State-of-the-art biomedical applications such as targeted drug delivery and laparoscopic surgery are extremely challenging because of the small length scales, the requirements of wireless manipulation, operational accuracy, and precise localization. In this regard, miniaturized magnetic soft robotic swimmers (MSRS) are attractive candidates since they offer a contactless mode of operation for precise path maneuvering. Inspired by nature, researchers have designed these small-scale intelligent machines to demonstrate enhanced swimming performance through viscous fluidic media using different modes of propulsion. In this review paper, we identify and classify nature-inspired basic swimming modes that have been optimized over large evolutionary timescales. For example, ciliary swimmers like Paramecium and Coleps are covered with tiny hairlike filaments (cilia) that beat rhythmically using coordinated wave movements for propulsion and to gather food. Undulatory swimmers such as spermatozoa and midge larvae use traveling body waves to push the surrounding fluid for effective propulsion through highly viscous environments. Helical swimmers like bacteria rotate their slender whiskers (flagella) for locomotion through stagnant viscid fluids. Essentially, all the three modes of swimming employ nonreciprocal motion to achieve spatial asymmetry. We provide a mechanistic understanding of magnetic-field-induced spatiotemporal symmetry-breaking principles adopted by MSRS for the effective propulsion at such small length scales. Furthermore, theoretical and computational tools that can precisely predict the magnetically driven large deformation fluid–structure interaction of these MSRS are discussed. Here, we present a holistic descriptive review of the recent developments in these smart material systems covering the wide spectrum of their fabrication techniques, nature-inspired design, biomedical applications, swimming strategies, magnetic actuation, and modeling approaches. Finally, we present the future prospects of these promising material systems. Specifically, synchronous tracking and noninvasive imaging of these external agents during in vivo clinical applications still remains a daunting task. Furthermore, their experimental demonstrations have mostly been limited to in vitro and ex vivo phantom models where the dynamics of the testing conditions are quite different compared the in vivo conditions. Additionally, multi-shape morphing and multi-stimuli-responsive modalities of these active structures demand further advancements in 4D printing avenues. Their multi-state configuration as an active solid-fluid continuum would require the development of multi-scale models. Eventually, adding multiple levels of intelligence would enhance their adaptivity, functionalities, and reliability during critical biomedical applications.

B

Magnetic field

Co

Cobalt

CNN

Convolution neural network

DNA

Deoxyribonucleic acid

Fe

Ferrum (Iron)

FSI

Fluid–structure interactions

Ga

Gallium

GI

Gastro-intestinal

MHD

Magneto-hydrodynamics

MR

Magnetic resonance

MSRS

Magnetic soft robotic swimmers

Nd

Neodymium

Ni

Nickel

O

Oxygen

PLA

Polylactic acid

Pt

Platinum

RFT

Resistive force theory

SBT

Slender body theory

Ti

Titanium

US

Ultrasound

UV

Ultraviolet

2D

Two-dimensional

3D

Three-dimensional

4D

Four-dimensional

Soft robotics is an emerging field of inter-disciplinary research in the soft matter community that has seen enormous progress over the last couple of decades.1–6 This includes the design, fabrication, modeling, and control of compliant multi-functional structures for diverse biomedical and microfluidic applications.7–12 In contrast to their traditional rigid (hard) counterparts, soft robots are highly deformable and possess large degrees of freedom.13–17 Miniaturization, system engineering and full-scale integration have further increased the applicability of soft robots for potential in vivo sensing applications and micro-manipulation.18–23 

Today, state-of-the-art biomedical and microfluidic applications such as targeted drug delivery,24–30 cell-loaded micro-transportation through confined tortuous channels,31–33 on-demand orbital maneuvering and collective behavior,34 soft suction grippers,35,36 tissue engineering and bionics,37 robot-assisted surgery,38–45 and small-scale bio-manipulation46–49 demand untethered miniaturized soft robots that allow noninvasive control and contactless remote operation with minimum error and quick response time.50–55 This has led to the development of miniaturized magnetic soft robotic swimmers (MSRS) that can propel through narrow confinements (e.g., blood vessels and vascular channels) inside the human body as well as lab-on-a-chip devices (or microfluidic assays).56–66 

From a materials perspective, MSRS are compliant multi-functional composites that comprise external magnetic filler particles impregnated into an elastomeric (polymeric) matrix.67–72 The magnetic fillers either include soft magnetics with a weak coercive strength (e.g., Co, Ni, Fe, etc.), hard magnetics with a strong coercive strength (e.g., FeCo, FePt, FeNdB, etc.), or superparamagnetics with zero coercive strength (e.g., Fe3O4, Fe2O3, etc.).73 Considering their fabrication, a wide range of emerging technologies have been adopted to develop multifunctional nanocomposites that are capable of cross-domain energy transduction and spatiotemporal shape morphing in a pre-defined manner upon being subject to external stimuli.74,75 Here, three advanced fabrication techniques have been discussed—magnetic hydrogelation76 (where magnetic fields are used during the curing/gelation phase for appropriate aligning of magnetic filler particles), additive manufacturing of magnetic materials77 (where 3D printing is used to assign pre-programmed magnetic profiles), and magnetic additive manufacturing78–80 (where anisotropic magnetic profiles are obtainable during the printing process). Subsequently, the architecture, emergent properties, and magneto-responsiveness of these materials have been explained.

Owing to their unique magneto-mechanical coupling, these multi-functional composites can shape-morph in a pre-defined manner when subjected to an external magnetic field (see Fig. 1), and can even propel through a viscous medium under the combined action of viscous drag and external magnetic toques/forces.81–91 Furthermore, magnetic fields allow for a real-time contactless manipulation with a high accuracy and precise motion control with minimal delay, closed-loop feedback positional control.92–100 In addition, these untethered tiny machines offer a clean, wireless, and contact-free actuation because they do not involve on-board electronic, pneumatic, electrical, hydraulic, or optical components.101–110 As a result, magnetic actuation is the most-preferred choice for applications that demand noninvasive operation and remote control in confined and inaccessible target locations.111–118 

FIG. 1.

Schematic representation of a magnetically actuated soft robotic swimmer approaching tumor sites through a confined vascular channel. The inset at the top left demonstrates the applicability of 3D printing to fabricate these magneto-responsive materials. The inset at the bottom center depicts the pre-defined shape morphing of the MSRS under external magnetic fields. Chung et al., Adv. Intell. Syst. 3, 2000186, 2021; licensed under a Creative Commons Attribution (CC BY) license.

FIG. 1.

Schematic representation of a magnetically actuated soft robotic swimmer approaching tumor sites through a confined vascular channel. The inset at the top left demonstrates the applicability of 3D printing to fabricate these magneto-responsive materials. The inset at the bottom center depicts the pre-defined shape morphing of the MSRS under external magnetic fields. Chung et al., Adv. Intell. Syst. 3, 2000186, 2021; licensed under a Creative Commons Attribution (CC BY) license.

Close modal

Recent studies have reported the development and entire assembly–disassembly procedure for a magnetically actuated gearbox for wireless remote control of MSRS.119–123 For instance, polarized MSRS has been successfully integrated within a microfluidic chip to enable external control using magnetic waves.124 Similarly, artificial magnetic micrometer-sized cilia have been fabricated with pre-defined programmability to shape-morph under magnetic actuation for net fluidic propulsion and particle manipulation at low Reynolds number flows using metachronal waves.125–131 The actuation setups and control strategies implemented for these miniaturized magneto-responsive systems have been explained.132 The idea of re-configurable magnetic domains and domain switching have been utilized to obtain magnetic soft robots with adaptive structures that can exhibit shape morphing under externally varying magnetic fields to demonstrate sophisticated functionalities.133–135 

A comprehensive review of three-dimensional navigation, fabrication, and functionalization, and motion planning through viscous fluids has been reported for MSRS that exhibited sub-micrometer precision.136,137 Motion control and precise path maneuvering have been experimentally demonstrated for magneto-responsive swimmers subjected to external actuation.138–144 Actuation, visual tracking, and feedback control have been extensively discussed for in vivo applications of MSRS.145–147 In a recent review, a thorough insight into the fundamentals of magnetic soft matter, their sensing modalities, material composition, fabrication methods, design principles, actuation, and control of magneto-active soft materials and robots have been elaborated.148 Magnetically driven catheters, guide-wires, capsules, grippers, and soft robotic structures have been successfully propelled using path-following strategies for surgical tool navigation, biopsy, cellular manipulation, minimally invasive cardiovascular interventions, weight loss balloons, arterial stenosis, endoscopic laser steering, and microswimmer magnetic activities.149–159 Material transport and mixing of chemical species has been carried out using deformable magnetic soft robots swimming through confined microfluidic channels.160–162 

Sheet-shaped MSRS has been fabricated using solution casting technique followed by thermal curing and laser cutting into desired shapes for multi-modal locomotion under different forms of external magnetic actuation and fluidic confinements (see Fig. 2).163 Indeed, unprecedented progress in the design, fabrication, actuation, and control strategies of stimuli-responsive soft materials, magnetic soft robots, and MSRS has been witnessed over the last decade. From the transformation of passive structures into active (smart) intelligent systems (often embedded with physical and computational intelligence) to system engineering, miniaturization, and full-scale integration, magnetic soft robots have seen an enormous and steep progress.164–166 In this regard, the foundation of system-engineered miniature machines has been explained with emphasis on their morphology, kinematics, transduction, efficiency, and intelligence.167–169 An in-depth review featuring several methods of magnetic actuation and control techniques for untethered bio-inspired soft robots has been presented.170 The locomotion strategies and gait analysis of miniature smart material systems under external stimuli have been reported for potential minimally invasive medical treatments and lab-on-chip applications.171–173 

FIG. 2.

(A) Fabrication of a sheet-shaped MSRS from a solution-cast magnetic composite elastomer; after thermal curing, the desired shape of the specimen is laser-cut, followed by wrapping the specimen around a non-magnetic rod to induce a sinusoidal patterned remnant magnetization upon subject to strong magnetic fields. (B) Structural configurations of the MSRS for varying spatial confinements: (i) big gap, (ii) small gap, and (iii) cylindrical tube. Scale bars, 1 mm. (C) Schematic representation of the adaptive multimodal locomotion when the MSRS propels through different narrow confinements with varying cross sections. Ren et al., Sci. Adv. 7, eabh2022, 2021; licensed under a Creative Commons Attribution (CC BY) license.

FIG. 2.

(A) Fabrication of a sheet-shaped MSRS from a solution-cast magnetic composite elastomer; after thermal curing, the desired shape of the specimen is laser-cut, followed by wrapping the specimen around a non-magnetic rod to induce a sinusoidal patterned remnant magnetization upon subject to strong magnetic fields. (B) Structural configurations of the MSRS for varying spatial confinements: (i) big gap, (ii) small gap, and (iii) cylindrical tube. Scale bars, 1 mm. (C) Schematic representation of the adaptive multimodal locomotion when the MSRS propels through different narrow confinements with varying cross sections. Ren et al., Sci. Adv. 7, eabh2022, 2021; licensed under a Creative Commons Attribution (CC BY) license.

Close modal

The design strategies for biomedical applications of MSRS, in vivo and in vitro, have been thoroughly reviewed for drug delivery, cellular manipulation, endoscopy, and cardiovascular disease treatments.174–176 Indigestible magnetic capsules have been developed for noninvasive ex vivo human intestine as well as in vivo porcine intestine biopsy of the gastrointestinal (GI) tract.177–179 On-demand in vitro mucus collection in the human intestine for diagnosis has been conducted with a reduced risk of tissue damage.180 These miniaturized machines implemented a passive mode of locomotion and they collected the samples when triggered by external magnetic fields generated by a permanent magnet placed on the skin near the point of interest. The capsule contained a soft vacuum chamber that was sealed with wax impregnated with nichrome wax. When subjected to magnetic actuation, the heat generated by the wires melted the wax. This allowed the mucus to be sucked inwards into the vacuum rendering reliable sample collection. These capsules with tunable morphological adaptation and wireless actuation have been maneuvered through the GI tract for faster (and more accurate) endoscopy, minimally invasive surgery through untethered cardiovascular intervention, online diagnosis, and sensing.181–184 

Furthermore, untethered in-vivo manipulation and guidance of catheters and capsules using external magnetic actuation have been demonstrated for a suture needle by steering it through narrow holes or penetration through excised tissues.185–187 Magnetic catheters have been developed for stimulating the spinal cord for refractory pain syndromes, in order to improve physical and coordinated movements.188–190 Highly integrated MSRS composites have shown promising results for in vitro targeted neuronal cell delivery, on-demand localized wireless neuronal electro-stimulation, and post-delivery enzymatic degradation.191 Soft hydrogels with magneto-electric nanoparticles have been used where the hydrogel supported cell growth, while the nanoparticles were used for magnetic transportation and subsequent neural stimulation. Magneto-electric nanoelectrodes have been successfully injected into a freely moving mouse for wireless deep-brain stimulation.192 The transmission of an electrical impulse to the brain was demonstrated by means of an external magnetic field. In vitro neuronal modulation and minimal invasive in vivo deep brain stimulation have been performed for the mice leading to a change over time. Synchronous fluorescence imaging was employed to image a swarm of micrometer-sized artificial magnetic swimmers inside the intra-peritoneal cavity of a mouse.193, In vivo fluorescence imaging has been adopted to track microbots inserted into a mouse for stem cell transplantation.194 

Recent developments have been quite promising in demonstrating the myriad possibilities and unparalleled potential of MSRS for catering to the state-of-the-art challenging biomedical and microfluidic applications.195–198 However, we feel that there is still a gap in identification and proper classification of the nature-inspired basic swimming modes, and a rudimentary understanding of their magnetic-field-induced spatiotemporal symmetry-breaking mechanisms adopted (by MSRS during helical, ciliary, and undulatory modes of swimming) for effective propulsion at such small length scales, which hampers fast progress in the field. Furthermore, modeling approaches that can precisely predict the magnetically driven large deformation fluid–structure interaction of MSRS, are only slowly starting to emerge. Furthermore, an overview of the various fabrication techniques adopted for the development of advanced shape-tunable miniaturized MSRS has not been reported to date, which we feel has hindered their further progress.

Considering the gap between their unprecedented potential and current state of the art, a systematic review is, therefore, urgent. Here, we present a holistic review of the recent developments in these smart material systems covering the wide spectrum of their fabrication techniques, nature-inspired design (e.g., magnetic swarms, cell-based MSRS, etc.), biomedical applications, swimming strategies, magnetic actuation, and modeling approaches (see Fig. 3). Our primary objective is to cater to the early-stage researchers entering into this exciting field of MSRS and to provide them with a descriptive summary of the vast literature encompassing MSRS. Since the development of next-generation MSRS heavily depends upon our current understanding and successful implementations that have been achieved to date, this review thoroughly addresses the praiseworthy achievements in a comprehensive manner and addresses promising developments that lay ahead as future perspectives.

FIG. 3.

A schematic representation of the current review that encompasses the various facets involving MSRS: biomedical applications, nature-inspired design, fabrication techniques, swimming strategies, magnetic actuation, and modeling approaches.

FIG. 3.

A schematic representation of the current review that encompasses the various facets involving MSRS: biomedical applications, nature-inspired design, fabrication techniques, swimming strategies, magnetic actuation, and modeling approaches.

Close modal

First, we highlight the different fabrication routes, followed by their nature-inspired design strategies. Next, we explain the three basic modes of swimming for effective propulsion through a viscous medium using magnetic-field-induced spatiotemporal symmetry-breaking mechanisms. Then, we report the significant developments and recent progress made in the design of efficient actuation strategies. Moving further, we report the modeling approaches undertaken by researchers to study the underlying principles of magnetic-field-induced propulsion that give rise to distinct swimming behaviors. Finally, we summarize our observations before describing the future perspectives and scopes for further research.

Various strategies have been adopted for fabricating MSRS that range from additive manufacturing methods such as direct-ink writing and photolithography, to subtractive methods like solution casting and molding followed by thermal curing and laser cutting.199–205 

Magnetically driven microswimmers have been developed using a two-photon-based 3D printing technique for controlled drug release.206 3D printing of programmed ferromagnetic domains for shape morphing has been reported using a direct-ink writing technique for an elastomer composite containing ferromagnetic microparticles.207 In this case, a magnetic field was applied to re-orient the particles to impart a patterned magnetic polarity to the printed filaments.208 Two-photon polymerization of gelatin methacryloyl hydrogels has been reported, where, the polymer base was coated with magnetic nanoparticles to exhibit magneto-responsiveness.209 A method for patterning hard-magnetic microparticles into an elastomer matrix has been demonstrated using ultraviolet lithography technique.210 Here, the magnetic particles were oriented in a controlled manner to encode anisotropic remnant magnetization.

A novel technique has been reported to fabricate cellularized anisotropic hybrid hydrogel that can be driven by an external magnetic field.211 Here, a low-intensity magnetic field was used to align mosaic iron oxide nanoparticles into filaments with tunable size within a gelatin methacryloyl matrix. Magnetic motion control and collective behavior of 3D-printed lithography-based polymeric tubular micromotors, ranging from microjets to spermbots, and synthesized using high-power light-emitting-diode writing and two-photon absorption 3D laser lithography techniques, have been discussed.212 Standard photolithography has also been undertaken to develop sperm-inspired MSRS (see Fig. 4).213 Elsewhere, MSRS have been fabricated using a micro-electromechanical system-based fabrication technique.214 Ti and Ni were deposited onto the protruding structures for rendering magneto-responsiveness to these active material systems.

FIG. 4.

Schematic illustration of the fabrication technique used for developing magnetic sperm-inspired soft robots. [(a) and (b)] An SU-8 layer is spin-coated on a silicon support wafer. [(c) and (d)] Standard photolithography patterning is performed. [(e) and (f)] Using a resist liftoff mask, a Co–Ni MSRS head is created using electron-beam evaporation. (g) The magnetic sperm is released into liquid by etching the entire silicon wafer. An optical image shows the ellipsoidal head of the MSRS. Reproduced from Khalil et al., Appl. Phys. Lett. 104, 223701 (2014) with the permission of AIP Publishing.

FIG. 4.

Schematic illustration of the fabrication technique used for developing magnetic sperm-inspired soft robots. [(a) and (b)] An SU-8 layer is spin-coated on a silicon support wafer. [(c) and (d)] Standard photolithography patterning is performed. [(e) and (f)] Using a resist liftoff mask, a Co–Ni MSRS head is created using electron-beam evaporation. (g) The magnetic sperm is released into liquid by etching the entire silicon wafer. An optical image shows the ellipsoidal head of the MSRS. Reproduced from Khalil et al., Appl. Phys. Lett. 104, 223701 (2014) with the permission of AIP Publishing.

Close modal

Jellyfish-inspired MSRS has been developed by mixing NdFeB magnetic microparticles with silicone elastomer, followed by thermal curing at 65°C before laser-cutting them into desired shapes.163 These fabricated soft magnetic composites were then subjected to high magnetic fields in order to induce a remnant magnetization profile for pre-programmed shape morphing (see Fig. 5).83 Often, patterned magnetization for a quick transformation of the inactivated structure into activated three-dimensional shapes has been utilized to achieve the desired shape-programmability and locomotion.215 Here, magnetized NdFeB patterns have been selectively embedded into the adhesive elastomer network to generate the required shape.

FIG. 5.

