actuation [4] relies on robot deflection to create mo-tion, although predicting the magnetostrictive behavior is critical to these systems. Piezo-electric actuation [5] relies on the

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Journal of Micro-Nano Mechatronics ISSN 1865-3928 J. Micro-Nano Mech.DOI 10.1007/s12213-012-0048-y

An overview of multiple DoF magneticactuated micro-robots

Soukeyna Bouchebout, Aude Bolopion,Jean-Ochin Abrahamians & StéphaneRégnier

1 23

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J. Micro-Nano Mech.DOI 10.1007/s12213-012-0048-y

RESEARCH PAPER

An overview of multiple DoF magnetic actuatedmicro-robots

Soukeyna Bouchebout · Aude Bolopion ·Jean-Ochin Abrahamians · Stéphane Régnier

Received: 29 February 2012 / Revised: 7 August 2012 / Accepted: 25 September 2012© Springer-Verlag Berlin Heidelberg 2012

Abstract This paper reviews the state of the art ofuntethered, wirelessly actuated and controlled micro-robots. Research for such tools is being increasinglypursued to provide solutions for medical, biological andindustrial applications. Indeed, due to their small sizethey offer both high velocity, and accessibility to tinyand clustered environments. These systems could beused for in vitro tasks on lab-on-chips in order to pushand/or sort biological cells, or for in vivo tasks likeminimally invasive surgery and could also be used in themicro-assembly of micro-components. However, thereare many constraints to actuating, manufacturing andcontrolling micro-robots, such as the impracticabilityof on-board sensors and actuators, common hysteresisphenomena and nonlinear behavior in the environ-ment, and the high susceptibility to slight variationsin the atmosphere like tiny dust or humidity. In thiswork, the major challenges that must be addressedare reviewed and some of the best performing mul-tiple DoF micro-robots sized from tens to hundredsμm are presented. The different magnetic micro-robotplatforms are presented and compared. The actuationmethod as well as the control strategies are analyzed.The reviewed magnetic micro-robots highlight the abil-ity of wireless actuation and show that high velocities

S. Bouchebout (B) · J.-O. Abrahamians · S. RégnierInstitut des Système Intelligents et de Robotique (ISIR),Université Pierre et Marie Curie/CNRS UMR-7222,BC 173, 4 Place Jussieu, 75005 Paris, Francee-mail: [email protected]

A. BolopionFEMTO-ST Institute, UFC, ENSMM, UTBM,CNRS UMR-6174, 24 rue Alain Savary,25000 Besançon, France

can be reached. However, major issues on actuationand control must be overcome in order to performcomplex micro-manipulation tasks.

Keywords Micro-robot · Magnetic actuation · Control

1 Introduction

The promising field of micro and nano technologiesbased on wirelessly powered and maneuvered submil-limeter devices has recently been developed. As thesemicro-robots have a small size and are untethered, theycan fit in fluidic systems and manipulate micro-objects,likewise they can experience very high velocities andcarry out many actions in a short time. Several areaswill benefit from these advanced technologies.

As for potential applications, advanced manufac-turing relies on the micro-assembly of small me-chanical components, using micro-agents manipulat-ing micro-objects in order to build assembled systems.For example, Micro-Opto-Electro-Mechanical Systems(MOEMS) sense or manipulate optical signals on avery small size scale using integrated mechanical, op-tical, and electrical systems, therefore their fabricationrequires a precise micro-assembly system. Another ex-ample is the fabrication, packaging and interconnectionof different micro-components in the MEMS (Micro-Electro-Mechanical-Systems) where micro-assembly isvital. Modular robotics can also benefit from micro-robotics. Reducing the size of individual robotic mod-ules increases the spatial resolution of reconfigurablerobots, hence it adds to their versatility and range

Author's personal copy

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of tasks. Industrial biotechnology and medicine arealso suitable fields for micro-robot use. Indeed, micro-robots operate at the same scale as organic cells, al-lowing efficient in vitro interaction in order to moveand/or sort cells. Hence they can fit in lab-on-chipsand perform adaptable tasks on corpuscles such asblood cells sized from 6 to 10 μm. Minimally InvasiveSurgery (MIS) greatly reduces patient trauma and timerecovery through the use of smaller tools, in the futuremicron-sized robots could be inserted in the humanbody to reach locations that conventional surgery can’taccess [1], and used in targeted drug delivery to sicklycells or tumors.

The reduced size makes it impractical to powermicro-devices through built-in energy sources, as theyare currently hard to achieve at this scale. However,offboard actuation processes can be used that cannot beapplied on macro scale systems. Significant progress hasbeen realized in this regard using various methods. Theelectrostatic effect [2] powers scratch drive actuators,although these devices need a patterned surface tooperate on. The dielectrophoresis forces generated byan electric field can also be used to position a microdielectric particle [3], however this method providesshort courses for the micro-devices. Magnetostrictiveactuation [4] relies on robot deflection to create mo-tion, although predicting the magnetostrictive behavioris critical to these systems. Piezo-electric actuation [5]relies on the robot distorting to create motion butrequires a high voltage. Thermal actuation [6], whileunsuitable for biological purposes, would be adaptedto actuate submillimiters devices—since thermal ca-pacity depends on volume, heating and cooling timesare greatly reduced for micro-devices [7]. The maindifficulty for thermal actuators is to apply and mea-sure two different temperatures locally in a controlledmanner [8]. Biological properties can also be used toactuate micro-robots, like bacteria’s properties [9, 10]which present great potential for future research indrug delivery. The main issue with these systems is tomaintain low cytotoxicity induced by the bacteria whilethe detection and required payloads are guaranteed.Other actuation methods can be used such as laserbeams [11, 12], but this method offers a low rangeof forces ∼pN. Electromagnetism can be used as apower source in several ways. Swimming micro-robots[13–15] employ magnetic actuation as a propulsionmethod in a fluidic environment: the micro-robot iswirelessly pulled. Though, the swimming micro-robotscan be fitted with helical propellers [16–18]. Thesemicro-robots are well suited for in vivo medical ap-plications. The Magnetically driven MicroTool (MMT)which showed good performances in interacting with

biological cells [19] also uses magnetic actuation, usu-ally with permanent magnets. The MMT is mainlyaimed to fit in fluidic systems to perform a specific taskon cells. Moreover, various mobile micro-robots useelectromagnets as power sources [20–22].

