Reconfigurable Liquid‐Bodied Miniature Machines: Magnetic Control and Microrobotic Applications

Soft miniature machines demonstrate multimodal actuation and morphology change capabilities in narrow spaces smaller than their dimension. The wirelessly controlled soft‐bodied features make them promising candidates for microrobotic manipulation and targeted operation in a noninvasive manner. Liquid‐bodied machine offers an ultrasoft body with extreme deformability owing to its fluid nature, enabling adaptive navigation with smooth contact with objects and environmental restrictions. Over the last decade of development, significant research progress has been achieved in wirelessly controlling liquid‐bodied machines for diverse manipulation applications. Herein, an overview of the recent research results in magnetic control methods and diverse microrobotic applications of liquid‐bodied machines is provided. Considering the control mechanisms and application challenges, ferrofluid‐based, liquid metal‐based, and liquid marble‐based machines are mainly discussed with a brief discussion on droplet‐based machines. The connection between control methods and applications is highlighted with a detailed analysis of machine–object and machine–environment interactions. The current challenges and research opportunities on liquid‐bodied miniature machines are outlined, aiming at designing intelligent liquid‐bodied machine‐based microrobotic systems and promoting the development of small‐scale robotics.

In nature, living things show adaption behavior to the fast-changing environment.For example, mollusks and invertebrates show surrounding environment-triggered behaviors, such as stretching and curling up, relying on a complex mixture of biophysical and chemical signals. [39]Phylum mollusks, such as leeches, can behave deformations and multimodal moving patterns in response to environmental stimuli. [40]Besides single body-based adaption, a swarm of Bacillaria paradoxa diatom can reversibly transform between a fully stretched and a contracted pattern in response to light stimulation. [41,42]The demonstrated adaptability of these living things indicates that miniature machines with ultrasoft bodies and nondefined shapes can dramatically improve the application range and benefit robotic manipulation in narrowed spaces.Liquid-bodied miniature machines demonstrate high softness and promising deformability owing to the fluid-based main body. [43]54][55][56] This review summarizes the recent research achievements on liquid-bodied miniature machines with a focus on their magnetic control methods and microrobotic applications (Figure 1).Four types of liquid-bodied machines are discussed, including ferrofluid-based, liquid metal-based, liquid marble-based machines, and a brief discussion on magnetic droplet-based machines.We start with the magnetic control methods of ferrofluid-based machines, including motion and deformation control, followed by morphology control, splitting/coalescence control, and state transition control.Representative applications are introduced, which bridge magnetic control methods and practical applications.Besides, the self-assembly and collective behaviors of ferrofluid droplets are highlighted, and the underlying mechanisms and their applications in the microrobotics area are summarized.Next, attention moves to motion, deformation, and transformation control of liquid metal-based machines.The conductive feature-based manipulation of liquid metal is summarized and compared to show the internal connection between control and applications.After that, we introduce liquid marble-based machines with unique magnetic opening/close behavior and their applications in chemical reactions, cell culturing, and centrifuge processing.We provide key equations for the fundamental understanding of the machine behaviors under magnetic control and provide a foundation for building control systems.In the last part, we conclude with our perspective on the challenges and research opportunities on liquid-bodied miniature machines as well as the directions for designing liquid-bodied machine-based microrobotic systems with autonomy and intelligence.

Ferrofluid-Based Machines 2.1. Ferrofluid under External Magnetic Fields
[59] Chemical coating (e.g., surfactant, polymer) on the particle's surface prevents agglomeration in the carrier fluid.Considering a typical isothermal incompressible ferrofluid with monodisperse particles and constant mass density distribution, the continuity equation is expressed as ∇ ⋅ v ¼ 0, where v is the translational velocity.Thus, the linear momentum equation is obtained from the general balance for the linear momentum pðx, tÞ ¼ ρðx, tÞvðx, tÞ with ρ the density as [60] ρ Dv Dt where ω is the mean rotation rate, p is the pressure; μ 0 is the permeability of free space, M and H are the magnetization of suspension and the magnetic field; λ, η, ζ are the bulk viscosity, shear viscosity, and vortex viscosity, respectively.The changing rate of the internal angular momentum density sðx, tÞ ¼ ρðx, tÞIðx, tÞωðx, tÞ can be calculated by subtracting the moment of the linear momentum density from the total angular momentum density as [61] ρI where Iðx, tÞ is the particle's moment of inertia density; λ 0 and η 0 are the bulk spin viscosity and shear spin viscosity.Under an external magnetic field, the field obeys Maxwell's equations: [62] ∇ Â H ¼ 0 and ∇ ⋅ ðM þ HÞ ¼ 0. The applied field changes the inner magnetization density.The magnetization relaxation equation is expressed as τ B refers to the effective relaxation time of the particles, and M eq is the equilibrium magnetization of the suspension.The above equation is suitable for cases with low magnetic field strengths [63][64][65] ; ref. [66] accurately describes ferrofluid's behavior under fields with high strengths and frequencies.Then, the equilibrium magnetization of the assumed noninteracting monodisperse particles is expressed as [58] M eq ϕM d where α ¼ mH k B T and LðαÞ are the Langevin parameter and Langevin function, respectively; ϕ is the particle concentration; and M d is the domain magnetization of particle.With a low-strength field input (α ( 1), we have M eq ¼ χ 0 H with χ 0 the suspension's magnetic susceptibility.The ferrohydrodynamic equations we listed above describe the flow of a ferrofluid under an external magnetic field, providing the fundamental understanding for magnetic control of ferrofluid-based miniature machines. [67]hen applying ferrofluid-based machines for microrobotic applications, dynamic magnetic fields with time-dependent strength or frequency are widely used, such as rotating, oscillating, and precessing fields, resulting in a new equilibrium magnetization state.The inner particles exhibit rotation under the hydrodynamic resistance of the carrier fluid, governed by the Brownian relaxation with the relaxation time of τ B ¼ 3V h η 0 k B T , where V h is the hydrodynamic particle volume, and η 0 is the carrier fluid's viscosity. [58]From the particle's aspect, when the magnetic dipole rotates, the state is characterized by Néel relaxation with the time τ N ¼ 1 , where f 0 ¼ 10 9 Hz, K a is the material's anisotropy constant, and V is the particle's volume of the magnetic part. [58]Therefore, by considering the two mechanisms, the relaxation time is The above analysis indicates that the relevant effect of the relaxation mechanism exists when ferrofluid is under different dynamic magnetic fields.

