Magnetically actuated momentum-driven millirobots

Domain: chemistry
Published: 2025-12-27
Editorial outcome: major_revision

Abstract
Designing millirobots capable of navigating high-friction environments remains a significant challenge due to limitations in force output and the absence of efficient transmission mechanisms at small scales. In this study, we introduce a magnetically inner actuated millirobot capable of generating a thrust force exceeding 15 N with a body weight of 5.82 g for moving across diverse frictional terrains. The inner-actuated millirobot features a dual-coil array positioned at each end of a plastic skeleton and a permanent magnet accommodated in the center channel of the body. When powered by a 0.5 A current, the internal magnetic interaction propel the magnet to a velocity of 2.10 m/s within 17 ms, striking the end wall to produce a powerful instantaneous thrust that overcomes friction forces. Experimental results demonstrate the millirobot’s ability to operate in viscous oil, traverse sand and granular media, and transport cargo exceeding 300 times its body weight. Furthermore, the magnetically inner actuated millirobot shows promising potential for accessing confined tubular environments. This magnetically inner-actuated design, leveraging momentum conservation for propulsion, enables millirobots with high force capacity for high-friction and confined-space applications.

Introduction
Millirobots exhibit remarkable capabilities in navigating challenging and hazardous environments, such as subterranean spaces, disaster sites, and tubular structures. Recent advances in miniature robotics have enabled a range of applications, including wall-climbing1–3, pipeline inspection4, drug delivery5,6, deep-sea inspection7 and cargo transportation8,9. However, due to the scaling effect, current millirobots face limitations in force and energy output at small scales (e.g., less than 10 cm in length and 10 g in mass), which constrain their broad applicability. Developing a millirobot capable of generating sufficient force and energy remains challenging but is crucial for expanding their use in high-friction environments and confined spaces10.

Various efforts have been made to improve the load-bearing capacity of millirobots11,12. For example, hydraulically amplified self-healing electrostatic actuators have demonstrated the ability to lift over 200 times their weight13. In addition, 3D-printed pneumatic actuators have demonstrated the ability to lift cargo weighting more than hundreds of times their own body weight14. Moreover, reconfigurable modular robots have been built by attaching magnetic units to a plastic robot frame to deliver the cargo of various shapes15. However, achieving effective locomotion with a high load-to-weight ratio remains unsolved due to significant friction forces. Although several millirobots demonstrated impressive cargo delivery capabilities on the ground16,17, most actuation mechanisms restrict their movement to wide, flat terrains and fail to adapt to high-resistance environments, particularly when robots are tested in confined spaces like granular medium and collapsed tubular structures.

High-friction environments, such as viscous oil, subterranean mediums, and rough ground, are challenging for millirobotic navigation. Several actuation mechanisms have been proposed to address these challenges. For example, flagella-inspired millirobots have demonstrated locomotion in viscous environments18. The explosion and jumping actuation in granular media were demonstrated using a magnetic phase-change actuator19. In addition, pneumatic-driven expanding robots have been designed for operation in granular environments20. These studies succeeded in overcoming high friction forces in specific environments. However, a universal design and actuation mechanism capable of generating sufficient force for traveling through diverse high-friction terrains remains undeveloped.

To enhance the thrust force of magnetic systems, propulsion mechanisms based on the principle of momentum conservation have proven to be effective. Typically, magnetic robots driven by the magnetic field gradients are limited in their ability to achieve high force output for tissue penetration. To address this limitation, researchers have developed a magnetic hammer actuation system, which employs an MRI system to accelerate a magnet, generating large impulse forces upon impact with the robot frame21. Similarly, a pulse-actuated collision robot has been introduced to overcome the force limitations of magnetic robotic surgery, and this robot has been demonstrated in biological tissue suturing applications10. After that, researchers developed a triple-magnet system to improve the thrust force. By adjusting the orientation of the external magnet, the Newton-level forces through the attraction between embedded magnets were achieved for potential applications in tissue biopsy22. While the pulse impact mechanism has significantly improved actuation force, these systems remain limited by their small working range due to reliance on a fixed external magnetic source. They also suffer from high power consumption, as the magnetic actuation force decreases inversely with the fourth power of the distance between the robot and the magnetic source23.

To address the aforementioned limitations, we propose a magnetically inner-actuated millirobot (MiaBot) with integrated actuation coils and a magnet. As depicted in Fig. 1A, the millirobot consists of an inner permanent magnet, a tube frame to accommodate the magnet, two stoppers to limit the stroke, and two electromagnetic coils positioned at either end with opposite winding directions. To build the MiaBot, the plastic frame with a central channel is first made of polyetheretherketone (PEEK) by 3D printing and polishing to minimize the friction, from K&J Ltd.) is embedded within the center channel for inner actuation. After that, two stoppers are attached to the two ends of the robot frame using super glue. The resulting MiaBot is lightweight (5.82 g) and compact (+12 mm × 32 mm). The Detailed design principles, assembly process and dimensions of components are summarized in Supplementary Fig. S1.

When the MiaBot is driven by a square wave ranging from 0.5 A to −0.05 A. Figure 1C depicts the snapshots of the inner magnet and MiaBot during one cycle actuation. During propulsion, the magnet traverses the central channel in 14 ms, generating a strong impact force that propels the MiaBot forward. For the reposition process, the impact force is insufficient to overcome static friction, preventing backward displacement. Figure 1D demonstrates that the magnet can pass through the center channel of the robot frame within 20 ms, causing a theoretical thrust of up to 19.01 N. By leveraging local magnetic field actuation and momentum conservation, the robot overcomes substantial environmental resistance to perform challenging tasks, including navigation through granular media, operation in high-viscosity silicone oil, and cargo transport exceeding 300 times its weight (Fig. 1E). Figure 1B compares MiaBot’s load-carrying capability with that of state-of-the-art millirobots (weighing less than 10 grams) using various actuation mechanisms, including shape memory alloy24–26, dielectric elastomer actuators27–30, piezoelectric actuators31–34, magnetic robots17,35–39, and photothermal actuators40–43. Moreover, we also compare the loading performance with natural creatures like insects and mammals (data in Supplementary Tables S2 and S3). The results show that MiaBot outperforms most miniature robots and surpasses the majority of natural creatures, falling short only of beetles.

In summary, MiaBot, which utilizes local magnetic field actuation and a momentum conservation-based propulsion mechanism, offers three advantages: (1) Lightweight and compact design: The simple energy conversion mechanism eliminates the need for complex transmission components such as gears and bearings. (2) Unrestricted workspace: By integrating electromagnetic coils and a magnet, MiaBot operates with a self-contained actuation system without relying on external magnetic sources that confines the workspace. (3) High force and payload capacity: The rapid movement of the internal magnet generates a powerful inertial impact, enabling operation in high-friction environments. Overall, MiaBot advances the design of next-generation millirobots with a large force output for applications in high-friction environments and confined spaces.

Results
Robot actuation mechanism and kinematic characterization
The actuation coils are placed symmetrically at each end of the millirobot frame and are wound in opposite directions. This configuration allows the same magnetic pole (either north or south) to face inward when supplied with the same current, resulting in the same actuation force on the magnet by the left and right coils (e.g., left repulsion/right attraction or left attraction/right repulsion, as shown in Fig. 1D). When an electric current is applied to the electromagnetic coils, the theoretical magnetic force on the inner magnet at any given position along the center axis is calculated by

F z=∇ m·B z (1)

where m represents the magnetic moment of the sliding magnet. The calibration of m is shown in Supplementary Fig. S2. B z is the overall magnetic field generated by two coils. The overall magnetic field generated by the left coil set and right coil set can be expressed as

B z= 2L w μ 0 n l n t I Z 0 Lw Z R 1 R 2 B @(z−l) R 2 2 +R2 1.5 − L c − L w+l R 2 z 2+R2 1.5 C AdRdl (2)

where μ 0 is the vacuum permeability, n l is the coil’s turns of each layer, n t is the layer number of the coil, I is the input current, R 1 and R 2 are the inner and outer radius of the coil, z is the distance from the calculated point to the end of the coil, L C is the length of the center channel, L w is the width of a coil set R is the radius of the integral coil and l represents the distance from the end of the coil to the center of the integral coil loop. A detailed distribution of the magnetic field generated by the coils is shown in Supplementary Fig. S3, and the calculated interaction force between the coils and the magnet can be referred to Supplementary Fig. S4.

To sustain continuous locomotion, the MiaBot is actuated using a square wave with a bias current as the input signal. The polarity with a larger amplitude (denoted as I l) is used to actuate the inner magnet, serving as the primary contributor to MiaBot’s locomotion. Meanwhile, the opposite polarity with a smaller amplitude (denoted as I s) repositions the magnet, ensuring periodic and continuous movement. The resulting actuation force by I s is carefully controlled to reposition the inner magnet while minimizing the impact force to remain below the static friction force to avoid unwanted cancellation of the positive movement. Accordingly, I s is set to −0.05 A in this paper unless otherwise stated in the following experiments. This paper focuses on investigating the effect of I l and input frequency on MiaBot’s locomotion, as they are the primary factors influencing robot displacement.

The MiaBot is observed to have two distinct locomotion modes as the load increases with the input current. As illustrated in Fig. 2A, when MiaBot carries no load, the attraction force between the magnet and the coils dominates its locomotion. The reason is that the static friction between the robot frame and the ground is insufficient to counteract the attraction force, causing the magnet and the frame to move toward each other. Conversely, when carrying a heavy load, the inertial impact force of the magnet becomes the primary factor on the robot’s locomotion, resulting in a consistent movement direction for both the inner magnet and the robot frame. In addition, a critical region emerges where locomotion exhibits directional instability as environmental resistance approaches the magnetic actuation force. Within this region, the system oscillatory motion or unsteady swaying rather than stable unidirectional movement. Fig. S5 provides signal selection guidelines to avoid this unstable operational zone across varying environments. Then, we test input currents I l ranging from 0.1 A to 0.5 A and loads from 0 g to 100 g, as illustrated in Fig. 2B. The results indicate that the attraction-dominated region occurs only when the load is below 40 g. The MiaBot offers distinct advantages in these two modes. When the attraction force dominates, the MiaBot achieves a large displacement and high speed. In contrast, when the inertial force dominates, the robot generates a significant instantaneous output force, enabling MiaBot to operate in high-frictional environments (The locomotion process of this locomotion mode is shown in Fig. S6).

To study the kinematics and increase the actuation power, we develop a theoretical model to optimize the design parameters of center channel length (L c) and the wideness of the actuation coil set (L w) simultaneously. A longer L c can increase the magnet’s acceleration time, resulting in a more significant impacting force. However, if the channel length is excessively long, the pair of coils are separated too far apart, leading to a diminished magnetic gradient for driving the inner magnet. A narrow yet thick coil set yields a strong magnetic field nearby, but the magnetic field strength decreases in the near-central region. In contrast, wide and flat coils enhance the magnetic density near the central area while reducing the density near the coil. Given a constant input of 1.0 A, Fig. 2C explores the effect of L c ranging from 20 mm to 35 mm, and L w ranging from 3 mm to 8 mm on the inertial impact speed of the magnet. The optimal configuration yields an impressive impact velocity of the magnet at 3.11 m/s. As expected, the impact speed demonstrates an increased trend with the length of the channel. However, this rate of increase gradually diminishes once the length reaches 30 mm, with only a marginal 0.36% increase observed between 30 mm and 35 mm. Based on these results, and to simplify the design, a coil width of 5 mm and a channel length of 30 mm were selected as the design parameters for the MiaBot in the following work.

To validate the simulation results, we experimentally measured the travel time of the inner magnet with varied coil set widths and input currents ranging from 0.1 A to 1.0 A. As shown in Fig. 2D, the experimental results align with the simulation and confirm that the robot with a 5 mm coil set propel the magnet faster than those with 3 mm and 8 mm wide coils. Moreover, the results indicate that the magnet can pass the center channel in a short time. Specifically, with an input current of 0.1 A, the inner magnet traverses the center channel in less than 50 ms, while at 1.0 A, the time reduces to under 15 ms. We also observed that only minor fluctuations occurred when the coil width varied between 4 mm and 6 mm (Supplementary Fig. S7), indicating that manual coil set wiring is a viable fabrication method for the MiaBot. Subsequently, we calculated the velocity of the inner magnet before impacting under the input currents ranging from 0.1 A to 1.0 A (Fig. 2E). The results show that the inner magnet passes through the center channel at high speed. Specifically, the theoretical impact speed increases from 0.98 m/s to 3.10 m/s as the input current is increased from 0.1 A to 1.0 A. The measured results indicate that the magnet takes longer to traverse the channel and impacts at a lower speed (0.98 m/s and 2.93 m/s by 0.1 A and 1.0 A excitation, respectively) than predicted by the simulation. This discrepancy among experimental measurements can be attributed to the neglect of friction between the inner magnet and the frame in the simulation and the idealized assumption of perfect alignment between the magnet’s axis and the coil axis. With the optimized design parameters, the velocity of the unloaded MiaBot was measured at frequencies from 1 Hz to 15 Hz (with I l=0.5 A) as depicted in Fig. 2F. The results demonstrate that MiaBot can reach a maximum speed of 113.66 mm/s, equal to 3.55 body length per second, at a frequency of 9 Hz.

In addition to the current input and the design parameters of the robot frame, the size of the magnet significantly influences the dynamic performance of MiaBot. The scalability of the magnet in terms of diameter and length is examined in Supplementary Fig. S8. This analysis assumes a consistent gap between the magnet and the frame and a consistent traveling distance of the magnet. The results indicate that an increase in diameter leads to a decrease in impact velocity but an increase in impact energy. However, the impact energy initially increases and then decreases with the length of the magnet because a longer central channel always comes along with a smaller magnetic field gradient. In addition, MiaBot’s efficiency decreases as the input current increases. At the efficiency is 10.41% when the input current is 0.1 A, which declines to 6.32% as the input current increased to 0.5 A. The thermal effects and actuation efficiency of MiaBot are presented in Fig. S9. Following 300 seconds of actuation, the temperature rises by less than 5 °C with an input current of 0.1 A, while reaching 48 °C at 0.5 A. This temperature regime neither damages the robot’s frame material nor alters the permanent magnets’ magnetic properties. However, to ensure the thermal stability of the enamel insulation on the copper winding, continuous operation exceeding 300 s is not recommended, as prolonged thermal loading may degrade the insulation’s performance and compromise winding reliability. As a result, the 0.5 A was selected as the input current (I l) in the following experiments unless otherwise stated.

Inertial impact force and loading performance
To quantify the powerful inertial impact force, a high-frequency force sensor was employed to measure the thrust force. The description and specifications of the measuring setup can be referred to Supplementary Fig. S10A and Fig. S10B. The measurement was repeated ten times with input currents ranging from 0.2 A to 0.6 A with increments of 0.05 A. The resulting average impact forces and their corresponding standard deviations for robots with coil sets wide of 3 mm, 5 mm, and 8 mm are illustrated in Fig. 3A. The experimental results indicate that the MiaBot with a coil set wide of 5 mm exhibits the strongest impact among the different configurations. At an input current of 0.2 A, the average impact force measures 8.42 N, which increases to 16.67 N when the input current reaches 0.6 A. Although the impact force is slightly lower when coil set wides are 3 mm and 8 mm, it remains consistently above 13 N. Figure 3B showcases the repeatability of the impacting behaviors of MiaBot, where the forward actuation current (I l) is set between 0.2 A and 0.6 A, while the backward current (I s) remains constant at 0.05 A. The actuation frequency is set at 2 Hz for one minute to evaluate the impact performance. The variance in impact force measurements is attributed to the ultra-short impact duration (typically less than 1 ms) between rigid bodies (magnet and robot stopper), which may introduce measurement errors in the force sensor.

The force of inertial impact is also affected by the material of the end cover. We compare the impact force using end covers made of different materials, including silicon, plastic, and metal (Shown in Supplementary Fig. S10C). The results show that the robot with a silicon cover can significantly reduce the impact force because most energy can be absorbed by the silicon cover. The aluminum end cover delivers the highest impact force, and the PLA cover is slightly inferior to the aluminum cover. Finally, the 3-D printed PLA cover is utilized as the stopper because of its convenience and cost-effectiveness in fabricating. We then tested its reliability and durability by up to 10,000 impacts (Supplementary Fig. S10D). No significant changes in the permanent magnet’s magnetic properties or physical appearance were observed after 10,000 impacts with an input current of 0.5 A, indicating the magnet can maintain a high and stable thrust force output under prolonged usage.

The high-impact force of the design empowers MiaBot with a strong loading capability. Firstly, we investigated the locomotion performance of the robot with a load of 500 g (85.91 times its body weight). The quantitative investigation was conducted by applying a square wave signal with frequencies ranging from 1 Hz to 35 Hz, along with an I l of 0.5 A. As shown in Fig. 3C, the optimal actuation frequency is dependent on the magnitude of the input current. Overall, the velocity increases with the applied frequency during the initial stage (below 10 Hz) because more impacting and locomotion cycles occur in a fixed period. As the frequency increases, a decline in the velocity occurs due to the frequent backward impacting process, which plays a role in canceling the forward motion. In the third stage, the velocity rises again as the applied frequency increases because the inner magnet does not have sufficient time to contact and impact the back stopper, thus preventing the cancellation of the robot’s forward motion. However, this upward trend is confined by an upper limit that can restrict the forward acceleration distance, resulting in reduced impact velocity and final impact force output. Detailed analysis and optimal selection of the input frequency can be found in Supplementary Fig. S11. As shown in Supplementary Fig. S11, we repeated experiments using I l ranging from 0.3 A to 0.6 A. The four stages of frequency response are observed in all tested currents, and the most favorable choices of the driving currents converge around 25 Hz. Therefore, the optimized 25 Hz is set as the input frequency in the following experiments unless otherwise stated.

The locomotion performance with high loading capacity was subsequently assessed on a polymethyl methacrylate plate with the actuation frequency at the optimized frequency, i.e., 25 Hz (Fig. 3D). The results reveal a decrease in moving speed as the load increases from 100 g to 1000 g. With a load of 100 g, the millirobot achieves an average velocity of 618.74 mm/min. The speed decreases to 67.3 mm/min when the payload increases to 1000 g (171.82 times its body weight). We calculate energy loss as the input energy minus the load kinetic energy, defining the loss rate as this deficit relative to the input energy. The results in Fig. 3D show the loss rate increases under heavier loads due to the enhanced robot-ground contact, which creates additional friction and results in greater frictional loss.

To investigate the robot’s locomotion capability on different surfaces, we tested the MiaBot carrying 250 g of cargo on various surfaces. Figure 3E demonstrates the locomotion speed of MiaBot on various sandpapers, with insets showing physical images (5x magnification) of four different roughness levels (i.e., 180 mesh, 400 mesh, 800 mesh, and 1000 mesh). The results show MiaBot maintains high payload capacity on rough surfaces, whereas faster locomotion occurs on smoother surfaces. In addition, we observed that velocity variance increases with surface roughness, which was attributed to irregular particulate protrusions that induce unstable friction forces on the robot. Furthermore, to assess the locomotion reliability, the millirobot with a 500 g payload is tested on various surfaces such as metal, plastic, fabric, and wood (Fig. 3F, Video 1). The results prove that the millirobot is capable of carrying a heavy payload to move at a speed constantly above 110 mm/min on variety rigid surfaces. The mean cost of transportation is 178.1 (detailed data and definition is shown in Fig. S9C), which is relatively low for miniature robots of the comparable weight32,44. We observed that MiaBot’s load-bearing capacity significantly decreases on flexible surfaces due to energy absorption by surface deformation and increased adhesion. As indicated by the small error bar in Fig. 3F, the locomotion is stable across most substrates, particularly on smooth surfaces that are not adhesive, such as fabric, wood, Teflon, and polyethylene. The snapshots of the robot moving on different surfaces are shown in Supplementary Fig. S12.

Locomotion steerability
Bi-directional control is a highly desirable feature for miniaturized robots to complete point-to-point transportation tasks or navigate in confined environments (e.g., biological tubular organs or pipelines). In this study, the bi-directional control of the millirobot can be achieved by simply reversing the biased direction of the input signal (i.e., square wave). The snapshots in Fig. 4A (i) reveal that the MiaBot can move back to the initial position after one minute of forward and then one minute of backward locomotion. The experiments were conducted using different bias currents and repeated ten times. Figure 4A (ii) shows the real-time displacement of the MiaBot. The results show that the MiaBot can return to its initial position under various current inputs. The distance between the final positions and the starting points is less than 5 mm, demonstrating that the MiaBot exhibits simple but high-precision directional control capabilities.

Maintaining a straight trajectory with heavy cargo by a single actuator-based robot is challenging, as misaligning the center of mass can create unwanted torque to disrupt locomotion. Full directional maneuverability is also essential for millirobots to perform complex tasks, such as trajectory following and navigating unstructured environments. In this study, the full-orientation adjustment is achieved by assembling two individual actuation units in parallel, and each of them can be controlled independently. The control system of the parallel units is illustrated in Supplementary Fig. S13. To evaluate MiaBot’s directional maneuverability, we compared two strategies in Fig. 4B. Figure 4B (i) shows the conventional turning strategy commonly adopted by those actuators without bi-directional control capability. We can also use this method by activating one of the actuators. In this way, the turning radius can be adjusted by varying the input frequency and current of the active actuator. In contrast, Fig. 4B (ii) demonstrates MiaBot’s ability to perform in-place turning by simultaneously controlling both actuators with opposite input signals, which allows the MiaBot to be deployed in more confined spaces.

To quantitatively evaluate the maneuverability, the millirobot was tested to turn 180° on a polyvinyl chloride plate carrying payloads of 70 grams (Fig. 4C) and 500 grams of payload (Supplementary Movie 2). In Fig. 4C (i), we compare the time cost for turning under two strategies: conventional single-side actuation and the proposed synergy actuation. Experimental results show that the in-place turning mode achieves approximately 1.5 times higher turning efficiency than the conventional mode. Figure 4 (ii) evaluates the drift of the robot’s center during the 180° turn. The input current (I l) is kept at the same level of 0.5 A. Under conventional mode, the robot exhibits a significant drift of 361.12 mm, whereas synergy actuation reduces this drift to just 9.44 mm. The highly efficient, low-drift turning capability enabled by the proposed in-place turning control is useful for delivering heavy cargo in confined spaces.

