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1 This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier s archiving and manuscript policies are encouraged to visit:

2 Sensors and Actuators A 163 (2010) Contents lists available at ScienceDirect Sensors and Actuators A: Physical journal homepage: EMA system with gradient and uniform saddle coils for 3D locomotion of microrobot Hyunchul Choi a, Kyoungrae Cha a, Jongho Choi a, Semi Jeong a, Seungmun Jeon b, Gunhee Jang b, Jong-oh Park a,, Sukho Park a, a Dept. of Mechanical Engineering, Chonnam National University, Gwangju , Republic of Korea b Dept. of Mechanical Engineering, Hanyang University, Seoul , Republic of Korea article info abstract Article history: Received 2 March 2010 Received in revised form 14 July 2010 Accepted 9 August 2010 Available online 14 August 2010 Keywords: Microrobot Electromagnetic Uniform saddle coil Gradient saddle coil 3D locomotion Intravascular In this paper, we study the 3 dimensional (D) locomotion of a microrobot using an electromagnetic actuation (EMA) system with gradient and uniform saddle coils. Generally, previous EMA systems have used Helmholtz and Maxwell coil pairs. For 3D locomotion of a microrobot, two pairs of coils were perpendicularly positioned and one pair of the two pairs had a rotational mechanism. With such structure, the EMA system had a large volume and consumed much driving energy. To overcome these undesirable properties, we propose an EMA system driven by saddle coils, which has the same functions as the previous EMA system but a smaller volume and less consumption of driving energy. Firstly, the locomotion mechanisms of the proposed EMA system in 2D and 3D spaces are explained. Secondly, for the accurate locomotion of the microrobot by the EMA system in a 3D space, gravity compensation is executed. Thirdly, by 3D locomotion tests of the microrobot in a test bed cube and a blood vessel phantom, the performance of the proposed EMA system is evaluated. Lastly, the proposed EMA system and the previous EMA system are compared with respect to structure and energy consumption. The results showed that the proposed EMA system has smaller volume and higher energy saving capabilities than the previous EMA system. Crown Copyright 2010 Published by Elsevier B.V. All rights reserved. 1. Introduction Minimally invasive surgery has become the focus of much interest because of its short operational time, recovery period and minimal scar. Hence, for the treatment of coronary arterial diseases, microrobot technologies that allow microrobots to move in the blood vessel have been developed [1]. Generally, due to the size limitation of the microrobot, the actuation part including the power source is difficult to integrate into the microrobot. Therefore, several actuation mechanisms have been developed and used to propel the microrobot from a remote site [2]. We focused on the development of an electromagnetic actuation (EMA) system that uses an electromagnetic field to produce external propulsion forces. Recently, EMA methods of a microrobot in the 2D plane have been studied extensively [3 6]. However, because a blood vessel in human body is a 3D structure, the microrobot should have 3D locomotion capability. Therefore, a variety of 3D locomotion methods for the intravascular microrobot have been proposed [7 9]. Corresponding authors at: Chonnam National University, Mechanical System Engineering, 300, Yongbong-dong, Buk-gu, Gwangju , Republic of Korea. Tel.: ; fax: addresses: jop@jnu.ac.kr (J.-o. Park), spark@jnu.ac.kr (S. Park). Martel et al. used the magnetic field generated by medical magnetic resonance imaging (MRI) gradient coils to drive a microrobot [8]. This MRI based actuation method has the advantages of position recognition and paramagnetic microrobot manipulation at the same time. However, because the MRI based actuation system of a microrobot uses one fixed Helmholtz coil, the degrees of freedom of actuation for the alignment of the microrobot are limited. Therefore, this system cannot be applied to the 3D actuation of a microrobot. Previously, we proposed an EMA system using stationary Helmholtz Maxwell coil pairs and rotational Helmholtz Maxwell coil pairs for 3D locomotion of a microrobot [9]. This EMA system uses one pair of stationary Helmholtz Maxwell coils in the x-axis and one pair of rotational Helmholtz Maxwell coils around the x- axis to achieve 3D locomotion of a microrobot. This EMA system can realize the 3D locomotion of a microrobot, but it has a large volume and requires high power consumption. In addition, we proposed a new EMA system for 2D locomotion, which is composed of one conventional pair of Maxwell and Helmholtz coils and one pair of newly developed gradient and uniform saddle coils [10]. Compared with the previous EMA system using Maxwell and Helmholtz coils, this EMA system has a smaller volume and requires less driving power consumption. However, the one pair of Maxwell and Helmholtz coils and one pair of gra /$ see front matter. Crown Copyright 2010 Published by Elsevier B.V. All rights reserved. doi: /j.sna

