Agile robotic fish based on direct drive of continuum body

Agile robotic fish based on direct drive of continuum body | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Agile robotic fish based on direct drive of continuum body Keisuke Iguchi, Taiki Shimooka, Hiroto Tanaka, Yusuke Ikemoto, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3699820/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 8 You are reading this latest preprint version Abstract Fish-like agile movements, such as fast forward swimming and rapid turning, are essential for robots to perform a wide variety of tasks in aquatic environments. However, achieving these locomotion capabilities simultaneously in existing biomimetic underwater robots has proven challenging. Here, we present a self-contained robotic fish capable of swimming at a speed of 6.3 body length per second and pivot turning at an angular speed of 1450° per second. These fast motions, which compare well with those of real fish, are realized by directly oscillating a flexible body using an electromagnetic motor. This direct-drive (DD) method eliminates the need for transmission parts, simplifies the robotic structure, improves mechanical robustness, and enables the use of a flexible continuum body that passively interacts with water, generating fish-like body deformations and subsequent rapid swimming. This also allows the robot to have the Strouhal and swimming numbers that match the typical values observed in nature. Moreover, the observed frequency peaks in swimming are similar to computed values using a model, which guides the design of the robot. These results illustrate the DD method as a promising framework for the creation of highly versatile biomimetic underwater robots. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Underwater robots have significant utility for tasks in aquatic environments, including artifact inspection, ecology investigation, resource exploration, and rescue operations. Biomimetic underwater robots that ingeniously incorporate biological structures and functionalities offer the potential to achieve high mobility and efficiency similar to aquatic organisms 1 – 4 . Furthermore, traditional propeller-equipped underwater robots have faced challenges related to the entanglement of marine life and environmental disruption caused by strong water currents, highlighting environmental concerns. Accordingly, biomimetic robots, which are based on biological emulation, have been actively pursued as a solution to address these issues 1 – 4 . Underwater robots based on the biomimetic approach are paving the way for advanced underwater systems capable of a wide range of tasks in various liquid environments. Many robots inspired by various aquatic organisms 1 – 5 , such as fish 6 – 11 , eel 12 – 14 , ray 15 – 17 , and jellyfish 18 – 20 , have been developed. These robots may be broadly classified as being based on two approaches depending on their architecture. One is the so-called rigid robotic approach, in which electromagnetic motors or servos and their associated rigid transmission components form the active moving body to generate swimming motions 2 – 4 . The other is the soft robotic approach, in which a soft actuator that deforms itself, such as electroactive polymers 6 , 14 , 15 , 18 , 21 and fluid-driven soft actuators 9 , 13 , 20 , forms a portion of or the entire body and directly moves it 1 , 5 . The advantages of the rigid robotic approach are associated with the features of motors, such as ease of integration, high energy density, efficiency, positioning accuracy, and frequency response. However, the presence of a transmission mechanism including gears, cranks, sliders, hinges, linkages, and wires introduces complexities in the robotic structure. This makes the robots susceptible to damage from severe impacts, potentially compromising mechanical robustness 1 , 22 . Furthermore, although the motors themselves are highly efficient, energy losses in the transmission mechanism and its weight reduce the resulting efficiency and specific output 23 . Meanwhile, the soft robotic approach has the advantage that the actuator can achieve a type of automatically generated swimming motion because of the interaction between the continuous, simple, and flexible body and the surrounding water. This implies that the control input can also be simplified, resulting in a simple on-off in extreme cases. In addition, the softness contributes to improving the mechanical robustness of the structure. However, in many cases, individual soft-actuator technologies present one or more of the following challenges: low response speed, low efficiency and energy density, and small deformation and force output. In this study, we hypothesize that when both rigid and soft robotic approaches are combined, that is, when a robot has a flexible continuum body directly driven by a motor, the simplified high-energy-density structure and its interaction with the surrounding water provide the robot with high-performance swimming capability. As a specific way to verify this hypothesis, we propose direct-drive (DD) as an actuation method for motor-driven biomimetic underwater robots. As the name implies, DD moves the robotic body directly, eliminating the need for transmission parts. This results in the expected improvement in the output performance and mechanical robustness of the robots. Moreover, DD enables the motor to directly interact with the surrounding water through the body. Because of this functionality, we expect DD to also be capable of simplifying the complex control often required for traditional motor-driven underwater robots. This is analogous to the simplification of control through the passive deformation of the structure, which is well known in the soft robotic approach. In the literature, DD has demonstrated validity in legged terrestrial robots 23 ; however, to the best of our knowledge, no case of implementation in biomimetic underwater robots has been reported. In this context, the focus of the present study is to investigate the swimming characteristics that can be achieved by the DD approach through the characterization of a robotic fish platform. Results The robot developed in this study has a morphology inspired by the anatomy of Carangiform swimmers (Fig. 1 a) 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. 1 b, 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. 1 c, 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. 1 d). The experimental setup used for this observation is shown in Fig. 2 a-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. 3 a, 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 2 b 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. 2 a-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. 3 b). 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. 2 a-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. 3 c). 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. 2 a-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. 3 b) 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. 3 a, 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. 3 c. 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. 3 e, 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. 3 g), \(m\) 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. 3 h). 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. Discussion The simplicity of the fundamental architecture of the robot, that is, the brushless DC motor directly connected to the passive, flexible continuum body, ensures transmission of the power of the motor to the body and tail as well as assures mechanical robustness under external impacts. The observed rapid swimming of the fish robot, 6.3 BL/s (2.6 m/s) in the forward direction and 1450°/s in turning (110 ms to achieve a 90° pivot turn from a static position), is rarely achieved within a single system. The swimming speed of the robot compares well with that of real fish (Fig. 5 , data adopted and replotted from references 8 , 35 ), illustrating its high performance comparable with its natural counterpart. Moreover, the turning speed is more than four times higher than that of a fish robot capable of escape maneuvers 33 . At a speed of 6.3 BL/s observed at the tail beat frequency of 10 Hz, a minimum COT of 5.9 is achieved owing to the resonance mode of the body, which directly interacted with the surrounding water and facilitated elastic energy storage. Around this frequency (~ 10 Hz), the Strouhal and swimming numbers fall within the typical range observed for real fish. Both numbers reach the typical range at a low frequency as well (~ 1 Hz). These results suggest that the robot achieved swimming characteristics similar to those of real fish. The two frequency domains (~ 1 and ~ 10 Hz), where rapid and efficient swimming is achieved, are similar to the resonant frequency predicted by the model ( \({f}_{w1}^{{\prime }}=1.8\) Hz, \({f}_{w2}^{{\prime }}=11.6\) Hz). This implies that robots based on the DD method can be designed to a given