To evaluate the trajectory-following capability, we conduct experiments by controlling the millirobot to follow a Z-shaped trajectory, including horizontal, vertical, left-turn, and right-turn tracks, using an open-loop control scheme. The input current for the left and right actuators is illustrated in Fig. 4D (i). Initially, both actuators are operated with positive bias currents to move horizontally. As the robot approaches the left turn corner, the bias current of the left actuator is switched to a negative direction. In the subsequent vertical locomotion stage, both actuators’ bias currents return to positive. During the right-turning process, the bias current of the right actuator is switched to the negative direction. Finally, the robot completes another horizontal locomotion stage using the same input current as the first stage. The process of the robot moving following the Z-shaped trajectory is shown in Fig. 4D (ii) and Supplementary Movie 3.

Locomotion in high frictional terrains
In this section, we present a series of experiments to demonstrate MiaBot’s locomotion capability on various terrains to overcome the high friction force. The demonstrated challenging tasks include transportation of heavy cargoes (Fig. 5A and Supplementary Movie 4), locomotion in viscous liquid (Fig. 5B and Supplementary Movie 5), operation in granular mediums (Fig. 5C, D and Supplementary Movie 6, 7), and drilling out through natural sand from a depth exceeding 100 mm (Supplementary Movie 8).

To optimize the performance of MiaBot in a liquid environment, slanted fins pointing backward were integrated into the millirobot to increase the drag force and improve locomotion efficiency. In contrast, a smooth surface was designed on MiaBot to minimize friction when traversing within granular media. In addition, all the tested millirobots were equipped with conical heads to reduce the resistance drag force between the robot and the surrounding media.

Figure 5A shows that the MiaBot is capable of carrying an 1800 g (309.28 times the robot’s body weight) payload on a wooden surface. To the best of our knowledge, this work achieves a load-to-weight ratio exceeding 300 for a miniature robot, a performance that has not been previously reported. Theoretically, MiaBot could achieve a higher load-to-weight ratio as the impact force is higher than the static friction force between MiaBot and the ground (Supplementary Fig. S14). We only test 1800 g here as a proof of concept to verify the capability of navigating in a high-friction environment. As a universal design for high-friction environments, the MiaBot was also tested in a tank containing high-viscosity silicone oil (1000 cSt) (Fig. 5B). Despite the intermittent backward tendencies during the oscillating impact process, the presence of slanted fins effectively counteracts any backward movement owing to their greater resistance in the backward direction. The optimization design of slanted fins was proved through simulation, and the steerability of MiaBot is demonstrated with the assistant of an external magnetic field (Supplementary Fig. S15). The findings suggest that the MiaBot holds the potential for applications in viscous environments (e.g., in crude oil pipelines). The MiaBot was also tested to traverse within a granular medium such as ceramic particles (diameter: 0.5 mm − 1.0 mm), as shown in Fig. 5C. A red flag was attached to the robot for demonstration purposes. Eventually, the robot emerged from the medium owing to the asymmetric resistance between its bottom and top surrounding environment (17). To simulate a natural environment, the robot was then tested underground amidst soil, sand, ceramic particles, and plants, as depicted in Fig. 5D. The results demonstrate the capability to navigate through various complex environments. Furthermore, the MiaBot’s climbing performance was evaluated under high-friction conditions, including ascending steep 10° inclines and traversing gravel-filled environments with depths exceeding 100 mm (Supplementary Fig. S16 and Supplementary Movie 8).

Potential applications of MiaBot in flexible tube inspection
Regular inspection and maintenance of small-diameter pipelines in high-end equipment, particularly for detecting internal blockages and cracks, are critical to operational efficiency and safety. However, traditional endoscopic probes cannot navigate deep tortuous segments, whereas the proposed MiaBot demonstrates high efficacy in traversing these constrained environments despite gravitational loads and wall pressures. As illustrated in Fig. 6A, small robots face significant challenges in overcoming high-friction environments when the flexible tube walls press against them. For the proposed MiaBot, the internal magnet achieves a speed of 2.93 m/s under the influence of the inner actuation force generated by a 0.5 A input current. The instantaneous propulsion force resulting from collisions enables the MiaBot to overcome frictional resistance, facilitating its locomotion within flexible tubular environments. Vertical and three-dimensional tubular navigation poses significant challenges for millirobots, as their limited actuation force often fails to overcome the resistance from high friction and gravitational effects. This typically results in downward sliding and insufficient upward mobility. However, the spatially distributed complex tubing systems are widely employed in high-end equipment for gas-liquid transportation. To enable the deployment in such environments, we implemented the MiaBot with a resistance regulation strategy in the flexible tubes. The system’s strong instantaneous propulsion enables MiaBot to achieve rapid motion against both gravity and pipeline friction. In the experiment, MiaBot successfully navigated through a 60 cm vertical pipeline in 60 s with a 10 Hz square wave driving signal at +0.5 A forward and −0.05 A reverse (see Fig. 6B and Supplementary Movie 9). For equivalent-length three-dimensional spatial navigation, the robot required approximately 100 s (Fig. 6C), with this delay attributed to high frontal resistance from the narrow inner surface of the silicone tube. In addition, Fig. 6D and Supplementary Movie 10 present the process of the MiaBot navigating through a narrow silicone tube environment with an integrated camera. Experimental results demonstrate that the MiaBot successfully traverses a 680 mm silicone tube with straight and curved trajectories in under 200 s. Insets in Fig. 6D highlight the narrow and deformable nature of the silicone tube, which tightly envelopes the robot. With the compact camera, the MiaBot has the potential for applications in pipeline inspection. Figure 6E illustrates the inspection process, with the top images (Fig. 6E (i)) showing the MiaBot’s position via external views, while the bottom photos (Fig. 6E (ii)) display corresponding inspection results captured by the onboard camera. Moreover, the robot’s real-time position can be tracked using a magnetic tracking system (Supplementary Fig. S16), demonstrating the potential of closed-loop control for precise navigation. This is particularly useful for performing tasks at designated locations in tubular environments without an external line of sight. The demonstration indicates that MiaBot has the potential to detect and location the defects in industrial pipeline systems.

Methods
Materials for fabricating the MiaBot
Magnet: The permanent magnet used in MiaBot is made of NdFeB, Grade N52 (K&J Magnetics, Inc., USA). The cylindrical magnet is used in this paper with an overall dimension of 6.35 mm in diameter and 6.35 mm in thickness. The surface field of the magnet is 6619 Gauss. The calibration process of the magnetic moment is available in supplementary materials (Supplementary Fig. S2). The skeleton used for housing the permanent magnet and mounting the electromagnetic coil is Polyetheretherketone (PEEK), which is machined with a center channel of 6.5 mm for passing through the magnet. The PEEK has the properties of a smooth surface and high-temperature resistance (260° for long-time operating). Two end covers are printed by a commercial FDM printer (Method, MakerBot Inc., USA). The filament is made of Polylactic acid (precision material, Method series). And the printed layer thickness layer is 0.06 mm. The end cover is firmly attached to the frame using super glue (Loctite® 406). The wire for forming the electromagnetic coil is an enamel-insulated wire with a diameter of 0.15 mm. The copper wire has the properties of good conductivity and flexibility (Baoling Jiang Shu, China).

Signal-generating and validation
A three-channel wave generator is used to generate the desired signal (FY8300, FeelElec Inc., China). The three channels can provide any waveforms according to the generating commands and can be independently controlled. The controllable parameters include frequency, duty cycle, bias voltage, etc. The generated wave is then amplified to a suitable voltage via an amplifier with a limited voltage of 50 V and a current of 4 A (PS-LG504, HuNan PaiSheng Elegance Technology CO., LTD). On the one hand, the output voltage is connected to the MiaBot to drive the robot. On the other hand, the real-time current is also monitored by an oscilloscope (TBS 1102C, Tektronix) to determine whether the waveform meets the driving requirements.

Acceleration time of the permanent magnet
The acceleration time of the permanent magnet from one end of the center channel to the other is reflected by a high-speed camera (pco. dimax S4, PCO.). The high-speed camera can record videos at 4500 fps with 1008 × 1008 pixels.

Impact force measurement
A piezoelectric force sensor is applied to measure the impact force of the permanent magnet (1051V1, DYTRAN, USA). The sensor can measure the force up to 10 Lb with a frequency of 50 kHz. The measured signals are then stored in a data acquisition system (IOLITE i-1xACC, Althen sensors & controls).

Position and speed measurement
The real-time state of the MiaBot is captured by a CMOS camera (JW-02, tiantianquan). The figures are then transferred to the host computer and processed by MATLAB (MathWorks. Inc) for real-time position and orientation detection.

Thermal and magnetic field measurement
The temperature of the electromagnet is measured by an infrared thermal imager (UTi260B, UNI-T). The magnetic field density is detected by a Gaussmeter (HGM09s from MAGSYS) with a measuring range from 1 mT to 4.5 T and a resolution of 1 μT.

Experimental adaptability of the MiaBot
The silicon oil used for evaluating the experimental adaptability of the MiaBot is PX-200 (DOW CORNING). The granular medium used here is hollow ceramic microbeads with a diameter of 20–40 mesh (Henan Hengyuan New Material Co., Ltd). The natural sand is from the Tengger Desert (Gan Su province).

