Wireless Motion Control of Paramagnetic Microparticles usinga Magnetic-Based Robotic System with an Open-Configuration
Islam S. M. Khalil,Bishoy E. Wissa, and Bola G. Salama
The German University in Cairo,New Cairo City, Egypt
Stefano StramigioliMIRA–Institute for Biomedical
Technology and Technical Medicine,University of Twente, Enschede, The Netherlands
Abstract—In this work, motion control of paramagnetic mi-croparticles is achieved using a magnetic system with an open-configuration. This control is done using a permanent magnetand an electromagnetic coil under microscopic guidance. Thepermanent magnet and the electromagnetic coils are fixed to theend-effector of a robotic arm with 4 degrees-of-freedom to controlthe motion of the microparticles in three-dimensional (3D) space.A closed-loop control of the robotic arm is done at the joint-space to orient the magnetic field gradients of the permanentmagnet and the electromagnetic coil towards a reference pointin 3D space. Point-to-point motion control is achieved at anaverage speed of 117 µm/s using the permanent magnet andthe robotic arm, whereas the electromagnetic coil and the roboticarm achieve average speed of 46 µm/s. In addition, the permanentmagnet and the robotic arm achieves maximum position errorof 600 µm, in the steady-state, as opposed to 100 µm for theelectromagnetic coil and the robotic arm. We also demonstrateexperimentally that our control system moves the microparticlestowards a reference position in the presence of a constrain onthe motion of the end-effector. The precise motion control ofparamagnetic microparticles using a magnetic system with open-configuration provides broad possibilities in targeted therapy andbiomedical applications that cannot be achieved using magneticsystems with closed-configurations.
I. INTRODUCTION
Cancer is the second leading cause of death, following heartdisease, in many parts of the world [1]. Survival rates areincreasing for many types of cancer due to improvements incancer screening and treatment. This treatment has negative-side effects such as fatigue, pain and blood disorders. Theseside-effects can be mitigated using targeted drug delivery [2]by localizing the drug only within the vicinity of the dis-eased region. This localization can be achieved using mag-netic drug carriers such as ferromagnetic, superparamagnetic,and paramagnetic particles [3], [4], [5], [6]. Motion controlof these particles and other microrobotic systems has beenonly demonstrated using electromagnetic coils with closed-configurations [7]-[14] that cannot be scaled-up to be viablefor clinical applications [15].
Mahoney et al. [16], [17] have proposed a combination ofmagnetic field-driven helical robots [19], [20] and a roboticarm. The helical robot (with length and diameter of 26 mmand 18 mm, respectively) overcomes the problem of the limited
This work was supported by funds from the German University in Cairoand the DAAD-BMBF funding project.
The authors would like to thank Mr. Marcos Tawdros for the assistancewith the experimental work.
Fig. 1. Motion control of paramagnetic microparticles ¬ using a permanentmagnet and a robotic arm (not shown). The permanent magnet is fixed tothe end-effector ® of the robotic arm and the microparticles are containedinside a glass tube ¯ that is filled with water. Closed-loop motion control ofthe microparticles is achieved using microscopic ° feedback. The red-dashedline indicates the upper edge of the glass tube. The open-configuration ofthis magnetic-based robotic system allows us to control the motion of themicroparticles throughout a relatively large workspace with a field of viewof 13 mm×10 mm×10 mm. The maximum magnetic field of the permanentmagnet is 85 mT.