3 H. Choi et al. / Sensors and Actuators A 163 (2010) g m = 16 3 ( 3 ) 5/2 i m 7 rm 2 (6) where g m is the field gradient along its x-axis and i m and r m are the current and radius of the Maxwell coil, respectively. Since a Maxwell coil generates a uniform gradient magnetic near the center of the coil along the x-axis, the Maxwell coil can generate the magnetic force to propel the microrobot located near the center of the coil along the x-axis. The magnetic fields generated by Helmholtz and Maxwell coils were shown in our previous work [6,7] Theory of uniform and gradient saddle coils Fig. 1. Schematic diagram of the proposed EMA system. dient and uniform saddle coils are perpendicularly fixed, and thus can realize only 2D locomotion of the microrobot. In this paper, we expanded this 2D locomotion EMA system using saddle coils to 3D actuation by adding a rotational (-) axis pair of saddle coils, as shown in Fig. 1. If the saddle coil pairs can rotate around the x-axis, the actuating plane of the microrobot can be rotated, and the microrobot can move in 3D space. For accurate actuation of the microrobot in 3D space, the gravitational force exerted on the microrobot is also analyzed and compensated. The 3D locomotion performance of the microrobot using the proposed EMA system is evaluated, and the tracking errors are analyzed. Lastly, the proposed EMA system and the previous 3D EMA system [9] are compared with respect to system structure and energy consumption to evaluate the effectiveness and advantages of our newly proposed EMA system. Previously, we proposed a uniform saddle coil and a gradient saddle coil, which have the same functions as the Helmholtz and Maxwell coils [6]. Firstly, the uniform saddle coil is used to generate a uniform magnetic flux in the Region of Interest (ROI) shown in Fig. 2. The magnetic flux ( H us ) produced by the uniform saddle coil is described as follows: H us = [ 0 d us 0 ] T (7) d us = i us (8) r us where d us is the magnetic flux intensity of the uniform saddle coil along the y-axis, i us is the current of the uniform saddle coil, and r us is the radius of the uniform saddle coil. The gradient saddle coil is used to generate a uniform magnetic flux in the ROI, as shown in Fig. 3, and the magnetic flux ( H gs ) produced by the gradient saddle coil is as follows: H gs = [ g gs x g gs y g gs z ] T (9) 2. Theoretical background of proposed EMA system 2.1. Theory of Helmholtz and Maxwell coils g gs = cos 1 (1 ) 3 16 ( 3 ) 5/2 i gs rgs 2 (10) Magnetic force and torque applied to a microrobot composed of a permanent magnetic material in a magnetic field can be expressed by the following equations [11]. T = 0 V M H (1) F = 0 V( M ) H (2) where 0, V, and M are the magnetic permeability of free space, and the volume and magnetization vector of the microrobot, respectively. The magnetic force is proportional to the magnetic field gradient, and the magnetic torque is proportional to the magnetic field intensity. Generally, Helmholtz coils are used to generate a uniform magnetic flux and to align the microrobot. The magnetic flux ( H h ) produced by a Helmholtz coil is described as follows: H h = [ d h 0 0] T (3) ( 4 ) 3/2 i d h = h (4) 5 r h where i h and r h are the current and radius of the Helmholtz coil, respectively. Since the Helmholtz coil generates a uniform magnetic field intensity near the center of the coil along the x-axis, it can generate a uniform magnetic torque to align the microrobot located near the center of the coil along the x-axis. Maxwell coils are used to generate a uniform gradient magnetic flux and propel the microrobot. The magnetic flux ( H m ) produced by a Maxwell coil is as follows: H m = [ g m x 0.5g m y 0.5g m z ] T (5) Fig. 2. Schematic diagram and field map of uniform saddle coil. (a) Schematic diagram and (b) field map.

