Magnetically Actuated Continuum Medical Robots: A Review

The magnetic field has unique advantages in manipulating miniature robots working inside the human body, such as high transparency to biological tissue and good controllability for field generation. Generally, the actuated magnetic robot can be classified into two categories: tethered devices like intravascular microcatheters and untethered devices like helical swimmers. Among these, the tethered devices have a long history and good clinical application prospects, considering their high‐dose delivery and easy removal after the procedure. As an evolution of traditional continuum medical devices, the integration with magnetic actuation provides them with better scalability and improved dexterity. Although rapidly developed in the last two decades, the field of tethered magnetic robots requires further advancements in terms of design, fabrication, modeling, and control, especially for clinical applications. Herein, the recent progress of magnetically actuated continuum medical robots is focused on, intending to offer readers a comprehensive survey of the state‐of‐the‐art technologies and an information collection for future system design.

The magnetic field has unique advantages in manipulating miniature robots working inside the human body, such as high transparency to biological tissue and good controllability for field generation. Generally, the actuated magnetic robot can be classified into two categories: tethered devices like intravascular microcatheters and untethered devices like helical swimmers. Among these, the tethered devices have a long history and good clinical application prospects, considering their high-dose delivery and easy removal after the procedure. As an evolution of traditional continuum medical devices, the integration with magnetic actuation provides them with better scalability and improved dexterity. Although rapidly developed in the last two decades, the field of tethered magnetic robots requires further advancements in terms of design, fabrication, modeling, and control, especially for clinical applications. Herein, the recent progress of magnetically actuated continuum medical robots is focused on, intending to offer readers a comprehensive survey of the state-of-the-art technologies and an information collection for future system design.
designed to cure cardiac arrhythmia and has treated over 130 000 patients at more than 100 hospitals worldwide. [19] In contrast, the exploration of magnetically actuated miniature robots (MMRs) has facilitated the booming of MCRs. Generally, MMRs refer to tiny agents controlled by external magnetic fields with dimensions ranging from micrometers to millimeters, which could be further classified into two categories: tethered devices and untethered devices. [20,21] MCRs belong to the tethered ones and have good clinical application prospects, considering their high-dose delivery and easy removal after the procedure. The design with no bulky onboard power or actuation components makes miniaturization possible. [22] Furthermore, the external magnetic field has unique superiority for manipulating devices inside the human body, which is transparent to biological tissue and can be accurately controlled, thus ensuring enhanced flexibility and multifunctional design. [21,23] CRs and magnetic actuation are two of the decade's popular topics in medical robotics. [24] As a hybrid technology, MCRs possess integrated advantages that include the following: 1) less stiffness reduces the risk of tissue trauma and puncture; 2) simple structure without complex inner channels allows for extreme miniaturization; and 3) rapid response to the external magnetic field increases flexibility. Therefore, MCRs have been widely studied for minimally invasive procedures, especially endoluminal and intravascular, where instrumental flexibility is crucial for safe access and navigation to the lesion over long distances, considering the intricate nonlinear luminal boundaries. [25][26][27] Although surveys of magnetic microrobots and continuum manipulators have been presented separately in previous reviews, [2,3,20,22,23,[28][29][30][31][32][33] a comprehensive investigation on the overlapping topic that is MCRs is still absent, which is necessary considering its great attention and rapid development.
This review focuses on the recent progress of MCRs for medical applications, intending to provide readers with a comprehensive survey of the state-of-the-art technologies and an information collection for future system design. To begin with, the physics behind and implementation of magnetic control are briefly introduced. Then, state-of-the-art MCRs are introduced by category according to their structure and function. Subsequently, mainstream modeling, localizing, and control method are presented. Finally, conclusions and outlooks are discussed.

Force and Torque
Generally, external magnetic fields are designed for transmitting power through the following two technologies. One method is using high-frequency time-varying magnetic fields to induce currents, offering a wireless method for electricity generation. The other way is utilizing low-frequency quasi-static magnetic fields, directly applying force and torque to the magnetic component. [28,34,35] Most designs of MCRs adopt the second approach with governing equations written as ( Figure 1) where F m is the magnetic force in Newton (N); T m is the magnetic torque in Newton meter (N·m); V m is the magnetization volume in cubic meters (m 3 ); m is the internal magnetization in Ampere per meter (A m À1 ); B is the flux density of the external field at the integral point in Tesla (T), which can also be described by where μ 0 is the permeability of the free space that equals 4π Â 10 À7 T m A À1 ; H is the field intensity in Ampere per meter (A m À1 ). [36] When the overall dimension of the magnetic object is relatively small compared with the spatial variation of the external magnetic field, the aforementioned relation can be simplified as where M is the total dipole moment of the controlled object, the unit of which is in Ampere meter (A m). Maxwell's equations could be utilized for simplification, and Equations (4) and (5) An intuitive explanation could be presented from the relationship: the magnetic force exists only in the presence of the field gradient, which tends to move the object in the magnetic field to the position of local maximum; the magnetic torque exists when there is an intersection angle between the magnetization of the object and that of the magnetic field, which tends to align the former with the latter. Adapted under the terms of the CC BY 4.0 license. [21] Copyright 2022, The Authors, Published by Wiley.

Classification
Generally, magnetic tools can be subdivided into two categories: tethered devices and untethered devices ( Figure 2). [20] Tethered devices refer to those wired tools composed of the magnetic tip and the following continuum structure, which immerse a section of the instrument inside the human body and leave a segment outside, with a diameter ranging from micrometers to millimeters. The magnetic part remains inside for angle steering and other magnetic response. The continuum structure can be designed for various purposes, such as delivering drugs, transmitting power and signal, and providing working channels for tools. Examples of the tethered device include but are not limited to magnetic catheters, [37,38] magnetic endoscopes, [27,39] and magnetic probes. [40,41] Untethered devices refer to those wireless robots that fully immerse in the human body during the procedure, with an overall dimension ranging from micrometers to millimeters. The absence of wire constraints and miniatured size enable these tiny agents to go through narrow and tortuous human body regions where traditional surgical approaches are hard to reach. [42,43] Various untethered devices are developed, such as screw-like swimmers mimicking bacteria, [44][45][46] flexible oar-like swimmers imitating spermatozoa, [47,48] surface walkers using even boundary effect, [49][50][51] soft-bodied robots locomoting by self-deformation (e.g., insect-like crawling, multilegged walking, a jellyfish-like swimming), [52][53][54][55] and microrobot swarm utilizing the combination of agent-agent effect, fluidic force, and other interactions. [56][57][58][59]

Design Concept
MCRs belong to the tethered category, having higher dose delivery, faster movement speed, less sensitivity to the flow rate, and better reliability that can be easily taken out from the human body through pulling. For most MCRs, the forward-backward movement is mainly dominated by the tether via manual operation or mechanical advancers. The latter solution could free physicians from radiation and offer accurate insertion control, for example, a modified linear feed mechanism and a compact box with pairs of drive pulleys. [37,38] Meanwhile, tip steering is primarily accomplished by the magnetic wrench, which is the combined force and torque that the external magnetic field exerts on the magnetized object. Also, there are soft-tethered MCRs, of which proximal end feeding control is to assist in advancing the tethered into the human body with the distal end magnetic dragging force. [60,61] In addition, there are novel designs with hybriddriven strategies, which will be introduced in Section 3.1.
Magnetic components must be integrated into the MCRs to respond to the external magnetic fields. There are mainly four types, with the latter two designed for magnetic resonance imaging (MRI) scanners ( Figure 3). The most commonly used one is the permanent magnet. In these designs, one or multiple smallscale permanent magnets with a size ranging from micrometers to millimeters are attached to the distal of the MCR. Permanent magnets have high saturation magnetization, enabling the robot to respond strongly to external magnetic fields, for example, a large deforming angle or dragging force during actuation. This feature is important considering the magnetic field and field gradient attenuate rapidly with the distance, leading to increasing the density of the external field challenging, especially for largeworkspace implementation. [62,63] In addition, permanent magnets can be custom designed and mass-produced, making them good candidates for commercial products. In recent years, magnetic micro-or nanoscale particles have been widely used in MCRs, which are dispersed in and trapped by the soft polymer matrix to form the magnetic elastomer. The overall structure serves as the steerable tip, making minimization down to the submillimeter possible. The distribution density of the particles and the magnetization orientation of the elastomer can be programmed to deform into task-oriented shapes, further increasing its flexibility.
The third type uses ferromagnetic spheres that have no magnetization in magnetic field-free spaces but can be magnetized in the magnetic field. It has configurations similar to permanent magnet-based ones, and the mounted magnetic component can induce a large magnetic force when exposed to the magnetic field gradient. Micro coils are the fourth type that can be single or multiple axial according to the number and distribution of coils. The magnetic moment of each coil is proportionate to the current, and the overall magnetic moment obeys the superposition law, decided by powering currents as Figure 2. The classification of magnetically actuated miniature robots (MMRs) according to configuration and operating mode: tethered devices and untethered devices.
where k is the number of coils; N i is the turn of the i th coil; I i is the input current of the i th coil in Amperes (A), A i is the crosssectional vector area of the i th coil in square meters (m 2 ). [64] These instruments can be manipulated under constant magnetic fields by changing their owing magnetization.

