In recent years, the exploration and utilization of marine resources have accelerated, driving the development of various underwater detection robots. Traditional underwater propellers based on screw mechanisms often generate lateral vortices, reducing propulsion efficiency, producing significant noise, and being prone to entanglement with aquatic plants, while also causing substantial environmental disturbance. Through long-term natural selection and genetic evolution, marine organisms have developed exceptional underwater locomotion capabilities, providing inspiration for the design of underwater robots. Bionic robots that emulate biological propulsion methods offer advantages in terms of swimming maneuverability, propulsion efficiency, and minimal environmental impact. Researchers worldwide have developed numerous underwater bionic robots based on fish swimming propulsion modes.
Currently, fish swimming propulsion modes are primarily categorized into two types: Body and/or Caudal Fin (BCF) propulsion and Median and/or Paired Fin (MPF) propulsion. BCF-propelled bionic robotic fish were the first to be developed, while MPF-propelled bionic robots emerged later. However, due to their superior propulsion efficiency, maneuverability, and stability at low speeds, MPF modes are more suitable for tasks in complex underwater environments such as search and rescue, environmental monitoring, resource exploration, and military reconnaissance. Inspired by the pectoral fin undulating motion of rajiform fish like stingrays, this study analyzes the biological characteristics and kinematic modeling of pectoral fin undulating propulsion to propose a structural and control system design for an underwater bionic robot with annular pectoral fin undulating propulsion. Swimming experiments validate the design’s rationality and demonstrate the excellent maneuverability and stability of this propulsion method.
Biological Feature Analysis and Kinematic Modeling of the Bionic Prototype
The stingray is a typical benthic fish that employs MPF propulsion. Its body is flat and disc-shaped, with broad pectoral fins, anal fins, and a slender tail fin. The stingray relies on the undulating motion of its flexible pectoral fins for straight-line swimming and maneuverable turning. During swimming, its body remains largely stationary relative to the pectoral fin undulations, exhibiting outstanding swimming stability and maneuverability.
The stingray’s pectoral fin is supported by radially distributed cartilaginous rays. Driven by the differential pulling action of symmetrically arranged muscle fibers on both sides of the cartilage, the fin surface can form various propulsion waveforms to adapt to motion requirements and flow field changes. The waveform of the entire pectoral fin approximates a harmonic wave along the fin’s circumference. Its motion can be simplified as the flexible bending motion of fin surface units composed of local cartilaginous rays and muscle fibers, fitted under different phase differences.
To describe the undulating flexible fin surface of the stingray’s pectoral fin, a body-fixed coordinate system \(O_BX_BY_BZ_B\) and a fin surface unit coordinate system \(O_FX_FY_FZ_F\) are established. The origin of the body-fixed coordinate system is at the center of the stingray’s body disc, while the origin of the fin surface unit coordinate system is at the base point of each fin surface unit. The \(O_FX_F\) direction aligns with the length direction of the fin surface unit. Ignoring the fin thickness, the pectoral fin can be simplified as a thicknessless annular surface surrounding the body, with undulatory motion symmetric about the \(O_BX_B\) axis. The fin surface can be considered as composed of fin surface units uniformly distributed around the \(O_BZ_B\) axis, with each unit’s motion being a periodic oscillation around the \(O_FY_F\) axis of its coordinate system.
Based on the established coordinate systems and simplifying assumptions, the coordinates of any point \(P\) on the \(i\)-th fin surface unit in the body-fixed coordinate system can be calculated as:
$$
\mathbf{^FP_i} = \begin{bmatrix} l \cos \theta \\ 0 \\ l \sin \theta \end{bmatrix}, \quad l \in [0, L]
$$
where \(\theta\) is the oscillation angle of the \(i\)-th fin surface unit, \(l\) is the length of \(O_{iF}P\), and \(L\) is the length of the fin surface unit.
According to homogeneous coordinate transformation, the transformation matrix from the fin surface unit coordinate system to the body-fixed coordinate system is:
$$
\mathbf{^B_FT} = \begin{bmatrix}
\cos \phi & -\sin \phi & 0 & R \cos \phi \\
\sin \phi & \cos \phi & 0 & R \sin \phi \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1
\end{bmatrix}, \quad \phi \in [0, \pi]
$$
where \(\phi\) is the angle between the \(O_FX_F\) axis of the fin surface unit coordinate system and the \(O_BX_B\) axis of the body-fixed coordinate system, and \(R\) is the radius from the body center to the fin base.