As the most often magnetic micro-robots used aremade of a soft magnetic material, both a high magneticgradient and magnetic field magnitude are suitable.However, the systems providing high homogeneousmagnetic field with a weaker magnetic gradient, likethe Magnetic Resonance Imaging (MRI) benefit froma large workspace but are limited in DoF. Whereas,the electromagnetic systems allowing high DoF within asmaller workspace, lake of magnetic field homogeneityand use high gradient field or larger volume of micro-robots. Such compromises are critical in the electro-magnetic systems and can be addressed according to themicro-robot application. These systems can performtasks both in dry and wet surfaces. The magneticallyactuated micro-robots are force-controlled with posi-tion feedback, in contrast with macro scale robotictools which are position-controlled with force sensingor visual feedback. Thus limitations on generated forcescan be imposed to allow, besides performing industrialtasks, safe interactions with living biological micro-objects. Regarding the advantages of magnetic actu-ation, this review approaches magnetically actuatedmicro-robots.

The aim of this review is to highlight the main chal-lenges facing magnetically actuated micro-robots, andsolutions that have been proposed through some ex-amples of the most successful magnetic actuated micro-robots. The systems discussed in this work are restrictedto untethered micro-robots sized between tens to hun-dreds μm that can generate important forces comparedto their reduced size. The addressed systems can beconsidered as multipurpose, accessible, i.e. simple fab-rication processes, and having more than one degreeof freedom (DoF). These micro-robots are actuatedby electromagnets as they offer a convenient controlsystem by current signals. The four systems consideredin this paper are: the Mag-μBot from Carnegie MellonUniversity, the OctoMag of the ETH Zurich, a para-magnetic particles control system from the Universityof Twente, and the MagPieR of the ISIR and FEMTO-st laboratories. There are many challenges in achiev-ing such systems. The design of magnetic micro-robotsystems is divided between designing the actuators, andthe microfabrication of the micro-robots. Currently, di-mensioning the electromagnets and optimizating theirconfiguration are among the concerns in designing thesystems. Besides, the manufacturing of micro-robotsis today possible with the emergence of new micro


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fabrication techniques, however controlled surface con-ditions are difficult to achieve. Moreover, the challengein fulfilling micro-robotic applications is to have theability to position, and for anisotropic shapes orientate,micro-robots with micron accuracy, in order to interactwith micro-objects. Hence, a robust and efficient con-trol system is required, more so because of the non-linearities that occur at the micro scale: predominantadhesion forces, significant hysteresis phenomena, andthe high sensibility of micro systems to environmentvariables, such as humidity, residues, dust etc. The con-trol system must be robust to these environment noises,and as the micro world allows for very high velocities, afast control response is also required. Therefore, a goodcompromise between command robustness and speedis critical. In addition to these environment-relateddrawbacks, on-board sensors or controllers are hard toachieve on micro-robots due to the small scale. Thus,a fast and efficient external sensing and motion track-ing method is needed to locate the micro-robot. Sev-eral detection methods can be used, like cameras [21],x-rays, laser scanning, MRI [23–25], and fluoroscopy.The choice of the imaging systems is important anddepends on the environment of the micro-device, rangeof detection field, cost, tracking speed and flexibility.Perception feedback can be exploited by a user in ateleoperation mode while the control system enhancesmanipulating precision at a micro scale, as is ideally thecase for MIS. Camera frames can also be used in a fullyautomated manner, which is required for autonomousindustrial micro-assembly or operations on cells due tothe high number of repetitive tasks.

This work is organized as follows. Section 2 de-tails the major challenges that need to be addressed.Sections 3–6 illustrate how four micro-robot systems,the Mag-μBot from Carnegie Mellon University, theOctoMag of the ETH Zurich, a paramagnetic parti-cles control system from the University of Twente,and the MagPieR of the ISIR and FEMTO-st labo-ratories, approach micro-robotic challenges, with fo-cus on the micro-robot platforms, motion mechanismsand force/position controls. This review is concludedin Section 7 with a comparison between the discussedsystems.

2 Challenges of magnetically actuated micro-robots

Usually, the studied magnetic micro-robots systemsconsist in electromagnets surrounding the micro-robotworkspace, as depicted in Fig. 1. The micro-robotevolves in a workspace we will call the arena, which caninclude a fluid (liquid or gas). The scene is observedusing a camera fitted with a microscope objective. Inthis section the main issues in designing, actuating andcontrolling such systems are discussed.

2.1 Challenges of magnetic micro-robot actuation

An object with a non-zero internal magnetization ex-periences magnetic forces and torques when exposedto a magnetic field B, and thus exhibits motion [26]. B[T] is characterized by its directions represented as fieldlines, and by its value called flux density. It is a function

Fig. 1 An example of a magnetic actuated micro-robot


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of the magnetic H [T] field called field strength. It isproportional to the magnetization field M [A m] ofits source, which is the density vector field of localmagnetic moments inside its volume V. The magneticmoment m [A m2] is a vector quantity resulting fromthe motion of charges within a magnetized object, anddescribes its ability to magnetically interact with othermagnetized objects or magnetic fields.

Several types of magnetized materials can be used[27]. In ferromagnetic and ferrimagnetic materials,magnetic domains locally regroup large numbers ofatomic magnetic moments, which describes an ele-ment’s ability to magnetically interact with magne-tized objects or magnetic fields, pointing towards thesame directions. These magnetic domains result in anoverall magnetic moment in permanent magnets, orcompensate each other in other materials. An exter-nal magnetic field can realign these magnetic domainsaccording to its directions which may result in forcesand torques on the object: these materials are at-tracted towards stronger values of the magnetic field.The stronger the exciting field is, the more magneticdomains realign, until it reaches magnetic saturationas all the domains point towards the same direction.Thus, a ferromagnetic object which produces no mag-netic field on its own can also be used to enhance anexternal magnetic field. Residual magnetization mayremain when the exciting field is switched off, andmay be permanent. Ferromagnetic and ferrimagneticmaterials are classified as soft magnetic if the remainingmagnetization is small and dissipates very fast, whichis suitable for use in micro-robotics, or hard magneticwhen residual magnetization is significant, which canproduce permanent magnets. The advantage of usingferromagnetic micro-robots is to generate significantforces that can be used in the assembly or handling ofmicro-components.

