It shows two components of the force, FL1 and FL2. Using the time-average value of field and current in (1), the magnitude of FL1 and FL2 acting on a wire length l1 and l2 can be expressed as

(A-7) (A-8)

To simplify the calculation, we assume a region of the relatively uniform fields having a radius rB = l1 sin(φ) = l2 sin(φ), which is approximately 1 cm for the electromagnet used in this work. Outside this region, the magnetic field decreases rapidly 11

12 and the contribution to FL is small. The result is confirmed using the result obtained by the field calculation software, Vizimag [45]. Because of the opposite direction, the x-component of the force cancels out. Then, net FL can be rearranged as 2 2 FL  FL1y  FL2y  BMagn IL l1sin()  BMagn IL l2sin()   , (A-9) 2 2 2  BMagn IL rB  BMagn IL rB  BMagn IL lEff,side





References [1] A. Kiourti, K. S. Nikita, A Review of in-body biotelemetry devices: implantables, ingestibles, and injectables, IEEE Trans. Biomed. Eng. 64 (2017) 1422. https://doi: 10.1109/TBME.2017.2668612 [2] R. Puers, R. Carta, J. Thone, Wireless power and data transmission strategies for next-generation capsule endoscopes, J. Micromech. Microeng. 21 (2011) 054008. http://dx.doi.org/10.1088/0960-1317/21/5/054008 [3] R. Carta, G. Tortora, J. Thoné, B. Lenaerts, P. Valdastri, A. Menciassi, P. Dario, R. Puers, Wireless powering for a self-propelled and steerable endoscopic capsule for stomach inspection, Biosensors and Bioelectron. 25 (2009) 845. http://dx.doi.org/10.1016/j.bios.2009.08.049 [4] H. Li, G. Go, S. Y. Ko, J. O. Park, S. Park, Magnetic actuated pH-responsive hydrogel-based soft micro-robot for targeted drug delivery, Smart Mater. Struct. 25 (2016) 027001. https://doi.org/10.1088/0964-1726/25/2/027001 [5] M. Sitti, H. Ceylan, W. Hu, J. Giltinan, M. Turan, S. Yim, E. Diller, Biomedical applications of untethered mobile milli/microrobots, Proc. IEEE 103 (2015) 205. https://doi.org/10.1109/JPROC.2014.2385105 [6] B. J. Nelson, I. K. Kaliakatsos, J. J. Abbot, Microrobots for minimally invasive medicine, Annu. Rev. Biomed. Eng. 12 (2010) 55. https://doi.org/10.1146/annurev-bioeng-010510-103409 [7] M. P. Kummer, J. J. Abbott, B. E. Kratochvil, R. Borer, A. Sengul, B. J. Nelson, OctoMag: An electromagnetic system for 5-DOF wireless micromanipulation, IEEE Trans. Robot. 26 (2010) 1006. https://doi.org/10.1109/TRO.2010.2073030 [8] A. W. Mahoney, N. D. Nelson, K. E. Peyer, B. J. Nelson, J. J. Abbott, Behavior of rotating magnetic microrobots above the step-out frequency with application to control of multi-microrobot systems, Appl. Phys. Lett. 104 (2014) 144101. https://doi.org/ 10.1063/1.4870768 [9] X. Yan, Q. Zhou, M. Vincent, Y. Deng, J. Yu, J. Xu, T. Xu, T. Tang, L. Bian, Y. J. Wang, L. Zhang, K. Kostarelos, Multifunctional biohybrid magnetite microrobots for imaging-guided therapy, Sci. Robot. 2 (2017) eaaq1155. https://doi.org/10.1126/scirobotics.aaq1155 [10] J. Li, I. Rozen, J. Wang, Rocket science at the nanoscale, ACS Nano 10 (2016) 5619. https://doi.org/ 10.1021/acsnano.6b02518 [11] A. T. Baisch, P. S. Sreetharan, R. J. Wood, Biologically-inspired locomotion of a 2g hexapod robot, IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE, Taipei, Taiwan), 2010, pp. 5360-5365. [12] J. Sikorski, I. Dawson, A. Denasi, E. E. G. Hekman, S. Misra, Introducing bigmag-a novel system for 3d magnetic actuation of flexible surgical manipulators, IEEE Int. Conf. Robotics Automation (ICRA) (IEEE, Singapore), 2017, pp. 3594–3599. [13] S. Floyd, E. Diller, C. Pawashe, M. Sitti, Control methodologies for a heterogeneous group of untethered magnetic micro-robots, Int. J. Robotics Res. 30 (2011) 1553. https://doi.org/10.1177/0278364911399525 [14] C. Pawashe, S. Floyd, M. Sitti, Multiple magnetic microrobot control using electrostatic anchoring, Appl. Phys. Lett. 94 (2009) 164108. https://doi.org/10.1063/1.3123231 [15] C. Chen, L. Chen, P. Wang, L. F. Wu, T. Song, Steering of magnetotactic bacterial microrobots by focusing magnetic field for targeted pathogen killing, J. Magn. Magn. Mater. 479 (2019) 74. https://doi.org/10.1016/j.jmmm.2019.02.004 [16] L. Chen, C. Chen, P. Wang, C. Chen, L. F. Wu, T. Song, A compound magnetic field generating system for targeted killing of Staphylococcus aureus by magnetotactic bacteria in a microfluidic chip, J. Magn. Magn. Mater. 427 (2017) 90. https://doi.org/10.1016/j.jmmm.2016.10.109



where lEff,side = 2rB is the effective length.

FL1

FL1

i B field

FL1y

FL2y

l1

l2

FL1x

lEff,side i = 2rB

FL2x

φ = 45o Electromagnet

i

rB

Approximte B field region y

FL2

Load coil

x Fig. A2. Geometry used to calculate the overall Lorentz force.

In the current experiment, all the electromagnets receive the same current IMagn. And the attitude of the microrobot is determined by FL1 and FL2. When the attitude of the microrobot deviates from the center, asymmetric Lorentz forces are generated. Figure A3 shows the case of |FL2|> |FL1| and the microrobot moves to the right direction, eventually following the expected moving path. When we modify the experiment setup so that IMagn of each electromagnet can be separately adjusted, we can control the attitude of microrobot and it can move along the oblique line path. FL1

FL1y

FL1x

l1

i FL1

FL2y

FL2 FL2x

l2

Moving direction FL2

i

(FL2 > FL1)

Load coil

Expected moving path

Fig. A3. Attitude control of the microrobot.

12

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Highlight • Investigation of a new type of non-uniform metamaterial working at low MHz frequency for magnetic field focusing • The first demonstration of the propulsion and direction control of a microrobot using field-focused reconfigurable magnetic metamaterials • Active and reconfigurable magnetic metamaterial applied for wireless power transfer • Propose a new method of generating both wireless power and propulsion for a tiny untethered microrobot. • A defect cavity is introduced for localization of the magnetic field into the deep subwavelength scale • Propose a simple method to break the symmetry needed for generating a net force using a static field • Proposed method of closed-loop propulsion control for accurate robot positioning

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