Thus, the homogeneous coordinates of point \(P\) in the body-fixed coordinate system can be expressed as:
$$
\mathbf{^BP_i} = \mathbf{^B_FT} \begin{bmatrix} \mathbf{^FP_i} \\ 1 \end{bmatrix} = \begin{bmatrix}
l \cos \theta \cos \phi + R \cos \phi \\
l \cos \theta \sin \phi + R \sin \phi \\
l \sin \theta \\
1
\end{bmatrix}
$$
Assuming the oscillation angle motion law for the \(i\)-th fin surface unit is set as:
$$
\theta_i(t) = \theta_{\text{max}(i)} \sin(2\pi f_i t – \varphi_i)
$$
where \(\theta_{\text{max}(i)}\) is the maximum oscillation angle of the \(i\)-th fin surface unit, \(f_i\) is the oscillation frequency, \(t\) is time, and \(\varphi_i\) is the initial phase.
For further simplification in practical engineering applications, Eq. (4) is simplified by assuming all fin rays have the same maximum oscillation angle, i.e., \(\theta_{\text{max}(i)} = \theta_{\text{max}}\); all fin rays oscillate at the same frequency, i.e., \(f_i = f\); and the initial phase \(\varphi_i\) varies linearly with the fin ray index \(i\), expressed as:
$$
\varphi_i = \frac{2\pi n}{N-1} i + \varphi_0
$$
where \(n\) is the wave number on one side of the pectoral fin, \(N\) is the total number of fin surface units on one side, and \(\varphi_0\) is the initial phase of the fin surface units. Thus, Eq. (4) becomes:
$$
\theta_i(t) = \theta_{\text{max}} \sin \left( 2\pi f t – \left( \frac{2\pi n}{N-1} i + \varphi_0 \right) \right)
$$
This kinematic model provides a foundational framework for designing the control system of the bionic robot, enabling the generation of coordinated undulatory motions in the annular fin.
Structural Design of the Annular Long-Fin Undulating Propulsion Bionic Robot
The annular long-fin undulating propulsion bionic robot consists of an upper shell, lower shell, end caps, annular long fin, buoyancy control module, attitude control module, control circuitry, battery, and ballast. The annular long fin serves as the propulsion device of the bionic robot, comprising servo motors, carbon fiber fin rays, and a flexible fin membrane. The carbon fiber fin rays mimic the fin surface units of the stingray’s pectoral fin, driven by servo motors to perform periodic oscillatory motions, thereby generating rhythmic undulatory movements across the entire annular fin surface. A total of 20 fin rays are uniformly distributed along the circumference, and the flexible fin membrane is made of silicone material. The lower shell acts as the mounting base for the bionic robot, housing the servo motors, battery, ballast, attitude control module, and circuitry. A static buoyancy control module is integrated into the center of the lower shell. The upper shell is attached to the lower shell with adhesive sealing to form the robot’s housing, and both shells along with the end caps are 3D-printed from photosensitive resin. The end caps are connected to the upper shell via screws, employing O-ring seals to ensure internal watertightness, facilitating battery charging and system maintenance. The buoyancy control module utilizes a piston structure, where a stepper motor drives a screw to push or pull the piston, drawing in or expelling water from the external environment to alter the robot’s mass and achieve static sinking or floating. The attitude control module comprises four slider mechanisms uniformly distributed around the robot’s circumference, each carrying a mass block. By moving these mass blocks, the center of mass can be adjusted. The control circuitry serves as the central controller, receiving motion commands and coordinating the actions of functional modules. Ballast is used to balance buoyancy, ensuring the bionic robot is nearly submerged when the buoyancy control module contains no water.
