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Nat Commun
Nat Commun
Nature Communications
2041-1723
Nature Publishing Group UK London

39237505
51648
10.1038/s41467-024-51648-4
Article
Transformable 3D curved high-density liquid metal coils – an integrated unit for general soft actuation, sensing and communication
http://orcid.org/0000-0001-5045-4383
Li Nan 12
Zhou Yingxin 12
Li Yuqing 12
Li Chunwei 12
http://orcid.org/0000-0003-1137-473X
Xiang Wentao 12
Chen Xueqing 12
Zhang Pan 3
Zhang Qi 12
Su Jun 12
Jin Bohao 12
Song Huize 12
Cheng Cai 12
Guo Minghui 1
http://orcid.org/0000-0001-6674-1205
Wang Lei leiwangns@bjfu.edu.cn

4
http://orcid.org/0000-0002-0844-5296
Liu Jing jliu@mail.ipc.ac.cn

123
1 grid.9227.e 0000000119573309 State Key Laboratory of Cryogenic Science and Technology, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing, China
2 https://ror.org/05qbk4x57 grid.410726.6 0000 0004 1797 8419 School of Future Technology, University of Chinese Academy of Sciences, Beijing, China
3 https://ror.org/03cve4549 grid.12527.33 0000 0001 0662 3178 Department of Biomedical Engineering, School of Medicine, Tsinghua University, Beijing, China
4 https://ror.org/04xv2pc41 grid.66741.32 0000 0001 1456 856X Beijing Key Laboratory of Lignocellulosic Chemistry, Beijing Forestry University, Beijing, China
5 9 2024
5 9 2024
2024
15 76799 4 2024
15 8 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
Rigid solenoid coils have long been indispensable in modern intelligent devices. However, their sparse structure and challenging preparation of flexible coils for soft robots impose limitations. Here, a transformable 3D curved high-density liquid metal coil (HD-LMC) is introduced that surpasses the structural density level of enameled wire. The fabrication technique employed for high-density channels in elastomers is universally applicable. Such HD-LMCs demonstrated excellent performance in pressure, temperature, non-contact distance sensors, and near-field communication. Soft electromagnetic actuators thus achieved significantly improved the electromagnetic force and power density. Moreover, precise control of swinging tail motion enables a bionic pufferfish to swim. Finally, HD-LMC is further utilized to successfully implement a soft rotary robot with integrated sensing and actuation capabilities. This groundbreaking research provides a theoretical and experimental basis for expanding the applications of liquid metal-based multi-dimensional complex flexible electronics and is expected to be widely used in liquid metal-integrated robotic systems.

Developing flexible coils for soft robotic applications is challenging due to their sparse structure. Here, the authors present a design of transformable 3D curved high-density liquid metal coils, surpassing the structural density level of enameled wire for soft actuation, sensing, and communication.

Subject terms

Electronic devices
Actuators
Sensors and biosensors
https://doi.org/10.13039/501100001809 National Natural Science Foundation of China (National Science Foundation of China) 91748206 Liu Jing issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

The past few decades have witnessed the remarkable potential of soft robots in diverse application scenarios, owing to their exceptional safety features and adaptability to environmental conditions1–4. Systems resembling living organisms, capable of environmental sensing, self-awareness, and controlled motion, have long been a sought-after goal5–7. In general, advanced soft robots require high precision, a large working range, multi-physics sensing capabilities8–11, high response speeds, large power densities, and strong driving force actuation capabilities12–14. Moreover, it is challenging to find a single unit that can integrate both sensing and actuation functions; typically, multiple units need to work in tandem for such capabilities. For instance, flexible pressure and temperature sensors usually lack motion capabilities15–17, while soft actuators like dielectric elastomers, pneumatic or hydraulic muscles do not typically incorporate sensing functions18–23. This inevitably leads to an excessively bulky robot. Fortunately, among the various types of sensors and actuators, soft actuators utilizing electromagnetic force-driven mechanisms hold greater potential for integration.

This soft actuator comprises a soft coil that generates a force in the presence of an external magnetic field, thus triggering the motion of the robot. Thanks to the recent advancements in liquid metal technology, this electromagnetic actuator can seamlessly transition from copper coils to liquid metal coils24–28. The high-power electromagnetic actuator exhibits not only exceptional flexibility but also possesses a splendid sensing capability. For instance, the application of pressure induces a change in its resistance, thereby facilitating the detection of external forces29,30. Compared to actuators such as dielectric elastomers, ionic electroactive actuators, hydraulic muscles, and liquid crystal elastomers, robots equipped with soft electromagnetic actuators typically exhibit a better combination of response speed, motion displacement, and force output capabilities12,14. Consequently, they can be effectively employed for the development of soft grippers, land-running robots, and water-swimming robots26–28. Furthermore, precise motion control can be accomplished by adjusting the input electrical signal, enabling programmed operation25. The lower operating voltage of the actuator facilitates seamless integration with smaller batteries26. However, unlike rigid coils wound with copper wire, the fabrication of liquid metal soft coils poses significant challenges. The similar formation of liquid metal wires is unattainable due to the material’s fluidity and high surface tension. Instead, it can be infused into soft silicone tubes featuring a helical structure to generate coils31. The liquid state of soft silicone materials such as polydimethylsiloxane (PDMS), Ecoflex, and human silicone prior to curing poses challenges in the formation of channels. Consequently, most current research on liquid metal coils focuses on single-layer two-dimensional planar coils. However, these coils not only face difficulties in achieving curved surfaces but also exhibit a significant width for the insulating layer between the channels, which significantly impacts the utilization of soft electromagnetic elastomers in soft robots.

In recent years, the development of soft robotics has necessitated the integration of multifunctional components capable of performing sensing, communication, and actuation. The 3D curved high-density liquid metal coil (HD-LMC) introduced in this study offers a solution to these requirements through its unique structural and material properties. Additionally, we present a universal method for creating intricate channels within flexible silicone to produce high-density, three-dimensional multilayer, curved liquid metal flexible coils without the risk of short-circuiting. The 3D curved HD-LMC, constructed using liquid metal (EGaIn) and an elastic PDMS substrate, ensures exceptional flexibility. The minimum insulation thickness of 0.1 mm can be achieved for three wire diameters (D = 0.68, 1.2, 1.7 mm), resulting in wire diameter to corresponding insulation ratios (defined as parameter k) of 7, 12, and 17 respectively. These densities are consistent with those of enameled wires (approximately 10) and surpass the densities previously reported for liquid metal coils (highest being 1.25) or wires (highest being 5.75). A range of environmental sensing capabilities with HD-LCM unit, i.e., encompassing pressure, temperature, distance sensing and signal interaction are implemented. Moreover, we have successfully showcased a puffer fish robot capable of swimming in water and a wheel-shaped robot that can traverse land. Interestingly, even robots composed solely of HD-LMC units can achieve sensing and motion capabilities, showcasing an impressive level of integration between sensing and actuation.

Results

3D curved high-density liquid metal soft coil

Figure 1a illustrates the design concept of an integrated unit of 3D curved HD-LMCs. This unit features a stacked structure consisting of three layers of curved HD-LMCs, all enveloped by PDMS for insulation and isolation to achieve a highly resilient performance. The coil channels are filled with liquid metal (EGaIn) for the conductive core. The design of coils with three distinct wire diameters (D = 0.68, 1.2, and 1.7 mm be tagged as HD-LMC0.68, LMC1.2, and LMC1.7, respectively) was accomplished within a confined volume (20 mm in length and a sector with a 60° radius of r = 11 mm in cross-section), as shown in Supplementary Fig. 1. All of these HD-LMCs have achieved the maximum density of triple stacking.Fig. 1 Basic characteristics of the transformable 3D Curved High-Density Liquid Metal Coils (HD-LMC) integrated unit.

a. Structural design and composition of HD-LMC. The EGaIn is encapsulated with PDMS, resulting in an overall softness. The Ball represents the magnetic field generated by its energization. b. HD-LMC real cross-section. There are three configurations for wire diameter D = 0.68, 1.2, and 1.7 mm. c. SEM images of two neighboring liquid metal channels in three structures. The thickness of the insulation layer between the channels reaches 0.1 mm for all three wire diameters. d. Optical image showing the mechanical flexibility of the HD-LMC being stretched, compressed, twisted, and bent. e. Factors influencing the performance of coils. The findings indicate a positive correlation between Ball and both D and k. The significance of this change is more pronounced when k is small. When the insulation thickness δ = 0.1 mm, an increase in D leads to a corresponding increase in Ball. f. The present work demonstrates higher values of D and k compared to the reported research, surpassing even the structural density of enameled wires. Source data are provided as a Source Data file.

Additionally, the real cross sections of three HD-LMCs with different conductive path diameters are shown in Fig. 1b. The Scanning Electron Microscope (SEM) images and Energy Dispersive Spectrometer (EDS) based element mapping provide a clear visual representation of the PDMS elastomer and liquid metal channels, demonstrating its universality in fabricating HD-LMC with a consistent minimum insulation layer thickness of 0.1 mm, irrespective of the channel diameter (Fig. 1c and Supplementary Fig. 2). Additionally, Fig. 1d showcases the exceptional mechanical compliance of the transformable soft HD-LMC, which allows for stretching, compression, twisting, and bending without incurring any damage.

It is widely acknowledged that coils exhibiting superior performance should have a greater number of turns within a constant volume, and finer wire diameters are commonly employed to achieve this objective. However, contrary to conventional belief, as elucidated in Supplementary Note 1, employing a finer wire diameter for a given volume and heating power leads to increased resistance (Supplementary Eq. 5) and decreased excitation current (Supplementary Eq. 9). This clearly presents a highly disadvantageous impact on it.