Motion and Deformation Control
The extremely soft body of ferrofluid provides omnidirectional deformation under external magnetic fields.Because of the Brownian motion and the low volume fraction of the superparamagnetic nanoparticles (V p ), ferrofluid does not show magnetism without external field input. [58]Under a magnetic field, the magnetization direction of ferrofluid can be adjusted by changing the field direction with the magnetization intensity of with α ¼ μ 0 mH 0 =k 0 T, where M is the magnetization of a single particle and H 0 is the field strength.Assuming a ferrofluid droplet is driven under an external field with magnetic flux density B, the magnetic moment becomes where χ is the magnetic permeability of a ferrofluid droplet.A magnetic gradient generated by a permanent magnet or an electromagnetic coil system exerts a magnetic force on the ferrofluid body as [68] F This linear relationship is guaranteed assuming that the ferrofluid is in the saturation magnetization state.By exploiting the deformable and self-adaptive features of ferrofluid, a ferrofluid microrobot can navigate in a narrow, tortuous maze (Figure 2A-i).By applying a four-coil electromagnetic system, 3D navigation in a vascular model is conducted with real-time controllability (Figure 2A-ii).
The controllability of the ferrofluid-based microrobot is affected by the unstable shape of the fluid, limiting active deformation when performing microrobotic manipulation tasks.Sun et al. propose a magnetic slime robot with both elastomer-like stability and liquid body-like large deformations. [69]Synthesis of the slime robot involves adding borax and NdFeB particles into a polyvinyl alcohol (PVA) solution.The interaction between the tetrafunctional borate ions with the -OH group of PVA yields the slime formation.The slime robot consists >90 wt% water; thus, it is categorized as a hydrogel.The soft body exhibits elongation under a magnetic attraction.Adding another magnetic field source allows the slime robot to be locked on the substrate and perform controlled elongation (Figure 2B-i).The body provides environmental adaptability when navigating in a narrow environment with sharp curves.The robot can squeeze through the confined tube smaller than the robot body (Figure 2B-ii).The flexible body enables object manipulation with multiple functionalities.The body can extend its tentacles in different directions and capture wires under a rotating magnetic field.During manipulation, the remanent magnetism of the inner magnetic nanoparticles remains for a short time after removing the magnet because of the non-Newtonian behavior-induced limited dimensional stability. [70]The robot exhibits endocytosis-like object manipulation under the control of a ring-shaped magnet (Figure 2B-iii).By tilting the magnet, a C-shaped robot wraps the object, followed by spreading to enclose the object.The slime robot curls using a rotating magnetic field and swallows the object.Such microrobotic manipulation capability can be extended to electronic applications.The broken circuit is repaired by wrapping the two ends of the wires.Combined with the elongation control, 3D circuit connections are performed with ease.Besides the application in lab-made environments, ferrofluid micromachines have been used for spatiotemporal measurements of mechanical properties in vivo.Serwane et al. apply Motion and deformation control of ferrofluid-based miniature machines.A) Adaptive navigation of a ferrofluid-based microrobot in a complex maze and 3D channel.Reproduced with permission. [68]Copyright 2022, AIP Publishing.B) Magnetic control of a reconfigurable slime robot for microrobotic and electronic manipulation.Adapted with permission. [69]Copyright 2022, Wiley.C) In vivo quantification of mechanical properties of zebrafish using a ferrofluid droplet.μ and k are the viscous and elastic elements for describing the viscosity η and elastic modulus E, respectively.Adapted with permission. [71]Copyright 2017, Springer Nature.
biocompatible fluorocarbon-based ferrofluid droplet as the tool. [71]n array of eight permanent magnets is designed to control the magnetic field direction and flux density.To measure the mechanical properties of the surrounding environment, a key issue remains in reducing the 3D droplet's deformation information to the 1D formulation, which allows using 1D rheological diagrams to conduct the sensing or measurement tasks (Figure 2C-i).When the droplet is in a Newtonian fluid, the relationship between strain response εðtÞ and applied magnetic stress σ M becomes where α NF ¼ 1=k d and τ NF α ¼ μ=k d ; t on represents the switch-on time of the magnetic field.When the droplet is in purely elastic material, the equilibrium strain ε under a constant σ M becomes For in vivo and in situ quantification during zebrafish tailbud elongation, the mechanical response of the living materials exhibits viscoelastic behavior (Figure 2C-ii).Thus, without the magnetic stress σ M , the tissue stress σ T deforms the droplet, and the applied stress should be considered in different time slots.During the wait and relaxation time slots (i.e., 0 < t < t on and t ≥ t off ), we have σ 0 ¼ σ T , whereas σ 1 ¼ σ T þ σ M during the creep time slot (i.e., t on ≤ t < t off ).The ferrofluid-based measuring method allows investigation of mechanobiology in vivo, showing potential applications when combined with microrobotic control systems.

