Agile robotic fish based on direct drive of continuum body

Underwater robots are useful for inspection, ecology, resource exploration, and rescue, but conventional propeller-driven systems can entangle marine life and disturb environments. Biomimetic approaches aim to replicate aquatic organisms’ high mobility and efficiency. Existing bioinspired robots generally follow two architectures: rigid motor-driven designs with transmissions (gears, linkages) and soft robots using deformable actuators. Rigid robots offer ease of integration, high energy density, efficiency, and fast response but suffer from structural complexity and transmission losses, reducing robustness and overall efficiency. Soft robots provide passive structural deformation that simplifies control and enhances robustness but often face limitations in response speed, efficiency, and output. The study hypothesizes that combining both approaches—directly driving a flexible continuum body with a motor (direct drive, DD)—can yield simplified, high-energy-density structures that interact favorably with surrounding water to deliver high-performance swimming. The research question is whether a DD fish robot can simultaneously achieve fish-like speed and agility with robust, simple mechanics and whether resonance-informed design can guide its performance.

The paper situates the work among prior biomimetic underwater robots inspired by fish, eels, rays, and jellyfish, which use either rigid transmissions or soft actuators (electroactive polymers, fluidic soft actuators). It highlights the trade-offs: rigid systems’ efficiency and control fidelity versus transmission complexity and fragility; soft systems’ passive, continuous deformation and robustness versus limited bandwidth and energy density. Previous studies indicate efficient swimming emerges near structural resonance modes and that high-frequency operation can yield agile locomotion. Direct drive has proven effective in legged robots but, according to the authors, had not been implemented in biomimetic underwater robots. The paper also references biological metrics such as Strouhal and swimming numbers, which in nature cluster around 0.2–0.4 and 0.6–0.7, respectively, for efficient cruising, and notes prior work on tunable stiffness improving efficiency and thrust in fish-like robots.

Robot design and components: The robot is inspired by Carangiform swimmers, with total length 412.5 mm and mass 1.1 kg. It comprises a head (batteries, receiver, microcontroller, motor driver), a brushless DC motor (U8II Lite 100KV, T-MOTOR), a flexible continuum body, and a CFRP tail fin (aspect ratio 3.5). The motor directly drives the flexible body and tail, eliminating transmissions. The motor has high torque and frequency response (360° at 20 Hz) and minimal waterproofing needs. The motor mass is 242 g (≈21.6% of total, similar to fish muscle mass ≈20%). The body is silicone rubber (Dragon Skin 30) encapsulating a 1-mm CFRP sheet, molded to 10-mm thickness; the tail fin is 1-mm CFRP. The body and fin were designed so that the first two resonance modes fall within a tail-beat range up to ~20 Hz, with predicted natural frequencies: fixed condition f1 ≈ 3.3 Hz, f2 ≈ 21.9 Hz; free swimming f1 ≈ 1.8 Hz, f2 ≈ 11.6 Hz. Control and actuation: The robot uses onboard control (SparkFun DEV-14483 microcontroller) and a BLDC driver (FSESC6.7 or FSESC 7550 in some tests). Commands are sent via a 27 MHz R/C link (Sanwa RP-101 transmitter, RX-101 receiver). The motor is position-controlled with PD control; gains tuned at 10 Hz and then fixed. The body swing angle command was typically ±30° for all experiments except turning. Two drive waveforms were used: square and sine waves. Power is supplied by a 6S LiPo (25.2 V max, 1050 mAh), allowing ~9 minutes at maximum power; onboard logging (SparkFun DEV-13712) records power. Experimental setups: Measurements were conducted in a water tank (1800 × 750 × 600 mm) and a 25-m swimming pool.

• Thrust measurement (tank): Robot tethered to a lever pushing a waterproof load cell (FUTEK LSB210, 445 N). Sampling at 100 Hz; 2 s baseline, then 5 s drive; average over 1.5 s used for thrust. Frequencies 0–25 Hz (1 Hz steps), ±30° command.
• Tail amplitude (tank): Robot fixed; acrylic plate at surface to suppress waves. Overhead high-speed camera (Photron INFINICAM) at 1000 fps tracked tail-tip peak-to-peak amplitude using Photron software. Frequencies 0–25 Hz, ±30°; average of three trials.
• Low-frequency swimming speed (tank): Untethered, with 100-mm styrofoam float for buoyancy/stability. Two synchronized GoPro Hero10 Black at 240 fps outside the tank (lens separation 0.3 m) measured time to traverse their centerlines; speed computed. Tail amplitude during swimming recorded from above with Photron camera. Frequencies 0–5 Hz (1 Hz steps), ±30°; averages over three trials.
• Turning speed (tank): From rest, clockwise pivot turn recorded at 1000 fps (Photron), tracking two markers on the float to compute angle and angular rate. Similar setup to amplitude measurement but untethered; ±90° command; average of three trials.
• High-frequency swimming speed (pool): Robot suspended and balanced via fishing lines on a rod (no float) to reduce drag; conductor ran along pool with rod tip slightly behind robot, so measured speed could decrease but not increase. Two underwater synchronized GoPros at 240 fps with 1.0 m lens separation captured motion; time to traverse camera centerlines measured. Frequencies: 7.5, 10, 12.5, 15, 20 Hz; ±30°; average of three trials. Head and sealing: Head made from UV-curable resin (Formlabs Clear Resin v4) with silicone gasket (Dragon Skin 30) and sealing washers for screws. Derived metrics: Strouhal number St = f A / U and swimming number Sw = U / (f L) computed from measured speed U, frequency f, amplitude A (above 3 Hz, A estimated from fixed-condition amplitude due to surface wave distortions). Cost of transport COT = P / (m g U) computed from onboard power P, mass m, and speed U.