4 412 H. Choi et al. / Sensors and Actuators A 163 (2010) Once the torque aligns the microrobot along the direction, the microrobot can be propelled by the magnetic force which is generated along the aligned direction. The magnetic force should satisfy the following condition to propel the microrobot at angle of from the x-axis. F y = sin F x cos = MV sin ( g gs 0.5g m ) (13) MV cos (g gs + g m ) Eq. (13) provides the following relationship between the magnetic gradients of the Maxwell coils and the gradient saddle coils in the proposed EMA system. g m = g gs (14) The following relationship between the current applied to the Maxwell coil and that applied to the gradient saddle coil can be derived from Eqs. (7) and (9) to satisfy Eq. (14). ( ) 2 rm i m = i g (15) r g Then, from Eq. (2), a propulsion force for the microrobot is generated at an angle of from the x-axis. Therefore, the microrobot can be aligned and propelled by using the proposed EMA system composed of the gradient saddle coil, uniform saddle coil, Maxwell coil, and Helmholtz coil D locomotion using proposed EMA system Fig. 3. Schematic diagram and field map of gradient saddle coil. (a) Schematic diagram and (b) field map. where g gs is the gradient of the magnetic flux intensity produced by the gradient saddle coil along the x-axis, i gs is the current of the gradient saddle coil, r gs is the radius of the gradient saddle coil. The gradient saddle coil generates a uniform gradient magnetic around the central region D locomotion using proposed EMA system 2D locomotion of the microrobot using one conventional pair of Maxwell and Helmholtz coils and one pair of gradient and uniform saddle coils was proposed [10]. The generated magnetic flux ( H) in this EMA system can be expressed as follows: [ (g gs + g m )x + d h ] H = ( g gs 0.5g m )y + d us (1.4398g gs 0.5g m )z (11) The previous 2D EMA system [6,10] limits the microrobot to 2D locomotion. As shown in Fig. 1, the proposed EMA system has a pair of stationary Helmholtz Maxwell coils and a pair of rotational uniform and gradient saddle coils. By using the pair of rotational uniform and gradient saddle coils, the actuation mechanism of the 2D EMA system can be extended to 3D actuation. In Fig. 4, the actuation planes of the EMA system for each rotational angle are described. The rotational angles of = 0 and = 90 mean the x y actuation plane and the x z actuation plane, respectively. Therefore, the desired actuation plane is determined by the pair of rotational saddle coils, and the microrobot is directly actuated by the 2D actuation mechanism, which was explained in Section 2.3. Finally, the 3D actuation of the microrobot can be achieved by our proposed EMA system. However, for the actuation of a microrobot in 3D space, the gravitational force exerted on the microrobot should be compensated. In the next section, we analyze and compensate the gravity in the locomotion of a microrobot in 3D space. If the microrobot is located in the ROI, it can be aligned along the direction of the magnetic field. From Eq. (1), a uniform magnetic flux is generated along the desired direction using the Helmholtz and uniform saddle coils, and the difference between the magnetization direction of the microrobot and the direction of the magnetic field generates the rotational torque. The microrobot initially positioned along a random direction in 2D space is to be aligned at an angle of. Using Eqs. (3) and (7), the condition of the uniform magnetic field along the direction produces the following relationships of the currents between the uniform saddle coil and Helmholtz coil. i us = tan r us r h i h (12) Fig. 4. Rotation plane of the 3D space.