Morphology and Motion Control
The shape-programmable capability of ferrofluid-based miniature machines plays an essential role from both control and application aspects, which takes the unique features of the reconfigurable and reversible body.Patterned magnets or electromagnets enable spatiotemporal field control that can adjust the morphology and motion state of ferrofluid-based machines, thanks to the relatively fast response of ferrofluid to magnetic fields.The magnetic potential energy distribution is adjusted by controlling the current input (distribution) of the electromagnetic coil array or using permanent magnets with varied shapes [72] (Figure 3A-i).Robot splitting is performed by applying currents in two coils.The field gradient-induced splitting force at the robot's two sides elongates the body and results in body splitting (Figure 3A-ii).The shapes of the robot can be adjusted by programming the magnetic potential energy, e.g., by using permanent magnets with different shapes.The robot shows similar morphology to the shape of the magnet because the inner particles tend to move toward the region of the lowest magnetic potential energy.This mechanism can also be applied for motion control: navigation is achieved by shifting the magnetic potential energy well across the array.Furthermore, by activating different regions of the array, simultaneous coordinated motion of multiple robots is demonstrated.Together with the adaptive deformation in a confined environment, these control mechanisms provide manipulation strategies in cargo transportation, cargo caging, and fluidic mixing (Figure 3A-ii).
A ferrofluid robot carries flexible electronic devices and shows controlled motion on a 10 Â 10 array of electromagnets. [73]he flexible device floats on the top surface of the robot because of the surface tension and the device's large surface area to mass ratio (Figure 3B-i).The flexible device is compatible with the robot's deformation, especially during navigation in multipleobstacle and confined environments.Moreover, no interfacial separation is observed because of the adhesion forces between water molecules and the device.The sensing capability of the flexible device-embedded droplet robot relies on the functionality of flexible electronics, e.g., temperature and humidity sensing.The robot performs electrochemical sensing by glucose concentration monitoring (Figure 3B-ii).The robot merges three glucose droplets and two PBS droplets in a one-by-one order by controlling the motion direction and recording the current signal.The signal changes by 0.2 μA when merging glucose droplets and a reverse response is recorded when merging PBS droplets.The robot can identify specific mycotoxins from interfering ones: the I/V curves of the electrochemical sensor only changes with merging Aflatoxin B1 droplets.This work shows that ferrofluidbased miniature robots are able to be used as robotic carriers for functional devices, especially those flexible ones compatible with the deformation of the soft body.
To form ferrofluid-based robots with arbitrary shapes, Chen et al. propose a mold-based morphology control method. [74]esearchers fabricate customized magnets in a batch by pouring polydimethylsiloxane (PDMS) and NdFeB microparticles into the mold.After curing, any shapes of magnets can be fabricated after magnetizing them in a 2 T magnetic field.Essentially, the magnets determine the magnetic potential energy distribution; thus, ferrofluid robots with demanded shapes are displayed (Figure 3C-i).The robot deformability benefits manipulation in complex environments.The contact area between the robot and the environment or the object can be adjusted, providing cargo transportation capability in different environments, for example, pushing cargo and squeezing through narrow channels (Figure 3C-ii).The output force of the robot is adjusted by adjusting the robot-magnet distance.Changing the volume of the robot leads to different output forces, which provide multiple choices according to the object.
Taking advantage of the independent control feature of an electromagnet array, the cooperation of multiple ferrofluid-based miniature robots is demonstrated. [75]Inspired by an automated vehicle system used for autonomous cargo carrying and distribution in industries, the system involves an electromagnetic coil array (32 Â 32) to generate a localized field for controlling a permanent magnet, which attracts and moves the ferrofluid-based robots to conduct programmable tasks (Figure 3D-i).Direct driving of ferrofluid-based robots above the coil array can be conducted; the intermediary permanent magnet amplifies the actuation efficiency.Through the multiple functional regions, microrobotic manipulation is able to be achieved in a controlled manner, such as droplet splitting, coalescence, dispensing, and step-by-step transportation (Figure 3D-ii).Moreover, the system level of package sorting is designed using a cross-collaborative robot network.Copyright 2020, The Authors, published by PNAS.B) Controlling a ferrofluid droplet as a carrier for flexible devices.Adapted under the terms of the CC BY 4.0 license. [73]Copyright

Splitting and Coalescence Control
[78] Decreasing the distance between the droplet and a cylindrical permanent magnet increases the field strength (H) and gradient, which lead to droplet deformation and then splitting. [79]Interestingly, droplet splitting does not happen when they are actuated by a uniform magnetic field.The splitting is related to Rosensweig instability with the critical wavelength as where σ is the surface tension of fluid and M is the magnetization.The analysis indicates that droplet splitting occurs when λ c becomes smaller than the droplet's diameter, and a larger number of droplets can be observed by increasing the field strength (Figure 4A-i).After splitting, an ordered pattern is formed by minimizing the energy U.By summing the dropletdroplet dipolar repulsion and the gradient-induced attraction as Splitting and coalescence control of ferrofluid-based miniature machines.A) Splitting and coalescence under the reversible switching between static and dynamic self-assembly.Adapted with permission. [79]Copyright 2013, Springer Nature.B) Trans-scale state and motion control of ferrofluid microrobots in a dimension-varying structure.Reproduced with permission under the CC BY-NC 4.0 license. [82]Copyright 2022, The Authors, published by AAAS.C) Wettability-based control of ferrofluid body.Reproduced under the terms of the CC BY 4.0 license. [83]Copyright 2022, The Authors, published by Springer Nature.
where m and r represent the magnetic moment and position of the ith and jth droplets; c ¼ À d 2 H dr 2 is the confining curvature of the applied field.Therefore, a static self-assembly system is established and governed by energy minimization.The static system can transfer to dynamic self-assembly ones by providing continuous energy to keep the system away from energy minimum, i.e., applying oscillating motion to the magnet (Figure 4A-ii).The dynamic system is strongly affected by the energy feed rate (oscillating amplitude and frequency).The pattern remains stable when applying small amplitude and frequency and coalesces when the energy feed rate is above a critical value.The timedependent dissipative magnetic forces decrease the distance among droplets because the energy input frees the system from the kinetic trap, resulting in the coalescence. [80]A numerical investigation of the splitting phenomenon in a simple shear flow under a uniform magnetic field has been proposed, providing a fundamental analysis in low Reynolds number conditions. [81]esides using permanent magnets, Fan et al. combine electromagnets and a permanent magnet for the ferrofluid body control. [82]The actuation system consists of four orthogonal solenoids and one spherical NdFeB magnet, and the system is controlled by a motorized translation stage (Figure 4B).The solenoid-generated background field adjusts the direction of the magnet's moment, providing on-demand field control or even dynamic fields (e.g., rotating field).The system applies the relatively weak field to adjust the magnet-generated fields applied for ferrofluid control.The weak-strong field combination system also provides a new approach for indirect controlling objects with relatively weak magnetism.The droplet robot splitting and coalescence control and the deformable body enable adaptive navigation in a complex maze.The robot is stretched along the channel to squeeze through the narrowed region, exhibiting splitting to pass through an extremely narrowed region.This step is achieved by shortening the distance between the robot and the magnet, where the λ c approaches the robot diameter, and splitting occurs.By moving the magnet, the droplet propulsion transports into a new region.2D oscillating fields have been applied for manipulating a ferrofluid body. [83]The field consists of orthogonal constant and sinusoidal components as where A O and C O are the field amplitudes, and θ is the angle between the constant component and the y axis.By increasing the driven frequency, the viscous drag from water increases and the surface tension fails to maintain the intact shape, leading to the splitting (Figure 4C).The alignment direction is controlled by the oscillating direction of the field.By decreasing the frequency, the interagent magnetic attraction becomes dominant, and droplets contact the neighbors.Then, the coalescence is denominated by the van der Waals intermolecular forces.A further splitting behavior can be conducted by increasing the distance of subdroplets.A 3D dynamic field consists of 1D oscillation and a 2D rotation component is applied as where B m denotes the maximum strength, αðtÞ is the precession angle, and f 1 and f 2 are the input frequencies. [84,85]The droplet splits into 17 subdroplets that exhibit a spreading state and then gradually merge to the initial state by decreasing the input frequency.

