Machine learning–driven design of engineered cilia enables hybrid operations in acoustic microrobots

Domain: physics
Published: 2026-03-12
Editorial outcome: major_revision

Abstract
Microrobotic systems offer significant potential for precision medicine by enabling minimally invasive interventions in complex fluidic environments. However, effective operation in these settings requires actuators capable of more than simple linear or rotational motion, often necessitating programmable changes in both direction and shape. This remains a major challenge due to fundamental constraints in the design and control of microscale actuators, particularly in acoustic systems. Here, we introduce engineered cilia for hybrid operations microrobots, a class of acoustic microrobots that use geometry-tuned cilia and resonance-induced forces to execute complex motions such as bidirectional bending, controllable rotation, and adaptive morphing. The microrobots design is driven by a self-augmenting machine learning framework integrated with finite element analysis, enabling rapid prediction and optimization of geometry-resonance relationships across design space. This approach achieves >10⁵-fold reduction in prediction time and over 20-fold in memory savings, while maintaining >90% accuracy in peak amplitude and >98% in resonance frequency. Compliant mechanism strategies further expand the mechanical versatility of the microrobots, enabling programmable shape transformations tailored to specific tasks. These advances establish acoustic-driven microrobots as a scalable and efficient platform for intelligent microrobotic actuation in biomedical and microfluidic applications.

Introduction
Microrobotics has made progress in recent years, enabling diverse applications across multiple disciplines1-4. Examples range from biomedical uses such as targeted therapy and minimally invasive procedures5-7 to environmental remediation8-11, microassembly12, 13, and microscale inspection14, 15. In the biomedical field, microrobotic systems enable highly precise interventions at scales where conventional surgical techniques cannot reach, thereby minimizing physiological disruption and improving therapeutic outcomes4, 7, 16-20. Although recent progress has greatly advanced microrobotic technologies, achieving consistent and precise control in dynamic environments continue to be a primary hurdle to real-world translation. Researchers have explored a broad spectrum of actuation mechanisms, each developed to overcome specific physical, checmical, or biological constraints3-5, 21. Photothermal actuation, for example, allows fine and localized manipulation through laser heating of asymmetric Janus microstructures. In practice, however, its utility is limited by shallow optical penetration, which makes operation in deep tissue difficult7, 22, 23. Magnetic actuation allows for remote, wireless control and has been widely adopted, but it requires strong magnetic fields, and spatial precision deteriorates with increasing distance due to magnetic field decay24-28. Chemical actuation provides self-sustained mobility through catalytic reactions or electrokinetic propulsion, but it depends on highly specific biochemical conditions, limiting adaptability across biological environments29, 30. Biohybrid microrobots offer biocompatibility and autonomous motion by integrating living cells with synthetic materials, yet their reliance on complex biological processes makes precise and responsive control more difficult in complex environments31, 32.

Acoustic actuation, which utilizes sound-induced vibrations and streaming to generate controlled forces, has enabled precise manipulation of microrobots in confined fluidic environments33-48. Current acoustic actuation methods include bubble-based actuation and non-bubble-based microstructure oscillations. Bubble-based acoustic actuation exploits the primary and secondary Bjerknes acoustic forces to achieve controlled fluidic transport and object manipulation33-35, 49-53. Non-bubble-based acoustic actuation primarily utilizes cilia-inspired microstructures, where high-frequency acoustic fields induce asymmetric vibratory motion, driving directed locomotion54-57. However, existing acoustic microrobots are constrained by simple geometry and limited control, restricting them to linear or rotational motion and preventing the complex shape transformations that would significantly enhance their functional adaptability in biomedical settings35, 49-51. Recent works, such as SonoTransformers, have enabled acoustically actuated shape transformations using resonance-tuned soft-hinge joints40. This design, however, relies on closed-loop connections between rigid and soft segments, which limits certain key deformations such as asymmetric folding or reconfigurable shapes.

In recent years, researchers have begun to incorporate machine learning into acoustic microrobotics, particularly in control-oriented tasks such as navigation and swarm coordination. Examples include reinforcement learning strategies for ultrasound-guided microswimmers and data-driven approaches for modeling the collective behavior of microrobotic swarms20, 58, 59. Although recent studies highlight the growing role of machine learning in acoustic microsystems, most efforts have focused on swimming control, with relatively little attention to AI-assisted structural design or fine-grained deformation control. Designing acoustic microrobots to meet prescribed resonance and deformation targets typically relies on extensive finite element simulations with iterative experimental testing. This slow and costly workflow limits systematic exploration of high-dimensional design spaces and makes nonlinear geometric effects hard to resolve. Cilia-based structures are a natural fit: they are simple to fabricate, inherently liquid compatible, and their vibrating tips generate strong acoustic streaming for propulsion and surface self-cleaning, providing a large design space for exploration across geometry, acoustic parameters, and collective behavior. Combining AI-driven design with cilia-based actuation leverages these advantages to accelerate development and expand the functional versatility of microrobotic systems in biomedical applications60.

Here, we present Engineered Cilia for Hybrid Operations microrobots (ECHObots), a class of acoustic microrobots designed to address the limited actuation versatility of current microscale systems. ECHObots utilize geometry-tuned cilia that harness resonance-induced forces to achieve diverse deformation behaviors, including directional bending, controlled rotation, and morphing of complex geometries in a single design. They can perform diverse actions such as bending, rotation, opening, and closing. The design process is guided by a self-augmenting machine-learning framework integrated with finite element analysis, which predicts and optimizes resonance across the geometric design space, significantly accelerating the iterative design process61-65. Compared with finite element analysis alone, this approach reduces computation time by more than 105-fold and memory usage by over 20-fold, while maintaining high predictive accuracy (98% for frequency and 90% for amplitude). To further enhance functional adaptability, we incorporate compliant mechanism strategies that support diverse and reversible morphologies, such as soft robotic arms opening, closing, and multi-segmented soft actuation66, 67. With these capabilities, ECHObots are no longer limited to straight-line or rotational motion, instead providing a programmable and scalable actuation platform tailored to a wide range of tasks. This versatility positions them for potential use not only in biomedical contexts but also in microscale manufacturing and environmental monitoring.

Results
Machine learning accelerated computing enables controlled shape deformation. The ECHObots utilize acoustic induced deformation to achieve dynamically tunable and responsive soft robotic motion. Fig. 1a presents an optical image of the device positioned next to a coin to highlight its minimal physical dimensions, measuring less than 1 mm and nearly invisible to the naked eye. Despite their microscopic scale, ECHObots can be driven by acoustic fields, allowing deformation to be tuned and actuation to be controlled. We illustrate the process in Fig. 1b and Supplementary Movie 1. The left panel provides a schematic emphasizing cilia resonance, with an inset schematic defining the main geometric parameters (i.e., the aspect ratio AR and the cilia length L). The right panel shows optical micrographs of the soft robotic arm bending when the field is applied. The oscillatory motion of the cilia induces microstreaming and generates a reaction force that drives structural bending. Fig. 1c (left) shows the flow field distribution under acoustic excitation, which closely matches the FEA simulation results in Fig. 1c (right). This fluid reaction force around the microstructures is sufficient to cause deformation of the flexible microstructures (Supplementary Fig. 1). To evaluate the performance of the ECHObot, different voltages were applied to induce bending in the soft robotic arm (cilia parameters: aspect ratio = 5.5, length = 200 μm), as shown in the data of Fig. 1d. Here, “cilia” denotes the small resonant appendage on a flexible rod, and “soft robotic arm” refers to the integrated assembly of the rod and its cilia. The cilia act as the local actuator that drives deformation of the entire arm. Bending is the foundation actuation mode of ECHObots and underpins the hybrid deformation behaviors described below. The results indicate a clear correlation between applied voltage and bending angle, demonstrating the controllability of the ECHObot under acoustic actuation.

Reversible deformation is a key metric for advanced soft robotics24, 25, 53, 68. As shown in Fig. 1e, we evaluated ECHObots under repeated actuation. The devices sustained more than 200 deformation cycles with consistent recovery, indicating high controllability with strong reversibility and repeatability. The soft robotic structure was fabricated using UV-photopolymerized polyethylene glycol diacrylate (PEGDA), as described in Supplementary Fig. 2. PEGDA exhibits great mechanical stability in aqueous environments. The Young’s modulus of ECHObots can be tuned by adjusting the UV exposure time and PEGDA700/PEGDA250 ratio (Supplementary Figs. 3). Longer UV exposure or higher fraction of short-chain PEGDA increases the modulus, but excessive exposure leads to light scattering and trapezoidal profiles in height direction (along z-axis). Furthermore, excessive PEGDA250 results in immiscible suspensions (Supplementary Fig. 4). Since a higher modulus hinders deformation and a lower modulus reduces restoring force, we selected an optimized composition and exposure time that balance deformability with structural recovery. Due to PEGDA’s elastic deformation properties, the robotic arm bends under an acoustic field and generates an equal restoring force upon field removal. In most cases, the micro-robot rapidly returns to its original shape; for instance, the flexible robotic arm bends up to 60° and fully recovers. In rare cases, viscous drag from the surrounding fluid or minor plastic deformation results in incomplete or slower recovery.

With material flexibility and stability defined, we further tailor the ECHObots geometry to achieve resonance-tuned, controllable deformation. Conventional microrobotic optimization typically combines FEA with empirical parameter tweaking, which constrains controllability and prevents systematic tuning of geometric parameters. This issue is especially acute for ECHObots, where cilia geometry governs the resonant frequencies and the peak amplitudes. Running FEA across the full geometric design space is computationally expensive, so comprehensive structural optimization is not practical. To overcome this, we employed a self-augmenting machine learning framework to accelerate the computational process. The methodology and workflow are illustrated in Fig. 1f. We first fixed external factors such as solution parameters and material modulus, focusing solely on optimizing the geometric parameters: aspect ratio and cilia length. Our workflow starts with a sparse sweep of FEA runs over a gently varying parameter grid. For each run, we extract the peak frequencies and amplitudes through signal processing, as shown in Supplementary Fig. 5. Using this curated set, a Random Forest model learns the underlying trends from geometry changes to the resonance features and predicts the responses in unsampled regions of the parameter space. As shown in Fig. 1g, memory per prediction dropped from about 1.2 GB for FEA to about 50 MB for the Random Forest, a reduction of more than twenty-fold measured across ten independent geometric configurations. This smaller footprint supports deployment on portable devices and on platforms with limited computational resources.

Self-augmenting machine learning predicts resonance peak efficiently and accurately. To support the accurate prediction and optimization of geometric-actuation relationships, we now elaborate on the design and implementation of the self-augmenting machine learning method. Unlike linear models or kernel-based approaches like Gaussian Process Regression, Random Forest does not assume any predefined functional kernel between input and output and can effectively capture both gradual trends and sharp local variations. By constructing an ensemble of decision trees and partitioning the input space through data-driven splits, it models complex nonlinear resonance behaviors with high fidelity61.

To ensure an accurate ground truth dataset, resonance peak features are extracted from FEA simulations, as shown in Fig. 2a. Starting from a specific geometry, we measure the resonance spectrum and use FEA insets to show how the stress is distributed and what the cilia look like at selected modes. When we sweep aspect ratio and cilia length, the peak frequencies and amplitudes do not change linearly; instead, both quantities change in nonlinear ways. This is illustrated in Fig. 2b, where varying the aspect ratio at a fixed length markedly shifts the resonance peaks. A complementary sweep, in which the aspect ratio is held constant while the length is varied, is shown in Supplementary Fig. 6. Taken together, the two sweeps demonstrate that each parameter modulates the peak response nonlinearly. Other geometric parameters, such as cilium-attachment positions, different supporting framework lengths, and structure heights, also affect resonance peaks. Here we focus on aspect ratio and length of the cilia, because FEA shows the attachment position has only a secondary effect on peak amplitude and frequency (Supplementary Fig. 7a). Different supporting frameworks lengths can also shift the resonance frequencies (Supplementary Fig. 7b). In practice, however, the framework is dictated by application needs, for example the target arm length and the intended bending direction are usually treated as fixed rather than modified. Theoretically, the structural height does not affect the resonance frequency but linearly influences the resonance amplitude (Supplementary Fig. 8a).

The structural height of ECHObots is constrained by the microchannel depth. At low heights, the cross-section of ECHObots remains uniform, whereas deeper channels cause light attenuation during UV curing, producing a tapered profile with a wider base and narrower top that complicates characterization and modeling69. However, a very small height makes the rods overly compliant, increasing their susceptibility to random bending or fracture. With these trade-offs in mind, we kept the height at 50 μm across all experiments and simulations. Resonance is also sensitive to the material modulus (Supplementary Figure 8b). When selecting the materials modulus, we balanced reversibility of deformation and fabrication complexity. Reversibility of deformation requires a sufficiently high modulus, as overly soft structures fail to recover under viscous drag, while excessively stiff ones hinder deformation. Furthermore, fabrication constraints limit the realization of devices with higher moduli, since UV exposure time leads to wider structures due to light scattering. Accordingly, we fixed the material modulus to 590 kPa.

Under such conditions, quantifying the degree of nonlinearity becomes practically important. Fig. 2c presents both Pearson correlation coefficients and mutual information (MI) to evaluate the linear and nonlinear dependencies, respectively. The Pearson correlation coefficient C(X, Y) characterizes linear relationships and is computed as:
𝐶(𝑋,𝑌) = ∑(𝑋𝑖−𝑋̄)(𝑌𝑖−𝑌̄) / √∑(𝑋𝑖−𝑋̄)2√∑(𝑌𝑖−𝑌̄)2 (1)
where X and Y represent the geometric parameters and peak features, respectively. While Pearson correlation captures linear dependence, it does not reflect nonlinear interactions. We therefore quantify such interactions using mutual information (MI):
𝑀𝐼(𝑋,𝑌) = ∑ 𝑝(𝑥,𝑦)log (𝑝(𝑥,𝑦) / 𝑝(𝑥)𝑝(𝑦)) (2)
where p(x, y) is the joint probability distribution of X and Y, and p(x) and p(y) are their respective marginal distributions. The relatively high values of mutual information between cilia length and both resonance frequency and amplitude indicate strong nonlinear relationships. In contrast, the negative high Pearson correlation coefficient between aspect ratio and frequency indicates that linear relationships also exist between geometric parameters and peak features. Because the data contains both linear trends and sharp nonlinearities, standard regression is not suitable to analyze this data. This is because standard regression tends to fit either straight lines or one globally smooth curve. Sweeping the entire geometry space with FEA is likewise impractical. Random Forests addresses these issues. Because the Random Forests model interactions and nonlinear effects without choosing a kernel in advance, it can be trained on a sparse set of FEA runs and accurately predict responses for unsampled designs. The result is high predictive accuracy with a substantially smaller computational footprint than using FEA alone.

Another key advantage of the Random Forest method lies in its computational efficiency. The prediction process operates with a fixed complexity of O(m⋅d), where m = 100 is the number of trees and d = 10 is the tree depth, is over six orders of magnitude lower than the complexity of FEA simulations in our system, as illustrated in Fig. 2d (left). Consequently, the prediction runtime is drastically reduced, from 1620 ± 176 seconds per geometry for FEA to just 8.1 ± 0.18 ms using Random Forest, as shown in Fig. 2d (right). In addition, memory usage is reduced by more than 20-fold (Fig. 1g), enabling deployment on miniaturized or resource-constrained hardware platforms. Full complexity derivations and implementation details are provided in the Supplementary Information.