projection distance of the magnetic field gradient, whereasthe robotic arm (with open-configuration) holds a perma-nent magnet and generates rotating dipole field over a largeworkspace, as opposed to electromagnetic coils with closed-configurations. Therefore, this combination allows magnetic-based manipulation systems to be scaled-up and used indiverse biomedical applications. It has also been demonstratedthat the attractive forces acting on a magnetic microrobot canbe converted into a lateral force by rotating the actuator dipoleaccording to an open-loop trajectory [21], [22]. In this work,we achieve the following:
• Motion control of paramagnetic microparticles in three-dimensional (3D) space using a robotic arm with apermanent magnet and an electromagnetic coil;
• Point-to-point closed-loop positioning of a microparticleunder the influence of the gradients that are controlledusing the input current to the electromagnetic coil andthe spatial orientation of the end-effector;
• Closed-loop motion control of microparticles in the pres-ence of a constrain (sinusoidal-wave and square-wavetrajectories) on the motion of the end-effector that hold
2015 International Conference on Manipulation, Manufacturing and Measurement on the Nanoscale (3M-NANO)5-9 October 2015, Changchun
Fig. 2. Magnetic-based robotic system for the motion control of paramagneticmicroparticles using a permanent magnet. The microparticles are containedin water inside a glass tube and their position (P) is determined usinga microscopic system and a feature tracking software. The control systempositions the microparticles (based on the given reference position Pref ) bycontrolling the position of the permeant magnet through the robotic arm. qand U represent vectors of the generalized coordinates of the robotic arm andcontrol inputs, respectively. The red arrow indicates the microparticles.
the electromagnetic coil.Point-to-point closed-loop control of paramagnetic microparti-cles is achieved in 3D space using a magnetic-system with anopen-configuration [18]. This system allows us to control theposition of a permanent magnet and an electromagnetic coilthat are fixed to the end-effector of the robotic arm (Fig. 1).The motion control is achieved such that the microparticles arelocalized at the reference position without contact with thesurrounding glass tube. This motion control is achieved bypulling the paramagnetic microparticles towards a referenceposition using the magnetic field gradients. These gradientare controlled using two methods. The first method dependson controlling the position of the permanent magnet withrespect to the position of the microparticle and the givenreference position. The second method depends on controllingthe position of an electromagnetic coil and its input current.In addition, we experimentally demonstrate the motion controlof microparticles in 3D in the presence of a constrain on themotion of the end-effector.
The remainder of this paper is organized as follows: SectionII provides a model for the magnetic-based robotic systemusing the forward and inverse kinematics of the robotic arm.In addition, we study the characteristics of the magnetic fieldsgenerated using a permanent magnet and an electromagneticcoil that are controlled using a robotic arm with 4 degrees-of-freedom (DOF). The experimental results using the permanentand electromagnetic coil are included in Section III. Motioncontrol of microparticles in the presence of a constrain onthe motion of the end-effector of the magnetic-based roboticsystem is also included in this Section. Finally, Section Vprovides conclusions and directions for future work.
II. MODELING AND CONTROL OFTHE MAGNETIC-BASED ROBOTIC SYSTEM
Motion of a paramagnetic microparticle (Fig. 2) in a lowReynolds number regime under the influence of the magneticfield gradients is given by
∇ (m(P) ·B(P)) + 6πηrpP+ V (ρp − ρf)g = 0, (1)
where m(P) and B(P) are the magnetic dipole moment ofthe microparticle and the induced magnetic field at a point P,
Fig. 3. The magnetic fields generated using a permanent magnet along x-,y-, and z-axis are measured using a calibrated 3-axis digital Teslameter (Se-nis AG, 3MH3A-0.1%-200mT, Neuhofstrasse, Switzerland). The permanentmagnet is fixed parallel to z-axis using the end-effector of the robotic arm.The magnetic fields are measured by moving the probe of the Teslameterusing a planar motion stage throughout the workplace of the microparticle(indicated using the red arrow). The permanent magnet generates magneticfields of 39.4 mT, 38.2 mT, and 64.5 mT along x-, y-, and z-axis, respectively,at 10 mm along xp. xi, yi, zi represent the frames of the robotic arm, fori = 1, 2, 3. Further, xj , yj , zj represent the base and permanent magnetframes for j = b and p, respectively. qk are the generalized-coordinates ofthe robotic arm, for k = 1, . . . , 4.