Liquid-Solid State Transition Control
A magnetorheological millimeter-scale robot exhibits liquid (Newtonian fluid) and solid (Bingham plastic) states under magnetic fields with strengths of %0 and 100 mT, respectively. [86]he inner Fe particles and starch granules are randomly dispersed in fluids without magnetic field; thus, a flow-like state is demonstrated (Figure 5A-i).Fe particle chains and clusters are formed along the applied field direction due to the dipolar attraction, which extrudes the starch granules between the chains and increases the inherent stiffness.Such solid-liquid state transition provides foundation for conducting complex tasks by utilizing the advantages of both liquid and solid properties.The robot passes through a narrow channel under a weak magnetic field, and then splits into two bodies by the magnetic pulling forces (Figure 5A-ii).The two strong field-induced solid bodies work cooperatively to push a metal bar to connect the electrical circuit and light up the LED.The two bodies merge again to pass through narrow regions or deform into a C-shaped tool for robotic manipulations, demonstrating a reversible, on-demand transition capability between different states.By exploiting the deformability and adaptive mobility, the robot is suitable for manipulation in confined environments, such as vascular-like structures (Figure 5A-iii).Unlike soft robots, the solid state enables operation with a relatively large force, showing potential for thrombus clearance and bloodstream blockage.A magnetoresponsive and reconfigurable interfacial self-assembly (MRRIS) process has been designed for state transition. [87]The Fe 3 O 4 nanoparticles are stabilized by oleic acid in mineral oil.The ferrofluid body is in a water phase that consists of silica nanoparticles.Under an external magnetic field gradient, the Fe 3 O 4 nanoparticles deform the water-oil interface and cause assembly of silica nanoparticles at the interface.After removing the field, the silica nanoparticles jam at the interface, resulting in a stable solid-like shape (Figure 5B-i).Such state transition will not occur if the ferrofluid body is immersed in pure water.The reconfiguration is applied for microrobotic cargo transportation of oil droplets (Figure 5B-ii).Unlike the methods in ref. [86], this transition control and manipulation need specific environments that can trigger the MRRIS process.
State transition of temperature-sensitive soft robots has been demonstrated. [88]The soft composite contains magnetic particles and a polymer matrix.The exchange reaction of disulfide bonds inside the matrix is triggered by heat and infrared irradiation, and the materials behave like ferrofluids.When cooling to room temperature, the material behaves like a magnetic-responsive elastomer (Figure 5C-i).Therefore, the soft robots are able to exhibit deformation due to the temperature-sensitive rheological behavior [89] and shape change with self-healing capability under a temperature change.The soft robot transforms into an on-demand shape by applying localized heating with a laser beam.With the guidance of external magnetic fields, the temperature-responsive soft robots can carry out various A B C Figure 5. Liquid-solid state transition control of ferrofluid-based miniature machines.A) Liquid-solid state transition control by applying a strong magnetic field (% 100 mT).Reproduced with permission. [86]Copyright 2022, American Chemistry Society.B) State transition of a ferrofluid robot under various external magnetic fields.Reproduced with permission. [87]Copyright 2022, American Chemistry Society.C) State transition between elastomer and viscous fluid by changing the temperature.Reproduced with permission. [88]Copyright 2022, Royal Chemistry Society.microrobotic manipulation, including object grasping, welding/ unwelding, and targeted transportation along a planned path (Figure 5C-ii).
[92][93] Zhang et al. propose a PDMS-ferrofluid-based soft miniature robot that can be actuated by magnets or electromagnetic coils. [94]PDMS wrap ferrofluid inside for magnetic actuation: the robot can generate net forward or backward movement with switchable capability.The robot exhibits inchworm-inspired movement: after magnetically inducing a bending deformation, a forward movement generates by anchoring the posterior leg and detracting the deformation.Besides the microrobotic applications, ferrofluidbased soft robot has been applied for energy conversion.Ma et al. propose a ferrofluid robot-based energy transducer. [95]he robot exhibits motion under an external field and across a coil, which changes the magnetic flux, providing a mechanism for converting mechanical energy to electricity.The system consists of the robot, a superhydrophobic pedestal, and a coil/ magnet base.The output voltage e is calculated by the total change of magnetic flux during the droplet movement as where N is the number of coil turns, ΔΦ denotes the magnetic flux change, and Δt denotes the working time, i.e., the robot contact time of the magnetic plate.The mechanical-to-electrical transduction can be used as a wave monitor by transducing the wave mechanical energy to electricity.A sealed superhydrophobic space allows energy conversion where the status is monitored by connecting to a LED.

Collective Behaviors in Ferrofluid-Based Machines
Under an external magnetic field, the ferrofluid-based machines are magnetized, yielding the magnetic interactions between agents.Taking two machines i, j with magnetic moment m and location vector r, the magnetic interaction energy U i,j and force F i,j are express as Thus, a chain of ferrofluid agents is formed under a static magnetic field due to the magnetic attraction. [96]Driven under an in-plane (xy-plane) rotating magnetic field, the interagent magnetic force between ferrofluid droplets becomes timedependent.From a time-averaged aspect, the energy becomes U i,j ¼ Àμ 0 m 2 =8πðx þ γÞ 3 . [97,98]Thus, a droplet chain is formed by magnetic attraction.A magnetic disassembly is demonstrated by inducing the interagent repulsion, which is conducted by adding an out-of-plane field (Figure 6A-i).
The assembled chain can be navigated in a glass slice-sealed microfluidic chip.It can pass through a narrow, low tunnel without collisions (Figure 6A-ii).The strong interagent attraction stabilizes the chain-like structure when navigating over a series of adjacent deep grooves and prevents falling into the trenches.Fan et al. use a sphere magnet to achieve swarm control. [82]wo methods are applied for the droplet splitting and merging.The mechanism of the first approach relies on adjusting the distance between the magnet and droplets, as discussed in Figure 4A. [79]By vertically rotating the magnet, the in-plane attraction leads to the droplet merging (Figure 6B-i).The second approach relies on the rotating speed of the magnet (Figure 6B-ii).During rotation, the droplets are stretched to ellipsoids and subjected to shear forces that are larger at the ends, resulting in the splitting effect (Figure 6B-iii).14 sub-droplets are demonstrated by increasing the magnet's rotating frequency from 1 to 120 Hz, and they merge again by gradually decreasing the frequency to 1 Hz.Collective pattern transformation is conducted by adjusting the magnet's rotating axis, yielding vortex and matrix swarm patterns.
Swarming behaviors of ferrofluid droplets are demonstrated under dynamic magnetic fields. [99]The microswarm is formed under a rotating magnetic field, and it exhibits transformation by modulating the input field, benefiting adaptive navigation in multiple terrains (Figure 6C-i).The bending behavior can be applied for microrobotic manipulation.The circular swarm pattern exhibits elongation by polarizing the rotating field to an elliptic rotating field ( f = 8 Hz).The swarm acts like a liquid by increasing the frequency to 200 Hz, and the swarm states to bend clockwise from top to bottom and confines the microparticle (Figure 6C-ii).The manipulation approach can be successfully conducted in a channel; a 10 μm-diameter SiO 2 microparticle is picked from the 20 μm-width channel.The microswarm acts like a soft manipulator with input frequency-dependent flexibility.