An Ephyra jellyfish-inspired MSRS with (a) design parameters and (b) fabrication procedure - (i) First, the magnetic composite elastomer is cast onto a poly(methyl methacrylate) plate, followed by thermal curing at 60 °C; (ii) next, the active parts of the MSRS are laser-cut; (iii) then, these active parts are shaped into an ellipsoid prior to being magnetized by a strong magnetic field; (iv) finally, the gaps between the active parts are filled with a nonmagnetic elastomer. Reproduced with permission from Ren et al., Robot.: Sci. Syst. (2019). Copyright 2019 The Authors.

FIG. 5.

An Ephyra jellyfish-inspired MSRS with (a) design parameters and (b) fabrication procedure - (i) First, the magnetic composite elastomer is cast onto a poly(methyl methacrylate) plate, followed by thermal curing at 60 °C; (ii) next, the active parts of the MSRS are laser-cut; (iii) then, these active parts are shaped into an ellipsoid prior to being magnetized by a strong magnetic field; (iv) finally, the gaps between the active parts are filled with a nonmagnetic elastomer. Reproduced with permission from Ren et al., Robot.: Sci. Syst. (2019). Copyright 2019 The Authors.

Close modal

Similarly, porous silica spheres have been impregnated into a NdFeB–silicone elastomer matrix to fabricate highly flexible MSRS capable of multi-modal locomotion.216 Magnetic microrobots have been fabricated using a thermoresponsive hydrogel nanocomposite with a polyethylene glycol diacrylate layer.217 This enabled spontaneous and reversible folding from a planar rectangular structure to a tubular morphology under an opto-magnetic actuation.218 

Self-assembly fabrication technique has been reported to develop sperm-shaped MSRS (see Fig. 6).219 In another study, chiral miniature MSRS has been fabricated by self-aligning magnetic nanoparticles into parallel chains under external magnetic fields.220 The fabricated swimmers were highly flexible when subjected to a rotating magnetic field, thereby generating a body twist to ensure a nonreciprocal motion for net propulsion at low Reynolds numbers.

FIG. 6.

(a) Schematic representation of self-assembly fabrication technique employed to develop sperm-shaped MSRS. [(b) and (c)] SEM and energy-dispersive x-ray spectroscopy images of the Au/PPy nanowire. [(d) and (e)] A schematic depiction and SEM image of the self-assembled sperm-shaped MSRS. Celi et al., Scient. Rep. 11, 1–11, 2021; licensed under a Creative Commons Attribution (CC BY) license.

FIG. 6.

(a) Schematic representation of self-assembly fabrication technique employed to develop sperm-shaped MSRS. [(b) and (c)] SEM and energy-dispersive x-ray spectroscopy images of the Au/PPy nanowire. [(d) and (e)] A schematic depiction and SEM image of the self-assembled sperm-shaped MSRS. Celi et al., Scient. Rep. 11, 1–11, 2021; licensed under a Creative Commons Attribution (CC BY) license.

Close modal

Briefly, a plethora of fabrication routes have been undertaken for developing MSRS. While several successful endeavors have been discussed above, there are a lot more being researched currently that remain to be explored and investigated. The current developments and future ideas for fabrication (such as 4D printing) certainly open up vast possibilities for better design, performance, and control with enhanced multi-adaptive shape-tunable features.221–223 

Through evolution and body adaptation over millions of years, life forms in nature have gradually developed the ability to move through complex fluidic environments and respond to external changes for predating or seeking shelter.224,225 In doing so, they have armored self-organization techniques and equipped themselves with suitable mechanisms for efficiently propelling through viscid environments.226–228 This has often been a source of motivation for researchers trying to develop miniature untethered soft robotic swimmers for potential biomedical applications (see Fig. 7).66,229–236 Often, bio-hybrid and nature-inspired approaches have been undertaken to develop MSRS that can swim and navigate through harsh, dynamic, hard-to-reach, and confined environments.237–241 The propulsion mechanisms adopted by these MSRS have been categorized below according to their biological template or inspiration.242 

FIG. 7.

Naturally occurring microorganisms (top row) and their MSRS counterparts (bottom row). (a) E. coli with helical flagella, (b) spermatozoa with flexible flagellum, (c) Spirulina cells in water, (d) a Paramecium ciliate, (e) lotus-root-based helical magnetic microswimmers, (f) magnetically actuated robotic sperm, (g) Spirulina-templated magnetic helical microswimmer, and (h) a magnetically actuated ciliary microrobot. [(a) is reproduced with permission from Nakamura et al., Biomolecules 9, 279 (2019). Copyright 2019 MDPI. (b) is reproduced with permission from Ebrahmi et al., Adv. Funct. Mater. 31, 2005137 (2021). Copyright 2021 American Institute of Physics. (c) is reproduced with permission from Gong et al., J. Magn. Magn. Mater. 468, 148–154 (2018). Copyright 2018 Elsevier. (d) is reproduced with permission from Valentine et al., Cilia 1, 1–16 (2012). Copyright 2012 BioMed Central Ltd. (e) is reproduced with permission from Liu et al., Micromachines 8, 349 (2017). Copyright 2017 MDPI. (f) is reproduced with permission from Khalil et al., PloS One 13, e0206456 (2018). Copyright 2018 PLOS. (g) is reproduced with permission from Gong et al., J. Magn. Magn. Mater. 468, 148–154 (2018). Copyright 2018 Elsevier. (h) is reproduced with permission from Kim et al., Scient. Rep. 6, 1–9 (2016). Copyright 2016 Nature Portfolio.].

FIG. 7.

Naturally occurring microorganisms (top row) and their MSRS counterparts (bottom row). (a) E. coli with helical flagella, (b) spermatozoa with flexible flagellum, (c) Spirulina cells in water, (d) a Paramecium ciliate, (e) lotus-root-based helical magnetic microswimmers, (f) magnetically actuated robotic sperm, (g) Spirulina-templated magnetic helical microswimmer, and (h) a magnetically actuated ciliary microrobot. [(a) is reproduced with permission from Nakamura et al., Biomolecules 9, 279 (2019). Copyright 2019 MDPI. (b) is reproduced with permission from Ebrahmi et al., Adv. Funct. Mater. 31, 2005137 (2021). Copyright 2021 American Institute of Physics. (c) is reproduced with permission from Gong et al., J. Magn. Magn. Mater. 468, 148–154 (2018). Copyright 2018 Elsevier. (d) is reproduced with permission from Valentine et al., Cilia 1, 1–16 (2012). Copyright 2012 BioMed Central Ltd. (e) is reproduced with permission from Liu et al., Micromachines 8, 349 (2017). Copyright 2017 MDPI. (f) is reproduced with permission from Khalil et al., PloS One 13, e0206456 (2018). Copyright 2018 PLOS. (g) is reproduced with permission from Gong et al., J. Magn. Magn. Mater. 468, 148–154 (2018). Copyright 2018 Elsevier. (h) is reproduced with permission from Kim et al., Scient. Rep. 6, 1–9 (2016). Copyright 2016 Nature Portfolio.].

Close modal

Spermatozoa are highly efficient microswimmers that have the ability to make its way toward the ovum even through the highly viscous fluid using a flagellar motion.243,244 Motivated by the motility of the sperm cells, a microscopic artificial swimmer with magnetic multilayers comprising of a magnetic head and a passive tail has been designed (see Fig. 8).200,245–247 The swimming behavior and closed-loop motion control of a micro-robot driven by a sperm flagella has successfully demonstrated under low magnetic fields.248 Contrary to the existing magnetically actuated or bacteria-driven systems,233 this sperm-driven micro-machine came up with a promising motivation for developing new fertilization methods. Therefore, in principle, a single spermatozoon could potentially be transported to the egg cell location in a noninvasive manner.249 Sperm-inspired MSRS have been developed for efficient propulsion under magnetic fields (of strength 5 mT) with the capability of steering.213,250,251 In a recent study, the swimming of a magnetic sperm cell has been demonstrated through transverse bending wave propagation.252 Similar studies have been reported for potential drug delivery systems using magnetic nanoparticles, magnetotactic bacteria, and self-propelled microjets.253–259 

FIG. 8.

Schematic representation of a cryo-scanning electron micrograph shows a sperm-templated MSRS: 100 nm magnetite nanoparticles are attached to the head, mid-piece, principal piece, and distal end of a bovine sperm cell. Magdanz et al., Sci. Adv. 6, eaba5855, 2020; licensed under a Creative Commons Attribution (CC BY) license.

FIG. 8.

Schematic representation of a cryo-scanning electron micrograph shows a sperm-templated MSRS: 100 nm magnetite nanoparticles are attached to the head, mid-piece, principal piece, and distal end of a bovine sperm cell. Magdanz et al., Sci. Adv. 6, eaba5855, 2020; licensed under a Creative Commons Attribution (CC BY) license.

Close modal

Emulating the swimming behavior of a bacteria in motion, researchers have fabricated MSRS consisting of polystyrene microbeads and magnetic nanoparticles via a flagellar filament231; avidin–biotin linkages were used in order to propel the MSRS through a low Reynolds number fluid flow. Inspired by bacterial flagella, several other helical MSRS have been developed for net propulsion through a viscous fluid.260–264 Through these studies, it was inferred that the hydrodynamics and magneto-elastic forces interacted with each other, and as a natural consequence of fluid–structure interaction, they determined the swimming kinematics of the MSRS. Swimming kinematics of motile bacterial flagellar motors and their alignment with the magnetic field have also been reported.265 When propelled by rotating a bunch of slender flagella, these swimmers developed magnetic micro-torques for effective low Reynolds number fluidic propulsion.266 Bio-hybrid microswimmers consisting of several Serratia marcescens bacteria attached to a superparamagnetic microbead have been demonstrated to achieve high swimming speeds with steering control.267 Bacteria-templated micro-cleaners have been developed for their magnetic photo-catalytic ability268; in this study, core-shell micro-helical robots have been fabricated using Fe3O4–TiO2 for degrading organic pollutants using UV–visible light.

Inspired by a Chlamydomonas reinhardtii microalga, a cytocompatible microswimmer has been fabricated and subsequently magnetized by incorporating terbium.269 These magnetized algae could align themselves with the field lines of an applied external magnetic field in order to swim in a directional manner.270 Mimicking the breaststroke of an alga,271 ferromagnetic filaments have demonstrated structural instability-based swimming, thanks to their filament-buckling mechanisms.272 In a recent study, octopus-inspired MSRS has been developed for swimming under a time-asymmetric gradient-based magnetic field.273 Live microbial Tetrahymena pyriformis cells have been impregnated with artificial magnetic dipoles so that they could be actively steered under external magnetic actuation.274,275 Arguably one of the most energy-efficient aquatic lifeforms, jellyfish Ephyra-inspired MSRS have been fabricated using a solution casting method and studied for their enhanced swimming kinematics and ability of multi-modal locomotion.83,90

Nature-inspired coordinated pattern formation and (emergent) collective behavior owing to fluid-mediated hydrodynamic interactions are ubiquitous in a school of fish or in bacterial swarms.276 This has been emulated for active artificial microswimmers based on identical individuals.277 Here, randomly shaped magnetic micro-propellers have shown dynamic and reversible pattern formation. Even the synchronized motion of bacterial swarms has motivated researchers to develop their magnetotactic bacterial counterparts that could locomote in a synchronous manner.278 During their motion, hydrodynamic interactions lead to temporal synchronization in addition to their self-organizing swarm behavior. Iron-oxide nanoparticles have been inserted into cells to impart a remnant magnetization.279,280 Subsequently, the collective behavior and swarm control of these individual cells have been studied under rotating magnetic fields.

Similarly, bio-inspired acousto-magnetic robotic microswarms have demonstrated upstream motility.281 Recent studies on the cooperative motion and interactive behaviors of multiple disk-shaped micromotors have modeled their distinct dynamic self-organizing behaviors using physical models.282,283 Furthermore, the collective behavior and swimming kinematics of drug-loaded sperm-templated swarms have been studied for potential targeted and controlled drug delivery applications.284 Magnetically articulated robots have demonstrated multimodal collective swimming, clustering, and on-demand switching between translational and rotational swimming.285 In this study, the nanocomposite robots comprised a stiff lightweight carbon nanotube yarn framework that was surrounded by a magnetic polymer composite. Agglomeration-free magnetic swarms have been developed by enzyme-modified magnetite nanoparticles for small-dose fast thrombolysis and on-demand tasks in biological fluids.286 

Molecular cargo delivery has been achieved by employing cell-based magnetic microswimmers with inspiration from multi-cellular Spirulina.287 These swimmers were actuated by low-strength magnetic fields to navigate through a model intestinal tract for molecular transport.288 Cell erythrocyte-based bacterial MSRS has been fabricated as cargo vehicles for drug delivery.289,290 Recently, a review on biomedical applications and fabrication methodologies of bio-hybrid magnetic microrobots have been reported.291 Elsewhere, inspired by midge larva's distinct swimming gaits (e.g., side-to-side flexures and rotation) and their ability to couple their locomotion strategy, researchers have developed a pre-programmed magnetic soft robot that could optimally couple body curling as well as rotation to enhance mobility.292 

Clearly, several instances of biological inspiration serve as design strategies for the development of nature-inspired MSRS. In Sec. IV, we explain the swimming behavior of these magnetic swimmers with emphasis on their basic (primary) swimming modes (that are adopted by both real-life aquatic species and their robotic counterparts). We further attempt to unravel the coupled physics, swimming behavior, and magnetic field-induced propulsion of MSRS using principles of magnetic actuation, symmetry-breaking mechanisms, and fluid–structure interactions (that dictate their overall propulsion dynamics). Finally, we discuss the influence of the interplay between magnetic, elastic, and viscous forces that are simultaneously present in these magneto-responsive soft robotic swimmers.

Nature-inspired designs provide us with swimming strategies at miniaturized length scales.293 Over the years, researchers have used these as inspiration to generate the structural kinematics of a soft elastica for enhancing the swimming performance and net fluidic propulsion of magnetic swimmers. Owing to their miniaturized length scales, MSRS often find themselves in low Reynolds number fluid flows that have negligible inertial effects on offer.171,294 Hence, the sole contribution for net propulsion comes from breaking the spatial symmetry. This is a direct consequence of Purcell's scallop theorem (see Fig. 9), which states that a microorganism with a reciprocal stroke in a Stokes fluid would not be able to travel until it exerts thrust against the flow by employing a nonreciprocal motion.295 Nevertheless, at moderate to high Reynolds number fluid flows, inertial effects are not insignificant and contribute to the net propulsion.296–298 

FIG. 9.

Schematic representation of Purcell's scallop theorem: a reciprocal motion in a low Reynolds number fluid flow results in no net displacement; however, when the Reynolds number is high, there is a net propulsion even with a reciprocal motion owing to temporal symmetry breaking. Zhou et al., Chem. Rev. 121, 4999–5041, 2021; licensed under a Creative Commons Attribution (CC BY) license.

FIG. 9.

Schematic representation of Purcell's scallop theorem: a reciprocal motion in a low Reynolds number fluid flow results in no net displacement; however, when the Reynolds number is high, there is a net propulsion even with a reciprocal motion owing to temporal symmetry breaking. Zhou et al., Chem. Rev. 121, 4999–5041, 2021; licensed under a Creative Commons Attribution (CC BY) license.

Close modal

Depending upon the fabrication technique adopted to develop a magnetic swimmer and their targeted application, the size of magnetic particles used and the length scales of the robotic swimmer vary.299 In this review, we focus mostly on miniaturized magnetic robots that have sizes typically in micrometers to a few millimeters. However, notable exceptions have also been discussed when their length scales are orders of magnitude different. For example, sperm-inspired magnetic swimmers have a length scale of micrometers, while jellyfish ephyra-inspired magnetic swimmers are a few millimeters in length. Notably, nanoscale magnetic machines have also been reported,300–302 although they were rigid helices and clearly do not fit in the scheme of “soft” robots. A systematic representation of different magnetic soft robots and robotic swimmers in relation to their length scales and magnetic particles sizes have been listed in Table I.

TABLE I.

A systematic description of size information of MSRS: fabrication technique, biological inspiration, swimming mode, and characteristic lengths of magnetic soft robotic swimmer and magnetic filler particles.

Reference Fabrication technique Inspiration Swimming mode MSRS length Size (type) of magnetic particles
Kim et al.303   3D laser lithography  Paramecium  Ciliary  200 μ 0.2 μm (Ni–Ti) 
Ren et al.83   Solution casting  Ephyra  Ciliary  5 mm  5–10 μm (NdFeB) 
Garstecki et al.304   Photolithography  Bacteria  Helical  2–10 mm  1 μm (Fe2O3
Liu et al.305   Magnetic coating  Bacteria  Helical  1–4 mm  0.1–1 μm (Fe3O4
Magdanz et al.200   Self-assembly  Spermatozoa  Undulatory  60 μ 1 μm (Fe2O3
Manamanchaiyaporn et al.306   Solution casting  Fish  Undulatory  10 mm  0.5 μm (Fe3O4
Reference Fabrication technique Inspiration Swimming mode MSRS length Size (type) of magnetic particles
Kim et al.303   3D laser lithography  Paramecium  Ciliary  200 μ 0.2 μm (Ni–Ti) 
Ren et al.83   Solution casting  Ephyra  Ciliary  5 mm  5–10 μm (NdFeB) 
Garstecki et al.304   Photolithography  Bacteria  Helical  2–10 mm  1 μm (Fe2O3
Liu et al.305   Magnetic coating  Bacteria  Helical  1–4 mm  0.1–1 μm (Fe3O4
Magdanz et al.200   Self-assembly  Spermatozoa  Undulatory  60 μ 1 μm (Fe2O3
Manamanchaiyaporn et al.306   Solution casting  Fish  Undulatory  10 mm  0.5 μm (Fe3O4

It is important to note that all these swimmers typically undergo structural deformations and are therefore active elastica. They are flexible and deform under magnetic actuation to push (sweep or sway) the surrounding fluid for effective propulsion through the viscous medium. During their swimming cycle, they change their shape. For example, the ciliary swimmers have flexible lappets that continually deform to manipulate the surrounding fluid. The undulatory swimmers undergo flexural body deformations in the form of traveling waves (i.e., they are flexural swimmers), or sway the surrounding fluid using oar-like motion. These swimmers can be classified as both flexural and shape-changing swimmers.

However, the situation is somewhat different in the case of helical swimmers: e.g., when their magnetic flagella change shape under different magnitudes of external actuation, these flaps deform following the principles of magneto-dynamics. Therefore, they are elastic, flexible and can change their shape depending upon the interplay between (and dominance of) elastic, viscous, and magnetic forces. However, in some helical swimmers, they have a constant body profile where the chirality is fixed during their fabrication. Therefore, under external magnetic actuation, neither do they change shape, nor are they flexible.300 These swimmers are not discussed here in detail because the primary focus of this review is on nature-inspired” soft” robots that are inevitably elastic and flexible.

Microorganisms in nature (e.g., bacteria, spermatozoa, ciliates, etc.) as well as MSRS break spatial symmetry (i.e., they adopt a nonreciprocal motion) for propulsion through a viscous medium. However, exceptions to this have been reported. For example, in the case of microswimmers propelling through non-Newtonian shear-rate-dependent fluids, where net propulsion is achievable even in the Stokes regime by employing a reciprocal motion.301,307,308 Swimming behavior of MSRS through viscoelastic biological gels, non-Newtonian fluids, and other heterogeneous media have been reported.309–314 Inspired from nature, there exist three basic (primary) modes of propulsion for MSRS at such miniature length scales: helical,57,300 undulatory,198,306 and ciliary90,214 (see Fig. 10). Often, a combination of these modes (secondary) is employed by MSRS for enhancing their swimming speed and precision of maneuverability through a viscous medium.163,315

FIG. 10.