respectively. Further, η and rp are the fluid dynamic viscosityand radius of the microparticle, respectively. Furthermore,V and ρp are the volume (rp = 50 µm) and density(1.4×103 kg/m3) of the microparticle, respectively. In (1),g and ρf are the acceleration due to gravity and the densityof the fluid, respectively [23]. The magnetic force in (1) isgenerated using a permanent magnet or an electromagneticcoil that can be attached to the end-effector of the robotic armwith the following kinematical equations, respectively, in theposition and velocity levels [24]:
x = ϕ(q) and x = J(q)q, (2)
where x =[xp,c yp,c zp,c
]Tis the generalized coordinates
of the task-space, and xp,c, yp,c, and zp,c represent the framesof the end-effector for the permanent magnet and the electro-
magnetic coil, respectively. Further, q =[q1 q2 q3 q4
]Tis a vector of generalized coordinates, and qk are the gener-alized coordinates, for k = 1, . . . , 4. Further, ϕ(q) and J(q)are the kinematical equations and the Jacobian matrix of therobotic arm, respectively. Motion control of the microparticleis achieved by controlling the generalized coordinates at thejoint space to orient the magnetic fields (Fig. 3) and magneticfield gradients of the permanent magnetic and electromag-netic coil towards a reference position.
A. Motion Control using a Permanent Magnet
Control of the magnetic force in (1) is achieved usingthe position of the end-effector of the robotic arm (Fig. 2).
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Fig. 4. Magnetic-based robotic system for the motion control of paramagneticmicroparticles using an electromagnetic coil. The microparticles are containedin water inside a glass tube and their position (P) is determined usinga microscopic system and a feature tracking software. The control systempositions the microparticles (based on the given reference position Pref ) bycontrolling the position of the coil through the robotic arm and its currentinput (I). q and U represent vectors of the generalized coordinates of therobotic arm and control inputs, respectively. The red arrow indicates themicroparticles.
The robotic arm changes the position of the end-effector,and hence controls the magnetic field gradient exerted onthe microparticle. We devise a proportional-derivative (PD)magnetic force as follows [25]:
∇ (m(P) ·B(P)) = Kpe+Kde, (3)
where Kp and Kd are the proportional and derivative gainmatrices, respectively. Further, e and e are position andvelocity errors, respectively, and are given by
e = P−Pref and e = P. (4)
In (4), Pref is a fixed reference position (Pref=0). Substituting(3) in (1) yields the following error dynamics:
e+ ΓKpe+ ΓV (ρp − ρf)g = 0, (5)
where Γ is given by
Γ = (Kd + 6πηrpΠ)−1
, (6)
where Π is the identity matrix. Based on (5), the controlgain matrices must be selected such that the matrix ΓKp ispositive-definite. The magnetic field gradients (∂B(P)
∂x , ∂B(P)∂y ,
and ∂B(P)∂z ) that are required to pull the microparticle towards a
reference position (Pref ) are determined by solving (3). Thesegradients are generated by controlling the position of the end-effector of the robotic arm with respect to the microparticle.Fig. 3 shows the magnetic fields generated using the perma-nent magnet within a workspace of 13 mm×10 mm. Thesemagnetic fields are measured using a calibrated 3-axis digitalTeslameter (Senis AG, 3MH3A-0.1%-200mT, Neuhofstrasse,Switzerland) throughout a grid that spans the workspace of themicroparticles. Fifth order polynomials (yield minimum sumsquares for error) are used to provide best fits for the measuredmagnetic fields along x-, y- and z-axis. The permanent magnetprovides maximum magnetic fields of 45 mT, 70 mT, and 75mT along x-, y- and z-axis, respectively. Within the vicinityof the workspace (13 mm×10 mm) of the microparticles, themagnetic field components are 39.4 mT, 38.2 mT, and 64.5 mTalong x-, y- and z-axis, respectively (Table I). The magnetic
Fig. 5. The magnetic fields generated using an electromagnetic coil along x-,y-, and z-axis are measured using a calibrated 3-axis digital Teslameter (SenisAG, 3MH3A-0.1%-200mT, Neuhofstrasse, Switzerland). The electromagneticcoil is fixed parallel to z-axis using the end-effector of the robotic arm. Themagnetic fields are measured by moving the probe of the Teslameter using aplanar motion stage throughout the workplace of the microparticle (indicatedusing the red arrow). The electromagnetic coil generates magnetic fields of4 mT, 4 mT, and 5 mT along x-, y-, and z-axis, respectively, at 10 mmalong xp. The input current to the coil is 0.6 A. xi, yi, zi represent theframes of the robotic arm, for i = 1, 2, 3. Further, xj , yj , zj represent thebase and permanent magnet frames for j = b and c, respectively. qk are thegeneralized-coordinates of the robotic arm, for k = 1, . . . , 4.