Potential Application
MCRs have demonstrated high potential in medical applications across the body (Figure 4), which enables safe diagnosis and therapy by improving the flexibility of instruments and reducing the physical stress on tissue and organ. [65] Conventional brain surgery employs rigid and straight devices, constraining the possible paths between the entry point and the target point to a straight line. [66] The development of flexible magnetic probes and needles allows for various curved paths, providing more freedom for the surgeon to select the entry point and the access path. Therefore, a safer route can be planned to avoid damage to vital tissue and neural structures. [40,41,67] Transoral bronchoscopy is widely used in respiratory system pathologies. For example, effective lung biopsy is important evidence for early lung cancer diagnosis. [68] However, traditional bronchoscopy can only move along the bronchial tree of the lung while leaving the deeper region unreachable. Magnetic bronchoscopy is a promising candidate for providing a Figure 3. The concept diagram of magnetically actuated continuum robots (MCRs). Mainstream designs consist of a flexible body at the base for forward-backward motion and a magnetic component at the tip for magnetic actuation. The magnetic components are mainly four types: permanent magnet, magnetic particle (mixed into polymer matrix), ferromagnetic sphere, and micro coil. www.advancedsciencenews.com www.advintellsyst.com more consistent and stable intervention procedure, benefitting from its smaller diameter and enhanced flexibility. [39,69] Continuum instruments have a long history of treating vascular disease. In a conventional procedure, physicians deliver guidewires and catheters to the target lesion within the aorta and peripheral vascular system, [38,[70][71][72] the cerebral vascular system (interventional neuroradiology), [17,73] and the cardiac vascular system (interventional cardiology), [37,74,75] by manual operation at the proximal end with combined back-and-forth pushing and base rotation. [76] Lots of magnetic guidewires and catheters have been developed for endovascular interventions. The magnetic solution allows for improved accuracy and precision that enables better outcomes. It also reduces radiation exposure and contrast agent dosage by adopting remote control and cutting procedural times.
Steerable devices also possess the potential for the intervention of the urogenital system, such as the bladder, kidney, and fallopian tube. [77] The small diameter and good flexibility allow for the surgery to further reduce invasiveness via natural orifices for accessing pathology. For example, travel through the narrow and long ureter to perform retrograde intrarenal surgery. [78] In addition, MCRs have been explored to enter small organs of the sensory system for various treatments. Examples include the endolaser probe for panretinal photocoagulation and the microcannula for subretinal injections to treat retinal disorders, [79,80] the micro driller for nasolacrimal duct recanalization, [81] and the slotted tube for placing cochlear-implant electrode arrays (EAs). [82] These small-scale steerable apertures demonstrate high dexterity and considerable safety advantages over rigid tools, potentially reducing the risk of complications and improving precision.
Most of the current screening of the gastrointestinal (GI) tract is conducted via conventional gastroscopes and colonoscopes. Although clinically effective, the diagnostic procedure may cause tissue damage and patient discomfort. Wireless capsule robots are an alternative solution and have scored tremendous achievements, whereas most of their applications are limited to screening. [83,84] The development of MCRs shows advantages to making the surgery procedure safer and more comfortable without sacrificing the necessary functions, such as imaging, suction, biopsy, and delivery. [60,65,85] In addition, the miniature size and enhanced flexibility enable the device to enter complex structures such as the bile duct and gallbladder. [86]

Magnetic-Actuation Platform
The magnetic-actuation platforms have been summarized in previous surveys. [21,62] This section briefly reviews the existing systems, providing a general view of driven implementation. For more technical details, readers could refer to mentioned surveys on the specific topic. Especially, the description of the platforms is categorized according to the field generation ability, some recently developed systems are included, and commercial platforms are highlighted.

Platform with Flexible Field Generation
Numerous magnetic-actuation systems have been developed that can produce magnetic fields and/or field gradients with a desired magnitude and orientation. They can be further classified into different groups according to the type of magnetic source (e.g., permanent magnet, electromagnet), the feature of configuration (e.g., single, paired), and the ability of motion (e.g., stationary, movable). For most permanent magnet-based platforms, the magnetic field at the working point is adjusted by changing the position and/or orientation of one or multiple permanent magnets. The multi-DOF industrial robotic arm is commonly used as the driven mechanism of permanent magnets to produce static magnetic fields (Figure 5a). [27,60,[87][88][89][90] A customized mechanism can be further introduced as the end actuator to provide extra DOFs, through which the permanent magnet can rotate along itself when driven by the robotic arm to produce dynamic magnetic fields. [91][92][93] Recently, a dual-arm robotic platform has been proposed, realizing control with a maximum of 8 DOF through collaborative magnetic manipulation, which is up to 5 DOF in the previous single permanent magnet system (Figure 5b). [94,95] For most electromagnet-based platforms, the magnetic field at the working point is decided by powering different currents into the paired coils or distributed electromagnets. Examples of paired coils include the Helmholtz coil pair, Maxwell coil pair, uniform saddle coil pair, gradient saddle coil pair, Golay coil pair, and their combinations. [96][97][98][99][100][101][102] The scale-up issue, increasing the workspace from on-table equipment to clinical applications, is still challenging due to limitations of energy efficiency and configuration layout. The systems with paired coils usually tend to enclose the workspace via coils that are generally in discal shape, allowing convenient control since the magnetic field is insensitive to the working position, while most of the systems with distributed electromagnets have columnar coils inserted with soft-iron cores that position around and point to the workspace, mitigating the limitation of energy efficiency and configuration layout limitations. The OctoMag system is the first representative system with eight electromagnets designed for intraocular treatment ( Figure 5c). [103] Following this idea, diverse systems using distributed electromagnets have been developed, possessing different numbers of coils and layouts ( Figure 5d). [104][105][106][107][108][109][110][111] Systems with different configurations show one or multiple priorities among magnetic torque control, magnetic force control, accommodation to the human body and imaging equipment, scaling issues, and energy efficiency.
Recently, some newly devised mobile electromagneticactuation systems have been proposed, which have simultaneous good on-off manipulability and can cover a working area with tens of centimeters, showing potential MCR steering tasks for clinical applications. One example is the advanced robotics for magnetic manipulation (ARMM) system, in which an electromagnet is mounted on a serial robotic arm. The direction of the magnetic field still depends on the pose adjustment, while the lightweight may offer enough space for medical operation (Figure 5e). [71,112,113] Another platform is the DeltaMag system, which integrates an array of three electromagnets into a parallel manipulator (Figure 5f ). [114][115][116] The enlarged workspace is realized by motion control, and the field generation is achieved by current control. It has the ability to produce both static and dynamic magnetic fields. The RoboMag system also has three electromagnets that are driven by three serial robotic arms separately ( Figure 5g). [117][118][119] The configuration enables multimode magnetic control and integration with clinical imaging equipment.