The performance of the electromagnetic elastomer is significantly influenced by both the insulation thickness δ and the coil channel diameter D. Therefore, a structural evaluation parameter k = D/δ is defined to more effectively reflect the coil density. The magnetic field B excited by the solenoid coil increases with a larger value of k, as depicted in Fig. 1e and Supplementary Eq. 15. Additionally, when the thickness of the insulation layer δ (the intersection of the black arrow with the curve in the figure indicates the case of δ = 0.1 mm) or the value of k remains constant, there is a positive correlation effect between the diameter D and the magnetic field B. Therefore, when selecting a solenoid coil with a constant volume and a large k, it is advisable to opt for the largest possible diameter within the limits of the required inductance value (L) and maximum current (Isupply) that can be supplied (refer to Supplementary Note 1, Supplementary Fig. 3 and Supplementary Fig. 4 for more details).

The flexible coil compositions with large cross-sections of conductive pathways can be broadly classified into two types. One type involves the fabrication of flexible wires that are subsequently wound to form coils27,32. The k of the coils formed by this method is dependent on the wire insulation. Furthermore, elastic wires are generally incapable of achieving coil fabrication with significant curvature. This limitation can lead to the collapse of the runners, causing a sudden spike in resistance or even circuit breakage (Supplementary Fig. 5). The second approach involves the construction of the coil channel within the elastomer, followed by filling it with liquid metal to create the coil24,25,28. This methodology is also employed here. A comparison was made with previously reported work in Fig. 1f using k-D plots that incorporated coils24–26,28,33–36, flexible wires27,32,37–45, and enameled wires (refer to Supplementary Table 1 for further details). The HD-LMC in this study exhibits higher D and k values, surpassing even the structural density of enameled wires (refer to Supplementary Fig. 6).

The utilization of water-soluble materials, such as poly vinyl acetate (PVA), poly acrylic acid (PAA), poly acryla mide (PAM), and poly ethylene oxide (PEO)46, along with high-temperature sacrificial materials like paraffin wax and low-melting-point metals47, is deemed more appropriate for the fabrication of intricate internal cavities. The cavities required in this work, however, are more intricate. They encompass not only curved surfaces but also multilayer structures. Furthermore, the diameter of the channels is small and the spacing between them is a mere 0.1 mm. These factors pose challenges for various sacrificial materials to effectively fulfill their task. For instance, paraffin wax is prone to breakage. And utilizing PVA materials for 3D printing lacks the required precision, often leading to PVA flocculation issues (Supplementary Fig. 7). A solution to this problem can still be found in the low melting point metal Bi32In51Sn17, which has a melting point of approximately 60.5 °C and exhibits high toughness and stiffness in its solid state (Supplementary Fig. 8 and Supplementary Table 2).

The liquid alloy of Bi32In51Sn17 was poured into the silicone tube and subsequently peeled off after cooling and solidification to obtain the metal wires utilized for fabricating HD-LMC channels (Supplementary Fig. 9 and Supplementary Table 3). Subsequently, the metal wire was enveloped with a PDMS film obtained through spin-coating and curing, and pressed into a coil using a mold. Next, it was placed in a 3D printing mold to introduce PDMS before undergoing curing. Finally, by rinsing off the Bi32In51Sn17 alloy in a water bath and infusing it with EGaIn, the HD-LMC could be successfully produced (Supplementary Fig. 10). The Supplementary Fig. 11 presents photographs of the physical HD-LMC featuring three distinct runner diameters, both with and without liquid metal infusion. Therefore, this approach enables precise control of the channel diameter through manipulating the BiInSn wire diameter and accurate regulation of the insulating layer thickness via modulation of the PDMS film thickness.

The SEM images of the channel diameter and insulating layer were captured at multiple locations for various samples of the three coils, respectively. It can be inferred that employing the methodology outlined in this study results in a high level of structural uniformity for 3D curved HD-LMC (Supplementary Fig. 12). Additionally, based on the non-uniformity data obtained from SEM analysis, HD-LMC0.68 was employed to generate 100 random structures for 1× non-uniformity and 5× non-uniformity, respectively. By calculating the magnetic field excited at a current of 2 A, it has been determined that there is a maximum error of 0.82% in the 1× non-uniformity and 3.35% in the 5× non-uniformity (Supplementary Fig. 13). Finally, Supplementary Fig. 14 showcases the exceptional reproducibility of the BiInSn coil structures, which is pivotal for ensuring consistent formation of the channel structure in the HD-LMC.

The proposed method in this study has demonstrated its universal applicability for fabricating 3D curved HD-LMCs. It enables the creation of coil structures with any desired number of turns on various surfaces. As shown in Supplementary Fig. 15, two complex supercoils have been successfully fabricated to illustrate this point. Firstly, a multi-layer tapered coil has been successfully fabricated on the surface of a cone using PDMS, while maintaining its central hollow structure. Secondly, it has demonstrated the fabrication of a multi-layer planar coil consisting of approximately 30 turns per layer and achieving a minimum wire spacing of 0.1 mm.

To further demonstrate the universality of our method, we also fabricated HD-LMCs using epoxy resin (hard), human silicone (soft), and Ecoflex 00-30 (soft) as the matrix materials (Supplementary Fig. 16). The process involved the same steps of creating intricate channels and filling them with liquid metal (EGaIn). This confirms that our fabrication technique is versatile and applicable to a wide range of elastomers.

Mechanical-electrical-magnetic-thermal characterization of HD-LMC integrated units

The performance of the transformable HD-LMC as a fundamental integrated unit for flexible actuation and sensors is directly linked to its mechanical, electrical, magnetic, and thermal characteristics. The mechanical properties reflect the softness of the HD-LMC and its susceptibility to mechanical damage. The electrical properties dictate its impact on the circuit when connected. Magnetic characteristics reveal the strengths and limitations of the HD-LMC on performance. Furthermore, thermal characteristics determine the potential for overpowering during operation and the overall stability of the HD-LMC during use.

The conceptual diagram of the HD-LMC undergoing compression testing is illustrated in Fig. 2a. Due to the small modulus and soft behavior (HD-LMC0.68), the compression rate has minimal impact on the test results (Supplementary Fig. 17a). Their successive multiple compressions at a compression rate of 5 mm/min demonstrated favorable agreement (Supplementary Fig. 17b). Moreover, HD-LMC1.7 with a larger wire diameter displays a higher modulus for pressures up to 63 kPa, with a reversal in behavior for pressures exceeding 63 kPa (Supplementary Fig. 17d). The simulation analysis reveals that the stresses are primarily concentrated in the central region during compression (Fig. 2b and Supplementary Fig. 17e). The mesh-independence verification (Supplementary Table 4) and its consistency with the experimental findings (Fig. 2c) ensure the reliability for these results. Furthermore, the HD-LMC can endure an ultimate pressure exceeding 357 kPa and an ultimate compression of 2.4 mm, underscoring its exceptional mechanical reliability. Simultaneously, the performance of the HD-LMC was unaffected when dropped from a height equivalent to 233.28 times its body height, as evidenced by the undamaged internal coil and normal conductivity observed in the test (Fig. 2d).Fig. 2 Mechanical-electrical-magnetic-thermal characterization of 3D Curved High-Density Liquid Metal Coils (HD-LMC) integrated unit.

a. Conceptual diagram of the HD-LMC compression process. b. Stress distribution of HD-LMC at a compression of 2 mm. c. The pressure-compression curve of the HD-LMC0.68 demonstrates excellent agreement between experimental results and theoretical calculations. d. The HD-LMC undamaged after dropping from a height equivalent to 233.28 times its own height. e. Potential distribution of HD-LMC0.68 with 1 A current applied. f. Impedance characteristics, including impedance and impedance angle, exhibited by the three HD-LMCs at different frequencies. g. The inductance values of the three HD-LMCs exhibit good agreement between theoretical and experimental results. h. Resistance values of HD-LMC, theoretical and experimental (measured by the four-wire method) are in good agreement. i. Magnetic field distribution at the center cross-section of HD-LMC0.68 at 2 A. j. The magnetic field strengths excited at the centers of the three HD-LMCs, with a current of 2 A, exhibit exponential decay with distance. k. Transmission of energy by electromagnetic radio. l. A LED board with a driving voltage of 3 V is successfully lit. m. Thermograms of the three HD-LMCs with current incrementing every 5 minutes. n. Temperature evolution curves for the three HD-LMCs upon energizing the current, with gradual current increments every 5 minutes. o. The HD-LMC0.68 was tested for the cyclic stability of its Joule heating performance by alternately switching the current between 0 and 1.5 A. All error bars are the standard deviation of three independent samples. Source data are provided as a Source Data file.

The potential distribution of the HD-LMC0.68 is depicted in Fig. 2e after a current of 1 A has passed through it, which can also be interpreted as the variation of resistance with length (refer to Supplementary Fig. 18 for other HD-LMCs). Figure 2f illustrates that the impedance characteristics of the three distinct HD-LMCs at varying frequencies show low-frequency impedance dominance and high-frequency inductive impedance dominance. The inductance at different frequencies can be determined by fitting the impedance characteristics with a series equivalent model, which demonstrates consistent values for frequencies exceeding 1000 Hz (Supplementary note 2 and Supplementary Fig. 18). Furthermore, the HD-LMC0.68 showcases an inductance value of 1.37 μH, highlighting its elevated coil turn density (Fig. 2g). The measured inductance is consistent with the theoretical calculations, which have also been validated for grid-independence (Supplementary Table 5). The obtained results further elucidate the more pronounced augmentation in impedance and phase angle observed in HD-LMCs with higher inductance at elevated frequencies. While the other two HD-LMCs exhibit lower inductance, they can handle higher currents due to their thicker wire diameters with reduced resistance. The resistance of HD-LMC0.68 is significantly high, reaching 391 mΩ, as depicted in Fig. 2h. In contrast, the resistance of HD-LMC1.7 is merely 22 mΩ.