field gradients of these fields are relatively large enough toovercome the gravitational and drag forces.
The position of the end-effector is used to calculate thegeneralized coordinates at the joint space by integrating thekinematical equation in the velocity level (2). This integrationis done by setting, q 7−→ J−1(q)Ks, to achieve stableintegration of (2) [26].
q 7−→ J−1(q)Ks. (7)
where K is a positive-definite matrix, and s is given by
s = x− ϕ(q), (8)
we define a Lyapunov function (v(t)) as follows:
v(t) =1
2sTs. (9)
Taking the time-derivative of (9) yields
v(t) = sTs = sTJ(q)q. (10)
Substituting (7) in (10) yields
v(t) = −sTKs, (11)
Therefore, setting q = J−1(q)Ks, as in (7) results in anegative-definite time-derivative of the Lyapunov function.This procedure allows us to integrate (2) and solve for thegeneralized coordinates that achieves a desired spatial orienta-tion of the end-effector and the permanent magnet with respectto the position of the microparticles. This spatial orientation
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TABLE ISPECIFICATIONS OF THE MAGNETIC-BASED ROBOTIC SYSTEM USING
PERMANENT MAGNET AND AN ELECTROMAGNETIC COIL. THE MAGNETICFIELDS ARE MEASURED AT THE CENTER OF THE WORKSPACE USING A
CALIBRATED 3-AXIS DIGITAL TESLAMETER (SENIS AG,3MH3A-0.1%-200MT, NEUHOFSTRASSE, SWITZERLAND).
Parameter Value Parameter Value
|B(P)| [mT] 85 ∇|B(P)| [T.m−1] 1.62
Bx(P) [mT] 39.4 ∂B(P)∂x
[T.m−1] 0.49
By(P) [mT] 38.2∂B(P)
∂y[T.m−1] 0.37
Bz(P) [mT] 64.5∂B(P)
∂z[T.m−1] 1.52
max Ii [A] 0.6 Number of turns 1600|B(P)| [mT] 7.5 ∇|B(P)| [T.m−1] 0.9
Bx(P) [mT] 4.0 ∂B(P)∂x
[T.m−1] 0.27
By(P) [mT] 4.0∂B(P)
∂y[T.m−1] 0.20
Bz(P) [mT] 5.0∂B(P)
∂z[T.m−1] 0.84
rp [µm] 50 Workspace [mm3] 10× 10× 10η [mPa.s] 1.0 Frame per second 10
directs the magnetic field gradients towards the referenceposition. This level of control allows the microparticles tobe suspended inside the glass tube and move towards thereference positions under the influence of a constant magneticfield gradient. The gradient is kept constant by the closed-loop control on the joints of the robotic arm based on therelative position between the microparticle and the permanentmagnet. The magnitude of the magnetic field gradient canbe controlled by using an electromagnetic coil instead of thepermanent magnet.