MRI Scanner
MRI was introduced into standard medical practice in the 1980s. This technology is based on the phenomenon of nuclear magnetic resonance (NMR) that utilizes strong magnetic fields and radio waves to image nuclei of atoms inside the body, providing good contrast between different soft tissues. [120] A typical MRI scanner has a main magnetic body for generating a strong static field, shim coils for increasing the uniformity of the main field, gradient coils for briefly adjusting the magnetic field, and radio-frequency (RF) coils for transmitting and recording signals. The main magnetic body can be further divided into three categories: standard electromagnet, permanent magnet, and superconducting magnet.
Researchers have found that this widely used clinical equipment can be employed for simultaneous magnetic actuation and imaging with software and/or hardware upgradation ( Figure 5h). [121][122][123] From the actuation point of view, a typical MRI scanner during operation can generate a single-directional high-intensity uniform magnetic field and a 3D controllable magnetic field gradient. Because the magnetic field generation of the MRI scanner is not as flexible as that of the aforementioned customized platforms, potential MCRs need to be specially designed, for example, the ferromagnetic spheres-based instrument that is driven by the magnetic field gradient, and the micro coil-based device with current-decided magnetization that is actuated by the constant magnetic field.
Recently, the fringe field has been proposed and investigated, which emanates outside a clinical MRI scanner and is produced by the superconducting magnet, featured by strong magnetic gradients. [124,125] Since superconducting magnets are bucky Figure 5. Laboratorial magnetic-actuation platforms. a) The system with one robotic arm and a permanent magnet. b) The system with dual robotic arms and two permanent magnets. c) OctoMag system with eight electromagnets. d) Schematic diagram showing platforms with different coil numbers and distributions. e) Advanced robotics for magnetic manipulation (ARMM) system with a robotic arm-driven electromagnet. f ) DeltaMag system with three parallel mechanism-driven mobile electromagnets. g) RoboMag system with three robotic arm-driven mobile electromagnets. h) Small-animal magnetic resonance imaging (MRI) scanner. Panel (a): Adapted with permission. [27] Copyright 2020, Springer Nature. Panel (b): Adapted with permission. [94] Copyright 2022, IEEE. Panel (e): Adapted with permission. [72] Copyright 2022, IEEE. Panel (f ): Adapted with permission. [38] Copyright 2021, IEEE. Panel (g): Reproduced with permission. [117] Copyright 2021, IEEE. Panel (h): Adapted under the terms of the CC BY license. [121] Copyright 2021, The Authors, published by Wiley. and fixed, the operation relies on the positioning and orientation of the patient around the MRI scanner, pulling the magnetic tip of instruments toward the desired direction.

Commercial Platform
Commercially available preclinical and clinical magneticactuation platforms have been proposed. The most famous one is the Niobe system released by Stereotaxis Inc. (Missouri, USA) in 2003 (Figure 6a). [19,126,127] The core of magnetic actuation has two focused-field permanent magnets that are mounted separately on two customized robotic arms. The permanent magnets can rotate inside the housing, and each hous ing is tiltable, creating a uniform magnetic field in the central region with controllable orientation. This system is initially designed for guiding magnetic catheters to treat cardiac arrhythmia, which has treated over 130 000 patients at more than 100 leading hospitals worldwide. Results show improved safety, precision, efficacy, and outcome. [128,129] Recently, Stereotaxis Inc. released the Genesis system with a lighter, faster, and more flexible architecture with smaller magnets that rotate along their center of mass ( Figure 6b). The entire system is significantly smaller, allowing for greater access to the patient and allowing for unprecedented responsiveness to the physician's command. It is reported that the Genesis system is 70-80% faster than the Niobe system.
The catheter guidance control and imaging (CGCI) system developed by Magnetecs Corp. (California, USA) is electromagnet based, which is designed for use in catheter ablation. The system is composed of eight electromagnets that are distributed spherically, with four arranged above and four placed below the patient bed ( Figure 6c). [130][131][132] The configuration of the electromagnets fulfills isotropic magnetic field generation.
However, the huge electromagnets almost encapsulate the workspace, limiting access to the patient during the operation. Aeon Scientific AG (Zurich, Switzerland) released the Aeon Phocus system, which is used for the treatment of cardiac arrhythmias. The system has seven electromagnets fixed on two movable frames, with four arranged on one side and three placed on the other (Figure 6d). [16,74,133] During operation, the frames enclose the patient body from both sides for magnetic actuation and separate to offer space for medical imaging and surgeon intervention.

Magnetic Continuum Robot
This section will summarize the state-of-the-art MCRs. It will begin with the routine designs that perform as conventional continuum devices but with the capacity of active angle steering, followed by functional instruments with better performance or clinical treatment. The last part is about devices with hybridactuation designs that integrate the benefits of other driven mechanisms, such as tendon driven, concentrate tube driven, and flow driven. In the first part, the MCRs are subdivided into three categories according to the applications.

