2. Design structure

A streamlined robotic fish design employing laterally undulating pectoral fins for propulsion is presented in Figure 1. Each fin is actuated with a single degree of freedom, enabling the generation of bidirectional thrust to drive the main body in planar motion. Additionally, an expansive module can be integrated into the ventral section of the robot, mechanically coupled to the main body, for the purpose of environmental sensing or water sample collection.

Figure 1.

Schematic diagram of the operating principle.

Figure 2.

Kinematic diagram of a single-fin module.

An efficient propulsion system is essential for robotic fish. This section presents a novel modular propulsion design for the pectoral fins. The robot features two propulsion modules, symmetrically positioned on either side beneath the head, emulating the morphology of natural fish. Figure 2 depicts a propulsion module, consisting of a single motor, five gear transmission pairs, and five fin-ray crank mechanisms. A crank-slider mechanism, coupled with gear pairs, converts the motor’s rotary motion into oscillatory motion of the fin rays. The fin rays are arranged in a fan-shaped configuration, enabling a compact transmission design while allowing manual adjustment of phase angles between fin rays through angular positioning of drive gears on a shared motor-driven shaft. This setup converts rotational motion from a single motor into oscillatory motion of five compact fin rays with adjustable phase offsets.

Figure 3 presents the 3D structural model of the propulsion module, developed using a commercial computer-aided design and analysis tool (Autodesk Inventor). The module is designed as an independent unit, enabling easy and rapid attachment or detachment from the robot’s body. The motor is housed within the robot’s head for waterproofing and is connected to the module’s drive shaft via a magnetic coupling. Additionally, the fin rays can be detached from their base using a hexagonal threaded connector, facilitating robot compaction for transport. The gear reduction ratio is 21:64. The driving gears (smaller gears) can be angularly adjusted around the drive shaft to modify the phase difference between fin rays. These features enable rapid deployment, compaction, and adjustment of kinematic parameters.

Figure 3.

Structure of the propulsion module.

Figure 4.

Structure of the head and tail shell of the robot.

Figure 4. Long description

The image presents a cross-sectional view of a robotic fish, focusing on the head and tail shell. Panel A shows the head shell, which is a complex structure with various internal components. The outer shell is depicted in a solid, reddish-brown color, with internal compartments and support structures visible. Panel B illustrates the tail shell, which is shown in a color-coded displacement map. The tail shell is predominantly blue, indicating minimal displacement, with regions of green, yellow, and red showing increasing levels of displacement. The color scale on the right ranges from blue (0 mm) to red (1.05 mm), indicating the magnitude of displacement. The internal structure of the tail shell includes several ribs and support beams, which are integral to its function and movement.

To ensure waterproofing of the robot’s internal components, such as the motor and electrical systems, the design of the outer shell was meticulously considered. As illustrated in Figure 4, the robot’s structure comprises two primary sections: the front and rear compartments. To evaluate its structural response, finite element analysis (FEA) was conducted using a simulation tool (Autodesk Inventor). This static analysis assesses the deformation behavior of the compartments under external hydrostatic pressure. The front section houses two propulsion module chambers, fully isolated from the internal space containing the electrical circuits, motors, and counterweights. The rear section accommodates the battery, sensors, microcontroller, and external cable connectors for interfacing with optional measurement modules. Static deformation simulations under hydrostatic pressure (equivalent to a 2-meter water column) were performed to identify the weakest points in the designed shell framework. The two halves of the robot body are fastened together using 44 M3 bolts and a 5.10 $^{-4}$ m thick silicone gasket, resulting in the robot’s overall length of 0.45 m.

In addition to the mechanically designed hull, the electrical, control, and sensor systems were proposed. The central control unit interfaces with two motors driving the left and right fin modules, an Inertial Measurement Unit (IMU), a pressure sensor, and an RF LoRa communication module. Furthermore, a design for an optional measurement expansion module was proposed. This module incorporates two water-sampling motors, a total dissolved solids sensor, a turbidity sensor, and a laser-based obstacle detection sensor. The schematic diagram of the proposed system is presented in Figure 5.