Data availability
The original experimental data generated in this study have been deposited in the Figshare database under accession code: 10.6084/m9.figshare.30598439.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript discusses the invention of a “MiaBot” which is magnetically driven using a permanent magnet and magnetic\ncoils that allow the robot to move by overcoming static friction. The authors demonstrate that the “MiaBot” can operate in a\nvariety of different working environments (surfaces, granular, & viscous fluids), demonstrates payload carrying of sufficient\nweight, and also presents a lightweight and simple to fabricate design. They also demonstrated the customization of the\nplatform by introducing it with fins and other add-ons to make it more robust and demonstrate a real-world\napplication (swimming, pipeline inspection). The videos were also very cool to watch and the paper was\nvery well written altogether.\nOverall I personally feel the paper presents novel and interesting results that advances the field of small-scale robotics and\nthe authors included several impressive demonstrations showing the robots utility. I have included below a list of comments\nand criticisms that are geared towards improving the manuscripts fitness for publication in Nature Communications. Authors\nare encouraged to address these concerns.\n1) The term “microbot” is used prolifically throughout this manuscript and relies on several publications regarding the\ntechnology. Microbots or “microrobots” typically refer to robots that are sub-millimeter in size in at least one dimension. The\ndimensions provided in the manuscript of Ø 12 mm x 30 mm for the MiaBot would make me more inclined to refer to this as a\n“millibot” or “millirobot” instead. I would strongly encourage the authors to make this change throughout the manuscript to be\nmore dimensionally accurate.\n2) I’ve provided a list of papers below that I feel would increase the strength of the introduction if overviewed & discussed.\nThis is an optional suggestion to the authors as these specifically deal with millirobots:\na. Bhattacharjee, Anuruddha, et al. \"Magnetically controlled modular cubes with reconfigurable self-assembly and\ndisassembly.\" IEEE transactions on robotics 38.3 (2021): 1793-1805.\nb. Rogowski, Louis William, et al. \"Magnetically programmable cuboids for 2d locomotion and collaborative assembly.\" 2020\nIEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2020.\nc. Al Khatib, Ehab, et al. \"Magnetically actuated simple millirobots for complex navigation and modular assembly.\" IEEE\nRobotics and Automation Letters 5.2 (2020): 2958-2965.\n3) Listed below are papers discussing a conceptually similar millirobot that should be included:\na. Leclerc, Julien, et al. \"Magnetic hammer actuation for tissue penetration using a millirobot.\" IEEE Robotics and\nAutomation Letters 3.1 (2017): 403-410.\ni. Can the authors comment on how the impact force of the MiaBot compares?\n4) Applications for the MiaBot are not discussed in any great depth at any point in the manuscript. The pipeline inspection as\na proof of concept was a good addition, but can the authors comment on current limitations with pipe inspections and where\nthis robot would be useful as a substitute? I believe that the authors should highlight at least one potential application in\ndepth in the discussion section and provide comparison to existing methods.\n5) Were there any design considerations on the type of magnet used inside the MiaBot? Fig. S7 discusses the diameter\nscaling and length scaling changes, but what about overall magnet shape? In this case it looks like a cylindrical magnet but\nwould there have been significant difference with a spherical magnet? Any effects investigating on adding lubrication to the\nmagnet inside the MiaBot?\na. Kindly change the x-label’s in Figure S7 such that the scaling factor for each is symbolically labeled instead of written out.\n6) Fig. S9 (c) make no reference to what the individual colors on the graph represent, please add a legend. I’m assuming\nthese are the materials of the covers on the MiaBot?\n7) Fig. S9 (d) were there any physical changes to the frame of the MiaBot after 10,000 impacts?\n8) Fig 3 (f), please consider using different colors for each of the labels or the bar graph.\n9) Please make sure that all figure references are consistent in labeling throughout the paper (fig   Fig).\n10) When the MiaBot is moving along different surfaces, can you reiterate the experimental current limits and frequency\nsomewhere as a reminder to the reader?\n11) Please specify in figures with error bars whether these error bars represent standard error or standard deviation. Please\nspecify the number of repeated trials used to generate the error bars in the caption.\n12) Please specify if the Z-pattern followed by the MiaBot in Figure 4 (d,ii) is open loop or closed loop control. If closed loop\ncontrol, please provide equations and parameters for PID control.\n13) Can the authors comment on the maximum depth the robot could safely operate in its current configuration, for\nmovement through viscous fluids? Did the fins require any design or calculations on the parts of the authors? If so, please\ninclude in the SI. Please comment on future work to get this robot steerable in viscous fluids and granular media.\n14) For pipeline navigation have you considered adding wheels or bearings to improve navigation in combination with your\nexisting propulsion mechanism?\n15) For next steps, have you considered on scaling down this design to be more ‘micro sized’, if so please comment on next\nsteps.\n16) Table S2 and S3 do a good job of comparing against existing motors and animals in size to weight ratios. However,\nplease include a more detailed analysis discussing the MiaBot against other robots of similar size in terms of load / weight\nratio.\n17) Different types of weights were used (liquid, solids, etc.) to act as loads throughout the manuscript to affect the\nMiaBot. Can the authors comment on why these specific type of weights were tested and not consistent throughout? For example\none figure shows a weight and another shows a glass of water.\n18) Please proofread captions and figures, several had missing periods and other mistakes. Fig. S5 is missing a period at\nthe end of the paragraph.\nOverall, this was a nice introduction to the robot and I’m curious on the future of the work going forward. If any of my\ncomments were already addressed inside the paper and I just missed it, please comment in the response.", "reviewer_2": "In the manuscript, the authors present an actuation approach for miniaturized magnetic robots using a permanent magnet\ngenerating thrust driven by magnetic interactions with surrounding electromagnetic coils. Despite the robot capability to carry\nheavy payload, the manuscript has fundamental issues that do not meet the standards of Nature Communications:\nThe key concept of ‘microrobot’ is not clearly defined or aligned with a criterion. The actuation relied on millimeter-scale\nNdFeB magnets (6.35 mm) and centimeter-scale robot dimensions which differ significantly from conventional microrobots\ntypically characterized by sub-millimeter or microscopic sizes. This raises questions about the relevance of the work to\nmicrorobotics. In microrobotics, microrobot operation in a high friction environment or at low Reynolds number causes a\nchallenge of forward movement. However, the manuscript does not consider the size aspect of robots despite the emphasis\non the use of microrobots. Furthermore, the reliance on inertia-driven motion contradicts the focus on lightweight design of a\n‘microrobot’. The ability to generate thrust is dependent on the load mass, which is needed to be counted for robot mass,\nweakening the core arguments about the advantages of the proposed design.\nThe highlight of ‘multi-terrain locomotion’ is overstated. While MiaBot achieved bi-directional control in sand, the\ndisplacements were demonstrated by using the corkscrew shape of the robot. The translational motion restricts adaptive\nlocomotion (i.e., climbing obstacles), limiting steering functionality in multi-terrain locomotion beyond granular media. The\nlimitation conflicts with claims of locomotion in unrestricted workspace.\nAdditionally, the manuscript juxtaposes tethered and untethered robot systems to compare ‘high force’ capability, which\ninherently differ in power sources and operational constraints. The comparison results in an overstatement of the proposed\n‘high force’ capabilities without sufficient justification. Overall, the authors would be recommended to address these\nshortcomings and consider resubmitting it to a journal more aligned with the current stage of their research.", "reviewer_3": "The manuscript presents the development of a magnetically inner-actuated microrobot (MiaBot) capable of high-force output\nfor multi-terrain locomotion. While the work demonstrates some interesting experimental results, it lacks critical scientific\nrigor in several areas, leading to significant concerns about novelty, theoretical justification, reproducibility, and practical\napplicability. Below are major issues that substantiate the rejection of this paper.\nClearly the concept cannot be downscaled and it is misleading to name it microrobot.\nThe paper claims to introduce a new actuation mechanism, but the proposed approach is a variation of existing\nelectromagnetic actuation methods. Previous works (e.g., magnetic pulse-actuated robots and magnetically controlled soft\nrobots) have already demonstrated force amplification techniques for microrobotic applications. The authors fail to clearly\ndifferentiate their work from existing literature in terms of unique theoretical insights or practical advancements. The claimed\nadvantage of high-force output has been explored in previous studies, and the manuscript does not convincingly\ndemonstrate how MiaBot significantly advances the state of the art.\nThe study lacks rigorous theoretical validation of its proposed propulsion mechanism. While some equations are presented\nto describe the interaction between the internal magnet and the electromagnetic coils, they are insufficient to fully\ncharacterize the system. Specifically:\n1- The derivation of force equations does not account for realistic effects such as eddy currents, magnetic hysteresis, and\nnon-linearities in the electromagnetic response.\n2- The dynamics of the impact force generation and its relation to microrobot stability are not analyzed beyond empirical\nobservations.\n3- No analytical or numerical modeling is provided to predict the performance of the robot in different environmental\nconditions.\nThe experimental results lack rigorous control and reproducibility. Several aspects of the methodology raise concerns:\n1- The actuation mechanism is tested in highly controlled environments that do not sufficiently represent real-world\napplications such as the human gastrointestinal tract or complex unstructured terrains.\n2- The experiments rely on manual actuation and observation, with limited statistical analysis to ensure reproducibility and\nsignificance.\n3-The comparison with natural creatures (e.g., ants and beetles) lacks scientific rigor and does not contribute meaningful\ninsights into the practical relevance of MiaBot.\n4- The load-carrying performance lacks a detailed discussion of how frictional losses, compliance of surfaces, and real-time\ncontrol strategies affect performance.\n5- The lack of a comprehensive error analysis undermines the reliability of the reported data.\nThe claimed applications, such as pipeline inspection and medical interventions, are not adequately justified.\nLack of In Vivo Validation. The robot's ability to navigate complex biological environments is speculative, as it is only tested\nin artificial setups.\nEnergy Efficiency Concerns. The high-impact actuation mechanism may introduce excessive energy dissipation, vibration,\nand instability, limiting its practicality for precision applications.\nBiocompatibility and Safety Issues. he potential for damage in medical applications due to high-impact forces is not\ndiscussed.\nScalability. The feasibility of scaling this actuation mechanism for different sizes and environments is not explored.\nThe manuscript includes excessive and irrelevant comparisons, such as those with animal species, which do not strengthen\nthe scientific arguments."}, "author_response": "Authors’ Response to Reviews of\nMagnetically Inner Actuated Microrobot with High Force Out-\nput for Multi-Terrain Locomotion\nMin Wang, Wenlong Wu, Zeju Zheng, Wei Dai, Tianyi Wu, Rui Liu, Yuxuan Xiang, Steven Wang, Jiachen Zhang∗,\nZuankai Wang∗, Jun Liu∗\nNature Communications, Ref: NCOMMS-24-57990A-Z\nRC: Reviewers’ Comments, AR: Authors’ Response, : Authors’ Action\nThe authors would like to thank the Editor, Nature Communications, for allowing a major revision of our\nmanuscript (ID: NCOMMS-24-57990A-Z). We also thank the reviewers for their insightful comments and\nsuggestions. We have addressed all the comments in this revised version. The point-by-point response to the\ncomments and detailed explanations of changes are attached below.\n1. Reviewer #1\nThis manuscript discusses the invention of a “MiaBot” which is magnetically driven using a permanent\nmagnet and magnetic coils that allow the robot to move by overcoming static friction. The authors\ndemonstrate that the “MiaBot” can operate in a variety of different working environments (surfaces,\ngranular, & viscous fluids), demonstrates payload carrying of sufficient\nweight, and also presents a lightweight and simple to fabricate design. They also demonstrated the\ncustomization of the platform by introducing it with fins and other add-ons to make it more robust and\ndemonstrate a real-world\napplication (swimming, pipeline inspection). The videos were also very cool to watch and the paper was\nvery well written altogether.\nOverall, I personally feel the paper presents novel and interesting results that advances the field of small-\nscale robotics and the authors included several impressive demonstrations showing the robots utility. I\nhave included below a list of comments and criticisms that are geared towards improving the\nmanuscript’s fitness for publication in Nature Communications. Authors are encouraged to address\nthese concerns.\nAR: Thank you for your positive evaluation. Following your constructive suggestions and comments, we have\naddressed the limitations by including additional simulation and experiments. As shown below, we provide\npoint-by-point responses to your comments and have revised the manuscript to improve its fitness for\npublication in Nature Communications.\n1.1 Comment #1\nRC: The term “microbot” is used prolifically throughout this manuscript and relies on several publications\nregarding the technology. Microbots or “microrobots” typically refer to robots that are sub-millimeter in size\nin at least one dimension. The dimensions provided in the manuscript of ϕ12mm × 30mm for the MiaBot would\nmake me more inclined to refer to this as a “millibot” or “millirobot” instead. I would strongly encourage the\nauthors to make this change throughout the manuscript to be more dimensionally accurate.\nAR: Thank you for the suggestion. We acknowledge that the term \"millirobot\" is indeed a more accurate description\nof the proposed design compared to \"microrobot\". Following your suggestion, we have revised the manuscript\nby replacing all instances of \"microrobot\" with \"millirobot\" throughout the manuscript.\n1.2 Comment #2\nRC: I’ve provided a list of papers below that I feel would increase the strength of the introduction if overviewed &\ndiscussed. This is an optional suggestion to the authors as these specifically deal with millirobots:\na. Bhattacharjee, Anuruddha, et al. \"Magnetically controlled modular cubes with reconfigurable self assembly\nand disassembly.\" IEEE transactions on robotics 38.3 (2021): 1793-1805.\nb. Rogowski, Louis William, et al. \"Magnetically programmable cuboids for 2d locomotion and collaborative\nassembly.\" 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2020.\nc. Al Khatib, Ehab, et al. \"Magnetically actuated simple millirobots for complex navigation and modular\nassembly.\" IEEE Robotics and Automation Letters 5.2 (2020): 2958-2965.\nAR: The suggested papers are relevant to the background of the research, especially in the application of millirobot\nand load capability. Therefore, the three additional references are added to the revised version in the first\nparagraph and the second paragraph as:\nPaper \"b\" and \"c\" are cited as Ref. 8 and 9 in the first paragraph of Introduction section:\nRecent advances in miniature robotics have enabled a range of applications, including wall-climbing1,2,3,\npipeline inspection4, drug delivery5,6, deep-sea inspection7 and cargo transportation8,9.\nPaper \"a\" is cited as Ref. 15 in the second paragraph of Introduction section:\nAdditionally, 3D-printed pneumatic actuators have demonstrated the ability to lift cargo weighting more than\nhundreds of times their own body weight14. Moreover, reconfigurable modular robots have been built by\nattaching magnetic units to a plastic robot frame to deliver the cargo of various shapes15.\n1.3 Comment #3\nRC: Listed below are papers discussing a conceptually similar millirobot that should be included: a. Leclerc,\nJulien, et al. \"Magnetic hammer actuation for tissue penetration using a millirobot.\" IEEE Robotics and\nAutomation Letters 3.1 (2017): 403-410. i. Can the authors comment on how the impact force of the MiaBot\ncompares?\nAR: Thank you for the suggestion. The referenced work also utilizes magnetic fields to generate actuation force\nbased on momentum conservation. However, our proposed design differs significantly in its actuation\nmechanism. Specifically, we employ embedded coils to generate the magnetic field, whereas the cited study\nrelies on external MRI equipment. In our design, the active magnet is driven by the magnetic field gradient\ngenerated by the nearby embedded coils, which diminishes with the inverse fourth power of the distance\nbetween the magnet and the coil. Since the distance between the embedded coil and the magnet is much shorter\nthan that between the MRI coils and the magnet, our proposed design is capable of generating a significantly\nhigher impact force. Quantitatively, the MRI-based magnetic hammer produced an impact force of 0.0273 N\n(mass of the magnet: 1.05 g) with an input of 0.96 A, while our millirobot produces an impact force of 16.67\nN (mass of the magnet: 1.51 g) with an input of 0.6 A. The powerful impact force and self-actuation\nmechanism allow the proposed MiaBot to be deployed in various environments that require high force and\npayload capacity.\nTo clarify this novel design, we have cited the suggested article as Ref. 21 in the Introduction section to\nstrengthen the background and related work of our research. A detailed discussion of the reference paper has\nbeen added in the fourth paragraph, as follows:\nTo enhance the thrust force of magnetic systems, propulsion mechanisms based on the principle of momentum\nconservation have proven to be effective. Typically, magnetic robots driven by the magnetic field gradients\nare limited in their ability to achieve high force output for tissue penetration. To address this limitation,\nresearchers have developed a magnetic hammer actuation system, which employs an MRI system to accelerate\na magnet, generating large impulse forces upon impact with the robot frame21. Similarly, a pulse-actuated\ncollision robot has been introduced to overcome the force limitations of magnetic robotic surgery, and this\nrobot has been demonstrated in biological tissue suturing applications10.\nWhile the pulse impact mechanism has significantly improved actuation force, these systems remain limited\nby their small working range due to reliance on a fixed external magnetic source. They also suffer from high\npower consumption, as the magnetic actuation force decreases inversely with the fourth power of the distance\nbetween the robot and the magnetic source23.\n1.4 Comment #4\nRC: Applications for the MiaBot are not discussed in any great depth at any point in the manuscript. The pipeline\ninspection as a proof of concept was a good addition, but can the authors comment on current limitations with\npipe inspections and where this robot would be useful as a substitute? I believe that the authors should\nhighlight at least one potential application in depth in the discussion section and provide a comparison to\nexisting methods\nAR: Thank you for pointing this out. Navigation in 3D space and confined environments remains a challenge for\npipe inspection technologies. Designing a robot capable of such navigation requires a mechanism that can\neffectively counteract the influence of gravity. Traditional actuation mechanisms tend to be bulky and require\ncomplex control methods, making them unsuitable for narrow and spatially constrained pipelines. For instance,\nresearchers have equipped pipe robots with embedded motors for power and wheel-legged mechanisms that\npress against pipe walls to counteract gravity [1-3]. However, these conventional designs struggle to adapt to\nnarrow vertical-pipe environments. In fact, narrow pipes distributed in 3D space are commonly found in oil\nnetworks, hydraulic systems, and chemical plants. The proposed MiaBot leverages the pressure from the pipe\nwalls to resist gravitational forces, therefore preventing slippage during vertical and inclined movement.\nFurthermore, MiaBot’s strong impact force enables efficient locomotion in high-friction environments that are\ntypically difficult for other miniaturized robots to operate. In the revised manuscript, we have included vertical\nand 3D navigation experiments (See Fig. 6B, 6C and Video 9) and discussed the advantages of MiaBot over\nexisting methods. A detailed summary of the revisions is shown below:\nFig. R1 (Fig. 6 in the Manuscript): Millirobot inspection in a confined flexible tubular environment. (A)\nSchematic of MiaBot navigating a narrow and flexible silicone tube. (B) Locomotion in a vertical tube. (C)\nLocomotion through a tube in 3D space. (D) Snapshots of MiaBot traversing straight and curved trajectories\nwith an onboard camera. Inset: comparison of MiaBot and the flxible tube. (E) The external and internal view\nduring tube inspection: (i) external view showing the position of MiaBot within the tube; (ii) internal view\ncaptured by the camera showing the interior conditions of the tube.\nSection \"Potential applications of MiaBot in flexible tube inspection\":\nVertical and three-dimensional tubular navigation poses significant challenges for millirobots, as their limited\nactuation force often fails to overcome the resistance from high friction and gravitational effects. This typically\nresults in downward sliding and insufficient upward mobility. However, the spatially distributed complex\ntubing systems are widely employed in high-end equipment for gas/liquid transportation. To enable the\ndeployment in such environments, we implemented the MiaBot with a resistance regulation strategy in the\nflexible tubes. The system’s strong instantaneous propulsion enables MiaBot to achieve rapid motion against\nboth gravity and pipeline friction. In the experiment, MiaBot successfully navigated through a 60 cm vertical\npipeline in 60 s with a 10 Hz square wave driving signal at +0.5 A forward and -0.05 A reverse (see Fig. 6B,\nVideo 9). For equivalent-length three-dimensional spatial navigation, the robot required approximately 100 s\n(Fig. 6C), with this delay attributed to high frontal resistance from the narrow inner surface of the silicone\ntube.\nIn addition to the 3D and vertical navigation, we have further applied magnetic tracking for localization of\nMiaBot in the pipe (shown in Fig. S16). This advancement addresses the critical challenge of position\nperception in optically inaccessible environments, where conventional optical tracking methods are ineffective\ndue to ambient light limitations. The technical implementation and validation metrics are further explained in\nthe response to your Comment #12.\nReferences:\n[1] T. Zheng, H. Li, X. Wang, Z. Jiang, M. Ceccarelli, and Q. Huang, “Smooth motion control policy of wall-\npressing pipeline robots,” IEEE Transactions on Industrial Electronics, vol. 71, no. 6, pp. 6005–6012,\n2024.\n[2] O. Inbar and D. Zarrouk, “Analysis of climbing in circular and rectangular pipes with a reconfigurable\nsprawling robot,” Mechanism and Machine Theory, vol. 173, p. 104832, 2022.\n[3] J. Wang, Y. Wang, L. Peng, H. Zhang, H. Gao, C. Wang, Y. Gao, H. Luo, and Y. Chen, “Transformable in-\nspection robot design and implementation for complex pipeline environment,” IEEE Robotics and\nAutomation Letters, vol. 9, no. 6, pp. 5815–5822, 2024.\n1.5 Comment #5\nRC: Were there any design considerations on the type of magnet used inside the MiaBot? Fig. S7 discusses the\ndiameter scaling and length scaling changes, but what about overall magnet shape? In this case it looks like\na cylindrical magnet but would there have been significant difference with a spherical magnet? Any effects\ninvestigating on adding lubrication to the magnet inside the MiaBot?\na. Kindly change the x-label’s in Figure S7 such that the scaling factor for each is symbolically labeled instead\nof written out\nAR: Yes, MiaBot incorporates a cylindrical magnet because of two major considerations. First, the cylindrical shape\nof the MiaBot is chosen to improve adaptability in pipeline environments and granular media, where\nstreamlined geometry reduces mechanical interference. So, the circular cross section aligns seamlessly with\nthe overall cylindrical structure of the robot. Second, a cylindrical magnet inside the cylindrical center channel\nhas a larger magnetic volume compared to spherical or cuboid magnets of the same cross-sectional dimensions.\nThis increased volume translates into a stronger impact force, which is essential for navigating high-friction\nenvironments. Furthermore, the axial length of the magnet is designed to be longer than the diameter of the\ncenter channel to prevent free rotation under the influence of magnetic torque. In contrast, a spherical magnet\ntends to rotate in place without generating an acceleration impact. Therefore, the cylindrical magnet was\nselected as the active unit in our design.\nTo clarify the rationale behind the choice of magnet shape, we have revised the manuscript as follows:\nIntroduction:\nThe design principles, assembly process, and dimensions of all components are summarized in Fig. S1.\nSupporting Information:\nThe entire structure of MiaBot is designed with a cylindrical shape to enhance its adaptability in high-friction\nenvironments such as pipelines and granular media, where streamlined geometry reduces mechanical\ninterference. This design choice extends to both the central channel and the embedded permanent magnet to\nmaximize the spatial efficiency and improve the actuation performance. Additionally, the axial length of the\ncylindrical magnet is selected to exceed the diameter of the central channel to prevent free rotation under\nmagnetic torque and generate directional impact forces along the axial direction.