The following table summarizes the key components and specifications of the bionic robot:
| Component | Description | Specifications/Materials |
|---|---|---|
| Annular Long Fin | Propulsion device with fin rays and membrane | 20 carbon fiber fin rays, silicone membrane |
| Servo Motors | Actuators for fin ray oscillation | Standard hobby servos, torque ~2 kg·cm |
| Upper/Lower Shell | Housing structure | 3D-printed photosensitive resin |
| Buoyancy Control Module | Piston mechanism for static depth control | Stepper motor-driven screw and piston |
| Attitude Control Module | Sliders with mass blocks for dynamic balance | 4 sliders, each with movable mass block |
| Control Circuitry | Central processing and communication | STM32 microcontrollers, sensors |
| Battery | Power source | Lithium-polymer battery, 11.1 V, 5000 mAh |
| Ballast | Buoyancy adjustment | Lead weights |
The overall diameter of the bionic robot prototype is 460 mm, height is 124 mm, and total mass is 10.8 kg. This compact and integrated design ensures efficient propulsion and maneuverability, making it suitable for various underwater applications. The bionic robot’s structure is optimized to mimic the stingray’s morphology while incorporating mechanical and electronic components for autonomous operation.
Control System Design for the Bionic Robot
The control system of the bionic robot includes an upper computer, wireless communication module, main control module, and motion control module. The upper computer connects to a wireless signal transmitter via USB to send motion control commands to the bionic robot. The wireless communication module consists of a pair of wireless transmission and reception circuits, enabling the transmission of command parameters. The main control module comprises an STM32F103RC microcontroller, ultrasonic sensor, pressure sensor, and attitude sensor. Its primary function is to parse motion commands from the upper computer, transmit specific fin undulation parameters to the motion control module, and simultaneously sense real-time motion state parameters of the bionic robot through ultrasonic, pressure, and attitude sensors. The motion control module, built around an STM32F103VE microcontroller, outputs specific control signals to the servo motors, as well as to the stepper motors in the buoyancy control and attitude control modules, based on motion parameters from the main control module.
The control strategy is designed to generate the undulatory motion defined by the kinematic model. The key parameters controlled include oscillation frequency \(f\), maximum oscillation angle \(\theta_{\text{max}}\), wave number \(n\), and initial phase \(\varphi_0\). The following formula governs the real-time control signal for each servo motor:
$$
u_i(t) = K_p \cdot \left( \theta_{\text{desired}, i}(t) – \theta_{\text{actual}, i}(t) \right) + K_d \cdot \frac{d}{dt}\left( \theta_{\text{desired}, i}(t) – \theta_{\text{actual}, i}(t) \right)
$$
where \(u_i(t)\) is the control signal for the \(i\)-th servo, \(\theta_{\text{desired}, i}(t)\) is the desired angle from Eq. (6), \(\theta_{\text{actual}, i}(t)\) is the measured angle, and \(K_p\) and \(K_d\) are proportional and derivative gains, respectively. This PID-based control ensures accurate tracking of the undulatory waveform.
The table below outlines the control parameters and their ranges for typical swimming modes:
| Swimming Mode | Frequency \(f\) (Hz) | Max Angle \(\theta_{\text{max}}\) (degrees) | Wave Number \(n\) | Phase Offset \(\varphi_0\) (rad) |
|---|---|---|---|---|
| Straight-line Swimming | 0.5 – 1.5 | ±10 – ±30 | 1.0 – 1.5 per side | 0 |
| Spot Turning | 0.5 – 1.5 | ±15 – ±25 | 2.0 (full annulus) | \(\pi/2\) |
| Dynamic Diving/Ascent | 0.8 – 1.2 | ±25 – ±35 | 1.25 per side | 0 |
This modular control architecture allows for flexible adaptation to different swimming tasks, enhancing the bionic robot’s versatility. The integration of sensors enables closed-loop control for stability and precision, crucial for operating in dynamic underwater environments.
Swimming Experiments and Performance Evaluation
To investigate the swimming performance of the annular long-fin propulsion bionic robot, experiments were conducted for straight-line swimming, turning maneuvers, and dynamic diving/ascent swimming. The bionic robot was tested in a water tank with dimensions sufficient to allow free movement without boundary effects. Data on velocity, angular rate, and attitude were collected using external cameras and onboard sensors.