Magnetic Guidewire and Catheter
Permanent Magnet Based: The earliest attempt at magnetically guided catheterization could date back to the 1950s when Tillander attached small steel links to the tip of a catheter and used electromagnets to explore magnetic steering. [18] From the 1960s to 1980s, several groups explored various magnetically Figure 6. Commercial magnetic-actuation platforms. a) Niobe system. b) Genesis system. c) The catheter guidance control and imaging (CGCI) system. d) Aeon Phocus system. e) Concept diagram of the magnetic field sources with respect to the patient for systems (a)-(d), respectively. Panel (c): Reproduced with permission. [131] Copyright 2013, Elsevier. Panel (d): Reproduced under the terms of the CC BY 4.0 license. [16] Copyright 2019, The Authors, published by Wiley.
www.advancedsciencenews.com www.advintellsyst.com steered continuum instruments, as discussed in a review provided by Driller et al. [134] In recent years, catheters, guidewires, and flexible mock-up tubes have been equipped with permanent magnets at the tip for magnetic steering. These devices can align themselves with external magnetic fields for different deflection orientations, delivering significant progress in improving flexibility and accuracy. [112,[135][136][137][138][139] Neodymium magnet (NdFeB), an alloy of neodymium, iron, and boron, is widely utilized due to its advantages of strong magnetization and easy fabrication. [140] An example is the magnetic micro guidewire composed of a 0.014 in. guidewire and a 2 mm long small permanent magnet ( Figure 7a). [135] The configuration of equipping multiple permanent magnets distributed along the tip has also been explored. [106,111,141,142] For instance, Armacost et al. proposed Figure 7. Magnetic guidewires and catheters based on permanent magnets and magnetic particles. a) A magnetic micro guidewire with a permanent magnet. b) A magnetic catheter with three permanent magnets. c) A magnetic catheter with a string-like tether. d) A magnetic guidewire with a core-shell structure. e) A magnetic guidewire with a large deformation angle. f ) A ferromagnetic soft CR. g) The soft robot for minimally invasive bioprinting. h) A magnetic catheter with braided reinforcement. i) A patient-specific magnetic catheter. Panel (a): Reproduced with permission. [135] Copyright 2006, Springer Nature. Panel (b): Adapted with permission. [106] Copyright 2016, Wiley. Panel (c): Reproduced with permission. [133] Copyright 2017, IEEE. Panel (d): Reproduced with permission. [38] Copyright 2021, IEEE. Panel (e): Adapted under the terms of the CC BY 4.0 license. [37] Copyright 2019, The Authors, published by Mary Ann Liebert. Panel (f ): Adapted with permission. [17] Copyright 2019, AAAS. Panel (g): Adapted under the terms of the CC BY license. [145] Copyright 2021, The Authors, published by Springer Nature. Panel (h): Reproduced with permission. [86] Copyright 2022, IEEE. Panel (i): Reproduced with permission. [73] Copyright 2020, IEEE.
www.advancedsciencenews.com www.advintellsyst.com a three-magnet-tip catheter, which had the ability to generate a more significant deflection and a more rapid turning compared with the single-magnetic design (Figure 7b). [106] They also derived a comprehensive mathematical model to predict the position and deflection of the catheter, taking both the magnetic torques and forces into consideration. Lin et al. devised a catheter with two opposite-magnetized magnets. Different from the design in which all magnetizations of magnets are in the same direction, this device possessed multiple control modalities under the control of an external mobile magnet. [142] The deflection shapes among C-shape, S-shape, and J-shape were achieved by applying different magnetic torques and forces. This catheter showed superiority in obstacle avoidance to reach the target region behind, improving dexterity and a larger reachable workspace than uniform-magnetized MCRs. They further developed a mathematical model coupling point-dipole field model and energy-based kinematics to describe the multimode deformation, which could be modified to calculate deformation for other CRs. Derivative designs are investigated from the basic concept. Chautems et al. devised a catheter for treating cardiac arrhythmias, in which a magnet was connected to its distal end by a string-like tether (Figure 7c). [133] The tethered magnet could extend from the distal end. Therefore, the tension on the tether would be transferred to the force on the contact point with the heart wall while the tether was extended, enabling precise force control independent of the catheter bending radius and insertion length. This innovative concept provided a controlled space with additional DOFs and force control. They also presented a steerable magnetic sheath. [75] In specific, a permanent magnet was attached to the distal tip of the introducer sheath rather than the catheter. In this design, the tip orientation was decoupled from the catheter insertion, enabling more robust and intuitive manipulation of the catheter.
Soft materials, such as elastomers and hydrogels, are good candidates for fabricating steerable tips due to their good elasticity and deformability. Yang et al. proposed a magnetic steerable guidewire composed of a rigid shaft and a flexible tip (Figure 7d). [38] The tip was made of polydimethylsiloxane (PDMS) via the replica-molding method. The guidewire had a core-shell structure, balancing the stiffness of the two parts for effective steering and avoiding tip fracturing during operation. Furthermore, ultrasound (US) imaging was introduced into the intervention procedure for real-time monitoring. Jeon et al. presented a magnetic guidewire, the attached tip component of which consisted of a beam silicone (PDMS), two NdFeBs, and a connection microspring (Figure 7e). [37,143] The magnetic guidewire has an overall diameter of less than 1 mm. They developed a finite-element analysis (FEA)-based mathematical model, successfully estimating its deformation with high accuracy. The prototype guidewire had large deformation with a maximum angulation of 132.7°, and showed good performance when evaluated in 2D and 3D blood vessel phantoms.
Liu et al. proposed a robotic catheter with tuning steerability. [144] Instead of using soft materials as the deforming segment, this manipulator adopted heat shrink tubing with different flexural patterns. Except for the external magnetic interaction loads acting on the robot, the designed flexural patterns had a critical role in the deformation behavior and steerability. They further developed a novel and generic multiphysical framework and iterative solution algorithm to evaluate the performance influenced by different involved parameters, such as flexure patterns, notch geometry, and catheter size. In this study, though they mainly focused on flexure patterns of catheters that enabled planar deformations, the proposed approach could be readily extended for modeling and evaluations of such robot bending in 3D.
Magnetic Particle Based: Magnetic micro/nanoparticles are dispersed into the polymer matrix to form steerable elastomers. Kim et al. proposed a submillimeter ferromagnetic soft CR using magnetic elastomeric fibers (Figure 7f ). [17] The composite ink was prepared by mixing the unmagnetized NdFeB particles with the uncured elastomer. Then, the uncured mixture was further magnetized using the impulse magnetic field and made into elastomeric fibers by printing/extrusion or injection molding approach. Later, the same group presented a system consisting of a developed magnetic guidewire, a robot arm with a magnet, a set of motorized linear drives, and a remote-control console. They demonstrated the capability of navigating the magnetic guidewire through narrow and winding pathways both in vitro and in vivo, using realistic human neurovascular phantoms and the porcine brachial artery, respectively. [89] Following this idea, Zhou et al. reported a ferromagnetic soft catheter robot that was able to perform on-site bioprinting based on magnetic actuation ( Figure 7g). [145] The robot was made of the composition of dispersing ferromagnetic particles in a fiber-reinforced polymer matrix. The embedded fiber enabled stable ink extrusion, allowing to print of different materials in desired shapes.
Aside from the magnetic elastomer with axial magnetization, attempts have been made to further extend flexibility. Zhang et al. developed a magnetic guidewire consisting of a commercial guidewire and a soft actuator made of Ecoflex and magnetic powder. [146] Different from the forward magnetic moment, the magnetization profile of the soft tip actuator was nonhomogenous, benefiting a large deformation angle to help access the branch with an acute angle. It was observed a compound deformation behavior combining bending and twisting happened under a large bending angle, and this phenomenon hindered further deformation. Lloyd et al. proposed a magnetic catheter with braided reinforcement, causing an increase in the twisting stiffness 20 times larger than that in the bending stiffness (Figure 7h). [86] With a curved magnetization profile, this catheter could perform up to 180°bending without the aid of anatomical interaction.
Programmable strategies have been proposed for oriented design. Wang et al. reported a catheter with enhanced flexibility and enlarged workspace, benefiting from nonuniformly distributed magnetic particles. [147] They also investigated a model-based evolutionary design strategy that integrates the theoretical model and the genetic algorithm, focusing on the magnetization and rigidity patterns of the catheter. This work achieved the optimal workspace of the catheter and provided a powerful tool for the efficient design and optimization of future MCRs. Lloyd et al. presented a multi-segment continuum device composed of the pure Ecoflex segments and the magnetic Ecoflex segments (Figure 7i). [69,73] The magnetization direction of each magnetic segment could be separately processed. They also reported a design methodology using FEA-based neural network training, through which the magnetization profiles could be patientspecifically customized for a designed trajectory.
Ferromagnetic Sphere Based: MRI scanner provides a unique environment and opportunity for developing interventional devices, featuring simultaneous magnetic steering and real-time localization. Ferromagnetic components could be navigated by MRI gradient forces and imaged with dedicated MR sequences. Zhang et al. presented a ferromagnetic sphere-based catheter in which a single ferromagnetic sphere was attached to the tip of an 8 Fr catheter via a highly flexible silicone tube (Figure 8a). [148] Another souter guiding tube was placed around the catheter to improve stiffness and to facilitate insertion, which could be retracted when the catheter reached the vessel branching. Phantom studies and animal studies showed that the flexible tip could be navigated by magnetic forces imposed by the gradient coil. Gosselin et al. further explored the deflections of such catheters with different tip designs. In their study, one or two ferromagnetic spheres are mounted on the tip of catheters with various inner spacing (Figure 8b). [149,150] It was concluded that more ferromagnetic materials would induce larger magnetic forces; however, the undesired dipole-dipole interactions might be problematic while navigating into small branches. In addition, two ferromagnetic spheres would generate a single large artifact when closely placed.
Lalande et al. proposed a ferromagnetic guidewire by gluing a 0.9 mm diameter ferromagnetic bead to the tip of a 0.007 in. guidewire (Figure 8c). [151] The size of the bead was maximized in the premise of fitting in the introducer catheter to allow for the Reproduced with permission. [148] Copyright 2010, Springer Nature. Panel (b): Reproduced with permission. [149] Copyright 2011, Wiley. Panel (c): Adapted with permission. [151] Copyright 2015, Wiley. Panel (d): Reproduced with permission. [152] Copyright 2014, RSNA. Panel (e) and (f ): Adapted under the terms of the CC BY license. [155] Copyright 2022, The Authors, published by Wiley.
www.advancedsciencenews.com www.advintellsyst.com largest steering force. During operation, the bead was magnetized to its saturation by the permanent magnetic field. Subsequently, the guidewire was deflected by the field gradient in the desired direction. It was observed that the bead was anisotropic, leading to a small but noticeable preferential magnetization direction. The direction perpendicular to the guidewire was viewed as the preferential magnetization orientation, and a hook appeared when the guidewire was placed parallel to the main field. The deformation caused by anisotropy was considerably less than that imposed by the field gradient. Micro Coil Based: Different from the magnetic instrument mentioned before, one or multiple micro coils can be integrated into the continuum device, enabling its current-dependent magnetization. These devices are often navigated by MRI main field and imaged with fewer artifacts. Settecase et al. proposed a steerable catheter by wounding solenoids of 50, 100, or 150 turns on 1.8 and 5 Fr catheters, which could be remotely steered and monitored under MRI guidance. [64] They further derived and validated the relationship between deflection and a series of physical factors, thereby providing a framework for modeling the behavior of similar catheter tips. Losey et al. later evaluated the performance of such a catheter using an in vitro abdominal aortic phantom (Figure 8d). [152] Results showed that the catheter could be clearly visualized under real-time MRI. Furthermore, magnetically assisted catheterization was faster than manual catheterization while both were under MRI guidance, and was comparable to the standard operation under X-ray guidance.
The problem with the single-coil design is that no torque can be generated in the direction of the symmetry axis, causing actuation singularity. This can be overcome by introducing multiple coils with different dipoles. Roberts et al. wounded a three-axis coil on a 1.5 Fr cylindrical catheter for MRI navigation. [153] The z-axis coil was solenoidal, and the two orthogonal coils were modified from Helmholtz coils. A concept diagram of x-and y-axis coils is shown (Figure 8e-I). By applying direct currents up to 100 mA, the catheter could achieve arbitrary 3D deflection and was successfully guided through a 3D vascular-mimicking phantom maze. Liu et al. developed an MRI-actuated steerable catheter by embedding two sets of three-axis coils into the tip of a microcatheter, each with one axial coil and two orthogonal side coils. [154] They further built a 3D kinematic model utilizing the finite differences approach. The quasi-static torque-deflection equilibrium equation for each finite segment was calculated by the beam theory.
Except for the manually wounded micro coils, novel fabrication techniques have been utilized for processing. Wilson et al. fabricated coils in a novel manner via plasma vapor deposition of a copper layer and followed laser lithography of the copper sheet. All coils were manufactured by the laser lathe process, including a single orthogonal helical coil and two side-by-side saddle-shaped coils, which were manufactured on individual tubes with different diameters and further assembled by inserting one inside another. A concept diagram of x-and y-axis coils is illustrated in Figure 8e-II. Phelan et al. later introduced micro coils via the conventional flexible circuit fabrication approach (Figure 8f ). [155] A quad-configuration micro coil design was introduced with a concept diagram of x-and y-axis coils shown in Figure 8e-III. Especially, the two saddle coils are laser machined on the same copper layer, allowing for more compact micro coil designs and tip weight reductions. This scheme enabled the miniaturization of existing MRI driven, Lorentz force-based catheters scale down to 1 mm diameter.