Fundamentals in Liquid Metal
[105] Room-temperature liquid metals have a melting point below 30 °C.In nature, Hg, Cs, and Ga elements have melting points of À38.8, 28.65, and 29.8 °C, and are holding liquid state at 30 °C.However, the high-toxic vapors of Hg and active reaction of Cs in water make Hg and Cs hard to be applied.Ga and Ga-based liquid metal alloys with stable properties have been widely studied.At room temperature, several liquid metal alloys have a comparable flowability to water; for example, the viscosities of GaIn, GaInSn, and GaInSnZn are 2.7, 2.98, and 0.71 m 2 s À1 , respectively (water: 11.2 m 2 s À1 ). [106]109] A B C Figure 6.Collective control of ferrofluid droplets.A) Assembly and disassembly of ferrofluid droplets for microrobotic applications.Reproduced with permission. [96]Copyright 2020, Wiley.B) Splitting and merging control of ferrofluids with collective control capability.Reproduced with permission under the CC BY-NC 4.0 license. [82]Copyright 2022, The Authors, published by AAAS.C) Controlling a ferrofluid swarm with adaptive locomotion in multiterrain conditions.The swarm acts like a soft manipulator to grab a microsphere.Reproduced with permission. [99]Copyright 2021, Wiley.
When attaching liquid metals to soft or membrane-shaped materials, the outstanding flexibility enables various manipulation with conductive capability, which provides soft electronics with properties that traditional electrical circuits are hard to achieve. [110,111]One can stretch or press the devices without breaking the conductivity by printing liquid metals on a flexible substrate, such as Ecoflex silicon rubber and PDMS.Liquid-solid phase transition occurs by lowering the temperature below the melting point.Thus, it is easy to reshape liquid metals to the desired structures with plasticity and metallic properties.By embedding magnetic particles in liquid metal, magnetoactive phase transitional matter is observed.For example, the neodymium-iron-boron microparticle-embedded liquid metals show 21.2 MPa mechanical strength and 1.98 GPa stiffness in the solid phase.After heating with an alternating magnetic field, the liquid metal transits to the liquid phase with morphological adaptability. [112]Liquid metals hold high electroconductivity compared with electrical flexible materials. [113]The material's conductivity is affected by adjusting the ratio of liquid metals based on the task's requirements.By mixing other materials into liquid metals, conductive materials with other properties can be obtained.For example, magnetic-responsive liquid metals are obtained by mixing metal particles (e.g., Fe, Ni); [114] enhanced electroconductivity and thermal conductivity are presented by adjusting the doping ratio of Cu. [115] One of the critical factors in controlling liquid metal-based machines is the driving force of the miniature soft devices.Various driven mechanisms have been proposed, including selfpropulsion (e.g., bubble propulsion, [116][117][118][119] self-electrophoretic propulsion, [120][121][122][123][124][125] enzyme-powered robots [126,127] ), Marangoni effect-based locomotion, [128][129][130] and external fields-driven navigation (e.g., magnetic field, [131][132][133][134] electric field, [135][136][137][138][139][140][141][142] ultrasound, [143,144] light [145][146][147] ).Magnetically driven liquid metal-based robots are usually driven by permanent magnets or electromagnets. [148]We categorize the magnetic actuation strategy as direct and indirect actuation, depending on whether the liquid metalbased robots are directly actuated by the external field.Direct actuation requires the robot to be magnetic, and the indirect involves a magnetic-responsive environment. [149]

Magnetic Mechanism and Motion Control
Wang et al. fabricate magnetic liquid metal droplets by mixing carbonyl iron particles into Galinstan. [150]Compared to magnetite particles, the carbonyl iron microparticles are easier wrapped and wetted by the liquid metal.The mixing of magnetic particles affects the conductivity of liquid metals; therefore, the mixing ratio should be tested.Interestingly, the particle-liquid metal composite behaves in a liquid-like state at low mass ratios (e.g., particle-liquid metal ratio = 1:8 or 2:8) and can be extruded from a syringe (Figure 7A).It becomes solid-like and deforms plastically under an external force with a higher ratio, and the particle aggregation leads to a rough surface.Driven by a permanent magnet, the liquid metal-based robot exhibits controlled motion, and splitting occurs if the robot's diameter breaks the critical wavelength of the Rosensweig pattern, as we discussed in Figure 4A.Assembling a hollow internal framework into a liquid metal droplet provides magnetism for further magnetic actuation, which also allows cargo carrying and transportation toward on-demand releasing (Figure 7B). [151]Disassembly of the framework is able to be magnetically conducted, adding more operation possibilities.Liu et al. exploit the gallium oxide layer on the surface of the liquid metal to preserve the magnetic beads inside. [152]This approach enables liquid metal droplet manipulation on solid substrates and in fluidic environments (Figure 7C).
The magnetic features of liquid metals enable motion control for patterning and microrobotic applications.By programming the on-off state of the electromagnet array, pattering and dynamic collective motion control of Galinstan droplets are carried out (Figure 7D).The interplay between surface tension and magnetic forces governs the droplet behavior. [153]Taking advantage of the programmable control strategy and conductivity of liquid metal, manipulation of copper wire for connecting and disconnecting electronic circuits can be achieved.The magneticcontrolled locomotion is converted for wheel movement. [154]he wheel rolls forward under the actuation of a permanent magnet (Figure 7E).Liquid metal-based wheel actuation can also be performed by electrical actuation. [155]