\nRegarding lubrication：the permanent magnet used in the experiments is coated with a protective and polished\nlayer. Additionally, PEEK has been chosen as the material for the robot frame due to its low coefficient of\nfriction, making it ideal for oil-free sliding parts. In contrast, conventional grease or oil lubrication could cause\nthe channel to become sticky, thereby reducing the magnet’s motion performance. For these reasons, we did\nnot use any lubrication in our experiments. However, it is noticeable that friction between the permanent\nmagnet and the robot frame significantly affects the thrust force during experiments. As a result, we emphasize\nthe importance of keeping the permanent magnets free from contamination. When using adhesive to assemble\nthe end caps, special care was taken to prevent glue from leaking into the channels of the frame, as this could\nintroduce additional resistance during the movement of the magnets. The description is included in part of\n\"Supporting Information Fig. S1\" as:\nIt is important to note that the center channel of the robot frame should be polished after printing, and the\nmagnet must be kept free from contamination to minimize friction between the magnet and the frame.\nAdditionally, when using adhesive to assemble the end caps, special care should be taken to prevent the glue\nfrom leaking into the center channels, as this could introduce unnecessary resistance during the movement of\nthe magnets.\nRegarding the \"x-label\" in Figure S8: we thank the reviewer for the suggestions and have corrected in the\nrevised manuscript accordingly. In the revised Fig. S8, we use 𝑘 and 𝑘 to represent the scaling factor in\nd 𝑙\ndiameter and axial length. The updated figure is shown below:\nFig. R2 (Fig. S8 in the Supporting Information): The scalability of MiaBot in diameter and length aspects. (A)\nScalability in diameter direction. (i) Schematic diagram; (ii) The effect of the diameter scaling factor on the\nmagnet’s impact velocity; (iii) The effect of the diameter scaling factor on the magnet’s impact kinetic energy.\n(B) Scalability in length direction. (i) Schematic diagram; (ii) The effect of the length scaling factor on the\nmagnet’s impact velocity; (iii) The effect of the length scaling factor on the magnet’s impact kinetic energy.\n1.6 Comment #6\nRC: Fig. S9 (c) make no reference to what the individual colors on the graph represent, please add a legend. I’m\nassuming these are the materials of the covers on the MiaBot?\nAR: Thanks for your review. Yes, different colors represent different cover materials. We have added the legend on\nFig. S9 (now Fig. S10) in the revised manuscript to indicate the materials used in the experiments:\nFig. R3 (Fig. S10 in the Supporting Information): Impact force measuring experiments. (A) The schematic\nview of the force measuring device. (B) The physical view of the testing device. The load cell and the MiaBot\nare attached on two ends of a plastic connector, respectively. The magnetic impact force of the MiaBot can be\nreflected as pressing and pulling forces on the load cell. (C) The effect of cover material on the impact force.\n(D) The durability test of the magnet by thousands of times of impact. (E) The force curve of a one-time impact\nprocess. Error bar conventions, as described in Fig. 2.\n1.7 Comment #7\nRC: Fig. S9 (d) were there any physical changes to the frame of the MiaBot after 10,000 impacts?\nAR: Thank you for the question. The repeated impact experiments showed no observable physical deformation in\nthe robot frame. To clarify this point, we have updated the description in the Supporting Information (Fig.\nS9) as follows:\nAs a result, 3D-printed PLA was chosen as the material for the stopper in the performance experiments, as it\nis a readily available and easy-to-fabricate material. In the fatigue tests, no visible physical changes were\nobserved in either the PLA stoppers or the robot frame after more than 10,000 impact cycles.\n1.8 Comment #8\nRC: Fig 3 (f), please consider using different colors for each of the labels or the bar graph\nAR: Thanks for your suggestion. Different colors have been adopted to represent different surfaces in the bar graph.\nThe revised figure is shown as:\nFig. R4 (Fig. 3 in the Manuscript): Inertial impact force and loading performance of MiaBot. (A) Relationship\nbetween impact force and applied current for different widths of coil set (3 mm, 5 mm, and 8 mm). (B)\nRepeatability of impact force under various actuation currents. (C) Locomotion velocity as a function of\nexcitation frequency with a 500 g load. (D) The relationship between locomotion velocity, loss rate and loaded\nweight. (E) Locomotion velocity on sandpaper surfaces with varying grit sizes (180, 400, 800, and 1000).\nInsets: 5x magnified images of sandpaper textures. (F) Locomotion velocity on different surface materials.\nError bar conventions, as described in Fig. 2.\n1.9 Comment #9\nRC: Please make sure that all figure references are consistent in labeling throughout the paper (fig ->Fig).\nAR: Thank you for your careful review and valuable suggestion. To ensure consistency and maintain proper\nformatting, all figure references have been revised to use the format \"Fig. *\" throughout the manuscript.\n1.10 Comment #10\nRC: When the MiaBot is moving along different surfaces, can you reiterate the experimental current limits and\nfrequency somewhere as a reminder to the reader?\nAR: Thanks for pointing this out. We have clarified the parameters of the input square wave current and frequency\nutilized in the experiments at different locations of the manuscript. In general control principle, the\npositive/forward current 𝐼 is limited by thermal effect, whereas the negative/backward current 𝐼 with a\nl 𝑠\nsmall amplitude is carefully set to reposition the magnet while not causing unwanted locomotion. For\nfrequency, it is optimized through validation experiments. In details, we have added the following\nclarifications in the manuscript as:\nIn the first paragraph of the Results section:\nThe resulting actuation force by 𝐼 is carefully controlled to reposition the inner magnet while minimizing\ns\nthe impact force to remain below the static friction force to avoid unwanted cancellation of the positive\nmovement. Accordingly, 𝐼 is set to -0.05 A in this paper unless otherwise stated in the following experiments.\ns\nIn the last paragraph of the Results section:\nAfter 300 seconds of operation, the temperature rises by less than 5°C when the input current is 0.1 A, and\nreaches 48°C at an input current of 0.5 A, which remains within the safe tolerance limit of 300°C for the robot\nframe. As a result, the 0.5 A was selected as the input current (𝐼) in the following experiments unless otherwise\nl\nstated.\nIn the last paragraph of Inertial impact force and loading performance section:\nThe four stages of frequency response are observed in all tested currents, and the most favorable choices of\nthe driving currents converge around 25 Hz. Therefore, the optimized 25 Hz is set as the input frequency in\nthe following experiments unless otherwise stated.\n1.11 Comment #11\nRC: Please specify in figures with error bars whether these error bars represent standard error or standard\ndeviation. Please specify the number of repeated trials used to generate the error bars in the caption.\nAR: In this work, all the error bars represent the standard deviation calculated from five independent experiments.\nWe added the statement as follows:\nIn Fig. 2: Error bars represent the standard deviation, based on five independent experiments.\nIn other figures with error bars: Error bar conventions are consistent with those described in Fig. 2.\n1.12 Comment #12\nRC: Please specify if the Z-pattern followed by the MiaBot in Figure 4 (d,ii) is open loop or closed loop control. If\nclosed-loop control, please provide equations and parameters for PID control\nAR: Thank you for this insightful question. In experiments shown in Fig. 4, an open-loop control strategy was used\nto show the reliability and steerability of the new MiaBot. The primary focus of this study is to highlight the\nadvantages of the new actuation mechanism, particularly its high force output for deployment in high-friction\nenvironments, as well as its bidirectional steerability and in-place turning capabilities. We agree that closed-\nloop control is critical for robotic operations. To further address this, we have conducted additional\nexperiments to demonstrate the feasibility of position feedback using a magnetic sensor array. This tracking\nsetup enables accurate determination of both position and orientation, demonstrating the unique advantage for\napplications in occluded environments.\nTo clarify this, we further revised the manuscript and added the magnetic tracking experiments in the\nsupplementary information as follows:\nFig. R5 (Fig. S17 in the Supporting Information): Tracking of MiaBot with a magnetic sensor array. (A)\nSchematic illustration of the magnetic localization principle. (B) Comparison of the localization results with\nthe actual trajectory.\nSection \"Locomotion steerability\"(Line 283-285):\nTo evaluate the trajectory-following capability, we conduct experiments by controlling the millirobot to follow\na ‘Z’-shaped trajectory, including horizontal, vertical, left-turn, and right-turn tracks, using an open loop\ncontrol scheme.\nSection \"Potential applications of MiaBot in flexible tube inspection\"(Line 350-354):\nMoreover, the robot’s real-time position can be tracked using a magnetic tracking system (Fig. S17),\ndemonstrating the potential of closed-loop control for precise navigation. This is particularly useful for\nperforming tasks at designated locations in tubular environments without an external line of sight. The\ndemonstration indicates that MiaBot has the potential to detect and location the defects in industrial pipeline\nsystems.\nSupporting Information: Part: \"Localization through magnetic sensor array\":\nAccurate position tracking of pipeline robots remains a critical challenge, particularly in nonilluminated\ntubular environments where optical tracking methods prove ineffective. To overcome the limitations, we use\nthe magnetic localization method, which does not rely on optical or vision-based methods for target tracking.\nWe model MiaBot as a permanent magnetic dipole and deploy an external sensor array for magnetic flux\ndensity detection (Fig. S17(A)). The magnetic field intensity at the 𝑙−𝑡ℎ sensor position is given by:\n𝜇 3(𝐦 ∙𝑹)𝑹 −𝐦\n0 𝑎 𝑙 𝑙 𝑎\n𝑩 =𝐵 𝒊+𝐵 𝒋+𝐵 𝒌= [ ] (𝑠49)\n𝑙 𝑙𝑥 𝑙𝑦 𝑙𝑧 4𝜋 ‖𝑹‖3\n𝑙\nwhere 𝑩 denotes the magnetic flux density at the 𝑙−𝑡ℎ sensor, 𝜇 is the vacuum permeability (4π × 10−7\n𝑙 0\nH/m), 𝐦 represents the magnetic moment vector, 𝑹is the unit vector from the dipole to the sensor, and\n𝑎 𝑙\n‖𝑹‖ is the source-to-sensor distance.\n𝑙\nThen, we define an error function as:\n𝐸𝑟𝑟 =(𝑉 −𝐵 )2+(𝑉 −𝐵 )2+(𝑉 −𝐵 )2 (𝑠50)\n𝑙 𝑙𝑥 𝑙𝑥 𝑙𝑥 𝑙𝑥 𝑙𝑥 𝑙𝑥\nWhere (𝑉 ,𝑉 ,𝑉 )𝑇 is the measured data from the 𝑙−𝑡ℎ sensor and (𝐵 ,𝐵 ,𝐵 )𝑇 is the estimated\n𝑙𝑥 𝑙𝑦 𝑙𝑧 𝑙𝑥 𝑙𝑦 𝑙𝑧\nvalue generated by the magnetic dipole model. The position and orientation of the magnet can be obtained by\nminimizing 𝐸𝑟𝑟 using the particle swarm optimization algorithm.\n𝑙\nFig. S17(B) demonstrates that MiaBot moves through a silicon tube from left to right. A magnetic tracking\nsystem formed by eight magnetic sensors is deployed outside the tube. The black dashed line in the figure\nrepresents the real trajectory that the robot passes through during its movement, and the red line represents the\ntracking result of the robot. The experiment results demonstrate a high degree of overlap between the tracking\nlocations and the actual trajectory (with a root mean square error of 4.53 mm). This precise localization\ncapability enables future implementation of closed-loop control strategies for improved robotic navigation.\n1.13 Comment #13\nRC: Can the authors comment on the maximum depth the robot could safely operate in its current configuration,\nfor movement through viscous fluids? Did the fins require any design or calculations on the parts of the authors?\nIf so, please include in the SI. Please comment on future work to get this robot steerable in viscous fluids and\ngranular media.\nAR: Thank you for your comments. The maximum distance that robots can safely operate in viscous liquids is\nmainly determined by the material of the robot frame. In our design, PEEK material is used as the robot frame.\nFor simplicity, the robot is considered a cylindrical shell structure with a length of 𝐿, a thickness of 𝑡, and an\nouter diameter of 𝐷. The elastic modulus of PEEK material is 𝐸 =3600 𝑀𝑃𝑎, and the Poisson’s ratio is ν =\n0.39. For a thin-walled long tube structure, the critical buckling pressure can be calculated by:\n2.2𝐸 𝑡 2.2×3600 0.7 3\n𝑃 = ( )3 = ×( ) ≈6.49𝑀𝑃𝑎\n𝑐𝑟 1−𝜈 2 𝐷 (1−0.392) 7.9\nThe safety factor 𝐹 is set to 4 here. The density of silicon oil is: 𝜌=0.96 𝑘𝑔/𝑚3 . The gravitational\n𝑠\nacceleration is: 𝑔=0.981 𝑚/𝑠2. As a result, the safely operating depth is:\n𝑃 6.49×106\n𝑐𝑟\nℎ= = ≈172.28 𝑚\n𝐹𝜌𝑔 4×960×9.81\n𝑠\nTherefore, MiaBot can theoretically operate safely in silicone oil deeper than 170 meters. Under practical\nconditions, other risks such as silicone oil infiltration into internal compartments may arise, inducing elevated\ninternal friction and damping that could compromise permanent magnet actuation efficiency.\nFor the second question about the fins, theoretical and finite element analyses reveal that reducing the tilt angle\ndecreases hydrodynamic resistance when moving forward. However, excessively low tilt angles result in\nunintended trade-offs, including diminished resistance asymmetry between forward and backward locomotion\nand compromised horizontal stability due to the front-rear imbalance in a fluidic environment.\nFor the third question of steerability in viscous fluids and granular media, additional experiments demonstrated\nthat the MiaBot can be controlled to turn with the assistance of an external magnetic field in a viscous\nenvironment.\nTo clarify the above issues, we have revised the SI documents, as shown in Supporting Information,\nFig.\nS15(B) and Fig. S15(C):\nFig. R6 (Fig. S15 in the Supporting Information): Simulation and experiments in a viscous environment. (A)\nThe heat map of simulation results shows the force distribution. (B) The heat map of simulation results shows\nthe pressure distribution at the fin tips with varied angles. (C) The average resistive force plot shows an\nincreasing trend with elevated scaling factors. (D) The extracted average pressure plot shows an increasing\ntrend with the elevated fin angles. (E) The diagram of the steering principle with an external magnetic field.\n(F) Experimental snapshots show the robot is turning counterclockwise by 180 degrees.\nFig. S15(B) and Fig. S15(D) further quantify the relationship between hydrodynamic pressure and the\ninclination angle of the robot’s fins. The analysis reveals a positive correlation between the inclination angle\nand resistance magnitude: as the angle was increased from 40° to 80°, the average pressure on the conical\nsurface escalated from 6.47 Pa to 39.48 Pa. In addition, the simulation shows most hydrodynamic pressure\naccumulates on the first fin, which means that the number of fins does not significantly affect the resistance\nof the robot. While reducing the fin angle minimizes forward resistance, this configuration introduces trade-\noffs, including diminished differentiation between forward and backward motion resistance and compromised\nhorizontal stability due to the front-rear balance in a fluidic environment.\nA single MiaBot unit inherently provides bidirectional horizontal propulsion, limiting its capability for planar\nsteering. As demonstrated in Fig. 4, planar steering can be achieved by coordinating two millirobots in parallel.\nHowever, this strategy amplifies hydrodynamic resistance in viscous media. To address this limitation, an\nexternal magnetic field-assisted steering mechanism can be used. By applying a controlled magnetic torque\n(𝑇=𝑀×𝐵) via a rotating external magnetic field (Fig. S15(E) and Fig. S15(F)), the robot gains\nmaneuverability for directional adjustments. Crucially, the magnetic field intensity must be optimized to avoid\nintroducing destabilizing forces that interfere with propulsion; the uniform rotational magnetic field generated\nby Helmholtz coils could be another solution for programmed steerability.\n1.14 Comment #14\nRC: For pipeline navigation have you considered adding wheels or bearings to improve navigation in combination\nwith your existing propulsion mechanism?\nAR: In this study, we introduced a new design paradigm for a millirobot that can effectively utilize local magnetic\nfield drive and momentum conservation law to improve the instantaneous output force of robots and adapt to\napplications in high-resistance environments. In specific applications, follow-up work can still be\nsupplemented to improve its performance. Undoubtedly, setting small wheels or bearings around the robot can\nchange the sliding friction between the robot and the inner wall of the pipeline to rolling friction, which can\nfurther improve the robot’s operating speed in restricted pipelines. In future designs, we will conduct a\nthorough analysis of integrated MiaBot with wheels and bearings. To clarify this issue, we added a discussion\nin the revised manuscript on the future work in the pipeline system. The revision is added to the Discussion\nsection (Line 406-411) as:\nAlthough MiaBot has shown great performance in high-resistance environments, it can be further improved in\nspecific scenarios. For instance, in liquid environments, optimization of the robot’s fin angle and scale could\nimprove its propulsion efficiency. In pipe environments, adding wheels or bearings mechanisms could enhance\nthe locomotion efficiency and adaptability. Additionally, reducing the robot’s size could open up potential\nmedical applications in human organs, such as the gastrointestinal tract or cardiovascular system.\n1.15 Comment #15\nRC: For next steps, have you considered on scaling down this design to be more ‘micro sized’, if so please comment\non next steps.\nAR: In future work, we aim to miniaturize MiaBot to enable deployment in more confined spaces, such as the\ngastrointestinal tract and cardiovascular systems. For instance, reducing the robot’s size could involve using\na smaller permanent magnet, a shorter and thinner plastic frame, and fewer coil turns to achieve a micro-scale\ndesign. We have expanded our discussion of future applications for such micro-sized robots in medical\ncontexts, as detailed in our response to Comment #14.\n1.16 Comment #16\nRC: Table S2 and S3 do a good job of comparing against existing motors and animals in size to weight ratios. However,\nplease include a more detailed analysis discussing the MiaBot against other robots of similar size in terms of load /\nweight ratio.\nAR: Thanks for your positive comments and suggestions. A detailed discussion has been added to compare the\nload-to-weight ratio of the proposed MiaBot with other robots of similar size. The revision can be found in\nthe Manuscript and Supplementary Information:\nManuscript: Discussion and Conclusion:\nThe results show that the majority of existing small robots are capable of transporting cargo weighing less than\n50 times their own weight. Only two studies report load capacities exceeding 100 times body weight, but their\nminiature size (<0.05 g) restricts absolute payloads to <5 g. The SMA-, DEA-, and PZT-driven robots, which\nshare comparable scales and similar wired actuation systems with our design, exhibit the load-to-weight ratios\nbelow 30. In contrast, the proposed MiaBot achieves a payload of 1800 g, corresponding to a load ratio of\n309.28.\nSupporting Information: Table S2\nIn recent years, small robots driven by functional materials (e.g., SMA, DEA, PZT, or magnetic/thermal fields)\nhave been developed to accomplish various tasks due to their gear-free design and ease of miniaturization.\nHowever, existing miniaturized robots are limited in load capacity, restricting their ability to carry heavy cargo\nin confined environments.\nTable S2 summarizes representative studies in recent years, including robots driven by SMA, DEA, PZT, as\nwell as those powered by magnetic and thermal fields. Most of these robots can carry less than 50 times their\nbody weight. Only two studies report load capacities exceeding 100 times body weight, but these robots are\nextremely small (under 0.1 g), resulting in relatively low payload capacities (both under 5 g).\nSMA-, DEA-, and PZT-driven robots typically rely on wired actuation, similar to our approach. Among them,\nDEA-powered robots exhibit the weakest payload capacity, with most carrying less than five times their own\nweight due to the flexibility of DEA materials. SMA-driven robots demonstrate higher load capacity but still\nunder 50 times their body weights. In contrast, our 5.82 g MiaBot is able to carry a load of 1,800 g (309.28\ntimes its own weight), significantly outperforming existing small robots in both absolute and relative load\ncapacity.\n1.17 Comment #17\nRC: Different types of weights were used (liquid, solids, etc.) to act as loads throughout the manuscript to affect\nthe MiaBot. Can the authors comment on why these specific type of weights were tested and not consistent\nthroughout? For example one figure shows a weight and another shows a glass of water.\nAR: Actually, all experiments were conducted using liquid as the loaded weight, except for Fig. 4. The reason for\nthis exception is that top-view images are needed to demonstrate the robot’s maneuverability. Due to the\nrobot’s small size, we used a small but heavy copper weights as the load to highlight the new millirobot’s\npayload capacity. Otherwise, a large liquid container covers the small MiaBot and makes it invisible, which\nmay confuse readers.\n1.18 Comment #18\nRC: Please proofread captions and figures, several had missing periods and other mistakes. Fig. S5 is missing a period at\nthe end of the paragraph.\nAR: Thank you for your careful review. We have carefully proofread and double checked all captions and figures.\nNow all typos and grammar errors have been corrected.\n1.19 Comment # Overall\nRC: Overall, this was a nice introduction to the robot and I’m curious on the future of the work going forward. If\nany of my comments were already addressed inside the paper and I just missed it, please comment in the\nresponse.\nAR: Thank you for recognizing our work. We hope this revised version has addressed your comments.\n2. Reviewer #2\nIn the manuscript, the authors present an actuation approach for miniaturized magnetic robots using a\npermanent magnet generating thrust driven by magnetic interactions with surrounding electromagnetic\ncoils. Despite the robot capability to carry heavy payload, the manuscript has fundamental issues that\ndo not meet the standards of Nature Communications:\nAR: Thank you for your time and valuable suggestions on our work. We have carefully revised the manuscript to\naddress your concerns and provided detailed point-by-point responses as follows. Specifically, we have\nrevised the description of \"microrobots\" to \"millirobots\" to more accurately convey the advantages of our\nwork, offered a comprehensive explanation of the relationship between the weight of the magnets and the\nrobot’s load ratio, and included additional climbing experiments and turning experiments in gravel\nenvironments to better support our claims regarding multi-terrain locomotion.\nWe believe these revisions have significantly enhanced the quality of the article, and we are grateful for your\nconstructive feedback, which has contributed to improving our work.\n2.1 Comment #1\nRC: The key concept of ‘microrobot’ is not clearly defined or aligned with a criterion. The actuation relied on\nmillimeter-scale NdFeB magnets (6.35 mm) and centimeter-scale robot dimensions which differ significantly\nfrom conventional microrobots typically characterized by sub-millimeter or microscopic sizes. This raises\nquestions about the relevance of the work to microrobotics.\nAR: Thank you for pointing this out. We have modified the term \"microrobot\" throughout the revised paper to\nreflect the scale of the proposed robot. To better align with the actual scale, we have replaced \"microrobot\"\nwith \"millirobot\". Specifically, we have systematically revised the manuscript in over 30 places by replacing\nall instances of \"microrobot\" with \"millirobot\" throughout the title, manuscript, and supporting information.\n2.2 Comment #2\nRC: In microrobotics, microrobot operation in a high friction environment or at low Reynolds number causes a\nchallenge of forward movement. However, the manuscript does not consider the size aspect of robots despite\nthe emphasis on the use of microrobots.\nAR: Thanks for your question. The analysis of the size effect on the locomotion in a low Reynolds number\nenvironment have been added in Fig. S14. Moreover, we also show the effect of the fin angle on the pressure.\nOur detailed action can be found in Fig. S14 as\nFig. R7 (Fig. S15 in the Supporting Information): Simulation and experiments in a viscous environment. (A)\nThe heat map of simulation results shows the force distribution. (B) The heat map of simulation results shows\nthe pressure distribution at the fin tips with varied angles. (C) The average resistive force plot shows an\nincreasing trend with elevated scaling factors. (D) The extracted average pressure plot shows an increasing\ntrend with the elevated fin angles. (E) The diagram of the steering principle with an external magnetic field.\n(F) Experimental snapshots show the robot is turning counterclockwise by 180 degrees.\nFor a robot moving in a silicon oil environment, the locomotion state of the robot can be determined by\ncalculating the Reynolds number as follows:\n𝜌𝑣𝐿\n𝑅𝑒= (𝑠47)\n𝜂\nwhere 𝜌 is the density of the liquid, 𝑣 is the velocity of the robot, 𝐿 is the character length of the robot, and\n𝜂 is the dynamic viscosity of silicone oil.\nAs shown in Fig. 5(B), the movement speed of MiaBot in silicone oil is approximately 2.5mm/s. For low-\nspeed movement in high-viscosity environments (e.g., 𝑅𝑒≪1), it can be considered as laminar flow. In this\ncase, the friction force can be expressed as:\n𝐹=𝐾∙𝜂∙𝑣∙𝐿 (𝑠48)\nwhere 𝐾 is the shape correction factor. For spherical robots, the value is 𝐾=3𝜋, while for other shapes,\nsuch as the conical head used in this article, the value needs to be determined by experiments or numerical\nsimulations.\nIn this study, finite element analysis (FEA) was conducted using ANSYS 2022 to simulate hydrodynamic\nforces acting on the robot. As illustrated in Fig. S15(A) and Fig. S15(C), the resistance force exhibits a positive\ncorrelation with the characteristic length of the robot, aligning with the theoretical predictions derived from\nEq. s48. When the robot’s diameter was scaled from 0.5× to 2.0× the baseline design, the resistance increased\nproportionally from 1.05 mN to 3.36 mN. These results suggest that minimizing the cross-sectional area of\nMiaBot is critical for enhancing actuation efficiency in highly viscous fluid environments.