Despite the computational advantage of machine learning prediction, the training process still relies on a sufficiently rich set of FEA-derived samples. Dense global sampling is unnecessary and inefficient, since large nonlinear shifts in peak features are confined to pockets of the design space. We therefore use localized refinement to balance cost and accuracy. A self-augmenting learning loop expands the training set where the model errors the most. This is done by mapping the residuals across the parameter space after an initial FEA-based pass. The high-residual regions are then resampled, and the model is retrained. Figure 1f and Figure 2e show that this adaptive strategy markedly reduces frequency prediction error. After five iterations, the global residual stabilizes, with the average frequency prediction error falling below 2% and the amplitude prediction residual around 10%, as shown in Fig. 2f. The small mismatch comes from the 10 Hz resolution in the FEA sweep. If the actual resonance falls between sample points, the peak is not captured exactly and its amplitude is underestimated. The effect is modest and stays within experimental tolerance. In Fig. 2g, predictions for L = 80 µm and 200 µm show peaks that are clearly separated across geometries, which allows selective actuation without interference. Further implementation details are given in the Supplementary Information (Supplementary Figs. 9–10). By contrast, other machine learning models, such as XGBoost and a multilayer perceptron model, performed worse under sparse sampling, largely due to noise sensitivity and overfitting (supplementary text and Supplementary Table 1).

Refined design of ECHObots enables versatile manipulation in microrobotic systems. Using the self-augmenting machine learning pipeline, we select geometries that produce the desired resonance and, in turn, the required deformation. As shown in Fig. 3a, modest changes in cilia shape shift both the frequency and amplitude of the resonance peaks. The FEA insets visualize the corresponding stress patterns, and the colored arrows mark the parameter sets. Since the resonance features is tunable, the robotic arm can be driven in a controlled, predictable way, allowing motion to be customized. A concrete example is shown in Fig. 3b, where two cilia of different sizes are placed on opposite sides of a flexible arm. At 5 kHz, the larger cilium resonates and drives a rightward bend, while the smaller cilium has little influence on the deformation. At 7.2 kHz, the roles reverse, and the arm bends to the left. The spacing minimizes coupling, keeping the peaks separate and allowing bidirectional actuation from a single acoustic driver. The underlying mechanism can be understood as geometry–frequency coupling: at different excitation frequencies, one cilium resonates more strongly than the other, creating unbalanced hydrodynamic forces that drive the structure to bend in the corresponding direction. Intuitively, the system behaves like a lever under opposing forces, where the side experiencing stronger resonance acts as the dominant force that tilts the balance of bending. These results indicate the ability to predictably select distinct deformation modes by tuning excitation frequency according to the designed cilia geometry. To further investigate the structural and fluidic responses under different excitation frequencies, FEA simulations in Fig. 3c visualize the corresponding stress distribution and acoustic streaming fields. In the stress distribution maps, the color scale indicates the magnitude of local stress during cilia resonance. Regions in red mark the stress concentrations associated with larger local deformation. Each panel includes an enlarged inset of the cilium at resonance: the black outline shows the undeformed shape and the colored map shows the stress under acoustic drive.

We next examined how material properties and the surrounding fluid influence the resonance spectrum and mode shapes of the same flexible rod-cilia system. FEA results (Supplementary Fig. 11) indicate that even small increases in material relaxation time broaden and flatten the peaks, underscoring the central role of viscoelastic damping. Changing the fluid viscosity and density similarly alters the resonance spectrum, as shown in simulations (Supplementary Fig. 12) of biomedical-relevant environments, such as water, ethanol, blood, and phosphate-buffered saline.

We also varied the incidence angle of the acoustic wave, with 0° defined as propagation perpendicular to the cilium (Fig. 3d). Spectra at 0°, 20°, and 40° show large changes in peak amplitude but little shift in peak frequency, confirming that frequency is set primarily by the material and fluid rather than the incidence angle of the acoustic wave. Leveraging this property, we designed a rotating flower-shaped structure, as shown in Fig. 3e. When an acoustic signal is applied, it rotates, with low-voltage excitation resulting in slow rotation (16 rpm) and negligible structural deformation, as shown in Supplementary Movie 2. As the driving voltage increases, the flexible arms contract inward, reducing the overall structure size and leading to a marked increase in rotational speed (110 rpm) as reflected in Supplementary Movie 3. The rotational acceleration is primarily driven by the reaction force from the vibrating cilia, and it is aided by two secondary effects: drag is reduced, and the effective moment of inertia decreases as the structure deforms. Paired with bidirectional bending, this controlled rotation shows how ECHObots behavior can be altered by applying varying acoustic amplitudes. Therefore, a single acoustic driver can support a broad set of hybrid operations. To verify the coupling between the drive and cilia dynamics, we performed FEA on the same geometry (Fig. 3f). The measured resonances closely track the predictions, within approximately 2% (≈200 Hz). Rotating the cilia orientation produces clearly different mode shapes, in line with experiment (Supplementary Fig. 13). The right panel of Fig. 3f and Supplementary Fig. 14 add a circular “wall,” where the driven flow generates particle paths with localized swirl. Particles circulate along the wall in closed loops, much like a tiny mill that repeatedly sweeps the boundary. These simulations match the experimental observations in Fig. 3e and point to cilia-generated reactive forces as the driver of both rotation and deformation. As shown in Fig. 3g, the rotation is voltage dependent, with speed rising in a controlled, systematic way as the drive increases. Together, the frequency-selective and the amplitude-dependent deformation tuning demonstrate the potential of ECHObots as a programmable platform for microscale soft robotics.

Structural diversity in ECHObots enabled by compliant mechanisms. Diverse deformation modes are central to the versatility of microrobots. In complex, unstructured environments, the ability to change shape passively and adaptively allows microrobots to move effectively and interact with their surroundings70. To realize this, we incorporate soft mechanisms in a controlled manner, enabling precise tuning of both geometry and motion. Figure 4a shows two approaches. Type-I relies on modulus modulation, where patterned exposure produces softer segments that bend preferentially. This reduces local stress and restoring force, enhancing durability and minimizing the risk of plastic deformation. However, material and fabrication constraints limit the achievable modulus reduction, so the decrease in actuation force is modest. Type-II, in contrast, modifies the geometric layout: narrow joints act as hinges, substantially lowering the required actuation force and enabling large bending at relatively low power. The trade-off is that stress concentrates at the hinges, and recovery after acoustic excitation is less effective, potentially shortening device lifetime. In summary, Type-II maximizes flexibility for biomimetic motion, while Type-I sacrifices some flexibility for greater stability and repeatability.

To quantitatively assess the mechanical response of these compliant mechanisms, we measured the maximum stress and corresponding recovery force under a 45° bending deformation of the upper segment (relative to the x-axis). As shown in Figure 4b, the two designs present distinct differences in stress distribution and restoring forces. Those differences explain the balance of each design between flexibility, robustness, and power efficiency. Building on this insight, we extended the approach to a set of ECHObot configurations, shown in Figure 4c. The designs include Closure-type and Open-type-I configurations derived from the original structure; Open-type-II, which incorporates Type-I compliant mechanisms to improve adaptability (see Supplementary Movie 4); and Type-II connection-based designs such as the Curved Hemisphere and Multi-Segmented Arm. In the Curved Hemisphere design, cilia at the bases of the small triangular units generate upward reactive forces under acoustic excitation. With the leftmost large triangle held fixed and the smaller triangles connected by flexible hinges, the net forces pull the small triangles inwards, contracting the array into a hemisphere-like dome.

The Multi-Segmented Arm design (Supplementary Movie 5) further demonstrates the potential for complex morphing and diverse transformation modes. Under repeated actuation at 20 V, the multi-segment arms exhibit slightly larger deformation after ~20 cycles compared to the initial response, while still recovering to their original shape. The minor shift likely reflects localized plastic deformation at the hinge regions, consistent with the stress concentrations in Fig. 4b. For each architecture, we measured recovery time at its designated driving frequency (as labeled in the figures) under 20 V. The recovery times are as follows: Closure-type, 1.5 s; Open-type-I, 1.0 s; Open-type-II, 3.5 s; Curved Hemisphere, 6.0 s; Multi-segmented Arms, 1.0 s. The spread underscores the dependence of recovery on geometry and drive conditions. In addition, the recovery times for these structures provide a quantitative measure of controllability, showing that different morphologies return to their original configurations within predictable timescales. To demonstrate the capabilities of the robots, we pair experiments with FEA stress fields and simulations of the streaming flow. Together, they reveal the variety of deformations that can occur and how recovery and drive conditions impact controlled motion, and on-demand shape change. By integrating Type-I and Type-II compliant mechanisms, ECHObots strike an elegant balance between flexibility and control, achieving tunable, energy-efficient, and mechanically robust deformations. By selecting the appropriate bending mechanism, we can program the system to favor either fine, precise actuation or large, multi-state transformations tailored to diverse tasks. These programmable architectures unlock structural diversity and complex deformation in ECHObots, enabling soft robotic arms that open and close with lifelike motion and multi-segmented structures that morph dynamically to meet the challenge of their environment.

Methods
Materials and reagents. Polyethylene glycol diacrylate (PEGDA700 and PEGDA250), photo initiator(2-Hydroxy-2-methylpropiophenone), TE buffer (pH 8.0), Poly(vinyl alcohol) (PVA, Mw 13,000-23,000, 87-89% hydrolyzed), 2-Propanol (IPA, 99.5%) were purchased from Sigma-Aldrich. PDMS (Sylgard 148) was purchased from Dow Inc. Transducer (7BB-27-4C) was purchased from Murata.

Fabrication of ECHObots. ECHObots were fabricated using a UV photolithography technique. The PEGDA precursor solution was prepared by mixing 40% (v/v) PEGDA700, 30% (v/v) PEGDA250, 15% (v/v) photoinitiator, and 15% (v/v) TE buffer. PEGDA-based resin was injected into a 50 μm-high microfluidic channel, whose substrate had been pre-coated with PDMS to prevent the polymer from adhering. Assisted with an inverted microscope setup, a high-resolution photomask (ArtnetPro Inc.) was employed which was positioned within the field stop of a Nikon Eclipse Ti inverted microscope. A mercury lamp (Intensilight C-HGFI, Nikon Inc.) was mounted onto the microscope, delivering UV light through the photomask. A 20× objective lens was used to focus the UV light. The polymerization process was finely controlled by an electric shutter system (Smart Shutter, Sutter Instrument), which regulated the UV exposure to a precise duration of 500 ms at full light intensity, ensuring complete polymerization of the PEGDA. After UV exposure, the device was washed with isopropyl alcohol to remove any residual PEGDA. The microchannel was then carefully covered with a glass slide, the isopropyl alcohol was replaced with deionized water, and the device was transferred under a microscope for further observation. The heights and geometric parameters of the ECHObots were determined using optical microscopy, as shown in Supplementary Fig. 15.

ECHObot triggering and testing. We performed all tests on an inverted microscope with the devices mounted on glass slides. After gluing the transducer in place, the device was transferred to the slide, sandwiched with cover slips, and filled with deionized water to a depth of roughly 100 μm. When particle tracking was required, the medium consisted of a 10:1 volume mixture of deionized water and 5.7 μm tracer particles from Polysciences. A Tektronix AFG 3102C, driving a Krohn-Hite 7620, provided the acoustic signal, and both frequency and voltage were adjusted for each experiment. PEGDA stiffness was measured by nanoindentation using an Optics11 Piuma.

FEA simulation. We computed the acoustic flow in COMSOL Multiphysics (v6.1) by coupling the Pressure Acoustics, Thermoviscous Acoustics, and Laminar Flow interfaces. The acoustic source was prescribed with a 1 μm boundary displacement, consistent with related studies60. First, the Pressure Acoustics interface provided the time-harmonic, first-order field. This solution then served as the forcing for the time-averaged Navier–Stokes equations to obtain the steady streaming velocity. Reaction forces on the cilia were evaluated by applying the acoustic–structure boundary condition and integrating the traction on the cilium. Further details are given in the Supplementary Information.

Machine learning analysis. All analyses were performed in Python 3.11. We first trained a Random Forest model as an initial predictor. A sparse sweep of the geometric space (aspect ratio and cilia length) was run with FEA to extract resonance peak frequency and amplitude. To simplify training, we modeled only peak frequency and amplitude, and grouped the resonances into four principal sets to clearly show the trending of the peaks. Prediction residuals were then used to guide adaptive sampling: regions with high residuals received denser sampling, the new data points were added, and the model was retrained. This loop continued until residuals reached a target value, such as under 5% for frequency prediction, or reach a plateau for amplitude prediction. This approach yields a practical balance between computational cost and accuracy. Full details are provided in the Supplementary Information.