performance specification. These outcomes validate the successful implementation of the DD method derived from the conceived concept that combines the rigid and soft robotic approaches and that the proposed DD method can be employed as a framework for biomimetic underwater robotic systems. From an energetics viewpoint, the efficiency of the robot (COT of 5.9) is on the same or higher order of magnitude as that of robots in other studies (0.4 15 , 2.8 8 , 1.9 35 , and 1.7 26 ), further away from real fish, indicating room for improvement. Modification of the shape of the body and tail fin will contribute to increasing the efficiency. Moreover, hypotheses propose that fish actively control muscle contractions during swimming to regulate body stiffness. For instance, tuna adjusts the stiffness of its tail for high-speed and steady-state swimming, and this mechanism has been successfully implemented in a robotic fish 25 . Incorporation of such variable stiffness into our robot may further improve the swimming performance by modulating the frequency response characteristics. The DD method also requires investigation and establishment of robotic architecture and a control method for multi-degree-of-freedom motion because the primary locomotion of the robot presented herein is forward movement. Swimming with multi-degree-of-freedom motion can be achieved by introducing pectoral fins and a buoyancy control unit as reported in a previous study 9 . When considering the environment in which the robot performs its tasks, protection of the motor plays a particularly important role. As mentioned in the previous section, the brushless DC motor used in this study required almost no waterproofing. However, this may only be valid in tap water; seawater, which many robots often come in contact with in actual tasks, can corrode motor parts and eventually cause them to fail. To address this issue, an additional structure would need to be placed around the motor such that it does not inhibit its rotation and movement of the flexible body while providing physical insulation from the surrounding water, such as a compliant bag filled with insulating oil. The agility of the developed robot provides the opportunity for implementing advanced functionalities. A typical example is gliding in the air after taking off from underwater, the same functionality as that of flying fish 36 . Flying fish are known to glide over water surfaces to evade predators and facilitate movement. They exhibit high swimming speeds exceeding 10–20 m/s at tail beat frequencies of 20–40 Hz 36 – 38 . To achieve swimming speeds similar to those of flying fish, an actuator with a power density of 4150 W/kg is necessary 37 . The brushless DC motor used in this study consumed a maximum power of 1450 W 39 , resulting in a power density of 5992 W/kg. This exceeds the reported values and provides high feasibility from the viewpoint of power density. Further, the robot exhibited a swimming speed of 6.3 BL/s, clearly lower than that of flying fishes. Although the brushless DC motor used in this study allows a driving voltage of up to 48 V, for safety reasons all the experiments described herein were conducted at a voltage of 25.2 V. Thus, there remains room for dramatically increasing the swimming speed even with the current robot, and the same is true for its potential as a gliding platform. We believe that by including systems with such advanced features, the proposed DD method will contribute to the creation of highly versatile biomimetic underwater robots. Methods Measurements in the water tank In a water tank having dimensions of 1800 × 750 × 600 mm (L×W×H) and filled with tap water, the thrust force, tail amplitude, forward speed in the low-frequency domain (0–5 Hz), and turning speed were measured. Aluminum frames were placed around the water tank to provide structural support for measurement equipment (Fig. 2 a). The driving voltage for the robot was maintained at 25.2 V for all the experiments. In the measurement of the thrust and tail amplitude, an external microcontroller board (DEV-14483, SparkFun), a motor driver (FSESC 7550, Flipsky), and a power supply (PWR801ML, Kikusui) were used to drive the robot body. The brushless DC motor equipped with an encoder (AS5047D-TS_EK_AB, ams OSRAM) was connected to the driver, and the microcontroller board controlled the motor’s position by providing angle commands to the driver, thus driving the robot. Thrust force measurement In the thrust force measurement, a waterproof load cell with a capacity of 445 N (LSB210, FUTEK) was used as a force sensor. The measurement setup involved attaching the robot to a lever mechanism that indirectly pushed the force sensor (Fig. 2 a-ⅰ) 40 . When the robot generated a thrust, the lever attached to the robot rotated around an axis, pressing the other lever against the force sensor. The output signal of the load cell was recorded using a digital multimeter (2100/100, Keithley) controlled by PyVISA and saved on a PC. The sampling rate was set at 100 Hz. To account for the sensor’s initial output voltage when the robot was not driven, a 2-s baseline data recording was conducted without robot propulsion, and the average voltage was taken as the reference. The robot was then driven for 5 s, and the sensor output was recorded. The average of the recorded sensor output over 1.5 s was calculated and used as the thrust force value at the respective frequency. The driving frequency applied to the robot ranged from 0 to 25 Hz with 1-Hz increments, and the angular command to the motor was set at ± 30°. Tail amplitude measurement In the tail amplitude measurement, above the underwater robot, an acrylic plate was placed and fixed at the water surface level to remove waves that could distort the images taken from above. In this setup, the robot was driven for 3 s and its behavior was recorded using a high-speed camera (INFINICAM, Photron) positioned directly above it (Fig. 2 a-ⅱ). The frame rate for this camera was set at 1000 fps. The recorded video data were analyzed using image-processing software (Photron Fastcam Analysis, Photron Fastcam Viewer, Photron) to track the coordinates of the tip of the tail fin. The peak-to-peak distance of these coordinate data was recorded as the amplitude value. The driving frequency of the robot ranged from 0 to 25 Hz with 1-Hz increments, and the angular command to the motor was set at ± 30°. The results were reported as the average of three measurements at each frequency. Low-frequency swimming speed measurement In the low-frequency swimming speed measurement, the wireless-enabled robot was allowed to swim inside the water tank, and its movement was recorded using two synchronized high-speed video cameras (Hero10 Black, GoPro) with a frame rate of 240 fps. A styrofoam ball of 100-mm diameter was attached to the robot to ensure buoyancy and stability. The cameras were positioned outside the tank, fixed to the aluminum frame to maintain a lens separation distance of 0.3 m (Fig. 2 a-ⅲ). The time taken by the robot to traverse both cameras was measured from the recorded video and used to calculate the swimming speed. The initial state of the robot was at one end of the tank, and the first camera was placed approximately 1.2 m from that position. Additionally, the tail amplitude during swimming was recorded using a high-speed camera (INFINICAM, Photron) fixed to the top of the water tank. Image-processing software (Photron Fastcam Viewer, Photron) was used to track the coordinates of the tail fin’s tip from the recorded video and calculate the peak-to-peak distance, which was then recorded as the tail amplitude. The driving frequency of the robot ranged from 0 to 5 Hz with 1-Hz increments, and the angular command to the motor was set at ± 30°. The results were reported as the average of three measurements at each frequency. Turning speed measurement In the turning speed measurement, the motion of the robot, i.e., turning in clockwise direction from a stationary position, was captured using a high-speed camera (INFINICAM, Photron) fixed to the top of the water tank. The frame rate for this camera was set at 1000 fps. After the rotation, two markers attached to the float of the robot were tracked using image-processing software (Photron Fastcam Analysis, Photron), and the change in angle of the vector formed by these markers was used to calculate the rotation speed. The angular command to the motor was set at 90°. The experimental setup used in this measurement was the same as the one presented in Fig. 2 a-ⅱ, except that the robot was not fixed. The results were reported as the average of three measurements. Measurement in the swimming pool In a 25-m-long swimming pool, the forward speed in the high-frequency domain (5–20 Hz) was measured. In preliminary tests, a difficulty was encountered, wherein the float attached to the robot for buoyancy and stabilization purposes created significant fluid resistance and disturbed swimming in unexpected directions. Moreover, the fast movements of the robot