## 5 Experimental Results  
During the experiments (see video S1 published as Supplementary Material), the angular velocity of the eccentric mass is controlled by the voltage applied to the DC motor. The aquatic and terrestrial locomotion of the robot is recorded with a high-speed camera while the robot is moving in a 0.7 \(\times\) 1.5 m aquarium, and the locomotion speed, the rotating mass rotational speed, and the robot foot positions are measured thanks to high-speed camera recordings. The DC motor voltage is increased from 0.8 V to 2.7 V in 0.1 Volt increments. In Figure 9, the experimental and numerical aquatic locomotion speed as a function of \(\omega\) (counterclockwise rotation) are overlapped. The numerical curve has been derived using the WM model presented in Section 4. It can be observed that there is good agreement between the resonance frequencies of the numerical and experimental model. A first resonance peak appears at about 26.5 rad/s and a second resonance peak appears at about 33-35 rad/s in both cases. These values are also in good agreement with the resonance frequencies computed with the linear model of Section 3.2 (28.8 rad/s and 34.2 rad/s). Moreover, the numerical and experimental curves are in good agreement and nearly overlapped. For higher values of \(\omega\) (>40 rad/s), the numerical model cannot be used due to the increasing importance of the effect of waves generated by the robot (which are observed in the experiments). It is worth noting that the natural frequencies of aquatic locomotion are well below the natural frequencies of the structural modes studied in Section 3.1. Hence, the assumption of rigid robot in the model of aquatic locomotion is consistent with the actual operation of the robot. In Figure 10, the displacements of the hind foot are presented both for terrestrial and aquatic locomotion, which have been measured in experiments with \(\omega\) = 38 rad/s. The experimental curves are almost linear, and this is related to constant locomotion speeds. In the case of aquatic locomotion, the experimental points are overlapped with the numerical curve, which is almost linear with small local peaks due to the periodic locomotion. The  
Figure 8: Locomotion speed (**left**) and motor speed (**right**) using a motor torque of 0.00005 Nm as an input. experimental and numerical results are in good agreement. A more detailed comparison between the experimental and numerical positions of the robot feet is depicted in Figure 11, considering a couple of periods of motion. Experimental and numerical data are in good agreement in this time scale as well: the period of the oscillations is the same and the error between the numerical curve and the experimental points is always less than 1.3 mm. Figure 10: Displacements of the hind foot in terrestrial and aquatic locomotion. Figure 9: Simulated vs. experimental locomotion speed. The differences between numerical and experimental data in Figures 9-11 are mainly due to all the simplifying assumptions (detailed in Section 4), the disturbance forces related to the electrical cables of the motor, and the effect of the small waves present in the experiment, which are not considered in the numerical model. The overlap between the experimental points and numerical curves could be improved by using computational fluid dynamics to simulate the flow around feet for different relative velocities and angles, or by using experimentally determined drag and lift coefficients. However, these activities are beyond the scope of the present work. Figure 12 shows both the terrestrial and aquatic locomotion speed as a function of \(\omega\), as measured in the experiments. The figure shows that the robot reaches the highest speed on the ground when the eccentric mass rotates at an angular velocity of about 38 rad/s, and it reaches the highest speed on the water when the eccentric mass rotates at an angular velocity of about 35 rad/s, which is in accordance with the resonance peak found with the mathematical and numerical models of Sections 3 and 4.