The robot developed in this study has a morphology inspired by the anatomy of Carangiform swimmers (Fig. 1a)24, measuring a total length (head-to-tail) of 412.5 mm and weighing 1.1 kg (see Supplementary Fig. 1 for the detailed dimensions). It mainly comprises a head, motor, flexible body, and tail fin (Fig. 1b, see Supplementary Information for more details). The head part accommodates drive control components such as a set of batteries, receiver, microcontroller, and motor driver. To simplify the experimental design, the primary mode of robot swimming is set as forward. Therefore, the components required to achieve multi-degree-of-freedom motion, such as pectoral fins, are absent. The control system embedded in the head part allows the generation of driving signals to the motor with different waveforms of input current as a function of time. In this study, we employ two waveforms: square and sine waves. Square waves are frequently used in soft underwater robots 6,13–15, and sine waves are typically used in rigid underwater robots 10,25–27. This is because soft robots exploit passive structural deformation to reproduce fish-like undulating motions, while in rigid robots such motions are realized by transmission mechanisms in which the input and output are mechanically matched. To reveal the swimming characteristics derived from the DD method, which combines rigid and soft robotic approaches, it is important to use both square and sine waves for driving the robot.
A high-torque, high-energy-density brushless DC motor (U8II Lite 100KV, T-MOTOR) is employed, which directly moves the flexible body followed by a tail fin. The DD method aligns well with brushless DC motors—known for their high torque and responsive frequency characteristics (e.g., ability to produce an amplitude of 360° at 20 Hz 24)—rendering them suitable for our DD method, which achieves high-power, high-speed swimming. Moreover, this type of motor, being devoid of rotor–stator contact, requires minimal waterproofing treatment, further contributing to structural simplicity. The motor used in this study weighs 242 g and constitutes 21.6% of the total weight of the robot. This aligns closely with the biological observation that fish muscles account for approximately 20% of their total body mass 28.
The flexible body is made of silicone rubber encapsulating a thin sheet of carbon fiber reinforced polymer (CFRP) by a molding process (Supplementary Fig. 2). Forming the body as a flexible continuum ensures simplicity, flexibility, mechanical robustness to external impacts, and durability to deal with operation in a wide frequency range. The tail fin, designed with an aspect ratio of 3.5 employed on the basis of preliminary experiments (see Supplementary Information for more detail), is made from the same thin CFRP sheet. The reason behind using CFRP is to exploit the resonance modes in the relatively high frequency domain. Researchers have demonstrated that efficient swimming emerges with natural vibration modes and that agile locomotion can be achieved at high frequencies 6,8,11,29–31. We designed the body and tail to have the first and second resonance modes within the tail beat frequency range of up to ~ 20 Hz according to a previously reported analytical approach 32. In particular, from the designing result, we expected the first and second natural frequencies as 3.3 Hz (\({f}_{w1}\)) and 21.9 (\({f}_{w2}\)) Hz, respectively, in the case where the robot was fixed in the experiments (discussed later), and as 1.8 Hz (\({f}_{w1}^{{\prime }}\)) and 11.6 Hz (\({f}_{w2}^{{\prime }}\)), respectively, in free swimming (see Materials and Methods for more details).
With the aid of DD and the flexible continuum body, the fish robot has a high backdrivability that provides high mechanical robustness; it can dissipate external impacts without causing any mechanical failures even when hit by a hammer (Fig. 1c, see also Supplementary Video S1). This feature is often difficult to realize with traditional motor-driven fish robots that have low backdrivability and a body consisting of several transmission parts and structural components, which face the risk of damage upon impact.
The robot achieved fish-like motion and subsequent swimming locomotion by oscillating the brushless DC motor with a given operating angle, which in turn generated thrust through the passive deformation of the flexible body and tail fin (Fig. 1d). The experimental setup used for this observation is shown in Fig. 2a-i. In the robot, the angular command to the motor, i.e., the swing angle of the body, was set as ± 30° for all experiments except for the measurement of turning speed (described later) according to the preliminary test (Supplementary Fig. 7). A previous study reported ± 30° (swing angle of 60°) as an optimal value for a servomotor-driven fish robot 26, which motivated us to use the same value. The nature of the robot to directly drive the flexible structure suggests that the resonance oscillation of the continuum body contributes to the swimming performance. In the tested tail beat frequency range of 7.5–20 Hz, the measured swimming speed of the robot reached a peak of 2.6 m/s at 10 Hz, corresponding to 6.3 body length (BL)/s (Fig. 3a, Supplementary Video S2) with square waves. In the case of sine waves, the swimming speed reached 2.4 m/s (5.8 BL/s) at 12.5 Hz. Figure 2b presents the experimental setup used for this measurement. The peaks for the square and sine waves appeared at 10 and 12.5 Hz, respectively, which were around the second natural frequency of \({f}_{w2}^{{\prime }}=11.6\) Hz predicted by the model, indicating the presence of a resonance likely to be the second mode.