did not permit the use of water tanks or water tunnels because of their limited size or achievable fluid speed. Therefore, the measurement was performed by balancing the robot with fishing lines through a rod (Fig. 2 b), and a conductor of the experiment holding the rod ran along the pool while matching the swimming speed of the robot. Because the position of the conductor (i.e., the tip of the rod) was slightly behind the robot, the swimming speed could decrease but never increase. This method has also been used in other studies 10 . In this measurement, two synchronized waterproof high-speed cameras with a frame rate of 240 fps (Hero10 Black, GoPro) were fixed to an aluminum frame with a lens separation distance of 1.0 m. These cameras were positioned underwater to capture the swimming motion of the robot (Fig. 2 b). The time taken by the robot to traverse the center line of both cameras was measured from the recorded video and used to calculate the swimming speed. The driving frequency of the robot was set at 7.5, 10, 12.5, 15, and 20 Hz, and the angular command to the motor was set at ± 30°. The results were reported as the average of three measurements at each frequency. Structure and components of the fish robot The robot was controlled by an onboard microcontroller board (DEV-14483, SparkFun). The commands to the robot were sent using a 27-MHz-band R/C transmitter (RP-101, Sanwa). The commands were received by a receiver (RX-101, Sanwa) and then sent to the microcontroller board, which sent position commands to the brushless DC motor driver (FSESC6.7, Flipsky). A schematic diagram of the control system of the robot is shown in Supplementary Fig. 4. The robot swam at a given driving frequency for the specified duration. It was powered by a six-cell lithium-polymer battery with a maximum charged voltage of 25.2 V (6S 1050 mAh LiPo-Battery, Sunpadow), allowing approximately 9 min of swimming at the maximum power consumption. The power consumption of the robot during swimming was recorded using an onboard logger (DEV-13712, SparkFun). The body of the robot was designed to be both flexible and durable for high-frequency operation by encapsulating a thin CFRP plate in a 10-mm-thick silicone structure via a molding process. After investigating the impact of stiffness differences of the CFRP on swimming in preliminary tests, a thickness of 1 mm was selected. Dragon Skin 30 (Smooth-On) was used for the silicone structure, which was poured in a mold and cured in an oven at 60 ℃ for more than 6 h (Supplementary Fig. 2). The mold was made of an ultraviolet (UV)-curable resin (Clear Resin v4, Formlabs) and printed by a three-dimensional (3D) printer (Form 3, Formlabs). The tail fin was crafted by cutting a 1-mm-thick CFRP plate. The aspect ratio of the fin was determined as 3.5 from preliminary tests. The fin was connected to the body using a 3D-printed part made of the UV-curable resin. The head was made of the UV-curable resin and comprised top and bottom parts that were fixed by screws. To ensure a waterproof head, a molded gasket made of silicone rubber (Dragon Skin 30, Smooth-On) was inserted between the top and bottom parts (Supplementary Fig. 3). Water infiltration through the screw holes in the head parts was prevented by using sealing washers during screw fastening. Declarations Acknowledgments The authors thank the University of Electro-Communications, Tokyo Institute of Technology, Japan Agency for Marine-Earth Science and Technology for swimming speed measurements and preliminary tests. Funding Nagamori Foundation Research Grant 2021, 2022, and 2023. Japan Science and Technology Agency (JST) Fusion Oriented Research for Disruptive Science and Technology (FOREST) (grand number JPMJFR2126). Japan Society for the Promotion of Science (JSPS) KAKENHI Grant-in-Aid for Scientific Research on Innovative Areas “Science of Soft Robot” project (grant number 21H00324 and JP18H05468). Japan Society for the Promotion of Science (JSPS) KAKENHI Grant-in-Aid for Scientific Research (grant number 23H03480). Author contributions Conceptualization: KI, YI, JS Methodology: KI, TS, HT, YI, JS Investigation: KI, TS Visualization: KI, JS Funding acquisition: JS Project administration: JS Supervision: HT, YI, JS Writing – original draft: KI Writing – review & editing: TS, HT, YI, JS Competing interests The authors declare that they have no competing interests. Data and materials availability All data needed to evaluate the conclusions presented in this paper are included in the article and/or Supplementary Information. References Wang, R. et al. Soft Underwater Swimming Robots Based on Artificial Muscle. Adv. Mater. Technol. 8 , 2200962 (2023). Scaradozzi, D., Palmieri, G., Costa, D. & Pinelli, A. BCF swimming locomotion for autonomous underwater robots: a review and a novel solution to improve control and efficiency. Ocean Eng. 130 , 437–453 (2017). Li, Y. et al. A comprehensive review on fish-inspired robots. Int. J. Adv. Robot. Syst. 19 , (2022). Raj, A. & Thakur, A. 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Optimal Soft Composites for Under‐Actuated Soft Robots. Adv. Mater. Technol. 6 , (2021). Wang, Y., Zhang, P., Huang, H. & Zhu, J. Bio-Inspired Transparent Soft Jellyfish Robot. Soft Robot. 10 , 590–600 (2023). Nawroth, J. C. et al. A tissue-engineered jellyfish with biomimetic propulsion. Nat. Biotechnol. 30 , 792–797 (2012). Frame, J., Lopez, N., Curet, O. & Engeberg, E. D. Thrust force characterization of free-swimming soft robotic jellyfish. Bioinspir. Biomim. 13 , 064001 (2018). Berlinger, F. et al. A Modular Dielectric Elastomer Actuator to Drive Miniature Autonomous Underwater Vehicles. in 2018 IEEE International Conference on Robotics and Automation (ICRA) 3429–3435 (IEEE, 2018). doi:10.1109/ICRA.2018.8461217. Pratt, G. A. & Williamson, M. M. Series elastic actuators. in Proceedings 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots vol. 1 399–406 (IEEE Comput. Soc. Press, 1995). Kenneally, G., De, A. & Koditschek, D. E. Design Principles for a Family of Direct-Drive Legged Robots. IEEE Robot. Autom. Lett. 1 , 900–907 (2016). Sfakiotakis, M., Lane, D. M. & Davies, J. B. C. Review of fish swimming modes for aquatic locomotion. IEEE J. Ocean. Eng. 24 , 237–252 (1999). Zhong, Q. et al. Tunable stiffness enables fast and efficient swimming in fish-like robots. Sci. Robot. 6 , (2021). Zhong, Y., Li, Z. & Du, R. A Novel Robot Fish With Wire-Driven Active Body and Compliant Tail. IEEE/ASME Trans. Mechatronics 22 , 1633–1643 (2017). Ijspeert, A. J., Crespi, A., Ryczko, D. & Cabelguen, J. M. From swimming to walking with a salamander robot driven by a spinal cord model. Science (80-. ). 315 , 1416–1420 (2007). Azuma, A. The Biokinetics of Flying and Swimming, Second Edition . The Biokinetics of Flying and Swimming, Second Edition (American Institute of Aeronautics and Astronautics, 2006). doi:10.2514/4.862502. Tytell, E. D., Hsu, C. Y. & Fauci, L. J. The role of mechanical resonance in the neural control of swimming in fishes. Zoology 117 , 48–56 (2014). Quinn, D. B., Lauder, G. V. & Smits, A. J. Scaling the propulsive performance of heaving flexible panels. J. Fluid Mech. 738 , 250–267 (2014). Daou, H. El, Salumäe, T., Chambers, L. D., Megill, W. M. & Kruusmaa, M. Modelling of a biologically inspired robotic fish driven by compliant parts. Bioinspiration and Biomimetics 9 , (2014). Van Eysden, C. A. & Sader, J. E. Resonant frequencies of a rectangular cantilever beam immersed in a fluid. J. Appl. Phys. 100 , (2006). Marchese, A. D., Onal, C. D. & Rus, D. Autonomous Soft Robotic Fish Capable of Escape Maneuvers Using Fluidic Elastomer Actuators. Soft Robot. 1 , 75–87 (2014). Taylor, G. K., Nudds, R. L. & Thomas, A. L. R. Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency. Nat. 2003 4256959 425 , 707–711 (2003). White, C. H., Lauder, G. V. & Bart-Smith, H. Tunabot Flex: a tuna-inspired robot with body flexibility improves high-performance swimming. Bioinspir. Biomim. 16 , 026019 (2021). Davenport, J. How and why do flying fish fly? Rev. Fish Biol. Fish. 4 , 184–214 (1994). Gao, A. & Techet, A. H. Design considerations for a robotic flying fish. Ocean. - MTS/IEEE Kona, Progr. B. (2011) doi:10.23919/OCEANS.2011.6107039. Makiguchi, Y., Kuramochi, K., Iwane, S., Kojima, T. & Naito, Y. Take-off performance of flying fish Cypselurus heterurus doederleini measured with miniature acceleration data loggers. Aquat. Biol. 18 , 105–111 (2013). U8Ⅱ Lite_U Efficiency Type_U Type_Motors_Multirotor_T-MOTOR Store-Official Store for T-motor drone motor,ESC,Propeller. Hu, D. et al. Micro thrust measurement experiment and pressure field evolution of bionic robotic fish with harmonic actuation of macro fiber composites. Mech. Syst. Signal Process. 