B. Motion Control using an Electromagnetic Coil
An electromagnetic coil is attached to the end-effector ofthe robotic arm (Fig. 4). Therefore, the equation of motion (1)can be written as follows:
∇(m(P) · B(P)I
)+ 6πηrpP+ V (ρp − ρf)g = 0, (12)
where I and B(P) are the current input to the electromagneticcoil and the magnetic field-current map, respectively. Theequation of motion (12) is used to derive a similar errordynamics to (5) when an PD magnetic force input is appliedusing (3). Unlike the motion control using the robotic armand the permanent magnet, (12) indicates that using an elec-tromagnetic coil with the robotic arm allows us to change themagnitude of the pulling magnetic force that is exerted on themicroparticles. However, the direction of this pulling magneticforce can only be controlled using the position of the end-effector of the robotic arm. Fig. 4 shows the configuration ofthe closed-loop control system of the microparticles using theelectromagnetic coil. The magnetic fields generated using theelectromagnetic coil with the configuration shown in Fig. 5.The magnetic field components are 4 mT, 4 mT, and 5 mTalong x-, y-, and z-axis, respectively, for an input current of0.6 A.
Fig. 6. A magnetic-based robotic system for the wireless motion controlof paramagnetic microparticles ¬. The inset shows a pair of microparticlesmoving towards a reference position (red crosshair) under the influence ofthe controlled magnetic field gradient. A permanent magnet is fixed to theend-effector ® of the robotic arm. The microparticles are contained in waterinside a glass tube ¯ and are tracked using a microscopic system °. Thepermanent magnet generates maximum magnetic fields of 85 mT. The whitesquare indicates the microparticles and is assigned using a feature trackingalgorithm. An electromagnetic coil ² (inset in the upper-left corner) can bealso attached to the end-effector of the robotic arm ±. The electromagneticcoil generates magnetic field of 7.5 mT for current input of 0.6 A.
The position of the microparticles is determined using themicroscopic system and used to determine the position ofthe electromagnetic coil with respect to the microparticles. Inaddition, the input current of the electromagnetic coil is usedto change the magnitude of the pulling magnetic force towardsthe reference position.
III. EXPERIMENTAL MOTION CONTROL RESULTS
Our experimental point-to-point motion control results aredone using a magnetic-based robotic system. This systemconsists of a robotic arm that controls the position of apermanent magnet or an electromagnetic coil.
A. Magnetic-Based Robotic System
Our system consists of a robotic arm with 4 DOF, asshown in Fig. 6. The end-effector of this robotic arm canbe adapted to hold a permanent magnet or an electromag-netic coil. The control of the robotic arm and the elec-tromagnetic coil is implemented using an Arduino controlboard (Arduino Mega 2560, Arduino, Memphis, Tennessee,U.S.A). Position of the microparticles is determined usinga microscopic system and a feature tracking algorithm. Themicroparticles are paramagnetic with saturation magnetizationof 6.6 × 10−3 Am2/g, consisting of iron-oxide in a poly(lactic acid) matrix (PLAParticles-M-redF-plain from Micro-mod Partikeltechnologie GmbH, Rostock-Warnemuende, Ger-many). The magnetic field gradients that are generated usingthe permanent magnet or the electromagnetic coil are used
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(a) Position of the microparticle along x-axis (b) Position of the microparticle along z-axis
Fig. 7. A representative closed-loop motion control of a paramagnetic microparticle using a permanent magnet. The permanent magnet is fixed to theend-effector of a robotic arm. The microparticle is positioned within the vicinity of the reference position at an average speed of 117 µm/s, and the controlachieves maximum position error of 600 µm in the steady-state. This experiment is done in water inside a glass tube with inner diameter of 40 mm.
to control the microparticles inside the glass tube in 3Dspace. The workspace of our magnetic-based robotic systemis 13 mm, 10 mm, and 10 mm along x-, y-, and z-axis,respectively. The field-of-view of the microscopic system isset to 13 mm, 10 mm, and 10 mm along x-, y-, and z-axis,respectively. The maximum magnetic fields generated usingthe parament magnet and the electromagnetic coil are 85 mTand 7.5 mT, respectively. The magnetic fields are measured atthe center of the workspace using a calibrated 3-axis digitalTeslameter (Senis AG, 3MH3A-0.1%-200mT, Neuhofstrasse,Switzerland). The maximum magnetic field gradients withinthe workspace of the system are calculated to be 1.6 T/m and0.9 T/m for the permanent magnet and electromagnetic coil,respectively. Characteristics of our magnetic-based roboticsystem are provided in Table I.
