IROS2019国际学术会议论文集 0839

Permanent Magnets based Actuator for Microrobots Navigation Manel Abbes1 2 Karim Belharet3 Hassen Mekki1and Gerard Poisson2 Abstract This paper presents a novel design of four per manent magnet based actuator for magnetic drug targeting of therapeutic microrobots Drugs are transported through therapeutic magnetic boluses composed of magnetic particles controlled by magnetic gradients In this study to maximize the effect of the treatment and minimize adverse effects on the patient a magnetic actuator have been developed to wirelessly control microrobots in a fl uidic environment using four external magnets Experimental validation is carried using the robotic arm Fanuc LR Mate 200iD to demonstrate the steerability of the magnetic microrobots under different trajectory constraints in viscous fl uidic environment Index Terms Magnetic actuator permanent magnet micro robot I INTRODUCTION Targeted drug delivery is a fi eld in full expansion leading to the ability to treat only the infected zones This helps minimizing drugs poor diffusion in targeted cells avoid ing risks of toxicity and maximizing the cures effi ciency Drug targeting using magnetic nanoparticles represents a promising and challenging new avenue for controlled drug delivery 1 2 They have a considerable capacity to easily cross tissue and blood barriers offering an intended delivery of drug to the infected cells This technique lasts for a short period of time and allows the diffusion of drugs in only targeted cells without causing any damage to the healthy ones Several researches have been conducted on the control of targeted drug delivery into the human body using magnetic source Mainly two solutions have proven to be the most interesting Electromagnetic Actuation EMA systems and permanent magnet actuation systems EMA systems are generally obtained with Helmholtz and or Maxwell coils The combination of these coils allows the manipulation of magnetic microrobots In 3 4 5 the authors used a combination of Helmotz and Maxwell coils for 2D actuation of magnetic microrobots inside body fl uids In 6 an EMA actuation system using the differential current coil approach was developped for steering magnetic nanoparticles in ves sels An EMA system with saddle coils was used in 7 for 3D locomotion of microrobot OctoMag a 5 DOF EMA system to wirelessly control microrobots was introduced in 8 However for the control of the microrobots in the case of biomedical applications these EMA systems require high 1 are with Laboratoire NOCCS Univ de Sousse Rue Khalifa Karoui 4054 Sousse Tunisie 2 are with the Laboratoire PRISME Univ Orl eans 18020 Bourges France 3 arewithLaboratoirePRISME Hautes Etudes d Ing enieur campusCentre SiteBalsan 2all eeJeanVaill e36000 Chateauroux France Correspondingauthor ManelABBES Email manel abbes yncrea fr Permanent Magnets Permanent Magnets Mechanical Structure Fig 1 Four permanent magnets based actuator prototype power consumption which results in the liberation of intense heat in the workspace and the need of a cooling system This will lead to a large systems volume and a very congested workspace Using permanent magnets instead of EMA devices allows to generate stronger magnetic fi elds and magnetic fi eld gra dients by a factor of 10 20 and 2 3 respectively depending on the workspace size 9 with no supplied power leading to no increase in temperature in the workspace Increasing the amplitude of the magnetic fi eld ensures faster motions for swimming robots 10 and magnetic crawling 11 12 while increasing the magnitude of the magnetic fi eld gradient results in stronger forces for magnetic pulling of microrobots Several systems using one more permanent magnets have been developed for micro robotic manipulation 13 used one single permanent magnet coupled to a robotic manipu lator to control the position 3 DOF and the orientation 2 DOF of a magnetic capsule endoscope in a fl uid A small permanent magnet was manipulated for three dimensional levitation movement of a microrobot was described in 14 Permanent magnet devices have shown the ability of 4 DOF capsule endoscopes control by using a hand held 15 or a robotic actuation 16 17 permanent magnet positioned outside the body But in many medical applications the abil ity of pushing away therapeutic microparticles is necessary whereas single magnets are only able to pull them in owing to magnetic fi elds and forces physics New confi gurations using several permanent magnets