153 , 107538 (2021). Additional Declarations No competing interests reported. Supplementary Files DDfishrobotSInpjR.docx Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 28 Mar, 2024 Reviews received at journal 27 Feb, 2024 Reviewers agreed at journal 21 Feb, 2024 Reviewers agreed at journal 06 Feb, 2024 Reviewers invited by journal 22 Jan, 2024 Editor assigned by journal 04 Dec, 2023 Submission checks completed at journal 04 Dec, 2023 First submitted to journal 03 Dec, 2023 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3699820","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":278410440,"identity":"171922f4-59ba-4a9c-854a-fe9b6bacfedf","order_by":0,"name":"Keisuke Iguchi","email":"","orcid":"","institution":"The University of Electro- communications","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Keisuke","middleName":"","lastName":"Iguchi","suffix":""},{"id":278410441,"identity":"9f374d4c-5092-4a24-bd5b-f195ebffe962","order_by":1,"name":"Taiki Shimooka","email":"","orcid":"","institution":"Tokyo Institute of Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Taiki","middleName":"","lastName":"Shimooka","suffix":""},{"id":278410442,"identity":"d059e3c7-db0e-4eaf-8d09-e55791746b4c","order_by":2,"name":"Hiroto Tanaka","email":"","orcid":"","institution":"Tokyo Institute of Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Hiroto","middleName":"","lastName":"Tanaka","suffix":""},{"id":278410443,"identity":"28ecd801-f70d-4e9a-8e4e-bc2ede7801c2","order_by":3,"name":"Yusuke Ikemoto","email":"","orcid":"","institution":"Meijo University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Yusuke","middleName":"","lastName":"Ikemoto","suffix":""},{"id":278410444,"identity":"5f990b79-7a6f-4299-83bc-9b78d554f325","order_by":4,"name":"Jun Shintake","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA10lEQVRIiWNgGAWjYDACCcYGIJnAwA8TAPMJajkA1CIJU0mEFiAGaTE4QKy75Gc3tz3+UJMmZ3wj+eAHhho7BubZBKwxuHOw3eDAsRxjsxtpyRIMx5IZGOcQsM9AIrFN4gBbReK2GzlmDAxsBxgYZyQQcNgMkJZ/FfWbZ+R/Y2D4R4QWhhtALQfbchIMJHLYGBjbiNBiANJyti/NcMaZZ8YSiX3JPAT9Ij8j/ZlExbdkef725IcfPnyzkzMkFGKoAOgkHsMZpOiA2CtBspZRMApGwSgY5gAA0FpF1KRsdYsAAAAASUVORK5CYII=","orcid":"","institution":"The University of Electro- communications","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Jun","middleName":"","lastName":"Shintake","suffix":""}],"badges":[],"createdAt":"2023-12-03 08:29:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3699820/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3699820/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":52743669,"identity":"f7240977-ff08-4071-a24b-498f5fe803a6","added_by":"auto","created_at":"2024-03-15 08:39:45","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1982199,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDirect-drive (DD) biomimetic underwater robot.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e Developed robot designed with a streamlined shape resembling a real fish to minimize fluid resistance. \u003cstrong\u003eb\u003c/strong\u003eSchematics illustrating the components in the robot. A brushless DC motor equipped with an encoder is directly connected to a flexible body and tail fin. The motor is also connected to a head part, in which control and communication modules are placed (see Supplementary Information for more detail). \u003cstrong\u003ec\u003c/strong\u003e High backdrivability and simplified structure facilitated by the DD architecture enable the robot to withstand external impacts (in this case, hitting by a hammer; see also Supplementary Video S1). \u003cstrong\u003ed\u003c/strong\u003e Swimming motion of the robot at a driving frequency of 2 Hz (see also Supplementary Video S5).\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-3699820/v1/a527ea3128e8294a98f28420.png"},{"id":52743668,"identity":"e1dc09a1-cf09-479c-bbd7-62edce286262","added_by":"auto","created_at":"2024-03-15 08:39:45","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":912065,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExperimental setups. a\u003c/strong\u003eExperimental setup using a water tank (750 × 600 × 1800 mm (W × H × L)). In this setup, (i) swimming speed in the low-frequency domain (0–5 Hz), (ii) thrust force, and (iii) tail amplitude as well as turning speed are measured (see Materials and Methods for more details). \u003cstrong\u003e\u0026nbsp;b\u003c/strong\u003e Experimental setup used for measurement in a pool. The robot is suspended on a rod using a fishing line, with the swimming speed in the high-frequency domain (7.5–20 Hz) is measured. The bottom-right image shows a picture taken during the experiment (see also Supplementary Video S2). During the experiment, a conductor holding the rod runs along the pool while following the swimming speed of the robot. Two synchronized waterproof video cameras placed at the side wall of the pool measure the speed of the robot passing in front (see Materials and Methods for more details). Because the position of the conductor (i.e., the tip of the rod) is slightly behind the robot, the swimming speed can decrease but cannot increase.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-3699820/v1/9ffddff947cbbd4d63023fef.png"},{"id":52743670,"identity":"f30184c4-991a-4c68-87cb-15d446c0abec","added_by":"auto","created_at":"2024-03-15 08:39:45","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":990930,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-3699820/v1/8de85c2048cd6cd988159487.png"},{"id":52743671,"identity":"0308db3f-f7e4-473a-a2de-398ff3972472","added_by":"auto","created_at":"2024-03-15 08:39:46","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":445534,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eMeasured turning speed. \u003c/strong\u003eData are presented as angle and angular rate as functions of time (see also Supplementary Video S4). The robot achives a turn of approximately 90° within 110 ms from an initial static state, resulting in an angular rate of 1450°/s.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-3699820/v1/8d993895ece0263cffc177d7.png"},{"id":52743672,"identity":"12b87698-d8a1-4f8d-ad91-fc9cb9a6ef30","added_by":"auto","created_at":"2024-03-15 08:39:46","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":369402,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSwimming speed as a function of the tail beat frequency for real fish and robots. \u003c/strong\u003eThe speed of the robot developed in this study compares well with that of real fish. The data of real fish are adopted and replotted from the study of Zhu et al. \u003csup\u003e8\u003c/sup\u003e. The data of the robot are adopted and replotted from the study of White et al. \u003csup\u003e35\u003c/sup\u003e.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-3699820/v1/9adcc033ff722f72d5e3d3ed.png"},{"id":52744494,"identity":"8799535f-653b-4d6b-8e58-f18c5ac34617","added_by":"auto","created_at":"2024-03-15 08:47:47","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2560439,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3699820/v1/bcb71dd1-cadb-4346-be92-6cef09f295ad.pdf"},{"id":52743673,"identity":"60c9db2b-933b-4881-9be5-78713a4fe1b7","added_by":"auto","created_at":"2024-03-15 08:39:46","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":3991054,"visible":true,"origin":"","legend":"","description":"","filename":"DDfishrobotSInpjR.docx","url":"https://assets-eu.researchsquare.com/files/rs-3699820/v1/0b4fa3a734a62117145cc6cc.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Agile robotic fish based on direct drive of continuum body","fulltext":[{"header":"Introduction","content":"\u003cp\u003eUnderwater robots have significant utility for tasks in aquatic environments, including artifact inspection, ecology investigation, resource exploration, and rescue operations. Biomimetic underwater robots that ingeniously incorporate biological structures and functionalities offer the potential to achieve high mobility and efficiency similar to aquatic organisms \u003csup\u003e\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. Furthermore, traditional propeller-equipped underwater robots have faced challenges related to the entanglement of marine life and environmental disruption caused by strong water currents, highlighting environmental concerns. Accordingly, biomimetic robots, which are based on biological emulation, have been actively pursued as a solution to address these issues \u003csup\u003e\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. Underwater robots based on the biomimetic approach are paving the way for advanced underwater systems capable of a wide range of tasks in various liquid environments.