\n2.3 Comment #3\nRC: Furthermore, the reliance on inertia-driven motion contradicts the focus on lightweight design of a\n‘microrobot’. The ability to generate thrust is dependent on the load mass, which is needed to be counted for\nrobot mass, weakening the core arguments about the advantages of the proposed design.\nAR: Thanks for pointing this out. We agree that the MiaBot relies on the mass of the permanent magnet to provide\nkinetic energy and impact force. However, its key advantage lies in its minimalist structural design, eliminating\nthe need for energy conversion components like gears or bearings while directly outputting impact force.\nMoreover, the momentum conservation rules allow the energy stored in the accelerating magnet to be released\ninstantaneously, significantly increasing the instantaneous output of the robot.\nAs suggested in your comment #1, we replaced the term \"microrobot\" with \"millirobot\" throughout the\nmanuscript to reflect the scale of the proposed robot. For a millirobot, the dimensions of the permanent magnet\n(ϕ6.35 mm × 6.35 mm) and its weight (1.51 g) are acceptable. With the 1.51 g magnet, the measured impact\nforce exceeds 15 N at an input current of 0.5 A. Additionally, we compared the proposed MiaBot with existing\nsmall robots weighing less than 10 g in terms of carrying capability. The MiaBot demonstrates a significantly\nhigher load-to-weight ratio than these robots of comparable self-weight (MiaBot: 309.28; most existing models:\n< 30).\nIn the revised manuscript, we integrated the quantitative relationship between the magnet’s specific impact\npower (impact power per unit mass) and its mass into the scaling effect analysis, as shown by the red curve in\nFig. S7. While the impact energy per unit mass varies with magnet scale, the variation range of impact energy\nper unit volume is within an order of magnitude within the scale coefficient range of 0.2-5 for diameter and\nlength dimensions. Additionally, the impact energy per unit mass can be further optimized by adjusting the\ncoil configuration as the permanent magnet’s dimensions are modified. The revised figure is provided below:\nFig. R7 (Fig. S8 in the Supporting Information): The scalability of MiaBot in diameter and length aspects. (A)\nScalability in diameter direction. (i) Schematic diagram; (ii) The effect of the diameter scaling factor on the\nmagnet’s impact velocity; (iii) The effect of the diameter scaling factor on the magnet’s impact kinetic energy.\n(B) Scalability in length direction. (i) Schematic diagram; (ii) The effect of the length scaling factor on the\nmagnet’s impact velocity; (iii) The effect of the length scaling factor on the magnet’s impact kinetic energy.\n2.4 Comment #4\nRC: The highlight of ‘multi-terrain locomotion’ is overstated. While MiaBot achieved bi-directional control in\nsand, the displacements were demonstrated by using the corkscrew shape of the robot. The translational\nmotion restricts adaptive locomotion (i.e., climbing obstacles), limiting steering functionality in multi-terrain\nlocomotion beyond granular media. The limitation conflicts with claims of locomotion in an unrestricted\nworkspace.\nAR: We are sorry for the confusion. Actually, the bidirectional control is demonstrated in Fig. 4A on the ground.\nThe slanted fins and a conical head were attached to the robot to fit the specific environment, while we did\nnot use a corkscrew structure.\nComment #4.1 Climbing capability\nWe acknowledge that the climbing and steering functions are important for a multi-terrain robot. To\ndemonstrate these capabilities, the obstacles climbing experiments in the tubular environment (Fig.6),\nground (Fig.S16), and granular medium (Fig.S16) have been included in the revised version as follows:\nClimbing in the tubular environment:\nFig. R8 (Fig. 6 in the Manuscript): Inspection in a confined flexible tubular environment. (B) Locomotion in\na vertical tube. (C) Locomotion through a tube in 3-D space.\nSection: “Potential applications of MiaBot in flexible tube inspection” :\nVertical and three-dimensional tubular navigation poses significant challenges for millirobots, as their limited\nactuation force often fails to overcome the resistance from high friction and gravitational effects. This typically\nresults in downward sliding and insufficient upward mobility. However, the spatially distributed complex\ntubing systems are widely employed in high-end equipment for gas/liquid transportation. To enable the\ndeployment in such environments, we implemented the MiaBot with a resistance regulation strategy in the\nflexible tubes. The system’s strong instantaneous propulsion enables MiaBot to achieve rapid motion against\nboth gravity and pipeline friction. In the experiment, MiaBot successfully navigated through a 60 cm vertical\npipeline in 60 s with a 10 Hz square wave driving signal at +0.5 A forward and -0.05 A reverse (see Fig. 6B,\nVideo 9). For equivalent-length three-dimensional spatial navigation, the robot required approximately 100 s\n(Fig. 6C), with this delay attributed to high frontal resistance from the narrow inner surface of the silicone\ntube.\nClimbing on the ground and within the granular medium:\nFig. R9 (Fig. S16 in the Supporting Information) Climbing experiments. (A) Climbing to overcome the\nobstacles. (B) Climbing through the 100-mm-depth sand environment. Input square wave: 0.5A/-0.05A, 10Hz.\nSupplementary Information: Climbing tests using MiaBot\nIn this section, we evaluate the climbing performance of the MiaBot on both silicone surfaces and granular\nsubstrates. As shown in Fig. S16(A), two robots carrying a 70 g payload (6× their body weight) successfully\nascended slopes of 5° and 10°. However, experimental observations revealed that slopes exceeding 20°\ninduced instability due to torque imbalances caused by the payload, resulting in tipping events. To address this\nlimitation, future implementations should incorporate passive stabilizing mechanisms (e.g., deployable\nanchors or adhesive pads) to ensure static stability on steep inclines without active propulsion.\nFurthermore, the MiaBot demonstrated the ability to traverse gravel environments with depths exceeding 100\nmm. To track its real-time position, a lightweight copper rod was mounted vertically on the robot. Notably, the\ntethered configuration of the current prototype introduced significant frictional resistance between the\nactuation cables and the gravel during locomotion. To mitigate this issue, the driving cables were routed along\nthe fixed copper rod, minimizing contact with the substrate. For deployment in sandy or loosely packed\ngranular terrains, future iterations should explore wireless actuation schemes (e.g., embedded battery and\nactuation circuit) to eliminate cable-induced friction and enhance mobility robustness.\nComment #4.2 Steering capability\nThe steering function can be achieved with the assistance of an external magnetic field, which is included in\nFig. S15(C) (refer to your Comments #2). The description is shown as below:\nA single MiaBot unit inherently provides bidirectional horizontal propulsion, limiting its capability for planar\nsteering. As demonstrated in Fig. 4, planar steering can be achieved by coordinating two millirobots in parallel.\nHowever, this strategy amplifies hydrodynamic resistance in viscous media. To address this limitation, an\nexternal magnetic field-assisted steering mechanism can be used. By applying a controlled magnetic torque\n(𝑇=𝑀×𝐵) via a rotating external magnetic field (Fig. S15), the robot gains maneuverability for directional\nadjustments. Crucially, the magnetic field intensity must be optimized to avoid introducing destabilizing forces\nthat interfere with propulsion; the uniform rotational magnetic field generated by Helmholtz coils could be\nanother solution for programmed steerability.\nComment #4.3 Overstated of multi-terrain\nTo enhance the precision of our statement, we have included a more detailed description of multi-terrain\nlocomotion in the revised manuscript. Specifically, the original title, ’Magnetically Inner Actuated Microrobot\nwith High Force Output for Multi-Terrain Locomotion,’ has been updated to ’Magnetically Inner Activated\nMicrorobot with High Force Output for Extreme Friction and Constrained Environments’. This adjustment\nbetter reflects the microrobot’s capabilities in navigating challenging conditions.\nOriginal title:\n\"Magnetically Inner Actuated Microrobot with High Force Output for Multi-Terrain Locomotion\"\nUpdated title:\n\"Momentum-Driven Millirobotics: Magnetically Inner-Actuated Design for High-Friction and Confined\nEnvironments\"\n2.5 Comment #5\nRC: Additionally, the manuscript juxtaposes tethered and untethered robot systems to compare ‘high force’\ncapability, which inherently differ in power sources and operational constraints. The comparison results in an\noverstatement of the proposed ‘high force’ capabilities without sufficient justification.\nAR: Thanks for your comments. First, we acknowledge that we agree that it is not fair to compare our work with\nuntethered robots. We now focus on our comparison with the tethered ones. Next, (also the most important\nthing), we need to emphasize that our robot still has a dramatic advantage over the tethered robots. In the\nrevised version, we have carefully re-evaluated the value of our work and made necessary changes. We\nremoved some comparisons with the untethered robot system. Instead, we focused on highlighting the unique\nfeatures of a simple yet effective propulsion method based on local magnetic actuation and momentum\nconservation enabling MiaBot to achieve high output forces in a variety of challenging terrains.\nOur action can be referred to section “Discussion and Conclusion”:\nIn this study, we developed a new millirobot using the robot’s inner magnetic interaction force as the actuation\nforce. The proposed actuation method, based on local magnetic forces and the momentum conservation\nprinciple, offers several significant benefits. First, the straightforward energy conversion mechanism of the\nproposed MiaBot allows it a direct, powerful force output at a smaller scale than conventional electromagnetic\nmotors that output torque and rely on complicated gears and bearing systems. Second, the momentum\nconservation-based impact motion enables the MiaBot to have a strong instantaneous propulsion force,\nallowing it to be deployed in various high-frictional environments. Third, the robot is not restricted to a limited\nworkspace, as the inner actuation mechanism can propel the robot regardless of the millirobot’s position and\nget a higher actuation force with lower power consumption due to the close distance between the coils and the\ninner magnet.\nMoreover, we conducted a comparative analysis of robots with varying configurations, including wired and\nwireless actuation systems. The results demonstrate that our design significantly outperforms existing models\nin force output performance, as reflected by the load-carrying capability.\nSection: Discussion and Conclusion (Line 373-378):\nThe results show that the majority of existing small robots are capable of transporting cargo weighing less than\n50 times their own weight. Only two studies report load capacities exceeding 100 times body weight, but their\nminiature size (<0.05 g) restricts absolute payloads to <5 g. The SMA-, DEA-, and PZT-driven robots, which\nshare comparable scales and similar wired actuation systems with our design, exhibit the load-to-weight ratios\nbelow 30. In contrast, the proposed MiaBot achieves a payload of 1800 g, corresponding to a load ratio of\n309.28. force output performance, as reflected by load-carrying capability.\nSupplementary Information Table S2: Comparison of load capability of proposed MiaBot with the state-\nof-the-art small robots:\n2.6 Comment #Overall\nRC: Overall, the authors would be recommended to address these shortcomings and consider resubmitting it to a\njournal more aligned with the current stage of their research.\nAR: Thanks for your comments on the manuscript, which helped us greatly improve the quality of this work. After\npoint-by-point revision, we hope this revised version meets your expectations.\n3. Reviewer #3\nThe manuscript presents the development of a magnetically inner-actuated microrobot (MiaBot)\ncapable of high force output for multi-terrain locomotion. While the work demonstrates some\ninteresting experimental results, it lacks critical scientific rigor in several areas, leading to significant\nconcerns about novelty, theoretical justification, reproducibility, and practical applicability. Below are\nmajor issues that substantiate the rejection of this paper.\nAR: Thanks for your time and insightful suggestions. We have carefully revised the manuscript to address your\nconcerns and provided detailed point-by-point responses as follows. Specifically, we conducted more theoretical\nanalyses of factors affecting magnetic actuation forces, including eddy currents, magnetic hysteresis and\nelectromagnetic nonlinearities. Furthermore, we analyzed conditions where impact/vibration-based actuation\nmay induce robotic instability and proposed active control strategies to mitigate this risk. To demonstrate the\nimpact of the new robot design, we rewrote the applications section to emphasize value in industrial scenarios\nrather than in medical settings. We conducted additional experiments on navigation through vertical and twisted\nconduits with magnetic tracking of the new robot, while toning down the claims regarding biomedical\napplications.\nWe believe these revisions have improved the quality of the article, and we sincerely appreciate your\nconstructive feedback, which has been instrumental in guiding these improvements.\n3.1 Comment #1\nRC: Clearly the concept cannot be downscaled and it is misleading to name it microrobot.\nAR: Thanks for pointing this out. We acknowledge that the term \"millirobot\" is a more accurate description of the\nproposed design compared to \"microrobot\". Following your suggestion, we have gone through the manuscript\nand replaced all instances of \"microrobot\" with \"millirobot\".\n3.2 Comment #2\nRC: The paper claims to introduce a new actuation mechanism, but the proposed approach is a variation of\nexisting electromagnetic actuation methods. Previous works (e.g., magnetic pulse-actuated robots and\nmagnetically controlled soft robots) have already demonstrated force amplification techniques for\nmicrorobotic applications. The authors fail to clearly differentiate their work from existing literature in terms\nof unique theoretical insights or practical advancements. The claimed advantage of high-force output has\nbeen explored in previous studies, and the manuscript does not convincingly demonstrate how MiaBot\nsignificantly advances the state of the art.\nAR: Thank you for your comments. We acknowledge that previous studies have proposed magnetic pulse-actuated\nrobots to enhance thrust force in magnetic actuation systems. For instance, Leclerc et al. [21] and Erin et al.\n[10] employed gradient magnetic fields from external coils to drive magnetic robots. Xiang et al. [22] proposed\na triple magnetic system utilizing an external permanent magnet to adjust the orientation of two embedded\nsmaller magnets, leveraging local interaction forces for acceleration.\nWhile these approaches improved actuation force compared to direct gradient field actuation, they face\nlimitations in constrained workspace due to reliance on bulky external magnetic sources. Furthermore, energy\nconsumption is high because magnetic field strength decays rapidly with distance. Another challenge lies in\nachieving bidirectional control within confined tubular environments. In obscured and tortuous pipelines, the\nrobot may need to reverse the movement directions without changing the location, which is not feasible with\nprevious designs.\nIn contrast, MiaBot overcomes these limitations. The stable relative position between its embedded coils and\nthe permanent magnet allows the robot to maintain movement towards the exit by keeping the bias direction\nof the input square wave signal constant. Additionally, the integrated design of near-field coils and permanent\nmagnet within the robot eliminates strict workspace limitations. Moreover, due to the short coil-to-magnet\ndistance, MiaBot requires relatively low power consumption.\nThe detailed description and brief discussion of these systems are shown in Section Introduction, paragraph 4:\nTo enhance the thrust force of magnetic systems, propulsion mechanisms based on the principle of momentum\nconservation have proven to be effective. Typically, magnetic robots driven by the magnetic field gradients\nare limited in their ability to achieve high force output for tissue penetration. To address this limitation,\nresearchers have developed a magnetic hammer actuation system, which employs an MRI system to accelerate\na magnet, generating large impulse forces upon impact with the robot frame21. Similarly, a pulse-actuated\ncollision robot has been introduced to overcome the force limitations of magnetic robotic surgery, and this\nrobot has been demonstrated in biological tissue suturing applications10. After that, researchers developed a\ntriple-magnet system to improve the thrust force. By adjusting the orientation of the external magnet, the\nNewton-level forces through the attraction between embedded magnets were achieved for potential\napplications in tissue biopsy22. While the pulse impact mechanism has improved actuation force, these systems\nremain limited by their confined workspace due to reliance on a fixed external magnetic source. They also\nsuffer from high power consumption, as the magnetic actuation force decreases inversely with the fourth power\nof the distance between the robot and the magnetic source23.\nReferences:\n[10] Erin O, et al. Overcoming the Force Limitations of Magnetic Robotic Surgery: Magnetic Pulse Actuated\nCollisions for Tissue-Penetrating-Needle for Tetherless Interventions. Advanced Intelligent Systems 4, (2022).\n[21] Leclerc J, Ramakrishnan A, Tsekos NV, Becker AT. Magnetic hammer actuation for tissue penetration\nusing a millirobot. IEEE Robotics and Automation Letters 3, 403-410 (2017).\n[22] Xiang YX, et al. MINRob: A Large Force-Outputting Miniature Robot Based on a Triple-Magnet System.\nIEEE Transactions on Robotics 40, 3127-3145 (2024).\n3.3 Comment #3\nRC: The study lacks rigorous theoretical validation of its proposed propulsion mechanism. While some equations\nare presented to describe the interaction between the internal magnet and the electromagnetic coils, they are\ninsufficient to fully characterize the system. Specifically:\nComment #3.1 The derivation of force equations does not account for realistic effects such as eddy currents,\nmagnetic hysteresis, and non-linearities in the electromagnetic response.\nAR: Eddy currents - Eddy current effects arise from two primary sources: (1) currents induced in the robot frame\nby rapid magnet motion, which dampen acceleration and impact dynamics, and (2) eddy currents generated\nwithin permanent magnets when alternating current powers electromagnetic coils. For frame-induced effects,\nwe did find that metallic frames substantially impede motion, critically justifying our selection of a non-\nconductive material, PEEK, for the robotic structure. Regarding the second source, theoretical analysis confirms\nnegligible skin effect in permanent magnets under applied currents. This indicates the magnetic fields generated\nby coils can penetrate permanent magnet uniformly, and the eddy current influence on magnet’s acceleration\ncould be ignored. The detailed analysis is added in Supporting Information: “Analysis of the interaction force\nbetween electromagnetic coils and the permanent magnet” as follows\nThe magnet's acceleration may also be influenced by eddy currents. To prevent such effects from high-speed\npermanent magnets, the robot frame is made of a non-conductive material, which is also an important reason to\nchoose PEEK as the frame material. Additionally, alternating currents in the electromagnetic coils may induce\neddy currents in the permanent magnet. To evaluate this potential impact on motion, we calculated the relevant\nskin depth for the eddy currents on the inner magnet. Under 𝑓=25𝐻𝑧 excitation, the permanent magnet’s\nskin depth is\n1\n𝛿=√ (𝑠28)\n𝜋𝑓𝜇 𝜇 𝜎\n𝑟 0\nwhere 𝜇 is the relative permeability (𝜇 ≈1.05 for NdFeB), 𝜇 is the vacuum permeability (𝜇 =\n𝑟 𝑟 0 0\n4𝜋×10−7𝐻/𝑚), and 𝜎 is the conductivity of permanent magnet (𝜎≈6×105𝑆/𝑚 for NdFeB).\nThe calculated skin depth 𝛿=129.95 𝑚𝑚 exceeds the permanent magnet's radius (𝑟=3.15 𝑚𝑚), indicating\nnegligible skin effect at this frequency. Consequently, the magnetic field penetrates the permanent magnet with\napproximately uniform distribution, and eddy current damping effects on the magnet are insignificant.\nAR: Magnetic hysteresis - Hysteresis losses predominantly affect soft magnetic materials, which experience\nsignificant magnetic changes under applied fields. However, the N52 NdFeB permanent magnet (hard magnetic\nmaterial) used in this study exhibits minimal hysteresis under the actuation field that is lower than 20 mT (i.e.,\n2×10−3𝑘𝑂𝑒). By comparing the applied magnetic field with B–H curve as shown in the follow dashed region,\nwe can confirm that external fields of this magnitude level induce negligible changes in its magnetic properties.\nFig. R10 B-H curve of the utilized permanent magnet\nAnd the detailed analysis is added in Supporting Information: “Analysis of the interaction force between\nelectromagnetic coils and the permanent magnet” as follows\nMagnetic hysteresis could potentially affect permanent magnet motion, though this phenomenon is primarily\npronounced in soft magnetic materials. For the N52 permanent magnet used in this study, the intrinsic\ncoercivity (𝐻 ) typically ranges from 1100 to 1500 kA/m (regarded as 1300 kA/m in the following discussion).\n𝑐𝑗\nAs shown in Fig. S3, the magnetic field (𝐵 ) generated by the energized coils ranges between -20 mT and +20\n𝑧\nmT. The ratio of this applied field strength to the magnet's coercive force is\n|𝐻 | |𝐵 |\n𝑐𝑜𝑖𝑙 𝑧\n𝜂= = (𝑠29)\n𝐻 𝜇 𝐻\n𝑐𝑗 0 𝑐𝑗\nQuantitative analysis confirms the ratio is lower than 1.2%. At low driving field strengths, the permanent\nmagnet remains near saturated magnetization. And the external electromagnetic field does not significantly\nalter its internal magnetic moment distribution. Therefore, the dynamics of the inner magnet and the entire\nrobot are not influenced by the magnetic hysteresis effects.\nAR: Non-linearities in the electromagnetic response - In the original version, we modeled and analyzed the\nmagnetic field distribution in the robot's center channel (Fig. S3) and the force on the permanent magnet (Fig.\nS4). The results showed that the magnetic field distribution in the center channel was nonlinear. When\ncalculating the force on the permanent magnet, we treated it as a magnetic dipole. Despite potential errors from\nthis simplification as the magnet was placed in a nonlinear region, its impact was minimal. We divided the\npermanent magnet into 100 equal parts along the central axis, calculated their individual forces, and summed\nthem to obtain the total force, as illustrated in Fig. R11. The blue line represents the magnetic force calculated\nusing the dipole model, while the red line shows the result from a discrete model using small permanent magnets,\nwhich accounts for magnetic field nonlinearity. The results show that the dipole model yields a higher force\nnear the coil region and a slightly lower force in the middle region compared to the discrete model. However,\nafter considering the offset in both regions, the overall results of the two models are consistent, with negligible\nerrors in estimating the transmitted magnetic power. The power exerted on the inner magnetic can be calculated\nby integrating the force along the position axis. As shown in Fig. R11, the areas under the red and blue curves\nare 5.724 N·mm and 5.955 N·mm, respectively. The results confirm that the simplified dipole model is\nsufficiently accurate for capturing the nonlinear magnetic field distribution. For future work requiring higher\nfidelity, a finer-resolution finite element simulation can be employed.\nFig. R11 Comparison of magnetic forces acting on the permanent magnet based on magnetic dipole model\nand discrete superposition method\nComment #3.2 The dynamics of the impact force generation and its relation to microrobot stability are not\nanalyzed beyond empirical observations.\nAR: We thank the reviewer for highlighting the need for analysis of robot stability. The instability in robot motion\nprimarily stems from two factors. First, when the frictional force between the robot and its environment is\ncomparable to the electromagnetic driving force, the robot enters a critical regime (Fig. 2B), exhibiting unstable\nforward or backward movement. To address this, the revised version includes a detailed derivation of this\nregime's conditions and provides guidelines for selecting the driving current to avoid it. Second, during high-\nload operation, the robot generates strong impact forces during movement. If its center of gravity deviates from\nthe geometric center, a moment of deviation is induced, causing unstable rectilinear motion. To mitigate this,\nthe real-time position and orientation feedback is necessary to adjust the control parameters. In the revised\nmanuscript, we developed a robot tracking platform based on magnetic sensor array, demonstrating that the\nposition and orientation of the MiaBot can be sensed in real-time.\nTo clarify this issue, the manuscript is revised as follows:\nCritical region analysis: Manuscript: Section: “Robot actuation mechanism and kinematic characterization”:\nAdditionally, a critical region emerges where locomotion exhibits directional instability as environmental\nresistance approaches the magnetic actuation force. Within this region, the system exhibits oscillatory motion\nor unsteady swaying rather than stable unidirectional movement. Fig. S5 provides signal selection guidelines to\navoid this unstable operational zone across varying environments.\nCritical region analysis: Supporting Information: Section: “Selection of locomotion modes”:\nFig. R12 (Fig. S5 in the Supporting Information): Motion modes of MiaBot under varying input and\nenvironmental conditions. (A) Phase diagram mapping motion regimes to input current magnitude and\nenvironmental friction. (B) Motion mode differentiation between high-friction (loaded) and low-friction\n(unloaded) states.