Figure 6 illustrates the robotic fish that includes the primary subsystems as follows: two propulsive modules, a balance module, an expansive measurement module, a battery, and a control and electrical system. These parts can be disassembled easily, especially the propulsive modules that can be removed or installed immediately when the robot needs to be deployed. The design parameters, including geometric dimensions, center of buoyancy, and moment components of mass inertia, are also extracted from the design.

To estimate the position of the Center of Buoyancy (CoB) during the initial design phase, the total vehicle hull was rendered as a solid water volume within the computer-aided design (CAD) environment. Additionally, external components, such as the two fin-actuated modules, were assigned material properties equivalent to water to account for displacement. This approach allowed for an accurate determination of the CoB position.

Figure 5.

Schematic diagram of the electrical system on the robot.

Figure 6.

3D design model of the robot with an extended measurement module.

Figure 6. Long description

A diagram of a robotic fish design model with labeled components. Panel A: Assembly model without the shell. The diagram shows the internal structure of the robotic fish, including the CoM adjustment module, propulsive module, BLDC geared motor, pressure sensor, and Arduino mini M0. Panel B: Assembly model with the shell. The diagram shows the external structure of the robotic fish, including the fin rays and extensive measurement module.

3. Dynamic analysis

This part presents a dynamic analysis for a fish robot propelled solely by dual undulating pectoral fins. The primary aim is to establish a computational model that describes the influence of fin oscillatory motion on the swimming speed and propulsive efficiency of the robotic fish, with the motion constrained to a two-dimensional horizontal plane for analytical simplification. To facilitate the development of the mathematical model, several assumptions are adopted: the robot’s buoyancy center is aligned with its mass center in the horizontal plane projection, and its weight is calibrated to achieve neutral buoyancy. Furthermore, the robot’s body is modeled as an ellipsoid, facilitating the calculation of fluid inertia and damping impacts on the structure.

To model the motion of the robotic fish’s pectoral fins and body in a fluid medium, three coordinate systems are defined: the inertial coordinate frame, the body-fixed coordinate frame, and the pectoral fin coordinate frames, denoted as $O_wXYZ$ , $O_B x_B y_B z_B$ , $O_L x_L y_L z_L$ , $O_R x_R y_R z_R$ , $O_{Li} x_{Li} y_{Li} z_{Li}$ , and $O_{Ri}x_{Ri}y_{Ri}z_{Ri}$ , respectively (see Figure 7). The body-fixed coordinate frame is aligned with the robot’s center of buoyancy. The coordinate frames of the right and left pectoral fins are anchored at the revolute joints of the respective fin rays, with subscripts $R$ or $L$ (collectively referred to as $K$ in subsequent equations) indicating the right or left fin and the subscript denoting the fin ray order. A detailed schematic of these notations is provided in Figure 7. Here, $\psi$ represents the body’s heading angle (defined as the angle between the $x_B$ and $X$ axes), and $\gamma _{Ki}$ indicates the oscillation angle of a fin ray. Unit vectors for the inertial and body–referenced coordinate frames are represented as $[\vec {i}_W,\vec {j}_W,\vec {k}_W]$ , and $[\vec {i}_B,\vec {j}_B,\vec {k}_B]$ , respectively. The connection between the unit vectors of the body-fixed and inertial coordinate frameworks is detailed in Appendix (Eqs. (A1, A2, A3)).

Figure 7.

Diagram illustrating fin motion analysis in a two-dimensional plane.

Figure 8.

Diagram of the swing arm mechanism.

Figure 8. Long description

A diagram of the swing arm mechanism. The diagram shows a circular gear mechanism with labeled components. The i-th fin ray extends from point O to the gear, where it connects to a slide pin. The slide pin moves along a circular path defined by the gear’s radius R. The distance d1 represents the length from point O to the center of the gear, labeled C. The distance d2 represents the radius of the circular path along which the slide pin moves. The angle Ki is formed between the fin ray and the line connecting O to C. The angle K’i is formed between the slide pin and the line connecting C to the slide pin. The diagram illustrates the mechanical interaction between the fin ray, slide pin, and gear, demonstrating how the fin ray’s movement is translated into the slide pin’s motion along the circular path.