The magnetic field distribution in Fig. 2i exhibits the highest magnetic field strength at the center of the HD-LMC, while experiencing significant attenuation as distance increases due to the low permeability of air and PDMS (Fig. 2j). Moreover, as depicted in Fig. 2j, the HD-LMC0.68 with more turns generates a stronger magnetic field at the same current (2 A). The current input needs to be increased in order to achieve the same magnitude of magnetic field for HD-LMCs with thicker wire diameters (Supplementary Fig. 19). The theoretical results also passed the network irrelevance analysis (Supplementary Table 6).

As demonstrated in Supplementary Note 1 and Supplementary Fig. 4, for coils with the same channel diameter, the k value results in a greater number of turns (n) within a limited volume, thereby enhancing the magnetic field generated under the same current. This finding is further validated by the model using the 3D curved HD-LMC0.68, which also demonstrates that a higher k value leads to increased inductance due to the higher number of turns (Supplementary Fig. 20). Additionally, under the same conditions, it is also imperative to consider the performance of coil structures ranging from 1-layer to 4-layer. The findings, as illustrated in Supplementary Fig. 21, demonstrate that augmenting the number of layers significantly amplifies the magnetic field generated by the coils and yields higher values of inductance. This enhancement is particularly useful when a single-layer structure has reached its maximum potential, yet further performance improvements are needed.

Additionally, a demonstration of wireless energy transfer utilizing an HD-LMC is employed to explore another magnetic characteristic of the integrated unit. The complete energy transfer device is illustrated in Fig. 2k. More specific circuit components and the wire connections between them are depicted in Supplementary Fig. 22. After the HD-LMC is energized with sinusoidal AC power, the LED board can be easily illuminated through wireless energy transfer (Fig. 2l and Supplementary Movie 1). The maximum induced voltage amplitude in the secondary coil reaches 10.6 V when the HD-LMC’s current is approximately 1 A, with the voltage amplitude at its terminals also approaching 1 V (Supplementary Fig. 23a-c). The mutual inductance coefficient of the HD-LMC0.68 can be determined by measuring the voltages across the primary and secondary coils, which exhibit a nearly linear decay as the distance between the two coils increases. This trend is also reflected in the amplitude of induced voltage (Supplementary Note 3 and Supplementary Fig. 23d-f). Furthermore, the HD-LMC0.68 shows a peak mutual inductance of 17.95 μH, outperforming the HD-LMC1.2 and HD-LMC1.7, which have maximum mutual inductances of 9.78 μH and 6.01 μH, respectively.

Joule heating behavior plays a crucial role in determining the maximum operating power of the HD-LMC. To prevent damage to the coil, the operational temperature should generally be kept below 150 °C (with PDMS being capable of withstanding high temperatures up to 200 °C). The HD-LMC0.68, depicted in Fig. 2m, achieves a temperature of 142.2 °C when subjected to a current of 2 A, whereas the other two variants (1.2 and 1.7 mm HD-LMCs) exhibit higher tolerance for current inputs (4 and 8 A respectively). The temperature evolution of the HD-LMC over time is depicted in Fig. 2n, with the current incrementing every 5 minutes. Supplementary Movie 2 showcases the infrared thermography of three HD-LMCs during both the warming and cooling processes. The HD-LMC0.68 underwent repeated cycles of warming (105 ± 1 s) and cooling (160 ± 1 s) by applying a current of 1.5 A, fluctuating between 40-60 °C.

Utilization of HD-LMC integrated units in a wide range of soft sensing and communication devices

The versatile properties of the HD-LMC make it an ideal candidate for various sensing applications. The capabilities of pressure sensing, temperature sensing, non-contact distance sensing, and near-field communication (NFC) are investigated. The flexibility of the HD-LMC enables it to enhance versatility compared to conventional rigid copper wire coils. Unless otherwise specified, the applications discussed in this section and beyond will primarily focus on HD-LMC0.68 with higher inductance and lower operating currents.

The spatial position of the channel inside the HD-LMC undergoes changes during the pressure application process, which can be accurately reflected in the alteration of the inductance signal. Figure 3a demonstrates its potential application in designing pressure sensors, a task that cannot be achieved with other single-layer flexible coils. The corresponding signal feedback can be obtained as long as the pressure applied to the HD-LMC does not result in physical damage. As shown in Supplementary Table 7, the proposed sensor exhibits a wider sensing range and superior signal linearity response compared to other previously reported pressure sensors17,29,30,39,48–56. The linear signal change over a wide pressure range (35.71-357.14 kPa, equivalent to 5-50 N) is depicted in Fig. 3b (refer to Supplementary Note 4 for detailed information on the rate of change and signal error). Additionally, linearly varying signals can be generated within the medium range of 7.14-71.43 kPa (1-10 N) and the ultra-small range of 0.714-7.14 kPa (0.1-1 N). A resolution as small as 0.357 kPa (0.05 N) is attainable. Moreover, the inductance values align with the theoretical calculations (Supplementary Fig. 24a-d).Fig. 3 The 3D Curved High-Density Liquid Metal Coils (HD-LMC) integrated unit can be used for pressure and temperature sensing, as well as distance sensing and near-field communication.

a. Conceptual design of pressure sensors. b. The value of the inductance change of the HD-LMC is linear over a wide range of applied pressure (35.71-357.14 kPa, corresponding to 5-50 N). c. 100 cycle tests were conducted at higher pressures (214.29 kPa, corresponding to 30 N) and stable inductive signal changes were observed. d. The inductive signal changes during a pressure cycle, with the signal increasing and decreasing relatively quickly. e. Conceptual design of temperature sensors. f. The inductance signal of HD-LMC from room temperature 27 °C to 100 °C also has a strong linear relationship. g. The inductance signal of HD-LMC exhibits a stable step-like shape with relatively consistent changes when the temperature is raised by 5 °C every 30 minutes. h. HD-LMC exhibited good cycling stability when heated and cooled in a water bath for 3 min between room temperature 27 °C and 80 °C. i. HD-LMC is used for non-contact sensing of distance to metal surfaces. j. HD-LMC is used to sense the distance of metal plates with high magnetic permeability. k. HD-LMC is employed to sense the distance of lower permeability metal plates. l. Conceptual diagram of the principle of non-contact eddy current detection. m. HD-LMC is used for Near Field Communication (NFC) for information exchange. n. Return loss S11 for different quality factors Q. o. Impedance characteristics exhibited by NFC with different Q. p. Utilize the HD-LMC integrated unit for a variety of functions such as receiving text messages, sending text messages, creating new contacts, making phone calls, opening emails, obtaining location information, accessing WiFi, and browsing websites. All error bars are the standard deviation of three independent samples. Source data are provided as a Source Data file.

The inductive signal changes remained stable during the testing of the HD-LMC for 100 cycles at pressures of 214.29 kPa and 71.43 kPa at a rate of 20 mm/min (Fig. 3c and Supplementary Fig. 24a-d). The signal rise and fall in Fig. 3d and Supplementary Fig. 24e is observed to be rapid, but constrained by the compression rate. Specifically, compressing the HD-LMC at pressures of 214.29 and 71.43 kPa resulted in displacements of 1.8 and 1.05 mm respectively, corresponding to compression times of 5.4 and 3.15 s respectively. Consequently, the hysteresis during compression was found to be 0.35 and 0.6 s, while during relaxation it was 0.75 and 0.9 s for the respective pressure levels.

The PDMS thermal expansion effect renders the inductance of the flexible HD-LMC highly responsive to ambient temperature, thereby enabling its application as a temperature sensor, as depicted in Fig. 3e. Similarly, as demonstrated in Supplementary Table 8, a comparative analysis with other previously reported temperature sensors reveals that the proposed sensor in this study exhibits an expanded sensing range and superior signal linearity response16,49,57–66. The inductive signal exhibits a good linear variation across a wide temperature range interval of 27-100 °C (Fig. 3f). The ambient temperature is increased by 5 °C per 30 minutes to monitor the inductance signal, resulting in a distinct and consistent step signal change (Fig. 3g). The HD-LMC exhibits excellent stability, as demonstrated in Fig. 3h through repeated temperature cycling tests. Furthermore, it possesses a high sensitivity to ambient temperature changes, capable of detecting variations as small as 0.2 °C (Supplementary Fig. 25).

The HD-LMC integrated unit effortlessly achieves non-contact distance sensing, a type of flexible sensor that is relatively rare, as illustrated in Fig. 3i. A variety of metal sheets were utilized for the experiments, and non-contact distance sensing was successfully achieved in all cases. As depicted in Fig. 3j, there exists a positive correlation between the magnetic permeability of the metal and the signal change. For instance, 1J85 alloy can increase the inductance value of HD-LMC by 17.71%, while iron can increase it by 2.05%. However, compared to these two metals, nickel and cobalt possess much smaller magnetic permeability, resulting in a reversed change in HD-LMC inductance. Notably, other metals with magnetic permeability similar to that of air, such as 304 stainless steel, aluminum, and molybdenum, exhibit a reduction in the inductance value of the HD-LMC (Fig. 3k). However, it is worth noting that different metals can display significant variations in signal changes, thereby enabling the detection of substance conductivity. The sensing ability, as illustrated in Fig. 3l, is attributed to the eddy current effect between the HD-LMC and the metal plate, which is directly influenced by the mutual inductance coefficient M (including the impact of metal magnetic permeability) and the electrical conductivity of the metal plate (refer to Supplementary note 5 for detailed information).