5 H. Choi et al. / Sensors and Actuators A 163 (2010) Gravity compensation As the microrobot, a cylindrical neodymium magnet with diameter, length, density, and magnetization of 1 mm, 5 mm, 7.4 g/cm 3, and 955,000 A/m along the axial direction, respectively, was used. Because the density of the microrobot was 7.4 times higher than that of water, the gravitational effect of the microrobot had to be considered. In the locomotion of the microrobot in the x y plane ( = 0 ), the gravitational force exerted on the microrobot was not considered, because the gravitational force was offset by the reaction force from the surface of the test bed. However, when the rotational angle () was 90, the gravitational force had to be totally compensated as follows: F z mg = tan (16) F x where F x, F z, and mg are the magnetic forces along the x-axis and z-axis and gravitational force, respectively. Next, when an arbitrary rotational angle () from 0 to 90 was given, the gravitation force could not be easily compensated. As shown in Fig. 5, based on the rotational angle, the actuation plane is defined as the x r plane and the gravitational force can be divided into a normal component and tangential component. Similarly, the normal component (mg cos ) is cancelled by the reaction force, but the tangential component (mg sin ) cannot be canceled. Therefore, the tangential component of the gravitational force should be compensated. To compensate the tangential component of the Fig. 6. Fabricated EMA coil system. gravitational force, Eq. (16) can be modified as follows: F r mg sin = tan, F x /= 0 (17) F x where F r is the propulsion force generated by the gradient saddle coil. Eq. (17) can be rewritten as: F r = mg sin + F x tan, F x /= 0 (18) If the magnetic field gradients, the volume and the magnetization values of the microrobot are introduced, Eq. (17) can be described as: MV sin ( g gs 0.5g m ) mg sin = tan (19) MV cos (g gs + g m ) From Eq. (19), the magnetic field gradient can be derived as follows: mg sin g gs = MV sin g m (20) where we can obtain the relations of g gs = g m for = 0 and g gs = (mg/3.4398mv sin ) g m for = 90. Finally, the gravitational force of the microrobot can be compensated by regulating the magnetic flux g gs of the rotational coil pairs. 3. Experiments 3.1. Experimental setup Based on the theoretical background in Section 2 and a schematic diagram in Fig. 1, we fabricated the EMA system as shown in Fig. 6 and the detailed specifications of the fabricated EMA system are described in Table 1. The body of the EMA system was fabricated with aluminum alloy for high thermal conductivity and low sensitivity toward a magnetic field. Fig. 7 shows the overall schematics of the experimental setup for the locomotion tests. The microrobot was positioned in the ROI on the test bed of the EMA system. We fabricated a cubical test bed of 20 mm in length. For the observation of the microrobot, the test Table 1 Specification of proposed EMA coil system. Coils Radius (mm) Diameter of copper wire (mm) Coil turns Fig. 5. Schematic modeling of 3D locomotion of microrobot. (a) Modeling in 3D Space and (b) modeling in x r plane. Maxwell coil Helmholtz coil Gradient saddle coil Uniform saddle coil

6 414 H. Choi et al. / Sensors and Actuators A 163 (2010) Fig. 7. Experimental setup. bed was made of transparent acrylic and filled with high viscosity silicone oil (350 cp) and it was rotated together with the rotation of the pair of saddle coils. As the microrobot, a cylindrical (diameter 1 mm, height 5 mm) neodymium magnet was used in these experiments. For the position recognition of the microrobot, still images of the microrobot were recorded by a camscope (Sometech Vision). The coil currents were supplied by power suppliers (Agilent 6675A), which were controlled by the PXI controller with LabVIEW software. For the direction control of the currents, an extra circuit, using relay components and a power supply (ADVANTEK P3030D), was fabricated and adopted. To confirm the 3D locomotion of the microrobot based on the proposed EMA system, we carried out locomotion tests of the microrobot in the desired tilted wall of the test bed. In order to record the locomotion of the microrobot in the tilted angle wall of the test bed, we made a fixture for the camscope camera, as shown in Fig. 8. The structure can be rotated together with the rotation of the pair of saddle coils and the camscope camera was positioned perpendicularly the pair of saddle coils. Therefore, using the camscope and the structure, the locomotion of the microrobot in the tilted plane was recorded and analyzed Basic 3D locomotion experiments For the evaluation of the locomotion performance of the proposed EMA system, we selected three representative rotation angles ( = 45,60,90 ) and executed the locomotion experiments Fig. 8. Structure for recording of microrobot s locomotion. Fig. 9. Experimental results: propulsion of microrobot in 3D Space( = 60 ). (a) Without gravity compensation and (b) with gravity compensation.