Magnetic Continuum Endoscope
In addition to intervention procedures, MCRs for endoscopic inspection and treatment have also been widely developed. Compared with traditional endoscopy procedures, the soft tether reduces the rate of tissue damage and occurrence of inner wall deformation and looping. Compared with wireless capsule endoscopes, the continuum magnetic endoscope maintains the functionalities of a traditional instrument, such as therapeutic channel, illumination, viewing, irrigation, suction, lens cleansing, and insufflation (Figure 9a). [156] The early concept was proposed by Valdastri et al., which was an endoscopic device consisting of a frontal capsule-like unit and a compliant multiluminal tether (Figure 9b). [157] The frontal unit included an integrated charge-coupled device (CCD) camera for illumination and real-time imaging, a custom-shaped permanent magnet for actuation, a magnetic field sensor for localization, and two channels for lens cleaning and insufflation/suction/irrigation/insertion of operative tools. The overall dimension of the front unit and the tether had an 11 mm diameter and a 26 mm length, and %5.4 mm diameter and a 2 m length, respectively. Later, based on this concept, a series of prototype magnetic endoscopes with improved performance have been proposed, exhibiting more compact distribution, enhanced encapsulation, brighter illumination, more precise localization module, and softer tether (Figure 9c,d). [27,60,85,110] Except for cylindrical or cylinder-like permanent magnets, ring-shaped magnets have also been utilized. Yen et al. proposed an endoscope using a magnetic ring with a 12 mm outer diameter, a 7.6 mm inner diameter, and a 12 mm length. The main components of the frontal unit included a high-definition (HD) complementary metal-oxide semiconductor (CMOS) camera, two white light-emitting diodes (LEDs), and a single working channel to perform operations such as biopsy, water supply, and air supply. [158] Li et al. developed an endoscope containing a ringshaped permanent magnet with a 14 mm outer diameter, a 10 mm inner diameter, and a 23 mm length (Figure 9e). [61] There were four functional channels inside the tether, designed for insufflation, irrigation, instrument insertion, and signal transmission, respectively. Note that these two designs had no inner localization module.
In addition to the monocular camera, stereo vision had also been considered for better visualization, as reported by Verra et al. (Figure 9f ). [159] In this design, the frontal capsule integrated two custom-made wide-angle lenses and two CMOS cameras, enabling stereoscopic vision. Furthermore, illumination was provided by four white LEDs and four green/blue UV-LEDs, enhancing the visibility of vessels and tissues on the mucosal surface that benefited from the narrow-band imaging-like functionality.