Magnetic Deformation and Transformation Control
Magnetic liquid robot is fabricated by mixing Fe nanoparticles and Galinstan for droplet manipulation. [156]The robot's shape is affected by surface tension, gravity, and the external field.The adhere surface area between the substrate and the robot increases by increasing the field strength, which enhances the droplet transport capacity (Figure 8A).By increasing the field strength from 55 to 145 mT, the maximum droplet volume that can be held on the inclined surface changes from 55 to 150 μL.Besides the field-induced active deformation, the passive deformation of the soft body enables droplet manipulation in narrow spaces.By splitting the metal body, cooperative manipulation of multiple water droplets is performed.The surface oxide over the liquid metal-based robot provides stretchability and the mechanic strength for 3D stretch in the free space. [134]The soft body can be magnetically guided to cross the air-liquid interface and perform reconfigurable shape deformation for connecting the circuits in 2D and 3D (Figure 8B-i).The oxide skin of Ga-based liquid metal has been exploited for reshaping. [150]The liquid metal elongates when controlled by a magnet, and its deformation maintains due to the oxide layer-yield stress.The shape is fixed using phase transition of Ga by adjusting the temperature (Figure 8B-ii).The melting temperature can be adjusted by alloying with In, Sn, and Cu. [157]Morphological transformation of a liquid-bodied robot is achieved by applying a high-frequency alternating magnetic field (20 kHz, 2 kW). [133]The metal absorbs and converts the magnetic energy to local heat, which breaks the oxide skin of the body and results in morphological transformation from a rod into a droplet (Figure 8C).Wang et al. proposed a ferromagnetic NdFeB-mixed liquid metal robot that can exhibit reversible transitions between solid and liquid phase. [112]They also utilize a high-frequency alternating magnetic field to heat the metal-based machine for the phase transition.Taking advantage of the high mechanical strength (solid phase) and the soft body (liquid phase), the shape-reconfigurable machine behaves as magnetic A) The liquid metal robot is fabricated by mixing and grinding carbonyl iron particles and Galinstan.Reproduced under the terms of the CC BY 4.0 license. [150]Copyright 2022, The Authors, published by Wiley.B) The robot is fabricated by assembling a magnetic internal framework into a liquid droplet.Adapted with permission. [151]2020, Elsevier.C) The liquid metal robot is controlled by two magnetic beads.Reproduced with permission. [152]Copyright 2018, Royal Society of Chemistry.D) Patterning of liquid metal droplets under the guidance of an electromagnet array.Reproduced with permission. [153]Copyright 2020, American Chemistry Society.E) Magnetically driven liquid metal robots for driving a wheel.Adapted with permission. [154]Copyright 2021, Elsevier.A) The liquid metal robot manipulates droplets in narrow space and splits for cooperative manipulation under magnetic guidance.Adapted with permission. [156]Copyright 2022, American Chemistry Society.B) (i) Magnetic liquid metal with 3D deformation control as a scalable conductor.Adapted with permission. [134]Copyright 2019, American Chemistry Society.(ii) Leechinspired deformation control of magnetic liquid metal for electricity connection.Adapted under the terms of the CC BY 4.0 license. [150]Copyright 2022, The Authors, published by Wiley.C) Magnetic navigation and morphological transformation under an elliptically polarized magnetic field and a 20 kHz alternating magnetic field, respectively.Reproduced with permission. [133]Copyright 2019, Wiley.D) Liquid-solid phase transition control of a liquid metalbased machine for robotic applications.Reproduced with permission. [112]Copyright 2023, Cell Press.solder and universal screws for robotic manipulation and object delivery (Figure 8D).

Liquid Marble-Based Machines
Liquid marbles are mainly composed of liquid droplets and lyophobic particles (ranging from nanometers to millimeters) that can encapsulate and stabilize the droplet at the liquid-air interface.[163][164][165][166][167] Besides the liquid body-enabled features, liquid marble can be actuated by external fields depending on the components of liquid and particles and the environments.

Magnetic Actuation and Control Methods
One typical method to form a magnetically controllable liquid marble-based machine is attaching hydrophobic magnetic particles to the droplets.][170] This method allows wireless magnetic actuation in a relatively straightforward manner with a longrange operation capability.However, a large force on the liquid marble may remove the particles from the liquid-air interface during the actuation process.Due to the low mass ratio of magnetic particles, the relatively long response time of liquid marbles may bring challenges to following dynamic magnetic fields (e.g., rotating and oscillating magnetic fields) and maintaining deformation.Wang et al. design a system for liquid marble formation and manipulation based on the centrifugal force and gravity. [171]The droplet formation is conducted by dropping liquid in the center of a spiral channel followed by turning on the shaker, and a liquid marble is formed on the bed of SiO 2 .The centrifugal force-driven circular motion ensures a uniform particle attachment on the droplet.By adding magnetic particles to the powder bed, magnetic liquid marble-based machines can be formed in a batch, providing a process for mass production.
The sliding motion of a floating magnetic marble (radius: r) is affected by the volume concentration of magnetic particles (V mag ) and the velocity and flux density (B) of the driving magnetic source. [172]Considering the surrounding environment is diamagnetic, the driving force (F m ) by a permanent magnet is expressed as where χ is the marble's magnetic susceptibility.Therefore, we have F m ∝ VB ⋅ dB= dx.The friction force (F f ) is calculated by adding a dimensionless correction factor β to the Stokes friction [173] as where μ is the dynamic viscosity and v is the moving velocity.
The drag force for a liquid marble inside a medium becomes According to the force balance, the demanding motion velocity can be estimated by applying a magnetic field gradient.
Compared with ferrofluid-based and liquid metal-based machines, magnetic marble machine has a unique magnetic opening feature.The Fe 3 O 4 nanoparticles on the marble are pulled down toward a magnet and expose the liquid medium on the top. [174,175]The nanoparticles recover after removing the magnet due to the minimization of surface free energy (Figure 9A).The reversible opening and closing features enable merging and medium replacement.By partially opening the particle shell, electrochemical detection of the medium is able to be conducted, providing convenience for "online" detection. [176]Besides, a fully opened marble benefits the detection of liquid optical absorbance.