7 H. Choi et al. / Sensors and Actuators A 163 (2010) Table 2 Experimental results. Rotation angle () Gravity compensation Desired direction () 30 (%) 40 (%) 50 (%) 60 (%) 45 W/O (40) W (12) 60 W/O (50) W (13) 90 W/O (56) W (9) (16) (8) (30) (6) (42) (3) (5) (1) (13) (1) (20) (0) (5) (1) (7) (1) (12) (0) for four desired direction angles ( = 30,40,50,60 ). In addition, two cases of with and without gravity compensation were tested. Fig. 9 shows the experimental results of the linear locomotion of the microrobot for the representative rotation angle, = 60. For the desired direction angles ( = 30,40,50,60 ), Fig. 9 (a) and (b) shows the experimental results without and with gravity compensation. In addition, Table 2 and Fig. 10 summarize the locomotion results of the microrobot with and without gravity compensation. Firstly, from the experimental results, the microrobot could follow the desired direction angles ( = 30,40,50,60 ) on the tilted angle plane ( = 45,60,90 ). In addition, the tracking angle error was reduced by the gravity compensation algorithm and the microrobot was controlled precisely with the compensation algorithm. Especially, as the tilted angle increased, the microrobot without the gravity compensation algorithm gave large tracking angle errors from 2.59 to That is, when the tilted angle was large, the gravity effect on the microrobot also increased. However, once the gravity compensation algorithm was applied, the microrobot gave small tracking angle errors below 3.82, regardless of the tilted angle. Fig. 10. Tracking angle error of experimental results. Values are expressed as mean ± S. E Locomotion in the phantom of blood vessel To confirm the possibility of 3D locomotion of the microrobot, we executed a locomotion test of the microrobot in the phantom of human blood vessel. Rendering data of the blood vessel were extracted from computed tomography (CT) images, which are shown in Fig. 11(a). With this data, a phantom of the blood vessel was fabricated by using the rapid prototype (RP) process. The phantom of the blood vessel was filled with silicone oil. As the microrobot, a cylindrical (diameter 1 mm, height 5 mm) neodymium magnet was used. The phantom of the blood vessel was installed in the proposed EMA system, and the microrobot was inserted into the phantom. The microrobot was manually controlled by using a joystick and its locomotion was observed and analyzed by a camscope. Experimental results are shown in Fig. 11. Propulsion of microrobot in blood vessel phantom. (a) CT image of blood vessel and (b) experimental result.

8 416 H. Choi et al. / Sensors and Actuators A 163 (2010) Table 3 Comparison of power consumption between two EMA systems. Previous EMA system Proposed EMA system HC1 HC2 MC1 MC2 USC HC3 GSC MC3 Radius r 2r r 2r r 1.82r 1.34r 1.82r Ratio of turns Ratio of power consumption 62.80r r 68.38r r Ratio of volume r r 3 Fig. 11(b). The experimental results showed that the microrobot was actuated by the proposed EMA system and could move freely in the phantom of the blood vessel at 3.75 mm/s. 4. Comparative analysis of proposed EMA system In this study, for the 3D locomotion of the microrobot, the proposed EMA system used a pair of stationary Helmholtz Maxwell coils and a pair of rotational uniform and gradient saddle coils. In our previous EMA system, we used a pair of stationary Helmholtz Maxwell coils and a pair of rotational Helmholtz Maxwell coils [9]. The proposed EMA system has similar locomotive functions of the previous one. However, there are several differences between the two systems with respect to volume and power consumption. In this section, we compared and analyzed the proposed EMA system with the previous system. For a precise and correct comparison, the two EMA systems, whose schematic diagrams are shown in Fig. 12, were compared under the following assumptions. The inner coils in both systems have the same radius. To generate the same uniform magnetic flux intensity in the Helmholtz and uniform saddle coils and the same uniform gradient magnetic field in the Maxwell and gradient saddle coils, we designed the number of coil turns for each coil. When constant coil current was applied to the coils, the power consumption became directly proportional to the coil s resistance, which was also proportional to the total length of the coil. According to the previous paper [8] and this paper, with respect to the physical structure of each coil, the radius of the outer uniform saddle coil was 1.34 times greater than that of the inner gradient saddle coil, and the radius of the Maxwell coil or Helmholtz coil was 1.36 times greater than that of the outer uniform saddle coil. Additionally, in the previous EMA system, the radius of the outer coil pairs (HC2 and MC2) is 2 times that of the inner coil pairs (HC1 and MC1). Based on the above assumptions, we could calculate the ratio of coils turns and the ratio of the total resistance and summarize the ratio of power consumption of each coil in Table 3. In addition, the ratio of the volumes of the two EMA systems could be compared. From the results, it was validated that the newly proposed EMA system gave about 8.9% torque degradation