\nAs illustrated in Fig. S5(A), the robot demonstrates diverse motion modes under varying input current\namplitudes and environmental friction conditions. First, when the robot is in a high-friction environment or the\ndriving current is extremely low, a \"dead zone\" occurs where the robot cannot move. Conversely, in frictionless\nor low-friction scenarios, where the environmental friction force is insufficient to counteract the electromagnetic\nattraction, the robot frame is attracted by the electromagnetic force (i.e., attraction-dominated region Fig. S5(B,\ni)). In contrast, under high resistance or heavy loads exceeding actuation forces, the robot remains stationary\nduring magnet acceleration but slides under subsequent impact-induced thrust (i.e., impact-dominated region\nFig. S5(B, ii)). An unstable \"critical region\" exists between these two states, where the robot may exhibit\nunstable left-right swaying motions. This section establishes current control strategies to mitigate critical region\ninstability and ensure stable locomotion across variable friction/load conditions.\nMagnetic tracking showcases the possibility of future close loop and stable control:\nFig. R13 (Fig. S17 in the Supporting Information): Tracking of MiaBot through magnetic sensor array. (A) The\ndiagram shows the principle of magnetic localization. (B) Comparison of the Localization results with the actual\ntrajectory.\nAccurate position and orientation feedback of MiaBot is important for precise and stable control to complete\ntasks in unstructured terrains. However, it remains a critical challenge, particularly in non-illuminated\ntubular environments where optical tracking methods prove ineffective. To overcome the limitations, we use\nthe magnetic localization method, which does not rely on line-of-sight, for target tracking. we model MiaBot as a\npermanent magnetic dipole and deploy an external sensor array for magnetic flux density detection (Fig. S17(A)).\nThe magnetic field intensity at the l-th sensor position is given by:\n𝜇 3(𝒎 ∙𝑹)𝑹 −𝒎\n0 𝑎 𝑙 𝑙 𝑎\n𝑩 =𝐵 𝑖+𝐵 𝑗+𝐵 𝑘= [ ] (𝑠49)\n𝑙 𝑙𝑥 𝑙𝑦 𝑙𝑧 4𝜋 ‖𝑹‖3\n𝑙\nwhere 𝑩 denotes the magnetic flux density at the l-th sensor, 𝜇 =4π × 10−7 H/m is the vacuum\n𝑙 0\npermeability, 𝒎 represents the magnetic moment vector, 𝑹 is the unit vector from the dipole to the sensor,\n𝑎 𝑙\nand ‖𝑹‖ is the source-to-sensor distance.\n𝑙\nThen, we define an error function as:\n𝐸𝑟𝑟 =(𝑉 −𝐵 )2+(𝑉 −𝐵 )2+(𝑉 −𝐵 )2 (𝑠50)\n𝑙 𝑙𝑥 𝑙𝑥 𝑙𝑦 𝑙𝑦 𝑙𝑧 𝑙𝑧\nwhere (𝑉 ,𝑉 ,𝑉 )𝑇 is the measured data from the l-th sensor and (𝐵 ,𝐵 ,𝐵 )𝑇 is the estimated value\n𝑙𝑥 𝑙𝑦 𝑙𝑧 𝑙𝑥 𝑙𝑦 𝑙𝑧\ngenerated by the magnetic dipole model. The position and orientation of the magnet can be obtained by\nminimizing 𝐸𝑟𝑟 using the particle swarm optimization algorithm.\n𝑙\nFig. S17(B) demonstrates that MiaBot locomotes through a silicon tube from left to right. A magnetic tracking\nsystem formed by eight magnetic sensors is deployed outside the tube. The black dashed line in the figure\nrepresents the real trajectory that the robot passes through during its movement, and the red line represents the\ntracking result of the robot. We can observe a high degree of overlap between the positioning results and the\nactual trajectory (with a root mean square error of 4.53 mm). This precise localization capability enables future\nimplementation of closed-loop control strategies for enhanced robotic navigation precision in unstructured\nterrains and non-illuminated environments.\nComment #3.3 No analytical or numerical modeling is provided to predict the performance of the robot in\ndifferent environmental conditions.\nAR: Thank you for your feedback. In the previous version, we identified three motion modes of the MiaBot (Fig.\n2A and Fig. 2B): 1) when the environmental friction is less than the electromagnetic actuation force, the robot\nmoves in the opposite direction to the magnet; 2) when the environmental friction exceeds the electromagnetic\ndriving force, the robot slides in the same direction as the magnet under the impact force of the permanent\nmagnet; and 3) unstable movements in the critical region. In the revised version, we performed a more in-depth\nanalytical modeling and provided specific recommendations for selecting actuation signals to optimize\nperformance.\nIn the revised supplementary material, the following analysis has been made:\nIn our design, the weight of the permanent magnet 𝑚 is larger than the mass of the robot frame 𝑚 (i.e.,\n1 2\n𝑚 >𝑚 . When input current 𝐼 activates the system, the electromagnetic force 𝐹 accelerates the permanent\n1 2 𝑚\nmagnet while simultaneously propelling the robot frame in the opposite direction against environmental friction\n𝐹. The dual motion of the permanent magnet and the robot frame is governed by\n𝑓\n𝑑2\n𝑚 𝑧1 =𝐹 (𝑧)−𝐹 (𝑠30)\n1𝑑𝑡2 𝑚 𝑓𝑖\n𝑑2\n𝑚 𝑧2 =−𝐹 (𝑧)+𝐹 +𝐹 (𝑠31)\n2𝑑𝑡2 𝑚 𝑓 𝑓𝑖\nwhere 𝑧=𝑧 −𝑧 denotes the relative position between the magnet and the end of the robot frame. 𝐹 is the\n2 1 𝑓𝑖\ninner friction between the magnet and the robot frame. Applying boundary conditions of z = 0, we discretize\nthese equations via the Euler method to solve for the magnet-frame encounter time (t).\nThe respective traveling distances of the permanent and the robot frame are\n𝑚 (𝐿 −𝑙) 𝐹\n𝑠 = 2 𝑐 + 𝑓 𝑡2 (𝑠32)\n1 𝑚 +𝑚 2(𝑚 +𝑚 )\n1 2 1 2\n𝑚 (𝐿 −𝑙) 𝐹\n𝑠 = 1 𝑐 − 𝑓 𝑡2 (𝑠33)\n2 𝑚 +𝑚 2(𝑚 +𝑚 )\n1 2 1 2\nwhere 𝐿 is the length of the robot frame, l is the length of the permanent magnet. Equations (S32) - (S33)\n𝑐\nreveal that for high 𝐹 (heavy loaded/high-friction environments), the relative motion between the permanent\n𝑓\nmagnet and the robot frame is mainly contributed by 𝑠 (impact dominance). While when the robot is not\n1\nloaded or moving in a smooth environment, the main displacement of the robot is attributed to 𝑠 (attraction\n2\ndominance).\nPost-collision, most of the energy will be canceled out due to the opposite direction of motion between the frame\nand the permanent magnet. The residual kinetic energy can be expressed as\n1 𝐹2\n𝐸 = 𝑓 𝑡2 (𝑠34)\n𝑘 2𝑚 +𝑚\n1 2\nAfter the permanent magnet collides with the robot end cover, they continue to slide as a combined system until\nthey rest. The sliding distance is\n𝐸\n𝑘\n𝑠 = (𝑠35)\n3 𝐹\n𝑓\nTo avoid unstable critical regions, modulate the input current to maximize |𝑠 −𝑠 | . Since 𝑠 and 𝑠 are\n2 3 2 3\ncorrelated with −𝑡2 and 𝑡2, respectively, the attraction-dominant displacement requires minimizing current to\nprolong 𝑡, ensuring that the magnet-frame attraction occurs gradually (i.e., the permanent magnet collides with\nthe end of the robot cover at a lower speed).\nWhen the electromagnetic driving force is less than the frictional force between the robot and the environment\n(i.e., 𝐹 <𝐹), the motion process of the robot becomes simpler as the environmental friction is high enough\n𝑚 𝑓\nto keep the robot in place in the attraction stage. The permanent magnet accelerates towards the end cover of\nthe robot under the action of electromagnetic force, and its impact velocity is expressed as\n2∫\n𝐿𝑐−𝑙\n𝐹 (𝑧)𝑑𝑧\n𝑣 =√ 0 𝑚 (𝑠36)\n1 𝑚\nunder the action of inertia. The sliding distance is\n𝑚2𝑣2\n𝑠= 1 1 (𝑠37)\n2𝐹(𝑚 +𝑚 )\n𝑓 1 2\nSince both the permanent magnet and the robot end cap are nonelastic bodies, their impact time 𝑡 is short to\n𝑖\ngenerate a strong instantaneous impact force for driving the millirobot in high frictional environments. One the\nother hand, the millirobot has a loading limit to ensure that the friction force is less than the instantaneous\npropulsive force generated by the impact (i.e., 𝐹 <𝑚 𝑣 /𝑡) to avoid the robot entering the dead zone.\n3.4 Comment #4\nRC: The experimental results lack rigorous control and reproducibility. Several aspects of the methodology raise\nconcerns:\nComment #4.1 The actuation mechanism is tested in highly controlled environments that do not sufficiently\nrepresent real-world applications such as the human gastrointestinal tract or complex unstructured terrains.\nAR: Thanks for your comments. In the previous version, we noted in one sentence that has over claim to indicate its\npotential applications in both industrial and biomedical systems. However, the core innovation of this work\nresides in the actuation mechanism, MiaBot design and its application in high frictional environments. Therefore,\nafter careful consideration, we have removed the claim on biological applications. Additionally, to better\nsimulate complex industrial environments in real world, we have incorporated additional navigation\nexperiments for the MiaBot to navigate in vertical and three-dimensional tortuous pipelines. To address this\nissue, the revisions have been made as follows\nTone down the references to biomedical applications in section “Potential applications of MiaBot in flexible\ntube inspection”:\nRevised version: Regular inspection and maintenance of small-diameter pipelines in high-end equipment,\nparticularly for detecting internal blockages and cracks, are critical to operational efficiency and safety. However,\ntraditional endoscopic probes cannot navigate deep tortuous segments, whereas the proposed MiaBot\ndemonstrate high efficacy in traversing these constrained environments despite gravitational loads and wall\npressures.\nVertical and three-dimensional tortuous pipeline navigation experiments\nFig. R14 (Fig. 6 in the Manuscript): Inspection in a confined flexible tubular environment. (B) Locomotion in\na vertical tube. (C) Locomotion through a tube in 3-D space.\nVertical and three-dimensional tubular navigation poses significant challenges for millirobots, as their limited\nactuation force often fails to overcome the resistance from high friction and gravitational effects. This typically\nresults in downward sliding and insufficient upward mobility. However, the spatially distributed complex\ntubing systems are widely employed in high-end equipment for gas-liquid transportation. To enable the\ndeployment in such environments, we implemented the MiaBot with a resistance regulation strategy in the\nflexible tubes. The system's strong instantaneous propulsion enables MiaBot to achieve rapid motion against\nboth gravity and pipeline friction. In the experiment, MiaBot successfully navigated through a 60 cm vertical\npipeline in 60 s with a 10 Hz square wave driving signal at +0.5 A forward and -0.05 A reverse (see Fig. 6B,\nVideo 9). For equivalent-length three-dimensional spatial navigation, the robot required approximately 100 s\n(Fig. 6C), with this delay attributed to high frontal resistance from the narrow inner surface of the silicone\ntube.\nComment #4.2- The experiments rely on manual actuation and observation, with limited statistical analysis to\nensure reproducibility and significance.\nAR: We apologize for this confusion. In fact, most experimental results were obtained using specialized instrument\nrather than manual observation. For instance: Impact time measurements (on the order of tens of milliseconds)\nemployed high-speed cameras. Impact forces were quantified using a 50-kHz high-frequency contact force\nsensor. Coil temperature data was acquired via thermal imaging devices. All experiments in Fig. 2, Fig. 3, and\nFig. 4 were repeated at least five times, with error bars in the data representing standard deviations to confirm\nreproducibility.\nComment #4.3-The comparison with natural creatures (e.g., ants and beetles) lacks scientific rigor and does\nnot contribute meaningful insights into the practical relevance of MiaBot.\nAR: Thank you for pointing this out. The data points in comparison with natural creatures in Fig.1D are all extracted\nfrom previous scientific papers. To eliminate the debating relevance to this work, this figure has been removed\nfrom Fig. 1 in the main manuscript. However, the loading performance are kept in supplementary materials to\ndiscuss and compare with natural creatures in Table. S2 to provide extra information to interested readers. The\nupdated Fig. 1 and the related text can be seen as follows:\nFig. R15(Fig. 1 in the Manuscript): Overview and locomotion mechanism of MiaBot. (A) An image of a\nMiaBot and an exploded view of the design. (B) Comparison of load-carrying capability between the proposed\nMiaBot with the existing millirobots less than 10 g. (SMA: Shape memory alloy, DEA: Dielectric elastomer\nactuators, PZT: Piezoelectric actuators). (C) The snapshot of one actuation cycle: MiaBot carrying 500 g load\nactuated by a biased square wave (0.5A and -0.05A) signal. (D) Position of the inner magnet and the\ncorresponding force on the MiaBot during one actuation cycle. When the applied current is 0.5 A, the magnet\naccelerates from one end to the other within 20 ms and generate a theoretical impact force greater than 19 N.\nThe magnet is repositioned to its initial position using a lower current (-0.05 A). (E) The schematic diagram\nshows that MiaBot is capable of exploring various terrains with high friction, such as granular medium, viscous\nliquids, and large payload transportation, due to the strong impact force.\nSection: “Introduction”:\nWhen the MiaBot is driven by a square wave ranging from 0.5 A to -0.05A. Fig. 1C depicts the snapthot of\nthe inner magnet and MiaBot during one cycle actuation. During propulsion, the magnet traverses the central\nchannel in 14 ms, generating a strong impact force that propels the MiaBot forward. For the reposition process,\nthe impact force is insufficient to overcome static friction, preventing backward displacement. Fig. 1D\ndemonstrates that the magnet can pass through the center channel of the robot frame within 20 ms, causing a\ntheoretical thrust of up to 19.01 N. By leveraging local magnetic field actuation and momentum conservation,\nthe robot overcomes substantial environmental resistance to perform challenging tasks, including navigation\nthrough granular media, operation in high-viscosity silicone oil, and cargo transport exceeding 300 times its\nweight (Fig. 1E). Fig. 1B compares MiaBot’s load-carrying capability with that of state-of-the-art millirobots\n(weighing less than 10 grams) using various actuation mechanisms, including shape memory alloy24, 25, 26,\ndielectric elastomer actuators27, 28, 29, 30, piezoelectric actuators31, 32, 33, 34, magnetic robots17, 35, 36,\n37, 38, 39, and photothermal actuators40, 41, 42, 43. Moreover, we also compare the loading performance\nwith natural creatures like insects and mammals (data in Tables S2 and S3). The results show that MiaBot\noutperforms most miniature robots and surpasses the majority of natural creatures, falling short only of beetles.\nComment #4.4- The load-carrying performance lacks a detailed discussion of how frictional losses,\ncompliance of surfaces, and real-time control strategies affect performance.\nAR: We deeply appreciate this insightful comment.\nFrictional loss: We agree that frictional loss significantly impacts load-carrying performance. As shown in Fig.\n3D, which plots locomotion velocity versus loaded weight, we observed a decrease in speed as the load increases.\nTo better illustrate the effect of frictional loss, we analyzed the relationship between the loss rate and load in\nFig. 3D. We define the effective energy as 𝐸 =0.5×𝑚 ×𝑣2 , the input energy as 𝐸 =𝐼2𝑅𝑡, and the\ne 𝑙𝑜𝑎𝑑 𝑙𝑜𝑎𝑑 𝑖\nloss rate as 𝜂=(𝐸 −𝐸 )/𝐸 . The results in one cycle of actuation show that the robot's effective power\ni e i\ndecreases and the loss rate increase as the load increases. The occurrence of this phenomenon is due to the fact\nthat as the weight increases, the robot and the ground bonded tightly, resulting in an increase in the friction force\nbetween the two surfaces.\nFig. R16 (Fig. 3(D) in the Manuscript). The locomotion velocity decreases with increased payload, while the\nenergy loss ratio rises due to the higher friction induced by the added weight.\nSection: “Inertial impact force and loading performance”:\nWith a load of 100 g, the millirobot achieves an average velocity of 618.74 mm/min. The speed decreases to\n67.3 mm/min when the payload increases to 1000 g (171.82 times its body weight). We calculate energy loss as\nthe input energy minus the load kinetic energy, defining the loss rate as this deficit relative to the input energy.\nThe results in Fig. 3D show the loss rate increases under heavier loads due to the enhanced robot-ground contact,\nwhich creates additional friction and results in greater frictional loss.\nCompliance of surfaces: We have also added a new Section “Inertial impact and loading performance” to\ndiscuss the compliant surfaces, which affect load-bearing capacity in two key ways: 1. Compliant surfaces\ntypically exhibit higher friction coefficients, increasing the locomotion resistance. 2. Surface deformation under\nimpact forces absorbs most energy, further reducing load-bearing capability.\nSection “Inertial impact force and loading performance”:\nFurthermore, to assess the locomotion reliability, the millirobot with a 500 g payload is tested on various surfaces\nsuch as metal, plastic, fabric, and wood (Fig. 3F, Video 1). The results prove that the millirobot is capable of\ncarrying a heavy payload to move at a speed constantly above 110 mm/min on variety rigid surfaces. In the\nexperiments, we observed that MiaBot's load-bearing capacity significantly decreases on flexible surfaces due\nto energy absorption by surface deformation and increased adhesion to paper and polymer-based materials.\nReal-time control strategies: Furthermore, implementing a real-time control strategy can correct the trajectory\ndeviation when the robot is carrying heavy cargos, we show the magnetic tracking results in this paper. Moreover,\nadjusting the input frequency is also a way to improve the MiaBot’s locomotion speed (Fig. 3C).\nSection: “Potential applications of MiaBot in flexible tube inspection”:\nMoreover, the robot's real-time position can be tracked using a magnetic tracking system (Fig. S16),\ndemonstrating the potential of closed-loop control for precise navigation. This is particularly useful for\nperforming tasks at designated locations in tubular environments without external line of sight. The\ndemonstration indicates that MiaBot has the potential to detect and location the defects in industrial pipeline\nsystems.\nComment #4.5- The lack of a comprehensive error analysis undermines the reliability of the reported data.\nAR: Thanks for pointing this out. In this study, we performed repeated experiments and derived the mean and\nstandard deviation of statistical data with a systematic error analysis. For example, in Fig. 2E, the discrepancy\nbetween the measured magnet velocity and theoretical value was attributed to neglected friction between the\nmagnet and robot frame. In Fig. 3A, the significant variance in impact force measurements was linked to the\nultra-short impact duration (typically <1 ms) between rigid bodies (magnet and robot stopper), suggesting\npotential measurement errors from the impact force sensor. Additionally, this revised version includes an\nexpanded analysis of the robot’s high velocity variance in rough environments (Fig. 3E), which we attribute to\nirregular protrusions on rough sandpaper acting as numerous tiny \"speed bumps,\" introducing randomness in\nthe contact forces experienced by the robot. To address this issue, we have made the following revisions:\nIn Section “Robot actuation mechanism and kinematic characterization”:\nThis discrepancy among experimental measurements can be attributed to the neglect of friction between the\ninner magnet and the frame in the simulation and the idealized assumption of perfect alignment between the\nmagnet’s axis and the coil axis.\nIn Section “Inertial impact force and loading performance”:\nThe variance in impact force measurements is attributed to the ultra-short impact duration (typically <1 ms)\nbetween rigid bodies (magnet and robot stopper), which may introduce measurement errors in the force sensor.\nFig. 3E demonstrates the locomotion speed of MiaBot on various sandpapers, with insets showing physical\nimages (5x magnification) of four different roughness levels (i.e., 180 mesh, 400 mesh, 800 mesh, and 1000\nmesh). The results show MiaBot maintains high payload capacity on rough surfaces whereas faster locomotion\noccurs on smoother surfaces. Additionally, we observed that velocity variance increases with surface roughness,\nwhich was attributed to irregular particulate protrusions that induce unstable friction forces on robot.\n3.5 Comment #5\nRC: The claimed applications, such as pipeline inspection and medical interventions, are not adequately justified.\nAR: Thank you for your feedback. In the revised manuscript, we have moderated claims regarding biomedical\napplications and emphasized industrial use cases such as pipeline inspection. We included a navigation\ndemonstration showcasing the robot’s operation in complex pipelines, including vertical sections and tortuous\n3D paths to validate its ability to operate in inclined pipelines while compensating for gravitational effects (Fig.\n6). Additionally, a magnetic sensor array and a tracking algorithm are integrated to the system to achieve\naccurate robot positioning even in obstructed pipelines (Fig. S17). These results establish a technical foundation\nfor future precise localization of millirobot in internal pipeline inspection. The action of “toning down the\nreferences to biomedical applications” and “extended pipeline application experiments” can be referred to our\nresponse to Comment #4.1. Additionally, the real-time tracking of MiaBot in a tubular environment is explained\nin our response to Comment #3.2.\n3.6 Comment #6\nRC: Lack of In Vivo Validation. The robot's ability to navigate complex biological environments is speculative, as it\nis only tested in artificial setups.\nAR: Thank you for your feedback. To better align with the manuscript's core focus, we have moderated discussions\nof biomedical applications. The revised version prioritizes analysis of the robot's propulsion mechanism and its\npotential in industrial pipeline applications. In the future, we will do more thorough research to study its\npotential in biomedical scenarios in an extra work.\n3.7 Comment #7\nRC: Energy Efficiency Concerns. The high-impact actuation mechanism may introduce excessive energy dissipation,\nvibration, and instability, limiting its practicality for precision applications.\nAR: Thank you for your comments. We agree the energy efficiency limitations of MiaBot. However, its permanent\nmagnet’s acceleration and instantaneous release mechanism offers unique advantages in specialized scenarios\nby generating exceptional propulsion forces. This capability proves critical for (1) extending maximum output\nforce thresholds; (2) locomotion in high-resistance environments; (3) preventing motor stall during starting in\nhigh-friction environment. To clarify the energy efficiency, additional quantitative efficiency analysis is added\nin Fig. 3D. The results indicated that as the payload weight increased from 100g to 1000g, the loss rate escalated\nfrom 39.5% to 91.3%, , which is a trade-off to improve its upper limit of certain capabilities. Our action:\nFig. R17 (Fig. 3(D) in the manuscript). The relationship between locomotion velocity, loss rate and loaded\nweight.\nSection: “Inertial impact force and loading performance”:\nWith a load of 100 g, the millirobot achieves an average velocity of 618.74 mm/min. The speed decreases to\n67.3 mm/min when the payload increases to 1000 g (171.82 times its body weight). We calculate energy loss as\nthe input energy minus the load kinetic energy, defining the loss rate as this deficit relative to the input energy.\nThe results show the loss rate increases under heavier loads due to the enhanced robot-ground contact,\nwhich creates additional friction and results in greater frictional loss.\n3.8 Comment #8\nRC: Biocompatibility and Safety Issues. the potential for damage in medical applications due to high-impact forces\nis not discussed.\nAR: In the prior version's section “Potential applications of MiaBot in flexible tube inspection”, we briefly\nreferenced potential biomedical applications. After careful consideration, we decided to remove that claim.\nMedical implementation would require substantial robot redesign and clinical validation, potential future work\nbeyond this study's scope. For transparency, we provide both original and revised statements below:\nPrior version: The flexible tubular environments in industrial systems, such as oil pipelines and biomedical\nsystems, like the gastrointestinal tract, are prone to deformation and collapse, causing the tube walls to envelop\nthe robot and generate significant frictional resistance. However, regular inspection is critical in these systems\nto prevent system failure or disease progression.\nRevised version: Regular inspection and maintenance of small-diameter pipelines in high-end equipment,\nparticularly for detecting internal blockages and cracks, are critical to operational efficiency and safety. However,\ntraditional endoscopic probes cannot navigate deep tortuous segments, whereas the proposed MiaBot\ndemonstrate high efficacy in traversing these constrained environments despite gravitational loads and wall\npressures.\n3.9 Comment #9\nRC: Scalability. The feasibility of scaling this actuation mechanism for different sizes and environments is not\nexplored.\nAR: We appreciate the reviewer’s feedback. We investigated the scaling effects of the robot in both length and\ndiameter directions (scaling factor range: 1/5 to 5) in Fig. S8. The numerical calculations theoretically\ndemonstrated that the robot's impact kinetic energy remains consistently high across this scaling range. In the\nrevised version, we also included additional simulations specifically focusing on diameter scaling within\nsilicone oil environments. The results indicate that the resistance significantly increases when increasing the\ndiameter in silicone oil. The results suggest that maintaining a smaller diameter configuration in silicone oil\nyields higher motion efficiency. The detailed simulation results can be seen as follows:\nFig. R18 (Fig. S8 in the Supporting Information): The scalability of MiaBot in diameter and length aspects.\n(A) Scalability in diameter direction. (i) Schematic diagram; (ii) The effect of the diameter scaling factor on\nthe magnet’s impact velocity; (iii) The effect of the diameter scaling factor on the magnet’s impact kinetic\nenergy. (B) Scalability in length direction. (i) Schematic diagram; (ii) The effect of the length scaling factor\non the magnet’s impact velocity; (iii) The effect of the length scaling factor on the magnet’s impact kinetic\nenergy.\nSupporting Information: Section08: Scalability of MiaBot.\nIn this section, we investigate the scalability of MiaBot in two dimensions, including the direction of diameter\nand length. In these two types of scalability, we keep the coil arrangement and input current constant. Moreover,\nthe distance between the center channel and the magnet in the direction of diameter and length also remains\nunchanged. The diameter/length of the magnet is changed to k (k = [1/5, 5.00]) times its original diameter to\nverify its scalability in two directions, as shown in Fig. S8(A, i) and Fig. S8(B,i).\nFig. S8(B, ii) shows that the impact velocity of the magnet decreases with the increased diameter of the magnet.\nThe reason is that a larger diameter can result in a larger mass and, thus, a lower acceleration value. Although\nthe impact velocity is lower, the impact kinetic energy increases with an increased diameter (Fig. S7(A, iii))\nbecause the kinetic energy is proportional to the magnet’s mass.