Three different swimming modes - undulatory, ciliary, and helical - adopted by natural lifeforms and artificial miniaturized magnetic soft robotic swimmers. For details on fabrication, magnetic actuation, swimming behavior, and computational modeling of MSRS, refer (a) Refs. 213 and 219, (b) Refs. 90 and 303 and (c) Refs. 304 and 316.

FIG. 10.

Three different swimming modes - undulatory, ciliary, and helical - adopted by natural lifeforms and artificial miniaturized magnetic soft robotic swimmers. For details on fabrication, magnetic actuation, swimming behavior, and computational modeling of MSRS, refer (a) Refs. 213 and 219, (b) Refs. 90 and 303 and (c) Refs. 304 and 316.

Close modal

In the ciliary mode,303 distinct effective and recovery strokes are used by a magnetic elastica to displace the surrounding fluid. Under a nonreciprocal magnetic actuation, a magneto-responsive elastica deforms and displaces a higher quantity of fluid to generate sufficient thrust during the effective stroke. A lesser fluid quantity is swept during the recovery phase only to bring the elastica back to its initial configuration for the next cycle to begin. As a result, there is a net quantity of the fluid swept, which generates a thrust. In the helical mode,304 an elastica deforms in the form of a helix (body twist/chirality) and swims through the fluid exhibiting a typical corkscrew motion. In the undulatory mode,317 a magnetic swimmer develops traveling waves through the body length that starts from the leading edge and travels until the trailing edge to push the surrounding fluid backward, or it propels through an oar-like whipping motion to sway the surrounding fluid backward, thereby generating net propulsion. In all these modes, there exists an interplay of magnetic, elastic, and viscous forces that dictate their overall swimming kinematics.318–320 

Microorganisms like ciliates (e.g., Paramecium and Coleps) possess naturally occurring membrane-bound hair-like tubular appendages (known as cilia) that have unequal relaxation (recovery) and contraction (effective) strokes within one swimming cycle to manipulate the surrounding fluid flow.321–323 Predominantly found in Chlamydia trachomatis, Paramecium aurelia, cartilaginous chondrocytes, tracheal respiratory epithelium, etc., a cilia renders them with motility and several important physiological functions. For example, during ciliary swimming, a large flexural (bending) deformation of the elastica is observed that helps it to displace large quantities of the surrounding fluid, thereby enabling higher swimming speeds. The fascinating manner in which a Paramecium or a Chlamydomonas swims through a viscous medium using their hair-like projections, has motivated researchers to design and fabricate ciliary swimmers.303 Owing to their miniature length scales (in micrometers), the above-mentioned swimmers and their robotic counterparts typically find themselves in low Reynolds number flows. Hence, they adopt a nonreciprocal motion to break spatial symmetry due to unavailability of inertial forces.

However, exceptions to these have been observed in nature for a jellyfish ephyra. Owing to their larger sizes and swimming behavior, they often swim at moderate to high Reynolds numbers. Inertia becomes relevant at these length scales (in millimeters). Therefore, they use both temporal as well as spatial asymmetries for net propulsion. For example, an aquatic jellyfish ephyra-inspired magnetic swimmer has been fabricated using eight flexible lappets that are fundamentally similar to cilia, but larger in size (around 5 mm). As a natural consequence, they have a moderate Reynolds number flow environment where they typically use inertial effects to their benefit for gliding through the viscous fluid.90 Inherently, they break temporal symmetry while gliding. Furthermore, they displace the surrounding fluid during the recovery (relaxation) and effective (contraction) strokes for generating a net displacement per swimming cycle.83 During the effective stroke, the lappets are wide open to enhance their interaction with the surrounding fluid (with an increased projection area) to displace a larger quantity of fluid for generating a higher thrust. However, the lappets close themselves during the recovery stroke by curling themselves significantly and return to their initial position, thereby reducing the projected area for minimizing fluidic interactions (see Fig. 11). This way, they also take full advantage of spatial asymmetry. Hence, they manipulate the surrounding fluid to propel themselves forward in an efficient manner by breaking both temporal and spatial symmetry.318 

FIG. 11.

(a) Schematic representation of an aquatic Ephyra jellyfish (left), the design (center), and its assembled MSRS version (right). (b) The motion sequence and kinematics of the robotic swimmer during one swimming cycle comprise distinct contraction (effective) and recovery (relaxation) strokes/phases, akin to a ciliate. Ren et al., Nat. Commun. 10, 1–12, 2019; licensed under a Creative Commons Attribution (CC BY) license.

FIG. 11.

(a) Schematic representation of an aquatic Ephyra jellyfish (left), the design (center), and its assembled MSRS version (right). (b) The motion sequence and kinematics of the robotic swimmer during one swimming cycle comprise distinct contraction (effective) and recovery (relaxation) strokes/phases, akin to a ciliate. Ren et al., Nat. Commun. 10, 1–12, 2019; licensed under a Creative Commons Attribution (CC BY) license.

Close modal

Inspired by the ciliary bending kinematics, the folding-bending and bending-only deformations of frog-inspired MSRS have been distinctly studied to emphasize the importance of the folding motion.91 The swimming kinematics improved when the MSRS propelled using the folding-bending motion kinematics compared to the bending-only motion due to higher spatial symmetry breaking (see Fig. 12). Often, these individual ciliary motion have been combined to display coordinated wave movements.324 For example, tiny soft ferromagnetic assemblies have been subjected to precessing magnetic fields to induce metachronal waves on their periphery (mimicking the ciliates), resulting in a sequential movement and net propulsion.325 

FIG. 12.

Schematic representation of an aquatic frog and its biomimetic swimming robot. The (b) propulsive mechanism, (c) geometry, programmed magnetization, and fabricated specimen, (d) magnetic actuation, [(e) and (f)] swimming performance with (e) biomimetic folding-bending and (f) bending-only system, (g) floating and sinking, [(h) and (i)] quantitative comparison between these in terms of (h) normalized displacement during one swimming cycle, and (i) swimming speeds. Reproduced with permission from Wu et al., ACS Appl. Mater. Interfaces, 11, 41649–41658 (2019). Copyright 2019 American Chemical Society.

FIG. 12.

Schematic representation of an aquatic frog and its biomimetic swimming robot. The (b) propulsive mechanism, (c) geometry, programmed magnetization, and fabricated specimen, (d) magnetic actuation, [(e) and (f)] swimming performance with (e) biomimetic folding-bending and (f) bending-only system, (g) floating and sinking, [(h) and (i)] quantitative comparison between these in terms of (h) normalized displacement during one swimming cycle, and (i) swimming speeds. Reproduced with permission from Wu et al., ACS Appl. Mater. Interfaces, 11, 41649–41658 (2019). Copyright 2019 American Chemical Society.

Close modal

Ciliary MSRS has been fabricated using three tubular protrusions (mimicking cilia) each on either side of the main body; further, a stepping (nonreciprocal) magnetic field was used to actuate the cilia with an asymmetric motion.214 As a result, the cilia possessed distinct contraction and relaxation strokes to generate a net propulsive thrust for efficient motility (see Fig. 13). In another study, the kinematics of a magnetically actuated microswimmer inspired by the Paramecium's metachronal wave has been discussed.326 Two-filament magnetic microswimmers have been proposed to swim through a viscous fluid using inter-filament hydrodynamic interactions, akin to a Chlamydomonas.327 Here, the filaments have been considered to be parallel, and they were attached to a rigid spherical head. The external magnetic actuation acted upon these filaments to deform them in a flexural manner. During this, the inter-filament hydrodynamic interactions modified the influence of drag forces due to one filament upon the other. Next, we discuss the helical mode of swimming.

FIG. 13.

Unequal power (contraction) and recovery (relaxation) strokes of a ciliary MSRS inspired from Paramecium. Kim et al., Scient. Rep. 6, 1–9, 2016; licensed under a Creative Commons Attribution (CC BY) license.

FIG. 13.

Unequal power (contraction) and recovery (relaxation) strokes of a ciliary MSRS inspired from Paramecium. Kim et al., Scient. Rep. 6, 1–9, 2016; licensed under a Creative Commons Attribution (CC BY) license.

Close modal

Helical propulsion has been regarded as the best strategy for efficient swimming,57 where a swimmer develops chirality and generates a body twist under a rotating magnetic field to propel forward. Generally, helical propellers are either partially magnetized or possess a nonhomogeneous distribution of the remnant magnetization (see Figs. 14 and 15).320 Chirality naturally facilitates directed propulsion and the use of an external rotating magnetic field actuates the soft miniature robot to locomote through the fluid in an efficient manner. In an experimental study,328 superparamagnetic filaments have been demonstrated to develop chirality on the fly due to the generation of magnetic torques. The spirals propagated from the leading edge to the trailing edge along the body length (i.e., in the direction opposite to swimming), thereby enabling the MSRS to propel forward.

FIG. 14.

(a) Partially magnetic elastica with only one end magnetized (grey region L0). (b) The development of the body twist is a natural consequence of fluid–structure interaction (acting on the entire swimmer) and magnetic torque (acting only on the magnetic portion). The trace and the swimming direction has been shown for clarity. Namdeo et al., Proc. R. Soc. A, 470, 20130547, 2013; licensed under a Creative Commons Attribution (CC BY) license.

FIG. 14.

(a) Partially magnetic elastica with only one end magnetized (grey region L0). (b) The development of the body twist is a natural consequence of fluid–structure interaction (acting on the entire swimmer) and magnetic torque (acting only on the magnetic portion). The trace and the swimming direction has been shown for clarity. Namdeo et al., Proc. R. Soc. A, 470, 20130547, 2013; licensed under a Creative Commons Attribution (CC BY) license.

Close modal
FIG. 15.

(a) Partially magnetic elastica with two ends oppositely magnetized (grey region L0). (b) The development of the body twist is dictated by the strength of the opposite magnetic torques acting at the two ends. The trace and the swimming direction has been shown for clarity. Namdeo et al., Proc. R. Soc. A, 470, 20130547, 2013; licensed under a Creative Commons Attribution (CC BY) license.

FIG. 15.

(a) Partially magnetic elastica with two ends oppositely magnetized (grey region L0). (b) The development of the body twist is dictated by the strength of the opposite magnetic torques acting at the two ends. The trace and the swimming direction has been shown for clarity. Namdeo et al., Proc. R. Soc. A, 470, 20130547, 2013; licensed under a Creative Commons Attribution (CC BY) license.

Close modal

In general, helical propellers display a linear velocity-frequency dependence.304 However, at higher frequencies, nonlinear velocity–frequency relationships often result in a wobbling motion. This is known as the step-out regime (see Fig. 16).305 The chirality of these helical structures could either be drag-induced (for uni-directional propellers) or field-induced (for bi-directional propellers).320 When a helix develops owing to the opposite magnetic torques acting at the two distal ends (with opposite remnant magnetization), it is a manifestation of field-induced chirality. The helicity reverses when the external field rotation is reversed (resulting in bi-directional swimming). However, when only one end of the MSRS is magnetized, magnetic torques act only upon that region locally. Due to structural elasticity, when this (magnetized) portion follows the external field, it tries to rotate the entire swimmer's body. However, the drag forces act throughout the body length. The fluid–solid interaction naturally and coherently generates the helix. This is known as drag-induced chirality. Notably, these swimmers have the ability to swim only along a specific direction (i.e., they are uni-directional), although they can be steered easily for a curved path maneuvering.

FIG. 16.

(a) Variation of swimming speed U as a function of actuation frequency ω. When ω > ω c, the swimmer wobbles (due to excessive viscous drag forces dominating over the swimmer's elastic forces—represented by the fluid number Fn) and the step-out regime begins. (b) The body twist θtwist (a measure of chirality) varies with the characteristic body length along the direction of swimming. Higher drag forces facilitate twisting, thereby resulting in higher swimming speeds but only to a certain critical value ( F n ) c. Namdeo et al., Proc. R. Soc. A, 470, 20130547, 2013; licensed under a Creative Commons Attribution (CC BY) license.

FIG. 16.

(a) Variation of swimming speed U as a function of actuation frequency ω. When ω > ω c, the swimmer wobbles (due to excessive viscous drag forces dominating over the swimmer's elastic forces—represented by the fluid number Fn) and the step-out regime begins. (b) The body twist θtwist (a measure of chirality) varies with the characteristic body length along the direction of swimming. Higher drag forces facilitate twisting, thereby resulting in higher swimming speeds but only to a certain critical value ( F n ) c. Namdeo et al., Proc. R. Soc. A, 470, 20130547, 2013; licensed under a Creative Commons Attribution (CC BY) license.

Close modal

Magnetotactic bacterium has been fabricated using an elongated bacteria and a long elastic flagella to propel under rotating magnetic fields.329 Typically, for magnetotactic bacteria and soft robotic miniature swimmers inspired by them, the field is basically the geomagnetic field that has a strength of merely 50 μT.238 Bacteria propel by rotating their slender flagella using a whipping helical stroke. While peritrichously flagellated Escherichia coli has the ability to swim back and forth by wrapping their flagella in the form of a helical bundle, monotrichous bacteria cannot do this using their single flagellum and planar wave propagation. This has motivated researchers to fabricate a two-tailed MSRS comprising a magnetic head and two collinear, unequal, and opposite ultra-thin tails.330 For a specific range of actuation frequency, either the first or the second tail was selectively excited to exhibit a planar wave propagation based on the tail-length ratio. This meant that below the (swimming direction) reversal frequency, the first tail provided a propulsive force, while the second tail was passive to generate a flagellated motion along one direction. However, above the reversal frequency, the second tail achieved a flagellated propulsion to demonstrate bi-directional locomotion.

Micro-swimmers with DNA self-assembled flagellar bundles have also been developed to mimic a self-propelling peritrichous bacteria.331 These swimmers were deformed by bending along the body length when subjected to a rotating uniform magnetic field. They outperformed their single-appendage counterparts as seen in monotrichous bacteria because of their well-controlled shape profile due to bundled flagellar assembly. Bio-inspired helical MSRS based on soft lotus root fibers have been characterized for their swimming performance.305 A corkscrew-type helical mode of propulsion has been adopted by magneto-active bacteria, where the flagellar motion kinematics have been studied using physics-based dynamic models.332 

Highly flexible helical MSRS have been subjected to rotating gradient magnetic fields to display special trajectories and complex paths.333 Here, the swimmer body was derived from the inner fiber structure of the lotus root. Flagellar nanorobots have been fabricated with avidin-coated magnetic nanoparticle head and a single biotin-tipped re-polymerized flagellum.334 This study analyzed the dependence of the swimming kinematics upon the magnetic field actuation frequency, flagellar length, and head size. Two-tailed soft microrobots have been developed to demonstrate frequency-dependent flow. Upon subject to external rotating magnetic fields, the magnetic swimmers exhibited a sprocket-like trajectory.335 

Undulation is usually the preferred swimming mode when the body aspect ratio is high, but the flexural rigidity is low enough to support the transmission of body waves.336 Sperm cells, flagella, and artificial MSRS inspired (or driven) by them classify themselves as undulatory propellers.337 Lampreys, eels, snakes, and several aquatic organisms (that have a slender morphology) swim using body undulations in the form of traveling wave propulsion with their passive elastic tails.338 The bending stiffness of their elastic tails is responsible for the development and propagation of the traveling wave along its length.339 

Owing to their low flexural rigidity, these structures can deform in a flexural manner when subjected to planar body loads. Traveling waves generate around the leading edge and propagates along the bodylength toward the trailing edge. This results in the generation of thrust required for forward propulsion.14,122,340 When the wavelength of the traveling wave is higher than the characteristic body length of the swimmer, the swimming mode is known as the oscillatory mode of propulsion. This is a sub-category of the undulatory mode of swimming. In such cases, the traveling wave is incomplete through the body length, thereby resulting in a whipping oar-like motion during propulsion (see Fig. 17).319 However, when the characteristic body length is higher than the wavelength, there is at least one complete traveling wave that propels through the swimmer body length.89,306,317

FIG. 17.

(a) Schematic of an undulatory MSRS. The magnetic portion (grey region) consists of a polymer matrix that is impregnated with external magnetic filler particles. This allows it to be remotely actuated using an external magnetic field. (b) The steady-state nonreciprocal undulatory motion of the MSRS. The induced bending curvature reverses halfway during the actuation cycle leading to its net propulsion. Reproduced with permission from Namdeo et al., Phys. Rev. E 88, 043013 (2013). Copyright 2013 American Physical Society.

FIG. 17.

(a) Schematic of an undulatory MSRS. The magnetic portion (grey region) consists of a polymer matrix that is impregnated with external magnetic filler particles. This allows it to be remotely actuated using an external magnetic field. (b) The steady-state nonreciprocal undulatory motion of the MSRS. The induced bending curvature reverses halfway during the actuation cycle leading to its net propulsion. Reproduced with permission from Namdeo et al., Phys. Rev. E 88, 043013 (2013). Copyright 2013 American Physical Society.

Close modal

Resembling a sperm cell, MSRS with a magnetic Co/Ni head and a passive elastomeric tail has been demonstrated to swim using an oscillatory mode of swimming under weak magnetic fields.213 In this study, a frequency sweep has been reported that showed an optimum value of actuation frequency resulted in the highest swimming speed. Under precessing magnetic fields, flexible sperm-templated MSRS exhibited bi-directional propulsion, where the magnetic head drove the flexible passive tail to rotate resulting in the generation of undulatory body waves.219 Sperm-templated flagellar propulsion based on the development of an undulatory traveling body wave has been observed for microbots with segmented magnetization, where the wave pattern on the individual cellular segment was shown to be dependent upon the location and quantity of the magnetic nanoparticles.341 

Magnetically driven nanoscale swimmers have emulated the body and caudal fin propulsion mechanism exhibited by fish.241 Here, opposite traveling waves were periodically generated to demonstrate forward propulsion. The soft swimmer deformed in the transverse direction due to generated body torques when subjected to an external oscillating magnetic field. MSRS has exhibited internal elastomeric undulatory deformations for propulsion through a viscous medium; this undulatory wave beating was attributed to the structural kinematics as a result of a remnant magnetization that was programmed into the swimmer.317 Furthermore, active head-passive tail morphology has been considered to fabricated undulatory MSRS.200 Here, the rigid triangular head geometry was magneto-responsive, while the passive tail was compliant and had no magnetization.316 Therefore, the slender tail waved passively (similar to a whipping motion), while the active head was driven by magnetic torques.

Flagella-inspired MSRS have been designed for their optimal swimming performance and the influence of various system parameters was thoroughly investigated.319 The hydrodynamic interactions were studied using the resistive force theory. The magnetic swimmer was subjected to a directional magnetic field for forward propulsion. Using a combination of a directed sinusoid magnetic field, it was possible to obtain a faster swimming speed. This was further validated experimentally.342 Millimeter-scale MSRS sheet with a distributed magnetization profile has been developed to propel using undulation.340 MSRS with a flexible slender cylindrical passive tail and an active (magnetic) spherical head has been actuated to propel by developing traveling body waves.343 Recently, undulatory swimming and surface crawling have been demonstrated for sheet-shaped MSRS inside viscous fluidic confinements (see Fig. 18).163 The body undulation and traveling wave propagation were attributed to a sinusoidal magnetization profile in combination with a rotating magnetic field.

FIG. 18.

Undulatory crawling (left) and swimming (right) modes of locomotion inside fluid-filled confined channels. Scale bars, 1 mm. Ren et al., Sci. Adv. 7, eabh2022, 2021; licensed under a Creative Commons Attribution (CC BY) license.

FIG. 18.