Applications of Liquid Marble-Based Machines
The spherical liquid body has been applied for 3D culture of stem cell spheroids. [171]The hydrophobic silica particle-wrapped body ensures the medium is separated from the contamination of the outer environment and permits gas exchange.Compared with nonadhesive plate-based culturing protocols, the splitting and coalescence capabilities enable medium manipulation: remove the spent medium via splitting and replenish fresh medium via coalescence (Figure 9B).Under a rotating magnetic field, the stationary rotation-induced centrifugal force by a liquid marble is applied as a microcentrifuge and localized viscosity sensor. [177]During rotation, the liquid body is stabilized by the hydrophobic Fe 3 O 4 nanoparticles.The induced centrifugal force on the AgNC nanocubes is large enough to overcome the fluidic drag and ensures mass transportation toward the marble interface (Figure 9C-i).The stationary rotation is applied to measure the viscosity.The rotating liquid marble floats on the aqueous solution and shows viscosity-dependent rotating behavior, i.e., it has a lower step-out frequency with a larger fluid viscosity due to the increased resistance of the fluid.Thus, this phase shift and maximum rotation speed are connected to the fluid viscosity (Figure 9C-ii).
Liquid metal marbles are droplets of liquid metal encapsulated by micro/nanoparticles.They show unique features due to the liquid-like body and the conductivity of metals and usually have high surface tension and density.Galinstan liquid metal can be coated with insulators (e.g., Teflon and Fe 3 O 4 ) and semiconductors (e.g., WO 3 , TiO 2 , MoO 3 , In 2 O 3 , carbon nanotubes). [178]he metal marble shows metal-semiconductor-metal junction behavior as a moveable soft electronic device, and the MoO 3 ,coated marble demonstrates enhanced sensing capability of heavy metals.When applying liquid marbles in fluidic environments, such as microfluidic channels, one of the challenges is maintaining the nonwetting properties.Jeon et al. coat liquid metal droplets with Fe particles and then treat them with HCI to generate bonding between Fe and the metal body, forming a stable liquid metal marble that can be magnetically controlled in microfluidic channels with widths of 0.5-2 mm [179] (Figure 9D-i).Thanks to its soft body, the marble acts like a navigable slug in cross-linked channels.The electrical conductivity and the mobility enable the sequential turning on of LEDs (Figure 9D-ii).Under the control of a magnet, the ferronickel Reproduced with permission. [174]Copyright 2010, Wiley.B) Culturing of stem cell spheroids in a liquid marble.Reproduced under the terms of the CC BY 4.0 license. [171]Copyright 2019, The Authors, published by Wiley.C) Stationary rotating liquid marble as a microcentrifuge and viscosity sensor.Adapted with permission. [177]Copyright 2016, American Chemistry Society.D) Magnetically controlled liquid metal marble for active blocking in microfluidic channel and sequential connecting LEDs.Adapted with permission. [179]Copyright 2017, Royal Society of Chemistry.and polyethylene particles mixture-coated liquid metal marble acts as a controllable obstacle-cleaning motor, demonstrating robotic locomotion and manipulation capabilities. [131]

Magnetic Droplets as Miniature Machines
A straightforward method to magnetically manipulate a droplet as a miniature machine is mixing or bonding magnetic particles inside the droplet.Wang et al. propose two magnetic water droplet-in-oil systems based on dynamic self-assembly.Unlike ferrofluids that have homogeneous properties, the magnetic droplets are formed beneath the air-liquid interface by adding ferromagnetic microparticle-water suspension into benzyl ether. [180]Without magnetic field, the microparticles sink to the bottom of droplets and form particle chains under a precessing magnetic field.The magnetic interactions between droplets with a separation distance r can be adjusted by modulating the precession angle (θ) as where m d is the induced magnetic dipole moment of a droplet.Therefore, the F m becomes repulsive (0 ∘ < θ< 54.7 ∘ ) or attractive (54.7 ∘ < θ< 90 ∘ ).The separation distance r is also affected by the capillary attraction at the interface and the hydrodynamic repulsion due to the fluid inertia.Under a precessing magnetic field, ordered patterns of droplets with different numbers are formed, and they are able to be automatically navigated along a preplanned path.Combined with the pattern expansion/shrinkage capability, microrobotic manipulation of cargo is performed.The second system involves a magnetic iron needle. [181]The needleinduced field gradient attracts droplets under a precessing field, accelerating the dynamic self-assembly process.Integrating with optimization algorithm and feedback control, the dynamic pattern can trap, encage, transport, and release cargo in a multiple-obstacle environment, working as an untethered end-effector for micromanipulation.Recently proposed paramagnetic-to-ferromagnetic transformable ferrofluid droplets also demonstrate dynamic patterns under a rotating bar magnet. [182]Besides using microparticles, two steel beads are embedded into a droplet to acquire magnetism. [183]By adjusting the ratio of beads' center-to-center distance (D) to the diameter (d), transportation and splitting of the droplet are conducted because of the resisting forces from the front and rear ends of the droplets.Si et al. use a superhydrophilic iron bead-embedded droplet as a remote manipulator to achieve microrobotic manipulation tasks, including object delivery, cargo release, and cleaning. [184]The adhesion between the bead and liquid acts as a motor for magnetically driving the droplet and as the braking force to stop the moving droplets.
A surface energy trap-based droplet manipulation strategy is proposed. [185]The trap is an area of high surface energy on a substrate coated with a low surface energy film.A magnetic particle drags a nonmagnetic droplet on the low-energy regions, and it can be extracted from the droplet when contacting the energy traps.The entire droplet is immobilized by pinning down the contact line.The combination of magnetic particles with energy traps enables droplet transport, fusion, particle extraction, and dispensing.While significant research has demonstrated the methods in acquiring magnetism, Guo et al. have approached this from a different angle. [186]The magnetic particle is put inside a channel with a superhydrophobic surface and interacts with a droplet through capillary interaction.By moving the particle using a relatively weak magnetic field, the nonmagnetic droplet is actuated by the capillary bridge.This method works on inclined surfaces where the droplet can self-lock without shedding off, enabling 3D and multiple droplet manipulation.In addition, droplets can be magnetically manipulated in an indirect manner.The magnetically controlled asymmetric deformation of a soft tubular microactuator exerts a capillary force on a droplet with a driving speed up to 10 cm s À1 . [187]ble 1 Magnetically actuated arrays and functional substrates have been proposed for driving droplets in microrobotic manipulation tasks Table 1 summaries the recent progress on magnetic dropletbased miniature machines.[188][189][190][191][192][193][194][195]