Other materials are susceptible to magnetic fields,like paramagnetic and diamagnetic materials. Thesematerials do not possess magnetic domains and are notsubject to magnetic remanence, but magnetic momentslinked to their unpaired electrons for paramagneticmaterials, or paired electron orbital motions for dia-magnetic materials, can likewise realign in the presenceof a magnetic field. Paramagnetic materials realigntheir magnetic moments in the direction of B, while

diamagnetic materials realign their magnetic momentsin the opposite direction of B. Hence, a diamagneticmicro-device can benefit from a point of equilibrium;which is suitable for the control. Diamagnetism can beobserved in all materials, but is very weak except insuperconductors: when paramagnetic properties existthey prevail over diamagnetic repulsion. Paramagneticmaterials themselves present a much weaker attractiontowards stronger values of the magnetic field than fer-romagnetic materials, and therefore require a strongermagnetic source to achieve similar results.

In practice, to express the forces exerted by a mag-netic field on a ferromagnetic object, constant experi-mental values can be used as a uniform magnetizationM for unsaturated materials. While, on a paramagneticbody, the local magnetic moment is proportional to theapplied magnetic field, where α is the proportionalityconstant measured by a magnetometer. The magneticforce Fm relies on the non-uniformity of the mag-netic field B and is proportional to the magnetic fieldgradient. The magnetic torque Tm is proportionalto the magnetic field and acts to bring the internalmagnetization of an object into alignment with thefield. The magnetic forces and torques are expressedin Table 1 for both ferromagnetic and paramagneticmaterial.

Regarding the effect of B on magnetic materials,the magnetic field can be employed to actuate micro-robots made of a magnetic material. B fields can beused to actuate micro-robots in several ways. Stick-slip motion induced by magnetic torques can producetranslation [28]. In addition to the stick-slip method,magnetic forces can produce a rolling motion on spher-ical magnetic micro-bodies [29]. Using magnetic forcesas a direct propulsion method requires a stronger mag-netic field to move the micro-device [21], but generateshigher magnetic forces when interacting with micro-objects. Besides, magnetic forces can be used to createvibrations in a micro-robot [30–32], leading to motionat its resonance mode. In the case of the magneti-cally actuated systems purposed for in vivo or in vitrobiomedical applications, the biocompatibility of mag-netic materials is important for such magnetic systems.Coating the magnetic material with polymer layers [33]can be used, to prevent the magnetic materials fromcorrosion and leaching. Moreover, some biocompatible

Table 1 Summary of the magnetic forces and torques on ferromagnetic and paramagnetic materials

Material m Fm Tm

Ferromagentic m = MV Fm = V(M · ∇)B (1) Tm = VM × B (2)

Paramagnetic m = αVB Fm = αV · ∇(B2) (3) Tm = 0


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magnetic materials exist [34] but there biocompatibilityis limited in time.

2.2 Challenges in designing magnetic actuationplatforms and micro-robots

The addressed magnetic actuation systems are basedon electromagnets which generate a magnetic field Bby applying a current I. The linearity and the strengthof B depends on the input I and the coil parameters,like the number of loops, size, geometry and core ofthe electromagnet. Designing magnetic micro-robotsinvolves the optimization of the electromagnets’ para-meters, thus maximizing the workspace and DoF of themicro-robots, the generated forces while manipulatingmicro-objects, as well as minimizing the latency andnon-linearities of the coils for a fast and robust controlof the micro-robots.

As B can be controlled by I, its intensity can be in-creased or turned off. Besides, the current signal can bemodulated through software and can exhibit differentforms: sinusoidal, sawtooth, square, triangle etc.. Thus,different magnetic fields can be produced to obtaintrajectory control. The maximum admissible currentintensity in the electromagnet depends on how muchheat the conductive material can withstand and howfast it can be dissipated by the coil. However, coolingsystems [21], or square waveform current instead ofcontinuous current [35] can be used.

Besides, the strength and linearity of the magneticfield depend on the core of the coil. The field gen-erated by a coil without a core (air-core) (Fig. 2a) isdirectly proportional to the applied current intensity.The generated magnetic field is strongest inside thecoil, and falls off rapidly outside of its volume. It is thenimportant to keep the micro-robot as close as possibleto the coil, which restrains its workspace. However, it ispossible to generate a stronger magnetic field outsideof the electromagnet by adding a soft magnetic coreat its center (Fig. 2b). If the core reaches magneticsaturation the magnetic field is no longer proportionalto the current intensity input.

In order to improve the micro-robot DoF, severalfixed electromagnets can be controlled to producedifferent fields one at a time, or more complex fieldswhen combined. The resulting field can then be con-sidered as the linear superposition of the effects ofeach individual electromagnet for air-core coils, eventhough a very weak mutual induction exists betweenthe coils. This approximation can also be applied toferromagnetic core coils, as long as the sources arefar enough from each other for the field generatedby an electromagnet not to affect another’s core [21].

The challenge in choosing the coils configuration andmicro-robot DoF is to reduce the distance betweenthe electromagnets and the micro-robot to increasethe available magnetic field strength, while keeping acertain distance to avoid overwhelming nonlinearities.Moreover, as one coil induces displacement of themicro-robot in one direction, the number of the usedcoils and their configuration influences the DoF of themicro-robot. Thus, to obtain controlled 2D motion atleast 4 coils are needed, and for 3D fully controlledmotion a minimum of 6 coils is required. Some typicalconfigurations can be used in the design. For exam-ple, in a method of actuation relying on propulsion,Helmholtz coils1 generate a uniform magnetic fieldintensity near the center of the coil to align the micro-robot located near the center of the coil along thecoil’s axis, and Maxwell coils2 are used to generate auniform gradient magnetic flux and propel the micro-robot in the desired direction [36]. However, due tothe electromagnets’ size, the admissible configurationsare restrained. This can be tackled by using a dynamicconfiguration of the coils i.e. moving the electromag-nets [38].