\nIn the length direction, we observed that the highest impact velocity appears near the original size (i.e., k = 1)\n(Fig. S8(B, ii)). Interestingly, we also observed that the magnet’s kinetic energy does not increase with increased\nmass. The reason is that when the length of the center channel increases, the coils at two ends increase, and the\nmagnetic field gradient at the center channel decreases simultaneously. In this way, the magnet can not keep a\nhigh velocity before impacting. From the simulation result, we can find that when k is about 2.0, the best impact\nkinetic energy appears (Fig. S8(B, iii)). The red line represents the impact energy generated per unit mass of the\nmagnet. As the magnet’s diameter and length increase, its per-unit-mass impact energy exhibits a general\ndownward trend. When the scale factor ranges from 1/5 to 5, the per-unit-mass impact energy predominantly\nremains above 1 mJ/kg. For specific scale factors, optimizing the coil configuration can enhance the per-unit-\nmass impact energy.\nSupporting Information: Section15: Locomotion in viscous environment.\nFig. S15: Simulation and experiments in a viscous environment. (A) The heat map of simulationresults shows\nthe force distribution. (B) The heat map of simulation results shows the pressure distribution at the fin tips with\nvaried angles. (C) The average resistive force plot shows an increasing trend with elevated scaling factors. (D)\nThe extracted average pressure plot shows an increasing trend with the elevated fin angles\nFor a robot moving in a silicon oil environment, the locomotion state of the robot can be determined by\ncalculating the Reynolds number as follows:\n𝜌𝑣𝐿\n𝑅𝑒= (𝑠47)\n𝜂\nwhere 𝜌 is the density of the liquid, 𝑣 is the velocity of the robot, 𝐿 is the character length of the robot, and\n𝜂 is the dynamic viscosity of silicone oil.\nAs shown in Fig. 5(B), the movement speed of MiaBot in silicone oil is approximately 2.5mm/s. For low-speed\nmovement in high-viscosity environments (e.g. Re ≪ 1), it can be considered as laminar flow. In this case,\nthe friction force can be expressed as:\n𝐹=𝐾𝜂𝑣𝐿 (𝑠48)\nwhere k is the shape correction factor. For spherical robots, the value is 𝑘=3𝜋, while for other shapes,\nsuch as the conical head used in this article, the value needs to be determined by experiments or numerical\nsimulations.\nIn this study, finite element analysis (FEA) was conducted using ANSYS 2022 to simulate hydrodynamic\nforces acting on the robot. As illustrated in Fig. S15(A) and Fig. S15(C), the resistance force exhibits a positive\ncorrelation with the characteristic length of the robot, aligning with the theoretical predictions derived from Eq.\nS48. When the robot’s diameter was scaled from 0.5× to 2.0× the baseline design, the resistance increased\nproportionally from 1.05 mN to 3.36 mN. These results suggest that minimizing the cross-sectional area of\nMiaBot is critical for enhancing actuation efficiency in highly viscous fluid environments.\n3.10 Comment #10\nRC: The manuscript includes excessive and irrelevant comparisons, such as those with animal species, which do\nnot strengthen the scientific arguments.\nAR: We appreciate this feedback. Per Comment #4.3, comparative analysis involving animal species has been\nremoved from the main Manuscript. The relevant performance data relative to biological systems are retained\nin Supporting Information (Table S3) for reference."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I believe that the authors made an honest, concise, and determined effort to address all of my concerns. They provided\nadditional experiments, simulations, and discussions which greatly improved the paper and increased its scientific merit. I\npersonally don't have any remaining serious complaints that need to be addressed. I recommend it for publication.", "reviewer_2": "The authors have responded clearly and constructively to the previous comments, significantly improving the quality of the\nmanuscript. The revised version shows the design rationale of the MiaBot system and highlights the role of momentum-\ndriven actuation strategy in overcoming the limitations of conventional actuators. The addition of simulation results and\nexperimental validations, including locomotion in high-friction conditions and confined tubular environments, demonstrates\nthe applicability of the system beyond the reach of traditional approach. The manuscript now is technically convincing and\npresents a novel approach in millirobotic actuation systems.\nMy remaining concern lies in the energy efficiency of the system whether the generated thrust is sufficiently high relative to\nthe electrical input required to drive the coils. While the demonstrated force output for load capability and load-to-weight ratio\nis impressive, a discussion on the input-output power ratio or energy conversion efficiency would provide a clearer\nunderstanding for system comparison and actuation efficiency.\nAdditionally, the authors briefly mention the potential for future wireless operation using onboard power sources. However,\ngiven the relatively high current required for internal electromagnetic actuation, the technical feasibility of wireless\nintegration remains unclear within the current range. A more detailed discussion on the challenges and potential strategies\nfor onboard battery systems, wireless power transfer, or energy efficiency optimization would strengthen the proposed\noutlook. Since many high-friction or confined-space applications demand untethered operation, the authors could discuss\nthe feasibility and enhance future directions of this work.\nIn particular, electromagnetic coil-based actuation generates Joule heat during operation, which may result in thermal\naccumulation or functional shutdown under prolonged usage. Although the manuscript describes impact experiments, it\nremains important to quantitatively evaluate long-term performance stability, including potential issues such as mechanical\ndegradation, thrust force reduction, or delayed actuation response over time. Because the actuation mechanism is based on\nhigh impact force to operate in high-friction and confined environments, further discussion on long-term performance would\nstrengthen the evaluation of durability.\nThe rationale behind the selected robot scale is not fully addressed. As magnetization and impact force are affected by\nmagnet sizes, decrease in robot size may compromise actuation efficiency.\nSeveral figures in the manuscript lack essential graphical clarity and unclear annotations, which hinders readability and\nreproducibility.\nFigure S5: The phase diagram uses qualitative terms such as “extremely low” and “insufficient” without clearly defined\nnumerical thresholds. The authors are encouraged to quantitatively define the critical values that determine the locomotion\ntransition.\nFigure S8: Specific numerical values or ranges are not provided although diameter scaling factors are discussed, making it\ndifficult to interpret the results and understand the underlying criteria.\nFigure S3 and S8: Legends are missing.\nIn addition to these examples, the authors should carefully review all figures and texts throughout the manuscript and\nsupplementary information to ensure that typo, scale bars, legends, units, and kye parameters are clearly presented.", "reviewer_3": "I have carefully reviewed the revised manuscript and the authors' response letter. While I sincerely appreciate the authors’\neffort to incorporate some of my previous comments—such as correctly referring to the robot’s scale and improving\nterminology—I still find that the manuscript suffers from several fundamental issues that were not adequately\naddressed in the revision.\nMost importantly, the authors do not provide a predictive model, dynamic simulation, or force–momentum-based analysis to\nsupport their design claims. This omission significantly limits the scientific value and reproducibility of the work. The\noriginality of the concept also remains unconvincing, especially given that some of the cited literature already covers similar\nideas. A more valuable contribution might have been to build on these concepts and apply them to a specific, well-motivated\nuse case.\nAdditionally, the manuscript lacks critical performance metrics such as force efficiency, energy usage per cycle, and\nactuation frequency. Without control experiments or comparative testing using other actuation strategies, it is difficult to\nevaluate the actual benefits of the proposed design.\nFinally, although the authors mention applications in confined or biological environments, the robot’s impulsive actuation\nmethod, high-speed internal impacts, and absence of steerability make it unlikely to be suitable for biomedical use. There is\nno discussion of biocompatibility, safety considerations, or integration with control and imaging systems, which weakens the\nbroader impact of the work.\nFor these reasons, I do not believe the manuscript is ready for publication in its current form."}, "author_response": "Authors’ Response to Reviews of\nMomentum-Driven Millirobotics: Magnetically Inner-Actuated\nDesign for High-Friction and Confined Environments\nMin Wang, Wenlong Wu, Zeju Zheng, Wei Dai, Tianyi Wu, Rui Liu, Yuxuan Xiang, Steven Wang, Jiachen Zhang∗,\nZuankai Wang∗, Jun Liu∗\nNature Communications, Ref: NCOMMS-24-57990B\nRC: Reviewers’ Comments, AR: Authors’ Response, : Authors’ Action\nThe authors would like to thank the Editor, Nature Communications, for allowing a major\nrevision of our manuscript (ID: NCOMMS-24-57990B). We also thank the reviewers for their\ninsightful comments and suggestions. We have addressed all the comments in this revised\nversion. The point-by-point response to the comments and detailed explanations of\nmodification are attached below.\nReviewer #1\nI believe that the authors made an honest, concise, and determined effort to address all of\nmy concerns. They provided additional experiments, simulations, and discussions which\ngreatly improved the paper and increased its scientific merit. I personally don't have any\nremaining serious complaints that need to be addressed. I recommend it for publication.\nAR: Thanks for your positive evaluation on our manuscript. Thanks again for your time and\nconstructive feedback on the manuscript throughout the whole review process.\nReviewer #2\nThe authors have responded clearly and constructively to the previous comments,\nsignificantly improving the quality of the manuscript. The revised version shows the\ndesign rationale of the MiaBot system and highlights the role of momentum-driven\nactuation strategy in overcoming the limitations of conventional actuators. The addition\nof simulation results and experimental validations, including locomotion in high-friction\nconditions and confined tubular environments, demonstrates the applicability of the\nsystem beyond the reach of traditional approach. The manuscript now is technically\nconvincing and presents a novel approach in millirobotic actuation systems.\nAR: Thanks for your positive comments on our previous revised manuscript. We have further\nimproved our manuscript according to your constructive suggestions and comments. As shown\nbelow, we provide point-by-point responses to your comments and have revised the manuscript\nto improve its fitness for publication in Nature Communications.\n2.1 Comment #1\nRC: My remaining concern lies in the energy efficiency of the system whether the generated thrust\nis sufficiently high relative to the electrical input required to drive the coils. While the\ndemonstrated force output for load capability and load-to-weight ratio is impressive, a\ndiscussion on the input-output power ratio or energy conversion efficiency would provide a\nclearer understanding for system comparison and actuation efficiency.\nAR: We thank the reviewer for this comment. The actuation efficiency is an important parameter to\ncharacterize the performance of a robot system. Here, we defined the actuation efficiency as\nthe ratio of the kinetic energy of the magnet before it impacts the end cover (propelling process)\nto the energy consumed by the coil array during one actuation cycle (propelling and\nrepositioning process). The results and discussion are shown in Fig. S9(C) as:\nFig. R1 (Fig. S9(C) in the Supplementary Materials). The power and efficiency of MiaBot\nunder the input currents from 0.1 A to 0.5 A.\nThe capability of locomotion in high-friction environments is attributed to the inertial impact\nprocess as the accelerated magnet collides with the front cover. Here, we define actuation\nefficiency as the ratio of the kinetic energy of the magnet before it impacts the front cover\n(propelling process) to the thermal energy consumed by the coil array during one actuation cycle,\nincluding propelling and repositioning process. Thus, the actuation efficiency is expressed as\n𝑚𝑣2\n𝜂 = (𝑠38)\n2(𝐼2𝑅 𝑡 +𝐼2𝑅 𝑡 )\n𝑝 𝑐 𝑝 𝑟 𝑐 𝑟\nwhere 𝑚 is the mass of the permanent magnet, 𝑣 is the magnet’s velocity before impacting\nthe front cover (propelling process). 𝐼 and 𝐼 are the input currents of the magnet’s\n𝑝 𝑟\npropelling and repositioning process, respectively. 𝑡 and 𝑡 are the time costs of the\n𝑝 𝑟\nmagnet’s propelling and repositioning process, respectively. 𝑅 is the resistance of the coil\n𝑐\narray.\nThe average traveling time in Fig. 2E is adopted here to calculate the coil’s energy consumption.\nHere, the input current of the magnet’s propelling process is set from 0.1 A to 0.5 A. In addition,\nwe maintain the reposition current at -0.05 A. The average speed in Fig. 2F is adopted here to\ncalculate the impact energy. The blue curves in Fig. R1 (fig. S9(C) in the supplementary\nmaterials) shows the cost energy in the coil array and the magnet’s kinetic energy. The orange\ncurve indicates the efficiency of MiaBot. The figure shows that the efficiency decreases with an\nincreased input current. When the input current is 0.1 A, the efficiency is 10.41%. The efficiency\ndecreases to 6.32% when the input current is set to 0.5 A. The present version of the robot is not\noptimized in terms of actuation efficiency; instead, it is optimized for the load-carrying\ncapability. In future, the energy efficiency can be improved by decreasing the current in\nmagnet’s reposition process or shorten the distance between the left coil and the right coil.\nMoreover, the energy and cost of transport (CoT) is another indicator to evaluate the energy\nconsumption of a miniaturized robot. In this revised manuscript, we calculated this CoT value\non various surfaces and compared our performance with other robots. The results are\nsummarized in Fig. S9(D). The CoT is defined as:\n𝑈 𝑃\n𝐶𝑜𝑇 = =\n𝑚𝑔𝑑 𝑚𝑔𝑣\nWhere 𝑈 is the energy consumed, 𝑚 is the mass of the robot, 𝑔 is the gravitational constant,\nand 𝑑 is the traveled distance of the robot. By dividing a unit time period for both the\ndenominator and the numerator, the 𝑈/𝑑 can also be rewritten as 𝑃/𝑣, where 𝑃 is the power\ninput and v is the moving velocity. The reported CoT of other miniature robots can be seen in\nthe following figures.\nPublished Data Figure Redacted\nFig. R2 The comparison of CoT among various miniature robots\nA detailed summary of the revisions in the updated manuscript is shown below:\nSection: “Inertial impact force and loading performance”: Furthermore, to assess the locomotion\nreliability, the millirobot with a 500 g payload is tested on various surfaces such as metal, plastic,\nfabric, and wood (Fig. 3F, Video 1). The results prove that the millirobot is capable of carrying\na heavy payload to move at a speed constantly above 110 mm/min on variety rigid surfaces. The\nmean cost of transportation is 178.1 (detailed data and definition is shown in Fig. S9(C)), which\nis relatively low for miniature robots of the comparable weight [32][46].\nFig. R3 (Fig. S9(D) in the Supplementary Materials). The cost of transport for MiaBot when\nmoving across various surfaces while carrying a 500 g cargo.\nSupplementary Materials: “S09: The thermal efficiency and cost of transport”: The cost of\ntransport (CoT) is a common metric used to evaluate energy consumption in miniature robot,\nwhich is defined as\n𝑃\n𝐶𝑜𝑇 = (𝑠39)\n𝑚𝑔𝑣\nwhere 𝑃 is the power input, 𝑚 is the mass of MiaBot, 𝑔 is the standard gravitational constant,\nand 𝑣 is the moving velocity of MiaBot.\nUsing a square wave with a current ranging from 0.5 A to -0.05 A as input signals, we calculated\nthe associated cost of transport (CoT) for MiaBot when carrying a 500 g cargo across various\nterrains. Results presented in Fig. S9(D) demonstrate stable CoT values across different surfaces,\nwith a maximum of 202.6 observed on paper and a minimum of 157.4 on polyethylene. In future\nwork, the CoT can be further reduced by replacing the square-wave input with pulse signals,\nthereby minimizing heat loss during the sliding process. Another feasible solution involves\nreducing unnecessary heat generation by optimizing the duty cycle and lowering internal friction\nthrough the application of dry lubricants (e.g., graphite) between permanent magnets and frames.\n2.2 Comment #2\nRC: Additionally, the authors briefly mention the potential for future wireless operation using\nonboard power sources. However, given the relatively high current required for internal\nelectromagnetic actuation, the technical feasibility of wireless integration remains unclear\nwithin the current range. A more detailed discussion on the challenges and potential strategies\nfor onboard battery systems, wireless power transfer, or energy efficiency optimization would\nstrengthen the proposed outlook. Since many high-friction or confined-space applications\ndemand untethered operation, the authors could discuss the feasibility and enhance future\ndirections of this work.\nAR: Thank you for bringing up this important question. In our MiaBot design, the total resistance\nof the coil array is approximately 12.4Ω, and input currents were tested across the range of\n0.05 A to 0.5 A. Under these conditions, a battery with an output voltage range of 0–6.2V and\na power output of at least 3.1W can satisfy the driving requirements for all scenarios. This\nactuation requirement can be met by connecting two 3.7V lithium batteries in series. For\n3.7\nexample, when a single 3.7V battery is used to produce an output current of ≈ 0.3𝐴, the\n12.4\nimpact force generated by the permanent magnet could reach 10.92N (Fig. 3A), which is a\nstrong instantaneous propulsion force for millirobots. Based on our measurements of the static\nfriction between the MiaBot and the ground (Fig. S14), this thrust is capable of transporting\ncargo weighing over 1000 g, demonstrating that the robot can meet actuation requirements in\nmost high-friction environments. Below are detailed parameters of two small rechargeable\nlithium batteries that meet these requirements.\nItem Product 1 Product 2\nSize (mm×mm×mm) 6.5×17×23 24.5 ×17 ×7.5\nWeight (g) 3 g 6 g\nVoltage (V) 3.7 V 3.7 V\nMaximum output current 3.2 A 3.0 A\n(A)\nCapacity 160 mAh 150 mAh\nReference website https://detail.1688.com/offer/ https://www.amazon.com/-\n598777999506.html /zh/dp/B07TXQ3GLF/\nUsing a square wave input with current from -0.05A to 0.3 A and a duty cycle of 0.5, the\noperational time of the lithium battery could be:\n150\n𝑡 = ×60 = 51.4 𝑚𝑖𝑛\n(300+50)/2\nMoreover, the operational time could also be improved by reducing the duty cycle or using an\nimpulse current as the input signal.\nFor onboard circuit systems, we need to convert the battery’s DC output into a controllable\nsquare wave signal. This can be achieved using an H-bridge circuit, where the alternating\nswitching of transistors reverses the output polarity. By applying a square wave control signal\nto the H-bridge, we can generate the desired controllable square wave signals. Therefore, the H-\nbridge power switch module must have a current rating exceeding 0.5A. the MOSFET witch\nlike the AO3401 and AO3400, with their 30V withstand voltage and 2.8A rated current, could\nbe used in the onboard circuit system.\nThe detailed discussion about future onboard systems is summarized in section “Discussion\nand Conclusion”\nThe applicability of MiaBot could be further expanded with onboard power solutions, as the\nmaximum operating voltage in this study is below 6 V, with a current of 0.5 A. Future work will\ninvolve implementing lithium battery power and developing onboard circuits with Bluetooth\ncommunication for remote control. This will enable remote switching of embedded H-bridge\ncircuits to generate the necessary square wave signals for actuating the robot.\n2.3 Comment #3\nRC: In particular, electromagnetic coil-based actuation generates Joule heat during operation,\nwhich may result in thermal accumulation or functional shutdown under prolonged usage.\nAlthough the manuscript describes impact experiments, it remains important to quantitatively\nevaluate long-term performance stability, including potential issues such as mechanical\ndegradation, thrust force reduction, or delayed actuation response over time. Because the\nactuation mechanism is based on high impact force to operate in high-friction and confined\nenvironments, further discussion on long-term performance would strengthen the evaluation\nof durability.\nAR: Thank you for your thorough analysis of the proposed robotic system. Temperature rise and\nmechanical impact are indeed two critical parameters affecting robotic performance, primarily\nthrough the following mechanisms:\n(1) Temperature Effects:\n1.1 Elevated temperatures can induce mechanical damage to the robot's structure.\n1.2 Generated heat may cause thermal agitation of molecules within the permanent magnet.\nThis could alter magnetic domain orientation, reduce molecular alignment, diminish magnetic\nmoment, and potentially lead to reduced actuation force and delayed actuation response.\n(2) Impact Effects:\n2.1 Severe impacts risk damaging the robot’s mechanical structure.\n2.2 Impact-induced vibrations can similarly disrupt molecular arrangements within magnets,\nreducing magnetic moment, actuation force and actuation response.\nIn response to the above mechanisms, we have conducted a detailed analysis in this revised\nversion, examining which factors contribute to the long-term instability in robot operation and\noffering recommendations for mitigating such instability. Additionally, we also analyzed which\nfactors have negligible impact and can thus be disregarded.\nFor mechanism 1.1: After continuous operation at 0.1A–0.5A for five minutes, the surface\ntemperature of the coil array showed a maximum rise below 50°C. Given the PEEK robotic\nframe’s 300°C thermal limit, these results confirm negligible risk of mechanical damage. Our\naction can be seen as follows:\nFig. R4 (Fig. S9(A) in the Supplementary Materials): The relationship between increased\ntemperature and the operation time under the input currents from 0.1 A to 0.5 A\nSection “Robot actuation mechanism and kinematic characterization”: Following 300 seconds\nof operation, the temperature rises by less than 5°C with an input current of 0.1 A, while reaching\n48°C at 0.5 A. This temperature remains far from the safe tolerance limit of 300°C for the frame\nmaterial (PEEK).\nFor mechanism 1.2: During the 30-minute operation of the robot, we measured the magnetic\nfield strength on the upper surface of the permanent magnet under two distinct operating modes.\nThe two modes tested were: continuous operation for 30 minutes, and intermittent operation (4\nminutes of actuation followed by a 1-minute pause). The results indicated that the surface\nmagnetic field strength of the permanent magnet remained nearly unchanged after 30 minutes\nwith intermittent operation. Even after 30 minutes of continuous operation, the measured surface\nmagnetic field intensity varied by less than 1%. This confirms that the robot exhibits good\nthermal stability. Although a temperature increase was observed in the coil, this rise was\nprimarily localized to the coil surface. Owing to the insulating properties of PEEK, the material\nused for the robot’s body frame, this temperature rise does not directly affect the permanent\nmagnet or induce significant changes in its magnetic domain orientation. A summary of the\nchanges in this regard is provided below:\nManuscript: Section “Robot actuation mechanism and kinematic characterization”:\nFollowing 300 seconds of actuation, the temperature rises by less than 5°C with an input current of 0.1 A,\nwhile reaching 48°C at 0.5 A. This temperature remains far from the safe tolerance limit of\n300°C for the frame material (PEEK). Moreover, owing to the isolation provided by the robot\nframe, the temperature rise of the coil will not be directly transferred to the permanent magnet,\nthereby avoiding significant changes in the magnetic properties of the permanent magnet.\nFig. R5 (Fig. S9(B) in the Supplementary Materials): The surface magnetic field intensity of\nthe magnet during actuation for 30 min\nSection Supplementary Materials “09 The thermal effect and cost of transport”: Although a\nsignificant temperature rise was observed on the coil surface, this increase did not notably affect\nthe magnetic properties of the magnet (Fig. S9(B)). We conducted a 30-minute operation test\nwith the robot, measuring the magnetic field strength on the surface of the permanent magnet\nunder two operating modes: continuous actuation and intermittent operation (4 minutes of\nactuation followed by a 1-minute pause). The results did not show detectable changes in the\nmagnetic field strength of the permanent magnet’s surface during intermittent operation. After\n30 minutes of continuous actuation, the surface magnetic field strength of the permanent magnet\ndecreased from 515.5 mT to 510.8 mT, a reduction of less than 1% (0.91%), demonstrating good\nthermal stability of the robot. This is likely because the coil is not in direct contact with the\npermanent magnet, and the robot’s frame, constructed by PEEK, provides thermal isolation,\npreventing a significant temperature rise in the permanent magnet.\nFor mechanism 2.1: We need to ensure a tight connection between the stopper and the robot\nframe during assembly to prevent the stopper from being ejected under the impact of the\npermanent magnet. In the future, the integrated molding technology will be considered instead\nof separately manufacturing these two parts and assembling them to improve the durability. Our\naction is summarized as follows:\nSection Supplementary Materials “01 Design parameters of the MiaBot”: Moreover, the outer\ndiameter of the stopper and the inner diameter of the center channel must maintain a tight\ntolerance or employ an interference fit to ensure long-term stability. A significant gap can reduce\nthe durability of robots, as the adhesive strength cannot counteract the impact forces of the\npermanent magnet. Experimental results show that gaps exceeding 0.5 mm between these\ncomponents induce stopper dislodgement within ten minutes.