Undulatory crawling (left) and swimming (right) modes of locomotion inside fluid-filled confined channels. Scale bars, 1 mm. Ren et al., Sci. Adv. 7, eabh2022, 2021; licensed under a Creative Commons Attribution (CC BY) license.

Close modal

Multi-link magnetic nanoswimmers have been fabricated using a segmented-chain approach.344 The tail mimicked a eukaryote-like elastica that had rigid magnetic Ni links connected through flexible polymer bilayer hinges to form the head (see Fig. 19). Planar undulations were observed for this MSRS composite when subjected to an oscillating magnetic field. In another study, MSRS has been demonstrated to navigate through the body lumen using undulatory swimming.345 A similar propulsion technique has been employed by an untethered nonmotile sperm-inspired microbot that showed bending waves along the passive flagellum for efficient swimming.346 

FIG. 19.

(a) Schematic representation, (b) SEM images, and (c) optical images of n-link nanoswimmers. (d) The 3-link undulatory MSRS subjected to an oscillating magnetic field; here, 2θ is the angular sweep of the magnetic field B, and τm is the magnetic torque. Reproduced with permission from Nano Lett. 15, 4829–4833 (2015). Copyright 2015 American Chemical Society.

FIG. 19.

(a) Schematic representation, (b) SEM images, and (c) optical images of n-link nanoswimmers. (d) The 3-link undulatory MSRS subjected to an oscillating magnetic field; here, 2θ is the angular sweep of the magnetic field B, and τm is the magnetic torque. Reproduced with permission from Nano Lett. 15, 4829–4833 (2015). Copyright 2015 American Chemical Society.

Close modal

The swimming performance of a magnetic flagellum (comprising of a paramagnetic microsphere with a ferromagnetic nanorod) under a swinging magnetic field has been reported.347 A reversal of the microswimmer velocity was observed upon varying the length of the nanorod and the effective direction of magnetic susceptibility.348 Nanoscale filaments have been designed using the DNA-origami technique that acted like asymmetric flagellar appendages to propel magnetic beads through a viscous medium.349 Self-folding hydrogel tubes with bacterial flagellar appendages have exhibited efficient swimming through viscous fluids.350 The influence of the flexible tail and its geometry upon propulsion has been discussed. While the flagella applied a forward thrust, a precession was induced on the swimmer's body because the tail wobbled. This enhanced the swimming performance.

Ferrogels in the form of long cylinders have been considered as artificial magnetic swimmers that undulated and swam like a worm.351 Under a transverse oscillating magnetic field operating beyond a critical limit, the swimmer undulated as a result of torsional buckling instability. In another study,352 undulatory body deformation in ferromagnetic filaments was characterized under transverse oscillating magnetic fields. At low frequencies, the filament synchronously rotated with the magnetic field. However, beyond a critical limit, an out-of-plane three-dimensional transition was observed at higher frequencies.353 A laterally undulating MSRS with a triangular head-tail morphology and sinusoidal magnetization has been developed for tunable body deformation-induced swimming.306 Under an oscillating magnetic field, higher dynamic torques acted on the head compared to the tail. This resulted in the development of traveling body waves that propagated through the entire body length enabling self-propulsion through the fluid.

Undulatory magnetic swimmers have demonstrated excellent control for both dry as well as wet working environments.354 They have demonstrated abilities of bi-directional locomotion and steering.355 Planar wave propulsion and swimming behavior have been observed for magneto-responsive soft robotic sperms at low Reynolds number flows.232 These swimmers were fabricated using polystyrene (dissolved in dimethyl formamide) and iron-oxide nanoparticles. The latter was concentrated within the sperm bead to provide a magnetic dipole. The deformable ultra-thin tail enabled a flagellar locomotion under external magnetic fields. In another study, a magnetically actuated soft robotic sperm has been reported to switch between helical and undulatory modes of swimming.315 Here, the MSRS had a magnetic head with a slender deformable flagellum. Upon magnetic actuation, an out-of-plane wobbling was observed in the head. This resulted in helical propulsion, whereas an in-plane wobbling gave rise to undulatory swimming.

Inspired by the undulatory motion of a larval zebrafish,356 researchers have fabricated magnetic swimmers that generated flexural body waves to propel through a fluid medium (Fig. 20).357 Furthermore, the design strategy was reported followed by a systematic kinematic comparison between them. MSRS with flexible flagellum have been developed to exhibit dexterous swimming behavior and accelerated maneuvering in a three-dimensional setting.358 In another study, multiple deformable flagella have been attached to a miniature MSRS to facilitate rotation and enhance swimming speed by generating higher thrust.359,360

A transition between helical and transverse wave propulsion has been demonstrated for a sperm-templated MSRS for different concentrations and profiles of remnant magnetization.252 Furthermore, based on the viscosity of the surrounding fluid, MSRS has been actuated using different external magnetic fields to undergo a transition between helical and undulatory modes of propulsion.361 A kinematic comparison of flexible undulatory swimmer and a helical swimmer has been reported362; in this study, the swimmers were immersed in a pure glycerol fluid to replicate a low Reynolds flow environment. It was observed that the helical swimmers were easier to experiment with compared to undulatory ones. The former displayed higher swimming speeds. However, the steerability of undulatory swimmers outperformed the helical ones.

FIG. 20.

A kinematic comparison between a larval zebrafish and its robotic counterpart in the form of an untethered undulatory MSRS during their swimming cycles with the magnetic flux density orientation indicated (by red arrows). Wang et al., Sci. Adv. 7, eabf7364, 2021; licensed under a Creative Commons Attribution (CC BY) license.

FIG. 20.

A kinematic comparison between a larval zebrafish and its robotic counterpart in the form of an untethered undulatory MSRS during their swimming cycles with the magnetic flux density orientation indicated (by red arrows). Wang et al., Sci. Adv. 7, eabf7364, 2021; licensed under a Creative Commons Attribution (CC BY) license.

Close modal

Furthermore, MSRS with freestyle swimming mode has been demonstrated to be highly efficient in low Reynolds number regime for a symmetric multi-linked two-arm nanoswimmer.363 Here, the synchronized oscillatory body deformations under the combined action of magnetic field and viscous forces were attributed as the fundamental driving force. It was demonstrated that the nonplanar propulsion swimming mechanism due to the cooperation between the two magnetic arms could be powered by a plane oscillatory magnetic field. Functionalization and biomedical applications of helical magnetic soft miniature robots have been discussed in a recent review, where these small corkscrew-type machines advance toward translational medicine and minimally invasive interventions for applications such as cell stimulation, targeted drug delivery, and in vivo medical imaging.262 

Different force- and torque-based actuation strategies have been proposed to propel MSRS using uniform fields, field gradients, and field patterns (see Fig. 21).114 Miniaturization of magnetic swimmers is mandatory for them to cater to challenging biomedical applications that involve reaching difficult-to-access body regions and microfluidic assays that have viscid environments). Consequently, there is a drastic reduction in the Reynolds number of the surrounding fluid.296 Therefore, minimal inertial contributions are on offer due to nonavailability of temporal asymmetry. Hence, torque-based methods are favored because this approach ensures lesser viscous drag forces compared to that of force-based actuation.57 Furthermore, large deformability of MSRS under magnetic body torque enhances spatial asymmetry leading to higher swimming speeds.318 Additionally, the penetration depth of torque-based methods are higher and they are relatively easy to control (and do not falloff quickly). Furthermore, we summarize below the actuation strategies and control techniques adopted during experimental procedures/demonstration of magneto-responsive swimmers.

FIG. 21.

A schematic representation of different field patterns for force- and torque-based actuation methods. (a) The torque τ is a cross product of magnetization M and magnetic field B. (b) The force F is a dot product of M and magnetic field gradient B. (c) Directional oscillating B. (d) Unidirectional oscillating B. (e) Rotating B. (f) Directional rotating B. (g) Stepping B. (h) On/off B. (i) Longitudinal/axial B. (j) Lateral/transverse B.

FIG. 21.

A schematic representation of different field patterns for force- and torque-based actuation methods. (a) The torque τ is a cross product of magnetization M and magnetic field B. (b) The force F is a dot product of M and magnetic field gradient B. (c) Directional oscillating B. (d) Unidirectional oscillating B. (e) Rotating B. (f) Directional rotating B. (g) Stepping B. (h) On/off B. (i) Longitudinal/axial B. (j) Lateral/transverse B.

Close modal

Magnetotactic bacteria with various morphologies and flagellar apparatus have been developed for sensing oxygen and cell motility in an oxygen gradient owing to magneto-aerotaxis.364 This is a phenomenon in microaerobic niches that describes the alignment of a cell impregnated with a magnetic dipole to migrate toward an environment with higher oxygen concentration.365 These magnetotactic bacteria formed assemblies of magnetic nanoparticles (magnetosomes) that displayed several organization templates.366 Mostly, they arranged in chains, although cluster assemblies have also been reported and quantitatively characterized.367 Researchers have studied the flexural rigidity of magnetosome chains.368 These were regarded as cellular compass needles consisting of a string of vesicle-enclosed magnetic nanoparticles aligned on a cytoskeletal filament. Here, the influence of the magnetic interactions on the bending stiffness, orientation, morphology, and persistence chain length has been discussed.

Self-assembly behavior of paramagnetic colloidal particles on magnetically vibrated stripes have been reported earlier.369 Pair interactions between magnetically driven colloidal microrotors subjected to an external precessing magnetic field have been studied.370 Here, the micro-rheological properties and collective dynamics of the colloidal aggregates were analyzed using optical microscopy. Magneto-responsive surface magnetic rotors in the form of spherical microparticles have demonstrated net translation upon subject to magnetic field.371 The magnetic modulation helped them to rotate, spin, and interact with other units of the collection using hydrodynamic effects. Highly dense permanently linked magnetic colloidal chains in the form of micro-sieves have been assembled.372 These were guided above a channel-free magnetic strip in order to precisely move and sieve nonmagnetic particles or tweeze microscopic cargos. Furthermore, chain-aligned magneto-responsive particles have shown controlled motion under external magnetic fields.373 

DNA-linked anisotropic particles composed of paramagnetic colloidal rotors have shown controlled propulsion when floating above a flat plate and subjected to a precessing magnetic field.374 MSRS swarms have been steered by dynamic magnetic actuation using a novel steering algorithm to reach a target region along curved trajectories.[375,376] Pattern formation, collective behavior, and clustering of assemblies have been studied for MSRS swarms.377 Paramagnetic microparticle clusters have been formed using a magnetic manipulation system to control their collective behavior and precise positioning, manipulation, and assembly.378 The of microscopic magneto-responsive clusters propelling close to a surface has been studied.379 Their collective dynamics was attributed to the fine balance between the magnetic dipolar interactions and hydrodynamic drag forces.

Dynamic behavior of particle-based paramagnetic microswimmers actuated using rotating magnetic fields has been studied for different frequencies.380–384 When the actuation frequency was below a threshold, the microswimmer exhibited a simple rotation upon the substrate. However, it propelled with varied morphology under higher frequencies. Suspended paramagnetic particles were shown to form a vortex-like swarm by appropriately tuning the pitch angle under the influence of an external rotating magnetic field.385 Further, pattern generation and motion control of vortex-like paramagnetic nanoparticle swarms from dispersed nanoparticles have been successfully reported.386 Contactless manipulation of paramagnetic microbead clusters via push-and-pull has been demonstrated.387 Varying concentrations of ferrimagnetic nanoparticle chains have been infused into a thermoreversible gelatin hydrogel matrix with varying cross-linking degrees to yield ferrogels using a green synthesis technique.388 Following this, crystallographic, morphological, magnetic, and mechanical characterizations have been reported.389 In addition, the interaction between the ferrimagnetic nanocrystals and the ferrogel magnetic anisotropy has been explained.390 

Paramagnetic nanoparticles have been shaped into ribbon-like swarms under oscillating magnetic fields.227 When the magnetic fields were tuned, the micro-swarms performed a reversible elongation with an extremely high aspect ratio with occasional splitting and merging. Furthermore, the colloidal micro-swarm was demonstrated to pass through confined microfluidic channels with high swimming speed while maintaining stability. Magnetic navigation and active generation of similar magnetic swarms have been reported in bio-fluids, wherein the effects of viscosity and chemical species have been discussed.391 Hematite colloidal rotors have been observed to form stable three-dimensional clusters when subjected to rotating magnetic fields.392 The applied field generated torques that forced rotation close to a surface resulting in a net translational motion. This study reported the cluster lifespan and its dependence on propulsion speed and stability.

Furthermore, swimming dynamics of dipolar rings of microscopic ferromagnetic ellipsoids have been discussed, where their shape evolution and cluster formation were precisely controlled using an external oscillating magnetic field.393 The microscopic rings captured, entrapped, and released microscopic objection through a remote magnetic command. The enhancement of diffusion and non-Gaussian dynamics in a magnetic colloidal cluster under a precessing magnetic field has been demonstrated.394 In addition, small hematite microdocker clusters in the form of anisotropic ferromagnetic particles have been actuated using a remote magnetic field.395 Effectively, this towed and induced a phoretic flow to dock and transport microscopic objects within confined microfluidic channels. Using a similar mode of actuation, magnetically twisted colloidal ribbons in the form of ferromagnetic micro-ellipsoids have been used to influence the hydrodynamic flow field and transport-and-release microscopic particles within a viscous fluid.396 

3D steering along tortuous paths has been realized using a visual feedback mechanism.397 Steering and nonholonomic position control have been demonstrated using a single pair of Maxwell coils.398 In this study, the millirobot exhibited a two-dimensional motion along the two axes under changing magnetic field gradients. A set of two synchronized permanent magnets has been used to radially steer a helical MSRS.399 With this actuation strategy, a higher motion stability was observed compared to that when a single rotating dipole field was used. Furthermore, the two synchronized dipole fields reduced the lateral oscillation, even when actuated at higher swimming speeds. Multi-microbot actuation, independent steering, and precise motion control have been demonstrated for magnetic micropropellars with varying magnetization profiles.400 Magnetic steering was precisely performed with directional control for CoO–TiO2 microswimmers under external magnetic fields.401 

Magnetically actuated screws have been driven through soft bovine tissues under external rotating magnetic fields.402 In this study, the influence of actuation frequency upon the destabilizing torque (that resulted in steering) was discussed. Wire-shaped magneto-electric nanoswimmers have been precisely steered toward the targeted location using the remote rotating magnetic field for on-demand magneto-electrically assisted drug release.403 Similarly, magnetic swimmers have been steered using external magnetic fields for targeted drug delivery and controlled navigation through blood flow.404 Wheel-shaped flaky magnetic microswimmers have been studied for their locomotion behavior upon subject to rotating magnetic fields.405 Here, two modes of propulsion were observed—tumbling and rolling. Microswimmers with a rolling motion were observed to propel and steer precisely with a higher swimming speed.

Based on geometric mechanics, an algorithmic framework has been developed to regulate the external magnetic fields to precisely control the desired locomotion of MSRS in a fluid medium.406 In this study, the swimming speed was optimized using a principled approach as a function of the remnant magnetization to encode the optimized magnetization profiles for two-link and three-link swimmers. 3D motion planning has been reported for a three-link two-joint planar MSRS for a low Reynolds number flow.407 Here, yaw-pitch movements at the two actuated joints were demonstrated during 3D swimming (in contrast to the traditional yaw–yaw movements) with only two active inputs.

Magnetic films have been maneuvered along arbitrary three-dimensional paths using a closed-loop control stereo-vision approach,408 online neural-network compensation update with proxy-based sliding mode control,409 and adaptive orientation compensation model.410 A similar study has been reported for ferromagnetic nanoparticle robots.411 Magnetic coil setups have been developed to control and maneuver jellyfish-inspired MSRS using ultrasound image-guiding for patching target surfaces within bladder phantoms (see Fig. 22).83 Pulsatile release of payloads and precise control over drug discharge kinematics have been successfully demonstrated for a magneto-electric composite.412 Simultaneous localization and propulsion of a magnetic capsule propelling through the lumen has been demonstrated.413,414

FIG. 22.

(a) Schematic representation of the experimental setup: (i) the magnetic coil system, and (ii) the phantom bladder model. (b) Ultrasonic image-guided robotic control for target surface patching—the robot is marked using thin red curves. Reproduced with permission from Ren et al., Robot.: Sci. Syst. (2019). Copyright 2019 The Authors.

FIG. 22.

(a) Schematic representation of the experimental setup: (i) the magnetic coil system, and (ii) the phantom bladder model. (b) Ultrasonic image-guided robotic control for target surface patching—the robot is marked using thin red curves. Reproduced with permission from Ren et al., Robot.: Sci. Syst. (2019). Copyright 2019 The Authors.

Close modal

Furthermore, using a combination of acoustic and magnetic fields, MSRS have demonstrated effective maneuverability.91 Specifically, the swimmers had micro-cavities at their body center, and superparamagnetic particles within its polymeric matrix. The micro-cavity had an air bubble trapped within it. When this was acoustically activated, there was a bubble oscillation that consequently resulted in their net propulsion. 2D magnetic actuation and precise positioning have been successfully performed for a surface roller at low Reynolds number flows.415 Here, a magnetic roller was actuated through a viscous fluid under rotating magnetic fields. Closed-loop motion control of microscopic jets through microfluidic channels (and mazes) has been demonstrated using external magnetic actuation. U-turn trajectories and precise maneuvering were achieved for high jet speeds at a low Reynolds number fluid flow.256 These self-propelled microjets have been controlled using haptic feedback that employed a teleoperation system along with force estimation.416 Consequently, this enabled an external user to appropriately control the position of the microjet.

Thin film MSRS has been fabricated to demonstrate multi-modal locomotion such as crawling, rolling, and swimming through narrow-walled confinements.163 Specifically, jellyfish-inspired and forklift truck modes have been illustrated for state-of-the-art cargo delivery applications and transporting heavier micro-objects even up to 10 times its own weight.90,417 Here, apart from the biomimetic mode, other modes of swimming have been reported for surrounding fluid manipulation and chemical species mixing. Bio-inspired hydrogel-based MSRS have been fabricated with magnetic actuation in the head region and a passive tail.418,419 This MSRS exhibited helical propulsion as well as multi-modal locomotion such as rolling, crawling, and swinging. Bi-directional locomotion has been achieved for a self-assembled nanorod-sphere propeller under a simple oscillating magnetic field tuning.420,421 However, in spite of these burgeoning achievements and steep progress in experimental approaches, nature-inspired design, additive manufacturing techniques, and state-of-the-art laboratory facilities, there is still a lacuna in the theoretical modeling and kinematic design of these fully coupled MSRS. Computational and numerical models have only started to emerge in order to comprehend the fundamentals of coupled physics in MSRS as well as their magnetic-field-induced propulsion using robust modeling approaches; this is discussed in Sec. VI.

Over the years, computational and numerical frameworks have been proposed to study the swimming behavior and kinematic performance of these magneto-responsive soft robotic swimmers.83,90,297,422–424 The spatial evolution of structural variables and the temporal evolution of the surrounding flow field due to an external magnetic actuation have been predicted using a wide range of empirical, semi-analytical, and numerical models. The most promising approaches are mentioned here: (i) slender body theory (SBT) has been used to capture the flagellar hydrodynamics and swimming behavior of undulatory MSRS;315 and, resistive force theory (RFT) has been proposed to estimate the drag forces offered by the surrounding fluid and estimate the steady-state kinematics of MSRS;316,424 (ii) reduced-order dynamic/physics-based models;83 and, (iii) robust computational models involving a full coupling between the fluid flow, solid deformation, and magnetic actuation have also been used for studying the large deformation fluid–structure interactions (FSI) in magnetic swimmers using the finite element method,319 lattice Boltzmann method,425 or boundary element method.163,313 A comparative study between SBT and RFT has been reported for a generic analysis of flagellar locomotion.426 It was concluded that the former was more accurate, but it involved a higher computational cost. Additionally, the error estimates could be reduced in RFT by appropriate manipulation of the drag coefficients.427 Dynamics-based reduced-order simplistic models have been proposed to study the swimming kinematics of a magnetic swimmer using Newton's laws of motion.21,198 In this section, we discuss these modeling approaches adopted for understanding the kinematics of MSRS.