Once the macro scale actuation system is designed,the micro-robot fabrication can be addressed. Mag-netic micro-robots are usually made of ferromagneticmaterials and have more or less simple geometricshapes depending on their intended purpose; for ex-ample they can have a crescent shape to clasp micro-devices. Micro-robots are sized from tens to hundredsμm. Since adhesion forces at this scale are very highand depend on surface roughness, the manufacturingmethod should offer accurately controlled micro-robotssurfaces. To machine such micro-devices, macro scaleprocesses can be used such as laser fabrication. Micro-fabrication process like lithography can also be used inmachining micro-devices. Laser fabrication consists incutting a large stock of a material using a small laserspot, whereas lithography-based fabrication combinesoperations of selective deposition and growth of mate-rials, like sputtering, chemical vapor deposition, elec-troforming, spin-coating, etc., and selective removal,such as deep-reactive ion etching (DRIE). Lithographyallows machining micro-objects with layers of different

1Helmholtz coil pair: two identical circular magnetic coils placedsymmetrically one on each side along a common axis, and sepa-rated by a distance equal to the radius of the coil. Each coil carriesan equal electrical current flowing in the same direction.2Maxwell coil pair: two identical circular magnetic coils placedsymmetrically one on each side along a common axis, and sep-arated by 1.73 times their radius. Each coil carries an equalelectrical current flowing in the opposite direction.


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(a) Air core electromagnet magnetic field lines. (b) Iron core electromagnet magnetic field lines.

Fig. 2 Field lines comparison between an air core and iron core electromagnet. Data obtained by FEMM software (http://www.femm.info/)

materials, and guarantees a smoother surface than laserfabrication, however the latter preserves magnetizationand density values of the material which is not thecase with a lithography-based process. The challengefor future magnetic micro-robots is to include inter-nal DoF, like active clamps which can be actuatedindependently to perform complex micro-manipulationtasks.

2.3 Challenges in controlling magnetic micro-robots

The first step in controlling micro-robots is to performopen loop control. The user applies a given I to bringthe micro-robot to a desired position Pdes = [

xdes ydes]T

in 2D.3 An I applied through a coil generates a mag-netic field B, the magnetic field applies a magnetictorque on the micro-robot following Eq. 2 and a mag-netic force according to Eq. 1. The orientation of thedevice θcurr is commonly assumed to be equivalent tothe magnetic field orientation [21], but the translationof the micro-device needs to be identified. The controlof the magnetic micro-robot can be based on I or B.In both cases, knowledge of the relation between themicro-robot velocity and the electric current input I orthe magnetic field B is essential. Controlling magneticmicro-robots with B relies on the evaluation of B usinghall sensors. In this case these sensors can be integratedall over the arena surface which is costly. However, theycan be placed next to the coils and by interpolation,estimate B. Besides, the latency of the hall sensorsshould be minimal to perform fast control. When con-trolling the micro-robot through I, the identification ofthe generated B by a current I flowing in the coil is

3Respectively Pdes = [xdes ydes zdes

]T in 3D.

important and must include the latency and the non lin-earity of the coil. This identification can be performedby an analytic model, which does not take all the coilproperties into account, or by a finite elements model(FEM), which is calculated off-line and cannot be usedin a real-time fashion. However, the combination of thetwo methods is possible, i.e. simulating the responseoff-line and then integrating it in an analytic model forreal-time computation.

In addition to the identification of the coil parame-ters, the computation of the direct/inverse model sys-tem, i.e the relation between the micro-robot velocityand B/I, or vice versa, is one of the main issues incontrolling magnetic micro-robots. Actually, magneticforces can induce the same accelerations regardless ofthe object’s size, therefore a micro-robot can expe-rience high accelerations relative to its reduced sizeHowever, depending on the environment, the micro-robot’s behavior is disturbed by high adhesion forcesin the air [37], which depends closely on the surfaceof the arena and fabrication of the micro-robot. Ad-hesion forces can be reduced at this scale by usingvibrations generated from a piezoelectric layer [35],or levitation using the electrostatic effect. In a liquidenvironment, the micro-robot experiences fluid dragforces [37], which increase with its velocity; as themicro-robot operates, the liquid state changes and leadsto system disturbances. Besides liquid drag forces, themicro-robot can experience adhesion forces if it sticksto the surface. To reduce or avoid surface adhesionforces in liquid, the surface of the micro-robot can beadapted to make it float [38]; or it can be maintainedin the fluid above the surface by capillary forces [22].The challenge in identificating the behavior of magneticmicro-robot systems lies in the significant influenceof non-linearities, although systems parameters can be


http://www.femm.info/

http://www.femm.info/

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evaluated theoretically and corrected by several repeat-able experiences. Other methods can be used such asneural networks [39] or learning machines [40], whichshowed good performance in identifying macro scalenonlinear systems.

To provide autonomy and time gain to the user, aclosed loop system is required. In this case, the con-troller automatically computes the I needed to reachthe desired position Pdes. Due to the reduced size ofthe robot, mounted sensors are impractical. The micro-robot position Pcurr = [

xcurr ycurr]T can be detected us-

ing various sensors. Although, cameras are widely useddue to the low cost and fast computational time. Thecamera should be fast enough (several hundreds ofHertz at least) to ensure a stable control law. Theimage processing can benefit from the contrast betweenthe micro-robot and its background environment, forexample by applying threshold and/or morphologicaloperations on arena captions. Predictive control is suit-able to speed up the control loop. Besides, other detec-tion methods can be used such as event-based sensors,which are faster but have a more complex processingand need to be calibrated with a classic camera. Event-based sensors mimic biological visual systems and reactto changes of contrast that are converted in a stream ofasynchronous time-stamped events [41]. The controlleruses the value returned by the detection method, andaccording to the desired position sets the input to theelectromagnets. It thus minimizes the error ε∗,4 whichis the difference between the current and desired po-sition values. The control of the micro-robot systemis achieved by specific software according to the tasksto be executed. Thus, the control of magnetic micro-robots, besides avoiding obstacles and performing tra-jectories, has to be adapted to the micro-robots’ tasks.Clearly, micro-objects manipulation differs dependingon the environment. In the air, the micro-robot needsto generate important forces to push/pull micro-devicesand contract the adhesion forces, whereas in liquidthe control of the micro-robot needs to adapt to thefluid movement carrying the micro-objects. Besides thecontrol of one micro-object, controlling multiple micro-robots in cooperation may allow to perform morecomplex tasks, like handling a bigger object, and coop-eratively handle an object.