Second, to generate the oscillatory motion of each fin ray, a gear-driven crank and slider mechanism is employed, as depicted in Figure 8. Let $\zeta _{Ki}$ represent the rotational position of the motor-driven crank connected to the pivot. The symbols $R$ and $D_{oc}$ express the crank radius and the distance from the fin-ray pivots to the big gear-driven crank pivot, respectively. The association between $\zeta _{Li}(t)$ and the oscillation frequency $f_K$ of the fin ray $i^{th}$ on the pectoral fin $K$ is expressed as follows: $\zeta _{Li}(t) = 2\pi f_L(t) t + \phi _{\gamma Li}$ , $\zeta _{Ri}(t) = -2\pi f_R(t) t + \phi _{\gamma Ri}$ , where $f_K(t) = n_K(t)/60$ , $n_K$ is the crankshaft $K$ ’s revolutions per minute, and $\phi _{\gamma Ki}$ represents the phase deviation between consecutive fin rays.

The angle, angular velocity, and angular acceleration of the fin ray $i$ belonging to the pectoral fin are computed as follows, respectively:

(1) \begin{equation} \gamma _{Ki} = \arctan 2\left ( {R\sin \zeta _{Ki}},{D_{oc}+R\cos \zeta _{Ki}}\right )\!, i = \overline {1,5} \end{equation}

(2) \begin{equation} \dot \gamma _{Ki} = \frac {-2\pi Rf_K(t)(D_{oc} \cos \zeta _{Ki}(t)+R)}{\big(D^2_{oc} + 2D_{oc}R \cos \zeta _{Ki}(t)+ R^2\big)} \end{equation}

(3) \begin{equation} \ddot \gamma _{Ki} = \frac {-4\pi ^2 R f_K^2(t) D_{oc} \sin \zeta _{Ki}(t)\big(D_{oc}^2 - R^2\big)}{\big(D^2_{oc} + 2D_{oc} R \cos \zeta _{Ki}(t)+ R^2\big)^2} \end{equation}

Thirdly, the motion of the robotic fish in the inertial frame can be described using the following coordinate transformation:

(4) \begin{equation} \begin{cases}\dot {X} = v_x \cos \psi - v_y \sin \psi , \\[5pt] \dot {Y} = v_x \sin \psi + v_y \cos \psi , \\[5pt] \dot {\psi } = \omega _z. \end{cases}\end{equation}

Here, $v_x$ , $v_y$ , and $\omega _z$ denote the velocities of surge, sway, and yaw motions of the body, respectively; $\psi$ represents the heading position, defined as the angle between the axis of the body-fixed coordinate system $x_B$ and the axis of the inertial frame system $X$ (refer to Figure 9).

Figure 9.

Planar dynamic analysis model of the fish robot with the fan-shaped pectoral fins.

Figure 9. Long description

A diagram of a fish robot with fan-shaped pectoral fins, showing various forces and moments acting on it. The diagram includes a coordinate system with axes labeled X, Y, and Z. The fish robot is depicted with its body axis labeled xB and yB. The pectoral fins are shown on both the left (L) and right (R) sides, with forces FL and FR acting on them in the x and y directions. Moments ML and MR are also shown acting on the fins. The diagram includes labels for various forces and moments, such as fD, τD, α, and Ψ. The fish robot’s center of rotation is marked as OB. The diagram illustrates the interaction between the fish robot’s body and the surrounding water, highlighting the dynamic analysis of the robot’s movement.

Fourthly, to describe the dynamic behavior of the fish robot in the body-fixed frame, Kirchhoff’s equation is utilized [Reference Fossen38]. The robot is assumed to operate with three degrees of freedom in the horizontal plane, namely surge ( $v_x$ ), sway ( $v_y$ ), and yaw ( $\omega _z$ ). The robot’s body is symmetric about the plane $O_Bx_Bz_B$ , allowing the off-diagonal terms of the inertial matrix with respect to the $y_B$ -axis to be set to zero. As the robot operates at low speeds, inertial coupling terms among surge, sway, and yaw motions are neglected. Consequently, the resulting equation is simplified as follows:

(5) \begin{equation} \begin{cases}(m_b+m_x)\dot {v}_x -(m_b+m_y)v_y\omega _z = F_x \\[5pt] (m_b+m_y)\dot {v}_y +(m_b+m_x)v_x\omega _z = F_y \\[5pt] (J_b+J_z)\dot \omega _z -(m_x-m_y)v_yv_y = M_z \end{cases} \end{equation}

Where $m_b$ and $J_b$ represent the robot’s mass and its moment of inertia about the $z$ -axis, respectively. The terms $m_x$ , and $m_y$ denote the added mass components associated with the $x_B$ -axis and $y_B$ -axis, while $J_z$ symbolizes the added inertia of the robot about the $z_B$ -axis. Additionally, $F_x$ and $F_y$ represent the external forces in surge and sway directions, respectively, while $M_z$ denotes the yaw moment acting on the robotic fish body due to the pectoral fins.