have been proposed to guide magnetic nanoparticles in biological fl uids Professor Shapiro has studied the possibility of in jecting magnetic particles in the inner ear of mousse using a combination of two permanent magnets 18 The work pre sented in 19 used an equivalent system to accumulate stem 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 978 1 7281 4003 2 19 31 00 2019 IEEE7062 cells coupled to Superparamagnetic Iron Oxide Nanoparticles SPION injected into cerebrospinal fl uid In our precedent work we have proposed a motorized actuator based on two permanent magnets to control the navigation of a microrobot in the cochlea 20 Although this confi guration based two permanent magnets has demonstrated its performances in the plane it does not ensure a symmetrical movement of the magnetic particle in the 3D space This can have conse quences on the accuracy of the magnetic particle control especially in the open loop navigation case as presented in 20 To ensure this symmetry in this work we propose a four permanent magnets based actuator for a wireless control of therapeutic microrobots Mounted on a robotic manipulator this actuator is able to guide magnetic particles in a fl uidic environment This paper is organized as follows Section I presents magnetic principles and modeling of the four magnets based actuator In section II simulations performed using MAT LAB software are discussed in order to evaluate the two magnets actuator and the proposed one Finally section III shows experimental results of actuating a spherical particle in a viscous fl uidic environment II MAGNETIC PRINCIPLE Magnetic control technique uses the magnetic interaction principle between two or more objects In our case perma nent magnets placed at a defi ned position in the workspace are the source of the generated magnetic fi eld while magnetic particles are subjected to the same fi eld Introducing the parameters of the magnetic fi eld B The magnetization M characterizes the magnetic object representing the magnetic moment density in a material The magnetic excitation H Thus the total magnetic fi eld B can be expressed as follows B 0 M H 1 where 0is the vacuum s magnetic permeability M depends on H and the magnetic susceptibility so that B can be written as B 0 1 H 2 The magnetic fi eld leads to the presence of a magnetic force applied to the different magnetic objects In the case of magnetic microrobots actuation we use magnetic force or and torque to guide particles The magnetic force and torque that act on the magnetized particle can be expressed as follows 21 Fm Vm M B Vm 1 3 H H 3 m Vm M B 4 Where Vmis the volume of the magnetized object B represents the magnetic fi eld s fl ux density and M the object s magnetization However when using spherical particles which is the case in our study a major simplifi cation takes place Due to the particle s shape the magnetic fi eld B and the vector of magnetization M are always aligned Thus the particle does not undergone any magnetic torque This allows to deduct that the magnetic force depends only on the magnetic fi eld s magnitude 22 such as Fm Vm M B 5 Using one single permanent magnet the magnetic gradient generated by the applied magnetic fi eld is oriented to this later So any particle positioned in the workspace will be attracted by the permanent magnet Indeed magnetic forces are proportional to the magnetic fi eld s gradient according to equation 3 This means that the force depends on the strength of the magnetic fi eld and directed from low to high region Therefore to create a push force we need to generate a local minimum of magnetic fi eld denoted Lagrange point where all the magnetic forces are cancelled Indeed the magnetic fi eld strength decreases until being canceled at this equilibrium node then increases again from the same point In 18 authors demonstrate the ability of creating this local minimum of magnetic fi eld using two permanent magnets So any particle positioned around this minimum will be pushed away to the zone of higher magnetic fi eld s strength Although the capacity of pushing and pulling particles using this structure of two permanent magnets the control is only possible along the actuator s axis In fact this capacity can only be achieved on the actuator s axis which means that to push a particle there is a need of a perfect positioning accuracy in order to align the axis of the actuator with the magnetic object Based on this we assume that when positioning