In the following sections, four magnetic micro-robotsare presented, and the approaches proposed to handlethe above mentioned challenges are highlighted.

4εx, εy, εz, εθ , are respectively the error along x, y, z direction andthe orientation.

3 Mag-μBot (Magnetic micro roBot)

3.1 Micro-robot design

The Mag-μBot was introduced in [20, 42]. The systemcontains six identical electromagnetic coils in an or-thogonal configuration. The coils surround the arena,wherein resides the magnetic micro-robot (Mag-μBot)(Fig. 3a). The maximum generated magnetic field andgradient field are respectively around 15 mT and0.65 T.m−1, these values being measured at the centerof the arena. A camera is located inside the top elec-tromagnet. It is a classic CCD camera coupled witha variable magnification microscope lens providing afield of view of 26 mm × 20 mm.

A Mag-μBot is a composite of Neodymium-Iron-Boron. Two fabrication processes can be used inmachining Mag-μBots. First, a laser micro-machiningsystem has been used in the fabrication of the Mag-μBot [20]. The second process relies on batch manufac-turing using molding techniques. The micro size mouldsare produced by a lithography based process. Theprocess allows the production of large numbers of Mag-μBots. To handle micro-components, the micro-robot’sshape can be adapted. Thus, the Mag-μBots is fabri-cated in several shapes (parallelepiped, cylinder etc.).Figure 3b depicts the Mag-μBots with claws to manip-ulate micro-objects.

3.2 Micro-robot actuation

The Mag-μBot’s movement is produced by applying atime varying magnetic field. Thus the Mag-μBot ex-hibits a non-uniform rocking behavior, which results ina stick-slip motion across the arena surface as shownin Fig. 4. However, this composite motion limits thevelocity of the Mag-μBot. The orientation of the micro-robot is produced by one of the in plane coils, while theMag-μBot is held down by the magnetic field generatedby the bottom coil. The translation of the micro-robotis achieved by out-of-plane pulses. The top coil appliesan alternating magnetic field leading the micro-robot torock downward when the field decreases, and upwardwhen it increases, and due to surface friction the micro-robot experiences stick and slip phases which result intranslating movement. As the motion of the Mag-μBotis composed of rotations, the torques are responsiblefor the micro-robot going forward or rotating. The mag-netic torques are given by Eq. 2. As the movement ofthe Mag-μBot is based only upon magnetic torques, thesystem requires a much smaller magnetic field strengththan magnetic gradient-based systems (i.e magneticforce-based systems). The velocity of the Mag-μBot


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Fig. 3 The Mag-μBot systemdesign

(a) Picture of the Mag-µBot system, A:Camera, B: Microscope,C: Top coil, D: Up-right coil, E: The arena, F: Bottom coil [43].

(b) The claw model of Mag-µBot:300 µm x 300 µm x 100 µm [44].

can reach 25 mm.s−1, as performed at the NIST IEEEMobile Microrobotics 2010 Challenge [44].

3.3 Motion control

In order to servo the system, a correlation is set upbetween the current signal input and the micro-robot’sbehavior. Simulations and experiments were done todetermine the velocity of the micro-robot as a func-tion of the signal frequency and surface roughness.Different waveform current signals (shape, frequencyand amplitude varying) were applied to the systemand the resulting velocities were measured from thecamera frames. Thus, multiple surfaces were tested:glass, rough silicone, smooth silicone. Besides, air,vacuum and nitrogen atmospheres were tested. TheMag-μBot was also used in water, where precautionswere taken to avoid the solid/liquid interface fromgetting the micro-robot stuck on the surface. TheMag-μBot showed lower velocities in water than inair, since the drag forces are more important in water.As the velocity of the micro-robot depends on thefrequency of the current signal, values are obtained

Fig. 4 Mag-μBot performing a translation. The solid line is theinitial micro-robot position, the dotted line is the position of themicro robot after movement. In the stick phase the micro-robotis stationary because of surface friction, as soon as the contactbetween the micro-robot and the surface slips, the Mag-μBottranslates [28]

from experimental frequencies relating to the surfaceit operates on. Figure 5 shows some results of theseexperiments and simulations. The effect of the mag-netic torques is predominant compared to other forces,thus the orientation of the Mag-μBot is assumed to beequivalent to the orientation of the magnetic field inthe -x,y- plane.

The control is performed using visual feedback. Theimage processing returns the current position of themicro-robot to the controller. Given the goal posi-tion, the controller sets the adequate current signalfrequency and amplitude. The image processing is aparticle filtering algorithm coupled with state predic-tion [45]. The controller is a proportional-integrator-derivative (PID), with additional imposed nonlinearlogic. The nonlinear logic regulates the orientation ofthe magnetic field and the velocity of the robot. Whentoo high angular accelerations are applied, the Mag-μBot can flip on its edge and its behavior becomesunknown. The aim of this block is to improve thestability of the micro-robot motion by limiting theseaccelerations. Figure 6 shows the block diagram of theMag-μBot control.

3.4 Experimental results and discussion

The reliable control of the micro-robot allows a higherlevel of Mag-μBot autonomy. The system is providedwith a motion planner. This module computes a freecollision path from an initial position to a goal position,in a clustered environment. In this case, the user definesin advance the obstacles in the environment of therobot. The planner sends to the controller the positionsto follow to reach the goal and the controller generatesthe needed current signal to the coils. The path is com-puted using the Wavefront algorithm [46]. The control


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Fig. 5 The Mag-μBotvelocities as a function of thecurrent signal frequency, bothexperimental and simulatedresults. The Mag-μBot istraveling on a rough siliconsurface in air

(a) Sawtooth and reverse sawtooth waveformssignal input [20].

(b) Square and sine waveforms signal input[20].

of the Mag-μBot generates sufficient forces and is accu-rate enough to perform interaction with micro-objects,such as pushing a 50 μm diameter sphere underwater.Moreover, as the Mag-μBot operates in liquid, themanipulation of micro-objects is performed using twostrategies. Non-contact handling is performed using theflow-field generated by the Mag-μBot [47]. A micro-object can be also moved by direct contact, in this casethe displacement of the micro-objects before contactdue the flow field is significant and needs to be takeninto account.