Characterizations and measurements. Scanning electron microscopy (SEM) was performed on an Apreo S (Thermo Fisher Scientific). UV–vis spectra were recorded with a Shimadzu UV-3600i, and optical micrographs were acquired using an Elikliv EM4K digital microscope. Temperature was monitored with an HT-19 thermal camera, and PEGDA moduli were measured with a Piuma nanoindenter (Optics11).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript titled \"Machine learning-driven design of engineered cilia enables hybrid operations in acoustic microrobots\" presents a novel approach for the design and optimization of cilia-enabled microrobots using machine learning, moving beyond traditional FEA-based design approaches. The multifunctionality demonstrated by the proposed microrobots offers promising application potential. The manuscript is well written and may be considered for publication in Nature Communications after the authors address the following comments:\n1. In the Introduction, while the authors have cited relevant prior work, they have not discussed the paper SonoTransformers: Transformable acoustically activated wireless microscale machines. This paper presents soft microrobots capable of transforming into different shapes. Including a brief summary of this work and contextualizing its limitations would provide a clearer contrast to the current study’s contributions.\n2. The authors should also briefly mention recent advancements in the use of machine learning within acoustic microrobotics. One or two sentences summarizing its growing role and relevance would provide important context for readers unfamiliar with the state of the art.\n3. Although the paper relies on machine learning for the design of engineered cilia, the Introduction lacks a clear explanation of the motivation for adopting this approach. It would be helpful to describe the conventional design methods currently used in the field, the limitations of those methods, and any existing algorithms used to design and control ciliary microrobots.\n4. The authors must also discuss other recent papers where artificial intelligence has been applied to cilia-inspired or structurally similar systems in the introduction. In particular, the paper \"AI-aided geometric design of anti-infection catheters\".\n5. While the FEA simulations and machine learning models are well described, the addition of a brief theoretical section in the Supplementary Information explaining the physical principles governing ciliary microrobot motion would benefit readers. This would allow for a more comprehensive understanding of the system’s operation.\n6. In Figure 1A (left panel), the microrobot is not clearly visible. It is suggested that the authors retake this image with higher contrast or enhanced visualization—for example, dipping the robot in dye to improve visibility—if possible. This would aid readers in better identifying and understanding the microrobot's structure from a macroscale perspective.\n7. In the Results section Machine learning-accelerated computing enables controlled shape deformation, the term “robotic arm” is used. To maintain consistency and clarity, it is recommended that the authors refer to this as “cilia,” aligning with the terminology used throughout the manuscript.\n8. The manuscript demonstrates optimization of cilia length; however, it would be beneficial to also explore results for the effect of cilia placement, as briefly illustrated in Figure 4 with cilia positioned at the middle of the microrobot’s length. A more detailed demonstration with their machine learning framework or discussion of such spatial optimization would enhance the completeness and applicability of the proposed design framework.\n9. In the Results section titled Refined design of ECHObots enables multimodal manipulation in microrobotic systems, it would be useful to include the governing equations related to rotational acceleration in the Supplementary Information. This would support readers seeking a deeper understanding of the underlying mechanics.\n10. While the benefits of having multiple cilia at different positions are discussed, a quantitative design study—based on the authors' machine learning framework—exploring the optimal number and positioning of cilia would strengthen the technical rigor. This analysis could be added to the Supplementary Information.\n11. In the Discussion section, a brief paragraph on the future potential of ML-based design tools in microrobotics would be valuable. For authors consideration, they could comment on the possibility of autonomous generative design workflows, highlighting the direction and opportunities for future research.", "reviewer_2": "In this manuscript, the authors explore a soft microrobot equipped with cilia, driven to rotate and notably deform using ultrasound. The study significantly broadens the motion capabilities and operational duration of existing microrobotic systems, expanding both the design possibilities and functionalities available to acoustically actuated microrobots. Additionally, the authors introduce a well-designed self-augmenting machine learning approach based on random forest methodology, effectively predicting resonance peaks from FEA simulation data. I appreciated that the authors did not use a more complex machine learning model just for the sake of it, but rather introduced model complexity only when necessary. Furthermore, the authors thoroughly investigate the effects of structural deformation on resonance frequencies, showcasing their approach through several impressive demonstrations of microrobots and related structures. Overall, the manuscript is clear, well-structured, and accessible to a broad scientific readership. I strongly recommend its publication after the authors consider following comments and suggestions:\n1. Some concepts are not well defined/explained\nThe authors use the terms \"hybrid operations\" and \"multi-model deformation,\" but both are ill-defined. Could you please define these two operations and the deformation modes used in this work?\nAnother slightly controversial concept in their work is \"reconfigurable.\" I suppose the authors mean the large deformation of the long beam with cilia. However, reconfigurable robots usually require that each configuration be stable when the actuator is turned off. This is certainly not the case for the robot in this paper; otherwise, every deformation could be called a reconfiguration.\nIn the introduction, the authors use \"controlled motion\" and \"controllable\" quite a lot, but they do not define how much control they have. The same applies to \"precise\": How precisely can they control it? I did not find such information in this paper.\n2. The prediction is compared between the FEA simulations and the ML model (Fig. 2e). However, the frequency-amplitude diagram is not compared to the experiments. Is it general practice in acoustic simulations for FEA to match reality so well? Perhaps the authors could provide readers with an idea of what to expect in the actual experiments.\nThis makes me wonder what the actual operating frequency is in all the demonstrations in Figures 3 and 4. What frequency is actually used to drive the microrobot in the experiments? Based on the authors' experience, how accurate is it?\n3. What is the height and thickness of the microrobot? What assumptions are made about oscillation modes in other directions? Is the FEA a 2D simulation? What is the actual height of the microfluidic chamber, and how thick is the fluidic layer above the microrobot in the z direction?\nThis is important because spatial confinement matters for such large beam deformation. When long, slender beams deform, could they buckle in other directions to release internal stress? The authors should elaborate more on the limitations of the system, which make it difficult to operate in 3D compared with other microrobots, as mentioned in the introduction.\n4. If the authors insist on the idea of a reconfigurable robot, perhaps they could consider creating a demonstration with a bistable mechanical structure that shows how cilia can switch between two stable configurations. This is just a suggestion if it is easy to do. I think the work is already very strong experimentally.\n5. Beginning of the Results section: \"ECHObots utilize acoustic induced deformation to achieve precise and controllable soft robotic motion, demonstrating strong potential for minimally invasive interventions, such as arterial cleaning.\" However, I think this speculation is a bit far-fetched since the authors did not provide a demo or reasoning as to why it is so promising. I would rephrase it to be less specific.", "reviewer_3": "This study presents a cilia-inspired soft actuator capable of acoustic field-responsive directional bending. The frequency-dependent bidirectional actuation of asymmetric structure is an impressive demonstration for motion control of soft actuators. In particular, FEA-based simulation with self-augmenting machine learning demonstrates high computational efficiency and predictive accuracy for acoustic actuator design. By selecting aspect ratio as the main design variable, the authors efficiently narrowed the design parameter space of microscale actuators. The methodology presents a promising approach to data-driven design in microscale robotics. However, several important concerns remain regarding the soft robotic demonstration.\n1-1. While the ECHObot demonstrates repeatable and controllable deformation by the acoustic field, directional propulsion and functional motion are not included, which is a fundamental characteristic of microrobots. Shape deformation in the absence of locomotion may be more accurate to classify it as a programmable microscale actuator rather than a microrobot.\n1-2. Propulsion in the medium, a crucial feature for functional soft robots, may be achieved through asymmetric design modifications.\n2-1. For shape morphing, robot dimension and physical properties are essentially considered. While aspect ratio is a primary determinant of bending stiffness and resonance behavior, bending motion is highly affected by other factors, such as Young’s modulus, cross-sectional thickness, and length of supporting framework. Discussion on the influence of the parameters can support broader applicability of this actuation methodology in soft robotics.\n2-2. Also, the manuscript presents only a cross-sectional schematic, making it difficult to figure out the geometric configuration. key geometric parameters for deformation are not mentioned, such as the cross-sectional thickness (or width and depth) of cilia and lengths of supporting framework.\n3-1. The effect of thermoacoustic coupling could be discussed for dimensional stability because long-term acoustic actuation of PEGDA structures may lead to mechanical deformation.\n3-2. The effect of polymer swelling is not addressed with respect to deformation and dimensional stability.\n4. Lower crosslinking density can allow more effective deformation due to lower bending stiffnesses. Therefore, the authors investigated the modulus of the PEGDA network by varying the curing time. However, the rationale behind the selected PEGDA700/250 composition is not clarified although the authors mentioned that the material property was optimized. In addition to curing time, change in PEGDA composition is the other strategy to decrease bending stiffness and determine actuation performance.\n5. Directional bending behavior in Figure 3 is demonstrated by distinct resonance of cilia. The detailed underlying physical explanation would enhance the overall understanding of the actuation performance.\n6. In Figure 3c and 4c, the stress distribution map is difficult to interpret. Because deformation behavior is affected by stress distribution of the structures, the images and description could be improved to provide comprehensive understanding.\n7. In Figure 3g, the descriptions in the graph are difficult to correlate with the experimental conditions. The terms slow, moderate, and fast rotation are subjective. Quantitative analysis such as angular velocity is suggested.\n8-1. Is the deformation associated with rotational, gripping, clamping, and stretching motions reversible and repeatable under repeated actuation cycles?\n8-2. The structures described as gripping and clamping exhibit only arm extension without shrinkage or reversible deformation. Since gripping or clamping typically involves holding an object through applied structural force, the demonstrations may not support the use of these terms. Alternative terminology may be more appropriate unless object engagement is demonstrated.\n8-3. For gripping and clamping functions, an additional example of object capture and release would help clarify the functionality of the actuator.\n8-4. The actuation behavior of the curved hemisphere structure is not clearly explained.\nMinor:\n9. The sentences explaining Figure 1b are repeated on page 3. Please revise to eliminate redundancy.\n10. Movie playback speeds and scale bars should be included for understanding actuation dynamics.\n11. The text and labels in the figures, particularly in Figure 1 and 4, are too small and difficult to read.\n12. In Figure 4c, key experimental parameters such as response time and applied acoustic conditions are not reported."}, "author_response": "Response to Reviews\nItemized list of response to reviewers’ remarks\n(Black italic: Reviewer’s remarks; Blue type: Our response; Yellow highlighted: Additions/modifications to reviewer’s comments in the manuscript)\nReviewer #1 (Remarks to the Author):\nThe manuscript titled \"Machine learning-driven design of engineered cilia enables hybrid operations in acoustic microrobots\" presents a novel approach for the design and optimization of cilia-enabled microrobots using machine learning, moving beyond traditional FEA-based design approaches. The multifunctionality demonstrated by the proposed microrobots offers promising application potential. The manuscript is well written and may be considered for publication in Nature Communications after the authors address the following comments:\nResponse:\nWe sincerely thank the reviewer for the positive comments and constructive feedback. In response to the reviewer’s suggestions, we have included a detailed, point-by-point reply to address each comment.\n1. In the Introduction, while the authors have cited relevant prior work, they have not discussed the paper SonoTransformers: Transformable acoustically activated wireless microscale machines. This paper presents soft microrobots capable of transforming into different shapes. Including a brief summary of this work and contextualizing its limitations would provide a clearer contrast to the current study’s contributions.\nResponse 1:\nWe appreciate the reviewer’s suggestion. “SonoTransformers: Transformable acoustically activated wireless microscale machines” is an important recent work in acoustically driven microrobots. We have now cited this paper as ref. 40 at Page 2, and briefly discussed its relevance and distinctions in the revised Introduction part in the second paragraph.\nChanges to the manuscript:\nAt Page 2, Line 66, “Recent works, such as SonoTransformers, have enabled acoustically actuated shape transformations using resonance-tuned soft-hinge joints (Ref. 40). This design, however, relies on closed-loop connections between rigid and soft segments, which limits certain key deformations such as asymmetric folding or reconfigurable new shapes.”\n2. The authors should also briefly mention recent advancements in the use of machine learning within acoustic microrobotics. One or two sentences summarizing its growing role and relevance would provide important context for readers unfamiliar with the state of the art.\nResponse 2:\nWe thank the reviewer for the suggestion. Recent studies have begun exploring the integration of machine learning into acoustic microrobotics. As the reviewer rightly pointed out, this is a rapidy evolving research direction. To reflect these advances, we have inserted a brief discussion at the end of the second paragraph in the Introduction, along with ref. 3, 48, 49. This addition provides a broader view of recent progress and highlights the distinct advantages of our approach in enabling resonance-based design and programmable structural deformation.\nChanges to the manuscript:\nAt Page 3, Line 70, “In recent years, researchers have begun to incorporate machine learning into acoustic microrobotics, particularly in control-oriented tasks such as navigation and swarm coordination. Examples include reinforcement learning strategies for ultrasound-guided microswimmers and data-driven approaches for modeling the collective behavior of microrobotic swarms (Ref. 20, 58, 59).”\n3. Although the paper relies on machine learning for the design of engineered cilia, the Introduction lacks a clear explanation of the motivation for adopting this approach. It would be helpful to describe the conventional design methods currently used in the field, the limitations of those methods, and any existing algorithms used to design and control ciliary microrobots.\nResponse 3:\nWe thank the reviewer for this helpful suggestion. To address this, we have added a short paragraph after the abovementioned discussion paragraph, the new text briefly discusses the limitations of conventional FEA-based design workflows, such as high simulation and experimental costs, limited scalability to complex geometries, and difficulty in capturing nonlinear effects and explains the motivation for adopting a machine learning-based framework in this context.\nChanges to the manuscript:\nAt Page 3, Line 74, “Although recent studies highlight the growing role of machine learning in acoustic microsystems, most efforts have focused on swimming control, with relatively little attention to AI-assisted structural design or fine-grained deformation control. Designing acoustic microrobots to meet prescribed resonance and deformation targets typically relies on extensive finite element simulations with iterative experimental testing. This slow and costly workflow limits systematic exploration of high-dimensional design spaces and makes nonlinear geometric effects hard to resolve.”