four permanent magnets as shown in Fig 4 at a defi ned distance each two opposite magnets will generate a magnetic fi eld resultant that is equal to zero at a distance This cancellation of the magnetic fi eld strength allows to create opposite forces around the local minimum of magnetic fi eld point Then since the four magnets structure is the assembly of two identical systems composed of two magnets each we will have the same behaviour on both planes xz and yz Its particularity is also the possibility of creating push and pull forces around the axis of the actuator with less movements that are also less complicated A single rectangular permanent magnet generates a mag netic fi eld in three dimensions at a point x y z such as Bi x y z f x y z px py pz 0 M 6 Where the position and orientation vectors of the magnet are respectively given by px py pz and 0denotes the permeability of the vacuum and M is the magnet s magnetization The directions of the resultant magnetic forces can be determined from the resultant magnetic fi eld strength expres sion as we mentioned before that magnetic force goes from 7063 low to high magnetic fi eld strength However calculating the total magnetic fi eld gradient at a point in the three dimensional space requires transformation between reference systems Therefore we express each magnet in its own frame then we calculate the total magnetic fi eld gradient in a common fi xed frame We express the magnetic fi eld of each magnet in the common frame using the following rotation matrix xn yn zn cos n sin n 0 sin n cos n 0 001 x y z 7 such as B xn yn zn Bxn xn yn zn xn Byn xn yn zn yn Bzn xn yn zn zn 8 Where n is the number of the magnet and is the magnet s angle of tilt Thus we obtain Btot x y z Btotx x y z x Btoty x y z y Btotz x y z z 9 Where due to magnetic fi elds additive property Btotx x y z P4 n 1Bxn x y z Btoty x y z P4 n 1Byn x y z Btotz x y z P4 n 1Bzn x y z 10 Then we can express the gradient of the magnetic fi eld as follows Btot Btot x Btot y Btot z 11 III FOUR PERMANENT MAGNETS BASED ACTUATOR A Two permanent magnets limits The 1 DOF permanent magnets based actuator cited pre viously was developed in our laboratory for targeted drugs delivery with magnetic particles in the inner ear Fig 2 The system is composed of two permanent magnets arranged in z cm x cm y cm Fig 2 Two magnets actuator confi guration a specifi c combination inspired by 18 This confi guration allows to generate both push and pull forces along the actuators s axis In fact the transition from an attractive force to a repulsive one takes place when arriving at a point where all the magnetic forces are null these points are called Lagrange points On the actuator s axis we have two exploitable lagrange points L1 and L2 see Fig 3 L1 is called unstable equilibrium point because of the divergence of magnetic forces from this position whereas L2 is called stable equilibrium point It represents a point of convergence of the magnetic forces which also corresponds ta a trapping zone of the magnetic microrobots Thus trapping micro robots in a defi ned workspace point allows their control until reaching the target The actuator is able to control the L2 point position in the workspace This allows steering magnetic particles to the target by exploiting the transition between push and pull forces However experiments and simulations showed some limits of this actuator We noticed that the magnetic forces converge to a fi xed point only in one single plane which means we can only control the particles in this plane see Fig 3 Thus it is compulsory to position the actuator s axis on the desired direction with signifi cant accuracy Indeed if the particle is off the axis the actuator is not able to neither push or pull microrobots So the actuator requires to be coupled to a positioning system with a very high accuracy to be effi cient Therefore a minimal error in the planning or in the positioning of the actuator may compromise the guidance procedure B Four permanent magnets combination The proposed system is a four magnets based actuator able to wirelessly steer particles in fl uidic environment Fig 4 Compared to the two magnets actuator it has a symmetrical behavior in the two planes xz and yz Fig 5 This allows to generate magnetic forces that converge to a fi xed point in both planes which facilitate the control of microrobots In addition this confi guration allows a margin of about 2cm around the axis where magnetic forces