The Mag-μBot system also offers the ability to con-trol multiple micro-robots, either by adapting the sur-face with electrodes and using the electrostatic effect toclamp all micro-robots except the one to move [48, 49],or by using micro-robots of different sizes, in whichcase each micro-robot has a specific actuation signalfrequency [42]. To control the micro-robot, it mustkeep contact with the surface. Indeed, if the contact isbroken, the robot flies during much of its travel dueto the magnetic gradient. The micro-robot will thenexperience high velocities which are impractical foruse from a controllability point of view. This behavioroccurs when using the top coil, which orients the micro-robot upwards and towards the in plane coils, makingthe micro-robot lose contact with the surface. Hence,with this method the Mag-μBot system is restricted to2D motion.

4 OctoMag


The OctoMag [21] micro-robot, an elliptical shapedmicro-device made of Nickel-Cobalt, is surrounded by 8soft-magnetic-core electromagnets (Fig. 7). These coilscan withstand a current intensity of 15 A provided bythe amplifiers. The temperature in typical operatingconditions is around 60◦ without a cooling system, andcan rise excessively if maximum magnetic forces areapplied. Thus, the coils require a cooling system. Thedisposition of the coils were defined in order to op-timize the force capability generation throughout thearena. To observe the micro-robot, two cameras aredisposed with additional optic zoom, one on the topof the arena and the other at the side of the scene.The micro-robot operates in a wet environment. TheOctoMag micro-robot is a three-dimensional structuremade of two micro-assembled individual parts. Micro-robot parts have been machined with electroplatednickel using a lithography process then laser cut steel[50].


The design of the OctoMag system allows the micro-robot to perform 6 DOF movements. However, the

Fig. 6 Block diagramdepicting the method ofcontrol for positioning aMag-μBot to a desired goallocation


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Fig. 7 The OctoMag electromagnetic system. Eight soft-magnetic-core electromagnets surround the arena containing themicro-robot. A camera is fitted down the central axis to imagethe micro-robot [21]

magnetic torque tends to align the longest axis of themicro-device with the magnetic field. Therefore, rota-tions along this axis are not practical, leading to theloss of one DOF. Hence, the control of the micro-robot is restricted to 5 DOF: 3 axis translation (Eq. 1)and 2 rotations (Eq. 2). For -n- electromagnets, eachelectromagnet -e- generates a magnetic field Be that canbe precomputed for every point P throughout the arena(Eq. 4).

Be(P) = Be(P)ie (4)

where Be [T.A−1] is a unit-current vector and ie[A] isa scalar current value. As the field generated by a coilis known and it is assumed that the soft magnetic coreused in the electromagnets is ideal, the superpositiontheorem can be applied i.e the field generated by sev-eral coils is the sum of the magnetic fields generated byeach coil. Thus, the magnetic field can be identified atany point of the arena as function of the current input.

B(P) =n∑

e=1

Be(P)ie = B(P)I (5)

where I is a vector of the unit current ie. As, theOctomag’s micro-robot is force controlled and the forceis related to B with Eq. 1, the derivative of the magneticfield is calculated for a given direction -x,y,z- at every

point in the workspace. According to Eq. 5, the mag-netic field and force is mapped through the arena for agiven current signal I by the following equation:

[B

Fm

]=

⎡

⎢⎢⎣

B(P)

MTBx(P)

MTBy(P)

MTBz(P)

⎤

⎥⎥⎦

⎡

⎢⎣

i1...

in

⎤

⎥⎦ = A(M, P) I (6)

4.3 Motion control

The system is controlled using micro-robot positionfeedback from a camera. The OctoMag’s micro-robothas 5 DoF, thus detection of the micro-robot inspace requires two cameras. The x,y position are de-duced from a top camera and the z position froma side camera. The tracking scheme of the Oc-toMag benefits from the use of adaptive thresh-olding and morphological operators, such as ero-sion and dilatation. The orientation of the micro-robot is controlled by an open loop assuming thatif the orientation of the magnetic field is changedslowly, the orientation of the micro-robot will be thesame as the orientation of the magnetic field. Hence,the micro-robot’s orientation is not measured. Themagnetic field and forces are proportional to I (Eq. 6).For a desired magnetic field and force, the current canbe computed for each coil by inverting the OctoMagmodel:

I = A(M, P)+[

Bdes

Fdes

](7)

Figure 8 depicts the block diagram of the OctoMag.


The main advantage of the OctoMag is to perform 3Dmotion, however only 5 DoF are fully controlled. Toevaluate the precision of the OctoMag’s positioning,the Octomag was controlled from a random position inthe workspace to the center of the arena. Positioningof the micro-robot showed a standard deviation of6.313, 4.757, and 8.951 μm along the x, y, and z axes,respectively, and a maximum Cartesian deviation of

Fig. 8 Block diagramrepresenting the method ofcontrol for positioning theOctoMag


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Fig. 9 OctoMag controlexperiments [21]

(a) The top and side view of the OctoMag controlled tofollow an ∞ -shaped trajectory. The micro-robot’s ori-entation is kept toward the center of the sphere.

(b) This trajectory was performed in anaverage time of 8.3 s.The black are setpath points and the red +

o

are the trackedpositions. The direction of displacement isshown by the arrows.

29.77 μm. The positioning error was measured from400 frames of the camera, collected at 30 Hz and theOctomag system was tested by keeping the absolutevalue of B constant (|B| = 15 mT) to guarantee thelinearization of the controller. Figure 9 shows a 3D ∞shaped trajectory performed in an automated mode.Due to the positioning error, the micro-robot deviatesfrom the desired path in some parts, however the micro-robot recovers from this drift and follows the trajectory.

One of the potential application of the OctoMag sys-tem is to perform in vivo ophthalmic procedures, likethe puncturing of retinal veins to inject thrombolyticdrugs. Thus, the system was tested in vitro. It suc-cessfully performed wireless vessel puncture of bloodvessels of the chorioallantoic membrane (CAM) on agrowing chicken embryo, which is considered a validtest setup for applications on human retinal vessels.In this experiment, another shape of the micro-robotwas used: two NdFeB cubes, of 800 μm edge, and aneedle tip were glued. The overall size of the robot ismore than 1,600 μm in length, the device can then applyenough force to puncture vessels.

