3.1. Deformation Response of the Magnetically Driven Quadruped Soft Robot
The effect of magnetic field strength on the bending deformation of the robot was investigated. As shown in
Figure 5A, the strength of the external DC magnetic field gradually increases while the robot is flipped and fixed on a flat surface. We also observed and counted the bending deformation angle of the foot. The deformation angle of the foot in the fixed attitude gradually increases with the gradual increase in the external magnetic field strength. The quadruped deformation angle of the robot gradually increases from the initial 45° to 55°. Moreover, the robot quadruped deformation angle is positively correlated with the magnetic field strength. It should be noted that the robot in the natural attitude may change its attitude due to the coupled magnetic response of the magnetic top cover, which, in turn, affects the deformation angle of the foot. In addition, to investigate the effect of magnetic field strength on the attitude of the robot, we applied a gradually increasing magnetic field to the robot in its natural position. We then observed and counted the robot’s attitude as well as the deformation angle of the top cover at each magnetic field strength. As shown in
Figure 5B, the extension inclination angle of the quadruped gradually increases with higher magnetic field strength, resulting in a downward compression of its attitude. Moreover, the magnetic top cover responds to the magnetic field drive and deforms under the action of torque to produce a certain inclination angle. With the increase in the inclination angle, the tumbling motion characteristic eventually appears. Furthermore, due to the coupling effect of the robot’s gravity and magnetic moment, the magnetic top cover establishes a specific angular relationship with the support plane. As the magnetic moment increases, the coupled attitude aligns more closely with the direction of the magnetic field. In general, the motion attitude of magnetic quadruped microrobots is positively correlated as a function of magnetic field strength. And the magnetic quadruped microrobots’ motion characteristics and attitude can be controlled by adjusting the magnetic field strength and direction. The magnetic field of the ENS is generated by an electromagnetic coil, and its strength can be controlled by adjusting the input current. The relationship between the input current and the magnetic field strength of the 3D Helmholtz coil triaxial is illustrated in
Figure 5C. By adjusting the size and direction of the triaxial magnetic field in space, a uniform magnetic field of any desired direction and size can be synthesized. In addition, the statistical data on how the magnetic field strength affects the robot were organized and are presented in
Figure 5D. From the intersection of the data in the figure, it can be seen that the robot used in the experiment tumbled and deformed, i.e., changed its attitude, at a magnetic field strength of 11.5 mT. At this strength, the magnetic field’s impact on the quadruped’s deformation also changes. Moreover, after the experimental test, it can be obtained that, under the action of the field strength at this transition point, 9 motion modal transitions occurred in 10 motion controls, and the stability is as high as 90%. Recognizing this will aid in analyzing the control and transformation between the robot’s two motion modes: crawling and tumbling. This will also help us further analyze how the magnetic field frequency affects the motion speed of the two motion modes in the corresponding magnetic field strength interval.
Since the motion of magnetic quadruped microrobots is mainly obtained by deforming the PDMS sheet wrapped with N52 magnetic particles, it is necessary to examine the deformation effect of the PDMS sheet under various ambient temperatures. Accordingly, only if the PDMS sheet maintains good deformation performance, the designed programmed motion can be realized. The material specification shows that the cured PDMS maintains stable mechanical properties in the temperature interval of −50 to 200 °C. In addition, its thermal conductivity is 0.17 W/(m‧K), which has a certain temperature resistance and can better meet the operational requirements. Combined with the characteristics of the operating environment, the PDMS sheet still maintains good elasticity and deformation ability under the environment of −4 °C after experimental testing. Moreover, since the PDMS sheet is cured by heating, it maintains stable mechanical properties even under a high-temperature environment. Therefore, the PDMS sheet for responding to magnetic torque deformation has good operational stability at various ambient temperatures.