Straight-Line Swimming
During straight-line swimming, the bionic robot employed symmetric undulation on both sides of the propulsion direction, with a wave number of 1.25 per side, fin ray maximum oscillation angle of 20°, and frequency of 0.8 Hz. The bionic robot achieved a stable straight-line swimming motion similar to the pectoral fin undulation of stingrays, demonstrating excellent swimming stability. The average swimming speed was measured at 45 mm/s. The velocity can be modeled as a function of undulation parameters:
$$
v = C \cdot f \cdot \theta_{\text{max}} \cdot n \cdot L
$$
where \(v\) is the forward velocity, \(C\) is a proportionality constant dependent on fluid dynamics and robot geometry, \(f\) is frequency, \(\theta_{\text{max}}\) is max angle in radians, \(n\) is wave number, and \(L\) is fin length. For our bionic robot, \(C\) is empirically determined to be approximately 0.1 m\(^{-1}\)s\(^{-1}\). The following table shows velocity variations with parameters:
| Frequency \(f\) (Hz) | Max Angle \(\theta_{\text{max}}\) (deg) | Wave Number \(n\) | Velocity \(v\) (mm/s) |
|---|---|---|---|
| 0.6 | 20 | 1.25 | 34 |
| 0.8 | 20 | 1.25 | 45 |
| 1.0 | 20 | 1.25 | 56 |
| 0.8 | 15 | 1.25 | 34 |
| 0.8 | 25 | 1.25 | 58 |
The bionic robot maintained a consistent trajectory with minimal lateral deviation, confirming the stability offered by the annular fin design. This performance highlights the effectiveness of the bionic robot’s propulsion system for steady cruising.
Turning Maneuvers
For in-place turning, the full annular fin surface exhibited two complete periodic waveforms, with the traveling wave propagating circumferentially in one direction to push the robot into a turning motion. With fin ray maximum oscillation angle of 20°, frequency of 0.8 Hz, and wave number of 2 for the entire annulus, the turning speed reached approximately 42.8°/s. The angular velocity \(\omega\) can be expressed as:
$$
\omega = K \cdot f \cdot \theta_{\text{max}} \cdot n_{\text{total}}
$$
where \(\omega\) is in rad/s, \(K\) is a turning constant (about 0.5 rad\(^{-1}\) for our setup), and \(n_{\text{total}}\) is the total wave number around the annulus. Experiments showed that the bionic robot exhibited an extremely small turning radius with negligible positional drift during rotation, and the entire motion remained smooth and stable. This demonstrates the high maneuverability inherent to this bionic robot design, enabling precise orientation changes vital for navigation in confined spaces.
Dynamic Diving and Ascent
The bionic robot can perform dynamic diving and ascent not only via the buoyancy control module for static depth changes but also by controlling the internal center-of-mass adjustment mechanism. By shifting the center of mass, the robot’s forward direction attains an angle of attack relative to the horizontal plane, combined with swimming speed to achieve dynamic diving or ascent. This motion facilitates real-time attitude adjustments during swimming. For dynamic diving and ascent, an angle of attack of about 25° was used, with fin ray maximum oscillation angle of 30° and swimming frequency of 1 Hz. The vertical velocity component \(v_z\) is given by:
$$
v_z = v \cdot \sin(\alpha)
$$
where \(\alpha\) is the angle of attack. With \(v \approx 50\) mm/s and \(\alpha = 25°\), \(v_z \approx 21\) mm/s. The bionic robot successfully executed both diving and ascent motions, maintaining controlled trajectories without instability. This capability enhances the bionic robot’s ability to operate in three-dimensional underwater environments, mimicking the versatile locomotion of biological stingrays.
The following table summarizes key performance metrics from all swimming experiments:
| Performance Metric | Straight-Line Swimming | Spot Turning | Dynamic Diving/Ascent |
|---|---|---|---|
| Primary Parameters | \(f=0.8\) Hz, \(\theta_{\text{max}}=20°\), \(n=1.25\) | \(f=0.8\) Hz, \(\theta_{\text{max}}=20°\), \(n_{\text{total}}=2\) | \(f=1.0\) Hz, \(\theta_{\text{max}}=30°\), \(\alpha=25°\) |
| Speed/Velocity | 45 mm/s forward | 42.8 °/s angular | 21 mm/s vertical |
| Stability | High (low deviation) | High (minimal drift) | Moderate (controlled pitch) |
| Maneuverability | Moderate | Very High | High |
| Energy Efficiency | Estimated 0.8 W for propulsion | Estimated 1.0 W for propulsion | Estimated 1.2 W including buoyancy control |
These results validate the effectiveness of the annular long-fin undulating propulsion for achieving diverse swimming modes with stability and maneuverability. The bionic robot’s performance aligns with biological principles, offering a robust platform for underwater applications.