RFT has often been used to analyze the movement of MSRS swimming through viscous fluids.232,361,428,429 In RFT (applicable mostly for slender members),430,431 the structural element is partitioned into infinitesimal segments. These individual units experience drag forces and generate thrust. Linear superposition of the force components from all these segmented lengths is used to estimate the effective swimming speed. This approach has not only been used to study the dynamics of MSRS inspired by flagella in Chlamydomonas432 or flagella of sperms,433,434 but also for analyzing the locomotion of animals (and their robotic counterparts)219,306,315,435 that even move through granular media.436 Very thin shell-type structures have been discretized using a nonlinear finite element framework to further couple it to RFT for the simulation of the surrounding flow field.429 ABAQUS subroutines have been developed to prescribe the external forces due to magnetic body couples and viscous drag forces. In this study, the swimming kinematics of a slender sheet-shaped MSRS under the helical mode of propulsion have been reported.

Based on RFT, a magneto-hydrodynamic model has been developed to study the kinematics of robotic swimmers through different viscous media and their transition into Newtonian-viscoelastic interfaces.437 An abrupt change in the viscosity of the surrounding fluid considerably affected the swimmer's ability to synchronously rotate with the rotating field. Subsequently, this resulted in a phase lag. The force-free steady-state condition was assumed to estimate the swimming speed using RFT in the case of a flagella-inspired MSRS.319 Using a similar strategy, kinematics of bi-directional locomotion was reported for independently controlled arc-shaped MSRS.316 Hydrodynamic interactions between a flagellar magnetic microswimmer and the surrounding fluid were successfully modeled using an RFT framework.342 Similarly, the swimming kinematics of a slender motile magneto-elastic microswimmer has been analyzed.431 Optimal actuation patterns for flagellar MSRS have been reported using this formulation.438 Shape discretization and approximation of hydrodynamical forces have been carried out to optimize the swimming speed involving constraints over the magnetic field amplitudes.

The low Reynolds number hydrodynamics and the induced flow fields around a magnetic swimmer has been studied for a variation of the Dreyfus microswimmer using RFT.245,439 This proof-of-concept study proposed a swimmer design that exceeded speeds of one body length per second under reasonable values of the driving magnetic field using appropriate geometric and material properties. Here, a discrete beam theory was used to account for the elasticity. The MSRS was considered to be permanently magnetic. Furthermore, the magnetic swimmer could swim straight, turn abruptly, and also swim in circles. The propulsion dynamics of a magneto-elastic 3-link artificial Purcell microswimmer with segmented remnant magnetization has been modeled using a modified RFT formulation.440 The control strategy for the optimal swimming dynamics of such a swimmer has been verified for real-life applications.441 

The swimming behavior of a beating flagellum in low viscous fluids has been modeled using a similar strategy.442 The findings were compared with experimental data of soft microrobotic sperms. It was inferred that this approach had estimated the flagellar deformation reasonably well. Numerical elastohydrodynamic models have been proposed to estimate the magnetic actuation and structural response of a magnetic nanoparticle-coated nonuniform flagella.339 The dynamics of bacterial flagellar swimming have been studied using SBT simulations incorporating full-field hydrodynamic interactions inside a bundle of parallel helical filaments that rotated in synchrony to push the fluid for efficient propulsion.443 

Model order reduction has been performed in order to reduce the computational complexity of mathematical models during numerical simulations for bio-inspired artificial microswimmers.444 Specifically, hydrodynamic analysis of a spermatozoa-like soft microrobot has been reported.445 Early works on the dynamic modeling of microscopic magnetic swimmers can be traced back to the early 2000s.446 For instance, the Dreyfus microswimmer, an elastic filament comprising of superparamagnetic particles linked together by DNA strands, has been actuated by an external oscillating field to demonstrate a nonreciprocal motion.439 In the dynamic model, the superparamagnetic filament was assumed to have a bead-spring configuration. Therefore, it that could resist bending (like a rigid rod), and the beads experienced friction with the surrounding fluid (due to hydrodynamic interactions). The bead dynamics were observed to be governed by the dimensionless sperm number, the magnetic field magnitude, and the angular amplitude of the field's oscillating direction.

Similar bead-spring models have been developed to study the hydrodynamics of artificial rigid magnetic micropropellers of arbitrary shapes.163,447 In these studies, the propellers were considered to be rigid spherical clusters interlinked via elastic chains. Similarly, Stokesian dynamics simulations have been performed to study the swimming kinematics of a single-flagellated magnetotactic bacterium.448 The cell body was assumed to be spherical and it had a single flagellum that was discretized as a chain of beads. Therefore, not only had it included its elasticity, but also considered the hydrodynamic and excluded volume interactions.449 A lattice-based reduced-order dynamic model has been proposed for hard-magnetic soft materials.425 This was used to study the structural kinematics of a jellyfish-inspired MSRS. Here, the elastic deformation energy was partitioned into lattice stretching and volumetric changes, and the external magnetic actuation was incorporated through prescribed nodal forces.

Balance of dynamic forces acting upon an accelerating system incorporating all the system forces such as gravity load, buoyancy effects, and fluid drag has been carried out for a magnetically actuated jellyfish-inspired soft robotic milli-swimmer.83 A comparison between the dynamic model prediction and the experimental observation for different magnetic fields and actuation frequencies is shown in Fig. 23. In this study, the drag coefficient was computed using an empirical relationship for the estimated drag force acting upon a half-hemisphere cavity.450 In another study, the elastic beam swimming model has been used to capture the dynamics of traveling wave propagation in a magnetic head elastic tail MSRS, using the Euler–Bernoulli beam model.451 Recently, a comprehensive dynamic model has been proposed to model the swimming kinematics of a magnetic helical microrobot consisting of a rigid helical flagellum.452 The influence of swimmer geometry and design upon the step-out frequency, swimming velocity, and optimum velocity at low Reynolds numbers have been explained.453 

FIG. 23.

Comparison of a jellyfish-inspired MSRS for different magnitudes of external magnetic fields (6 and 9 mT – top and bottom, respectively) with increasing actuation frequency; here, the standard deviation is represented by the error bars. Reproduced with permission from Ren et al., Robot.: Sci. Syst. (2019). Copyright 2019 The Authors.

FIG. 23.

Comparison of a jellyfish-inspired MSRS for different magnitudes of external magnetic fields (6 and 9 mT – top and bottom, respectively) with increasing actuation frequency; here, the standard deviation is represented by the error bars. Reproduced with permission from Ren et al., Robot.: Sci. Syst. (2019). Copyright 2019 The Authors.

Close modal

Kinematic modeling and optical closed-loop control have been reported for a magnetic cylinder swimming within a viscous fluid.423 The external magnetic field acting upon the microrobot was equated with the robot inertia using Newton's second law of motion. A time-delay estimation controller was formulated using the resulting motion kinematics.454 Further, a model predictive control approach has been adopted for motion planning of a rolling microrobot in a low Reynolds number fluid environment.455 Essentially, the framework incorporated the nonholonomic and kinematic constraints. The actuation limitations of the swimmer were taken into account for trajectory prediction and avoiding obstacles. Finally, in Sec. VI C, we discuss the fully coupled modeling approaches undertaken for MSRS.

Closed-form analytical solutions are seldom obtainable during high-fidelity mathematical modeling of MSRS. As a result, efficient numerical methods and computational models are employed to obtain numerical solutions of the coupled sets of nonlinear partial differential equations. Full coupling between solid mechanics, fluid dynamics, and magnetics is accounted for during the analysis of magnetic-field-induced propulsion, swimming behavior, and large deformation FSI of MSRS.318 Therefore, robust computational models are essential to obtain stable and efficient numerical techniques for a thorough and fundamental understanding of the MSRS propulsion kinematics. For magnetic actuation, the fundamental principle is the change in the spatial configuration of a magneto-responsive material due to a magnetic force and/or magnetic torque resulting in a net displacement. Using this concept, the swimming kinematics of a model 2D jellyfish-inspired MSRS (jellyfishbot) has been studied. Here, an oscillating magnetic field was used to actuate the two symmetric lappets that were pre-programmed with a specific remnant magnetization profile. The nonreciprocal magnetic field generated both spatial and temporal asymmetries. This study not only accounted for the strong two-way FSI and magnetics but also accounted for the large deformation geometric nonlinearity.298 Subsequently, the flow field around and the structural deformation of the MSRS was reported (see Fig. 24).

FIG. 24.

(a) Schematic representation of the fully coupled problem showing the Lagrangian solid and the Eulerian fluid domains along with the external magnetic field; (b) Snapshot of the MSRS configuration and the surrounding flow field visualized through streamlines. Reproduced with permission from Pramanik et al., Phys. Rev. E 107, 014607 (2023). Copyright 2023 American Physical Society.

FIG. 24.

(a) Schematic representation of the fully coupled problem showing the Lagrangian solid and the Eulerian fluid domains along with the external magnetic field; (b) Snapshot of the MSRS configuration and the surrounding flow field visualized through streamlines. Reproduced with permission from Pramanik et al., Phys. Rev. E 107, 014607 (2023). Copyright 2023 American Physical Society.

Close modal

A three-dimensional magnetostatic formulation based on a finite element analysis has been performed to estimate the magnetic forces/torques upon a Ni microrobot subjected to an external magnetic field.456 Under an oscillating field, the propulsion of a slender magnetic swimmer exhibiting a traveling wave motion have been studied using the immersed boundary method.241 Recently, an implicit finite difference method has been adopted to analyze the motion of MSRS propelling through a non-Newtonian fluid with complex wall features.457 In another study by the same research group, the Taylor's swimming sheet model was implemented,458 and the cervical mucus was modeled as the Oldroyd-4 constant fluid.459 The Eyring–Powell fluid model has also been considered to simulate the magnetic-field-actuated kinematics of self-propulsive sperm-inspired MSRS.460 

Magneto-hydrodynamics (MHD) of spermatozoa-like magnetic microswimmer propelling through the cervical canal was numerically investigated.461 It was inferred that MHD assisted the swimmer during propulsion. While the rheological properties of the surrounding fluid either helped or opposed swimming, the large undulation amplitude in the MSRS body significantly enhanced propulsion.462 In these studies, the solution obtained through the implicit finite difference method was further validated by a built-in MATLAB routine (that was based on the collocation technique). Furthermore, the interaction of thin shell-like elements with a low Reynolds number fluid flow has been discussed.463 Here, the slender structure was discretized by enhanced three-noded finite shell elements that were coupled with boundary element-based treatment of the surrounding fluid's Stokes flow in a monolithic manner. In another study by the same author, a flexible rod-type chiral MSRS has been studied using geometrically nonlinear shear-deformable beam elements along with regularized Stokeslets method in a monolithic implicit formulation.464 

Bi-directional locomotion of a jellyfishbot was numerically modeled using a robust fully coupled computational framework with a fixed-grid fictitious-domain technique.422 The evolution of structural kinematics and the surrounding flow field dynamics were studied to understand the relative importance of the individual system parameters upon the jellyfishbot swimming speed. The complex interplay of inertia, viscous, magnetic, and elastic forces was vividly discussed.318 Although this approach was benchmarked and validated for several reference cases,127,298 it involved a higher computational cost compared to RFT/SBT or reduced-order dynamic models. Therefore, the innate possibility of the development of a hierarchical multi-scale fully coupled model is, certainly, a future prospect.465 Particularly, when the Reynolds number is moderate to high, and the use of full Navier–Stokes becomes mandatory (instead of the linearized Stokes' equations), hierarchical models could come in handy.466–468 

Soft robots are gradually becoming ubiquitous in state-of-the-art biomedical and microfluidic applications such as targeted drug delivery, laparoscopic surgery, organ-on-a-chip devices, biopsy, etc. Although their clinical usage is still in its infancy due to cytotoxicity, biocompatibility, biodegradability, real-time tracking, and medical imaging challenges, they have shown promise in research laboratory settings for ex vivo and in vitro biomedical applications as well as on initial in vivo mouse trials. The praiseworthy achievements in this regard has been elaborately discussed in Sec. I A.

Owing to their ability of miniaturization, large degrees of freedom, compliance, ergonomics, large elongation-at-break strain alongside capability of withstanding high mechanical deformation prior to failure, and possibilities of untethered actuation through embedding of multi-functional filler materials, these stimuli-responsive elastica has seen burgeoning progress in the last few years.469–472 Noninvasive biomedical applications opt for a clean contact-free operation with a wireless mode of control to avoid excessive in-built components and electronics. Thanks to the magnetic field being a remote field actuation with high penetration depth, contactless manipulation of magnetic soft robots is possible without any compromise on the precise motion control and localization.

Over the years, this has led to the development of tiny untethered machines in the form of MSRS that deform in a pre-defined programmable manner under external magnetic fields to propel through a viscous medium. Their ever-increasing demand, noteworthy developments, and possible future explorations necessitate a thorough understanding of their state-of-the-art fabrication techniques, nature-inspired design strategies, physics behind their magnetic-field-induced propulsion, symmetry-breaking mechanisms for a net propulsion, and the mathematical frameworks proposed to unravel the complexities of their fully coupled kinematics. In this review, we have addressed these diverse aspects of MSRS by bringing these apparently standalone concepts under one broad-spectrum by connecting-the-dots and bridging-the-gaps between the pioneering works, noteworthy achievements over the years, as well as the most recent developments in this exciting field of multi-disciplinary research.

First, we briefly discussed the transition from the traditional hard robots to their softer deformable counterparts and introduced the concept of soft robotics. Then, we illustrated the special features that render them their cross-domain energy transduction (i.e., stimuli-responsiveness) through the use of multi-functional materials with a special emphasis on MSRS. We further discussed their exponentially increasing demand and widespread applications in the biomedical, health, microfluidic, and clinical sectors. Then, we highlighted the various fabrication techniques adopted to develop these magnetic swimmers inspired by nature, particularly from the aquatic life and marine environments. Specifically, bio-mimetic design strategies were illustrated through real-life examples.

Then, we explained the symmetry-breaking mechanisms that manifest in the three basic modes of swimming (i.e., helical, undulatory, and ciliary) adopted by MSRS for net propulsion through a viscous medium. We referred to the plethora of experimental characterization and magnetic actuation methods for noninvasive control and maneuvering of these tiny machines. Next, the theoretical frameworks to analyze the swimming kinematics of MSRS have been explained. Finally, the review has been concluded with several future perspectives and possibilities of further explorations. This review should serve as a holistic reference for mechanicians, material scientists, physicians, and young researchers interested in the design, fabrication, characterization, control, and modeling of MSRS for state-of-the-art biomedical applications and microfluidics.

In his classic lecture, There's plenty of room at the bottom, Feynman spoke about “swallowing the surgeon”.473 This was reinstated by Flynn in her 1987 paper “Gnat Robots (and How They Will Change Robotics)”.474 Although a highly futuristic idea at that point in time (1966), the movie Fantastic Voyage had imagined the entry of external agents inside the human body. Today, these concepts are no longer science fiction, but a reality to a great extent as has been discussed throughout the review.475–479 However, in spite of noteworthy advancements in magnetic soft robots over the last couple of decades, several challenges still remain. Here, we briefly mention some of the under-explored research topics and suggest potential directions for further developments.

For example, from the consideration of intricate unstructured biological workspace instead of phantom models for pragmatic in vivo testing to real-time tracking, from development of fully coupled multi-scale hierarchical models to 4D printing of magnetic matter with patterned magnetization, and to the development of new class of multi-state MSRS with combined intelligence for multi-shape morphing abilities, the opportunities are, indeed, endless. In order to live up to their true expectations and unparalleled potential, the next-generation MSRS must address the constraints and appropriately cater to the needs of the real-life in vivo clinical applications with integrated synchronous imaging modalities. Therefore, a significant leap must be made to shift the arena of MSRS from unrealistic laboratory setups to potential human working environments as life-savers.

Noninvasive treatment of tumorigenic cells is possible when MSRS are propelled into the bloodstream, liver, stomach channel, or reproductive tract for precise diagnosis and localized treatment.480 However, this simultaneously requires better imaging techniques with higher depth of penetration compared to what has been achieved to date.481 This is because motion accuracy and positional precision suffer a setback when the magnetic swimmers travel through a viscous bio-fluid (or any soft tissue-mimicking non-Newtonian rheological fluid) that lack high spatiotemporal resolution.482 Real-time digital holographic monitoring, control, and tracking of microrobots is limited to only low frequencies (approximately 40 Hz) with sufficient position accuracy in the imaging plane.483–485 

Noninvasive real-time detection strategies and medical imaging systems have been developed for active tracking of these magnetic microrobots.302 For example, optoacoustic tomography-based imaging has been used to track cell-sized magnetic microrobots maneuvering within both bloodless ex vivo phantom tissues and the rat brain vasculature.486 High-resolution 3D spatiotemporal information with a considerable penetration depth could be obtained with high specificity. Nevertheless, this is an open area of research with future prospects when the regions of interest are the confined hard-to-reach-and-locate body sites.487 For example, the position of MSRS during propulsion and the surrounding flow field dynamics have been imaged in real-time using multicolor fluorescence microscopy.488 In this study, the attachment of single and MSRS clusters to several organic bodies has been demonstrated as a proof-of-concept for targeted drug delivery applications.

Ultrasound (US) imaging has often been employed to track microbots during noninvasive biomedical applications.489–492 Thanks to the difference in the acoustic impedance between the magnetic soft robots and the biological tissues, US imaging and feedback is possible.493 The magnetic constituent in these miniaturized magnetic machines increases their acoustic impedance, which allows their easy detection and localization using US waves.494 Recently, machine learning models have been deployed for robotic US imaging and sonographers due to scarcity of medical data and for a better comprehension of the physical aspects involved.495–497 Synchronous magnetic navigation of an untethered miniature magnetically actuated robot has been demonstrated using US imaging.498 A movable electromagnetic coil setup has been used to track and control the robot in tissue-mimicking phantoms with tortuous confinements. Minimal path deviations were observed between the planned trajectory and tracked path.

Robot–tissue interactions have been studied using minimally invasive US imaging to sense the physiological properties of soft tissues499–501; e.g., the viscoelasticity of mice and porcine GI tissues has been estimated with minimal invasion. Closed-loop magnetic control, motion planning, and real-time imaging of untethered magnetic robots have been reported with the help of a camera-based tracker.502 Two methods, namely, the geometric approach and the convolutional neural network (CNN) method, were used to estimate the robot configuration and position with respect to the ground truth captured using a video camera. Later, CNN was used to predict the robot path and generate US images. External microscale agents inside vascular channels have been tracked for potential clinical applications using visual servoing.503 In this study, machine vision algorithms were reported for agent detection within phantom anthropomorphic surfaces and biological tissues.