Other Tethered Device
Optical images could offer important evidence for clinical diagnosis. Edelmann et al. proposed a magnetic miniature camera endoscope for inspecting the lungs (Figure 10a). [39] It contained www.advancedsciencenews.com www.advintellsyst.com a commercial miniature CMOS camera, 50 optical fibers, and 4 stacked permanent magnetic cubes. The main parts were ensheathed in a silicone rubber tube, and a halogen lamp was used to couple light into the optical fibers for illumination. The device had a 2 mm diameter and %30 cm length, including a 5.5 mm rigid tip and subsequent flexible body. The prototype device was demonstrated to flexibly arrive at the fourth-and fifthlevel bronchi, where the experimental phantom terminated. Magnetic needles have been proposed for tissue penetration. Hong et al. presented a steerable needle for neurosurgical procedures, offering more freedom for designing surgical trajectories and selecting possible targets (Figure 10b). [40,67] It consisted of a spherical permanent magnet as the ball joint, a cylindrical permanent magnet for actuation, a stainless steel adapter for attaching the magnetic tip, a Nitinol wire to provide the insertion force, and a silicone tube to prevent the thin wire from slicing the tissue. The magnetic needle had a 1.3 mm diameter tip and a 0.7 mm diameter flexible body, comparable to commercially available products. Ilami et al. also proposed magnetic needles for moving through soft tissue to solve problems caused by buckling and compression effects, torsion effects, and restricted radius of curvature (Figure 10c). [41] A cuboid-shaped magnet was chosen with dimensions of 3.2 Â 1.6 Â 1.6 mm. Different tips were fabricated and then attached to the magnet, with seven cut from various medical needle tips and three selected from standardized diamond-shaped needles.
Various MCRs have been developed to treat diseases occurring at small structures, potentially reducing the risk of complications and improving precision. Ullrich et al. developed a magnetic tool for capsulorhexis, showing the first catheter-based application for fast and safe ophthalmic surgery. [160] The customized end effector consisted of the bent tip of a 20 G injection needle and three cylindrical magnets with a 0.5 mm diameter and a 1.0 mm length, which was attached to a 2 Fr polyurethane catheter with a 0.3 mm diameter and a 0.6 mm outer diameter. Charreyron et al. investigated a flexible endolaser probe that performs panretinal photocoagulation (Figure 10d). [79,161] The probe included a fiber optic cannula, a polyimide tube, and a permanent magnet. The fiber had a 100 μm inner diameter and 125 μm outer diameter, which was placed in the tube with a 177 μm inner diameter and 215 μm outer diameter. Then, a customized magnet with a 450 μm inner diameter, an 850 μm outer diameter, and a 2 mm length was attached at the tip. The same group later integrated a 44 G capillary into the microprobe, through which fluid flowed. The capillary also created a retinomy, enabling fluid to enter the subretinal space. [80] Bruns et al. designed a device consisting of an insertion tool and a grasping mechanism for inserting cochlear-implant EAs (Figure 10e). [82] The tip of the insertion tool leveraged permanent magnets for actuation purposes. The following tube was chosen to accommodate the electrode. The distal end consisted of three nested Nitinol tubes, rods, and an outer polyimide sheath. These structures were used to grasp, guide, and detach the EA.
www.advancedsciencenews.com www.advintellsyst.com exposure to the surgeon. In addition to the comparative performance of conventional devices, MCRs with functional designs have been widely studied. Drilling motion is one of the widely studied functionalities. [70,72,81,[162][163][164][165] For example, Yang et al. developed a driller-tipped magnetic guidewire for peripheral vascular disease (PVD) treatment. The guidewire consisted of a magnetic driller tip, elastic neck, and base shaft (Figure 11a). [70] The ball-joint-like structure ensured dexterous axial rotation and minimum radial-free bending. The robot had two working modalities. In the bending mode, the tip direction was steered under directional magnetic fields to navigate in complex vasculature. In the drilling mode, the tip was spun under rotating magnetic fields to pass through clogged regions. They further explored the control under US image guidance. Jeon et al. proposed a magnetic micro active-guidewire composed of a ball joint and spiral-type magnetic microrobot. [164] The designed ball joint could provide an additional joint angle of up to 45°without wire deformation, providing a larger steering angle that was the sum of the joint and wire angles. Both directional magnetic field-driven and rotating magnetic field-driven modalities were analyzed and experimentally validated. Nguyen et al. presented a guidewired helical microrobot for percutaneous revascularization in chronic total occlusion (CTO). [165] The microrobot was fabricated with a spherical joint and a guidewire. Drilling performance with different driven parameters was tested, and in vivo demonstrations were conducted using rat models under X-ray guidance. Results showed that the devised strategy capacitated the robot to successfully unclog the thrombosis and navigate the target area. Yang et al. devised a drilling microrobot for nasolacrimal duct recanalization (Figure 11b). [81] The drilling microrobot consisted of a 3D-printed helical tip, a permanent magnet, and a guidewire. They further developed a force signal-based control strategy, through which the instrument could navigate through the nasolacrimal duct phantom and remove the blockage automatically.
Heunis et al. investigated an internally actuated magnetic rotablation robot for debulking stenosis (Figure 11c). [72] Different from the previous unclogging designs based on external magnetic actuation, this catheter was driven by internal electromagnetic coils and spring-loaded permanent magnets, which were embedded on its distal end. During actuation, the electromagnetic coils were powered by alternating currents, causing the plunger assembly to switch between retracting and releasing, and the screw hub turned linear motion into blade rotation. This device could generate enough axial force and torque for unclogging treatments, while miniaturization remained challenging due to the complicated structure. The same group also developed a magnetic tentacle catheter for object manipulation  [39] Copyright 2018, World Scientific Publishing. Panel (b): Reproduced with permission. [40] Copyright 2021, IEEE. Panel (c): Reproduced under the terms of the CC BY license. [41] Copyright 2020, The Authors, published by Spring Nature. Panel (d): Reproduced with permission. [79] Copyright 2019, IEEE. Panel (e): Reproduced with permission. [82] Copyright 2020, IEEE.
www.advancedsciencenews.com www.advintellsyst.com using a combination of electromagnetic coils and permanent magnets. [166] The catheter employed a bioinspired underactuated grasping, that is, the whole body of the catheter looped around the target object to form closure. The catheter adopted a permanent magnet for steering the tip position and an electromagnetic coil for strengthening the force external to the manipulated object, showing potential in MIS. Lee et al. proposed a multifunctional magnetic catheter robot to treat occlusive vascular disease, which was integrated with different motions, including steering, tunneling, and stent delivery ( Figure 11d). [167] The catheter was composed of a tube, tension spring, spring mount, magnetic joint, stent mounting body, stent cover, magnet holder, front magnet, and drill tip. All parts were threaded into the tube, and a self-expandable stent was mounted on the body and covered by the stent cover. First, the robot performed the steering motion to approach the target lesion in complex vascular environments. While reaching the occlusive lesion, the robot generated the tunneling motion to unclog the lesion. After this, a strong magnetic field was applied, and the robot executed the stent delivery motion to widen the lesion. Reproduced with permission. [81] Copyright 2022, IEEE. Panel (c): Reproduced with permission. [72] Copyright 2022, IEEE. Panel (d): Reproduced with permission. [167] Copyright 2021, IEEE. Panel (e): Reproduced under the terms of the CC BY license. [168] Copyright 2019, The Authors, published by AIP Publishing. Panel (f ): Reproduced with permission. [169] Copyright 2023, IEEE. Panel (g): Reproduced with permission. [170] Copyright 2022, IEEE.

Separatable MCR
Apart from synthesizing the function of treatment, separatable designs have also been proposed. These designs combine the advantages of wired and wireless robots, endowing them with high motion speed for long-distance navigation, operation reliability to be taken out, and extreme flexibility to access hard-toreach regions. Park et al. developed an integrated magnetic robot with selective separation and assembly (Figure 11e). [168] The proposed robot had a flexible-legged untethered magnetic robot and a delivery catheter. The external magnetic fields caused relative rotational movements of the two components, producing attractive and repulsive forces between assembled magnets. After separation, the untethered robot could propel, drill, or maintain a position using flexible legs. Yang et al. proposed a wired magnetic microrobot with an ejectable tip (Figure 11f ). [169] The robot had a clinical guidewire and an assembled tip module. The tip module was composed of three functional components: the base frame, rotary holder, and helical bullet. The ingenious structure of the rotating locker enabled the rotary holder to rotate along the axis within limits while restricting its radial deflection and axial movement. The magnetic ejector maintained the relative position between the rotary holder and the helical bullet while allowing axial rotation and movement. The combination of them enables selective ejection and retrieval. This robot could be omnidirectionally steered in the tethered mode, magnetically triggered for the tip ejection transition, and wirelessly propelled in the untethered mode.
Sikorski et al. presented a catheter capable of delivering magnetic projectiles (Figure 11g). [170] Different from the aforementioned designs using permanent magnet arrays, the delivery exploited the magnetic interaction between the miniaturized electromagnet and the loaded polymeric capsule. The loaded capsule could be trapped in the dock or delivered as a projectile by powering different currents into the electromagnet. A closedloop position controller was designed to steer the catheter, and a dynamic model of the capsule was established to predict the trajectory of the projectile.

MCR with Variable Stiffness
Another topic is the variable stiffness design that changes the mechanical property of one or multiple segments, which could further increase flexibility and benefit catheterization. Chautems et al. proposed a variable-stiffness magnetic continuum device using the phase change property of low-melting-point alloy (LMPA) (Figure 12a). [16] The LMPA was encapsulated by the silicon tube and heated by the enameled copper wire coil wrapped www.advancedsciencenews.com www.advintellsyst.com around the inner tube. The assembled robot had a 2.33 mm outer diameter and an inner working channel. It had multiple segments connected serially, which could be independently softened via electrical current. The softened segments were remotely deformed under a magnetic torque, whereas the rest kept being locked in place, thus increasing the DOFs. Following this idea, the same group later improved the fabrication technology, devising a submillimeter device fabricated through a repeatable extrusion process (Figure 12b). [171] It had an %900 μm outer diameter and 180 μm hollow working channel to deliver therapeutics or position instruments. In addition, the resistance-based heat-sensing method was discussed to decide the real-time electrical current, enabling different compliance states. Therefore, the device could be safely navigated in the soft state and apply the required force at the tip in the stiffness state.
Other variable stiffness materials have also been studied. Mattmann et al. presented a variable stiffness 4D robotic catheter utilizing the biocompatible thermoset polymer, the phase transition of which from the glassy state to the rubbery state was tunable ( Figure 12c). [65] The catheter had an embedded heating system to control the stiffness. In addition, it did not require the outer elastic material for encapsulation, which significantly reduced the final diameter, improved manufacturability, and increased safety in the event of complications. The device could be scaled down to a sub-millimeter scale while maintaining a high ratio of stiffness change. Piskarev et al. developed a magnetic catheter made of the conductive phase-change polymer (Figure 12d). [172] The polymer was nontoxic and simultaneously served as a heater, a temperature sensor, and a variable-stiffness substrate. For fabrication, the inner tube was dipped into the conductive shape memory polymer mixture, hung vertically, and cured in an oven. The aforementioned procedure could form a variable stiffness layer, which was repeated until the desired electrical resistance and thickness were obtained. Then, the structure was dipped into liquid silicone to form an encapsulation layer. The prototype catheter had a 0.75 mm lowest wall thickness and a 2 mm outer diameter.