5 Magnetic control of paramagnetic particles


An image-based magnetic control of paramagneticmicro-particles system was presented in [22, 51]. Inthis work, the micro-robot is a sphere of diameter∼100 μm made of a paramagnetic material (iron ox-ide). The paramagnetic particles are normalized andcommercially available. Four identical electromagnetsare responsible for the actuation of the micro-spheres,which lie in an arena (Fig. 10) containing a liquid (wa-ter), and are maintained in the water-to-air boundary.This configuration of the micro-spheres avoids the pres-ence of surface adhesion forces as the micro-spheresare not in contact with the bottom of the arena. Thecontained liquid forms a meniscus at the center ofthe arena. Thus, to reduce this liquid deformation thearena size is increased and only a parcel of the arenais observed. The particles are observed by a camerawith a 100 ms image period, fitted with a microscopeobjective.

Fig. 10 Design of theparamagnetic particlescontrolling system

(a) Scheme of the system, four coils surrounding anarena

(b) Picture of the controlled paramagnetic parti-cles. .


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Fig. 11 Schematic diagram ofthe control loop. Two PIcontrollers are used tocontrol the particle in both xand y directions


As the particles are made of a paramagnetic material,they exhibit a particular behavior under the influenceof a magnetic field. The magnetic forces (Eq. 3) onthese particles depend on the gradient field squared.Besides, the micro-spheres are held in the water-to-air layer by capillary forces, hence it is assumed theonly force opposing the micro-spheres’ movement isthe drag force induced by the liquid environment. Thedrag force increases with the velocity of the particle,thus the maximum speed of the particle is reached whenthe magnetic force equals the drag force.

5.3 Motion control

The control of paramagnetic particles relies on using atracking algorithm to detect particle motion. To benefitfrom a fast detection method, the tracking algorithmuses a region of interest, the center of which is eitherdefined by the user or assumed to be the last positionof the particle. Moreover, to overcome the lightingdisturbances, an adaptive thresholding is then appliedon this region. Afterwards, an erosion filter is appliedto reduce noise on the frame. As several micro-particlesare used once in a time, the particle is assumed to be thebiggest object on the frames. A size test is also appliedto verify that the detected particle has an acceptablesize, otherwise the particle is considered lost. In theexperiment, the environment was carefully preparedto avoid any disturbances. The image processing algo-rithm reaches its limit when several particles are usedand more than one particle is in the region of interest:the algorithm returns an inexact position, which is theaverage of the particle positions inside the region.

The tracking algorithm provides PI5 controllers—one for each axis (x, y)—with the difference betweenthe actual position and the desired position of the

5Proportional Integrator

particle. The PI controllers have the same gains for eachaxis (Fig. 11).


The experiments demonstrated in [22] show that con-trolling a particle towards a position takes around 15 sto reach a steady state. The current intensity appliedto the coils is 0.8 A which generates a gradient fieldsquared of 1.8 mT2.m−1. Under this condition, thespeed of a particle of 100 μm is 235 μm.s−1. Figure 12arepresents the positioning of a particle, the standard de-viation according to x and y is about 8.4 μm. Figure 12bshows movement of a particle around a path of presetpoints. The movement of the particle is not smoothdue to significant overshoot in particle positioning.Moreover, it is assumed that the controlled particlesare always held in the air-to-water boundary, avoidingbuoyancy forces. Thus, the experiments need to becarefully prepared, otherwise the proposed model ofthe system is not valid anymore.

6 MagPieR (Magnetic Piezo Robot)


The MagPieR is a micro-parallelepiped [35], composedof two heterostructure layers: a ferromagnetic material(Nickel) layer for magnetic driving on top of a bulkof PMN-PT (Pb(Mg1/3Nb2/3)O3-PbTiO3: a compositeof Lead-Magnesium-Niobium-Titane), a piezoelectricmaterial used to overcome surface friction (Fig. 13a).

The MagPieR is fabricated by electrodeposition of aNi layer on PMN-PT substrate and then by saw dicinginto small rectangular samples. In the Ni layer twotrenches are cut in order to align the micro-robot withthe magnetic field along the trenches. The MagPieRmoves inside a capacitor. The bottom electrode is thearena substrate itself, and the top electrode is an opti-cally transparent conductive glass (ITO glass) allowing


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(a) Positioning of a particle according to x and y directions[22] .

(b) The particles following a preset of points. The path isobtained from the image processing algorithm [22] .

Fig. 12 The control system performance in a positioning and in b following preset point paths

a visualization of the scene from above. The observa-tion of the MagPieR is done by a top situated highspeed camera (1,000 frames per second). The micro-robot then moves in a dry environment. The arena issurrounded by four identical electromagnets (Fig. 13b),the coils require less than 1 A to activate the micro-robot. The coils generate a magnetic field that allows3 DoF to the micro-robot: 2 translations in the x and ydirections, and a rotation in the -x,y- plane.


At the micro scale, the surface adhesion force is themain factor limiting the movement of a micro-devicein the air. To overcome this force the MagPier usesvertical vibration. High frequency, high voltage pulseson the bottom electrode actuate the piezoelectric effectto free the micro-robot from adhesion (Fig. 14a).

In-plane motion (translations and rotation) is thenobtained by applying an external magnetic field gener-ated by the coil. Only one electromagnet at a time is

used to actuate the robot. The magnetic field gradientinduces a magnetic force according to Eq. 1, whichresults in the micro-robot’s translation. The magneticfield exerts a magnetic torque on the micro-robot byEq. 2 orientating the robot in a given direction. Thesignal input to the coils is an impulse (Fig. 14b). Thevelocity of the micro-robot varies according to the am-plitude h and length u of this impulse.

6.3 Motion control

The behavior of the MagPieR is identified experimen-tally, thus the relation between the current intensityand the displacement of the micro-robot is known.As the micro-robots operates in a dry environment,adhesion forces are predominant and influence themodel of the system. In fact, the adhesion forces varythroughout the surface of the arena at this scale, henceit is difficult to simulate the micro-robot behavior witha high resolution. The controller is based on drivingthe micro-robot to a region the center of which is the

Fig. 13 The MagPieR design

(a) Image from Scanning Electronic Micro-scope of MagPieR

(b) Disposition of the coils surrounding theMagPieR arena


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Fig. 14 MagPieR actuation

(a) Externally induced vibration actuation (b) Signal current sent to the coil. .

desired position. The boundaries of this region aremarked by Xmin/Xmax and Ymin/Ymax, which are presetvalues obtained by the identification of the system. Inthis work, the visual feedback returns an (x,y) positionof the micro-robot in the workspace. The differencebetween the current position and the desired position isgiven to the PID controllers. The same PID controlleris used for each coil. Moreover, every coil controls themicro-robot in one direction on a given (x-y) axis. Oncethe position error is given to the controller, for each axisthe controller activates a coil, depending on the rangeof the error. Usable control laws are thus limited; si-multaneous control of several coils should improve themotion of the MagPieR. Depiction (Fig. 15) representsthe block diagram of the controlling system.