The corresponding expressions are derived as follows:

(6) \begin{equation} F_x = F^x_R + F^x_L + f_L\sin \alpha -f_D\cos \alpha , \end{equation}

(7) \begin{equation} F_y = F^y_R - F^y_L - f_L\cos \alpha -f_D\sin \alpha , \end{equation}

(8) \begin{equation} M_z = F^x_R b_1 + F^y_R a_1 - F^x_L b_1 - F^y_L a_1 + M^z_L - M^z_R + \tau _D. \end{equation}

Here, the fluid forces acting on the robot’s mass center, denoted as $f_D$ , $f_L$ , and $\tau _D$ , represent the drag force, lift force, and drag moment, respectively (refer to Figure 9).

(9) \begin{equation} f_D = 0.5C_DS\rho _H V^2, \end{equation}

(10) \begin{equation} f_L = 0.5C_LS\rho _H V^2 \alpha , \end{equation}

(11) \begin{equation} \tau = -C_M \text{sgn}(\dot {\psi }) \dot {\psi }^2 \end{equation}

Here, $C_D$ , $C_L$ , and $C_M$ represent the coefficients for drag, lift, and drag moment, respectively. The terms $S$ and $\rho _H$ indicate the submerged surface area of the robot’s body and the density of the water, respectively. The robot’s linear velocity, $V$ , is determined by the expression $V = \sqrt {v^2_x+v^2_y}$ . The angle of attack $\alpha$ is defined as the angle between the velocity vector $\vec {V}$ and $x_B$ -axis.

Fifthly, to determine the values of $F^x_K$ , $F^y_K$ , and $M^z_K$ , we integrate the forces and moments produced by each fin membrane. This enables the expression of the total components relative to $x_K$ , $y_K$ , and $z_K$ axes for each pectoral fin, as follows:

(12) \begin{equation} F^x_K = \sum _{i=1}^{N-1} \left ( \left ( \vec {n}_{Ki,i+1}\;.\;\vec {i}_B\right ) .\;F_{Ki,i+1}\right )\!, \end{equation}

(13) \begin{equation} F^y_K = \sum _{i=1}^{N-1} \left ( \left ( \vec {n}_{Ki,i+1}\;.\;\;\vec {j}_B\right ) .\;F_{Ki,i+1}\right )\!, \end{equation}

(14) \begin{equation} M^z_K = \sum _{i=1}^{N-1} \big( \big ( \vec {n}_{Ki,i+1}\;.\;\vec {k}_B\big)\;.\;M_{Ki,i+1}\big). \end{equation}

It is significant to observe that $i$ ranges from 1 to $N-1$ , with $N=5$ indicating the total count of fin rays in a pectoral fin. The force and the moment, corresponding, $F_{Ki,i+1}$ , $M_{Ki,i+1}$ , stemming from the engagement of the surrounding fluid with the fin webbing segment enclosed by two successive fin rays, are calculated as outlined below:

(15) \begin{equation} F_{Ki,i+1} = \displaystyle\int _{r^{min}_{Ki,i+1}}^{r^{max}_{Ki,i+1}} dF_{Ki,i+1}(r_{Ki,i+1},t), \end{equation}

(16) \begin{equation} M_{Ki,i+1} = \displaystyle\int _{r^{min}_{Ki,i+1}}^{r^{max}_{Ki,i+1}} r_{r_{i,i+1}}dF_{Ki,i+1} (r_{Ki,i+1},t). \end{equation}

Where,

(17) \begin{equation} {r^{max}_{Ki,i+1}} = \left ( L_0+L\right ) \cos {\frac {\lambda _{Ki,i+1}}{2}}, \end{equation}

(18) \begin{equation} {r^{min}_{Ki,i+1}} = L_0\cos {\frac {\lambda _{Ki,i+1}}{2}}. \end{equation}