Hybrid Robot
The magnetic actuation can be combined with other driven mechanisms, allowing the hybrid actuator to have the motion feature of individual manners, which could enhance the overall performance. Zhang et al. presented a hybrid CR synthesizing two actuation mechanisms (Figure 13a). [173] The main body was a 3D-printed millimeter-scale notched continuum manipulator with an ultrathin hollow skeleton wall of 300 μm. The structure was further coated with a thin ferromagnetic elastomer layer of 100-150 μm. The proposed robot had a tendon-driven and magnetic-driven hybrid strategy, thereby achieving simultaneous large-angle steering and high-precision manipulation up to 100°a nd low to 2 μm, respectively.
Peyron et al. proposed a magnetic concentric tube robot consisting of a telescopic set of pre-curved or straight tubes and one or several tip-attached magnetic elements (Figure 13b). [174] The robot could be actuated by both rotating and translating the tubes like the concentric tube continuum manipulators and adjusting the external magnetic field as the common magnetic devices.
The combined concentric tube mode and magnetic actuation retained the dexterity and stability of existing medical robots while fulfilling millimeter-sized outer diameters. In particular, the robot could achieve small distal radii of curvature down to 5.4 mm, and large angular displacements up to 160°, with an outer diameter of less than 1 mm.
Buckling of thin shell cylinders-based Kresling origami is an ideal building block for the CR because of its inherent capability of multimodal deformation. Based on this idea, Wu et al. investigated a magnetically controlled origami robot for multimodal deformations (Figure 13c). [175] The proposed device could perform stretching, folding, omnidirectional bending, and twisting. The robot had multiple serially connected Kresling units, each with specific geometries, materials, and magnetizations to perform different functions, fabricated from designed Kresling patterns with a magnetic plate attached. It allowed ultrafast on-demand control and small-scale device development with multiple functionalities.
The advancement of the following interventional instruments is independent of base insertion. These ideas were to overcome the challenge that many regions inside the body remain inaccessible due to complex anatomies. Pancaldi et al. proposed a flowdriven tethered ultra-flexible endovascular robot (Figure 13d). [176] The robot consisted of a so-called μ catheter and a magnetic head. Working principles were as follows: the motion of the robot relied on harnessing hydrokinetic energy; dynamic steering at bifurcations used magnetic actuation to deform the robotic head. Numerical simulations and ex vivo rabbit-ear experiments were conducted, showing that the probes could navigate through tortuous vascular networks with minimal external intervention. However, the navigation of the mentioned flow-driven robot totally relied on proper perfusion, while bottlenecks existed in the treatment of impaired flow conditions. Later, the same group proposed another robot by modifying the magnetic tip with an undulating magnetic head (Figure 13e). [177] The static magnetic field was used to position the head inside the obstructed channels during flow-driven navigation in perfusing channels; the rotating magnetic field was adopted for crawling locomotion to realize motion and steering in the absence of flow. The robot was further demonstrated inside the coronary arteries of an ex vivo porcine heart under X-ray guidance.

Kinematic Modeling
Different from conventional robots with separate joints and rigid links, continuum manipulators have high flexibility and redundancy, making them versatile in narrowed and complex environments. However, modeling could be intricate due to the continuum feature. Many strategies have been developed to predict the kinematics of MCRs. They are coincident with those developed for continuum manipulators with other actuation methods, which describe the outcome of equilibrium between internal forces and external magnetic wrenches. Several representative examples will be illustrated for modeling long slender objects.
One category is to use the classical elasticity theories. The rod theories, such as the Bernoulli-Euler beam theory and the www.advancedsciencenews.com www.advintellsyst.com Cosserat rod theory, are widely adopted for accurate load and strain analysis. The Bernoulli-Euler beam theory simplifies the linear theory of elasticity to calculate the relationship between load carrying and deflection, providing an analytical model. [75,106,162,163,[178][179][180] The Cosserat rod theory consists of solving a set of equilibrium equations between the position, orientation, internal force, and internal torque, providing complex and accurate geometries under complicated magnetic wrenches. [137,181] Although these methods based on rod theory can describe the deformation of a long and slender cantilever beam with satisfactory accuracy, numerical approaches, like finite difference methods, are also used to obtain proper solutions. [147,182] Subsequently, limited by time-consuming calculations, numerical approaches bring difficulty in efficiently controlling MCR tip position and orientation in a real-time way. In contrast, the energy-based method paves the way for kinematic modeling with a fast computation speed, featuring the stability analysis, that is, the system will lie in a stable equilibrium state when the minimum total potential energy of the whole system is obtained. [142,181,183,184] Note that the total potential energy, including magnetic potential energy, gravitational potential energy, elastic strain energy, etc., is involved in both the state of the MCR and the state of the external magnetic fields.
In addition, the constant curvature premise is widely used for reasonable simplification during kinematic modeling, which has the benefit of balancing computation cost and accuracy. [38,110,185] It is based on the assumption that the CR deforms as the arc of a circle, that is, the curvature keeps invariant along the lengths.
The assumption could also be extended to multiple segments, in which the deflected geometry has a finite number of mutually tangent curved segments, with each having a constant curvature.
Another approach is the pseudo-rigid-body model. [69,142,[186][187][188] The continuum manipulator is equivalent to a series of rigid links Figure 13. MCRs with hybrid-actuation strategy. a) Robot with tendon driven and magnetic driven. b) Robot with concentric tube driven and magnetic driven. c) Robot with origami structure driven and magnetic driven. d) Robot with flow driven and magnetic guidance. e) Robot with flow driven and selflocomotion. Panel (a): Reproduced under the terms of the CC BY 4.0 license. [173] Copyright 2021, The Authors, published by Wiley. Panel (b): Reproduced with permission. [174] Copyright 2022, SAGE. Panel (c): Reproduced under the terms of the CC BY 4.0 license. [175] Copyright 2021, The Authors, published by PNAS. Panel (d): Reproduced under the terms of the CC BY license. [176] Copyright 2021, The Authors, published by Springer Nature. Panel (e): Reproduced under the terms of the CC BY 4.0 license. [177] Copyright 2021, The Authors, published by Wiley.
www.advancedsciencenews.com www.advintellsyst.com connected by conventional joints so that the kinematics could be described by homogeneous transformations using standard Denavit-Hartenberg (D-H) parameter tables. Therefore, it is a helpful simplification since it permits utilizing well-established approaches for control and sensing. Finite-element models (FEM) have shown potential in analyzing the deformation performance of MCRs. [37,73,189,190] The simulation environment could be commercial software with appropriate packages or self-defined frameworks. This numerical technique offers a powerful tool to calculate the deformation of elastic materials with high nonlinearity under complex magnetic interactions. Moreover, neural network algorithms could be leveraged along with training data derived from FEM results to fit the real kinematics of MCRs, thus providing reliable strategies for predicting and controlling robot behaviors. [73]