X ray fluoroscopy produces continuous images by tracking real-time position and spatial configuration using X-rays in clinical workspace.504–507 For example, an x-ray reconstructed image using a principle component analysis of two perpendicular planes and x-ray devices has been reported for a milliscale robot.508 Radiology images of a magnetic capsule maneuvering inside a rabbit stomach has been produced using this imaging modality.509 Fluorescence images has been captured to reveal live actin protrusion during the crawling of a helical magnetic microswimmer.510 A swarm of porous spherical robots carrying targeted green fluorescence protein-positive tumorigenic cells for delivery and diagnosis has been continually tracked using fluorescence imaging.511 Real-time x-ray imaging has been illustrated for a magnetically actuated robotic system during potential drug delivery applications.512 In this study, the robot was loaded with Lipiodol (an x-ray contrast agent) to generate better images during its movement through a 2D phantom model. Yet, imaging miniaturized soft robots using x-ray fluoroscopy is still a challenge given the low robot body density and high permeability of X-rays.

Magnetic resonance (MR) image-guided tracking has come up as a promising tool for minimally invasive biomedical imaging.513 These have been successful in generating 2D MR images.514 Both MR and x-ray fluoroscopy imaging has been used in combination during an in vivo testing of biohybrid miniature helical robots.515 A deep learning-based tracking method using 2D MR images has been recently proposed using a CNN and complementary particle filter for 3D microrobot tracking.516 A probabilistic learning technique for a millimeter-scale MSRS has been proposed using Gaussian processes and Bayesian optimization to learn the gait control.517 Tissue-mimicking phantoms have been developed where Lanthanide-doped Up-conversion nanoparticles showed a unique luminescence property to be used as near-infrared fluorescent probes for optical imaging.518 The use of fluorescent magnetic spore-based microrobots has been successfully proven as a highly efficient portable sensing platform for toxin detection in the patients' stool.519 

Nevertheless, the task of building a fully autonomous system capable of reliably tracking, controlling, evaluating, and manipulating MSRS with minimal human intervention is still a rare possibility.520 While conventional optical microscopy techniques are able to generate spatiotemporal images, they are unable to reveal the encoded information required to distinguish the MSRS from their surroundings. Although portable microrobots have been demonstrated to successfully perform targeted cargo delivery and surgical micro-manipulations in difficult-to-reach body regions,521–523 high-resolution imaging and precise motion control of cell-sized microrobots in the in vivo vascular system is still a challenging task.524 

Although the efficacy and versatility of MSRS operating within phantom models have often been reported, nonetheless, the biodegradability, nontoxicity, physiological testing, and bio-compatibility for in vivo biomedical and clinical usage has not been realized extensively.525–527 For example, helical MSRS have been propelled through in vitro and ex vivo models of a rabbit aorta using rotating external magnetic fields.528 Here, the swimming speed was characterized by opposing flowing streams within a phosphate-buffered saline solution. However, the mechanical properties of the blood vessels were not taken into account. Furthermore, the MSRS was built using a nonbiodegradable material that had a higher thrombogenic response that rendered it vulnerable to platelet formation on the MSRS surface. Another study successfully reported the navigation of a magnetic swimmer through an additively manufactured cerebral aneurysm phantom with magnetic particle imaging.529 

MSRS have been successfully employed to clear clogged blood vessels in an in vitro phantom gelatin thrombus model using mechanical grinding.530 However, there is a clear lacuna in the in vivo testing of these MSRS for real-life clinical applications and human trials due to the toxic nature of the magnetic filler materials and insufficient tracking technologies. Recently though, a novel magnetically actuated hydrogel-based undulatory microswimmer has been fabricated integrally by 3D laser lithography based on two-photon polymerization from a biodegradable material.531 This swimmer degraded over time, thus proving its potential for future in vivo applications such as localized medicine, drug delivery, and real-time diagnosis. Specifically, this MSRS was fabricated using poly(ethyleneglyco) diacrylate and pentaerythritol triacrylate along with superparamagnetic Fe3O4 nanoparticles. Sheet-shaped MSRS has been actuated inside a phantom that mimicked the human brain cerebral aqueduct and other fluid-filled confined regions of the human body.163 Extracted coronary vessels have been used as phantoms during an optoacoustic tomography-based tracking.486 Here, a peristaltic pump was used to transport porcine blood into the phantom. MSRS was added into the phantom tube just before the blood entered the vessels. Inside the phantom, these magnetic particles were visualized and maneuvered using a permanent magnetic coil.

Complex 3D trajectory and steering capabilities of a millimeter-scale helical MSRS navigating in a blood-mimicking solution have been accomplished.532 3D navigation and blood clot removal have been demonstrated using a miniature magnetic swimmer for in vitro testing conditions.533 Complex paths have been maneuvered in an ex vivo porcine brain with extreme curvatures in sub-millimeter precision where the MSRS navigated through soft tissues via continuous penetration.50 Jellyfish-inspired MSRS has been successfully demonstrated to accomplish controlled steady-state swimming behavior inside artificial organs filled with a stagnant fluid.83 For example, the swimmer performed cargo delivery, clogged a narrow tube for embolization, and patched a cancer tissue region under external magnetic actuation. Furthermore, magnetically actuated capsule endoscopes have been developed for ex vivo fine-needle biopsy in the deep tissue of a porcine stomach.534 

When a 3D-printed magneto-responsive material undergoes shape transformation to generate a new morphology, this is known as the fourth dimension of printing (or, 4D-printing).535–537 4D printed high-performance magneto-responsive soft smart structures have been reported with further miniaturization for cellular bio-manipulation.538,539 4D printed magnetic polymer composite hydrogels have been fabricated using different state-of-the-art techniques for a plethora of biomedical applications and magneto-responsive remote structural manipulation.202,203,540 In 3D printing, there is only one distinctly programmable shape. However, 4D printing allows multiple shape transformations under different external magnetic fields.541,542 Therefore, this essentially combines the features of a conventional 3D printing methodology with an origami-based technique of remnant magnetization through patterned profiles.543 This unique state-of-the-art technique has the ability to create complex structures along with origami-based magnetization to generate different spatial configurations and shape morphing for programmable transformation and multi-modal locomotion.

Recently, multi-material patterned hydrogels have been fabricated to yield magnetically graded materials using magnetic inks with different ferrofluid concentrations.544 These macroscopically anisotropic magnetic hydrogels possessed a porous microstructure and were also noncytotoxic toward fibroblasts. Furthermore, they displayed considerable mechanical stability and enhanced magneto-responsiveness. Various patterns of magnetic and nonmagnetic materials were used to develop graded magnetic hydrogel composites. The kinematic performance of these active structures was demonstrated through bending, jumping, and rolling motions. Truly, these studies pave the path for further development of enhanced 4D printing opportunities for fabricating magnetically responsive hydrogels with programmable magnetization to fulfill the future demands of soft robotics.545–548 

Generally, magnetic soft robots and MSRS have a pre-defined shape that is pre-programmed. Therefore, upon being subject to an external magnetic field, they deform only in a specific manner. The magneto-responsive functionalities of MSRS are often restricted owing to their pre-defined shape-morphing. This offers serious challenges during their in situ navigation through confined body spaces. To address this, ferrofluid droplets have been developed as shape-programmable MSRS for successful navigation through confined tortuous channels.549 Furthermore, highly deformable non-Newtonian fluid-based magnetically driven adaptive MSRS have been developed to maneuver on different substrates in complex environments.550 Similarly, liquid metal-based MSRS has been controlled and maneuvered by electromagnetic fields.551 Re-programmable magnetization and stiffness have also been achieved with these robots.552 

In a recent study, a shape switching between liquid and solid states has been demonstrated for a miniature magneto-responsive material.553 Therefore, it possessed the potential benefits of both the solid as well as liquid phases, such as high mechanical strength and load-withstanding ability (in the solid state), and outstanding shape-changing ability like splitting and merging (in the liquid state). Specifically, this composite was composed of NdFeB microparticles embedded within a liquid metal (Ga). Beyond its (low) melting temperature, Ga is a liquid. At this point, the magnetic particles embedded in it could re-arrange themselves under an external field. However, it solidifies once the working temperature is lowered. This is when the arrangement of the magnetic filler materials is ideally locked, and the composite behaves as a solid. This arrangement is changed by first applying a thermal load to melt the liquid Ga, and then suitably arranging the magnetic phase. The temperature is reduced to lock the state. Such stimuli-responsive material architectures could further be explored for stretchable electronics, soft robotics, and healthcare.

Ferromagnetic shape memory polymer composites are another exciting area for further exploration into soft robotics with potential applications because these multi-functional materials possess the ability to remember their shape and hold onto it under certain combinations of thermo-magneto-mechanical loads.554 Magnetically triggered electromagnetic inductive heating shape memory properties of ferromagnetic microparticles-shape memory polymeric matrix composites have been reported.555 The influence of NdFeB magnetic filler concentration upon the shape recovery process and heat induction in NdFeB-impregnated cross-linked low-density polyethylene samples have been discussed.556 In a recent study, the behavior of thermo-electro-magneto-responsive shape memory polymers has been studied when subjected to electromagnetic fields and varying thermo-mechanical loads.557 Magneto-electroactive shape memory polymer composites have also been successfully fabricated using 4D printing.539 Here, iron-filled magnetic polylactic acid and carbon black-filled conductive PLA composites have been 3D-printed using fused deposition modeling. Subsequently, these multi-stimuli-responsive materials displayed shape-shifting under varying magnetic fields.

While several (full-field,558 lattice-based,559 continuum-based,112 continuum fully coupled,558 and analytical560) models have been developed to model magneto-responsive elastica, no hierarchical models have been proposed for studying the coupled physics in MSRS. Magneto-dynamics, solid dynamics, FSI and fluid mechanics become simultaneously relevant and decide the swimming kinematics of magnetic swimmers. Although physics-based computational models have been developed,318,425 there is still no report of a multi-scale hierarchical model that is irrespective of the length-scale effects. This is an open area for further research because significant outcomes from this development could not only reduce the computational complexity of the physical problem but also develop perspectives for patient-specific clinical treatments quite affordably and timely.

Miniature magnetic robots have generally been endowed with physical intelligence, which means the magneto-responsive systems respond to the magnetic field without generating/providing any feedback (or adjustments to its response for a similar event again in the future).561 Therefore, they respond in the same manner under an almost-identical environmental stimuli instead of adapting their behavior.166 This is because they do not have their own brain or any (central) processing unit within them that could have otherwise affected its response based on the altered system dynamics. This results in an inability to adapt appropriately and perform well in dynamic (and changing) environments, which is often the case during realistic applications. There is yet another level of intelligence in regard to these miniature machines—some sort of” adaptability” when the surroundings/environmental change.

For example, in a recent study, an actuation-enhanced multifunctional sensing alongside recognition of useful information by magnetic artificial sensor-integrated cilium arrays (together with conductive laser-induced graphene) have been proposed as a progressive step.562 Here, the cilia-graphene system demonstrated sensing of the surrounding fluid viscosity (which was seen as a system output), environmental boundaries, and fluid flow kinematics with a reconfigurable sensitivity. In principle, this endowed the system with the ability to estimate the required change (to be implemented) in their response for the altered (dynamic) environment. When this capability is incorporated into the stimuli–responsive system, the physical intelligence combines itself with computational intelligence.563 The third form of intelligence—artificial intelligence is to “learn” from the previous responses under actuation and correlate them with appropriate system parameters and architectures. The latter acts as input data points for being used as information for training purpose and adaptive behavior.564 In the near future, with all the three forms of intelligence (physical, computational, and artificial) innately incorporated into their buildup, magnetic soft robots and MSRS certainly have a strong possibility to become the next-generation materials for state-of-the-art and prospective biomedical and microfluidic applications.565–568 

The work is carried out within the research program of the Centre for Data Science and Systems Complexity (DSSC), Faculty of Science and Engineering, University of Groningen.

The authors have no conflicts to disclose.

Ratnadeep Pramanik: Conceptualization (equal); Investigation (lead); Writing – original draft (lead). Roel Verstappen: Conceptualization (equal); Supervision (equal); Writing – review & editing (equal). Patrick R. Onck: Conceptualization (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within this article.