\n4. The authors must also discuss other recent papers where artificial intelligence has been applied to cilia-inspired or structurally similar systems in the introduction. In particular, the paper \"AI-aided geometric design of anti-infection catheters\".\nResponse 4:\nWe thank the reviewer for this helpful suggestion. The paper \"AI-aided geometric design of anti-infection catheters\" is one of the most recent cilia-based microstreaming applications and fits our work very well, we have cited the paper as reference 50 at Page 3, and discussed cilia-based microrobots and other applications right after the above-mentioned inserted paragraph as following:\nChanges to the manuscript:\nAt Page 3, Line 80, “Cilia-based structures are a natural fit: they are simple to fabricate, inherently liquid compatible, and their vibrating tips generate strong acoustic streaming for propulsion and surface self-cleaning, providing a large design space for exploration across geometry, acoustic parameters, and collective behavior. Combining AI-driven design with cilia-based actuation leverages these advantages to accelerate development and expand the functional versatility of microrobotic systems in biomedical applications (Ref. 60).”\n5. While the FEA simulations and machine learning models are well described, the addition of a brief theoretical section in the Supplementary Information explaining the physical principles governing ciliary microrobot motion would benefit readers. This would allow for a more comprehensive understanding of the system’s operation.\nResponse 5:\nThanks to the reviewer's valuable suggestion. Per the reviewer’s comment, we have added a section of theoretical analysis at the beginning of the Supplementary Information to illustrate cilia vibration, which causes acoustic waves and generates an interaction force. The subtitle is “Theoretical Basis of Cilia Microrobots”.\nChanges to the manuscript:\nIn Supplementary Information, at Page 1:\nTheoretical Basis of the Engineered Cilia Enables Hybrid Operations\nMicrorobots (ECHObots)\nThe ECHObot is actuated by an oscillating acoustic field, which induces periodic deflection of the cilia through the acoustic radiation force and viscous coupling with the surrounding fluid. The time-harmonic acoustic pressure and particle velocity fields generate a steady, second-order body force in the fluid, often referred to as the acoustic streaming force, given by 𝑝1 𝑣1\n(1)\nwhere is the fluid density, is the sound speed, and denotes time averaging over one acoustic cycle. This volum𝐹e𝑣 𝑜fo𝑙r=ce− g𝛻e⟨n𝑝e1r⟩a/t(e2s𝜌 𝑐ste)a+dy𝜌 ⟨s(t𝑣re1a⋅m𝛻)in𝑣g1 ⟩flows at the tip of a cilium. And the stre𝜌aming flow generate𝑐s a hydrodynamic reaction ⟨f⋅o⟩rce on the supporting framework, which can be expressed as follows:\n(2)\nwhere is the fluid stress tensor and is the local outward normal. This reaction force\n𝐹𝑟𝑒𝑎𝑐𝑡 = ∬𝑆𝜎𝑓𝑙𝑢𝑖𝑑 ⋅𝑛𝑑𝑆\nacts along the axis of the cilium. Under resonant excitation, the displacement amplitude of the cilium i𝜎s 𝑓 a 𝑙𝑢 m 𝑖𝑑 plified according to the respons𝑛e function of a damped harmonic oscillator:\n(3)\n1\nwhere , and are the effective mass, stiffness, and damping of the cilium. This\n𝐴(𝜔)∝ √(𝑘−𝑚𝜔 2 ) 2 +(𝑐𝜔) 2\namplification\nincreas𝑚es, 𝑘the ma𝑐gnitude of the streaming-induced body force, thereby enhancing the deformation of the attached flexible elements through fluid–structure interaction. In this work, the interplay between cilia resonance, streaming-driven body forces, and elastic deformation of the microrobot body forms the physical basis for the finite element simulations and the machine learning-based design framework.\n6. In Figure 1A (left panel), the microrobot is not clearly visible. It is suggested that the authors retake this image with higher contrast or enhanced visualization—for example, dipping the robot in dye to improve visibility—if possible. This would aid readers in better identifying and understanding the microrobot's structure from a macroscale perspective.\nResponse 6:\nWe thank the reviewer’s valuable comments. We have re-taken the optical image in Fig. 1a, a flower-like structure that has been dyed with Rhodamine B, which now shows the outline of the flower-like structure more clearly.\nChanges to the manuscript:\nThe updated Figure 1 is as following:\n7. In the Results section Machine learning-accelerated computing enables controlled shape deformation, the term “robotic arm” is used. To maintain consistency and clarity, it is recommended that the authors refer to this as “cilia,” aligning with the terminology used throughout the manuscript.\nResponse 7:\nWe thank the reviewer for this helpful suggestion. We agree that the distinction between cilia and soft robotic arm could cause confusion. To clarify, we have explicitly defined these terms in the manuscript. Specifically, at the first appearance of soft robotic arm (Fig. 1d, end of the first paragraph in the Results section), we have added the following definition:\nChanges to the manuscript:\nAt Page 4, Line 122, “Here, “cilia” denotes the small resonant appendage on a flexible rod, and “soft robotic arm” refers to the integrated assembly of the rod and its cilia. The cilia act as the local actuator that drives deformation of the entire arm.”\n8. The manuscript demonstrates optimization of cilia length; however, it would be beneficial to also explore results for the effect of cilia placement, as briefly illustrated in Figure 4 with cilia positioned at the middle of the microrobot’s length. A more detailed demonstration with their machine learning framework or discussion of such spatial optimization would enhance the completeness and applicability of the proposed design framework.\nResponse 8:\nWe appreciate the reviewers' valuable suggestions. The attachment position of cilia does not significantly affect the resonance frequency and the peak amplitude of the structure. We have added this discussion to the supplementary information section. Please refer to Supplementary Fig. 7a for details. As shown in our simulations, the resonance frequency undergoes a slight shift when cilia are positioned at different locations on the flexible rod, and the amplitudes of the various resonance peaks also exhibit some variation.\nChanges to the manuscript:\nIn Supplementary Information, at Page 13:\nSupplementary Figure 7. Finite element simulations of cilium resonance on soft supporting frameworks. a, Effect of cilium placement (positions 1–4) on a single soft rod. Left: Schematic structures with stress distributions under vibration. Right: Corresponding resonance spectra. Cilium position has negligible effect on resonance frequency and only a minor impact on peak amplitude. b, Effect of supporting rod length. Left: Schematics with stress distributions for rods of different lengths. Right: Resonance spectra. Rod length significantly alters both resonance frequency and amplitude, but the supporting framework is predefined during device design and does not affect subsequent analysis of cilium geometry.\n9. In the Results section titled Refined design of ECHObots enables multimodal manipulation in microrobotic systems, it would be useful to include the governing equations related to rotational acceleration in the Supplementary Information. This would support readers seeking a deeper understanding of the underlying mechanics.\nResponse 9:\nWe would like to thank the reviewers for their valuable suggestions. We have added the control equations for the rotating flower pattern structure to the Supplementary Information (Governing Equation for Rotational Acceleration), which discusses the relationship between the rotational angular velocity of the flower-shape structure and various physical quantities, and provides the results of flower pattern cantilever contraction at high driven voltages and steady-state conditions. Please find the details in the SI.\nChanges to the manuscript:\nIn Supplementary Information, at Page 5:\nGoverning Equation for Rotational Acceleration\nWe assume that the rotor’s mean rotation occurs in the low-Reynolds-number (Stokes) regime—given its microscale size, moderate angular speeds, and viscous working fluids—so that the viscous torque varies linearly with angular velocity. The ultrasonic actuation is a harmonic (such as sinusoidal) signal at frequency , and the time-averaged driving torque is dominated by second-order acoustic effects (streaming and radiation pressure) that scale with the square of the drive amplitude and frequency ( 𝑓 , equivalently ). We further treat the flower-shaped rotor as near-axisymmetric model with effective radius . The governing\n2 2 2\nequation for rotational acceleration could be writte∝n 𝐴as𝑓: ∝ 𝑉\n𝑅 (5)\nwhere is the angular velo𝑑c𝜔ity, the drive voltage, and the acoustic\nincidence/orientation angle. Th 𝐼 e 𝑒𝑓 n 𝑓 , ( w 𝑅 e ) 𝑑w𝑡ri = te 𝜏 t 𝑎 h 𝑐 e ( 𝑓 fo , 𝑉 llo , w 𝜓 i ) n − g 𝜁 re 𝑟( la 𝑅 t ) io 𝜔 ns, which close the governing\nordinary𝜔 d(if𝑡f)erential equation by expressing𝑉 the acoustic torque, viscous dr𝜓ag, and effective\ninertia as functions of with geometric details absorbed into a few fitted constants.\n(6)\n(𝑓 , 𝑉 , 𝜓 , 𝑅)\n2\n(7)\n𝜏 𝑎𝑐(𝑓 , 𝑉 , 𝜓)= 𝐾𝜏𝜒(𝑓;𝑓0, 𝑄)𝑔\n3\n(𝜓 ) 𝑉 (8)\n𝜁𝑟(𝑅)= 𝐶𝑑𝜇𝑅\nHere is a Lorentzian-like resonance4 factor, 5 is a directional gain, is the\ndynamic viscosity, is the flu𝐼𝑒 i 𝑓 d 𝑓 (d𝑅e)n=sit𝐶y 𝐼 , 𝜌𝑠ℎ𝑅 an+d 𝐶2 2a𝜑re𝑅 the solid density and thickness,\nrespec𝜒t(iv𝑓e;l𝑓y 0 , , 𝑄an)d are geometry-dependent co𝑔n(𝜓st)ants to be fitted (or estim𝜇ated by\nFEA). 𝜌 𝜌𝑠 ℎ\nshaped arm tend𝐾s 𝜏,to𝐶 𝑑f,o𝐶l𝐼d, 𝐶i𝑎nward at high rotation speeds. The rotational model therefore\nrequires a morphology-drive correction. We write the following relation to close the new\ngoverning equation when voltage-induced in-folding is non-negligible:\n(9)\nSubstituting into and 2 2 yields:\n𝑅(𝑉)= 𝑅0(1−𝜅𝑉 ),0 < 𝜅𝑉 < 1\n3 4 5 (10)\n𝑅(𝑉) 𝜁𝑟(𝑅)= 𝐶𝑑𝜇𝑅 𝐼𝑒𝑓𝑓(𝑅)= 𝐶𝐼𝜌𝑠ℎ𝑅 +2 𝐶𝑎𝜌𝑅\n𝐾𝜏 𝜒(𝑓)𝑔(𝜓)𝑉\n𝜔𝑠𝑠(𝑓 , 𝑉 , 𝜓)= 𝐶𝑑𝜇 𝑅 3 ( 𝑉 ) (11)\n𝐼𝑒𝑓𝑓(𝑅(𝑉))\nHere, the steady-state angular velocity and rotational response time are defined as:\n𝜏𝑟𝑜𝑡(𝑉)= 𝜁𝑟(𝑅(𝑉))\n(12)\n𝜔𝑠𝑠(𝑓 , 𝑉 , 𝜓)=\n𝜏\n𝜁\n𝑎\n𝑟\n𝑐\n= 𝐶𝑑\n𝐾\n𝜇\n𝜏\n𝑅 3 𝜒(𝑓) 𝑔(𝜓)𝑉\n2 (13)\nThese equations account for the reduction in effective radius due to voltage-induced in-folding,\nproviding corrected prediction𝜏s 𝑟 𝑜 f 𝑡 or= s𝐼t 𝑒 e 𝑓 a 𝑓 d/y𝜁𝑟 -state rotation and response time under realistic\noperating conditions.\nIn summary, starting from an angular-momentum balance (acoustic driving torque minus\nviscous rotational drag equals the inertial term), small-amplitude harmonic actuation makes\nthe time-averaged acoustic torque scale as . Furthermore, the rotational drag\nis linear in with , and the effective inertia is the sum of structural and added-mass\n2\ncontributions. Substituting these relations int𝐾o 𝜏 𝜒th(e𝑓 )r𝑔o(ta𝜓t)io𝑉nal balance yields the steady-state\n3\nexpression𝜔 𝜁𝑟 ≈ 𝐶𝑑𝜇𝑅 and the response time , which\ntogether explain the quadratic3 trend, 2the separable effects of frequency and incidence,\nand the addi𝜔tio 𝑠𝑠 n=al (s𝐾p 𝜏 e⁄e(d𝐶u 𝑑 p𝜇 𝑅at h))ig𝜒h(𝑓 r)o𝑔ta(t𝜓io)n𝑉 speeds when petal in-folding𝜏 𝑟 re 𝑜𝑡 du=c𝐼e 𝑒 s 𝑓 𝑓 th/𝜁e 𝑟 effective\nradius. 𝜔−𝑉\n10. While the benefits of having multiple cilia at different positions are discussed, a quantitative\ndesign study—based on the authors' machine learning framework—exploring the optimal\nnumber and positioning of cilia would strengthen the technical rigor. This analysis could be\nadded to the Supplementary Information.\nResponse 10:\nWe thank the reviewer for the constructive suggestion. In the Supplementary Information, we\nadded a concise text titled “Comparison of Simple Single Cilium with Cilia-band Design.” We\nsummarize that cilia-bands can cooperatively reinforce acoustic streaming and thus produce a\nlarger net reaction force than a single cilium. However, there are several experimental\nconditions to consider in this design. First, tight spacing of a cilia photomask can lead to base\ncoalescence during UV polymerization, which shortens the free length and shifts resonance to\nhigher frequencies. Second, effective flow superposition typically requires an inclined bands\norientation rather than a normal-to-substrate layout; And thus, the resultant load on the flexible\nrod is angled, which increases design complexity but can enable richer multimodal bending.\nGiven the length of this article, the cilia-band structure will be discussed further in future\nresearch.\nChanges to the manuscript:\nIn Supplementary Information, at Page 2:\nComparison of Simple Single Cilium with Cilia-band Designs\nPrior work shows that arranging multiple cilia as a tightly spaced band enables cooperative\nstreaming and a larger reaction force1. Our current architecture can adopt this strategy to\nfurther increase net actuation. However, several experimental considerations arise. First,\nfabricating a cilia band requires closely spaced photomasks. During UV polymerization, light\nscattering can cause cilia bases to merge, effectively shortening the free length, reducing the\nresonant segment, and shifting the resonance to higher frequencies. This explains why the\ncilia-band structure exhibits a higher resonant frequency than a single cilium. Second,\neffective superposition typically requires inclined band orientations rather than a perpendicular\nlayout to the substrate. The resulting flow—and the corresponding load on the flexible rod—\nis angled, increasing design complexity in terms of force direction and boundary stresses, but\nalso enabling richer, multi-modal bending behaviors that warrant further investigation. In\nsummary, cilia bands are compatible with our system and can enhance thrust, but exploring\ntheir full potential is beyond the scope of this study.\n11. In the Discussion section, a brief paragraph on the future potential of ML-based design\ntools in microrobotics would be valuable. For authors consideration, they could comment on\nthe possibility of autonomous generative design workflows, highlighting the direction and\nopportunities for future research.\nResponse 11:\nWe appreciate the valuable suggestions from the reviewers. In the Conclusion section, we\ndiscussed the future direction of ML models for microrobots structural design, especially for\nautonomous generative design process, as shown below:\nChanges to the manuscript:\nAt Page 17, Line 387, “Looking ahead, we aim to improve structural stability, tighten\nsystem integration, and test performance in complex fluids, ultimately in vivo. We also expect\nthe design workflow to evolve: machine learning tools that began as surrogates can mature into\nfull platforms that suggest new structures within fabrication and stress limits. With FEA and\nexperimental results as training data, the models can optimize resonance, deformation, and\nactuation efficiency simultaneously and drive a closed-loop cycle of geometry creation,\nsimulation, testing, and continual improvement.”\nReviewer #2 (Remarks to the Author):\nIn this manuscript, the authors explore a soft microrobot equipped with cilia, driven to rotate\nand notably deform using ultrasound. The study significantly broadens the motion capabilities\nand operational duration of existing microrobotic systems, expanding both the design\npossibilities and functionalities available to acoustically actuated microrobots. Additionally,\nthe authors introduce a well-designed self-augmenting machine learning approach based on\nrandom forest methodology, effectively predicting resonance peaks from FEA simulation data.\nI appreciated that the authors did not use a more complex machine learning model just for the\nsake of it, but rather introduced model complexity only when necessary. Furthermore, the\nauthors thoroughly investigate the effects of structural deformation on resonance frequencies,\nshowcasing their approach through several impressive demonstrations of microrobots and\nrelated structures. Overall, the manuscript is clear, well-structured, and accessible to a broad\nscientific readership. I strongly recommend its publication after the authors consider following\ncomments and suggestions:\nResponse:\nWe sincerely thank the reviewer for the positive comments and constructive feedback. In\nresponse to the reviewer’s suggestions, we have included a detailed, point-by-point reply to\naddress each comment.\n1. Some concepts are not well defined/explained\nThe authors use the terms \"hybrid operations\" and \"multi-model deformation,\" but both are\nill-defined. Could you please define these two operations and the deformation modes used in\nthis work?\nResponse 1:\nWe thank the reviewer for highlighting the need for clearer definitions. In our revision, we\ndistinguish between hybrid operations and multi-modal deformation as follows: (i) Hybrid\noperations describe robotic functionalities enabled under a single acoustic driving system,\nwhere different microrobot designs or configurations can realize diverse functions (e.g.,\nbending, rotation, open, and closure, etc.). This emphasizes the capacity of one actuation\nsystem to support a broad functionality. (ii) Multi-modal deformation refers to the ability of\na single ECHObot to deform distinctly under varying acoustic conditions (frequency or\nvoltage), such as bidirectional bending, controllable rotation, or multi-segment morphing.\nThis highlights the versatility of individual devices.\nThese clarifications ensure consistent terminology throughout the manuscript. The\ninserted sentences as shown following:\nChanges to the manuscript:\nIn the Introduction section, we added an explanation sentence at the last paragraph, after first\nmention of ECHObots, at Page 3, Line 88, “ECHObots utilize geometry-tuned cilia that\nharness resonance-induced forces to achieve multimodal deformation, including directional\nbending, controlled rotation, and morphing of complex geometries in a single design. They\ncan perform diverse actions such as bending, rotation, opening, and closing.”\nIn the Results section, we added a sentence after Fig.1d mentioned, at Page 4, Line 124,\n“Bending is the foundation actuation mode of ECHObots and underpins the hybrid\ndeformation behaviors described below.”\nIn the Results section, after mentioned Fig.3g, we added a sentence at Page 13, Line 294, “We\nuse multi-modal deformation to describe a device that can switch between distinct\ndeformation modes under different acoustic conditions (e.g., varying frequency or voltage),\nsuch as alternating between bending in opposite directions and undergoing continuous\nrotation. Therefore, a single acoustic driver can support a broad set of hybrid operations.”