This was further supported by the data of thrust force of the robot measured in a fixed condition (Fig. 2a-ii). The thrust force increased with the increase in the tail beat frequency and reached a peak value of 63.2 N at 19 Hz (corresponding to a specific thrust of 0.36 N/W) for sine waves and 59.2 N at 18 Hz (0.32 N/W) for square waves (Fig. 3b). When considering the specific thrust (thrust/input power), peaks were observed around 2 and 19 Hz, suggesting efficient swimming and the presence of resonance modes. These peaks appeared near the predicted values of the body natural frequency (\({f}_{w1}=3.3\) Hz, \({f}_{w2}\)=21.9 Hz). See Supplementary Video S3 for the body deformations at 2 and 19 Hz.
We expected to observe the peaks when measuring the tail amplitude of the robot in a fixed condition (Fig. 2a-iii). However, after reaching an amplitude of 256.7 mm at 2 Hz, it gradually decreased with the increase in the tail beat frequency without any indication of other significant peaks (Fig. 3c). This suggests that the damping of the structure by the surrounding water is dominant, implying that even if resonance modes appear, they are not immediately apparent in amplitude.
The high response speed and backdrivability along with a wide range of operating angles of the robot owing to the DD method also enable rapid pivot turning, which is described as an escape maneuver 33. The experimental result, obtained using a setup similar to the one illustrated in Fig. 2a-iii, reveals that the robot achieved a turn of approximately 90° within 110 ms from an initial static state, with a maximum angular speed of 1450°/s (Fig. 4). See Supplementary Video S4 for the movement of the robot. Note that the robot would turn in the opposite direction when the tail swing back to the original position. Thus, asymmetry in the tail motion between the turning stroke and the recovery stroke needs to be considered in actual turning maneuvers.
As mentioned previously, the measured specific thrust (Fig. 3b) indicates efficient swimming around 2 and 19 Hz. This is probably consistent with the fact that aquatic organisms such as fish swim efficiently in steady-state swimming 24,28,34. The Strouhal and swimming numbers are quantitative expressions of stead-state fish swimming. In the literature, it has been observed that the Strouhal and swimming numbers of real fish typically converge within the range of 0.2–0.4 and 0.6–0.7, respectively 24,28,34. The Strouhal number is defined as \(St=fA/U\), where \(f\) is the drive frequency, \(A\) is the peak-to-peak amplitude distance of the tail, and \(U\) is the swimming speed. Further, the swimming number is defined as \(Sw=U/fL\), where \(L\) is the fish body length. By measuring the swimming speed (Fig. 3a, d, Supplementary Video S5) and tail amplitude, we calculated the \(St\) and \(Sw\) of the robot for the tail beat frequency range of 0–20 Hz. Above 3 Hz, \(St\) was calculated as a quasi-value using the amplitude data shown in Fig. 3c. The reason for this is that above 3 Hz, it was difficult to accurately observe the amplitude in free swimming owing to distortion caused by waves on the water surface. The results plotted in Fig. 3e, f show that \(St\) and \(Sw\) fall within their typical range observed in nature around the frequency values predicted by the model (\({f}_{w1}^{{\prime }}=1.8\) Hz, \({f}_{w2}^{{\prime }}=11.6\) Hz). These results imply that the swimming behavior of the robot closely approximates that observed in real fish, illustrating a functionality in addition to the rapid motions.
Next, we investigated the swimming behavior of the robot from an energy efficiency perspective by considering the cost of transport (COT). COT represents the energy consumed to travel a unit distance and is defined as \(\text{C}\text{O}\text{T}=P/mgU\), where \(P\) is the average power consumption (Fig. 3g), \(m\) is the mass, \(g\) denotes the gravitational acceleration, and \(U\) is the swimming speed. The COT reached a minimum value of 5.9 at 10 Hz for square waves and 6.1 at 12.5 Hz for sine waves (Fig. 3h). The COT values of the square and sine waves reached minima around the predicted frequency (\({f}_{w2}^{{\prime }}=11.6\) Hz). In the case of square waves, the COT also decreased toward the model prediction (\({f}_{w1}^{{\prime }}=1.8\) Hz). The low COT values obtained in this study suggest the effect of the DD method, where elastic energy is stored by the body under resonance modes, which reduces the load on the motor and thereby the power consumption, resulting in more efficient swimming. A comparison of the COT generated from square and sine waves revealed that the latter exhibited an overall lower trend. This indicates that sine waves are suitable for efficient swimming and square waves for agile movements. One possible reason is that sine waves excite shape deformation more smoothly, resulting in motions with less fluid resistance, whereas the opposite is true for square waves.