The MagPieR showed good velocity performance, in-deed it won the “2 mm dash” competition twice atthe NIST IEEE Mobile Microrobotics Challenge, beingthe fastest micro-robot by performing the 2 mm racein 15 ms. Figure 16a represents the resulting responseof serving the MagPier to an x-y position. The figuredemonstrates clearly that the x and y variables arecoupled. For example, at time 100 ms, the x positionhas reached its desired position but the y position hasnot. When a signal is sent to reduce the y error, the

generated magnetic force is in fact oblique and leadsto an additional movement of the micro-robot in thex direction.

The second figure (Fig. 16b) shows the control ofthe micro-robot through an ∞-shaped trajectory. Thesimulated trajectory is the continuous line, and the ex-perimental trajectory is the dotted line. The differencebetween the trajectories is due to the coupling of the -x,y- directions. Moreover, the control scheme is basedupon reaching a region rather than a trajectory, theresulting motion is irregular and lacks precision. Theuse of the gradient magnetic field in a dry environ-ment allows the micro-robot to experience high ac-celerations, though significant non-linearities inducedby this environment limit motion accuracy. Moreover,the close arrangement of the coils leads to large fieldgradients, but also leads to nonlinear field distributions.Thus, accurate control of the micro-robot is hard toachieve.

7 Comparison and conclusion

Characteristics of the previously presented magneticmicro-robots are summarized in Table 2. Magneticactuated micro-robots are made of ferromagnetic orparamagnetic materials. The shape is designed accord-ing to the application, and the robots usually have

Fig. 15 Controlling schemeof the MagPieR


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(a) Time responses to an x-y step input. The solid line isthe desired position and the dashed line is the experimentalresult [36] .

(b) An ∞ -shaped controlled trajectory of the micro-robot,the solid line is the planned trajectory and the dashed oneis the trajectory executed by the robot [36] .

Fig. 16 MagPieR control results. One pixel is ∼ 20 μm

parallelepiped, cylinder or claw geometries. The abovesystems’ coil setups respect the same configuration:four orthogonal electromagnets are used to produce 2Din plane motion; out of planes can be added to increasethe DoF of the micro-robots or to perform 2D using

only the magnetic torques. Besides, the average mag-netic field strength generated by the considered systemsis sufficient to induce motion in the magnetic micro-robot (∼10 mT). Some systems use ferromagnetic coresin their coils to increase the magnetic field strength,

Table 2 Summary of the magnetic micro-robots

Micro-robot Mag-μBot OctoMag Paramagnetic Sphere MagPieR

Micro-robot shape

Material NdFeB Ni Iron-oxide PMN-PT + NiEnvironment Dry/Wet Wet Wet DryMicro-robot dimension [μm] L = 130 ± 10 l = 500 r = 60∼110 L = 388

h = 100 ± 10 a = 375 h = 300 (100 of Ni)l = 250 ± 10 w = 250 l = 230

Coil number 6 8 4 4Number of DoF 3 5 2 3Coils position

Workspace size [mm × mm] 20 × 20 ∼20 × ∼20 10 × 10 20 × 35Coils dimension [mm] d_inner = – d_inner = 44 d_inner = 10 d_inner = 4

d_outer = – d_outer = 63 d_outer = 39 d_outer = 11l = – l = 210 l = 30 l = 17

Average magnetic field strength [mT] 15 15 6 15Coils core Air VACOFLUX 50 – FerromagneticMovement equation Eq. 2 Eq. 1 Eq. 3 Eq. 1Current signal Periodic waveform Continuous Continuous Square pulseCurrent intensity [A] 3 15 0.8 ≤1Velocity [mm.s−1] 25 ∼1.9 0.235 133


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though the saturation of the core needs to be taken intoconsideration in these systems. The maximum currentintensity admissible by a coil typically increases withits dimensions. However, the coils are subjected toexcessive heating, and require a cooling system whena significant gradient field is needed.

The systems presented above use several types ofactuation signals, such as continuous or periodic signals.Magnetic actuated micro-robots are mainly based onthe gradient of the magnetic field which induces mag-netic forces to translate the micro-device, the magneticfield being used to produce its orientations. However,the translation of micro-robots can also be inducedby magnetic torques, which requires lower magneticfield strengths but generates limited velocities. In adry environment, allow micro-robot experiences highaccelerations, unlike in a liquid environment wherethe drag forces decrease the micro-robot velocity. Al-though, in a dry environment the adhesion forces aresignificant and lead to non-linearity in the system inaddition to the non-linearity of the magnetic field dis-tribution. For most of the systems, the dynamic modelof the micro-robot is computed theoretically and cor-rected with experimental data.

Micro-robotic systems show high velocities com-pared to their reduced size. The controllers of theabove systems perform a relatively accurate position-ing, though the following of trajectories presents highlydiscontinuous behavior and irregularities. The controlsystems are, for the moment, insufficient to lead repeat-able tasks at a high speed with a high reliability. Thedynamics of the magnetic field and the micro-robot,established in an experimental way, do not reliably rep-resent the micro-robot’s behavior and non linearities.

The next challenges for untethered magnetic micro-robots are to benefit from 6 DoF navigation to fullyexplore the environment, and to be less sensitive toatmospheric variations. The coil setups can also benefitfrom optimized configurations in order to improve thetime response in generating the magnetic field andto increase the workspace of the micro-robot. In thefuture, these untethered micro-robots will have a greatpotential for many medical, biological and industrialapplications, thanks to their tiny size, wireless powerand control.

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http://www.nist.gov/el/isd/robotals.cfm

http://planning.cs.uiuc.edu/

http://planning.cs.uiuc.edu/

http://dx.doi.org/10.1109/BioRob.2012.6290856

Documents

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