\nOn the end Results section, we added a sentence at Page 16, Line 354, “These programmable\narchitectures unlock a new level of structural diversity and multi-modal deformation in\nECHObots, enabling soft robotic arms that open and close with lifelike motion and multi-\nsegmented structures that morph dynamically to meet the challenge of their environment.”\nAnother slightly controversial concept in their work is \"reconfigurable.\" I suppose the authors\nmean the large deformation of the long beam with cilia. However, reconfigurable robots\nusually require that each configuration be stable when the actuator is turned off. This is\ncertainly not the case for the robot in this paper; otherwise, every deformation could be called\na reconfiguration.\nResponse:\nWe thank the reviewer for this insightful comment. We agree that the term “reconfigurable”\nmay be misleading in the strict robotics sense, where each configuration should remain stable\nonce actuation is removed. To avoid confusion, we have revised the manuscript and replace\nthe term “reconfigurable” to another term, such as “durability”, “reversible deformation”,\n“reversibility”, and “reversible” in different conditions.\nChanges to the manuscript:\nIn Figure 1e caption, we changed reconfigurable to durability. “e, Durability performance of\nECHObots after 200 deformation cycles.”\nAt Page 3, Line 96, we changed reconfigurable to reversible and rephrase the sentence. “To\nfurther enhance functional adaptability, we incorporate compliant mechanism strategies that\nsupport diverse and reversible morphologies, such as soft robotic arms opening, closing, and\nmulti-segmented soft actuation.”\nAt Page 5, Line 128, we changed reconfigurable to reversible and rephrase the sentence.\n“Reversible deformation is a key metric for advanced soft robotics (Ref. 24,25,53,68). As\nshown in Fig. 1e, we evaluated ECHObots under repeated actuation. The devices sustained\nmore than 200 deformation cycles with consistent recovery, indicating high controllability\nwith strong reversibility and repeatability.”\nAt Page 16, Line 360, we changed reconfigurable to reversible and rephrase the sentence.\n“The frequency and amplitude of the applied acoustics drive cilia oscillation, enabling\nECHObots to undergo tunable and reversible shape change.”\nIn the introduction, the authors use \"controlled motion\" and \"controllable\" quite a lot, but they\ndo not define how much control they have. The same applies to \"precise\": How precisely can\nthey control it? I did not find such information in this paper.\nResponse:\nWe thank the reviewer for this valuable comment. In our work, the terms “controllable” and\n“precise” are defined by several quantifiable aspects. First, controllability is demonstrated\nthrough frequency-resolved mode selection, where distinct deformations such as bidirectional\nbending and controllable rotation are triggered at specific resonance frequencies. Second, our\nML-assisted design achieves high predictive accuracy, with resonance frequency errors below\n2% and amplitude residuals around 10% compared with FEA, ensuring reliable and precise\nfrequency control. Third, multimodal deformation—including bending, rotation, hemisphere\ncontraction, closure, and segmented arms—can be selectively activated by tuning the excitation\nfrequency. Fourth, reversibility and stability are confirmed by durability tests showing\nconsistent operation over 200 deformation cycles. Finally, the recovery times of different\ncompliant structures (1–6 s under 20 V) provide a quantitative measure of structural control,\ndemonstrating predictable and precisely quantifiable return to the initial state across\nmorphologies. We have now clarified these definitions in the revised Results and Discussion\nsections by adding some statements as following:\nChanges to the manuscript:\nAfter 1e, at Page 5, Line 129, “The devices sustained more than 200 deformation cycles with\nconsistent recovery, indicating high controllability with strong reversibility and repeatability.”\nAfter 3b, at Page 12, Line 256, “Since the resonance features is tunable, the robotic arm can be\ndriven in a controlled, predictable way, allowing motion to be customized.”\nAfter 3e, at Page 13, Line 293, “Paired with bidirectional bending, this controlled rotation\nshows how ECHObots behavior can be altered by applying varying acoustic amplitudes.”\nAfter 4c, at Page 15, Line 340, “For each architecture, we measured recovery time at its\ndesignated driving frequency (as labeled in the figures) under 20 V. The recovery times are as\nfollows: Closure-type, 1.5 s; Open-type-I, 1.0 s; Open-type-II, 3.5 s; Curved Hemisphere, 6.0\ns; Multi-segment Arms, 1.0 s. The spread underscores the dependence of recovery on geometry\nand drive conditions. In addition, the recovery times for these structures provide a quantitative\nmeasure of controllability, showing that different morphologies return to their original\nconfigurations within predictable timescales.”\nIn the Discussion section, after discussing multi-modal deformation, at Page 16, Line\n369, we added: “Altogether, we demonstrated precise and controllable actuation of ECHObots.\nMode selection is realized through frequency- and amplitude-resolved deformation behaviors,\nsuch as bidirectional bending and controllable rotation. There is only 2% mismatch in\nresonance frequency between the FEA predictions and the experimental results. Under a 20 V\ndriven voltage, the devices return to their original shape within 1–6 s, and the simplest design\ncould operate more than 200 cycles. These results establish reliable, predictable, and reversible\ndeformation control at the microscale. Furthermore, the actuation exhibits high spatial\nprecision, with bending angles controlled to within a few degrees (Fig. 1d and Fig. 3b), and\ntemporal precision, with recovery times of 1–6 seconds, providing clear quantitative\nbenchmarks for both spatial and temporal control.”\n2. The prediction is compared between the FEA simulations and the ML model (Fig. 2e).\nHowever, the frequency-amplitude diagram is not compared to the experiments. Is it general\npractice in acoustic simulations for FEA to match reality so well? Perhaps the authors could\nprovide readers with an idea of what to expect in the actual experiments.\nThis makes me wonder what the actual operating frequency is in all the demonstrations in\nFigures 3 and 4. What frequency is actually used to drive the microrobot in the experiments?\nBased on the authors' experience, how accurate is it?\nResponse 2:\nWe thank the reviewer’s valuable comments. When comparing FEA predictions with\nexperimental results, the experimentally observed resonance frequencies typically differ from\nFEA simulations by about 50–200 Hz (≈0.5–2% relative to a 9 kHz resonance), which is an\nacceptable margin of error. The error comes from two parts, (i) the material properties and\nliquid environment between fabrication and testing conditions can slightly shift resonance\nfrequencies; (ii) the acoustic transducer does not generate a perfectly narrowband signal, but\nrather emits wave packets with a certain bandwidth, meaning that microrobots begin vibrating\nas long as the driving frequency is close to the simulated resonance, making it difficult to\nresolve exact resonance frequencies with <10 Hz accuracy. This frequency tolerance is also\nthe reason why we choose two distinguishable (~5.0 kHz and ~7.2 kHz) resonance frequencies\nduring designing the bidirectional bending structure. This separation prevents cross-talk\nbetween the two actuators, ensuring clear, selective operation.\nMoreover, as our simulations show in Supplementary Fig. 3, 4, 6, 7, and 8, cilia resonance\nfrequencies are determined by material parameters, cilia geometric parameters, and the\nsupporting framework. Considering device reversibility and practical application scenarios, we\nfixed the material modulus during analysis. The working frequencies were then identified\nthrough frequency sweeps with a 50 Hz resolution. Experimentally measured resonance\nfrequencies are marked in Figure 3 and 4, which fall within 50–200 Hz of the FEA predictions,\nconfirming that the simulations capture the dominant resonance behavior with sufficient\naccuracy for design and demonstration purposes.\n3. What is the height and thickness of the microrobot? What assumptions are made about\noscillation modes in other directions? Is the FEA a 2D simulation? What is the actual height\nof the microfluidic chamber, and how thick is the fluidic layer above the microrobot in the z\ndirection?\nThis is important because spatial confinement matters for such large beam deformation. When\nlong, slender beams deform, could they buckle in other directions to release internal stress?\nThe authors should elaborate more on the limitations of the system, which make it difficult to\noperate in 3D compared with other microrobots, as mentioned in the introduction.\nResponse 3:\nWe thank the reviewer for these valuable comments. In the revised manuscript, we have\nclarified the relevant geometry in the Method, Fabrication of ECHObots section. The flexible\nrobotic arm has a height of 50 µm, and a thickness of a few micrometers. The liquid layer\nabove the device is estimated to be ~100 µm based on microscope focusing estimation. Under\nthese conditions, deformation is primarily confined to the in-plane direction. Out-of-plane\nbuckling was not observed experimentally, likely because the PEGDA material remains fully\nhydrated without swelling-induced curvature, and because a high height-thickness ratio\nprovides sufficient stiffness to resist z-axis instability. Indeed, we found that structures with\nsmaller heights (~25 µm) were prone to unpredictable out-of-plane bending, while larger\nheights (~100 µm) suffered from UV scattering during fabrication, resulting in trapezoidal\ncross-sections. Thus, a 50 µm height represents a practical balance between mechanical\nstability and fabrication fidelity. This issue was discussed in the main text Result, Self-\naugmenting machine learning predicts resonance peak efficiently and accurately, the end of the\nsecond paragraph as follows:\nChanges to the manuscript:\nAt Page 8, Line 187, “Theoretically, the structural height does not affect the resonance\nfrequency but linearly influences the resonance amplitude (Supplementary Fig. 8a). The\nstructural height of ECHObots is constrained by the microchannel depth. At low heights, the\ncross-section of ECHObots remains uniform, whereas deeper channels cause light attenuation\nduring UV curing, producing a tapered profile with a wider base and narrower top that\ncomplicates characterization and modeling (Ref. 69). However, a very small height makes the\nrods overly compliant, increasing their susceptibility to random bending or fracture. With these\ntrade-offs in mind, we kept the height at 50 μm across all experiments and simulations.”\nRegarding the simulations, we clarify that all finite element analyses were performed using a\n2D model with a prescribed thickness of 50 µm and discussed the model limitation at the end\nof the Finite Element Analysis (FEA) Simulation section of the supplementary information as\nfollows:\nChanges to the manuscript:\nIn Supplementary Information, Page 4, Line 99, “Deformation is limited by the chamber height\nand wall effects, so the present system is mainly contained within a single plane. Future designs\nwith multilayer composite structures may extend the approach to controlled 3D deformation.”\nTo assess sensitivity to thickness, we compared 2D simulations at 50 µm and 100 µm height\nand found negligible differences in resonance frequency and deformation profiles. While\nincreasing the structural height simply scales the magnitude of the amplitude of the reaction\nforces. This is because no additional degrees of freedom are introduced, and the resonance\nfrequency was determined by the material properties and in-plane geometry. Importantly, this\nlinear scaling has no impact on the conclusions of the present study, since all amplitude\nanalyses were performed at a fixed height (50 µm) and the machine learning framework was\ntrained to capture the non-linear relationship between geometries and the resonance features\nrather than the linear scaling of the geometrical height. We have added this clarification to the\nSupplementary Figure. S8a. The simulation results showed good agreement with experimental\nmeasurements, supporting that the 2D approximation is sufficient to capture the dominant\ngeometric effects in our system. We agree with the reviewer that a full 3D model would be\nvaluable for future work involving designs that are more sensitive to vertical confinement.\nChanges to the manuscript:\nSupplementary Figure 8. Finite element analysis of peak features identified by: a, Different structure\nheights. b, Different materials modulus. The simulations were performed on a simple soft rod.\n4. If the authors insist on the idea of a reconfigurable robot, perhaps they could consider\ncreating a demonstration with a bistable mechanical structure that shows how cilia can switch\nbetween two stable configurations. This is just a suggestion if it is easy to do. I think the work\nis already very strong experimentally.\nResponse 4:\nWe thank the reviewer for this thoughtful suggestion. To avoid potential confusion, we have\nrevised the manuscript to consistently use “reversible”, “reversibility” or “durability” instead\nof “reconfigurable,” as these terms more accurately describe the deformation behaviors of\nECHObots. Our focus here is on demonstrating frequency-selective programmability and\nelastic reversibility under acoustic actuation, rather than multi-stable reconfiguration. While\nthe concept of bistable structures is highly interesting and could indeed provide an additional\ndimension of reconfiguration, it lies beyond the scope of the current study. We agree it\nrepresents an exciting direction for future work.\nChanges to the manuscript:\nIn Figure 1e caption, we changed reconfigurable to durability. “e, Durability performance of\nECHObots after 200 deformation cycles.”\nAt Page 3, Line 96, we changed reconfigurable to reversible and rephrase the sentence. “To\nfurther enhance functional adaptability, we incorporate compliant mechanism strategies that\nsupport diverse and reversible morphologies, such as soft robotic arms opening, closing, and\nmulti-segmented soft actuation.”\nAt Page 5, Line 128, we changed reconfigurable to reversible and rephrase the sentence.\n“Reversible deformation is a key metric for advanced soft robotics (Ref. 24,25,53,68). As\nshown in Fig. 1e, we evaluated ECHObots under repeated actuation. The devices sustained\nmore than 200 deformation cycles with consistent recovery, indicating high controllability\nwith strong reversibility and repeatability.”\nAt Page 16, Line 360, we changed reconfigurable to reversible and rephrase the sentence.\n“The frequency and amplitude of the applied acoustics drive cilia oscillation, enabling\nECHObots to undergo tunable and reversible shape change.”\n5. Beginning of the Results section: \"ECHObots utilize acoustic induced deformation to\nachieve precise and controllable soft robotic motion, demonstrating strong potential for\nminimally invasive interventions, such as arterial cleaning.\" However, I think this speculation\nis a bit far-fetched since the authors did not provide a demo or reasoning as to why it is so\npromising. I would rephrase it to be less specific.\nResponse 5:\nWe thank the reviewer for this helpful suggestion. In the revised manuscript, we have\nremoved the overly specific example of “vascular cleaning” to avoid overstatement. We\nretained only the more general examples (controlled drug release and micro-scale particle/cell\nmanipulation), which are already discussed in the Conclusion.\nChanges to the manuscript:\nAt Page 17, Line 398, “By enabling programmable shape change and frequency-\naddressed control, these systems open new possibilities, from targeted drug delivery to precise\nmanipulation of particles or cells and other dynamic tasks at the microscale. With in vivo\nvalidation, these principles could transform microrobot behavior, paving the way for smart,\nadaptive, acoustically actuated manipulators capable of navigating and operating in complex\nbiological and technological environments with unprecedented precision and versatility.”\nReviewer #3 (Remarks to the Author):\nThis study presents a cilia-inspired soft actuator capable of acoustic field-responsive\ndirectional bending. The frequency-dependent bidirectional actuation of asymmetric structure\nis an impressive demonstration for motion control of soft actuators. In particular, FEA-based\nsimulation with self-augmenting machine learning demonstrates high computational efficiency\nand predictive accuracy for acoustic actuator design. By selecting aspect ratio as the main\ndesign variable, the authors efficiently narrowed the design parameter space of microscale\nactuators. The methodology presents a promising approach to data-driven design in\nmicrorobotics. However, several important concerns remain regarding the soft robotic\ndemonstration.\nResponse:\nWe sincerely thank the reviewer for the positive comments and constructive feedback. In\nresponse to the reviewer’s suggestions, we have included a detailed, point-by-point reply to\naddress each comment.\n1-1. While the ECHObot demonstrates repeatable and controllable deformation by the\nacoustic field, directional propulsion and functional motion are not included, which is a\nfundamental characteristic of microrobots. Shape deformation in the absence of locomotion\nmay be more accurate to classify it as a programmable microscale actuator rather than a\nmicrorobot.