Sensing and Localization
The sensing and localization strategy of MCRs could be classified into sensor based and image based. [191][192][193] Magnetic localization is a representative sensor-based one that can be subdivided into two main approaches. The first type consists of sensing modules (e.g., Hall-effect, magneto-resistive, or multiturn coils sensors) outside the human body to measure in-positioning magnetic sources inside the controlled device. [158,[194][195][196] For example, Son et al. proposed a 5D localization method for the magnetic robot. [196] The system utilized a 2D array of Hall-effect sensors to measure the related magnetic fields. The optimization methods were used to determine the position and orientation of the magnetic robot and minimize the effect of the electromagnetic field during positioning. The second-type comprises in-positioning sensing modules inside the controlled device that utilizes the outside actuation field or specially designed electromagnetic field for localization. [197][198][199][200][201] For instance, Fischer et al. presented a localization and navigation strategy of MCRs by using a Hall-effect sensor embedded into the catheter. The method could locate the catheter by measuring the magnetic field generated by the electromagnetic system, therefore estimating the position of the catheter without the need for an external device to obtain position feedback. [201] Another solution is using radio waves. [202][203][204] Usually, the controlled agents are integrated with an RF module, and sensors are placed outside to receive the strength of the RF signals for localization.
Fiber Bragg grating (FBG) sensors, a fiber-optic type of sensor, have been used for various purposes for CRs, such as estimating the muscular activity in the GI tract, [205] measuring contact force, [206] and sensing shape. [191] For example, Denasi et al. proposed a magnetic catheter with a multicore FBG fiber placed along the length of the catheter, which had four cores, and each core had 32 FBG sensors. [207,208] Three cores were placed around the center to measure the strains, whereas the center core was used for temperature compensation, enabling stable shape sensing.
A variety of clinical imaging techniques are good candidates. [192] Fluorescent imaging is the gold standard in interventional procedures for real-time monitoring. [89,135,136,139,165] For example, radiopaque catheters can be visualized easily in vascular structures filled with contrast agents. However, it exposes patients and surgeons to radiation that may lead to long-term health concerns. Kim et al. developed a magnetic catheter system that could access different branches of cerebral arteries with the imaging feedback of the fluoroscopy. The results showed the capability of coil embolization and clot retrieval. Further demonstrations were performed in the porcine artery with the X-ray fluoroscopy system providing real-time position feedback. [89] MRI has no ionizing radiation and high soft-tissue contrast to show blood vessels and tissue response, offering the visualization of the interaction effect. [64,[148][149][150][152][153][154][155]209,210] In addition to anatomical images, various MRI imaging techniques, such as perfusion, diffusion, and functional MRI, could increase the acquired information for diagnosis and treatment. It also has the potential for simultaneous imaging and magnetic control, while patients with cardiac pacemakers and metallic foreign bodies are not applicable. Plenty of examples have been discussed in Section 3.1.1.
Recently, studies of control continuum manipulators under 2D and 3D US imaging have been presented to mitigate radiation exposure in conventional procedures. [38,[70][71][72]113,169,211,212] US imaging is a high-portable and radiation-free medical imaging solution, also providing high temporal resolution, but the signalto-noise ratio (SNR) and targeted imaging region should be considered. An example is the magnetic driller-tipped guidewire that was actuated by the electromagnetic system and guided by the US imaging system. The proposed control strategy integrated all system modules and considered imaging noise, so that the catheter could be flexibly steered and remove the blood clot under US guidance. [70] Optical coherence tomography (OCT) imaging is mainly used in ophthalmology. This technology also has good imaging results in related ophthalmic surgery in recent studies, which can help surgeons obtain more precise position feedback during the manipulation of medical robots. [213,214] The magnetic microcannula for subretinal injections presented by Charreyron et al. allowed flexible position control and could perform subretinal injections in ex vivo porcine eyes with the assistance of OCT. The experimental results showed that OCT visualization could navigate the robotic intubation precisely and safely in most areas of the posterior eye. [80] Another solution is using the visual feedback from the instrument, such as the camera of the endoscope, to map the clinician commands to the tool workspace. [39,215] The kinematics of the system could be constantly estimated by directly relating the observed changes to the applied inputs. Therefore, the control requires neither prior anatomical information nor continuous device localization. For instance, Edelmann et al. utilized a model-free method, in which the position control was performed through images acquired by the endoscope integrated inside the catheter. Navigation experiments were performed in a lung phantom, verifying the catheter could access target bifurcations under the actuation of an electromagnetic field and feedback from the endoscope. [39]

Control Strategy
The control of MCRs could be divided into three layers according to their autonomous level. [27,[216][217][218] The first layer with low www.advancedsciencenews.com www.advintellsyst.com autonomy is defined as direct magnetic field control. In the layer, surgeons should simultaneously focus on magnetic field generation and real-time image feedback to make the decision. An example is the actuation system composed of a serial robotic arm and a mounted permanent magnet to manipulate a tethered magnetic endoscope ( Figure 14). During the operation, surgeons manipulated the position and orientation of the robotic arm intuitively to change the magnetic field generated at the working point. [157] The manipulator was an executor of the movements imparted by the human operator. Some safety constraints could be integrated into the system. The second layer with medium autonomy is called intelligent teleoperation, which enables the surgeons to focus on and operate the position and orientation of the continuum device directly. Surgeons only need to decide the motion of the continuum manipulator according to the surroundings, while the necessary magnetic field is automatically computed and generated. For instance, using the same system, surgeons only needed to instruct the bending and insertion of the endoscope, while the best motion strategy of the robotic arm to generate the required magnetic field was systematically decided and operated based on the localization information. [200] Note that a system carrying out semiautonomous motion for improving performance but dependent on a human-in-the-loop to indicate the end target also belongs to this category. [60,219] The third layer with high autonomy is defined as semiautonomous navigation, transferring the decision priority to the system. The computer governs all system modules and gives instruction according to real-time analysis of feedback. In this layer, both the motion planning of the device and the generation of the magnetic field are automatic. The system generates task strategies in most cases and only relies on the operator to approve or override the robotic choice. The overall procedure could be finished even without the human interface. For example, for an endoscopic system, the direction of motion could be computed by image analysis algorithms that detect the center of the lumen or polyp identification that decide the targeted lesion. [85,220,221]

Conclusion and Outlook
The MCRs have experienced fast and extensive development in the last two decades. The advanced design and fabrication enable the robots from initial angle steering to be integrated with more functions. Also, the potential application area extends from Figure 14. Schematic overview of the control layers using a permanent magnet-based actuation system. Panel: Adapted with permission. [27] Copyright 2020, Springer Nature.
www.advancedsciencenews.com www.advintellsyst.com intravascular and endoluminal to the whole body. Various developing magnetic-actuation systems allow for better manipulation performance. The exploration of localization and control strategy further improves the outcomes. The success of the magneticactuation platform named Niobe, launched in 2003, has opened an era and witnessed the development of magnetic techniques on CRs. Although with great potential to improve clinical procedures, the developing technique still has a long way to go before reaching medical specifications. The future focus may be fivefold ( Figure 15): First, the performance of the MCRs needs to be thoroughly evaluated. The prototype for most of the inventions is to prove the concept at the current stage, while the clinical requirements, such as sterilization, biocompatibility, and structure reliability, need to be considered for the design of the CR. Further miniaturization is also essential for some applications to fit the narrow structure, while the related mechanical structure should be maintained. To deal with these challenges, advanced processing methods, smart materials, and new structural design strategies are needed. In addition, most of the existing experimental settings are pretty ideal, while complex and highly dynamic in vivo anatomy needs to be included in the validation.
Second, potential medical applications should be explored and validated. One aspect is to focus on accessing hard-to-reach surgical points, such as neurovascular with small and tortuous anatomical structures, and pancreatic and bile ducts with narrow entrances and large deformation angles. Another aspect is to consider the clinical need and integrate the miniature-sized MCRs with one or compound functional designs for diagnosis and treatment, such as steering, tunneling, and stenting for occlusive endovascular treatment. Current studies have only offered preliminary concepts and demonstrations, while delicate design, quantitative analysis, and comprehensive validation are still necessary.
Third, the clinical magnetic-actuation platform needs further development. Most existing research in magnetic continuum robotic systems primarily focuses on the end effector, while the control platform is a significant part. Current preclinical and clinical systems still tend to be bulky and complex, which is hard to be installed in the operating room. Therefore, the next-generation platform should maintain a simultaneous small structure, good field generation ability, and high safety. A straightforward operation and user friendly interface are also necessary.
Fourth, the medical imaging methods should be considered. For example, in a conventional interventional procedure, X-ray fluoroscopy is utilized to monitor the interventional state and device. One aspect of real-time monitoring is the integration with imaging devices on the system level. For example, the imaging equipment and the magnetic-actuation platform should work collaboratively without mutual interference or physical collision. Also, other radiation-free imaging approaches could be introduced into the procedure, for example, MRI and US imaging. Except for the external US, internal US methods, such as intravascular ultrasound (IVUS) and endoscopic ultrasound (EUS), should be concerned, providing on-site endoluminal US images. Preliminary studies have been conducted and show great potential, but more in vivo experiments are necessary. In addition, through improvements in material selection, structural design, and sensor integration, the MCRs should have enhanced results under related imaging strategies, improving the accuracy of position and shape feedback.
Finally, the intelligent and autonomous level of manipulating the MCR should be improved. Despite the fact that developing autonomous driving capabilities has been a hot topic in the last decade, the use of which in the area of medical robots is still limited. The percentage is even low when it comes to magnetic control. Increasing intelligence and autonomy could help reduce the surgeon's workload, accelerate the operating procedure, and improve the surgical outcome. Moreover, this may also improve the medical level in underdeveloped regions with surgeon shortages.