1.
D.
Trivedi
,
C. D.
Rahn
,
W. M.
Kier
, and
I. D.
Walker
, “
Soft robotics: Biological inspiration, state of the art, and future research
,”
Appl. Bionics Biomech.
5
,
99
117
(
2008
).
2.
F.
Iida
and
C.
Laschi
, “
Soft robotics: Challenges and perspectives
,”
Procedia Comput. Sci.
7
,
99
102
(
2011
).
3.
N.
El-Atab
,
R. B.
Mishra
,
F.
Al-Modaf
,
L.
Joharji
,
A. A.
Alsharif
,
H.
Alamoudi
,
M.
Diaz
,
N.
Qaiser
, and
M. M.
Hussain
, “
Soft actuators for soft robotic applications: A review
,”
Adv. Intell. Syst.
2
,
2000128
(
2020
).
4.
Y.
Kim
,
G. A.
Parada
,
S.
Liu
, and
X.
Zhao
, “
Ferromagnetic soft continuum robots
,”
Sci. Robot.
4
,
eaax7329
(
2019
).
5.
L.
Wang
,
D.
Zheng
,
P.
Harker
,
A. B.
Patel
,
C. F.
Guo
, and
X.
Zhao
, “
Evolutionary design of magnetic soft continuum robots
,”
Proc. Nat. Acad. Sci. U.S.A.
118
,
e2021922118
(
2021
).
6.
N.
Bira
,
P.
Dhagat
, and
J. R.
Davidson
, “
A review of magnetic elastomers and their role in soft robotics
,”
Front. Robot. AI
7
,
588391
(
2020
).
7.
G.
Tortora
,
S.
Caccavaro
,
P.
Valdastri
,
A.
Menciassi
, and
P.
Dario
, “
Design of an autonomous swimming miniature robot based on a novel concept of magnetic actuation
,” in
2010 IEEE International Conference on Robotics and Automation
(
IEEE
,
2010
), pp.
1592
1597
.
8.
M.
Runciman
,
A.
Darzi
, and
G. P.
Mylonas
, “
Soft robotics in minimally invasive surgery
,”
Soft Robot.
6
,
423
443
(
2019
).
9.
C.
Xu
,
Z.
Yang
,
S. W. K.
Tan
,
J.
Li
, and
G. Z.
Lum
, “
Magnetic miniature actuators with six-degrees-of-freedom multimodal soft-bodied locomotion
,”
Adv. Intell. Syst.
4
,
2100259
(
2022
).
10.
G. S. C.
Bermúdez
,
M. N.
López
,
B. A.
Evans
,
K. V.
Yershov
,
D.
Makarov
, and
O. V.
Pylypovskyi
, “
Magnetic soft actuators: Magnetic soft robots from macro-to nanoscale
,” in
Curvilinear Micromagnetism: From Fundamentals to Applications
, edited by
D.
Makarov
and
D. D.
Sheka
(
Springer
,
Cham
,
2022
), Vol.
146
, p.
343
.
11.
H.
Ceylan
,
I. C.
Yasa
,
U.
Kilic
,
W.
Hu
, and
M.
Sitti
, “
Translational prospects of untethered medical microrobots
,”
Prog. Biomed. Eng.
1
,
012002
(
2019
).
12.
H.
Ceylan
,
J.
Giltinan
,
K.
Kozielski
, and
M.
Sitti
, “
Mobile microrobots for bioengineering applications
,”
Lab a Chip
17
,
1705
1724
(
2017
).
13.
F.
Ahmed
,
M.
Waqas
,
B.
Javed
,
A. M.
Soomro
,
S.
Kumar
,
H.
Ashraf
,
U.
Khan
,
K.
hwan Kim
, and
K. H.
Choi
, “
Decade of bio-inspired soft robots: A review
,”
Smart Mater. Struct.
31
,
073002
(
2022
).
14.
E. D.
Diller
,
J.
Giltinan
,
G. Z.
Lum
,
Z.
Ye
, and
M.
Sitti
, “
Six-degrees-of-freedom remote actuation of magnetic microrobots
,” in
Robotics: Science and Systems
(
Max Planck Institute for Intelligent Systems
,
2014
).
15.
X.
Wang
,
G.
Mao
,
J.
Ge
,
M.
Drack
,
G. S.
Cañón Bermúdez
,
D.
Wirthl
,
R.
Illing
,
T.
Kosub
,
L.
Bischoff
,
C.
Wang
et al, “
Untethered and ultrafast soft-bodied robots
,”
Commun. Mater.
1
,
67
(
2020
).
16.
Z.
Shen
,
F.
Chen
,
X.
Zhu
,
K.-T.
Yong
, and
G.
Gu
, “
Stimuli-responsive functional materials for soft robotics
,”
J. Mater. Chem. B
8
,
8972
8991
(
2020
).
17.
D.
Zhalmuratova
and
H.-J.
Chung
, “
Reinforced gels and elastomers for biomedical and soft robotics applications
,”
ACS Appl. Polym. Mater.
2
,
1073
1091
(
2020
).
18.
H.
Banerjee
,
M.
Suhail
, and
H.
Ren
, “
Hydrogel actuators and sensors for biomedical soft robots: Brief overview with impending challenges
,”
Biomimetics
3
,
15
(
2018
).
19.
X.
Li
and
T.
Fukuda
, “
Magnetically guided micromanipulation of magnetic microrobots for accurate creation of artistic patterns in liquid environment
,”
Micromachines
11
,
697
(
2020
).
20.
B.
Ahmad
,
M.
Gauthier
,
G. J.
Laurent
, and
A.
Bolopion
, “
Mobile microrobots for in vitro biomedical applications: A survey
,”
IEEE Trans. Robot.
38
,
646
663
(
2021
).
21.
F.
Kong
,
Y.
Zhu
,
C.
Yang
,
H.
Jin
,
J.
Zhao
, and
H.
Cai
, “
Integrated locomotion and deformation of a magnetic soft robot: Modeling, control, and experiments
,”
IEEE Trans. Ind. Electron.
68
,
5078
5087
(
2020
).
22.
E. B.
Joyee
,
A.
Szmelter
,
D.
Eddington
, and
Y.
Pan
, “
3d printed biomimetic soft robot with multimodal locomotion and multifunctionality
,”
Soft Robot.
9
,
1
13
(
2022
).
23.
K.
Mehta
,
A. R.
Peeketi
,
L.
Liu
,
D.
Broer
,
P.
Onck
, and
R. K.
Annabattula
, “
Design and applications of light responsive liquid crystal polymer thin films
,”
Appl. Phys. Rev.
7
,
041306
(
2020
).
24.
W.
Gao
,
D.
Kagan
,
O. S.
Pak
,
C.
Clawson
,
S.
Campuzano
,
E.
Chuluun-Erdene
,
E.
Shipton
,
E. E.
Fullerton
,
L.
Zhang
,
E.
Lauga
et al, “
Cargo-towing fuel-free magnetic nanoswimmers for targeted drug delivery
,”
Small
8
,
460
467
(
2012
).
25.
M.
Liu
,
L.
Pan
,
H.
Piao
,
H.
Sun
,
X.
Huang
,
C.
Peng
, and
Y.
Liu
, “
Magnetically actuated wormlike nanomotors for controlled cargo release
,”
ACS Appl. Mater. Interfaces
7
,
26017
26021
(
2015
).
26.
E. B.
Joyee
and
Y.
Pan
, “
Additive manufacturing of multi-material soft robot for on-demand drug delivery applications
,”
J. Manuf. Processes
56
,
1178
1184
(
2020
).
27.
M.
Luo
,
Y.
Feng
,
T.
Wang
, and
J.
Guan
, “
Micro-/nanorobots at work in active drug delivery
,”
Adv. Funct. Mater.
28
,
1706100
(
2018
).
28.
H.
Song
,
D-i
Kim
,
S. A.
Abbasi
,
N. L.
Gharamaleki
,
E.
Kim
,
C.
Jin
,
S.
Kim
,
J.
Hwang
,
J-y
Kim
,
X.
Chen
et al, “
Multi-target cell therapy using a magnetoelectric microscale biorobot for targeted delivery and selective differentiation of SH-SY5Y cells via magnetically driven cell stamping
,”
Mater. Horiz.
9
(
12
),
3031
3038
(
2022
).
29.
X.-Z.
Chen
,
J.-H.
Liu
,
M.
Dong
,
L.
Müller
,
G.
Chatzipirpiridis
,
C.
Hu
,
A.
Terzopoulou
,
H.
Torlakcik
,
X.
Wang
,
F.
Mushtaq
et al, “
Magnetically driven piezoelectric soft microswimmers for neuron-like cell delivery and neuronal differentiation
,”
Mater. Horiz.
6
,
1512
1516
(
2019
).
30.
P.
TirgarBahnamiri
and
S.
Bagheri-Khoulenjani
, “
Biodegradable microrobots for targeting cell delivery
,”
Med. Hypotheses
102
,
56
60
(
2017
).
31.
T.
Gopesh
,
J. H.
Wen
,
D.
Santiago-Dieppa
,
B.
Yan
,
J. S.
Pannell
,
A.
Khalessi
,
A.
Norbash
, and
J.
Friend
, “
Soft robotic steerable microcatheter for the endovascular treatment of cerebral disorders
,”
Sci. Robot.
6
,
eabf0601
(
2021
).
32.
I. C.
Yasa
,
A. F.
Tabak
,
O.
Yasa
,
H.
Ceylan
, and
M.
Sitti
, “
3d-printed microrobotic transporters with recapitulated stem cell niche for programmable and active cell delivery
,”
Adv. Funct. Mater.
29
,
1808992
(
2019
).
33.
F. Z.
Temel
and
S.
Yesilyurt
, “
Confined swimming of bio-inspired microrobots in rectangular channels
,”
Bioinspir. Biomim.
10
,
016015
(
2015
).
34.
S.
Won
,
S.
Kim
,
J. E.
Park
,
J.
Jeon
, and
J. J.
Wie
, “
On-demand orbital maneuver of multiple soft robots via hierarchical magnetomotility
,”
Nat. Commun.
10
,
4751
(
2019
).
35.
A.
Koivikko
,
D.-M.
Drotlef
,
M.
Sitti
, and
V.
Sariola
, “
Magnetically switchable soft suction grippers
,”
Extreme Mech. Lett.
44
,
101263
(
2021
).
36.
S. R.
Goudu
,
I. C.
Yasa
,
X.
Hu
,
H.
Ceylan
,
W.
Hu
, and
M.
Sitti
, “
Biodegradable untethered magnetic hydrogel milli-grippers
,”
Adv. Funct. Mater.
30
,
2004975
(
2020
).
37.
L.
Liu
,
J.
Wu
,
B.
Chen
,
J.
Gao
,
T.
Li
,
Y.
Ye
,
H.
Tian
,
S.
Wang
,
F.
Wang
,
J.
Jiang
et al, “
Magnetically actuated biohybrid microswimmers for precise photothermal muscle contraction
,”
ACS Nano
16
,
6515
6526
(
2022
).
38.
A. V.
Pozhitkova
,
D. V.
Kladko
,
D. A.
Vinnik
,
S. V.
Taskaev
, and
V. V.
Vinogradov
, “
Reprogrammable soft swimmers for minimally invasive thrombus extraction
,”
ACS Appl. Mater. Interfaces
14
,
20
(
2022
).
39.
A. W.
Mahoney
and
J. J.
Abbott
, “
Five-degree-of-freedom manipulation of an untethered magnetic device in fluid using a single permanent magnet with application in stomach capsule endoscopy
,”
Int. J. Robot. Res.
35
,
129
147
(
2016
).
40.
K.
Popek
and
J.
Abbott
, “
6-D localization of a magnetic capsule endoscope using a stationary rotating magnetic dipole field
,” in
Hamlyn Symposium on Medical Robotics
(Hamlyn Symposium on Medical Robotics,
2015
), pp.
47
48
.
41.
F.
Ullrich
,
S.
Schuerle
,
R.
Pieters
,
A.
Dishy
,
S.
Michels
, and
B. J.
Nelson
, “
Automated capsulorhexis based on a hybrid magnetic-mechanical actuation system
,” in
2014 IEEE International Conference on Robotics and Automation (ICRA)
(
IEEE
,
2014
), pp.
4387
4392
.
42.
G.
Chatzipirpiridis
,
O.
Ergeneman
,
J.
Pokki
,
F.
Ullrich
,
S.
Fusco
,
J. A.
Ortega
,
K. M.
Sivaraman
,
B. J.
Nelson
, and
S.
Pané
, “
Electroforming of implantable tubular magnetic microrobots for wireless ophthalmologic applications
,”
Adv. Healthcare Mater.
4
,
209
214
(
2015
).
43.
O.
Onaizah
,
L.
Xu
,
K.
Middleton
,
L.
You
, and
E.
Diller
, “
Local stimulation of osteocytes using a magnetically actuated oscillating beam
,”
Plos One
15
,
e0235366
(
2020
).
44.
J. A.
Steiner
,
L. N.
Pham
,
J. J.
Abbott
, and
K. K.
Leang
, “
Modeling and analysis of a soft endoluminal inchworm robot propelled by a rotating magnetic dipole field
,”
J. Mech. Robot.
14
,
051002
(
2022
).
45.
Z.
Yang
and
L.
Zhang
, “
Magnetic actuation systems for miniature robots: A review
,”
Adv. Intell. Syst.
2
,
2000082
(
2020
).
46.
B.
Özkale
,
R.
Parreira
,
A.
Bekdemir
,
L.
Pancaldi
,
E.
Özelçi
,
C.
Amadio
,
M.
Kaynak
,
F.
Stellacci
,
D. J.
Mooney
, and
M. S.
Sakar
, “
Modular soft robotic microdevices for dexterous biomanipulation
,”
Lab a Chip
19
,
778
788
(
2019
).
47.
O.
Youssefi
and
E.
Diller
, “
Dry surface micromanipulation using an untethered magnetic microrobot
,” in
Advances in Motion Sensing and Control for Robotic Applications
(
Springer
,
2019
) pp.
75
91
.
48.
V. M.
Fomin
,
M.
Hippler
,
V.
Magdanz
,
L.
Soler
,
S.
Sanchez
, and
O. G.
Schmidt
, “
Propulsion mechanism of catalytic microjet engines
,”
IEEE Trans. Robot.
30
,
40
48
(
2013
).
49.
C. K.
Schmidt
,
M.
Medina-Sánchez
,
R. J.
Edmondson
, and
O. G.
Schmidt
, “
Engineering microrobots for targeted cancer therapies from a medical perspective
,”
Nat. Commun.
11
,
5618
(
2020
).
50.
D.
Son
,
M. C.
Ugurlu
, and
M.
Sitti
, “
Permanent magnet array–driven navigation of wireless millirobots inside soft tissues
,”
Sci. Adv.
7
,
eabi8932
(
2021
).
51.
T.
Ashuri
,
A.
Armani
,
R.
Jalilzadeh Hamidi
,
T.
Reasnor
,
S.
Ahmadi
, and
K.
Iqbal
, “
Biomedical soft robots: Current status and perspective
,”
Biomed. Eng. Lett.
10
,
369
385
(
2020
).
52.
M.
Cianchetti
,
C.
Laschi
,
A.
Menciassi
, and
P.
Dario
, “
Biomedical applications of soft robotics
,”
Nat. Rev. Mater.
3
,
143
153
(
2018
).
53.
S.
Salmanipour
,
O.
Youssefi
, and
E. D.
Diller
, “
Design of multi-degrees-of-freedom microrobots driven by homogeneous quasi-static magnetic fields
,”
IEEE Trans. Robot.
37
,
246
256
(
2020
).
54.
S. L.
Charreyron
,
Q.
Boehler
,
A. N.
Danun
,
A.
Mesot
,
M.
Becker
, and
B. J.
Nelson
, “
A magnetically navigated microcannula for subretinal injections
,”
IEEE Trans. Biomed. Eng.
68
,
119
129
(
2020
).
55.
F.
Ullrich
,
S.
Fusco
,
G.
Chatzipirpiridis
,
S.
Pané
, and
B. J.
Nelson
, “
Recent progress in magnetically actuated microrobotics for ophthalmic therapies
,”
Eur. Ophthalmic Rev.
8
,
120
126
(
2014
).
56.
G.
Yan
,
A. A.
Solovev
,
G.
Huang
,
J.
Cui
, and
Y.
Mei
, “
Soft microswimmers: Material capabilities and biomedical applications
,”
Curr. Opin. Colloid Interface Sci.
61
,
101609
(
2022
).
57.
J. J.
Abbott
,
K. E.
Peyer
,
M. C.
Lagomarsino
,
L.
Zhang
,
L.
Dong
,
I. K.
Kaliakatsos
, and
B. J.
Nelson
, “
How should microrobots swim?
,”
Int. J. Robot. Res.
28
,
1434
1447
(
2009
).
58.
H.
Zhou
,
C. C.
Mayorga-Martinez
,
S.
Pané
,
L.
Zhang
, and
M.
Pumera
, “
Magnetically driven micro and nanorobots
,”
Chem. Rev.
121
,
4999
5041
(
2021
).
59.
X.-Z.
Chen
,
M.
Hoop
,
F.
Mushtaq
,
E.
Siringil
,
C.
Hu
,
B. J.
Nelson
, and
S.
Pané
, “
Recent developments in magnetically driven micro-and nanorobots
,”
Appl. Mater. Today
9
,
37
48
(
2017
).
60.
S.
Schürle
,
B. E.
Kratochvil
,
S.
Pané
,
M. A.
Zeeshan
, and
B. J.
Nelson
, “
Generating magnetic fields for controlling nanorobots in medical applications
,” in
Nanorobotics
, edited by
C.
Mavroidis
and
A.
Ferreira
(
Springer
,
2013
), pp.
275
299
.
61.
A. V.
Chesnitskiy
,
A. E.
Gayduk
,
V. A.
Seleznev
, and
V. Y.
Prinz
, “
Bio-inspired micro-and nanorobotics driven by magnetic field
,”
Materials
15
,
7781
(
2022
).
62.
T.
Luo
and
M.
Wu
, “
Biologically inspired micro-robotic swimmers remotely controlled by ultrasound waves
,”
Lab a Chip
21
,
4095
4103
(
2021
).
63.
S.
Fu
,
F.
Wei
,
C.
Yin
,
L.
Yao
, and
Y.
Wang
, “
Biomimetic soft micro-swimmers: From actuation mechanisms to applications
,”
Biomed. Microdev.
23
,
6
(
2021
).
64.
S. M.
Youssef
,
M.
Soliman
,
M. A.
Saleh
,
M. A.
Mousa
,
M.
Elsamanty
, and
A. G.
Radwan
, “
Underwater soft robotics: A review of bioinspiration in design, actuation, modeling, and control
,”
Micromachines
13
,
110
(
2022
).
65.
M.
Medina-Sánchez
,
V.
Magdanz
,
M.
Guix
,
V. M.
Fomin
, and
O. G.
Schmidt
, “
Swimming microrobots: Soft, reconfigurable, and smart
,”
Adv. Funct. Mater.
28
,
1707228
(
2018
).
66.
A.
Ghanbari
, “
Bioinspired reorientation strategies for application in micro/nanorobotic control
,”
J. Micro-Bio Robot.
16
,
173
197
(
2020
).
67.
S.
Wu
,
W.
Hu
,
Q.
Ze
,
M.
Sitti
, and
R.
Zhao
, “
Multifunctional magnetic soft composites: A review
,”
Multifunct. Mater.
3
,
042003
(
2020
).
68.
S.
Lucarini
,
M.
Hossain
, and
D.
Garcia-Gonzalez
, “
Recent advances in hard-magnetic soft composites: Synthesis, characterisation, computational modelling, and applications
,”
Composite Struct.
279
,
114800
(
2022
).
69.
R.
Zhao
,
Y.
Kim
,
S. A.
Chester
,
P.
Sharma
, and
X.
Zhao
, “
Mechanics of hard-magnetic soft materials
,”
J. Mech. Phys. Solids
124
,
244
263
(
2019
).
70.
V.
Manish
,
K. V.
Siva
,
A.
Arockiarajan
, and
G.
Tamadapu
, “
Synthesis and characterization of hard magnetic soft hydrogels
,”
Mater. Lett.
320
,
132323
(
2022
).
71.
H.
Meharthaj
,
S. M.
Sivakumar
, and
A.
Arockiarajan
, “
Significance of particle size on the improved performance of magnetorheological gels
,”
J. Magn. Magn. Mater.
490
,
165483
(
2019
).
72.
D.
Gutenko
, “
State of the art of soft robotic applications based on magneto-rheological materials
,” in
MATEC Web of Conferences
(
EDP Sciences
,
2020
), Vol.
322
, p.
01050
.
73.
M. K.
Purkait
,
M. K.
Sinha
,
P.
Mondal
, and
R.
Singh
,
Stimuli Responsive Polymeric Membranes: Smart Polymeric Membranes
(
Academic Press
,
2018
).
74.
J. K.
Wychowaniec
and
D. F.
Brougham
, “
Emerging magnetic fabrication technologies provide controllable hierarchically-structured biomaterials and stimulus response for biomedical applications
,”
Adv. Sci.
9
,
2202278
(
2022
).
75.
F.
Gang
,
L.
Jiang
,
Y.
Xiao
,
J.
Zhang
, and
X.
Sun
, “
Multi-functional magnetic hydrogel: Design strategies and applications
,”
Nano Select
2
,
2291
2307
(
2021
).
76.
H.
Lee
,
G. K.
Thirunavukkarasu
,
S.
Kim
, and
J. Y.
Lee
, “
Remote induction of in situ hydrogelation in a deep tissue, using an alternating magnetic field and superparamagnetic nanoparticles
,”
Nano Res.
11
,
5997
6009
(
2018
).
77.
B. R.
Rodriguez-Vargas
,
G.
Stornelli
,
P.
Folgarait
,
M. R.
Ridolfi
,
A. F.
Miranda Pérez
, and
A.
Di Schino
, “
Recent advances in additive manufacturing of soft magnetic materials: A review
,”
Materials
16
,
5610
(
2023
).
78.
V.
Chaudhary
,
S.
Mantri
,
R.
Ramanujan
, and
R.
Banerjee
, “
Additive manufacturing of magnetic materials
,”
Prog. Mater. Sci.
114
,
100688
(
2020
).
79.
E.
Périgo
,
J.
Jacimovic
,
F. G.
Ferré
, and
L.
Scherf
, “
Additive manufacturing of magnetic materials
,”
Addit. Manuf.
30
,
100870
(
2019
).
80.
D.
Goll
,
D.
Schuller
,
G.
Martinek
,
T.
Kunert
,
J.
Schurr
,
C.
Sinz
,
T.
Schubert
,
T.
Bernthaler
,
H.
Riegel
, and
G.
Schneider
, “
Additive manufacturing of soft magnetic materials and components
,”
Addit. Manuf.
27
,
428
439
(
2019
).
81.
H.-J.
Chung
,
A. M.
Parsons
, and
L.
Zheng
, “
Magnetically controlled soft robotics utilizing elastomers and gels in actuation: A review
,”
Adv. Intell. Syst.
3
,
2000186
(
2021
).
82.
C. S. X.
Ng
,
C.
Xu
,
Z.
Yang
, and
G. Z.
Lum
, “
Shape-programmable magnetic miniature robots: A critical review
,” in Field-Driven Micro and Nanorobots for Biology and Medicine (Springer, 2022); available at https://link.springer.com/book/10.1007/978-3-030-80197-7.
83.
Z.
Ren
,
T.
Wang
,
W.
Hu
, and
M.
Sitti
, “
A magnetically-actuated untethered jellyfish-inspired soft milliswimmer
,” in
Robotics: Science and Systems, Freiburg im Breisgau