\nResponse 1-1:\nWe thank the reviewer for the valuable comment. As outlined in the Introduction, a major gap\nin the field is the lack of systematic, programmable deformation compared with the extensive\nliterature on locomotion. Our goal here is therefore deformation-centric: to demonstrate\nfrequency-selective, programmable, and repeatable morphing and to show how an ML-\nassisted FEA workflow efficiently optimizes these deformation modes. To make this focus\nexplicit, we have added a short paragraph to the Discussion section to clarify our contribution\ncomplements propulsion-oriented microrobots. We also note that locomotion can be\nintegrated in future designs (e.g., via cilia arrays or bubble-based thrust) to realize systems\nthat combine directed movement and multimodal morphing on a single platform. The inserted\nparagraph in the Discussion section:\nChanges to the manuscript:\nAt Page 17, Line 393, “While most previous microrobotic studies have focused on directional\nlocomotion, our work takes a deformation-centric approach, exploring an underexamined\naspect of acoustic microrobotic functionality. Programmable, frequency-selective morphing\noffers a powerful complement to locomotion-focused designs, and integrating propulsion\nstrategies—such as cilia arrays or bubble-based thrust—within this deformation framework\ncould produce microrobots that combine precise, directed movement with versatile, multi-\nmodal shape changes.”\n1-2. Propulsion in the medium, a crucial feature for functional soft robots, may be achieved\nthrough asymmetric design modifications\nResponse 1-2:\nWe thank the reviewer for raising this important point. We fully agree that propulsion is a\ncrucial capability for many microrobotic systems, and asymmetric or banded designs are\nindeed effective strategies to achieve locomotion. However, the present work is intentionally\ndeformation-centric, aiming to address a challenge of programmable, frequency-selective\nmorphing has received far less systematic attention compared with propulsion. Considering\nthe scope and space limits of this study, a detailed exploration of propulsion mechanisms\nwould detract from the main theme. To acknowledge the reviewer’s suggestion, we have\nadded a new section “Future Integration of Locomotion with Programmable Deformation” to\nthe Supplementary Information where we summarize representative acoustic propulsion\nstrategies (cilia band-based and bubble-based) and discussed how their high-frequency\noperation could be integrated with our design. We emphasize that combining locomotion and\nprogrammable deformation represents an exciting direction for future work, but is beyond the\nscope of this manuscript.\nChanges to the manuscript:\nIn Supplementary Information, Page 2, Line 52:\nFuture Integration of Locomotion with Programmable Deformation\nThe present work is intentionally deformation-centric, while propulsion is a crucial capability\nfor many microrobotic systems. Prior literature has extensively explored acoustic locomotion,\nwhereas programmable shape deformation has received comparatively less attention,\nparticularly in the field of acoustic-driven microrobotics. Since propulsion and deformation are\ncomplementary design dimensions, we briefly summarize the main propulsion strategies here\nto discuss the potential integration of previous work with our ECHObot-based deformation\nframework. Here we outline two representative acoustic propulsion archetypes that can be\nintegrated with our deformation framework:\n1. Cilia-band–based propulsion. Arrays of cilia-like with geometric/asymmetric design can\ngenerate net streaming and thrust for directional locomotion. These systems typically operate\nat tens of kilohertz1.\n2. Micro-bubble–mediated propulsion. Entrapped or surface-attached bubbles excited by\nultrasound produce steady streaming and acoustic radiation forces that drive net propulsion.\nTypical drive frequencies of bubble-based propulsion span tens of kilohertz to the megahertz\nrange9, 10.\nBy contrast, the ECHObots reported here are tuned for low-kilohertz deformation ( 3–9\nkHz). By tuning low-frequency deformation, multiple frequencies can be utilized within in this\nsystem, such as a high-frequency channel could be dedicated to propulsion (cilia-ban∼d or\nbubble), while a low-frequency channel independently governs multimodal morphing (bending,\nrotation, opening, and closure). One conceptual embodiment is a hybrid device integrating a\ncilia-band module at one end (driven at tens of kHz for net thrust) and a flexible arm at the\nother end (driven at a few kHz for task-level manipulation). This spectral separation minimizes\nactuation cross-talk and allows time- and frequency-multiplexed control of movement and\ndeformation.\nIn practice, such co-integration introduces additional complexity, including geometrical\ndecoupling, actuation management, controller design, etc. Here, we concentrate on machine\nlearning-assisted FEA for design and optimization, which means that a full implementation of\nlocomotion and deformation is beyond the scope of the present study. Still, the machine\nlearning workflow presented in this work set the stage for hybrid microrobots that combine\ndirected locomotion with programmable, multimodal morphing.\n2-1. For shape morphing, robot dimension and physical properties are essentially considered.\nWhile aspect ratio is a primary determinant of bending stiffness and resonance behavior,\nbending motion is highly affected by other factors, such as Young’s modulus, cross-sectional\nthickness, and length of supporting framework. Discussion on the influence of the parameters\ncan support broader applicability of this actuation methodology in soft robotics.\nResponse 2-1:\nWe thank the reviewer for this constructive comment. In the revised Supplementary\nInformation, we have clarified the roles of several parameters in addition to aspect ratio.\nSpecifically:\nSupporting framework length: The FEA result in the Supplementary Fig. 7b indicates\nthat the length of the soft supporting rod (soft robotic arm) that anchors the cilia does affect\nresonance features, resonance features tend to exhibit a systematic shift.\nCross-sectional thickness (or structural height): Our FEA simulations shown in the\nSupplementary Fig. 8a indicate that the increasing thickness primarily scales the magnitude\nof the reaction force linearly, while the resonance frequency remains unchanged. This\nbehavior is consistent with the 2D simulation models, where thickness acts as a multiplicative\nfactor rather than introducing additional degrees of freedom.\nModulus: The FEA results in Supplementary Figure 8b show vibration characteristic\ncurves under different material moduli. It is clear that the modulus strongly affects the\nresonance peaks. Our experiments were performed after first determining the appropriate\nmaterial modulus, as recovery capability in the soft robotic arm requires a relatively high\nmodulus; overly soft materials fail to recover due to viscous drag of the working fluid. There\nare several methods to adjust the modulus of the device, while adjusting material ratios\n(PEGDA 700 and PEGDA 250) or extending UV exposure can increase the elastic modulus,\nboth approaches introduce new challenges. For example, longer UV exposure time causes\nlight scattering during polymerization, producing trapezoidal structures with broad bases and\nnarrow tops, we added a short discussion paragraph at the end of the subsection “Result -\nSelf-augmenting machine learning predicts resonance peak efficiently and accurately”.\nAltering precursor composition, such as increasing the PEGDA 250 fraction, can theoretically\nraise the modulus, as indicated in Supplementary Figure 3b. However, more PEGDA 250\nleads to suspended droplets in the precursor owing to incompatibility with photoinitiators and\nbuffer solutions, such as in Supplementary Figure 4. Thus, current modulus is a compromise\nsolution that balances fabrication feasibility with the requirement of the elastic modulus of\nthe material.\nIn the design of flexible robotic arms, we likewise prioritized creating distinct\nsupporting frameworks suited to specific applications before attaching cilia for evaluation.\nSupplementary Fig. 7a shows that on identical frameworks, changing cilia placement has only\na negligible effect on resonance characteristics, whereas cilia geometric parameters exert a\ndominant influence. This finding clarifies why the combined FEA+ML model uses only the\ngeometric parameters of the cilia themselves as input features.\nChanges to the manuscript:\nSupplementary Figure 3. Dependence of material Young’s modulus on: a, UV exposure time. b,\nPEGDA component ratios under a fixed UV exposure time of 500 ms.\nSupplementary Figure 4. Optical images of PEGDA700/PEGDA250 mixtures with varying\ncompositions. The 40%:30% mixture (left) shows a clear solution, indicating good miscibility. The\n30%:40% mixture (right) forms a suspension with dispersed droplets, suggesting phase separation.\nSupplementary Figure 7. Finite element simulations of cilium resonance on soft supporting\nframeworks. a, Effect of cilium placement (positions 1–4) on a single soft rod. Left: Schematic structures\nwith stress distributions under vibration. Right: Corresponding resonance spectra. Cilium position has\nnegligible effect on resonance frequency and only a minor impact on peak amplitude. b, Effect of\nsupporting rod length. Left: Schematics with stress distributions for rods of different lengths. Right:\nResonance spectra. Rod length significantly alters both resonance frequency and amplitude, but the\nsupporting framework is predefined during device design and does not affect subsequent analysis of\ncilium geometry.\nSupplementary Figure 8. Finite element analysis of peak features identified by: a, Different structure\nheights. b, Different materials modulus. The simulations were performed on a simple soft rod.\n2-2. Also, the manuscript presents only a cross-sectional schematic, making it difficult to figure\nout the geometric configuration. key geometric parameters for deformation are not mentioned,\nsuch as the cross-sectional thickness (or width and depth) of cilia and lengths of supporting\nframework.\nResponse 2-2:\nWe appreciate the reviewer’s comment regarding the dimensional accuracy of the flexible\nrobotic arm. We initially attempted SEM imaging for precise characterization; however, the\ninherently soft nature of the material and requirement of vacuum condition in SEM chamber\narises significant challenges. SEM requires a dry, vacuum environment, but dehydration and\nvacuum of the ECHObot device causes the structure to collapse, leading to unpredictable\ndistortions. The material also undergoes dehydration-induced deformation, bending, or\ndetachment from the substrate. The behaviors are similar to hydrogels, which makes SEM\nmeasurement impossible. In contrast, optical microscopy enables more accurate estimation of\nstructural dimensions. Because the ECHObot height is constrained by the microfluidic\nchannel during fabrication, the structural height is consistently ~50 μm. Height can also be\nestimated from intentionally “laid-flat” profile of the soft arms, and the thickness can be\ndirectly measured from optical images. As shown in the accompanying figure, the height is\nestimated as 50 ± 2 μm, and the width of a single flexible arm is 20 ± 0.5 μm (the error bar\ncomes from three independent measurements). These values, together with errors, are\nreported in Method section and the Supplementary Fig. 15.\nChanges to the manuscript:\nAt Page 18, Line 429: “After gluing the transducer in place, the device was transferred to the\nslide, sandwiched with cover slips, and filled with deionized water to a depth of roughly 100\nµm.”\nSupplementary Figure 15. Optical microscopy images used to estimate structural dimensions of soft\nrobotic arm based microstructures. a: laid-flat view showing a thickness of a rod side-view with 50 ± 2\nµm height. b: top-view image of a similar structure with 20 ± 0.5 µm width, where the error bar\nrepresents the standard deviation from three independent measurements.\n3-1. The effect of thermoacoustic coupling could be discussed for dimensional stability because\nlong-term acoustic actuation of PEGDA structures may lead to mechanical deformation.\nResponse 3-1:\nWe thank the reviewer for raising this point. In our experimental setup, the acoustic signals\nare generated from the transducer and delivered through the glass substrate, as illustrated in\nsupplementary information Fig. S2. The transducer itself is the primary heat source, but it\ndoes not directly contact the working area of the ECHObot. Any heat generated is transmitted\nthrough a thin glass slide, where obvious thermal accumulation is unlikely. Consistently, no\ntemperature rise of the local fluidic environment was observed during experiments, and no\nthermoacoustic-induced deformation was detected. Furthermore, our actuation is not a\ncontinuous signal but short bursts of excitation lasting only a few seconds. After removing\nthe acoustic triggering, the system is allowed to recover and “cool down”. This duty cycle\nkeeps the delivered power density below the threshold required to produce measurable\nheating. Indeed, Fig. 1e demonstrates that a simple soft rod structure maintains its\ndeformation amplitude even after ~200 cycles, supporting that thermal effects do not\ncompromise stability.\nAnd we do agree that structural stability issues can arise in some designs; however, in our\nobservations these are primarily due to plastic deformation under large deformation rather\nthan thermoacoustic effects. To illustrate this, we have added a supplementary Movie 5, the\nmovie shows the cyclic operation under 20 V driven voltage with 2x play speed. At the\nbeginning, the structure deforms slightly and the multi-segment arms are not fully “open”.\nAfter about 20 cycles, the structure could extend to larger deformations and we believe there\nare some plastic deformation inside the hinges part. The reason we select this structure is\nbecause the stress concentrated more than the original designs and reflect more plastic\ndeformation.\nChanges to the manuscript:\nIn Page 15, Line 336: “The Multi-Segmented Arm design (Supplementary Movie 5) further\ndemonstrates the potential for complex morphing and multi-modal transformations. Under\nrepeated actuation at 20 V, the multi-segment arms exhibit slightly larger deformation after\n~20 cycles compared to the initial response, while still recovering to their original shape. The\nminor shift likely reflects localized plastic deformation at the hinge regions, consistent with\nthe stress concentrations in Fig. 4b.”\n3-2. The effect of polymer swelling is not addressed with respect to deformation and\ndimensional stability.\nResponse 3-2:\nWe thank the reviewer for raising the important point regarding potential polymer swelling\nand its influence on deformation and dimensional stability. In our study, the ECHObots were\nfabricated from PEGDA solution and operated exclusively in aqueous environments. All\nrelevant material parameters (e.g., modulus characterization) and geometric measurements\nwere also conducted under stable aqueous conditions, rather than in dry or solvent-swollen\nstates. To further verify this, we compared representative microscopic images of the same\nstructure immersed in PEGDA precursor and in water, as shown in the following images. No\nnoticeable swelling or dimensional change was observed. Note: The apparent color difference\narises mainly from focal variations and optical reflections during imaging, rather than from\nstructural deformation. Importantly, both the overall structures and the hinge regions\nmaintained their integrity and shape fidelity. If substantial swelling had occurred,\nexpansion/contraction of the structure would have been inevitable, particularly at hinges\nwhere stress is concentrated. Such effects were not observed in the experiments.\nTherefore, swelling effects are negligible in the current system and not necessary to\nconsider for this study. We agree with reviewer’s comments that swelling could become\nimportant in future applications involving different physiological fluids, pH conditions, or\norganic solvents. This remains a guideline to design future relevant studies.\nFigure 1. Comparison of ECHObot in PEGDA liquid and in water.\n4. Lower crosslinking density can allow more effective deformation due to lower bending\nstiffnesses. Therefore, the authors investigated the modulus of the PEGDA network by varying\nthe curing time. However, the rationale behind the selected PEGDA700/250 composition is not\nclarified although the authors mentioned that the material property was optimized. In addition\nto curing time, change in PEGDA composition is the other strategy to decrease bending\nstiffness and determine actuation performance.\nResponse 4:\nWe thank the reviewer for this thoughtful comment. The selected PEGDA 700/250\ncomposition (40% PEGDA700, 30% PEGDA250, 15% (v/v) photoinitiator, and 15% (v/v)\nTE buffer) was chosen to balance flexibility and reversibility of the ECHObots. PEGDA700,\nwith its higher molecular weight, imparts greater chain mobility and lowers the network\nmodulus, whereas PEGDA250 provides sufficient crosslinking density to ensure robust\nstructural integrity and recover force (reversibility) in aqueous environments. To further\nillustrate the modulus of different PEGDA700/250 composition, we changed the ratio of\nPEGDA700 to PEGDA250 while keeping the UV exposure time constant (500 ms) and tested\nthe modulus in DI water. The results are presented in the Supplementary Figure. 3b (please\nrefer to the Response 2-1 section or to the revised Supplementary Information). As expected,\nincreasing the PEGDA700 component reduced the material modulus due to its longer\nmolecule chains and lower crosslinking density. Conversely, decreasing PEGDA700 (and\nthereby increasing PEGDA250) led to the formation of suspension with small droplets. This\nphenomenon is likely due to the shorter PEGDA250 chains, which reduce hydrophilicity and\npromote phase separation in the presence of TE buffer, causing PEGDA250 to partially\nprecipitate in aqueous environment. Reducing the TE buffer fraction can alleviate this\nphenomenon but significantly increases solution viscosity, making microchannel operation\nmore difficult.