\u003c/p\u003e \u003cp\u003eMany robots inspired by various aquatic organisms \u003csup\u003e\u003cspan additionalcitationids=\"CR2 CR3 CR4\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e, such as fish \u003csup\u003e\u003cspan additionalcitationids=\"CR7 CR8 CR9 CR10\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e, eel \u003csup\u003e\u003cspan additionalcitationids=\"CR13\" citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e, ray \u003csup\u003e\u003cspan additionalcitationids=\"CR16\" citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e, and jellyfish \u003csup\u003e\u003cspan additionalcitationids=\"CR19\" citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e, have been developed. These robots may be broadly classified as being based on two approaches depending on their architecture. One is the so-called rigid robotic approach, in which electromagnetic motors or servos and their associated rigid transmission components form the active moving body to generate swimming motions \u003csup\u003e\u003cspan additionalcitationids=\"CR3\" citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. The other is the soft robotic approach, in which a soft actuator that deforms itself, such as electroactive polymers \u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e,\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e,\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e,\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e and fluid-driven soft actuators \u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e,\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e,\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e, forms a portion of or the entire body and directly moves it \u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. The advantages of the rigid robotic approach are associated with the features of motors, such as ease of integration, high energy density, efficiency, positioning accuracy, and frequency response. However, the presence of a transmission mechanism including gears, cranks, sliders, hinges, linkages, and wires introduces complexities in the robotic structure. This makes the robots susceptible to damage from severe impacts, potentially compromising mechanical robustness \u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e. Furthermore, although the motors themselves are highly efficient, energy losses in the transmission mechanism and its weight reduce the resulting efficiency and specific output \u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. Meanwhile, the soft robotic approach has the advantage that the actuator can achieve a type of automatically generated swimming motion because of the interaction between the continuous, simple, and flexible body and the surrounding water. This implies that the control input can also be simplified, resulting in a simple on-off in extreme cases. In addition, the softness contributes to improving the mechanical robustness of the structure. However, in many cases, individual soft-actuator technologies present one or more of the following challenges: low response speed, low efficiency and energy density, and small deformation and force output.\u003c/p\u003e \u003cp\u003eIn this study, we hypothesize that when both rigid and soft robotic approaches are combined, that is, when a robot has a flexible continuum body directly driven by a motor, the simplified high-energy-density structure and its interaction with the surrounding water provide the robot with high-performance swimming capability. As a specific way to verify this hypothesis, we propose direct-drive (DD) as an actuation method for motor-driven biomimetic underwater robots. As the name implies, DD moves the robotic body directly, eliminating the need for transmission parts. This results in the expected improvement in the output performance and mechanical robustness of the robots. Moreover, DD enables the motor to directly interact with the surrounding water through the body. Because of this functionality, we expect DD to also be capable of simplifying the complex control often required for traditional motor-driven underwater robots. This is analogous to the simplification of control through the passive deformation of the structure, which is well known in the soft robotic approach. In the literature, DD has demonstrated validity in legged terrestrial robots \u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e; however, to the best of our knowledge, no case of implementation in biomimetic underwater robots has been reported. In this context, the focus of the present study is to investigate the swimming characteristics that can be achieved by the DD approach through the characterization of a robotic fish platform.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eThe robot developed in this study has a morphology inspired by the anatomy of \u003cem\u003eCarangiform\u003c/em\u003e swimmers (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea)\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e, measuring a total length (head-to-tail) of 412.5 mm and weighing 1.1 kg (see Supplementary Fig.\u0026nbsp;1 for the detailed dimensions). It mainly comprises a head, motor, flexible body, and tail fin (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb, 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 \u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan additionalcitationids=\"CR14\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e, and sine waves are typically used in rigid underwater robots \u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e,\u003cspan additionalcitationids=\"CR26\" citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e. 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.\u003c/p\u003e \u003cp\u003eA 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\u0026mdash;known for their high torque and responsive frequency characteristics (e.g., ability to produce an amplitude of 360\u0026deg; at 20 Hz \u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e)\u0026mdash;rendering them suitable for our DD method, which achieves high-power, high-speed swimming. Moreover, this type of motor, being devoid of rotor\u0026ndash;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 \u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe flexible body is made of silicone rubber encapsulating a thin sheet of carbon fiber reinforced polymer (CFRP) by a molding process (Supplementary Fig.\u0026nbsp;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 \u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e,\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e,\u003cspan additionalcitationids=\"CR30\" citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e. We designed the body and tail to have the first and second resonance modes within the tail beat frequency range of up to ~\u0026thinsp;20 Hz according to a previously reported analytical approach \u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e. In particular, from the designing result, we expected the first and second natural frequencies as 3.3 Hz (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{w1}\\)\u003c/span\u003e\u003c/span\u003e) and 21.9 (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{w2}\\)\u003c/span\u003e\u003c/span\u003e) Hz, respectively, in the case where the robot was fixed in the experiments (discussed later), and as 1.8 Hz (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{w1}^{{\\prime }}\\)\u003c/span\u003e\u003c/span\u003e) and 11.6 Hz (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{w2}^{{\\prime }}\\)\u003c/span\u003e\u003c/span\u003e), respectively, in free swimming (see Materials and Methods for more details).\u003c/p\u003e \u003cp\u003eWith 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.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec, 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.\u003c/p\u003e \u003cp\u003eThe 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.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed). The experimental setup used for this observation is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea-i. In the robot, the angular command to the motor, i.e., the swing angle of the body, was set as \u0026plusmn;\u0026thinsp;30\u0026deg; for all experiments except for the measurement of turning speed (described later) according to the preliminary test (Supplementary Fig.\u0026nbsp;7). A previous study reported\u0026thinsp;\u0026plusmn;\u0026thinsp;30\u0026deg; (swing angle of 60\u0026deg;) as an optimal value for a servomotor-driven fish robot \u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e, 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\u0026ndash;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.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea, 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\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb 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 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{w2}^{{\\prime }}=11.6\\)\u003c/span\u003e\u003c/span\u003e Hz predicted by the model, indicating the presence of a resonance likely to be the second mode.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThis was further supported by the data of thrust force of the robot measured in a fixed condition (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea-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.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb). 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 (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{w1}=3.3\\)\u003c/span\u003e\u003c/span\u003e Hz, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{w2}\\)\u003c/span\u003e\u003c/span\u003e=21.9 Hz). See Supplementary Video S3 for the body deformations at 2 and 19 Hz.