The HD-LMC not only facilitates physical interaction with the environment but also enables the exchange of information. The HD-LMC, shown in Fig. 3m, functions as the central component akin to a brain, enabling non-contact transmission of commands to electromechanical devices and facilitating interaction with the external world. In order to achieve NFC, HD-LMC necessitates impedance matching, as detailed in Supplementary Note 6. The self-resonant frequency of the HD-LMC is located at 52.54 MHz. At the operational frequency f0 = 13.56 MHz, the impedance measures Z = 13.127 + 99.379j Ω, and an inductance value of 1.1664 μH is obtained (Supplementary Fig. 26). As illustrated in Fig. 3n, the matched NFC can achieve a minimum return loss S11 exceeding -50 dB with a broad bandwidth. The impedance at the operating frequency f0 should ideally have a real part of approximately 50 Ω and an imaginary part close to 0 Ω (Fig. 3o). As shown in Fig. 3p, the HD-LMC is capable of a wide array of functions, such as receiving text messages, sending text messages, creating new contacts, making phone calls, opening emails, obtaining location information, accessing WiFi, and browsing websites (Supplementary Movie 3).

Precision-controlled HD-LMC magnetically actuated soft bionic pufferfish

Expanding upon the foundational understanding of the properties and sensing capabilities of HD-LMC, this study further investigates its potential application in soft actuation. The HD-LMC’s capacity to generate electromagnetic force renders it well-suited for the development of soft actuators. Additionally, The HD-LMC electromagnetic actuator features a fast response time and operates at a low drive voltage. It is highly programmable and offers precise control through current regulation. Unlike other soft actuators, this actuator is simpler and has fewer components.

Therefore, we presented a soft bionic pufferfish, fabricated using the HD-LMC electromagnetic actuator as depicted in Fig. 4a. The designed bionic pufferfish effectively achieves tail swing movement through the utilization of a simple lever principle, enabling it to attain the maximum swing angle of 22.8° (Fig. 4b).Fig. 4 Bionic pufferfish with electromagnetic actuator using 3D Curved High-Density Liquid Metal Coils (HD-LMC) integrated unit.

a. Structural design of the flexible bionic pufferfish. b. The internal motion frame can be swung at an angle of 22.8°. c. Conceptual diagram of HD-LMC as an electromagnetic actuator. d. Electromagnetic force of the actuator under different currents. The maximum can be 58.67 mN, and the experimental and theoretical results are in high agreement. e. Under a square wave signal, the bionic pufferfish can execute a tail-swinging motion. f. Square wave drive current at three different frequencies. g. Kinematic behavior of bionic pufferfish in water at three current frequencies. h. Kinematic displacement of bionic pufferfish in water. All error bars are the standard deviation of three independent samples. Source data are provided as a Source Data file.

The motion of the pufferfish is powered by the Lorentz force on the HD-LMC, which is energized by an electric current and influenced by a magnetic field (Fig. 4c). The impact of excitation current and distance on the HD-LMC electromagnetic actuator is illustrated in Fig. 4d. Both the experimental and the theoretical evidences that it can generate the maximum force of approximately 60 mN when operating at a current of 2 A. Indeed, if the HD-LMC had a larger surface area and volume, it would be capable of producing an even greater force. Since the HD-LMC possesses a near-limit k value and a substantial D, the maximum force generated per unit volume reaches 5.0455 × 104 N/m3, and the power density reaches 8279.6 W/m3 (Supplementary Note 7 and Supplementary Table 9). Moreover, the HD-LMC utilized in this study features a fan-shaped cross-section with a considerable amount of ineffective volume near the center of the circle. Consequently, the actual power density exceeds that calculated.

The bionic pufferfish demonstrates continuous tail swinging motion in response to a square wave current signal, as shown in Fig. 4e. Precise control over the tail swinging motion is achieved under an excitation current ranging from 0 to 5 Hz, with the frequency of the motion matching that of the driving current (Supplementary Movie 4). The square wave signal with a frequency range of 0-3 Hz is shown in Fig. 4f. Within this range, the pufferfish can achieve swimming motion in water; however, at frequencies of 4 and 5 Hz, only tail swinging motion can be realized in air. Beyond the frequency of 5 Hz, a perfect swinging motion cannot be achieved. Figure 4g illustrates that higher frequency drive currents enable faster swimming speeds (Supplementary Movies 5-7). We have employed the background difference technique for detecting moving objects, and accurately obtained the displacement time image of the bionic pufferfish in each frame, as depicted in Fig. 4h. The motion velocity was determined using the second-order difference format, as illustrated in Supplementary Fig. 27. For further details regarding the background difference method, please refer to Supplementary note 8.

Programmable control of soft high-speed rotary robot with position sensing and velocity feedback using HD-LMC

The collaborative function of multiple HD-LMC units facilitates the execution of complex programmable motion with real-time feedback. This section employs a high-speed rotating robot as an illustrative example to demonstrate the integration of sensing and actuation functions within a single entity. The HD-LMC soft high-speed rotary robot shown in Fig. 5a can be controlled by employing programmed current along with position sensing and velocity feedback. The perfect wheel shape is formed by utilizing six HD-LMC units, with two coils in each diagonal forming a connected group through wires. This configuration allows for high-speed rotation under the excitation of three-phase alternating current (Supplementary Fig. 28). The mechanism is illustrated in Fig. 5b, where the energization of Coil group A with current results in the generation of torque that drives the robot to rotate until alignment between the excited magnetic field lines and the background magnetic field is achieved.Fig. 5 Precision-controlled high-speed 3D Curved High-Density Liquid Metal Coils (HD-LMC) rotary robot with position recognition and velocity feedback.

a. Schematic of the structure of the HD-LMC integrated high-speed rotary robot. b. HD-LMC actuation principle for high-speed rotating robots. c. The ideal current waveform of a high-speed rotating robot with a 120° phase difference between the three. d. Characterization of the magnetic field distribution of the HD-LMC high-speed rotating robot. e. The HD-LMC high-speed rotary robot performs in-situ high-speed rotation. f. The rotational speed and driving frequency show consistency during in-situ rotation, and the experiments and simulations are in good agreement. g. Theoretically calculated rotating moments at different drive currents. h-k. Kinematic pictures for excitation currents of 2, 3, 4 and 5 Hz, respectively, and their corresponding displacement-time relationships. l. HD-LMC high-speed rotary robot realizes RPM feedback. m. HD-LMC high-speed rotary robot realizes its own position sensing. All error bars are the standard deviation of three independent samples. Source data are provided as a Source Data file.

The HD-LMC designed in this study features a sector angle of 60°, which corresponds to three groups of coils. Therefore, a three-phase drive is employed, and the operating current waveform is depicted in Fig. 5c. It exhibits a sinusoidal waveform with a phase difference of 120° between each pair. The sinusoidal excitation currents captured experimentally, ranging from 0.5 to 5 Hz, are presented in Supplementary Fig. 29.

The spatial distribution of the robot’s magnetic field under the excitation current (2 A) is illustrated in Fig. 5d, wherein the black lines depict its excited flux lines while the red lines represent the flux lines of the background magnetic field. In order to mitigate the issue of wire entanglement during high-speed rotation, high-speed electric slip rings are integrated at the centers of the robotic circles (refer to Supplementary Fig. 30 for detailed information on rotational resistance moments). Figure 5e displays an optical photograph of the HD-LMC high-speed rotary robot rotating in suspension in situ, while Supplementary Movie 8 captures its kinematic behavior at current drive frequencies ranging from 0.5 to 5 Hz.

We developed a kinematic theoretical computational model (Supplementary Note 9) to investigate the underlying mechanism of its in situ rotation behavior, which have also been validated for grid-independence (Supplementary Table 10). The rotational speed of the robot is determined by the frequency of the excitation current, as demonstrated by both the experimental and the theoretical evidence. These two values are found to be essentially equal, which greatly facilitates precise control programming (Fig. 5f). Additionally, as shown in Fig. 5g, the maximum rotational torque of the HD-LMC high-speed rotary robot was theoretically calculated to be 1.3 mN·m under varying current intensities. Moreover, we observed that when the resistive moment is smaller than the maximum dynamic moment (Mr < Md), the robot can achieve smooth and stable rotation. The transient moments exhibit high-frequency sinusoidal waves determined by the resistive moments. When Md < Mr < 2Md, the robot oscillates during rotation, yet a consistent upward trend in the angle of rotation is still observable. The transient moment, influenced by the maximum kinetic moment, displays a lower frequency compared to the drive current. In cases where Mr > 2Md, the robot exhibits violent shock motions, slow increases in the angle of rotation, and can be characterized as oscillating in place. The amplitude of the transient moment is dictated by the maximum dynamic moment, while its frequency corresponds to that of the drive current (Supplementary movie 9 and Supplementary Fig. 31).

The HD-LMC high-speed rotating robot can easily navigate on the road, with its speed primarily determined by the excitation current frequency and the circumference diameter. Figure 5h-k displayed optical photographs of the robot on a magnet track, running a distance of 300 mm in 0.9 s at 5 Hz, achieving a speed exceeding 14 body lengths per second. Supplementary movie 10 illustrates the kinematic behaviors of the HD-LMC high-speed rotating robot at excitation currents ranging from 0.5 to 5 Hz. Target capture recognition was conducted on each frame to extract displacement and velocity information, as elaborated in Supplementary Fig. 32.