B. Control using the Permanent Magnet
Point-to-point motion control of a paramagnetic microparti-cle is done by controlling the position of the permanent magnetsuch that the magnetic field gradients are oriented towardsthe reference position. Fig. 7 shows a representative motioncontrol result of a microparticles towards a fixed referenceposition. The microparticle is suspended and pulled towardsthe reference position at an average speed of 117 µm/s. Inaddition, we observe that the peak-to-peak amplitude of thesuspended microparticle along the z-component of the refer-ence position is 1.6 mm. Motion control of the microparticlescan be enhanced by reducing the attractive magnetic force.This reduction is done by replacing the permanent magnet withan electromagnetic coil. We repeat this motion control trial 20times and the average speed and position error in the steady-state are calculated to be 117 µm/s and 600 µm, respectively.
C. Control using the Electromagnetic Coil
Closed-loop motion control of paramagnetic microparticlesis achieved using an electromagnetic coil attached to the end-effector of the robotic arm. The position of the coil are
controlled to orient the magnetic field gradient towards thereference position. Also the current input to the electromag-netic coil is controlled to enhance the closed-loop controlcharacteristics of the controlled microparticles, as opposed tothe closed-loop control using the permanent magnet. Fig. 8shows a representative closed-loop control of a microparticles.The particles is controlled at an average speed of 255 µm/s,and the peak-to-peak amplitude along z-axis is calculated tobe 100 µm, in the steady-state. We repeat this motion controltrial 20 times and the average speed and position tracking errorin the steady-state are calculated to be 48 µm/s and 100 µm,respectively.
We observe that the speed of the controlled microparticlesusing the permanent magnet and the robotic arm is 41%higher than average speed of the microparticles driven usingthe electromagnetic coil (for maximum current of 0.6 A) andthe robotic arm. The difference in the average speed is dueto the maximum magnetic fields and field gradients that aregenerated using the permanent magnet and the electromagneticcoil, as shown in Figs. 3 and 5. The closed-loop control charac-teristics (steady-state error and peak-to-peak amplitude) of thecontrolled microparticles using the electromagnetic coil andthe permanent magnet are better than those of the permanentmagnet and robotic arm. The average peak-to-peak amplitudeof the controlled microparticles using the electromagnetic coilis 38% less than that achieved by the permanent magnet. Thisdifference is due to the current control input that allows usto change the magnitude of the pulling magnetic force bychanging the magnitude of the magnetic field gradient. Thisimprovement can not be done by controlling the microparticlesusing the permanent magnets.
D. Motion Control of the Microparticlesin the Presence of a Constrain on the End-Effector
We also demonstrate experimentally that microparticles canbe controlled in the presence of a constrain on the motion ofthe end-effector. We provide the end-effector with a reference
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(a) Position of the microparticle along x-axis (b) Position of the microparticle along z-axis
Fig. 8. A representative closed-loop motion control of a paramagnetic microparticle using an electromagnetic coil. The electromagnetic coil is fixed to theend-effector of a robotic arm. The microparticle is positioned within the vicinity of the reference position at an average speed of 48 µm/s, and the controlachieves maximum position error of 100 µm in the steady-state. This experiment is done in water inside a glass tube with inner diameter of 40 mm. (a)Position of the controlled microparticle along x-axis. (b) Position of the controlled microparticle along z-axis.