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWe expected to observe the peaks when measuring the tail amplitude of the robot in a fixed condition (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea-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.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec). 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.\u003c/p\u003e \u003cp\u003eThe 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 \u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e. The experimental result, obtained using a setup similar to the one illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea-iii, reveals that the robot achieved a turn of approximately 90\u0026deg; within 110 ms from an initial static state, with a maximum angular speed of 1450\u0026deg;/s (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). 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.\u003c/p\u003e \u003cp\u003eAs mentioned previously, the measured specific thrust (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb) 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 \u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e,\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e,\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. 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\u0026ndash;0.4 and 0.6\u0026ndash;0.7, respectively \u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e,\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e,\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. The Strouhal number is defined as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(St=fA/U\\)\u003c/span\u003e\u003c/span\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(f\\)\u003c/span\u003e\u003c/span\u003e is the drive frequency, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(A\\)\u003c/span\u003e\u003c/span\u003e is the peak-to-peak amplitude distance of the tail, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(U\\)\u003c/span\u003e\u003c/span\u003e is the swimming speed. Further, the swimming number is defined as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(Sw=U/fL\\)\u003c/span\u003e\u003c/span\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(L\\)\u003c/span\u003e\u003c/span\u003e is the fish body length. By measuring the swimming speed (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea, d, Supplementary Video S5) and tail amplitude, we calculated the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(St\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(Sw\\)\u003c/span\u003e\u003c/span\u003e of the robot for the tail beat frequency range of 0\u0026ndash;20 Hz. Above 3 Hz, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(St\\)\u003c/span\u003e\u003c/span\u003e was calculated as a quasi-value using the amplitude data shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec. 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.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ee, f show that \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(St\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(Sw\\)\u003c/span\u003e\u003c/span\u003e fall within their typical range observed in nature around the frequency values predicted by the model (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{w1}^{{\\prime }}=1.8\\)\u003c/span\u003e\u003c/span\u003e Hz, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{w2}^{{\\prime }}=11.6\\)\u003c/span\u003e\u003c/span\u003e 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.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eNext, 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 \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{C}\\text{O}\\text{T}=P/mgU\\)\u003c/span\u003e\u003c/span\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(P\\)\u003c/span\u003e\u003c/span\u003e is the average power consumption (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eg), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(m\\)\u003c/span\u003e\u003c/span\u003e is the mass, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(g\\)\u003c/span\u003e\u003c/span\u003e denotes the gravitational acceleration, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(U\\)\u003c/span\u003e\u003c/span\u003e 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.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eh). The COT values of the square and sine waves reached minima around the predicted frequency (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{w2}^{{\\prime }}=11.6\\)\u003c/span\u003e\u003c/span\u003e Hz). In the case of square waves, the COT also decreased toward the model prediction (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{w1}^{{\\prime }}=1.8\\)\u003c/span\u003e\u003c/span\u003e 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.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe simplicity of the fundamental architecture of the robot, that is, the brushless DC motor directly connected to the passive, flexible continuum body, ensures transmission of the power of the motor to the body and tail as well as assures mechanical robustness under external impacts. The observed rapid swimming of the fish robot, 6.3 BL/s (2.6 m/s) in the forward direction and 1450\u0026deg;/s in turning (110 ms to achieve a 90\u0026deg; pivot turn from a static position), is rarely achieved within a single system. The swimming speed of the robot compares well with that of real fish (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, data adopted and replotted from references \u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e,\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e), illustrating its high performance comparable with its natural counterpart. Moreover, the turning speed is more than four times higher than that of a fish robot capable of escape maneuvers \u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e. At a speed of 6.3 BL/s observed at the tail beat frequency of 10 Hz, a minimum COT of 5.9 is achieved owing to the resonance mode of the body, which directly interacted with the surrounding water and facilitated elastic energy storage. Around this frequency (~\u0026thinsp;10 Hz), the Strouhal and swimming numbers fall within the typical range observed for real fish. Both numbers reach the typical range at a low frequency as well (~\u0026thinsp;1 Hz). These results suggest that the robot achieved swimming characteristics similar to those of real fish. The two frequency domains (~\u0026thinsp;1 and ~\u0026thinsp;10 Hz), where rapid and efficient swimming is achieved, are similar to the resonant frequency predicted by the model (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{w1}^{{\\prime }}=1.8\\)\u003c/span\u003e\u003c/span\u003e Hz, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({f}_{w2}^{{\\prime }}=11.6\\)\u003c/span\u003e\u003c/span\u003e Hz). This implies that robots based on the DD method can be designed to a given performance specification. These outcomes validate the successful implementation of the DD method derived from the conceived concept that combines the rigid and soft robotic approaches and that the proposed DD method can be employed as a framework for biomimetic underwater robotic systems.\u003c/p\u003e \u003cp\u003eFrom an energetics viewpoint, the efficiency of the robot (COT of 5.9) is on the same or higher order of magnitude as that of robots in other studies (0.4 \u003csup\u003e15\u003c/sup\u003e, 2.8 \u003csup\u003e8\u003c/sup\u003e, 1.9 \u003csup\u003e35\u003c/sup\u003e, and 1.7 \u003csup\u003e26\u003c/sup\u003e), further away from real fish, indicating room for improvement. Modification of the shape of the body and tail fin will contribute to increasing the efficiency. Moreover, hypotheses propose that fish actively control muscle contractions during swimming to regulate body stiffness. For instance, tuna adjusts the stiffness of its tail for high-speed and steady-state swimming, and this mechanism has been successfully implemented in a robotic fish \u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e. Incorporation of such variable stiffness into our robot may further improve the swimming performance by modulating the frequency response characteristics. The DD method also requires investigation and establishment of robotic architecture and a control method for multi-degree-of-freedom motion because the primary locomotion of the robot presented herein is forward movement. Swimming with multi-degree-of-freedom motion can be achieved by introducing pectoral fins and a buoyancy control unit as reported in a previous study \u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWhen considering the environment in which the robot performs its tasks, protection of the motor plays a particularly important role. As mentioned in the previous section, the brushless DC motor used in this study required almost no waterproofing. However, this may only be valid in tap water; seawater, which many robots often come in contact with in actual tasks, can corrode motor parts and eventually cause them to fail. To address this issue, an additional structure would need to be placed around the motor such that it does not inhibit its rotation and movement of the flexible body while providing physical insulation from the surrounding water, such as a compliant bag filled with insulating oil.