Importantly, the HD-LMC high-speed rotary robot facilitates position sensing and velocity feedback. The eddy current effect of HD-LMC with the conductive substance is observed to cause a change in its inductance, as shown in Fig. 3i-l. Furthermore, the non-contact sensing capability allows for the measurement of the distance between them. Supplementary Fig. 33 illustrates the variation in inductance signal generated by a group of HD-LMC coils at different rotational speeds. The rotary robot can accurately achieve rotational speed detection feedback by detecting the period of the inductive signal, as illustrated in Fig. 5l. Furthermore, the variation in the waveform of the inductive signal in each period is not random; it correlates with the positional information of the rotating robot. By utilizing this feature, the HD-LMC high-speed rotary robot can effortlessly achieve self-position sensing, as illustrated in Fig. 5m depicting a signal cycle corresponding to one full rotation.

The high-speed rotary robot offers versatile applications across various fields. In inspection and maintenance, the robot can navigate confined or hazardous environments like pipelines, ventilation ducts, and industrial machinery with precise speed and position. When combined with sensors and cameras, it enables real-time data collection and remote assessment, thereby reducing the necessity for human intervention and enhancing safety as well as operational efficiency.

In agriculture, the robot has the potential to automate crop monitoring, pest control, and precision spraying. It can quickly traverse large fields and gather detailed data on crop health, soil conditions, and pest infestations, optimizing irrigation, fertilization, and pesticide application, thus improving yields and resource efficiency. Its flexibility enables it to adapt to various terrains and crop types.

In the entertainment and education sectors, the robot can be used in interactive exhibits, theme parks, and educational demonstrations. Its programmable nature allows for intricate movements, making it ideal for robotics competitions, workshops, and education programs. By engagingly showcasing advanced robotics, it serves as a source of inspiration and knowledge for aspiring engineers and scientists.

In summary, the robot’s integration of sensing and actuation functions, coupled with its exceptional speed performance and precise control, establishes it as a pioneering tool capable of enhancing efficiency, safety, and innovation across multiple fields.

Discussion

The utilization of soft liquid metal coils for integrated sensors and actuators is crucial in the development of soft robots, yet their implementation is hindered by the formidable challenge of designing high-density and intricate coil channels within elastomers. The present study demonstrates the successful design and fabrication of a HD-LMC that surpasses the structural density of enameled wires, thereby overcoming the limitations associated with planar single-layer structures and enabling the realization of curved multilayer three-dimensional structures. The structure comprises a helical conductive circuit, with a liquid metal (EGaIn) core, and an elastic shell made of PDMS material. Our approach to constructing HD-LMCs is universally applicable, resulting in coils with a consistent minimum insulation thickness of 0.1 mm for all three wire diameters (D = 0.68, 1.2, 1.7 mm). Those HD-LMCs are fundamental and versatile electromagnetic integrated components that possess excellent mechanical properties (able to withstand pressures up to 357 kPa and compression of 28.6%), exceptional electrical characteristics (including inductance values of 1.37, 0.41, and 0.14 μH, as well as resistances of 391, 75, and 22 mΩ respectively), impressive magnetic attributes (with an excited magnetic field strength of 2 mT), and the ability to withstand Joule heating at high currents (2, 4, and 8 A currents respectively).

As an integrated unit, the HD-LMC enables a diverse array of sensing and actuation functions. The initial design was focused on developing a pressure sensor capable of achieving a linear response of inductance across a wide range (0.714-357.14 kPa) with ultra-high resolution (0.357 kPa). As a temperature sensor, it can achieve a linear response of inductance within the range of 27-100 °C with an ultra-high resolution of 0.2 °C. The device is capable of non-contact distance sensing based on the eddy current effect and can accurately identify various conductive metal materials. Additionally, it can be utilized for NFC technology to enable non-contact information interaction and facilitate a wide range of communication functionalities. Furthermore, as a soft actuator, it can produce the maximum force of nearly 60 mN with a high-power density of 8279.6 W/m3. The bionic flexible pufferfish constructed using it can accurately control the swinging tail movement and swim through the water. Finally, we also present a programmable controlled HD-LMC high-speed rotary robot capable of traversing a distance of 300 mm in just 0.9 seconds while providing feedback for self-position recognition and rotational speed determination.

In summary, the HD-LMC demonstrates a remarkable ability to integrate multiple functionalities, including sensing, communication, and actuation, within a single unit. This versatility is also exemplified through various applications, from environmental sensing to complex robotic motion, highlighting the transformative potential of HD-LMCs in soft robotics. Moreover, its groundbreaking structural advancements are poised to revolutionize the realm of soft robotics.

Methods

Preparation of HD-LMC

PDMS (Dow Corning Sylgard 184 Silicone Elastomer was mixed at a 10:1 weight ratio) was first spin-coated onto the wafers in a homogenizer (EZ4-S, LEBO Science, China), and heated and cured to a 50 μm film. The Bi32In51Sn17 alloy (Bi: 32 wt%, In: 51 wt%, Sn: 17 wt%) was poured into the silicone tubes and subsequently cooled to form the metal wires. The metal wire wrapped with PDMS film is then pressed through a mold to form a coil, which is then placed into a 3D printing mold (printed by Shape 1 HD, RAYSHAPE, China) and added with PDMS to cure. HD-LMC was obtained by washing out the Bi32In51Sn17 alloy in a water bath and infusing it with EGaIn (Ga: 75.5 wt%, In: 24.5 wt%) (Supplementary Fig. 10). The performance of the soft coil system benefits from the liquid metal’s lower melting point (15.5 °C) and higher conductivity (3.4×106 S/m)67.

Characterization of HD-LMC cross-section morphology

The HD-LMC cross-sectional morphology and corresponding elemental mapping images were measured using field emission environmental scanning electron microscopes (FESEM, QUANTA FEG 250, America) and their energy spectra (EDS), respectively.

Mechanical testing of HD-LMC

Mechanical compression tests of HD-LMC, including pressure compression curves, multiple compression rate tests, and cyclic compression tests were performed on a universal stretching compressor (Shimadzu AGS-X Tester, SHIMADZU, Japan).

Electrical testing of HD-LMC

All inductance tests are measured at 1 V, 100 kHz with a precision inductance, capacitance, and resistance (LCR) meter (TH2832, Tonghui, China) unless otherwise noted. The inductance values were then obtained by fitting a series equivalent model. The resistance values were obtained using the four-wire method on a data acquisition system (Agilent 34420 A, Keysight, America). Current and voltage signals were acquired by a mixed signal oscilloscope (MSO2014, Tektronix, America).

Electromagnetic characterization of HD-LMC

The magnetic flux density of the HD-LMC after energization was measured by a digital Tesla meter (KT-102, KeOuTe, China). The excitation current was regulated by an adjustable direct current-regulated power supply (eTM-12020C, eTOMMENS, China). To accurately quantify the impact of distance, 3D-printed brackets with varying heights were utilized to position both the magnetometer and HD-LMC. Moreover, a 100 kHz sinusoidal AC signal is employed to excite the HD-LMC. Through mutual inductance, the secondary coil connects to the rectifier filter circuit, resulting in the illumination of the customized LED board. The sinusoidal AC signal is generated by an arbitrary signal generator (DG1022, Rigol Technologies, China) and then passed through a power amplifier (KD 5702, Ti Kedong Electronic, China) to regulate the voltage.

Joule heating behavior of HD-LMC

The Joule thermal behavior was obtained by video recording using a thermal imager (testo 890, Testo Inc., Germany). In the airless confined space, the HD-LMC is subjected to four levels of heating, starting from low to high current. Each level of energized current lasts for five minutes, followed by natural cooling after the heating process is completed. The circulating Joule heat behavior was controlled by using 1.5 A heating and natural cooling to circulate it between 40 °C and 60 °C. The excitation current is regulated by an adjustable direct current-regulated power supply (eTM-12020C, eTOMMENS, China).

Pressure sensors

The pressure exerted on the HD-LMC is measured and recorded along with its corresponding inductance value for sensor calibration. Larger forces were realized on a platform with a 0-500 N pull-pressure sensor (DS2-500N, ZhiQu, China). For precise application of smaller force, a universal tensioning machine with a 0-500 mN tensile transducer (FS05-012, Mark-10, America) was used.

Temperature sensors

The temperature sensors were calibrated in a thermostat (DHG-9070A, BluePard, China). Each temperature was maintained for 30 minutes to ensure internal equilibrium was achieved, with a 5 °C increment each time up to 100 °C. Rapid temperature cycling was done using a water bath. The temperature statements involved in the experiments were monitored by commercial thermocouples.

Non-contact distance sensors

A variety of 60 mm × 30 mm × 0.5 mm metal sheets (purchased from ShengShiDa, China) were used to realize the non-contact distance sensing test. To ensure distance accuracy, a series of highly 3D-printed brackets were taken for positional fixation.

Wireless near-field communication (NFC)

The HD-LMC was impedance-matched via a circuit board and employed for wireless near-field communication. All parameters, including impedance characteristics at high frequencies and return loss S11, were measured using an ENA network analyzer (E5063A, Keysight, America).

Bionic soft pufferfish

The constructed bionic soft pufferfish comprises an internal 3D-printed frame and a hollow silicone pufferfish (purchased from MoZhiJing, China). The actuated structure is created using two HD-LMCs with a diameter of 0.68 mm and a magnet (40 mm×20 mm×10 mm with a central surface flux of 356 mT). The bionic pufferfish was suspended in the water by connecting it to an air bladder floating on the water’s surface using a fine copper wire. The square wave signal was produced by an arbitrary signal generator (DG1022, Rigol Technologies, China), and the voltage was subsequently adjusted using a power amplifier (KD 5702, Ti Kedong Electronic, China) to drive the movement of the pufferfish robot.