Conclusion and Perspective
We have discussed the recent progress on reconfigurable liquid-bodied miniature machines that can perform microrobotic applications under magnetic control, including ferrofluid-based, liquid metal-based, and liquid marble-based machines ranging from millimeter to micrometer scales.The ferrohydrodynamic equations of ferrofluid under static and dynamic external fields are first discussed, which provides the fundamental understanding for magnetic control of ferrofluid droplets and ferrofluidbased machines.Starting from their magnetically responsive features, we first discuss the motion and deformation behaviors, followed by the morphology control, splitting/coalescence control, and state transition control.Some of the representative applications are summarized and compared to demonstrate the connection between magnetic control and practical applications in microfluidics, micromanipulation, and biomedical areas.Moreover, the self-assembly and collective behaviors of ferrofluid droplets are highlighted, and the underlying mechanisms and their applications in the microrobotics area are summarized.
As for liquid metal-based and liquid marble-based machines, we first focus on the approaches to acquire magnetism, i.e., the magnetic mechanism and actuation strategies.Their unique behaviors, such as the high conductivity of liquid metal-based machines and the magnetic opening/close behavior of liquid marble-based machines, are highlighted with the applications in electric area and chemical reactions, respectively.The growing research indicates that liquid-bodied miniature machines with wireless control capability have drawn increasing attention in the scientific community.Despite these accomplishments, key challenges remain and need to be tackled for building microrobotic systems for practical applications (Figure 10).
The first issue exists in the actuation strategy.Taking magnetic control as an example, many recent works rely on using permanent magnets to achieve the actuation and application requirements.[198][199] This also brings issues to the feedback control system because the applied field parameters are complex to be real-time recorded.Besides, generating complex dynamic fields is difficult using permanent magnets or magnet arrays.There is space for improving the control strategy, which may facilitate the 3D actuation that we consider the second issue.The 3D motion, deformation, and assembly control of these machines can maximize the advantages of the liquid-like body for application, including on-demand circuit connecting, blocking, and cargo transportation in complex environments.Modulating a magnetic field in 3D space and modeling the liquid body response under a dynamic field are the key challenges to achieve the 3D, precise state and motion control.Degree of freedom is one of the important indicators in robotic control.For these miniature machines with liquid-bodied behaviors, the capabilities of deformation, morphology adjustment, on-demand body splitting/coalescence, and state transition should be taken into account.Therefore, the control accuracy should be evaluated from more aspects, including accuracy of deformation rate, the response time of morphology change, and phase transition with different environmental conditions.
The fundamental research in liquid-bodied machines is insufficient.[202] To navigate or deliver these small-scale machines for complicated tasks in the vascular system or vascular-like scenarios, the machineenvironment interaction must be modeled first, which is essential for designing microrobotic systems.Furthermore, machine-machine interactions need investigation before designing collective machine-assisted manipulation systems.Estimation of the collective pattern formation, navigation, and even transformation relies on modeling the interactions, which also provides foundation for active pattern control in complex environments. [203]By evaluating the environment, manipulation tasks, and machine property, adaptive control with passive or active strategy can be determined to improve the operation efficiency.Additionally, the in vivo biosafety should be evaluated before applying these liquid-bodied machines in bioenvironments. [204]A toxicological study of both the medium and the particles is a must.Efforts should be focused more on cellular uptake and long-term monitoring by targeted labeling and imaging, which also evaluates the targeting ability of the applied particles.
The future liquid-bodied machine-based systems could involve different levels of autonomy, including precise path following, automated navigation, reconfigurable collective control, and batch manipulation.The ultrasoft liquid-like body may challenge the deformation control, but the unique features also enable adaptive control with high robustness.Hybrid control strategy, such as the magnetic-electric-hybrid control of liquid metal microrobots, combines the advantages of single-field control.The hybrid control approaches may tackle issues that traditional control methods find hard to conduct, such as manipulation in 3D.High energy density benefits manipulation capability and increases operation efficiency, which is important for designing a high-performance miniature machine.Hybrid control strategy may increase the energy density and change the energy density distribution of the machines, broadening the application range of liquid-bodied machine-based system.To date, most of the work relies on direct state feedback by camera or light microscope.Various imaging modalities, especially magnetic-compatible approaches, can be integrated with the manipulation system to provide both position and state feedback of the machines, which is essential for manipulation in opaque regions and in vivo conditions. [205,206]With more efforts devoted to investigating liquid-bodied machines, control systems, and feedback systems, research opportunities exist in system integration toward intelligent, adaptive, autonomous manipulation across scales.

Figure 1 .
Figure 1.Schematic illustration of untethered liquid-bodied miniature machines with magnetic controllability for microrobotic applications.

Figure 3 .
Figure 3. Morphology and motion control of ferrofluid-based miniature machines based on patterned magnetic substrates.A) Controlling reconfigurable ferrofluid microrobots for microrobotic applications.Adapted with permission under the CC BY-NC-ND 4.0 license.[72]Copyright 2020, The Authors, published by PNAS.B) Controlling a ferrofluid droplet as a carrier for flexible devices.Adapted under the terms of the CC BY 4.0 license.[73]Copyright 2019, The Authors, published by Wiley.C) Patterning magnetofluid-based robots for object manipulation in a complex maze.Adapted with permission.[74]Copyright 2021, AIP Publishing.D) Controlling ferrofluid droplets for automated microfluidic logistics.Adapted with permission.[75]Copyright 2020, AAAS.

Figure 7 .
Figure 7. Acquiring magnetism for motion control of liquid metal-based machines.A)The liquid metal robot is fabricated by mixing and grinding carbonyl iron particles and Galinstan.Reproduced under the terms of the CC BY 4.0 license.[150]Copyright 2022, The Authors, published by Wiley.B) The robot is fabricated by assembling a magnetic internal framework into a liquid droplet.Adapted with permission.[151]2020, Elsevier.C) The liquid metal robot is controlled by two magnetic beads.Reproduced with permission.[152]Copyright 2018, Royal Society of Chemistry.D) Patterning of liquid metal droplets under the guidance of an electromagnet array.Reproduced with permission.[153]Copyright 2020, American Chemistry Society.E) Magnetically driven liquid metal robots for driving a wheel.Adapted with permission.[154]Copyright 2021, Elsevier.

Figure 8 .
Figure 8. Deformation and transformation control of liquid metal-based machines.A)The liquid metal robot manipulates droplets in narrow space and splits for cooperative manipulation under magnetic guidance.Adapted with permission.[156]Copyright 2022, American Chemistry Society.B) (i) Magnetic liquid metal with 3D deformation control as a scalable conductor.Adapted with permission.[134]Copyright 2019, American Chemistry Society.(ii) Leechinspired deformation control of magnetic liquid metal for electricity connection.Adapted under the terms of the CC BY 4.0 license.[150]Copyright 2022, The Authors, published by Wiley.C) Magnetic navigation and morphological transformation under an elliptically polarized magnetic field and a 20 kHz alternating magnetic field, respectively.Reproduced with permission.[133]Copyright 2019, Wiley.D) Liquid-solid phase transition control of a liquid metalbased machine for robotic applications.Reproduced with permission.[112]Copyright 2023, Cell Press.

Figure 9 .
Figure 9. Magnetic control and applications of liquid marble-based machines.A) Magnetic opening of a liquid marble above a permanent magnet.Reproduced with permission.[174]Copyright 2010, Wiley.B) Culturing of stem cell spheroids in a liquid marble.Reproduced under the terms of the CC BY 4.0 license.[171]Copyright 2019, The Authors, published by Wiley.C) Stationary rotating liquid marble as a microcentrifuge and viscosity sensor.Adapted with permission.[177]Copyright 2016, American Chemistry Society.D) Magnetically controlled liquid metal marble for active blocking in microfluidic channel and sequential connecting LEDs.Adapted with permission.[179]Copyright 2017, Royal Society of Chemistry.

Figure 10 .
Figure 10.Key factors for designing liquid-bodied miniature machine-based microrobotic systems for practical applications.

.
Magnetic droplet-based miniature machines based on the magnetism, actuation methods, environment, and functionality.