\u003c/p\u003e \u003cp\u003eThe agility of the developed robot provides the opportunity for implementing advanced functionalities. A typical example is gliding in the air after taking off from underwater, the same functionality as that of flying fish \u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e. Flying fish are known to glide over water surfaces to evade predators and facilitate movement. They exhibit high swimming speeds exceeding 10\u0026ndash;20 m/s at tail beat frequencies of 20\u0026ndash;40 Hz \u003csup\u003e\u003cspan additionalcitationids=\"CR37\" citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. To achieve swimming speeds similar to those of flying fish, an actuator with a power density of 4150 W/kg is necessary \u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e. The brushless DC motor used in this study consumed a maximum power of 1450 W \u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e, resulting in a power density of 5992 W/kg. This exceeds the reported values and provides high feasibility from the viewpoint of power density. Further, the robot exhibited a swimming speed of 6.3 BL/s, clearly lower than that of flying fishes. Although the brushless DC motor used in this study allows a driving voltage of up to 48 V, for safety reasons all the experiments described herein were conducted at a voltage of 25.2 V. Thus, there remains room for dramatically increasing the swimming speed even with the current robot, and the same is true for its potential as a gliding platform. We believe that by including systems with such advanced features, the proposed DD method will contribute to the creation of highly versatile biomimetic underwater robots.\u003c/p\u003e"},{"header":"Methods","content":"\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003eMeasurements in the water tank\u003c/h2\u003e \u003cp\u003eIn a water tank having dimensions of 1800 \u0026times; 750 \u0026times; 600 mm (L\u0026times;W\u0026times;H) and filled with tap water, the thrust force, tail amplitude, forward speed in the low-frequency domain (0\u0026ndash;5 Hz), and turning speed were measured. Aluminum frames were placed around the water tank to provide structural support for measurement equipment (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea). The driving voltage for the robot was maintained at 25.2 V for all the experiments. In the measurement of the thrust and tail amplitude, an external microcontroller board (DEV-14483, SparkFun), a motor driver (FSESC 7550, Flipsky), and a power supply (PWR801ML, Kikusui) were used to drive the robot body. The brushless DC motor equipped with an encoder (AS5047D-TS_EK_AB, ams OSRAM) was connected to the driver, and the microcontroller board controlled the motor\u0026rsquo;s position by providing angle commands to the driver, thus driving the robot.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eThrust force measurement\u003c/h2\u003e \u003cp\u003eIn the thrust force measurement, a waterproof load cell with a capacity of 445 N (LSB210, FUTEK) was used as a force sensor. The measurement setup involved attaching the robot to a lever mechanism that indirectly pushed the force sensor (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea-ⅰ) \u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e. When the robot generated a thrust, the lever attached to the robot rotated around an axis, pressing the other lever against the force sensor. The output signal of the load cell was recorded using a digital multimeter (2100/100, Keithley) controlled by PyVISA and saved on a PC. The sampling rate was set at 100 Hz. To account for the sensor\u0026rsquo;s initial output voltage when the robot was not driven, a 2-s baseline data recording was conducted without robot propulsion, and the average voltage was taken as the reference. The robot was then driven for 5 s, and the sensor output was recorded. The average of the recorded sensor output over 1.5 s was calculated and used as the thrust force value at the respective frequency. The driving frequency applied to the robot ranged from 0 to 25 Hz with 1-Hz increments, and the angular command to the motor was set at \u0026plusmn;\u0026thinsp;30\u0026deg;.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003eTail amplitude measurement\u003c/h2\u003e \u003cp\u003eIn the tail amplitude measurement, above the underwater robot, an acrylic plate was placed and fixed at the water surface level to remove waves that could distort the images taken from above. In this setup, the robot was driven for 3 s and its behavior was recorded using a high-speed camera (INFINICAM, Photron) positioned directly above it (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea-ⅱ). The frame rate for this camera was set at 1000 fps. The recorded video data were analyzed using image-processing software (Photron Fastcam Analysis, Photron Fastcam Viewer, Photron) to track the coordinates of the tip of the tail fin. The peak-to-peak distance of these coordinate data was recorded as the amplitude value. The driving frequency of the robot ranged from 0 to 25 Hz with 1-Hz increments, and the angular command to the motor was set at \u0026plusmn;\u0026thinsp;30\u0026deg;. The results were reported as the average of three measurements at each frequency.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eLow-frequency swimming speed measurement\u003c/h2\u003e \u003cp\u003eIn the low-frequency swimming speed measurement, the wireless-enabled robot was allowed to swim inside the water tank, and its movement was recorded using two synchronized high-speed video cameras (Hero10 Black, GoPro) with a frame rate of 240 fps. A styrofoam ball of 100-mm diameter was attached to the robot to ensure buoyancy and stability. The cameras were positioned outside the tank, fixed to the aluminum frame to maintain a lens separation distance of 0.3 m (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea-ⅲ). The time taken by the robot to traverse both cameras was measured from the recorded video and used to calculate the swimming speed. The initial state of the robot was at one end of the tank, and the first camera was placed approximately 1.2 m from that position. Additionally, the tail amplitude during swimming was recorded using a high-speed camera (INFINICAM, Photron) fixed to the top of the water tank. Image-processing software (Photron Fastcam Viewer, Photron) was used to track the coordinates of the tail fin\u0026rsquo;s tip from the recorded video and calculate the peak-to-peak distance, which was then recorded as the tail amplitude. The driving frequency of the robot ranged from 0 to 5 Hz with 1-Hz increments, and the angular command to the motor was set at \u0026plusmn;\u0026thinsp;30\u0026deg;. The results were reported as the average of three measurements at each frequency.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003eTurning speed measurement\u003c/h2\u003e \u003cp\u003eIn the turning speed measurement, the motion of the robot, i.e., turning in clockwise direction from a stationary position, was captured using a high-speed camera (INFINICAM, Photron) fixed to the top of the water tank. The frame rate for this camera was set at 1000 fps. After the rotation, two markers attached to the float of the robot were tracked using image-processing software (Photron Fastcam Analysis, Photron), and the change in angle of the vector formed by these markers was used to calculate the rotation speed. The angular command to the motor was set at 90\u0026deg;. The experimental setup used in this measurement was the same as the one presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea-ⅱ, except that the robot was not fixed. The results were reported as the average of three measurements.