3.2. Kinematic Characterization of the Magnetically Driven Quadruped Soft Robot
Previous analyses and experiments indicate that the magnetic quadruped soft robot may experience tumbling attitude changes under a magnetic field strength of 11 mT. Therefore, in this section, we set the maximum magnetic field strength for crawling at 9 mT and the minimum for tumbling at 11 mT. We then further investigated the motion characteristics of these two motion modes by adjusting the magnetic field frequency and strength within the intervals. As shown in
Figure 6A, we statistically analyzed how the magnetic field frequency affects the motion speed of the magnetic quadruped soft robot within a magnetic field strength range of 4 mT to 9 mT. The figure shows that the magnetic quadruped soft robot exhibits lower motion velocity at all frequencies when the magnetic field strength is 9 mT. Observations during the experimental process reveal that this is due to the increased deformation angle of the magnetic top cover at larger magnetic field strengths. This greater deformation significantly reduces the stability and effectiveness of the robot’s motion and can even cause unexpected deformation during tumbling. The robot also moves at the same lower speed at all frequencies when subjected to a 4 mT magnetic field strength. However, the difference is that the smaller magnetic field strength results in a smaller deformation angle of the magnetic top cover, which limits the bending deformation of the foot and thus leads to a lower movement speed. The motion characteristics of the robot at each frequency under a magnetic field strength of 5 mT to 8 mT are also affected by the deformation angle of the magnetic top cover and the degree of foot bending deformation. Overall, the robot exhibits better motion speeds when subjected to 7 mT and 8 mT magnetic field strengths. However, at 8 mT, the robot may tumble and deform when driven in a lower-frequency magnetic field, which can prevent it from completing the crawling motion. Through observation and analysis of the experimental phenomena, we have identified a compelling reason: at 8 mT, the magnetic top cover exhibits a larger deformation angle, increasing the likelihood of tumbling deformation. Under high-frequency magnetic fields, the timely reversal of moments prevents tumbling deformation caused by inertia. Conversely, at low magnetic field frequencies, tumbling deformation occurs due to inertia. Therefore, for the purpose of crawling motion drive in this study, a magnetic field strength of 7 mT is more appropriate.
In general, as the magnetic field frequency increases, the motion cycle time decreases, resulting in faster speeds. However, observing the robot speed versus frequency curve in the figure reveals that, as the frequency increases, the motion speed first increases and then appears to decrease. Observations during the experiment indicate that, when the frequency increases to a certain degree, the deformation and recovery speed of the robot cannot keep pace with changes in the magnetic field frequency. Therefore, the stability and effectiveness of the motion decrease, leading to a natural reduction in speed. For this experimental phenomenon, we adopt the definition from other studies and refer to it as the cutoff frequency, i.e., the maximum frequency at which the robot can match changes in the magnetic field. Clearly, the cutoff frequency for the robot’s crawling motion in our study is 10 Hz. Through experimental analysis, we can further optimize the motion effect by choosing the appropriate magnetic field strength and frequency within the parameter interval of the crawling motion mode according to the operational requirements.
In addition, we conducted a statistical analysis of how the magnetic field frequency affects the robot’s tumbling motion mode within varying intervals of magnetic field strength. As shown in
Figure 6B, we tested the tumbling motion speed of the robot at each magnetic field frequency within the magnetic field strength varying from 11 mT to 14 mT. It can be seen that the motion speed of the robot increases gradually with the increase in the magnetic field strength. However, when the magnetic field strength reaches a certain degree, the motion speed of the robot shows little increase and even decreases at certain frequencies. Based on the experimental process, we found that the deformation of the robot’s feet also increases as the magnetic field strength increases. However, as the bending of the foot increases, the bending moment increases dramatically, leading to a dramatic increase in the required magnetic moment, which, in turn, requires a stronger magnetic field strength. At this stage, the regular incremental increase in magnetic field strength is insufficient to provide the required magnetic moment.
The robot’s speed is also affected by the magnetic field frequency, and we tested its movement speed across a frequency range of 0.5 to 3 Hz. As illustrated in the figure, the tumbling motion speed gradually increases as the magnetic field frequency increases. However, as the magnetic field frequency continues to increase, the speed of the tumbling motion starts to decrease. During the tumbling motion experiment, we observed a cutoff frequency phenomenon similar to that seen in the crawling motion. Additionally, due to the larger deformation involved in the tumbling motion, it is more sensitive to changes in the magnetic field frequency. According to the experimental data, the tumbling motions all showed a certain speed decrease at a magnetic field frequency of 1.5 Hz, with the speed continuing to decrease as the frequency increased. However, we also noticed that the robot reached a tumbling motion speed of 80 mm/s at 2 Hz under a magnetic field strength of 14 mT. Several experiments have confirmed that the robot does not exhibit a low tumbling motion speed. We found that, while higher magnetic field strength can cause instability in the tumbling motion, increasing the magnetic field frequency makes the acting time of the magnetic moment shorter. Instead of optimizing this problem, this results in an abnormal increase in speed.