, 22–26 June (
2019
).
84.
S.
Miyashita
,
S.
Guitron
,
M.
Ludersdorfer
,
C. R.
Sung
, and
D.
Rus
, “
An untethered miniature origami robot that self-folds, walks, swims, and degrades
,” in
2015 IEEE International Conference on Robotics and Automation (ICRA)
(
IEEE
,
2015
), pp.
1490
1496
.
85.
J.
Zhang
,
R. H.
Soon
,
Z.
Wei
,
W.
Hu
, and
M.
Sitti
, “
Liquid metal-elastomer composites with dual-energy transmission mode for multifunctional miniature untethered magnetic robots
,”
Adv. Sci.
9
,
2203730
(
2022
).
86.
J.
Cui
,
T.-Y.
Huang
,
Z.
Luo
,
P.
Testa
,
H.
Gu
,
X.-Z.
Chen
,
B. J.
Nelson
, and
L. J.
Heyderman
, “
Nanomagnetic encoding of shape-morphing micromachines
,”
Nature
575
,
164
168
(
2019
).
87.
Y.
Tang
,
M.
Li
,
T.
Wang
,
X.
Dong
,
W.
Hu
, and
M.
Sitti
, “
Wireless miniature magnetic phase-change soft actuators
,”
Adv. Mater.
34
,
2204185
(
2022
).
88.
M.
Boyvat
and
M.
Sitti
, “
Remote modular electronics for wireless magnetic devices
,”
Adv. Sci.
8
,
2101198
(
2021
).
89.
C.
Wang
,
V. R.
Puranam
,
S.
Misra
, and
V. K.
Venkiteswaran
, “
A snake-inspired multi-segmented magnetic soft robot towards medical applications
,”
IEEE Robot. Autom. Lett.
7
,
5795
5802
(
2022
).
90.
Z.
Ren
,
W.
Hu
,
X.
Dong
, and
M.
Sitti
, “
Multi-functional soft-bodied jellyfish-like swimming
,”
Nat. Commun.
10
,
2703
(
2019
).
91.
S.
Wu
,
Q.
Ze
,
R.
Zhang
,
N.
Hu
,
Y.
Cheng
,
F.
Yang
, and
R.
Zhao
, “
Symmetry-breaking actuation mechanism for soft robotics and active metamaterials
,”
ACS Appl. Mater. Interfaces
11
,
41649
41658
(
2019
).
92.
T.
Zhang
,
L.
Yang
,
X.
Yang
,
R.
Tan
,
H.
Lu
, and
Y.
Shen
, “
Millimeter-scale soft continuum robots for large-angle and high-precision manipulation by hybrid actuation
,”
Adv. Intell. Syst.
3
,
2000189
(
2021
).
93.
J. J.
Abbott
,
E.
Diller
, and
A. J.
Petruska
, “
Magnetic methods in robotics
,”
Annu. Rev. Control, Robot. Auton. Syst.
3
,
57
90
(
2020
).
94.
A.
Denasi
and
S.
Misra
, “
Independent and leader–follower control for two magnetic micro-agents
,”
IEEE Robot. Autom. Lett.
3
,
218
225
(
2017
).
95.
J.
Lee
,
X.
Zhang
,
C. H.
Park
, and
M. J.
Kim
, “
Real-time teleoperation of magnetic force-driven microrobots with 3d haptic force feedback for micro-navigation and micro-transportation
,”
IEEE Robot. Autom. Lett.
6
,
1769
1776
(
2021
).
96.
X.
Tang
and
L.
Manamanchaiyaporn
, “
Magnetic-powered swimming soft-milli robot towards non-invasive applications
,” in
2022 8th International Conference on Control, Decision and Information Technologies (CoDIT)
(
IEEE
,
2022
), Vol.
1
, pp.
1562
1566
.
97.
J.
Zhang
,
O.
Onaizah
,
K.
Middleton
,
L.
You
, and
E.
Diller
, “
Reliable grasping of three-dimensional untethered mobile magnetic microgripper for autonomous pick-and-place
,”
IEEE Robot. Autom. Lett.
2
,
835
840
(
2017
).
98.
M.
Salehizadeh
and
E.
Diller
, “
Three-dimensional independent control of multiple magnetic microrobots via inter-agent forces
,”
Int. J. Robot. Res.
39
,
1377
1396
(
2020
).
99.
J.
Zhang
,
P.
Jain
, and
E.
Diller
, “
Independent control of two millimeter-scale soft-bodied magnetic robotic swimmers
,” in
2016 IEEE International Conference on Robotics and Automation (ICRA)
(
IEEE
,
2016
), pp.
1933
1938
.
100.
I. S.
Khalil
,
V.
Magdanz
,
S.
Sanchez
,
O. G.
Schmidt
, and
S.
Misra
, “
Wireless magnetic-based closed-loop control of self-propelled microjets
,”
PloS One
9
,
e83053
(
2014
).
101.
P.
Sharan
,
A.
Nsamela
,
S. C.
Lesher-Pérez
, and
J.
Simmchen
, “
Microfluidics for microswimmers: Engineering novel swimmers and constructing swimming lanes on the microscale, a tutorial review
,”
Small
17
,
2007403
(
2021
).
102.
A. D.
Marchese
,
C. D.
Onal
, and
D.
Rus
, “
Autonomous soft robotic fish capable of escape maneuvers using fluidic elastomer actuators
,”
Soft Robot.
1
,
75
87
(
2014
).
103.
M.
Ariyanto
,
M.
Munadi
,
J. D.
Setiawan
,
D.
Mulyanto
, and
T.
Nugroho
, “
Three-fingered soft robotic gripper based on pneumatic network actuator
,” in
2019 6th International Conference on Information Technology, Computer and Electrical Engineering (ICITACEE)
(
IEEE
,
2019
), pp.
1
5
.
104.
A.
Sadeghi
,
L.
Beccai
, and
B.
Mazzolai
, “
Innovative soft robots based on electro-rheological fluids
,” in
2012 IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IEEE
,
2012
), pp.
4237
4242
.
105.
Q.
Shen
,
T.
Wang
,
J.
Liang
, and
L.
Wen
, “
Hydrodynamic performance of a biomimetic robotic swimmer actuated by ionic polymer–metal composite
,”
Smart Mater. Struct.
22
,
075035
(
2013
).
106.
L.
Sun
,
Z.
Chen
,
F.
Bian
, and
Y.
Zhao
, “
Bioinspired soft robotic caterpillar with cardiomyocyte drivers
,”
Adv. Funct. Mater.
30
,
1907820
(
2020
).
107.
H.
Niu
,
R.
Feng
,
Y.
Xie
,
B.
Jiang
,
Y.
Sheng
,
Y.
Yu
,
H.
Baoyin
, and
X.
Zeng
, “
Magworm: A biomimetic magnet embedded worm-like soft robot
,”
Soft Robot.
8
,
507
518
(
2021
).
108.
T. W.
Fountain
,
P. V.
Kailat
, and
J. J.
Abbott
, “
Wireless control of magnetic helical microrobots using a rotating-permanent-magnet manipulator
,” in
2010 IEEE International Conference on Robotics and Automation
(
IEEE
,
2010
), pp.
576
581
.
109.
E. B.
Joyee
and
Y.
Pan
, “
A fully three-dimensional printed inchworm-inspired soft robot with magnetic actuation
,”
Soft Robot.
6
,
333
345
(
2019
).
110.
C.
Yin
,
F.
Wei
,
S.
Fu
,
Z.
Zhai
,
Z.
Ge
,
L.
Yao
,
M.
Jiang
, and
M.
Liu
, “
Visible light-driven jellyfish-like miniature swimming soft robot
,”
ACS Appl. Mater. Interfaces
13
,
47147
47154
(
2021
).
111.
H.
Gu
,
E.
Hanedan
,
Q.
Boehler
,
T.-Y.
Huang
,
A. J.
Mathijssen
, and
B. J.
Nelson
, “
Artificial microtubules for rapid and collective transport of magnetic microcargoes
,”
Nat. Mach. Intell.
4
,
678
684
(
2022
).
112.
Y.
Kim
,
H.
Yuk
,
R.
Zhao
,
S. A.
Chester
, and
X.
Zhao
, “
Printing ferromagnetic domains for untethered fast-transforming soft materials
,”
Nature
558
,
274
279
(
2018
).
113.
Y.
Dai
,
D.
Chen
,
S.
Liang
,
L.
Song
,
Q.
Qi
, and
L.
Feng
, “
A magnetically actuated octopus-like robot capable of moving in 3d space
,” in
2019 IEEE International Conference on Robotics and Biomimetics (ROBIO)
(
IEEE
,
2019
), pp.
2201
2206
.
114.
K. E.
Peyer
,
L.
Zhang
, and
B. J.
Nelson
, “
Bio-inspired magnetic swimming microrobots for biomedical applications
,”
Nanoscale
5
,
1259
1272
(
2013
).
115.
G.
Dogangil
,
O.
Ergeneman
,
J. J.
Abbott
,
S.
Pané
,
H.
Hall
,
S.
Muntwyler
, and
B. J.
Nelson
, “
Toward targeted retinal drug delivery with wireless magnetic microrobots
,” in
2008 IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IEEE
,
2008
), pp.
1921
1926
.
116.
H.
Marino
,
C.
Bergeles
, and
B. J.
Nelson
, “
Robust electromagnetic control of microrobots under force and localization uncertainties
,”
IEEE Trans. Autom. Sci. Eng.
11
,
310
316
(
2013
).
117.
D.
Bobo
,
K. J.
Robinson
,
J.
Islam
,
K. J.
Thurecht
, and
S. R.
Corrie
, “
Nanoparticle-based medicines: A review of FDA-approved materials and clinical trials to date
,”
Pharm. Res.
33
,
2373
2387
(
2016
).
118.
R.
Khalesi
,
H.
Nejat Pishkenari
, and
G.
Vossoughi
, “
Independent control of multiple magnetic microrobots: Design, dynamic modelling, and control
,”
J. Micro-Bio Robot.
16
,
215
224
(
2020
).
119.
C.
Hong
,
Z.
Ren
,
C.
Wang
,
M.
Li
,
Y.
Wu
,
D.
Tang
,
W.
Hu
, and
M.
Sitti
, “
Magnetically actuated gearbox for the wireless control of millimeter-scale robots
,”
Sci. Robot.
7
,
eabo4401
(
2022
).
120.
J.
Zhang
,
Y.
Guo
,
W.
Hu
, and
M.
Sitti
, “
Wirelessly actuated thermo-and magneto-responsive soft bimorph materials with programmable shape-morphing
,”
Adv. Mater.
33
,
2100336
(
2021
).
121.
F.
Ongaro
,
D.
Niehoff
,
S.
Mohanty
, and
S.
Misra
, “
A contactless and biocompatible approach for 3d active microrobotic targeted drug delivery
,”
Micromachines
10
,
504
(
2019
).
122.
E.
Diller
,
C.
Pawashe
,
S.
Floyd
, and
M.
Sitti
, “
Assembly and disassembly of magnetic mobile micro-robots towards deterministic 2-D reconfigurable micro-systems
,”
Int. J. Robot. Res.
30
,
1667
1680
(
2011
).
123.
J.
Zhang
,
M.
Salehizadeh
, and
E.
Diller
, “
Parallel pick and place using two independent untethered mobile magnetic microgrippers
,” in
2018 IEEE International Conference on Robotics and Automation (ICRA)
(
IEEE
,
2018
), pp.
123
128
.
124.
H.
Salmon
,
L.
Couraud
, and
G.
Hwang
, “
Swimming property characterizations of magnetic polarizable microrobots
,” in
2013 IEEE International Conference on Robotics and Automation
(
IEEE
,
2013
), pp.
5520
5526
.
125.
E.
Milana
,
R.
Zhang
,
M. R.
Vetrano
,
S.
Peerlinck
,
M.
De Volder
,
P. R.
Onck
,
D.
Reynaerts
, and
B.
Gorissen
, “
Metachronal patterns in artificial cilia for low reynolds number fluid propulsion
,”
Sci. Adv.
6
,
eabd2508
(
2020
).
126.
S.
Zhang
,
X.
Hu
,
M.
Li
,
U.
Bozuyuk
,
R.
Zhang
,
E.
Suadiye
,
J.
Han
,
F.
Wang
,
P.
Onck
, and
M.
Sitti
, “
3d-printed micrometer-scale wireless magnetic cilia with metachronal programmability
,”
Sci. Adv.
9
,
eadf9462
(
2023
).
127.
S. N.
Khaderi
,
C.
Craus
,
J.
Hussong
,
N.
Schorr
,
J.
Belardi
,
J.
Westerweel
,
O.
Prucker
,
J.
Rühe
,
J.
Den Toonder
, and
P.
Onck
, “
Magnetically-actuated artificial cilia for microfluidic propulsion
,”
Lab a Chip
11
,
2002
2010
(
2011
).
128.
S.
Zhang
,
Y.
Wang
,
P.
Onck
, and
J.
den Toonder
, “
A concise review of microfluidic particle manipulation methods
,”
Microfluid. Nanofluid.
24
,
24
(
2020
).
129.
S.
Zhang
,
R.
Zhang
,
Y.
Wang
,
P. R.
Onck
, and
J. M.
den Toonder
, “
Controlled multidirectional particle transportation by magnetic artificial cilia
,”
ACS Nano
14
,
10313
10323
(
2020
).
130.
X.
Dong
,
G. Z.
Lum
,
W.
Hu
,
R.
Zhang
,
Z.
Ren
,
P. R.
Onck
, and
M.
Sitti
, “
Bioinspired cilia arrays with programmable nonreciprocal motion and metachronal coordination
,”
Sci. Adv.
6
,
eabc9323
(
2020
).
131.
J. M.
den Toonder
and
P. R.
Onck
, “
Microfluidic manipulation with artificial/bioinspired cilia
,”
Trends Biotechnol.
31
,
85
91
(
2013
).
132.
N.
Xia
,
D.
Jin
, and
L.
Zhang
, “
Magnetic soft matter toward programmable and multifunctional miniature machines
,”
Acc. Mater. Res.
5
(
2
),
173
183
(
2024
).
133.
S.
Wang
,
J.
Xu
,
W.
Li
,
S.
Sun
,
S.
Gao
, and
Y.
Hou
, “
Magnetic nanostructures: Rational design and fabrication strategies toward diverse applications
,”
Chem. Rev.
122
,
5411
5475
(
2022
).
134.
R.
Deng
,
Q.
Cao
,
G.
Gong
,
H.
Yang
,
T.
Shinshi
, and
D.
Han
, “
Multi-pole magnetization of ndfeb magnetic elastomers via a programmable magnetic stamp inspired by movable type printing
,”
Sens. Actuators A
366
,
114945
(
2024
).
135.
L.
Xu
,
L.
Yang
,
T.
Li
,
X.
Zhang
, and
J.
Ding
, “
Deformation and locomotion of untethered small-scale magnetic soft robotic turtle with programmable magnetization
,”
J. Bionic Eng.
21
,
266845556
(
2024
).
136.
F.
Qiu
and
B. J.
Nelson
, “
Magnetic helical micro-and nanorobots: Toward their biomedical applications
,”
Engineering
1
,
021
026
(
2015
).
137.
F.
Qiu
,
S.
Fujita
,
R.
Mhanna
,
L.
Zhang
,
B. R.
Simona
, and
B. J.
Nelson
, “
Magnetic helical microswimmers functionalized with lipoplexes for targeted gene delivery
,”
Adv. Funct. Mater.
25
,
1666
1671
(
2015
).
138.
M. P.
Kummer
,
J. J.
Abbott
,
K.
Vollmers
, and
B. J.
Nelson
, “
Measuring the magnetic and hydrodynamic properties of assembled-mems microrobots,” in Proceedings
of
2007 IEEE International Conference on Robotics and Automation
(
IEEE
,
2007
), pp.
1122
1127
.
139.
T.
Xu
,
J.
Yu
,
X.
Yan
,
H.
Choi
, and
L.
Zhang
, “
Magnetic actuation based motion control for microrobots: An overview
,”
Micromachines
6
,
1346
1364
(
2015
).
140.
J.
Liu
,
T.
Xu
,
C.
Huang
, and
X.
Wu
, “
Automatic manipulation of magnetically actuated helical microswimmers in static environments
,”
Micromachines
9
,
524
(
2018
).
141.
C.
Ye
,
J.
Liu
,
X.
Wu
,
B.
Wang
,
L.
Zhang
,
Y.
Zheng
, and
T.
Xu
, “
Hydrophobicity influence on swimming performance of magnetically driven miniature helical swimmers
,”
Micromachines
10
,
175
(
2019
).
142.
R.
Avaneesh
,
R.
Venezian
,
C.-S.
Kim
,
J.-O.
Park
,
S.
Misra
, and
I. S.
Khalil
, “
Open-loop magnetic actuation of helical robots using position-constrained rotating dipole field
,” in
2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
(
IEEE
,
2021
), pp.
8545
8550
.
143.
K.
Vollmers
,
D. R.
Frutiger
,
B. E.
Kratochvil
, and
B. J.
Nelson
, “
Wireless resonant magnetic microactuator for untethered mobile microrobots
,”
Appl. Phys. Lett.
92
,
144103
(
2008
).
144.
H.
Yu
,
W.
Tang
,
G.
Mu
,
H.
Wang
,
X.
Chang
,
H.
Dong
,
L.
Qi
,
G.
Zhang
, and
T.
Li
, “
Micro-/nanorobots propelled by oscillating magnetic fields
,”
Micromachines
9
,
540
(
2018
).
145.
K. B.
Yesin
,
P.
Exner
,
K.
Vollmers
, and
B. J.
Nelson
, “
Design and control of in-vivo magnetic microrobots
,” in
International Conference on Medical Image Computing and Computer-Assisted Intervention
(
Springer
,
2005
), pp.
819
826
.
146.
K. B.
Yesin
,
K.
Vollmers
, and
B. J.
Nelson
, “
Actuation, sensing, and fabrication for in vivo magnetic microrobots
,” in
Experimental Robotics IX
, edited by
M. H.
Ang
and
O.
Khatib
(
Springer
,
2006
), pp.
321
330
.
147.
A. G.
Alleyne
,
S.
Schurle
,
A.
Meo
, and
B. J.
Nelson
, “
Motion control for magnetic micro-scale manipulation
,” in
2013 European Control Conference (ECC)
(
IEEE
,
2013
), pp.
784
790
.
148.
Y.
Kim
and
X.
Zhao
, “
Magnetic soft materials and robots
,”
Chem. Rev.
122
,
5317
5364
(
2022
).
149.
B.
Dahroug
,
J.-A.
Séon
,
A.
Oulmas
,
T.
Xu
,
B.
Tamadazte
,
N.
Andreff
, and
S.
Régnier
, “
Some examples of path following in microrobotics
,” in
2018 International Conference on Manipulation, Automation and Robotics at Small Scales (MARSS)
(
IEEE
,
2018
), pp.
1
6
.
150.
J.
Sikorski
,
S.
Mohanty
, and
S.
Misra
, “
Milimac: Flexible catheter with miniaturized electromagnets as a small-footprint system for microrobotic tasks
,”
IEEE Robot. Autom. Lett.
5
,
5260
5267
(
2020
).
151.
C. M.
Heunis
,
K. J.
Behrendt
,
E. E.
Hekman
,
C.
Moers
,
J.-P. P.
de Vries
, and
S.
Misra
, “
Design and evaluation of a magnetic rotablation catheter for arterial stenosis
,”
IEEE/ASME Trans. Mechatron.
27
,
1761
1772
(
2021
).
152.
C. M.
Heunis
,
Y. P.
Wotte
,
J.
Sikorski
,
G. P.
Furtado
, and
S.
Misra
, “
The armm system-autonomous steering of magnetically-actuated catheters: Towards endovascular applications
,”
IEEE Robot. Autom. Lett.
5
,
705
712
(
2020
).
153.
T.-R.
Ger
,
H.-T.
Huang
,
W.-Y.
Chen
, and
M.-F.
Lai
, “
Magnetically-controllable zigzag structures as cell microgripper
,”
Lab a Chip
13
,
2364
2369
(
2013
).
154.
S.
Yim
and
M.
Sitti
, “
Shape-programmable soft capsule robots for semi-implantable drug delivery
,”
IEEE Trans. Robot.
28
,
1198
1202
(
2012
).
155.
V.
Iacovacci
,
G.
Lucarini
,
L.
Ricotti
,
P.
Dario
,
P. E.
Dupont
, and
A.
Menciassi
, “
Untethered magnetic millirobot for targeted drug delivery
,”
Biomed. Microdev.
17
,
1
12
(
2015
).
156.
E. B.
Joyee
and
Y.
Pan
, “
Multi-material additive manufacturing of functional soft robot
,”
Procedia Manuf.
34
,
566
573
(
2019
).
157.
T. N.
Do
,
K. Y.
Ho
, and
S. J.
Phee
, “
A magnetic soft endoscopic capsule-inflated intragastric balloon for weight management
,”
Sci. Rep.
6
,
39486
(
2016
).
158.
G.
Kósa
,
P.
Jakab
,
F.
Jólesz
, and
N.
Hata
, “
Swimming capsule endoscope using static and rf magnetic field of mri for propulsion
,” in
2008 IEEE International Conference on Robotics and Automation
(
IEEE
,
2008
), pp.
2922
2927
.
159.
A. J.
Petruska
,
F.
Ruetz
,
A.
Hong
,
L.
Regli
,
O.
Sürücü
,
A.
Zemmar
, and
B. J.
Nelson
, “
Magnetic needle guidance for neurosurgery: Initial design and proof of concept
,” in
2016 IEEE International Conference on Robotics and Automation (ICRA)
(
IEEE
,
2016
), pp.
4392
4397
.
160.
Q.-W.
Cai
,
X.-J.
Ju
,
S.-Y.
Zhang
,
Z.-H.
Chen
,
J.-Q.
Hu
,
L.-P.
Zhang
,
R.
Xie
,
W.
Wang
,
Z.
Liu
, and
L.-Y.
Chu
, “
Controllable fabrication of functional microhelices with droplet microfluidics
,”
ACS Appl. Mater. Interfaces
11
,
46241
46250
(
2019
).
161.
H.
Wang
,
M.
Totaro
, and
L.
Beccai
, “
Toward perceptive soft robots: Progress and challenges
,”
Adv. Sci.
5
,
1800541
(
2018
).
162.
R. Z.
Gao
and
C. L.
Ren
, “
Synergizing microfluidics with soft robotics: A perspective on miniaturization and future directions
,”
Biomicrofluidics
15
,
011302
(
2021
).
163.
Z.
Ren
,
R.
Zhang
,
R. H.
Soon
,
Z.
Liu
,
W.
Hu
,
P. R.
Onck
, and
M.
Sitti
, “
Soft-bodied adaptive multimodal locomotion strategies in fluid-filled confined spaces
,”
Sci. Adv.
7
,
eabh2022
(
2021
).