High-speed rotating robots

The high-speed rotary robot is composed of six HD-LMCs with D = 0.68 mm. A high-speed electric slip ring (purchased from SENRING, China) is used in the middle to solve the problem of wire winding. Frequency control is realized by using an inverter (380V-3kW, YINGSHIDA, China), and then connected to a three-phase voltage regulator (TSGC2-3KVA, ChengQiang, China) to realize the regulation of voltage. For safety, a 50 Ω 500 W high-power sliding varistor is connected for additional voltage division. The track for the high-speed rotating robot comprises multiple magnets (100 mm × 50 mm × 20 mm), with a central surface flux of 120 mT.

Electro-magnetic-mechanical behavior of HD-LMC by finite element analysis

Numerical theory simulations were performed using the commercial software COMSOL Multiphysics (Version 6.1, COMSOL Inc., Sweden). The geometric model of the HD-LMC was designed by SolidWorks (Version 2021, Dassault Systemes, France) and imported into the software. All computational models have been analyzed for mesh independence, and a medium number of meshes has been used after comprehensive consideration. See Supplementary Note 10 for more information.

Photography and video recording

All optical photographs were taken by a digital SLR camera (EOS90D, Canon, Japan) with a resolution of 6960 ×4640 pixels unless otherwise noted. All video information was also captured by a digital SLR camera (EOS90D, Canon, Japan) at a frame rate of 50 fps with a resolution of 1920 × 1080 pixels.

Supplementary information

Supplementary Information

Peer Review File

Description of Additional Supplementary Information

Supplementary Movie 1

Supplementary Movie 2

Supplementary Movie 3

Supplementary Movie 4

Supplementary Movie 5

Supplementary Movie 6

Supplementary Movie 7

Supplementary Movie 8

Supplementary Movie 9

Supplementary Movie 10

Source data

Source data

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-024-51648-4.

Acknowledgements

This work was partially supported by the NSFC Grant (No. 91748206) to J.L., the Frontier Project of the Chinese Academy of Sciences to J.L., and the Fundamental Research Funds for the Central Universities (BLX202343) to L.W.

Author contributions

Conceptualization: N.L., L.W., J.L. Methodology: N.L., Y.L., C.L., Y.Z., L.W., J.L. Experiment: N.L., Y.L., Q.Z., J.S, B.J., H.S., C.C. Validation: N.L., Y.Z., C.L., W.X., X.C. Investigation: N.L., P.Z., Y.Z., C.L. Writing—original draft: N.L. Writing—review and editing: L.W., J.L. Visualization: N.L., M.G. Supervision: L.W., J.L. All the authors agreed on the final manuscript.

Peer review

Peer review information

Nature Communications thanks Xuechang Zhou, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

The data generated in this study are provided in the Source Data file. Source data are provided with this paper.

Competing interests

The authors declare no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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References