\nTherefore, we selected PEGDA700: PEGDA250 = 40%: 30% as the optimal\ncomposition that balances structural recoverability and flexibility while maintaining\nprocessability. As also discussed above, longer UV exposure times can further increase the\nmodulus, but excessive exposure introduces light scattering that results in enlarged structures\nor tapered microstructures (wider at the base and narrower at the top), which compromises\nfabrication fidelity. These practical considerations guided us to adopt the current composition.\nDue to space constraints, we did not include every intermediate trial in the main text, but the\nrepresentative results are now added in Supplementary Figure 3&4 (please find them in\nResponse 2-1). We also added text in Result section after Figure 1e. The added paragraph is\nshown below:\nChanges to the manuscript:\nAnd in the Result Section, at Page 5, Line 133, “The Young’s modulus of ECHObots can be\ntuned by adjusting the UV exposure time and PEGDA700/PEGDA250 ratio (Supplementary\nFigs. 3). Longer UV exposure or higher fraction of short-chain PEGDA increases the modulus,\nbut excessive exposure leads to light scattering and trapezoidal profiles in height direction\n(along z-axis). Furthermore, excessive PEGDA250 results in immiscible suspensions\n(Supplementary Fig. 4). Since a higher modulus hinders deformation and a lower modulus\nreduces restoring force, we selected an optimized composition and exposure time that balance\ndeformability with structural recovery.”\n5. Directional bending behavior in Figure 3 is demonstrated by distinct resonance of cilia.\nThe detailed underlying physical explanation would enhance the overall understanding of the\nactuation performance.\nResponse 5:\nWe thank the reviewer for this valuable suggestion. In Figure 3, the directional bending\nbehavior arises from the asymmetric resonance of the two cilia. At 5 kHz, the larger cilium\nexhibits stronger vibrations and generates a dominant reactive force, while the smaller cilium\nshows only weak oscillations. This imbalance of reaction forces drives the soft robotic arm to\nbend toward the right. Conversely, at 7.2 kHz, the shorter cilium reaches resonance and\nproduces stronger vibrations, whereas the longer cilium responds only weakly, leading to an\nopposite imbalance that bends the soft rod toward the left. We have now clarified this\nexplanation in the corresponding part of Results section. In essence, the phenomenon reflects\ngeometry–frequency coupling: at different excitation frequencies, one cilium resonates more\nstrongly than the other, creating unbalanced hydrodynamic forces that determine the bending\ndirection. For intuitive understanding, this mechanism can be compared to a lever under\nopposing forces, where the side experiencing stronger resonance acts as the dominant force\nthat tilts the balance of bending. The added statement is in the Result section after first\nmentioned Figure 3b.\nChanges to the manuscript:\nAnd in the Result Section, at Page 12, Line 257, “A concrete example is shown in Fig. 3b,\nwhere two cilia of different sizes are placed on opposite sides of a flexible arm. At 5 kHz, the\nlarger cilium resonates and drives a rightward bend, while the smaller cilium has little\ninfluence on the deformation. At 7.2 kHz, the roles reverse, and the arm bends to the left. The\nspacing minimizes coupling, keeping the peaks separate and allowing bidirectional actuation\nfrom a single acoustic driver. The underlying mechanism can be understood as geometry–\nfrequency coupling: at different excitation frequencies, one cilium resonates more strongly\nthan the other, creating unbalanced hydrodynamic forces that drive the structure to bend in\nthe corresponding direction. Intuitively, the system behaves like a lever under opposing forces,\nwhere the side experiencing stronger resonance acts as the dominant force that tilts the balance\nof bending. These results indicate the ability to predictably select distinct deformation modes\nby tuning excitation frequency according to the designed cilia geometry.”\n6. In Figure 3c and 4c, the stress distribution map is difficult to interpret. Because\ndeformation behavior is affected by stress distribution of the structures, the images and\ndescription could be improved to provide comprehensive understanding.\nResponse 6:\nWe thank the reviewer for the insightful suggestion. To improve clarity, we have revised\nFigures 3c, 3f and 4c by replacing unclear images and including enlarged views of cilia\noscillation under resonance. In the revised manuscript, we also added explanatory text\ndescribing the stress distribution maps. Specifically, the color scale represents the magnitude\nof local stress, with red indicating regions of higher stress and larger local deformation, and\nblue denoting lower stress. For each design, we provide inset views where the black contour\noutlines the undeformed state and the colored map shows the resonant configuration, allowing\ndirect comparison of stress evolution with structural deformation. The added sentences are\nadded to the Result section just after Figure 3c was mentioned as following.\nChanges to the manuscript:\nAnd in the Result Section, at Page 12, Line 270, “In the stress distribution maps, the color scale\nindicates the magnitude of local stress during cilia resonance. Regions in red mark the stress\nconcentrations associated with larger local deformation. Each panel includes an enlarged inset\nof the cilium at resonance: the black outline shows the undeformed shape and the colored map\nshows the stress under acoustic drive.”\n7. In Figure 3g, the descriptions in the graph are difficult to correlate with the experimental\nconditions. The terms slow, moderate, and fast rotation are subjective. Quantitative analysis\nsuch as angular velocity is suggested.\nResponse 7:\nWe thank the reviewer for this helpful suggestion. In the revised manuscript, the labels “slow\nrotation” and “fast rotation” in Figure 3e are now accompanied by quantitative descriptions\nwith unit “rpm” (revolutions per minute): the slow case corresponds to 16 rpm (≈1.7 rad/s)\nand the fast case corresponds to 110 rpm (≈11.5 rad/s). A similar quantitative clarification has\nalso been added in Figure 3g, where the fitted curves show rotation speed under different\ndriving voltages. We also note that in the original submission, the unit of rotational speed in\nFigure 3g was mistakenly labeled as “Hz.” This was a typo, and we have corrected it to\n“Rotational Speed (rpm)” in the revised figure. Furthermore, to provide a clearer theoretical\nframework, we have included the governing equation and detailed physical analysis of\nrotational acceleration in the Supplementary Information (Governing Equation for Rotational\nAcceleration subsection). These revisions ensure that both Figures 3e and 3g are\nquantitatively consistent and aligned with the underlying physical principles.\nChanges to the manuscript:\nIn Supplementary Information, Page 5.\nGoverning Equation for Rotational Acceleration\nWe assume that the rotor’s mean rotation occurs in the low-Reynolds-number (Stokes)\nregime—given its microscale size, moderate angular speeds, and viscous working fluids—so\nthat the viscous torque varies linearly with angular velocity. The ultrasonic actuation is a\nharmonic (such as sinusoidal) signal at frequency , and the time-averaged driving torque is\ndominated by second-order acoustic effects (streaming and radiation pressure) that scale with\nthe square of the drive amplitude and frequency ( 𝑓 , equivalently ). We further treat\nthe flower-shaped rotor as near-axisymmetric model with effective radius . The governing\n2 2 2\nequation for rotational acceleration could be writte∝n 𝐴as𝑓: ∝ 𝑉\n𝑅 (5)\nwhere is the angular velo𝑑c𝜔ity, the drive voltage, and the acoustic\nincidence/orientation angle. Th 𝐼 e 𝑒𝑓 n 𝑓 , ( w 𝑅 e ) 𝑑w𝑡ri = te 𝜏 t 𝑎 h 𝑐 e ( 𝑓 fo , 𝑉 llo , w 𝜓 i ) n − g 𝜁 re 𝑟( la 𝑅 t ) io 𝜔 ns, which close the governing\nordinary𝜔 d(if𝑡f)erential equation by expressing𝑉 the acoustic torque, viscous dr𝜓ag, and effective\ninertia as functions of with geometric details absorbed into a few fitted constants.\n(6)\n(𝑓 , 𝑉 , 𝜓 , 𝑅)\n2\n(7)\n𝜏𝑎𝑐(𝑓 , 𝑉 , 𝜓)= 𝐾𝜏𝜒(𝑓;𝑓0, 𝑄)𝑔\n3\n( 𝜓 ) 𝑉 (8)\n𝜁𝑟(𝑅)= 𝐶𝑑𝜇𝑅\nHere is a Lorentzian-like resonanc4e factor, 5 is a directional gain, is the\ndynamic viscosity, is the 𝐼fl 𝑒 u 𝑓 i 𝑓 d( 𝑅d)e=ns𝐶it 𝐼 y𝜌, 𝑠ℎ𝑅 a+nd𝐶 22 𝜑ar𝑅e the solid density and thickness,\nrespec𝜒t(iv𝑓e;l𝑓y 0 , , 𝑄an)d are geometry-dependent co𝑔n(𝜓st)ants to be fitted (or estim𝜇ated by\nFEA). 𝜌 𝜌𝑠 ℎ\nshaped arm tend𝐾s 𝜏,to𝐶 𝑑f,o𝐶l𝐼d, 𝐶i𝑎nward at high rotation speeds. The rotational model therefore\nrequires a morphology-drive correction. We write the following relation to close the new\ngoverning equation when voltage-induced in-folding is non-negligible:\n(9)\nSubstituting into and 2 2 yields:\n𝑅(𝑉)= 𝑅0(1−𝜅𝑉 ),0 < 𝜅𝑉 < 1\n3 4 5 (10)\n𝑅(𝑉) 𝜁𝑟(𝑅)= 𝐶𝑑𝜇𝑅 𝐼𝑒𝑓𝑓(𝑅)= 𝐶𝐼𝜌𝑠ℎ𝑅 +2 𝐶𝑎𝜌𝑅\n𝐾𝜏 𝜒(𝑓)𝑔(𝜓)𝑉\n𝜔𝑠𝑠(𝑓 , 𝑉 , 𝜓)= 𝐶𝑑𝜇 𝑅 3 ( 𝑉 ) (11)\n𝐼𝑒𝑓𝑓(𝑅(𝑉))\nHere, the steady-state angular velocity and rotational response time are defined as:\n𝜏𝑟𝑜𝑡(𝑉)= 𝜁𝑟(𝑅(𝑉))\n(12)\n𝜔𝑠𝑠(𝑓 , 𝑉 , 𝜓)=\n𝜏\n𝜁\n𝑎\n𝑟\n𝑐\n= 𝐶𝑑\n𝐾\n𝜇\n𝜏\n𝑅 3 𝜒(𝑓) 𝑔(𝜓)𝑉\n2 (13)\nThese equations account for the reduction in effective radius due to voltage-induced in-folding,\nproviding corrected prediction𝜏s 𝑟 𝑜 f 𝑡 or= s𝐼t 𝑒 e 𝑓 a 𝑓 d/y𝜁𝑟 -state rotation and response time under realistic\noperating conditions.\nIn summary, starting from an angular-momentum balance (acoustic driving torque minus\nviscous rotational drag equals the inertial term), small-amplitude harmonic actuation makes\nthe time-averaged acoustic torque scale as . Furthermore, the rotational drag\nis linear in with , and the effective inertia is the sum of structural and added-mass\n2\n𝐾𝜏𝜒(𝑓)𝑔(𝜓)𝑉\n3\n𝜔 𝜁𝑟 ≈ 𝐶𝑑𝜇𝑅\ncontributions. Substituting these relations into the rotational balance yields the steady-state\nexpression and the response time , which\ntogether explain the quadratic3 trend, 2the separable effects of frequency and incidence,\nand the addi𝜔tio 𝑠𝑠 n=al (s𝐾p 𝜏 e⁄e(d𝐶u 𝑑 p𝜇 𝑅at h))ig𝜒h(𝑓 r)o𝑔ta(t𝜓io)n𝑉 speeds when petal in-folding𝜏 𝑟 re 𝑜𝑡 du=c𝐼e 𝑒 s 𝑓 𝑓 th/𝜁e 𝑟 effective\nradius. 𝜔−𝑉\n8-1. Is the deformation associated with rotational, gripping, clamping, and stretching motions\nreversible and repeatable under repeated actuation cycles?\nResponse 8-1:\nWe thank the reviewer for this important question regarding reversibility and repeatability.\nTo address this, we added a new Supplementary Movie 5. The video shows repeated actuation\n(>20 cycles) of the Multi-segment Arm. The structure can still recover to its original state.\nThis comparison highlights both the durability and reversibility, thereby clarifying the\nrepeatability concern. (Note: We changed some terms in our study, from “gripper, clamp, and\nsoft robotic arm”, to “Open-type-I, Open-type-II, Closure-type, and Multi-segment Arm”)\n8-2. The structures described as gripping and clamping exhibit only arm extension without\nshrinkage or reversible deformation. Since gripping or clamping typically involves holding an\nobject through applied structural force, the demonstrations may not support the use of these\nterms. Alternative terminology may be more appropriate unless object engagement is\ndemonstrated.\n8-3. For gripping and clamping functions, an additional example of object capture and release\nwould help clarify the functionality of the actuator.\nResponse 8-2 and 8-3 together:\nWe agree with the reviewer that the terms “gripping” and “clamping” may overstate the\ncurrent demonstrations, since actual object engagement has not yet been performed. In the\nrevised manuscript, we have moderated our terms and now describe these designs as “open-\ntype” or “closure-type” deformations instead of gripping or clamping. We have also clarified\nin the Discussion section that while the current work focuses on structural deformation, future\ndevelopments could integrate these soft robotic arms with object capture and release tasks,\nsuch as particle manipulation or controlled in vivo drug release. The following modified\nsentence was added at the end of the Discussion section:\nChanges to the manuscript:\nAt Page 17, Line 398, “By enabling programmable shape change and frequency-\naddressed control, these systems open new possibilities, from targeted drug delivery to precise\nmanipulation of particles or cells and other dynamic tasks at the microscale. With in vivo\nvalidation, these principles could transform microrobot behavior, paving the way for smart,\nadaptive, acoustically actuated manipulators capable of navigating and operating in complex\nbiological and technological environments with unprecedented precision and versatility.”\nUpdated Figure 4c:\n8-4. The actuation behavior of the curved hemisphere structure is not clearly explained.\nResponse 8-4:\nWe appreciate the reviewer’s request for the clarifying mechanism of the formation of Curved\nHemisphere actuation. In the revised text, we now explain it in the Result section after Fig.\n4c in more details:\nChanges to the manuscript:\nAt Page 15, Line 332, “In the Curved Hemisphere design, cilia at the bases of the small\ntriangular units generate upward reactive forces under acoustic excitation. With the leftmost\nlarge triangle held fixed and the smaller triangles connected by flexible hinges, the net forces\npull the small triangles inwards, contracting the array into a hemisphere-like dome.”\nMinor:\n9. The sentences explaining Figure 1b are repeated on page 3. Please revise to eliminate\nredundancy.\nResponse 9:\nWe thank the reviewer for carefully noting this redundancy. The repeated sentences\ndescribing Figure 1b on page 3 have been removed in the revised manuscript. We greatly\nappreciate the reviewer’s thorough and attentive reading.\n10. Movie playback speeds and scale bars should be included for understanding actuation\ndynamics.\nResponse 10:\nWe thank the reviewer for this helpful suggestion. In response, we have added on-screen text\nindicating the playback speed and included scale bars in the videos to improve clarity.\n11. The text and labels in the figures, particularly in Figure 1 and 4, are too small and difficult\nto read.\nResponse 11:\nWe appreciate the reviewer's attention to this issue. We have enlarged the font size in Figures\n1 and 4 and have a partial reformat to enhance text clarity. Additionally, we have adjusted\nsome text and had minor changes in Figures 2 and 3.\n12. In Figure 4c, key experimental parameters such as response time and applied acoustic\nconditions are not reported.\nResponse 12:\nWe thank the reviewer for this suggestion. In Figure 4c, we have added the driving frequency\nto clarify the applied acoustic conditions. Regarding response time, we have included a brief\ndescription at the end of Results section, since response time varies across structures and\ndepends on deformation scale and driving voltage. The added text as following:\nChanges to the manuscript:\nAt Page 15, Line 340, “For each architecture, we measured recovery time at its designated\ndriving frequency (as labeled in the figures) under 20 V. The recovery times are as follows:\nClosure-type, 1.5 s; Open-type-I, 1.0 s; Open-type-II, 3.5 s; Curved Hemisphere, 6.0 s; Multi-\nsegment Arms, 1.0 s. The spread underscores the dependence of recovery on geometry and\ndrive conditions.”\nResponse to Reviews\nItemized list of response to reviewers’ remarks\n(Black italic: Reviewer’s remarks; Blue type: Our response; Yellow highlighted:\nAdditions/modifications to reviewer’s comments in the manuscript)\nReviewer #1 (Remarks to the Author):\nThe authors have made substantial revisions that address the earlier concerns and improve the\nclarity and robustness of the work. In its current form, the manuscript meets the required\nscientific standards and can be considered suitable for publication.\nResponse：\nWe sincerely thank Reviewer #1 for the positive assessment and constructive comments,\nwhich have greatly strengthened the clarity and overall quality of our manuscript.\nReviewer #2 (Remarks to the Author):\nThe authors have addressed all of my comments and improved their manuscript. I am now\nhappy to recommend it for publication.\nResponse：\nWe sincerely thank Reviewer #2 for the positive assessment and constructive comments, which\nhave greatly strengthened the clarity and overall quality of our manuscript.\nReviewer #3 (Remarks to the Author):\n1. The manuscript has been clearly strengthened through the revisions, with constructive\nresponses to the earlier concerns regarding material design and acoustic actuation behavior.\nOne remaining issue concerns the use of the term multimodal deformation. Although the\nauthors suggest that a single architecture exhibits multiple deformation modes, the results\nindicate that bending, rotation, and opening behaviors arise from distinctly different\ngeometries, not from mode switching within a single design. Frequency-dependent modulation\nof bending amplitude does not constitute a change in deformation mode. In soft robotics,\nmultimodal actuation typically implies multiple deformation modes originating from the same\nstructure, for example, bending transitions to rotation, which does not appear to be the case\nhere. To avoid overstating the capability of the actuator, the authors are recommended to\nrevise it.\nResponse 1:\nWe sincerely thank the reviewer for the insightful comments regarding our use of the term\n“multi-modal.” We agree that the original wording may have overstated the capabilities of\nECHObots. In response, we have revised the terminology throughout the manuscript to ensure\naccuracy and consistency. Specifically, we replaced “multi-modal” with more precise and\nneutral terms such as “versatile” when describing deformation behaviors arising from\ndifferent structural or geometric architectures. The detailed revisions are as follows:\nChanges to the manuscript:\nAt Page 4, Line 89, we change the sentence: “ECHObots utilize geometry-tuned cilia that\nharness resonance-induced forces to achieve multimodal deformation, including directional\nbending, controlled rotation, and morphing of complex geometries in a single design.” to\n“ECHObots utilize geometry-tuned cilia that harness resonance-induced forces to achieve\ndiverse deformation behaviors, including directional bending, controlled rotation, and\nmorphing of complex geometries in a single design.”