\nFor mechanism 2.2: The permanent magnet was subjected to 10,000 times impacts at actuation\nof 0.5 A current. We measured the surface magnetic field of the permanent magnet; it shows no\nsignificant change in flux density. This confirms that continuous impact loading is not the\nprimary contributor to thrust force reduction. our action can be seen as follows:\nFig. R6 (Fig. S10(D) in the Supplementary Materials) The durability test of the magnet by\nthousands of times of impact\nContinuous high-impact forces may impair the performance of the permanent magnet,\npotentially leading to physical damage or a reduction in their magnetic moment. To investigate\nthis, a square wave input with 0.5 A in the positive direction and -0.5 A in the negative direction\nwas employed to actuate the magnet periodically. The magnet was subjected to 10,000 impact\ncycles, with surface magnetic flux density measured at intervals of 2,500 cycles (Fig. S10(D)).\nResults indicated no significant variations in magnetic flux density, and no visible damage was\nobserved on the magnet’s surface. These findings validate that the permanent magnet can be\nreliably utilized in our robotic system over extended operational periods.\n2.4 Comment #4\nRC: The rationale behind the selected robot scale is not fully addressed. As magnetization and\nimpact force are affected by magnet sizes, decrease in robot size may compromise actuation\nefficiency.\nAR: Thanks for the comments. The current scale of the proposed robot is primarily determined\nbased on the following considerations:\nFirst, for narrow-space scenarios such as pipeline environments, small-scale robots are required\nto perform challenging tasks (e.g., cargo transportation and navigation through high-resistance\nenvironments) within confined spaces. However, enhancing the force output capability of\nexisting small robots remains difficult due to spatial constraints. To address this, we developed\na magnetic inner actuation method. This design eliminates reliance on transmission components\n(e.g., gears and bearings), enabling miniaturization of the robot. Additionally, it enables direct\nforce output without torque conversion, thereby enhancing operational efficiency. So, we\ninitially targeted a scale range within ∅20 mm × 50 mm, as installing motors and transmission\ncomponents within this range is typically difficult, and the output energy of robots at such scales\nis often limited, this work aims to tackle this specific challenge.\nSecond, as you have also noted, the magnetic moment and impact force of the permanent\nmagnet decrease with reduced volume. According to Formula S38 (as referenced in Comment\n#1), actuation efficiency also declines with a smaller volume, leading to diminished actuation\nperformance. Thus, the overall size of the robot is referenced to that of capsule robot, rather\nthan those at the micrometer scale, to accommodate the constraints of most narrow pipelines.\nThird, considering the future feasibility of onboard power sources actuation (as discussed in\nComment #2), it should ensure that 3.7V–7.4V lithium batteries can power the robot to\ncomplete most tasks. This led us to set the coil resistance range to approximately 10–15 Ω.\nUltimately, we selected a 200-turn coil with a corresponding resistance of 12.4 Ω as the\nactuation electromagnet. Based on these coil parameters, we performed theoretical modeling\nand analysis on the length of the robot and the wide of coil array, as illustrated in Fig. 2C. This\nanalysis allowed us to determine the robot length (𝐿 ) and coil width (𝐿 , which defines the\nc 𝑤\ndiameter of the robot). We further characterized the magnetic field generated by the coil array\nalong the robot’s central axis (Fig. S3), which revealed a consistent gradient direction but\nnegligible gradient magnitudes in the middle region. This indicates that an excessively long\nrobot would result in insufficient actuation force on the permanent magnet in the middle region,\npotentially failing to overcome friction and causing deceleration. Conversely, an excessively\nshort robot would limit the permanent magnet’s acceleration distance, leading to collision with\nthe opposite end before reaching optimal speed. Based on the results in Fig. 2C, we therefore\ndetermined the robot dimensions as 30 mm in length and 12 mm in diameter.\nIn this revised version, we have added a summary of the rationale for this size selection, as\nfollows.\nSection: “Supplementary Materials 01 Design parameters of the MiaBot”. The proposed small-\nscale robot employs integrated coils and a permanent magnet for direct actuation, overcoming\nchallenges associated with installing traditional transmission components, such as motor gears\nand bearings, at the millimeter scale. Moreover, the millirobot in capsule size ensures its\nflexible maneuverability within confined, small-diameter pipelines while ensuring it has\nsufficient thrust to overcome environmental friction. More details about the selection of the\ndesign parameters can be referred to the section S-08 Scalability of Miabot.\n2.5 Comment #5\nSeveral figures in the manuscript lack essential graphical clarity and unclear annotations,\nwhich hinders readability and reproducibility.\nComment #5.1: Figure S5: The phase diagram uses qualitative terms such as “extremely low”\nand “insufficient” without clearly defined numerical thresholds. The authors are encouraged\nto quantitatively define the critical values that determine the locomotion transition.\nAR: Thanks for your rigorous review, which has helped us identify this potentially confusing part.\nIn this revised version, we have provided a clearer definition of this critical value to assist\nreaders in better understanding the localization transition process. Our specific revisions are as\nfollows:\nAs illustrated in Fig. S5(A), the robot demonstrates diverse motion modes under varying input\ncurrent amplitudes and environmental friction conditions. First, when the robot is in a high-\nfriction environment or the actuation current is extremely low, where the impact force generated\nby the acceleration of the permanent magnet is insufficient to overcome high-frictional\nenvironments or the high static friction between heavy objects and the ground (i.e.,𝐹 < 𝐹 ), a\n𝐼 𝑓\n\"dead zone\" occurs where the robot cannot move. Conversely, when the environmental friction\nforce is insufficient to counteract the electromagnetic attraction (i.e.,𝐹 < 𝐹 ), the robot frame\n𝑓 𝑚\nis attracted by the electromagnetic force (i.e., attraction-dominated region Fig. S5(B, i)). In\ncontrast, under high resistance or heavy loads exceeding actuation forces, the robot remains\nstationary during magnet acceleration but slides under subsequent impact-induced thrust (i.e.,\n𝐹 < 𝐹 < 𝐹), impact-dominated region Fig. S5(B, ii)). An unstable \"critical region\" exists\n𝑚 𝑓 𝐼\nbetween these two states, where the robot may exhibit unstable left-right swaying motions. In\nthis region, the static friction force (𝐹 ) is greater than the minimum value of 𝐹 yet less than\n𝑓 𝑚\nits maximum value since the magnetic field force 𝐹 varies along the axial direction. This\n𝑚\nsection establishes current control strategies to mitigate critical region instability and ensure\nstable locomotion across variable friction/load conditions.\nComment #5.2: Figure S8: Specific numerical values or ranges are not provided although\ndiameter scaling factors are discussed, making it difficult to interpret the results and understand\nthe underlying criteria.\nAR: Thanks for your careful review and pointing this out. The specific numerical values have been\nlabelled in X-axis of Figures S8, the scaling factor 𝑘 (𝑘 ) is kept in the title of X-axis as\nd 𝑙\n\"Diameter/length of the magnet with 𝑘 (𝑘 ) from 0.5 to 5”. The revised Figure S8 can be seen\nd 𝑙\nas follow:\nFig. R7 ((Fig. S8 in the Supplementary Materials): The scalability of MiaBot in diameter and length aspects.\n(A) Scalability in diameter direction. (i) Schematic diagram; (ii) The effect of the diameter scaling factor on\nthe magnet’s impact velocity; (iii) The effect of the diameter scaling factor on the magnet’s impact kinetic\nenergy. (B) Scalability in length direction. (i) Schematic diagram; (ii) The effect of the length scaling factor\non the magnet’s impact velocity; (iii) The effect of the length scaling factor on the magnet’s impact kinetic\nenergy.\nComment #5.3 Figure S3 and S8: Legends are missing.\nAR: Thanks for pointing this out. We added the legends accordingly. The revised Figure S8 can be\nseen in Comment #5.2. The revised Figure S3 can be seen as follow.\nFig. R8 ((Fig. S3(B) in the Supplementary Materials): B) The theoretical magnetic density and magnetic field\ngradient along the center channel with an input current of 1.0 A.\nComment #5.4 In addition to these examples, the authors should carefully review all figures\nand texts throughout the manuscript and Supplementary Materials to ensure that typo, scale\nbars, legends, units, and kye parameters are clearly presented.\nAR: Thanks for your suggestions. After carefully double-checking the figures and text. We\nimproved some expressions to make them clearer. Particularly, we also added legends to Fig.\n3D and Fig. S11 (A) to illustrate each line in the figures. The revised figures can be seen as\nfollows:\nFig. R9. The figures that we added legends\nReviewer #3\nI have carefully reviewed the revised manuscript and the authors' response letter. While\nI sincerely appreciate the authors’ effort to incorporate some of my previous comments—\nsuch as correctly referring to the robot’s scale and improving terminology—I still find\nthat the manuscript suffers from several fundamental issues that were not adequately\naddressed in the revision.\nAR: Thank you for your recognition of our previous revision and the constructive comments in this\nround. In response to the reviewer's comments and valuable suggestions, the detailed point-by-\npoint responses are shown below. We believe the revised manuscript addresses the additional\nconcerns raised and enhances the quality of the work.\n3.1 Comment #1\nRC: Most importantly, the authors do not provide a predictive model, dynamic simulation, or\nforce–momentum-based analysis to support their design claims. This omission significantly\nlimits the scientific value and reproducibility of the work. The originality of the concept also\nremains unconvincing, especially given that some of the cited literature already covers similar\nideas. A more valuable contribution might have been to build on these concepts and apply\nthem to a specific, well-motivated use case.\nAR: Thanks for pointing this out. The modeling analysis and the differences between this research\nand the cited literatures are summarized as follows:\nModeling analysis:\nIn terms of modeling, the process was conducted as follows: To begin with, we measured the\nmagnetic density of the permanent magnet at various positions using a magnetometer, which\nwas used to calibrate its magnetic moment 𝒎 (Supplementary Materials S2). Next, according\n𝒂\nto the parameters of the coil array, including the number of turns, winding direction, installed\nposition and input current, we modeled the spatial magnetic field it generates using the Biot-\nSavart law (Supplementary Materials S3). The magnetic field 𝑩 and axial magnetic field\ngradient 𝑑𝑩 along the robot’s central axis are presented in Fig. S3. Subsequently, leveraging the\ninteraction between the permanent magnet and the electromagnetic coil, we constructed the\n𝜕 𝜕 𝜕\nmagnetic force equation (𝑭 = (𝑚 +𝑚 +𝑚 )𝑩) (Supplementary Materials S4). Fig.\n𝑥 𝑦 𝑧\n𝜕𝑥 𝜕𝑦 𝜕𝑧\nS4(B) illustrates the theoretical force curves of the permanent magnet at different positions\nalong the central axis when the input current is 1 A. The kinematic equation describing the\nacceleration of the permanent magnet under electromagnetic force, as well as the friction\nbetween it and the robot frame, is given by Equation S30 (𝑚\n𝑑𝑧 2\n1 = 𝐹 (𝑧)−𝐹 ). As the\n1 𝑑𝑡2 𝑚 𝑓𝑖\npermanent magnet continues to accelerate, it collides with the robot’s stopper; by the principle\nof kinetic energy conservation, this collision enables the robot to generate a powerful\ninstantaneous propulsion force as illustrated in Equation S40 (∫\n𝑡𝑖𝐹(𝑡)𝑑𝑡\n= 𝑚 𝑣 −𝑚 𝑣 =\n0 1 1 1 2\n𝑚𝑣 ). The new design utilizes this powerful instantaneous propulsion force to allow the\n2\nminiaturized robot to carry loads exceeding 300 times its own weight and move effectively in\nvarious high-resistance environments.\nDifference between this research and the cited literatures:\nIn this manuscript, we referenced three studies (Refs. 10, 21, and 22) that enhance robot output\nforce via inertial actuation. However, their underlying principles, performance outcomes, and\napplication scenarios exhibit distinct differences from those of this study. Below are schematic\ndiagrams of the robots and actuation systems described in these three studies:\nPublished Data Figure Redacted\nFig. R10 The cited literatures that enhance robot output force via inertial actuation.\nAs observed in the above figures, these studies all utilize momentum conversion to enhance the\npropulsion force of magnetic robots. This highlights the prevalent challenge of limited actuation\nforce in magnetic actuation systems, preventing them from achieving optimal performance. The\ntarget application scenarios of the robots designed in these three studies are focused on puncture\nbiopsy applications within biomedical scenes, instead of the continuous actuation/locomotion\nof miniaturized robots.\nSpecifically, References 10 and 21 employ fixed coil arrays as the actuation source. Their robots\nare constructed by embedding soft and permanent magnets in hollow tubes, respectively, with\nneedles mounted at the tip. Under the magnetic field gradient generated by the electromagnetic\ncoils, the soft or permanent magnetic materials accelerate and collide toward the needle tip,\nthereby enhancing their instantaneous force. Reference 22 employs a needle tube consisting of\na fixed magnet and a movable magnet, actuated by an external permanent magnet. Under the\nmagnetic torque of the external permanent magnet, the movable magnet rotates and attracts the\nfixed magnet via opposite magnetic poles, accelerating toward the needle to generate an impact.\nWhile these methods effectively enhance the instantaneous force of magnetic actuation, they\nhave some limitations: reliance on fixed coils or permanent magnets results in highly restricted\noperating workspaces. Additionally, due to the distance between the magnetic field source and\nthe needle tube, energy attenuation is significant, leading to poor energy utilization efficiency.\nThe use of large external permanent magnets may also introduce safety risks associated with\nattracting metallic objects. In contrast, the robot designed in this study integrates actuation coils\nand permanent magnets, utilizing inertial impact for actuation. This design effectively improves\nboth the actuation efficiency and instantaneous propulsion force of the robot while overcoming\nthe workspace limitations of conventional systems and can be deployed in a wider frictional\nenvironment.\nIn this revised version, we have supplemented explanations regarding the modeling process.\nSpecifically, we have expanded the theoretical predictions of the impact force generated by the\npermanent magnet under different current-driven conditions. Our specific revisions are\nsummarized as follows:\nFig. R11 (Fig. S10(C) in the Supplementary Materials) The predicted impact force and the\neffect of the stopper material.\nFollowing the acceleration of the inner magnet, a powerful impact force is generated. According\nto the momentum conservation rules, the theoretical impact force can be expressed as:\n𝑡𝑖\n∫ 𝐹(𝑡)𝑑𝑡 = 𝑚 𝑣 −𝑚 𝑣 = 𝑚𝑣 (𝑆40)\n1 1 1 2 2\n0\nwhere 𝑚 represents the mass of the magnet, 𝑚 represents the mass of the robot and the\n1\nloaded weight, 𝑣 is the final velocity of the inner magnet before impact, 𝑣 is the velocity of\n1 2\nthe robot after impact, and 𝑡 is the duration time of the impact process. Considering the\n𝑖\nimpacting time 𝑡 is very short, as measured in Fig. S10(E). We assume the impact force 𝐹(𝑡)\n𝑖\nis independent of time and denoted as 𝐹. The impact force acts between the magnet and the end\ncover.\nFig. S10(E) illustrates the impact process using a 3D-printed PLA end cover with a 0.5 A input\ncurrent. The curve shows the immediate impact on the pressure sensor, followed by a gradual\nrelease. The thrust force at the moment of impact reaches 14.86 N, due to the very short impact\nduration (0.29 ms, as shown in the inset). During sensor release, several instances of abrupt\nincreases in sensing force were observed (indicated by dashed points), caused by the magnet\nrebounding and striking the end cover again. Since the rebound force is much smaller than the\ninitial impact force, it does not significantly affect the robot's movement in high-friction\nenvironments.\nBy substituting the impact time into Equation S40, we calculated the predicted curve of the\nimpact force generated by the permanent magnet during impact, as shown by the black curve in\nFig. S10(C). The blue bar chart depicts the measured impact force when a PLA material was\nused as the stopper. It can be observed that the predicted and measured values are in good\nagreement as the current varies from 0.1 A to 0.4 A. However, when the current increases to 0.5\nA, a noticeable discrepancy emerges between the theoretical and measured values, which is\nlikely attributed to our oversight of the rebound velocity of the permanent magnet during impact.\n3.2 Comment #2\nRC: Additionally, the manuscript lacks critical performance metrics such as force efficiency,\nenergy usage per cycle, and actuation frequency. Without control experiments or comparative\ntesting using other actuation strategies, it is difficult to evaluate the actual benefits of the\nproposed design.\nAR: Thanks for your comments. The actuation efficiency is defined as the ratio of the kinetic\n𝑚𝑣2\nenergy of the magnet before it impacts the end cover (propelling process: ) to the energy\n2\nconsumed by the coil array during one actuation cycle (propelling and repositioning process:\n𝐼2𝑅 𝑡 +𝐼2𝑅 𝑡 ). The results and discussion are shown in Fig. S9(B) as:\n𝑝 𝑐 𝑝 𝑟 𝑐 𝑟\nFig. R12 (Fig. S9(B) in the Supplementary Materials). The power and efficiency of MiaBot\nunder the input currents from 0.1 A to 0.5 A.\nThe capability of locomotion in high-friction environments is attributed to the inertial impact\nprocess as the accelerated magnet collides with the front cover. Here, we define actuation\nefficiency as the ratio of the kinetic energy of the magnet before it impacts the end cover\n(propelling process) to the energy consumed by the coil array during one actuation cycle,\nincluding propelling and repositioning process). Thus, the actuation efficiency is expressed as\n𝑚𝑣2\n𝜂 = (𝑠38)\n2(𝐼2𝑅 𝑡 +𝐼2𝑅 𝑡 )\n𝑝 𝑐 𝑝 𝑟 𝑐 𝑟\nwhere 𝑚 is the mass of the permanent magnet, 𝑣 is the magnet’s velocity before impacting\nthe end cover (propelling process). 𝐼 and 𝐼 are the input currents of the magnet’s propelling\n𝑝 𝑟\nand repositioning process, respectively. 𝑡 and 𝑡 are the time costs of the magnet’s\n𝑝 𝑟\npropelling and repositioning process, respectively. 𝑅 is the resistance of the coil array.\n𝑐\nThe average traveling time in Fig. 2E is adopted here to calculate the coil’s energy consumption.\nHere, the input current of the magnet’s propelling process is set from 0.1 A to 0.5 A. In addition,\nwe maintain the reposition current at 0.05 A. The average speed in Fig. 2F is adopted here to\ncalculate the impact energy. The blue curves in fig. S9(B) shows the cost energy in the coil array\nand the magnet’s kinetic energy. The orange curve indicates the efficiency of MiaBot. The figure\nshows that the efficiency decreases with an increased input current. When the input current is\n0.1 A, the efficiency is 10.41%. The efficiency decreases to 6.32% when the input current\nincreases to 0.5 A. In the future, we can decrease the current in magnet’s reposition process or\nshorten the distance between the left coil and the right coil to improve the efficiency.\nThe effect of the actuation frequency on locomotion performance is shown in Fig. 3C.\nFig. R13 (Fig. 3(C) in the Manuscript) Locomotion velocity versus excitation frequency with a\n500 g load.\nSection: “Inertial impact force and loading performance”: The quantitative investigation was\nconducted by applying a square wave signal with frequencies ranging from 1 Hz to 35 Hz, along\nwith an 𝐼 of 0.5 A. As shown in Fig. 3C, the optimal actuation frequency is dependent on the\nl\nmagnitude of the input current. Overall, the velocity increases with the applied frequency during\nthe initial stage (below 10 Hz) because more impacting and locomotion cycles occur in a fixed\nperiod. As the frequency increases, a decline in the velocity occurs due to the frequent backward\nimpacting process, which plays a role in cancelling the forward motion. In the third stage, the\nvelocity rises again as the applied frequency increases because the inner magnet does not have\nsufficient time to contact and impact the back stopper, thus preventing the cancellation of the\nrobot’s forward motion. However, this upward trend is confined by an upper limit that can\nrestrict the forward acceleration distance, resulting in reduced impact velocity and final impact\nforce output.\nRegarding control experiments or comparative tests using alternative actuation strategies, we\nface practical challenges due to the lack of necessary equipment and robot fabrication protocols\nrequired for other actuation methods (e.g., SMA, DEA, PZT, etc). As an alternative approach,\nwe directly used the reported data and compared our experimental results with other methods to\nvalidate the superiority of our proposed method.\nFig. R14 (Fig. 1(B) in the Manuscript). Comparison of load-carrying capability between the\nproposed MiaBot with the existing millirobots less than 10 g. (SMA: Shape memory alloy,\nDEA: Dielectric elastomer actuators, PZT: Piezoelectric actuators).\nFirstly, in Fig. 1B and Table S2, we have compared the load ratios of small-scale robots with\nself-weight less than 10 g across over 20 studies. The results demonstrate that our robot achieves\na load ratio of more than 309 times its own weight, which is significantly higher than the data\nreported in other literature, most of which fall below 50 times the robots’ own weight.\nMoreover, the energy and cost of transport is another important indicator to illustrate the\nperformance of a small robot. In this version, we calculated this value and compared our\nperformance with other robots. The results show that although our robot has a significantly\nbetter load-bearing ratio, this does not result in a higher CoT as shown in Fig. S9(D). The CoT\nis common metric used to evaluate energy consumption in small-scale robots and is defined as:\n𝑈 𝑃\n𝐶𝑜𝑇 = =\n𝑚𝑔𝑑 𝑚𝑔𝑣\nWhere 𝑈 is the energy input, 𝑚 is the mass of the robot, 𝑔 is the gravitational acceleration,\nand 𝑑 is the traveled distance of the robot. By multiplying a unit time period, the 𝑈/𝑑 can also\nbe rewritten as 𝑃/𝑣, where 𝑃 is the power input and v is the moving velocity. The reported\nCoT of other miniature robots can be seen as follow figures.\nPublished Data Figure Redacted\nFig. R15 The comparison of CoT among various miniature robots\nA detailed summary of our revision is shown below:\nSection: “Inertial impact force and loading performance”: Furthermore, to assess the locomotion\nreliability, the millirobot with a 500 g payload is tested on various surfaces such as metal, plastic,\nfabric, and wood (Fig. 3F, Video 1). The results prove that the millirobot is capable of carrying\na heavy payload to move at a speed constantly above 110 mm/min on variety rigid surfaces. The\nmean cost of transportation is 178.1 (detailed data and definition is shown in Fig. S9(C)), which\nis relatively low for miniature robots of the comparable weight [32][46].\nFig. R16 (Fig. S9(C)). The cost of transport for MiaBot when moving across various surfaces\nwhile carrying a 500 g cargo.\nSupplementary Materials: “S09: The thermal efficiency and cost of transport”: The cost of\ntransport (CoT) is a common metric used to evaluate energy consumption in miniature robot,\nwhich is defined as\n𝑃\n𝐶𝑜𝑇 = (𝑠39)\n𝑚𝑔𝑣\nwhere 𝑃 is the power input, 𝑚 is the mass of MiaBot, 𝑔 is the standard gravitational\nacceleration, and 𝑣 is the moving velocity of MiaBot.\nUsing an input square wave with a current ranging from 0.5 A to -0.05 A, we calculated\nthe associated cost of transport (CoT) for MiaBot when carrying a 500 g cargo across various\nterrains. Results presented in Fig. S9(C) demonstrate stable CoT values across different surfaces,\nwith a maximum of 202.6 observed on paper and a minimum of 157.4 on polyethylene. In future\nwork, the CoT can be further reduced by replacing the square-wave input with pulse signals,\nthereby minimizing heat loss during the sliding process. Another feasible solution involves\nreducing unnecessary heat generation by optimizing the duty cycle and lowering internal friction\nthrough the application of dry lubricants (e.g., graphite) between permanent magnets and frames.\n3.3 Comment #3\nRC: Finally, although the authors mention applications in confined or biological environments,\nthe robot’s impulsive actuation method, high-speed internal impacts, and absence of\nsteerability make it unlikely to be suitable for biomedical use. There is no discussion of\nbiocompatibility, safety considerations, or integration with control and imaging systems,\nwhich weakens the broader impact of the work.\nAR: Thanks for pointing this out. In the initial version of the manuscript, we considered that the\nproposed millirobot with high output force could be a promising candidate for specific\nbiological environments. However, we acknowledge that the preliminary attempts of using the\nMiabot in biomedical setting remain insufficient and not very suitable. Following the\nreviewers and editor’s suggestions, we have completely removed all biomedical related\nclaims and focused on the robot’s payload capacity and locomotion performance. Accordingly,\nthe biocompatibility, biosafety, and medical imaging systems are not related to the reported\nstudy."}, {"round": 3, "reviewer_comments": {"reviewer_2": "The authors have addressed the major concerns on energy efficiency, wireless feasibility, long-term stability, robot design,\nand figure clarity. However, regarding thermal issues, the manuscript only discusses the stability of polymers and permanent\nmagnets, which does not address the point of the earlier comment. The thermal stabilities of the used polymers and\npermanent magnets are high, not significantly affecting the magnetic performance. The more critical limitation is the self-\nheating of the conductive coils, which remains unconsidered. Local temperature rise can reduce coil conductivity and cause\ncircuit malfunction, becoming a bottleneck in long-term or high-frequency operation, particularly for momentum-driven\nmotions. This point would be clearer with further explanation."}, "author_response": ""}]

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