1. Wang RQ Soft underwater swimming robots based on artificial muscle Adv. Mater. Technol. 2023 8 2200962 10.1002/admt.202200962
Wang, R. Q. et al. Soft underwater swimming robots based on artificial muscle. Adv. Mater. Technol. 8, 2200962 (2023).10.1002/admt.202200962
2. Zhang WW Amoeba-inspired magnetic venom microrobots Small 2023 19 2207360 10.1002/smll.202207360
Zhang, W. W. et al. Amoeba-inspired magnetic venom microrobots. Small 19, 2207360 (2023).10.1002/smll.202207360
3. Ren ZY Soft-bodied adaptive multimodal locomotion strategies in fluid-filled confined spaces Sci. Adv. 2021 7 eabh2022 10.1126/sciadv.abh2022 34193416
Ren, Z. Y. et al. Soft-bodied adaptive multimodal locomotion strategies in fluid-filled confined spaces. Sci. Adv. 7, eabh2022 (2021).34193416 10.1126/sciadv.abh2022
4. Lu HJ A bioinspired multilegged soft millirobot that functions in both dry and wet conditions Nat. Commun. 2018 9 3944 10.1038/s41467-018-06491-9 30258072
Lu, H. J. et al. A bioinspired multilegged soft millirobot that functions in both dry and wet conditions. Nat. Commun. 9, 3944 (2018).30258072 10.1038/s41467-018-06491-9
5. Billard A Kragic D Trends and challenges in robot manipulation Science 2019 364 1149 10.1126/science.aat8414
Billard, A. & Kragic, D. Trends and challenges in robot manipulation. Science 364, 1149 (2019).10.1126/science.aat8414
6. Yang GZ The grand challenges of science robotics Sci. Robot 2018 3 eaar7650 10.1126/scirobotics.aar7650 33141701
Yang, G. Z. et al. The grand challenges of science robotics. Sci. Robot 3, eaar7650 (2018).33141701 10.1126/scirobotics.aar7650
7. Zhang JH Finger-inspired rigid-soft hybrid tactile sensor with superior sensitivity at high frequency Nat. Commun. 2022 13 5076 10.1038/s41467-022-32827-7 36038557
Zhang, J. H. et al. Finger-inspired rigid-soft hybrid tactile sensor with superior sensitivity at high frequency. Nat. Commun. 13, 5076 (2022).36038557 10.1038/s41467-022-32827-7
8. Gu LL A biomimetic eye with a hemispherical perovskite nanowire array retina Nature 2020 581 278 282 10.1038/s41586-020-2285-x 32433619
Gu, L. L. et al. A biomimetic eye with a hemispherical perovskite nanowire array retina. Nature 581, 278–282 (2020).32433619 10.1038/s41586-020-2285-x
9. Ma ZJ Permeable superelastic liquid-metal fibre mat enables biocompatible and monolithic stretchable electronics Nat. Mater. 2021 20 859 868 10.1038/s41563-020-00902-3 33603185
Ma, Z. J. et al. Permeable superelastic liquid-metal fibre mat enables biocompatible and monolithic stretchable electronics. Nat. Mater. 20, 859–868 (2021).33603185 10.1038/s41563-020-00902-3
10. Hegde C Sensing in soft robotics ACS Nano 2023 17 15277 15307 10.1021/acsnano.3c04089 37530475
Hegde, C. et al. Sensing in soft robotics. ACS Nano 17, 15277–15307 (2023).37530475 10.1021/acsnano.3c04089
11. Huang Y A skin-integrated multimodal haptic interface for immersive tactile feedback Nat. Electron 2023 6 1020 1031 10.1038/s41928-023-01115-7
Huang, Y. et al. A skin-integrated multimodal haptic interface for immersive tactile feedback. Nat. Electron 6, 1020–1031 (2023).10.1038/s41928-023-01115-7
12. Park J Soft sensors and actuators for wearable human-machine interfaces Chem. Rev. 2024 124 1464 1534 10.1021/acs.chemrev.3c00356 38314694
Park, J. et al. Soft sensors and actuators for wearable human-machine interfaces. Chem. Rev. 124, 1464–1534 (2024).38314694 10.1021/acs.chemrev.3c00356
13. Laschi C Mazzolai B Cianchetti M Soft robotics: Technologies and systems pushing the boundaries of robot abilities Sci. Robot 2016 1 eaah3690 10.1126/scirobotics.aah3690 33157856
Laschi, C., Mazzolai, B. & Cianchetti, M. Soft robotics: Technologies and systems pushing the boundaries of robot abilities. Sci. Robot 1, eaah3690 (2016).33157856 10.1126/scirobotics.aah3690
14. Ilami M Bagheri H Ahmed R Skowronek EO Marvi H Materials, actuators, and sensors for soft bioinspired robots Adv. Mater. 2021 33 2003139 10.1002/adma.202003139
Ilami, M., Bagheri, H., Ahmed, R., Skowronek, E. O. & Marvi, H. Materials, actuators, and sensors for soft bioinspired robots. Adv. Mater. 33, 2003139 (2021).10.1002/adma.202003139
15. Babatain W Buttner U El-Atab N Hussain MM Graphene and liquid metal integrated multifunctional wearable platform for monitoring motion and human-machine interfacing ACS Nano 2022 16 20305 20317 10.1021/acsnano.2c06180 36201180
Babatain, W., Buttner, U., El-Atab, N. & Hussain, M. M. Graphene and liquid metal integrated multifunctional wearable platform for monitoring motion and human-machine interfacing. ACS Nano 16, 20305–20317 (2022).36201180 10.1021/acsnano.2c06180
16. Zhang P Liquid-metal-based stretchable dual-parameter sensor for simultaneous detection of deformation and temperature Adv. Mater. Technol. 2023 8 2201264 10.1002/admt.202201264
Zhang, P. et al. Liquid-metal-based stretchable dual-parameter sensor for simultaneous detection of deformation and temperature. Adv. Mater. Technol. 8, 2201264 (2023).10.1002/admt.202201264
17. Li Y Ultrasensitive pressure sensor sponge using liquid metal modulated nitrogen-doped graphene nanosheets Nano Lett. 2022 22 2817 2825 10.1021/acs.nanolett.1c04976 35333055
Li, Y. et al. Ultrasensitive pressure sensor sponge using liquid metal modulated nitrogen-doped graphene nanosheets. Nano Lett. 22, 2817–2825 (2022).35333055 10.1021/acs.nanolett.1c04976
18. Kim S Laser-assisted failure recovery for dielectric elastomer actuators in aerial robots Sci. Robot 2023 8 eadf4278 10.1126/scirobotics.adf4278 36921017
Kim, S. et al. Laser-assisted failure recovery for dielectric elastomer actuators in aerial robots. Sci. Robot 8, eadf4278 (2023).36921017 10.1126/scirobotics.adf4278
19. Ji XB An autonomous untethered fast soft robotic insect driven by low-voltage dielectric elastomer actuators Sci. Robot 2019 4 eaaz6451 10.1126/scirobotics.aaz6451 33137720
Ji, X. B. et al. An autonomous untethered fast soft robotic insect driven by low-voltage dielectric elastomer actuators. Sci. Robot 4, eaaz6451 (2019).33137720 10.1126/scirobotics.aaz6451
20. Yang D Buckling of elastomeric beams enables actuation of soft machines Adv. Mater. 2015 27 6323 6327 10.1002/adma.201503188 26389733
Yang, D. et al. Buckling of elastomeric beams enables actuation of soft machines. Adv. Mater. 27, 6323–6327 (2015).26389733 10.1002/adma.201503188
21. Shin J Thermo-pneumatic artificial muscle: Air-based thermo-pneumatic artificial muscles for pumpless pneumatic actuation Soft Robot 2023 00 0229
Shin, J. et al. Thermo-pneumatic artificial muscle: Air-based thermo-pneumatic artificial muscles for pumpless pneumatic actuation. Soft Robot 00, 0229 (2023).
22. Smith GL Spider-inspired, fully 3d-printed micro-hydraulics for tiny, soft robotics Adv. Funct. Mater. 2023 33 2207435 10.1002/adfm.202207435
Smith, G. L. et al. Spider-inspired, fully 3d-printed micro-hydraulics for tiny, soft robotics. Adv. Funct. Mater. 33, 2207435 (2023).10.1002/adfm.202207435
23. Acome E Hydraulically amplified self-healing electrostatic actuators with muscle-like performance Science 2018 359 61 65 10.1126/science.aao6139 29302008
Acome, E. et al. Hydraulically amplified self-healing electrostatic actuators with muscle-like performance. Science 359, 61–65 (2018).29302008 10.1126/science.aao6139
24. Shin, G. et al. Soft electromagnetic artificial muscles using high-density liquid-metal solenoid coils and bistable stretchable magnetic housings. Adv Funct Mater, 2302895, (2023).
25. Li W Self-vectoring electromagnetic soft robots with high operational dimensionality Nat. Commun. 2023 14 182 10.1038/s41467-023-35848-y 36635282
Li, W. et al. Self-vectoring electromagnetic soft robots with high operational dimensionality. Nat. Commun. 14, 182 (2023).36635282 10.1038/s41467-023-35848-y
26. Mao GY Ultrafast small-scale soft electromagnetic robots Nat. Commun. 2022 13 4456 10.1038/s41467-022-32123-4 35945209
Mao, G. Y. et al. Ultrafast small-scale soft electromagnetic robots. Nat. Commun. 13, 4456 (2022).35945209 10.1038/s41467-022-32123-4
27. Do TN Phan H Nguyen TQ Visell Y Miniature soft electromagnetic actuators for robotic applications Adv. Funct. Mater. 2018 28 1800244 10.1002/adfm.201800244
Do, T. N., Phan, H., Nguyen, T. Q. & Visell, Y. Miniature soft electromagnetic actuators for robotic applications. Adv. Funct. Mater. 28, 1800244 (2018).10.1002/adfm.201800244
28. Ye J Lm-jelly: Liquid metal enabled biomimetic robotic jellyfish Soft Robot 2022 9 1098 1107 10.1089/soro.2021.0055 35486839
Ye, J. et al. Lm-jelly: Liquid metal enabled biomimetic robotic jellyfish. Soft Robot 9, 1098–1107 (2022).35486839 10.1089/soro.2021.0055
29. Wu H Ultrathin and high-stress-resolution liquid-metal-based pressure sensors with simple device structures ACS Appl Mater. Inter 2020 12 55390 55398 10.1021/acsami.0c16250
Wu, H. et al. Ultrathin and high-stress-resolution liquid-metal-based pressure sensors with simple device structures. ACS Appl Mater. Inter 12, 55390–55398 (2020).10.1021/acsami.0c16250
30. Zhang YQ Highly stretchable and sensitive pressure sensor array based on icicle-shaped liquid metal film electrodes ACS Appl Mater. Inter 2020 12 27961 27970 10.1021/acsami.0c04939
Zhang, Y. Q. et al. Highly stretchable and sensitive pressure sensor array based on icicle-shaped liquid metal film electrodes. ACS Appl Mater. Inter 12, 27961–27970 (2020).10.1021/acsami.0c04939
31. Ye J Xing ZR Gao JY Liu J Liquid metal coil Mater. Today Commun. 2022 32 104120 10.1016/j.mtcomm.2022.104120
Ye, J., Xing, Z. R., Gao, J. Y. & Liu, J. Liquid metal coil. Mater. Today Commun. 32, 104120 (2022).10.1016/j.mtcomm.2022.104120
32. Zhang Y Coaxially printed magnetic mechanical electrical hybrid structures with actuation and sensing functionalities Nat. Commun. 2023 14 4428 10.1038/s41467-023-40109-z 37481621
Zhang, Y. et al. Coaxially printed magnetic mechanical electrical hybrid structures with actuation and sensing functionalities. Nat. Commun. 14, 4428 (2023).37481621 10.1038/s41467-023-40109-z
33. Guo R Sheng L Gong H Liu J Liquid metal spiral coil enabled soft electromagnetic actuator Sci. China Technol. Sci. 2017 61 516 521 10.1007/s11431-017-9063-2
Guo, R., Sheng, L., Gong, H. & Liu, J. Liquid metal spiral coil enabled soft electromagnetic actuator. Sci. China Technol. Sci. 61, 516–521 (2017).10.1007/s11431-017-9063-2
34. Mao GY Soft electromagnetic actuators Sci. Adv. 2020 6 eabc0251 10.1126/sciadv.abc0251 32637626
Mao, G. Y. et al. Soft electromagnetic actuators. Sci. Adv. 6, eabc0251 (2020).32637626 10.1126/sciadv.abc0251
35. Fassler A Majidi C Soft-matter capacitors and inductors for hyperelastic strain sensing and stretchable electronics Smart Mater. Struct. 2013 22 055023 10.1088/0964-1726/22/5/055023
Fassler, A. & Majidi, C. Soft-matter capacitors and inductors for hyperelastic strain sensing and stretchable electronics. Smart Mater. Struct. 22, 055023 (2013).10.1088/0964-1726/22/5/055023
36. Lazarus N Meyer CD Bedair SS Nochetto H Kierzewski IM Multilayer liquid metal stretchable inductors Smart Mater. Struct. 2014 23 085036 10.1088/0964-1726/23/8/085036