\nAt Page 13, Line 250, we change the sentence: “Refined design of ECHObots enables\nmultimodal manipulation in micro robotics systems” to “Refined design of ECHObots\nenables versatile manipulation in microrobotic systems.”\nAt Page 14, last paragraph to describe Figure 3, we delete the sentence that describe the term\nmulti-model: “We use multi-modal deformation to describe a device that … in opposite\ndirections and undergoing continuous rotation”\nAt Page 14, Line 303, we change the sentence: “This frequency and amplitude resolved\nmultimodal actuation represents a powerful platform for programmable microscale soft\nrobotics.” to “Together, the frequency-selective and the amplitude-dependent deformation\ntuning demonstrate the potential of ECHObots as a programmable platform for microscale\nsoft robotics.”\nAt Page 15, Line 306, we change the sentence: “Multi-modal deformation and structural\ndiversity enabled by compliant mechanisms. Multi-modal deformation is central to the\nversatility of microrobots.” to “Structural diversity in ECHObots enabled by compliant\nmechanisms. Diverse deformation modes are central to the versatility of microrobots.”\nAt Page 16, Line 333, we change the sentence: “The Multi-Segmented Arm design\n(Supplementary Movie 5) further demonstrates the potential for complex morphing and multi-\nmodal transformations.” to “The Multi-Segmented Arm design (Supplementary Movie 5)\nfurther demonstrates the potential for complex morphing and diverse transformation modes.”\nAt Page 17, Line 351, we change the sentence: “These programmable architectures unlock a\nnew level of structural diversity and multi-modal deformation in ECHObots, enabling soft\nrobotic arms that open and close with lifelike motion and multi-segmented structures that\nmorph dynamically to meet the challenge of their environment” to “These programmable\narchitectures unlock a new level of structural diversity and complex deformation in\nECHObots, enabling soft robotic arms that open and close with lifelike motion and multi-\nsegmented structures that morph dynamically to meet the challenge of their environment.”\nAt Page 18, Line 392, we change the sentence: “Programmable, frequency-selective\nmorphing offers a powerful complement to locomotion-focused designs, and integrating\npropulsion strategies—such as cilia arrays or bubble-based thrust—within this deformation\nframework could produce microrobots that combine precise, directed movement with\nversatile, multi-modal shape changes.” to “Programmable, frequency-selective morphing\noffers a powerful complement to locomotion-focused designs, and integrating propulsion\nstrategies, such as cilia arrays or bubble-based thrust within this deformation framework could\nenable microrobots that combine precise, directed movement with versatile shape changes.”\nIn the Supplementary Information, at Page 3, Line 74, we change the sentence: “By contrast,\nthe ECHObots reported here are tuned for low-kilohertz deformation ( 3–9 kHz). By tuning\nlow-frequency deformation, multiple frequencies can be utilized within in this system, such as\na high-frequency channel could be dedicated to propulsion (cilia-band o∼r bubble), while a low-\nfrequency channel independently governs multi-model morphing (bending, rotation, opening,\nand closure)” to “By contrast, the ECHObots reported here are tuned for low-kilohertz\ndeformation ( 3–9 kHz). By tuning low-frequency deformation, multiple frequencies can be\nutilized within in this system, such as a high-frequency channel could be dedicated to\npropulsion (vi∼a cilia-band or bubble actuation), while a low-frequency channel independently\ngoverns diverse morphing, including bending, rotation, opening, and closure”\n2. The additional claim regarding broader applications in Results and Discussion, specifically\nthe statement of strong potential and several examples for minimally invasive medical\napplications, is overstated since the manuscript does not demonstrate clinically relevant tasks\nsuch as navigation in tissue-like environments, selective capture or manipulation of biological\ntargets, or any in-vivo functionality. In the absence of supporting data, this application\nstatement would be improved by focusing on broader conceptual impacts.\nResponse 2:\nWe appreciate the reviewer for this valuable comment. We fully agree that, because the\npresent manuscript focuses on demonstrating the deformation capabilities of ECHObots\nrather than validating clinically relevant tasks, our earlier statements regarding medical\napplications were overly specific. Following the reviewer’s suggestion, we have revised the\nmanuscript by removing overly definitive references to direct biomedical applications and\nreframing these points in terms of broader conceptual implications. The corresponding\nmodifications are listed below.\nChanges to the manuscript:\nAt Page 5, Line 102, we change the sentence: “This versatility positions them for applications\nnot only in non-invasive surgery, targeted drug delivery, and in vitro diagnostics but also in\nmicroscale manufacturing and environmental monitoring.” to “This versatility positions them\nfor potential use not only in biomedical contexts but also in microscale manufacturing and\nenvironmental monitoring.”\nAt Page 5, Line 106, we change the sentence: “The ECHObots utilize acoustic induced\ndeformation to achieve dynamically tunable and responsive soft robotic motion,\ndemonstrating strong potential for minimally invasive medical applications.” to “The\nECHObots utilize acoustic induced deformation to achieve dynamically tunable and\nresponsive soft robotic motion.”\nAt Page 18, Line 395, we change the sentence: “By enabling programmable shape change\nand frequency-addressed control, these systems open new possibilities, from targeted drug\ndelivery to precise manipulation of particles or cells and other dynamic tasks at the\nmicroscale.” to “By enabling programmable shape change and frequency-addressed control, these\nsystems open new possibilities for future microscale manipulation strategies, including\nparticle handling and other dynamic tasks.”\nResponse to Reviews\nItemized list of response to reviewers’ remarks\n(Black italic: Reviewer’s remarks; Blue type: Our response; Yellow highlighted:\nAdditions/modifications to reviewer’s comments in the manuscript)\nReviewer #3 (Remarks to the Author):\nThe authors have revised to address the main concerns and improved the clarity in the\nmanuscript. I recommend the publication.\nResponse：\nWe sincerely thank Reviewer #3 for the positive assessment and constructive comments,\nwhich have greatly strengthened the clarity and overall quality of our manuscript."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have made substantial revisions that address the earlier concerns and improve the clarity and robustness of the work. In its current form, the manuscript meets the required scientific standards and can be considered suitable for publication.", "reviewer_2": "The authors have addressed all of my comments and improved their manuscript. I am now happy to recommend it for publication.", "reviewer_3": "The manuscript has been clearly strengthened through the revisions, with constructive responses to the earlier concerns regarding material design and acoustic actuation behavior. One remaining issue concerns the use of the term multimodal deformation. Although the authors suggest that a single architecture exhibits multiple deformation modes, the results indicate that bending, rotation, and opening behaviors arise from distinctly different geometries, not from mode switching within a single design. Frequency-dependent modulation of bending amplitude does not constitute a change in deformation mode. In soft robotics, multimodal actuation typically implies multiple deformation modes originating from the same structure, for example, bending transitions to rotation, which does not appear to be the case here. To avoid overstating the capability of the actuator, the authors are recommended to revise it. The additional claim regarding broader applications in Results and Discussion, specifically the statement of strong potential and several examples for minimally invasive medical applications, is overstated since the manuscript does not demonstrate clinically relevant tasks such as navigation in tissue-like environments, selective capture or manipulation of biological targets, or any in-vivo functionality. In the absence of supporting data, this application statement would be improved by focusing on broader conceptual impacts."}, "author_response": "Response to Reviews\nItemized list of response to reviewers’ remarks\n(Black italic: Reviewer’s remarks; Blue type: Our response; Yellow highlighted:\nAdditions/modifications to reviewer’s comments in the manuscript)\nReviewer #3 (Remarks to the Author):\n1. The manuscript has been clearly strengthened through the revisions, with constructive\nresponses to the earlier concerns regarding material design and acoustic actuation behavior.\nOne remaining issue concerns the use of the term multimodal deformation. Although the\nauthors suggest that a single architecture exhibits multiple deformation modes, the results\nindicate that bending, rotation, and opening behaviors arise from distinctly different\ngeometries, not from mode switching within a single design. Frequency-dependent modulation\nof bending amplitude does not constitute a change in deformation mode. In soft robotics,\nmultimodal actuation typically implies multiple deformation modes originating from the same\nstructure, for example, bending transitions to rotation, which does not appear to be the case\nhere. To avoid overstating the capability of the actuator, the authors are recommended to\nrevise it.\nResponse 1:\nWe sincerely thank the reviewer for the insightful comments regarding our use of the term\n“multi-modal.” We agree that the original wording may have overstated the capabilities of\nECHObots. In response, we have revised the terminology throughout the manuscript to ensure\naccuracy and consistency. Specifically, we replaced “multi-modal” with more precise and\nneutral terms such as “versatile” when describing deformation behaviors arising from\ndifferent structural or geometric architectures. The detailed revisions are as follows:\nChanges to the manuscript:\nAt Page 4, Line 89, we change the sentence: “ECHObots utilize geometry-tuned cilia that\nharness resonance-induced forces to achieve multimodal deformation, including directional\nbending, controlled rotation, and morphing of complex geometries in a single design.” to\n“ECHObots utilize geometry-tuned cilia that harness resonance-induced forces to achieve\ndiverse deformation behaviors, including directional bending, controlled rotation, and\nmorphing of complex geometries in a single design.”\nAt Page 13, Line 250, we change the sentence: “Refined design of ECHObots enables\nmultimodal manipulation in micro robotics systems” to “Refined design of ECHObots\nenables versatile manipulation in microrobotic systems.”\nAt Page 14, last paragraph to describe Figure 3, we delete the sentence that describe the term\nmulti-model: “We use multi-modal deformation to describe a device that … in opposite\ndirections and undergoing continuous rotation”\nAt Page 14, Line 303, we change the sentence: “This frequency and amplitude resolved\nmultimodal actuation represents a powerful platform for programmable microscale soft\nrobotics.” to “Together, the frequency-selective and the amplitude-dependent deformation\ntuning demonstrate the potential of ECHObots as a programmable platform for microscale\nsoft robotics.”\nAt Page 15, Line 306, we change the sentence: “Multi-modal deformation and structural\ndiversity enabled by compliant mechanisms. Multi-modal deformation is central to the\nversatility of microrobots.” to “Structural diversity in ECHObots enabled by compliant\nmechanisms. Diverse deformation modes are central to the versatility of microrobots.”\nAt Page 16, Line 333, we change the sentence: “The Multi-Segmented Arm design\n(Supplementary Movie 5) further demonstrates the potential for complex morphing and multi-\nmodal transformations.” to “The Multi-Segmented Arm design (Supplementary Movie 5)\nfurther demonstrates the potential for complex morphing and diverse transformation modes.”\nAt Page 17, Line 351, we change the sentence: “These programmable architectures unlock a\nnew level of structural diversity and multi-modal deformation in ECHObots, enabling soft\nrobotic arms that open and close with lifelike motion and multi-segmented structures that\nmorph dynamically to meet the challenge of their environment” to “These programmable\narchitectures unlock a new level of structural diversity and complex deformation in\nECHObots, enabling soft robotic arms that open and close with lifelike motion and multi-\nsegmented structures that morph dynamically to meet the challenge of their environment.”\nAt Page 18, Line 392, we change the sentence: “Programmable, frequency-selective\nmorphing offers a powerful complement to locomotion-focused designs, and integrating\npropulsion strategies—such as cilia arrays or bubble-based thrust—within this deformation\nframework could produce microrobots that combine precise, directed movement with\nversatile, multi-modal shape changes.” to “Programmable, frequency-selective morphing\noffers a powerful complement to locomotion-focused designs, and integrating propulsion\nstrategies, such as cilia arrays or bubble-based thrust within this deformation framework could\nenable microrobots that combine precise, directed movement with versatile shape changes.”\nIn the Supplementary Information, at Page 3, Line 74, we change the sentence: “By contrast,\nthe ECHObots reported here are tuned for low-kilohertz deformation ( 3–9 kHz). By tuning\nlow-frequency deformation, multiple frequencies can be utilized within in this system, such as\na high-frequency channel could be dedicated to propulsion (cilia-band o∼r bubble), while a low-\nfrequency channel independently governs multi-model morphing (bending, rotation, opening,\nand closure)” to “By contrast, the ECHObots reported here are tuned for low-kilohertz\ndeformation ( 3–9 kHz). By tuning low-frequency deformation, multiple frequencies can be\nutilized within in this system, such as a high-frequency channel could be dedicated to\npropulsion (vi∼a cilia-band or bubble actuation), while a low-frequency channel independently\ngoverns diverse morphing, including bending, rotation, opening, and closure”\n2. The additional claim regarding broader applications in Results and Discussion, specifically\nthe statement of strong potential and several examples for minimally invasive medical\napplications, is overstated since the manuscript does not demonstrate clinically relevant tasks\nsuch as navigation in tissue-like environments, selective capture or manipulation of biological\ntargets, or any in-vivo functionality. In the absence of supporting data, this application\nstatement would be improved by focusing on broader conceptual impacts.\nResponse 2:\nWe appreciate the reviewer for this valuable comment. We fully agree that, because the\npresent manuscript focuses on demonstrating the deformation capabilities of ECHObots\nrather than validating clinically relevant tasks, our earlier statements regarding medical\napplications were overly specific. Following the reviewer’s suggestion, we have revised the\nmanuscript by removing overly definitive references to direct biomedical applications and\nreframing these points in terms of broader conceptual implications. The corresponding\nmodifications are listed below.\nChanges to the manuscript:\nAt Page 5, Line 102, we change the sentence: “This versatility positions them for applications\nnot only in non-invasive surgery, targeted drug delivery, and in vitro diagnostics but also in\nmicroscale manufacturing and environmental monitoring.” to “This versatility positions them\nfor potential use not only in biomedical contexts but also in microscale manufacturing and\nenvironmental monitoring.”\nAt Page 5, Line 106, we change the sentence: “The ECHObots utilize acoustic induced\ndeformation to achieve dynamically tunable and responsive soft robotic motion,\ndemonstrating strong potential for minimally invasive medical applications.” to “The\nECHObots utilize acoustic induced deformation to achieve dynamically tunable and\nresponsive soft robotic motion.”\nAt Page 18, Line 395, we change the sentence: “By enabling programmable shape change\nand frequency-addressed control, these systems open new possibilities, from targeted drug\ndelivery to precise manipulation of particles or cells and other dynamic tasks at the\nmicroscale.” to “By enabling programmable shape change and frequency-addressed control, these\nsystems open new possibilities for future microscale manipulation strategies, including\nparticle handling and other dynamic tasks.”\nResponse to Reviews\nItemized list of response to reviewers’ remarks\n(Black italic: Reviewer’s remarks; Blue type: Our response; Yellow highlighted:\nAdditions/modifications to reviewer’s comments in the manuscript)\nReviewer #3 (Remarks to the Author):\nThe authors have revised to address the main concerns and improved the clarity in the\nmanuscript. I recommend the publication.\nResponse：\nWe sincerely thank Reviewer #3 for the positive assessment and constructive comments,\nwhich have greatly strengthened the clarity and overall quality of our manuscript."}, {"round": 3, "reviewer_comments": {"reviewer_3": "The authors have revised to address the main concerns and improved the clarity in the manuscript. I recommend the publication."}, "author_response": "Response to Reviews\nItemized list of response to reviewers’ remarks\n(Black italic: Reviewer’s remarks; Blue type: Our response; Yellow highlighted:\nAdditions/modifications to reviewer’s comments in the manuscript)\nReviewer #3 (Remarks to the Author):\nThe authors have revised to address the main concerns and improved the clarity in the\nmanuscript. I recommend the publication.\nResponse：\nWe sincerely thank Reviewer #3 for the positive assessment and constructive comments,\nwhich have greatly strengthened the clarity and overall quality of our manuscript."}]

Decision letter