still converge 7064 5 4 3 2 101234 x c m 0 1 2 3 4 5 6 7 8 9 z c m M a g n e tic F o r c e 5 4 3 2 101234 y c m 0 1 2 3 4 5 6 7 8 9 z c m M a g n e tic F o r c e a b Linear vectors in the push zone No linear vectors in the push zone L2 L1 L2 L1 Fig 3 Magnetic forces vectors generated by two magnets actuator which dimensions are 1 5 5 1 5cm a xz plane b yz plane x cm y cm z cm Fig 4 Four magnets actuator confi guration towards the equilibrium zone see Fig 5 This margin makes possible to control the movement of a microrobot despite an error in the positioning of the actuator Increasing the number of the permanent magnets also makes it possible to move the position of the stable Lagrange point L2 from the center of the magnets frame as shown in see Fig 5 Here the point L2 is situated at 8cm from the structure s center whereas in the two magnet confi guration the stable point L2 is situated at a distance of 5 2cm from the magnets However while maximizing this distance we have to make sure that the magnetic fi eld strength generated by the magnets maintains suffi cient So it s clear that magnetic forces generated by the novel actuator are more important than the ones generated by the two magnets based actuator while ensuring that the magnetic force strength is suffi cient to steer the microrobot to the stable equilibrium node Fig 6 c d shows the distribution of magnetic fi eld vec tors around the stable equilibrium point L2 that represents the magnetic force s local minimum The stable equilibrium node is situated at a distance of 8cm from the center of the magnet s frame Analyzing the strength of the magnetic fi eld we noticed that the actuator s infl uence zone is situated between z 7cm and z 9cm with a margin along x axis of 2cm x 1cm to x 1cm 5 4 3 2 101234 x c m 2 3 4 5 6 7 8 9 z c m 5 4 3 2 101234 y c m 2 3 4 5 6 7 8 9 z c m Linear vectors in the push zone Linear vectors in the push zone a b L2 L1 L2 L1 Fig 5 Magnetic forces vectors generated by four magnets actuator which dimensions are 6 3 1 5cm a xz plane b yz plane Magnetic Force 2 1 5 1 0 500 511 52 y cm 4 5 5 5 5 6 6 5 z cm Magnetic Force 2 1 5 1 0 500 511 52 x cm 4 5 5 5 5 6 6 5 z cm Magnetic Force 2 1 5 1 0 500 511 52 y cm 6 5 7 7 5 8 8 5 9 9 5 z cm Magnetic Force 2 1 5 1 0 500 511 52 x cm 6 5 7 7 5 8 8 5 9 9 5 z cm a b c d Fig 6 Isolines of magnetic force strength around the convergence point with the direction of the magnetic force a two magnet system plane xz b two magnet system plane yz c four magnet system plane xz d four magnet system plane yz IV EXPERIMENTAL VALIDATION In this section two experiments were realized to validate the proposed four magnets actuator and its capacity to push and pull a particle toward and from the local minimum of the magnetic fi eld strength The fi rst experience aims to demonstrate the ability to push pull particles even though the later isn t positioned on the actuator s axis with a margin of about 6mm The second one shows the actuator s capacity of actuating particles along the vertical axis perpendicular to the actuator s axis To perform experiments we realized a fi rst prototype of the four permanent magnets based actuator using a 3D printer see Fig 1 The latter is mounted at the end effector of the robotic manipulator Fanuc LR Mate 200iD as a micropart to assure an accurate control of magnetic particles A microscope was used to track the particles motion The radius of the spherical particle used is r 0 25mm positioned in a viscous fl uidic environment a mixture of glycerin and water In the fi rst experience the particle is positioned in a linear microfl uidic chip with 3 channels see Fig 7 The actuator 7065 1st channel 2nd channel 3rd channel 6mm Workspace Magnetic Actuator Robotic Arm Microscopes x y z First stage Second stage Third stage Apex Artificial cochlea Linear chip with three channels Fig 7 Experimental setup used to validate the performances of the proposed magnetic actuator is positioned manually relative to the chip Then we slightly move the actuator only along the x axis towards the chip until getting a suffi cient force able to push magnetic particle We repeated the same experience in the three channels keeping the same y and z position of the actuator The results are shown in Fig 8 In each channel we extracted three positions of the particle during its motion towards and from the equilibrium point push pull force As predicted this experience shows the ability of the actuator to control particle