• High-speed swimming: Peak forward speed 2.6 m/s (6.3 BL/s) at 10 Hz with square-wave drive; 2.4 m/s (5.8 BL/s) at 12.5 Hz with sine-wave drive. Peaks occur near the predicted second free-swimming resonance f2 ≈ 11.6 Hz.
• Thrust and specific thrust: In fixed tests, peak thrust 63.2 N at 19 Hz (sine) and 59.2 N at 18 Hz (square). Specific thrust (thrust/input power) exhibited peaks near ~2 Hz and ~19 Hz, aligning with predicted fixed-body modes f1 ≈ 3.3 Hz and f2 ≈ 21.9 Hz.
• Tail amplitude: In water, amplitude reached ~256.7 mm at 2 Hz then decreased with frequency due to hydrodynamic damping; resonance peaks were not prominent in amplitude under water.
• Turning agility: From rest, the robot achieved ~90° turn in ~110 ms with a maximum angular rate of ~1450°/s.
• Bio-inspired performance metrics: Strouhal number (0.2–0.4) and swimming number (0.6–0.7) fell within typical biological ranges around ~1.8 Hz and ~11.6 Hz (model predictions) when using measured U and amplitude data (above 3 Hz, amplitude approximated from fixed measurements).
• Energetics: Power consumption peaked at 12.5 Hz. Minimum COT was 5.9 at 10 Hz for square waves and 6.1 at 12.5 Hz for sine waves, near the predicted second mode (~11.6 Hz). Sine waves tended to yield lower COT (greater efficiency), while square waves favored agility.
• Robustness: High backdrivability and simplified direct-drive architecture allowed the robot to withstand strong impacts (e.g., hammer hits) without mechanical failure.

The results demonstrate that directly driving a flexible continuum body with a high-torque brushless DC motor simplifies the mechanical architecture, enhances robustness, and leverages fluid–structure interaction to realize fish-like, high-performance locomotion. The robot achieved both rapid forward swimming (up to 6.3 BL/s) and agile turning (1450°/s), capabilities that are rarely combined in a single system. The peak speeds and efficiency minima occur near resonant frequencies predicted by a structural model, supporting the hypothesis that resonance-informed design can guide performance optimization for DD swimmers. The Strouhal and swimming numbers fall within natural ranges around the predicted resonant frequencies, indicating bio-like gait and efficiency characteristics. Energetically, sine-wave inputs promote smoother deformations and lower COT, whereas square waves are advantageous for agility. Compared with other robots and real fish data, the DD approach reaches competitive speeds, suggesting a compelling framework for versatile biomimetic underwater robots that integrates the advantages of rigid (energy density, bandwidth) and soft (passive deformation, robustness) paradigms.

This work introduces a direct-drive biomimetic fish robot that directly oscillates a flexible continuum body via a brushless DC motor, eliminating transmissions and achieving high robustness, rapid swimming (6.3 BL/s), and agile turning (1450°/s). Performance peaks align with model-predicted resonances, and Strouhal/swimming numbers match typical biological ranges, validating resonance-informed DD design. The method offers a simple, high-energy-density, and mechanically robust framework for underwater robots. Future directions include: optimizing body and tail stiffness distributions and geometries to improve efficiency; implementing variable stiffness for tunable frequency response; extending to multi-DOF swimming with pectoral fins and buoyancy control; employing CFD with fluid–structure interaction to quantify DD benefits; enhancing motor protection for corrosive environments (e.g., seawater); and exploring high-power operation to approach flying-fish-like speeds and aerial gliding transitions.

• Environmental robustness: The brushless DC motor required minimal waterproofing in tap water but may corrode in seawater; additional protective structures (e.g., compliant oil-filled enclosures) are needed.
• Control tuning: PD gains were tuned at 10 Hz and held constant; gains may not be optimal across frequencies, potentially limiting performance.
• Degrees of freedom: The presented system primarily demonstrates forward locomotion and pivot turns; multi-DOF swimming (e.g., with pectoral fins, buoyancy control) is not implemented.
• Measurement constraints: High-frequency speed measurements used suspension via a rod with the tip slightly behind the robot, allowing speed to decrease but not increase; free-swimming amplitude above 3 Hz was difficult to measure accurately due to surface waves, requiring approximation from fixed tests.
• Hydrodynamic damping: Strong damping in water masked resonance peaks in tail amplitude measurements, complicating direct identification of modal behavior from amplitude alone.