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003eMeasurement in the swimming pool\u003c/h2\u003e \u003cp\u003eIn a 25-m-long swimming pool, the forward speed in the high-frequency domain (5\u0026ndash;20 Hz) was measured. In preliminary tests, a difficulty was encountered, wherein the float attached to the robot for buoyancy and stabilization purposes created significant fluid resistance and disturbed swimming in unexpected directions. Moreover, the fast movements of the robot did not permit the use of water tanks or water tunnels because of their limited size or achievable fluid speed. Therefore, the measurement was performed by balancing the robot with fishing lines through a rod (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb), and a conductor of the experiment holding the rod ran along the pool while matching the swimming speed of the robot. Because the position of the conductor (i.e., the tip of the rod) was slightly behind the robot, the swimming speed could decrease but never increase. This method has also been used in other studies\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e. In this measurement, two synchronized waterproof high-speed cameras with a frame rate of 240 fps (Hero10 Black, GoPro) were fixed to an aluminum frame with a lens separation distance of 1.0 m. These cameras were positioned underwater to capture the swimming motion of the robot (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb). The time taken by the robot to traverse the center line of both cameras was measured from the recorded video and used to calculate the swimming speed. The driving frequency of the robot was set at 7.5, 10, 12.5, 15, and 20 Hz, and the angular command to the motor was set at \u0026plusmn;\u0026thinsp;30\u0026deg;. The results were reported as the average of three measurements at each frequency.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eStructure and components of the fish robot\u003c/h2\u003e \u003cp\u003eThe robot was controlled by an onboard microcontroller board (DEV-14483, SparkFun). The commands to the robot were sent using a 27-MHz-band R/C transmitter (RP-101, Sanwa). The commands were received by a receiver (RX-101, Sanwa) and then sent to the microcontroller board, which sent position commands to the brushless DC motor driver (FSESC6.7, Flipsky). A schematic diagram of the control system of the robot is shown in Supplementary Fig.\u0026nbsp;4. The robot swam at a given driving frequency for the specified duration. It was powered by a six-cell lithium-polymer battery with a maximum charged voltage of 25.2 V (6S 1050 mAh LiPo-Battery, Sunpadow), allowing approximately 9 min of swimming at the maximum power consumption. The power consumption of the robot during swimming was recorded using an onboard logger (DEV-13712, SparkFun).\u003c/p\u003e \u003cp\u003eThe body of the robot was designed to be both flexible and durable for high-frequency operation by encapsulating a thin CFRP plate in a 10-mm-thick silicone structure via a molding process. After investigating the impact of stiffness differences of the CFRP on swimming in preliminary tests, a thickness of 1 mm was selected. Dragon Skin 30 (Smooth-On) was used for the silicone structure, which was poured in a mold and cured in an oven at 60 ℃ for more than 6 h (Supplementary Fig.\u0026nbsp;2). The mold was made of an ultraviolet (UV)-curable resin (Clear Resin v4, Formlabs) and printed by a three-dimensional (3D) printer (Form 3, Formlabs). The tail fin was crafted by cutting a 1-mm-thick CFRP plate. The aspect ratio of the fin was determined as 3.5 from preliminary tests. The fin was connected to the body using a 3D-printed part made of the UV-curable resin.\u003c/p\u003e \u003cp\u003eThe head was made of the UV-curable resin and comprised top and bottom parts that were fixed by screws. To ensure a waterproof head, a molded gasket made of silicone rubber (Dragon Skin 30, Smooth-On) was inserted between the top and bottom parts (Supplementary Fig.\u0026nbsp;3). Water infiltration through the screw holes in the head parts was prevented by using sealing washers during screw fastening.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003eAcknowledgments\u003c/p\u003e\n\u003cp\u003eThe authors thank the University of Electro-Communications, Tokyo Institute of Technology, Japan Agency for Marine-Earth Science and Technology for swimming speed measurements and preliminary tests.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNagamori Foundation Research Grant 2021, 2022, and 2023.\u003c/p\u003e\n\u003cp\u003eJapan Science and Technology Agency (JST) Fusion Oriented Research for Disruptive Science and Technology (FOREST) (grand number JPMJFR2126).\u003c/p\u003e\n\u003cp\u003eJapan Society for the Promotion of Science (JSPS) KAKENHI Grant-in-Aid for Scientific Research on Innovative Areas \u0026ldquo;Science of Soft Robot\u0026rdquo; project (grant number 21H00324 and JP18H05468).\u003c/p\u003e\n\u003cp\u003eJapan Society for the Promotion of Science (JSPS) KAKENHI Grant-in-Aid for Scientific Research (grant number 23H03480).\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eConceptualization: KI, YI, JS\u003c/p\u003e\n\u003cp\u003eMethodology: KI, TS, HT, YI, JS\u003c/p\u003e\n\u003cp\u003eInvestigation: KI, TS\u003c/p\u003e\n\u003cp\u003eVisualization: KI, JS\u003c/p\u003e\n\u003cp\u003eFunding acquisition: JS\u003c/p\u003e\n\u003cp\u003eProject administration: JS\u003c/p\u003e\n\u003cp\u003eSupervision: HT, YI, JS\u003c/p\u003e\n\u003cp\u003eWriting \u0026ndash; original draft: KI\u003c/p\u003e\n\u003cp\u003eWriting \u0026ndash; review \u0026amp; editing: TS, HT, YI, JS\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no competing interests.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003cstrong\u003eData and materials availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll data needed to evaluate the conclusions presented in this paper are included in the article and/or Supplementary Information.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eWang, R. \u003cem\u003eet al.\u003c/em\u003e Soft Underwater Swimming Robots Based on Artificial Muscle. \u003cem\u003eAdv. 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Signal Process.\u003c/em\u003e \u003cstrong\u003e153\u003c/strong\u003e, 107538 (2021).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"npj-robotics","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"npjrobot","sideBox":"Learn more about [npj Robotics](http://www.nature.com/npjrobot/)","snPcode":"44182","submissionUrl":"https://mts-npjrobot.nature.com/cgi-bin/main.plex","title":"npj Robotics","twitterHandle":"@NaturePortfolio","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-3699820/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3699820/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eFish-like agile movements, such as fast forward swimming and rapid turning, are essential for robots to perform a wide variety of tasks in aquatic environments. However, achieving these locomotion capabilities simultaneously in existing biomimetic underwater robots has proven challenging. Here, we present a self-contained robotic fish capable of swimming at a speed of 6.3 body length per second and pivot turning at an angular speed of 1450\u0026deg; per second. These fast motions, which compare well with those of real fish, are realized by directly oscillating a flexible body using an electromagnetic motor. This direct-drive (DD) method eliminates the need for transmission parts, simplifies the robotic structure, improves mechanical robustness, and enables the use of a flexible continuum body that passively interacts with water, generating fish-like body deformations and subsequent rapid swimming. This also allows the robot to have the Strouhal and swimming numbers that match the typical values observed in nature. Moreover, the observed frequency peaks in swimming are similar to computed values using a model, which guides the design of the robot. These results illustrate the DD method as a promising framework for the creation of highly versatile biomimetic underwater robots.\u003c/p\u003e","manuscriptTitle":"Agile robotic fish based on direct drive of continuum body","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-03-15 08:39:41","doi":"10.21203/rs.3.rs-3699820/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-03-28T21:24:31+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-02-27T22:35:54+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"18bcc657-60ba-4c83-83de-f2ba37d12643","date":"2024-02-21T17:26:16+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"57eef833-4e16-48ba-86aa-9bf18c6f7599","date":"2024-02-06T16:16:11+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-01-22T12:10:37+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2023-12-05T00:57:58+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2023-12-04T11:04:25+00:00","index":"","fulltext":""},{"type":"submitted","content":"npj Robotics","date":"2023-12-03T08:19:41+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"npj-robotics","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"npjrobot","sideBox":"Learn more about [npj Robotics](http://www.nature.com/npjrobot/)","snPcode":"44182","submissionUrl":"https://mts-npjrobot.nature.com/cgi-bin/main.plex","title":"npj Robotics","twitterHandle":"@NaturePortfolio","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"7b9a156a-6c59-4a4e-b7bf-e49530f7fb86","owner":[],"postedDate":"March 15th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2024-08-28T20:09:25+00:00","versionOfRecord":[],"versionCreatedAt":"2024-03-15 08:39:41","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3699820","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3699820","identity":"rs-3699820","version":["v1"]},"buildId":"7rjqhiLT3MXkJMwkYKINL","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}