**4. Results**

Figure 7 shows the electrical conductance of a robot with 0.5-mm legs. Two peaks can be clearly identified corresponding to modes (50) and (60). Figure S1, included in the Supplementary Materials, compares the conductance of this device with and without legs. There was almost no difference between the two measurements, which corroborates the negligible impact of the legs on the standing waves corresponding to the modes. Once the resonant frequencies were known, the frequency of actuation was adjusted manually. For this sample, the actuation frequency was set to 161 kHz, close to the mid-frequency between the measured modes (50) and (60). It is important to notice that the frequency of actuation, 161 kHz, differed from the estimated frequency *f* 5–6, by just 10%. This difference might be attributed to the limitations of the 1D model at representing the 3D structure of the robot, as well as to uncertainties in the mechanical parameters of the materials. Table S1 of the Supplementary Materials compares the resonant frequency of different modes, found using both experimentation and calculated using the 1D model and a 3D finite element analysis. It also shows the values for *<sup>L</sup>*(n0), which is the first zero of the second derivative of the modal shapes deduced by the 1D and 3D models.

**Figure 7.** Electrical conductance of a robot with 0.5-mm legs.

Next, we present the characterization of the fabricated robots in terms of speed and force. Figure 8 shows the speed of the robot versus the applied voltage. Ten measurements were taken at each voltage and the standard deviation was about ±3.5 mm/s. The phase shift between patches was fixed to either 90◦ or −90◦ to confirm the bidirectional movement. Video S1, included with the Supplementary Materials, shows how the direction was reversed by changing the phase. The set-up for the speed measurement consisted of two infrared LEDs separated by 100 mm, where each was aligned with a photodiode. The set-up allowed for measurement of the time required by the robot to travel 100 mm along a rail on glass by tracking the light interruption events when the robot passed below the infrared LEDs with a frequency counter. Robots with legs of 1.5 mm showed a less uniform speed, with di fficulties in maintaining the rectilinear displacement, which might be related to the interference of an intrinsic mode of vibration of the legs. The modes of vibration of 0.5- and 1-mm legs were far away from the frequency of actuation. When comparing robots with 0.5- and 1-mm legs, a better performance was observed for the 1-mm leg, which might be attributed to an enhancement of the horizontal displacement at the tip of the leg, as mentioned previously. For the maximum voltage applied, namely 65 Vpp, the velocity for the 1-mm-legged structure reached 60 mm/s, which was equivalent to 3 BL/s (body lengths per second). These results are comparable to the state-of-the-art in miniature soft robotics, with performances similar to arthropods [29]. Furthermore, notice that the minimum voltage required to initiate movement with 1-mm legs was as low as 20 Vpp, which might facilitate the implementation of an untethered robot with an integrated driving signal.

**Figure 8.** Speed of the robots versus applied voltage for legs with different lengths: 0.5 mm (red), 1 mm (black), and 1.5 mm (blue). Circles represent experimental data and are joined with lines for guidance purposes. BL/s: Body lengths per second.

Furthermore, we investigated the e ffect of mass loading on the performance of the robot. Figure 9 shows the speed versus applied voltage for di fferent loading masses. The robot carried a mass of 7.5 g, which was 40 times its weight, at a speed of about 40 mm/s at the maximum voltage applied. This result shows the potential to incorporate electronic circuits on board, for communication, control, sensing, or other applications. Video S2 shows the locomotion with a mass of 7.5 g.

To complete the characterization of the robot, Figure 10 displays the blocking force under di fferent mass loadings. The force was measured while the robot contacted a force sensor (Honeywell FSG Series, Morris Plains, NJ, USA) with the actuation voltage applied. As expected, the blocking force increased as the mass loading increased [30].

Finally, Figure 11 shows the comparison between two and three pairs of 1-mm legs. A clear improvement can be seen when using three pairs of legs, with a speed as high as 5 BL/s. Further investigations are in progress to study the e ffect of increasing the number of legs.

**Figure 9.** Speed of the 1-mm-legged robot versus applied voltage for different masses: no load (blue), 1.2 g (pink), 3 g (black), and 7.5 g (red).

**Figure 10.** Blocking force of the robot for different masses: no load mass (blue) and 7.5 g (red).

**Figure 11.** Speed of the 1-mm-legged robot versus applied voltage for two (blue) and three (black) pairs of legs.