Through an in-depth investigation of the motion characteristics of the robot, we identified and summarized the characteristic parameters of effective motion. There is a situation where different parameters can achieve the same control effect for these motion control parameters. For this situation, we take improving the stability of motion manipulation and reducing the accidental damage to human organs and tissues as the guideline and choose as much as possible a low magnetic field frequency (improve the stability of the motion) and a small magnetic field strength (avoid the unknown damage under the high field strength). Moreover, according to the operational requirements, we flexibly adjust the parameters of the control variables so as to achieve the best control effect. Building on these parameters, we conducted an experimental test to investigate how adjusting the robot’s manipulation parameters according to its motion characteristics can enhance its ability to navigate through obstacles. The complete experimental procedure is detailed in
Video S1, and
Figure 6C,D provide representative screenshots of the experiments. As shown in
Figure 6C, the robot can pass through a bridge-shaped environment with a certain slope using a crawling motion. When facing a sloped environment, its motion capability can be enhanced by adjusting the inclination angle of its crawling motion, based on the crawling motion characteristics analyzed earlier, so as to navigate the slope smoothly. However, while it can navigate a slope through crawling, it takes a considerable amount of time. Therefore, further exploration and optimization are needed to maintain a stable attitude and movement speed. On the other hand, the robot can traverse a ramp with a cross-grain in 1.5 s and return to its initial upright attitude (
Figure 6D). In this case, the robot’s locomotion capability and speed are greatly improved. However, the tumbling process implies a drastic change in attitude, which can negatively impact cargo stability during transport. Therefore, it is important to find a balance between maintaining cargo stability and achieving movement speed in the tumbling motion mode. As the magnetic quadruped microrobots can flexibly change the two motion modes of crawling and tumbling, therefore, the motion characteristics can be flexibly adjusted according to the operational requirements during the actual operation so as to meet the positioning accuracy and speed requirements.
After experimental testing and analytical verification, our designed magnetic quadruped microrobots have two freely switchable motion modes and excellent motion characteristics. In order to further highlight the advantages of the motion characteristics, we made a comparison with some typical studies that have been reported. We selected some typical walking untethered magnetic microrobots as well as the locomotion characteristics of arthropods in nature for comparison. The comparisons were made in terms of body size and locomotion speed, respectively, to visualize the advantages and characteristics of each magnetically driven microrobot design. For the data to be more informative, we use the body length and the number of moving body lengths per second as comparison parameters. As can be seen from the data in
Figure 6E, the magnetic microrobots that currently exist include multiple orders of magnitude sizes ranging from 0.1 mm to 100 mm. Moreover, they have different motion characteristics based on design features, for example, triangular [
20], portal [
21], biconical [
12], multipedal [
22], crab [
23], and bionic crab shapes [
24] with walking ability. Among them, the magnetic quadruped bionic microrobots we designed have excellent locomotion characteristics by achieving the first gradient of locomotion speed while maintaining the more common body size. On the other hand, comparing with typical arthropods in nature, such as ants, spiders, web spinners, Hediste diadroma, etc., the magnetic quadrupedal microrobots still have comparable locomotion speeds and locomotion characteristics.
3.3. Transportation and Release of Cargo by the Magnetically Driven Quadruped Soft Robot
In the previous section, we explored and verified the kinematic properties and the obstacle-crossing ability of the designed robot. Based on this research and experimental observations, we designed in vitro simulated cargo transportation experiments. Considering the characteristics of the two motion modes, crawling and tumbling can be combined to effectively navigate a complex operating environment. First, the magnetic quadruped microrobots are maneuvered to the target location. Then, the magnetic quadrupedal microrobots’ tumbling motion characteristics are utilized to adjust the control signal so that they tumble rapidly and continuously at the targeted drug delivery position to achieve drug release. After realizing the targeted drug delivery operation, the magnetic quadruped microrobots’ tumbling motion control signal is restored. The magnetic quadruped microrobots are made to complete the tumbling motion, recover the attitude, and leave the operation area. As shown in
Figure 7A, by adjusting the control signal of the electromagnetic coil and the magnetic field strength, the characteristic attitude of the tumbling motion can be changed, thus realizing the half-tumbling motion with left and right swaying. Once the cargo has been released, restoring the magnetic field parameters of the tumbling motion will enable the soft robot to recover its attitude. Based on this control strategy, we designed and carried out experiments for cargo transportation and release. The complete experimental procedure can be seen in
Video S2, with representative screenshots provided in
Figure 7B. As shown in
Figure 7B, after crawling and tumbling to reach the target position, the robot performs a half-tumbling motion in response to the control signal of the tumbling motion (Target position). Then, the magnetic field strength and frequency are varied to perform a left–right swinging motion to release the transported cargo (Oscillation release). Finally, the tumbling motion is resumed to control the magnetic field, thus adjusting the robot’s attitude to upright (Targeted delivery). This process combines the stability and the ability of the crawling motion to handle small displacements with the ability of the tumbling motion to manage large displacements and release cargo through oscillation. Based on this mode of operation, the ability to achieve work accuracy and movement speed is greatly enhanced. From the experimental observations, we successfully applied the magnetic quadruped soft robot for cargo transportation and release following the designed experimental steps. However, several areas require improvement, such as enhancing the stability during cargo transportation and addressing challenges related to cargo release. In the future, our goals include further reducing the robot’s size, enhancing its movement ability based on its kinematic characteristics, and optimizing the methods for cargo transportation and release.