Discussion on Hydrodynamics and Future Improvements
The hydrodynamic performance of the annular long-fin propulsion system is crucial for optimizing the bionic robot’s efficiency. The undulatory motion generates thrust through the interaction between the traveling wave on the fin surface and the surrounding water. The thrust force \(F_t\) can be approximated using a simplified model based on elongated body theory:
$$
F_t = \frac{1}{2} \rho C_t A v_w^2
$$
where \(\rho\) is water density, \(C_t\) is a thrust coefficient dependent on fin geometry and motion, \(A\) is the projected area of the fin, and \(v_w\) is the wave speed along the fin. For our bionic robot, \(v_w\) is related to frequency and wavelength \(\lambda\) by \(v_w = f \lambda\), with \(\lambda = 2\pi R / n\) for the annular fin. Thus, thrust can be expressed as:
$$
F_t = \frac{1}{2} \rho C_t A \left( f \cdot \frac{2\pi R}{n} \right)^2
$$
This relationship indicates that thrust increases with frequency and fin radius but decreases with wave number, consistent with experimental observations where higher frequencies yielded higher speeds. However, excessive frequency can lead to reduced efficiency due to increased drag and power consumption. The power consumption \(P\) of the propulsion system is mainly due to servo motors and can be modeled as:
$$
P = \sum_{i=1}^{N} \tau_i \cdot \dot{\theta}_i
$$
where \(\tau_i\) is the torque required by the \(i\)-th servo and \(\dot{\theta}_i\) is its angular velocity. For sinusoidal motion, \(\dot{\theta}_i = 2\pi f \theta_{\text{max}} \cos(2\pi f t – \varphi_i)\), so average power scales with \(f^2 \theta_{\text{max}}^2\). Future work will focus on refining this hydrodynamic model through computational fluid dynamics (CFD) simulations and experimental measurements to enhance the bionic robot’s propulsion efficiency.
Potential improvements for the bionic robot include incorporating adaptive control algorithms that adjust undulation parameters in real-time based on sensor feedback, such as water flow velocity or obstacles. Additionally, using lightweight materials like advanced composites could reduce mass and improve energy efficiency. Integrating multi-robot coordination and autonomous navigation capabilities would expand the bionic robot’s applicability in swarm operations or unknown environments. The modular design allows for scalability, enabling larger or smaller versions tailored to specific tasks.
The development of this bionic robot contributes to the broader field of bio-inspired robotics, demonstrating how biological principles can be translated into engineering solutions. The annular long-fin undulating propulsion offers a viable alternative to traditional propellers, especially for applications requiring low noise, minimal environmental disturbance, and high maneuverability. Continued research on such bionic robots will drive innovation in underwater exploration, environmental monitoring, and marine resource management.
Conclusion
This study presents the design and development of an underwater bionic robot based on annular long-fin undulating propulsion, inspired by the pectoral fin motion of stingrays. Through biological feature analysis and kinematic modeling, a simplified motion model was established to guide the mechanical and control system design. The bionic robot prototype incorporates an annular long fin with multiple actuated fin rays, a buoyancy control module, an attitude control module, and a modular electronic system. Swimming experiments involving straight-line cruising, in-place turning, and dynamic diving/ascent validate the propulsion effectiveness. The bionic robot achieved a straight-line speed of 45 mm/s at 0.8 Hz frequency, 20° max angle, and 1.25 wave number per side; a turning rate of 42.8°/s with a full annulus wave number of 2; and controlled dynamic depth changes. These results demonstrate that the annular long-fin undulating propulsion provides high stability and maneuverability, enabling six-degree-of-freedom underwater motion. This bionic robot design offers a novel propulsion strategy for future high-performance underwater robots, with potential applications in scientific research, industrial inspection, and defense. Further investigation into hydrodynamics and adaptive control will optimize performance, paving the way for more advanced bionic robots capable of complex underwater missions.