trajectory and the microparticles with a reference position.Therefore, the motion control system must provide stableposition tracking error for the microparticles and the end-effector at the same time. Figs. 9(a), (b), and (c) shows arepresentative motion control result of a pair of paramagneticmicroparticles under the influence of the controlled magneticfiled gradient. The field gradients are controlled by the cur-rent provided to the electromagnetic coil and the positionof the end-effector with respect to the microparticles. Theend-effector is constrained to follow a reference sinusoidaltrajectory that is shown in Fig. 9(c). This representative ex-periment shows that the magnetic-based robotic system movesthe microparticles towards a reference position, while the end-effector is simultaneously following a sinusoidal trajectory. Weobserve that the microparticles are controlled at an averagespeed of 46 µm/s. The maximum position tracking error forthe microparticles is calculated to be 100 µm in the steady-state along x-axis.
We provide the end-effector with a square-wave referencetrajectory, as shown in Fig. 9(d), (e), and (f). The magnetic-based robotic system moves the microparticles towards thereference position at an average speed of 42 µm/s, whilethe end-effector is following the square-wave trajectory. Themaximum position tracking error of the microparticles iscalculated to be 100 µm along x-axis in the steady-state.
IV. CONCLUSIONS AND FUTURE WORK
Point-to-point motion control of paramagnetic microparti-cles is achieved using a magnetic-based robotic system withan open-configuration. This system enables suspension ofthe microparticles along z-axis and achieves point-to-pointmotion control along a tube with a diameter of 40 mm. Ourexperimental motion control trails show that the permanentmagnet and the robotic arm achieve motion control at anaverage speed of 117 µm/s, whereas the electromagnetic coilsand the robotic arm achieve average speed of 48 µm/s. How-ever, the electromagnetic coils and the robotic arm achieve
higher positioning accuracy than the permanent magnet, inthe steady-state. The maximum error and the average peak-to-peak amplitude of the controlled microparticle using theelectromagnetic coil are calculated to be 100 µm and 1 mm,respectively. In addition, we demonstrate experimentally thatmicroparticles are controlled in 3D space in the presence ofa constrain on the end-effector. In clinical application, theconstrain represents a curvature of the human body that hasto be considered by the motion of the end-effector during thesuspension of the microparticle.
As part of future studies, our motion control system andexperimental setup will be adapted to include physical con-strains on the motion of the end-effector in the task-space. Thiswould allow us to control the motion of the microparticlesinside the glass tube while following a trajectory in thetask-space (to achieve axillary task, e.g., obstacle avoidance).In addition, our system will be modified by replacing themicroscopic vision system with a clinical imagine modality,and the motion control will be done in the presence of aflowing stream of a fluid to mimic the required environmentduring in vivo applications.
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Fig. 9. Motion control of paramagnetic microparticles in three-dimensional (3D) space using a magnetic-based robotic system. An electromagnetic coil isfixed to the end-effector of the robotic system to control the magnetic field gradient and the pulling magnetic forces exerted on the cluster of microparticles.These experimental results are done in the presence of constrains on the motion of the end-effector. The constrains are a sinusoidal (top row) and square-wave(bottom row) trajectories. This experiment is done in water inside a glass tube with inner diameter of 40 mm. (a) Controlled position of the microparticlesalong x-axis in the presence of a sinusoidal reference trajectory on the end-effector. The particles are pulled towards the reference position at an average speedof 46 µm/s. (b) Controlled position of the microparticles along z-axis in the presence of a sinusoidal reference trajectory on the end-effector. (c) Controlledmotion of the end-effector during the motion control of paramagnetic microparticles. (d) Controlled position of the microparticles along x-axis in the presenceof a square-wave reference trajectory on the end-effector. The particles are pulled towards the reference position at an average speed of 42 µm/s. (e) Controlledposition of the microparticles along z-axis in the presence of a square-wave reference trajectory on the end-effector. (f) Controlled motion of the end-effectorduring the motion control of paramagnetic microparticles.
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