Lazarus, N., Meyer, C. D., Bedair, S. S., Nochetto, H. & Kierzewski, I. M. Multilayer liquid metal stretchable inductors. Smart Mater. Struct. 23, 085036 (2014).10.1088/0964-1726/23/8/085036
37. Chen MX Self-powered multifunctional sensing based on super-elastic fibers by soluble-core thermal drawing Nat. Commun. 2021 12 1416 10.1038/s41467-021-21729-9 33658511
Chen, M. X. et al. Self-powered multifunctional sensing based on super-elastic fibers by soluble-core thermal drawing. Nat. Commun. 12, 1416 (2021).33658511 10.1038/s41467-021-21729-9
38. Wu YH Liquid metal fiber composed of a tubular channel as a high-performance strain sensor J. Mater. Chem. C. 2017 5 12483 12491 10.1039/C7TC04311B
Wu, Y. H. et al. Liquid metal fiber composed of a tubular channel as a high-performance strain sensor. J. Mater. Chem. C. 5, 12483–12491 (2017).10.1039/C7TC04311B
39. Yu LT Highly stretchable, weavable, and washable piezoresistive microfiber sensors ACS Appl Mater. Inter 2018 10 12773 12780 10.1021/acsami.7b19823
Yu, L. T. et al. Highly stretchable, weavable, and washable piezoresistive microfiber sensors. ACS Appl Mater. Inter 10, 12773–12780 (2018).10.1021/acsami.7b19823
40. Xiong Y A multifunctional hollow tpu fiber filled with liquid metal exhibiting fast electrothermal deformation and recovery Soft Matter 2021 17 10016 10024 10.1039/D1SM01189H 34672302
Xiong, Y. et al. A multifunctional hollow tpu fiber filled with liquid metal exhibiting fast electrothermal deformation and recovery. Soft Matter 17, 10016–10024 (2021).34672302 10.1039/D1SM01189H
41. Lin RZ Digitally-embroidered liquid metal electronic textiles for wearable wireless systems Nat. Commun. 2022 13 2190 10.1038/s41467-022-29859-4 35449159
Lin, R. Z. et al. Digitally-embroidered liquid metal electronic textiles for wearable wireless systems. Nat. Commun. 13, 2190 (2022).35449159 10.1038/s41467-022-29859-4
42. Sin D Ultrastretchable thermo- and mechanochromic fiber with healable metallic conductivity Adv. Electron Mater. 2021 7 2100146 10.1002/aelm.202100146
Sin, D. et al. Ultrastretchable thermo- and mechanochromic fiber with healable metallic conductivity. Adv. Electron Mater. 7, 2100146 (2021).10.1002/aelm.202100146
43. Dong CQ High-efficiency super-elastic liquid metal based triboelectric fibers and textiles Nat. Commun. 2020 11 3537 10.1038/s41467-020-17345-8 32669555
Dong, C. Q. et al. High-efficiency super-elastic liquid metal based triboelectric fibers and textiles. Nat. Commun. 11, 3537 (2020).32669555 10.1038/s41467-020-17345-8
44. Leber A Soft and stretchable liquid metal transmission lines as distributed probes of multimodal deformations Nat. Electron 2020 3 316 326 10.1038/s41928-020-0415-y
Leber, A. et al. Soft and stretchable liquid metal transmission lines as distributed probes of multimodal deformations. Nat. Electron 3, 316–326 (2020).10.1038/s41928-020-0415-y
45. Zheng LJ Conductance-stable liquid metal sheath-core microfibers for stretchy smart fabrics and self-powered sensing Sci. Adv. 2021 7 eabg4041 10.1126/sciadv.abg4041 34049879
Zheng, L. J. et al. Conductance-stable liquid metal sheath-core microfibers for stretchy smart fabrics and self-powered sensing. Sci. Adv. 7, eabg4041 (2021).34049879 10.1126/sciadv.abg4041
46. Linder V Gates BD Ryan D Parviz BA Whitesides GM Water-soluble sacrificial layers for surface micromachining Small 2005 1 730 736, 10.1002/smll.200400159 17193516
Linder, V., Gates, B. D., Ryan, D., Parviz, B. A. & Whitesides, G. M. Water-soluble sacrificial layers for surface micromachining. Small 1, 730–736, (2005).17193516 10.1002/smll.200400159
47. Costa SC Kenisarin M A review of metallic materials for latent heat thermal energy storage: Thermophysical properties, applications, and challenges Renew. Sust. Energ. Rev. 2022 154 111812 10.1016/j.rser.2021.111812
Costa, S. C. & Kenisarin, M. A review of metallic materials for latent heat thermal energy storage: Thermophysical properties, applications, and challenges. Renew. Sust. Energ. Rev. 154, 111812 (2022).10.1016/j.rser.2021.111812
48. Chen MR An ultrahigh resolution pressure sensor based on percolative metal nanoparticle arrays Nat. Commun. 2019 10 4024 10.1038/s41467-019-12030-x 31492843
Chen, M. R. et al. An ultrahigh resolution pressure sensor based on percolative metal nanoparticle arrays. Nat. Commun. 10, 4024 (2019).31492843 10.1038/s41467-019-12030-x
49. Kim J Stretchable silicon nanoribbon electronics for skin prosthesis Nat. Commun. 2014 5 5747 10.1038/ncomms6747 25490072
Kim, J. et al. Stretchable silicon nanoribbon electronics for skin prosthesis. Nat. Commun. 5, 5747 (2014).25490072 10.1038/ncomms6747
50. Liu Z A three-dimensionally architected electronic skin mimicking human mechanosensation Science 2024 384 987 994 10.1126/science.adk5556 38815009
Liu, Z. et al. A three-dimensionally architected electronic skin mimicking human mechanosensation. Science 384, 987–994 (2024).38815009 10.1126/science.adk5556
51. Lee S Nanomesh pressure sensor for monitoring finger manipulation without sensory interference Science 2020 370 966 970 10.1126/science.abc9735 33214278
Lee, S. et al. Nanomesh pressure sensor for monitoring finger manipulation without sensory interference. Science 370, 966–970 (2020).33214278 10.1126/science.abc9735
52. Hao YF A soft gripper with programmable effective length, tactile and curvature sensory feedback Smart Mater. Struct. 2020 29 035006 10.1088/1361-665X/ab6759
Hao, Y. F. et al. A soft gripper with programmable effective length, tactile and curvature sensory feedback. Smart Mater. Struct. 29, 035006 (2020).10.1088/1361-665X/ab6759
53. Kim K Highly sensitive and wearable liquid metal-based pressure sensor for health monitoring applications: Integration of a 3d-printed microbump array with the microchannel Adv. Health. Mater. 2019 8 1900978 10.1002/adhm.201900978
Kim, K. et al. Highly sensitive and wearable liquid metal-based pressure sensor for health monitoring applications: Integration of a 3d-printed microbump array with the microchannel. Adv. Health. Mater. 8, 1900978 (2019).10.1002/adhm.201900978
54. Kim MG Alrowais H Brand O 3d-integrated and multifunctional all-soft physical microsystems based on liquid metal for electronic skin applications Adv. Electron Mater. 2018 4 1700434 10.1002/aelm.201700434
Kim, M. G., Alrowais, H. & Brand, O. 3d-integrated and multifunctional all-soft physical microsystems based on liquid metal for electronic skin applications. Adv. Electron Mater. 4, 1700434 (2018).10.1002/aelm.201700434
55. Jeong YR A skin-attachable, stretchable integrated system based on liquid gainsn for wireless human motion monitoring with multi-site sensing capabilities Npg Asia Mater. 2017 9 e443 10.1038/am.2017.189
Jeong, Y. R. et al. A skin-attachable, stretchable integrated system based on liquid gainsn for wireless human motion monitoring with multi-site sensing capabilities. Npg Asia Mater. 9, e443 (2017).10.1038/am.2017.189
56. Gao YJ Wearable microfluidic diaphragm pressure sensor for health and tactile touch monitoring Adv. Mater. 2017 29 1701985 10.1002/adma.201701985
Gao, Y. J. et al. Wearable microfluidic diaphragm pressure sensor for health and tactile touch monitoring. Adv. Mater. 29, 1701985 (2017).10.1002/adma.201701985
57. Hong SY Stretchable active matrix temperature sensor array of polyaniline nanofibers for electronic skin Adv. Mater. 2016 28 930 935 10.1002/adma.201504659 26630502
Hong, S. Y. et al. Stretchable active matrix temperature sensor array of polyaniline nanofibers for electronic skin. Adv. Mater. 28, 930–935 (2016).26630502 10.1002/adma.201504659
58. Shin J Sensitive wearable temperature sensor with seamless monolithic integration Adv. Mater. 2020 32 1905527 10.1002/adma.201905527
Shin, J. et al. Sensitive wearable temperature sensor with seamless monolithic integration. Adv. Mater. 32, 1905527 (2020).10.1002/adma.201905527
59. Zhang ZX Liquid metal-created macroporous composite hydrogels with self-healing ability and multiple sensations as artificial flexible sensors J. Mater. Chem. A 2021 9 875 883 10.1039/D0TA09730F
Zhang, Z. X. et al. Liquid metal-created macroporous composite hydrogels with self-healing ability and multiple sensations as artificial flexible sensors. J. Mater. Chem. A 9, 875–883 (2021).10.1039/D0TA09730F
60. Yang H Soft thermal sensor with mechanical adaptability Adv. Mater. 2016 28 9175 9181 10.1002/adma.201602994 27572902
Yang, H. et al. Soft thermal sensor with mechanical adaptability. Adv. Mater. 28, 9175–9181 (2016).27572902 10.1002/adma.201602994
61. Han SB Thermoelectric polymer aerogels for pressure-temperature sensing applications Adv. Funct. Mater. 2017 27 1703549 10.1002/adfm.201703549
Han, S. B. et al. Thermoelectric polymer aerogels for pressure-temperature sensing applications. Adv. Funct. Mater. 27, 1703549 (2017).10.1002/adfm.201703549
62. Chen QY Silk-based pressure/temperature sensing bimodal ionotronic skin with stimulus discriminability and low temperature workability Chem. Eng. J. 2021 422 130091 10.1016/j.cej.2021.130091
Chen, Q. Y. et al. Silk-based pressure/temperature sensing bimodal ionotronic skin with stimulus discriminability and low temperature workability. Chem. Eng. J. 422, 130091 (2021).10.1016/j.cej.2021.130091
63. Trung TQ Ramasundaram S Hwang BU Lee NE An all-elastomeric transparent and stretchable temperature sensor for body-attachable wearable electronics Adv. Mater. 2016 28 502 509, 10.1002/adma.201504441 26607674
Trung, T. Q., Ramasundaram, S., Hwang, B. U. & Lee, N. E. An all-elastomeric transparent and stretchable temperature sensor for body-attachable wearable electronics. Adv. Mater. 28, 502–509, (2016).26607674 10.1002/adma.201504441
64. Harada S Fully printed flexible fingerprint-like three-axis tactile and slip force and temperature sensors for artificial skin ACS Nano 2014 8 12851 12857 10.1021/nn506293y 25437513
Harada, S. et al. Fully printed flexible fingerprint-like three-axis tactile and slip force and temperature sensors for artificial skin. ACS Nano 8, 12851–12857 (2014).25437513 10.1021/nn506293y
65. Harada S Honda W Arie T Akita S Takei K Fully printed, highly sensitive multifunctional artificial electronic whisker arrays integrated with strain and temperature sensors ACS Nano 2014 8 3921 3927, 10.1021/nn500845a 24580035
Harada, S., Honda, W., Arie, T., Akita, S. & Takei, K. Fully printed, highly sensitive multifunctional artificial electronic whisker arrays integrated with strain and temperature sensors. ACS Nano 8, 3921–3927, (2014).24580035 10.1021/nn500845a
66. Kanao K Highly selective flexible tactile strain and temperature sensors against substrate bending for an artificial skin RSC Adv. 2015 5 30170 30174 10.1039/C5RA03110A
Kanao, K. et al. Highly selective flexible tactile strain and temperature sensors against substrate bending for an artificial skin. RSC Adv. 5, 30170–30174 (2015).10.1039/C5RA03110A
67. Wu YW Alkaraki S Tang SY Wang Y Kelly JR Circuits and antennas incorporating gallium-based liquid metal P IEEE 2023 111 955 977 10.1109/JPROC.2023.3285400
Wu, Y. W., Alkaraki, S., Tang, S. Y., Wang, Y. & Kelly, J. R. Circuits and antennas incorporating gallium-based liquid metal. P IEEE 111, 955–977 (2023).10.1109/JPROC.2023.3285400