but about 9.6% enhanced propulsion force for the microrobot from those of the previous EMA system, respectively. In the 3D locomotion of the microrobot in an intravascular vessel with pulsating blood flow, the driving force for propulsion of the microrobot is more important than the torque for rotation. Therefore, the energy reduction with respect to the propulsion force is very important for efficient electromagnetic actuation. That is, the proposed EMA system has more energy saving capabilities than the previous EMA system. In addition, the proposed EMA system is 16% smaller than the previous EMA system. The smaller volume of the proposed EMA system is suited for development as a medical apparatus. Consequently, from the comparison of the two EMA systems, we verified that our newly proposed EMA system has smaller volume and lower power consumption than the previous EMA system. Fig. 12. Schematic diagram of two EMA systems. (a) Previous EMA system and (b) proposed EMA system. 5. Conclusions We presented a newly proposed EMA system for the 3D locomotion for the intravascular microrobot. Previously, we developed an EMA system composed of a pair of stationary Helmholtz Maxwell coils and a pair of rotating Helmholtz Maxwell coils. In this study, the proposed EMA system had a pair of stationary Helmholtz Maxwell coils and a pair of rotating uniform and gradient saddle coils. Instead of the pair of rotating Helmholtz Maxwell coils in the previous EMA system, we adopted a pair of rotating uniform and gradient saddle coils. For 3D locomotion of the microrobot, an actuating algorithm including gravity compensation of the EMA system was derived. We executed locomotion tests in

9 H. Choi et al. / Sensors and Actuators A 163 (2010) D space and proved the feasibility of the proposed EMA system. The actuating algorithm including gravity compensation resulted in small tracking angle errors below 3.82 regardless of the tilted angles. In addition, through the locomotion test using a phantom of a blood vessel, the feasibility of the EMA system was demonstrated. Finally, we analyzed the benefits of the new proposed EMA system compared with the previous EMA system. The proposed EMA system has smaller volume and more energy saving capabilities than the previous EMA system. Consequently, we designed and fabricated the new EMA system for 3D locomotion of a microrobot and demonstrated the feasibility of 3D locomotion of the microrobot. Therefore, it is expected that the proposed EMA system would have much potential for use in many medical applications such as the vascular therapeutic microrobot, in active drug delivery, and in minimal invasive treatments of the brain and eyes, etc. We aim to develop a locomotive microrobot for use in the coronary arteries of the human body. For in vivo application in a human body, the size of EMA coils system should be increased. In addition, for the actuation of a microrobot in a patient body, more powerful current suppliers are necessary. Through various in vitro and in vivo tests, in the future, the detail specifications of the EMA system will be presented. Acknowledgment This work was supported by a Grant-in-Aid for Strategy Technology Development Programs (no ) from the Korea Ministry of Knowledge Economy. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi: /j.sna References [1] S. Park, J. Park, Frontier research program on biomedical microrobot for intravascular therapy, IEEE BIOROB 2008 (2008) [2] J.J. Abbott, Z. Nagy, F. Beyeler, B.J. Nelson, Robotics in the small Part I: microrobotics, IEEE Robotics and Automation Magazine 14 (2007) [3] K.B. Yesin, K. Vollmers, B.J. Nelson, Modeling and control of untethered biomicrorobots in a fluidic environment using electromagnetic fields, International Journal of Robotics Research 25 (2006) [4] K. Vollmers, D.R. Frutiger, B.E. Kratochvil, B.J. Nelson, Wireless resonant magnetic microactuator for untethered mobile microrobots, Applied Physics Letters 92 (2008) (No. 14). [5] S. Floyd, C. Pawashe, M. Sitti, An untethered magnetically actuated microrobot capable of motion on arbitrary surfaces, IEEE International Conference on Robotics and Automation (2008) [6] H. Choi, J. Choi, G. Jang, J. Park, S. Park, Two dimensional actuation of microrobot with stationary two-pair coils system, Smart Materials and Structures 18 (2009) 1 9. [7] B.H. Han, S. Park, S.Y. Lee, Gradient waveform synthesis for magnetic propulsion using MRI gradient coils, Physics in Medicine and Biology 53 (2008) [8] S. Tammz, R. Gourdeau, A. Chanu, J.B. Mathieu, S. Martel, Real-time MRI-based control of a ferromagnetic core for endovascular navigation, IEEE Transaction on Biomedical Engineering 55 (2008) [9] S. Jeong, H. Choi, J. Choi, C. Yu, J. Park, S. Park, Novel electromagnetic actuation method for 3 dimensional locomotion of intravascular microrobot, Sensors and Actuators 157 (2010) [10] S. Jeon, G. Jang, H. Choi, S. Park, Magnetic navigation system with gradient and uniform saddle coils for the wireless manipulation of a micro-robot in human blood vessel, IEEE Transactions on Magnetics 46 (2010). [11] W.H. Hayt, J.A. Buck, Engineering Electromagnetic, 7th Ed., McGraw-hill, New York, 2006.