A geometric depiction of a fin webbing enclosed by two successive fin rays is illustrated in Figure 10. To assess the external load applied to each unit length of a fin webbing segment, Morison’s hydrodynamic model is employed, with calculations as follows:

(19) \begin{equation} \begin{aligned} dF_{Ki,i+1} ( r_{Ki,i+1},t) &= -C_a \frac {\pi }{4} \rho _H d^2_{Ki,i+1} a_{Ki,i+1} ( r_{Ki,i+1},t) dr_{Ki,i+1} \\ &\quad - \frac {1}{2} C_d d_{Ki,i+1} \rho _H v_{Ki,i+1} ( r_{Ki,i+1},t) \left | v_{Ki,i+1} ( r_{Ki,i+1},t) \right | dr_{Ki,i+1}, \end{aligned} \end{equation}

where,

(20) \begin{equation} {r_{Ki,i+1}} = s_{Ki,i+1}\cos {\frac {\lambda _{Ki,i+1}}{2}}, \end{equation}

(21) \begin{equation} d_{Ki,i+1} =2 r_{Ki,i+1} \tan {\frac {\lambda _{Ki,i+1}}{2}}. \end{equation}

Here, $C_a$ , $C_d$ denote the coefficients representing the inertial and damping effects of fluid flow, respectively. The terms $a_{Ki,i+1}$ and $v_{Ki,i+1}$ indicate the acceleration and velocity of the segment center bounded by the $i^{th}$ and the $\left (i+1\right ) ^{th}$ fin ray (see Figure 10), with their magnitudes determined as follows: $a_{Ki,i+1} = ^W\mspace {-5mu}\ddot {\vec {p}}_{Ki,i+1}^T \vec {n}_{Ki,i+1}$ , $v_{Ki,i+1} = ^W\mspace {-5mu}\dot {\vec {p}}_{Ki,i+1}^T \vec {n}_{Ki,i+1}$ , here, $\vec {p}_{Ki} = P_{Ki}-P_{Ki}^0$ ; $P_{Ki}^0$ , and $P_{Ki}$ represent the coordinates of a point $s_{Ki,i+1} = L_0$ fin ray and a point $L_0 \lt s _{Ki,i+1} \leqslant L_0+L$ on the $i^{th}$ fin ray, respectively, of the pectoral fin $K$ (refer to Figure 10). To obtain the position coordinates of any point on the fin ray with respect to the inertial coordinate system, equations from Eqs. (A4) to (A15) in the Appendix are employed.

Figure 10.

Geometric representation of two fin webbing bounded by three sequential fin rays.

Furthermore, $\vec {n}_{Ki,i+1}$ represents the normal vector of the plane defined by the $i^{th}$ and $\left ( i+1\right ) ^{th}$ fin rays, calculated as $ \vec {n}_{Ki,i+1} = \vec {p}_{Ki} \times \vec {p}_{Ki+1}$ , where the operator “ $ \times$ ” signifies the cross-product of two vectors.

It is observed that the angle formed between two successive fin rays, constrained within the range of 0 to $ \pi /4$ radians, can be determined using the subsequent formula:

(22) \begin{equation} \lambda _{Ki,i+1} = \cos ^{-1} \left ( \frac {\vec {p}_{Ki}\;.\;\vec {p}_{Ki+1}}{\parallel \vec {p}_{Ki}\parallel . \parallel \vec {p}_{Ki+1}\parallel } \right ) \end{equation}

By consolidating Eqs. (20, 21), and (22) into Eq. (19) and merging them with Eqs. (15, 16), a collection of differential equations can be constructed to model the robot’s movement within the inertial reference framework (Eq. (5)). In this structure, the rotational rates of the motor shafts function as the driving variables. To evaluate the mechanical performance of the robot’s movement, the subsequent formula is applied:

(23) \begin{equation} \eta = \frac {\int _{0}^{T} P_{out}\left ( t\right ) dt}{\int _{0}^{T} P_{in}\left ( t\right ) dt} , \end{equation}

Here, $T$ signifies the testing timeframe, whereas $ P_{out}\left ( t\right )$ and $ P_{in}\left ( t\right )$ indicate the produced and supplied power, respectively, resulting from the function of the pectoral fins. These formulations are calculated as outlined below:

(24) \begin{equation} P_{out}\left ( t\right ) = f_D v_x , \end{equation}

(25) \begin{equation} \begin{aligned} P_{in}(t ) &= -( ( F_{xR} + F_{xL} ) v_x + ( F_{yR} + F_{yL} ) v_y ) \\ &\quad-( ( ( F_{xR} + F_{xL}) b_1 + ( F_{yR}+F_{yL} ) a_1 + M_{zR} + M_{zL} ) \omega _z ). \end{aligned} \end{equation}

The useful propulsive power is indirectly calculated based on the drag force generated by the fluid [Reference Suzuki, Kato and Suzumori37]. The mechanical efficiency provides a means to evaluate the robot’s energy utilization behavior and the effectiveness of the suggested fin configuration. To evaluate the quality of forward velocity performance of the robot, we apply the ripper factor in the steady state of robot motion that is defined as follows:

(26) \begin{equation} \gamma = \frac {v_{x,RMS}}{v_{x,a}} 100 \% \end{equation}

Where $v_{x,a}$ is the average value of the forward velocity of the robot in steady state time, determined by:

(27) \begin{equation} v_{x,a} = \frac {1}{T_S} \int _{t_{fm}-T_S}^{t_{fm}} {v_{x}}\left ( t\right ) dt \end{equation}

(28) \begin{equation} v_{x,RMS} = \sqrt {\frac {1}{T_S} \int _{t_{fm}-T_S}^{t_{fm}} ({v_{x}}\left ( t\right ) -v_{x,a}) ^2 dt} \end{equation}

Here, $t_{fm}$ and $T_S$ denote the final measurement time and the selected testing time, respectively.

4. Fabrication and experimental setup

In this section, the results of the fabrication of the modules are presented. Initially, the left and right propulsion modules are introduced. Subsequently, the fabrication of the structural frame is described. The installation and arrangement of motors and sensors are detailed comprehensively. Finally, several configurations for experimental testing and trial runs of the model are outlined. The process of testing with the expanded measurement module is also conducted. To realize the proposed designs, the fabrication of modules and experimental trials were conducted. Initially, the left and right propulsion modules were constructed. To achieve lightweight and rigid structural walls, the partition plates were fabricated using fused deposition modeling (FDM) 3D printing with polyethylene terephthalate glycol (PETG) filament, followed by a vacuum-assisted LRAB21H epoxy resin coating. These fabricated partitions were subsequently secured and aligned using four 8-mm-diameter aluminum rods, which were rigidly connected to the plates via M3 hexagonal socket screws to ensure structural integrity. The rotating shafts supporting the fin rays and the primary drive shaft, with corresponding diameters of 6 mm and 4 mm, were made of 304 stainless steel. Similarly, the five fin ray bases were also fabricated from stainless steel to mitigate oxidation in aqueous environments. Each fin ray base consisted of a 12 mm outer diameter stainless steel tube combined with a 4 mm stainless steel arm through a brazed joint. Additionally, two flanged ball bearings were employed for each fin ray base to ensure coaxial motion and reduce friction. The primary drive shaft, fitted with small gears, was constrained in five degrees of freedom using brass bearings to minimize friction. The spacing between the fin ray bases was achieved using thin stainless steel washers. A detailed illustration of this module is presented in Figure 11. To facilitate the assembly and disassembly of the fin membrane, the fin rays were manufactured as separate components, connected to the fin ray bases using threaded coupling nuts.

Table I.

Validation results of the TDS sensor.

Table I. Long description

A table comparing TDS pen measurements with a robot’s TDS module across six samples. The table has 6 rows and 3 columns. Column headers are No. sample, TDS pen, and The robot’s TDS module (mean ± standard deviation (SD)). Row labels are 1, 2, 3, 4, 5, and 6. Row 1: No. sample 1, TDS pen 111, The robot’s TDS module (mean 127.13 ± standard deviation (SD)) 0.92. Row 2: No. sample 2, TDS pen 162, The robot’s TDS module (mean 166.53 ± standard deviation (SD)) 1.13. Row 3: No. sample 3, TDS pen 206, The robot’s TDS module (mean 204.68 ± standard deviation (SD)) 1.32. Row 4: No. sample 4, TDS pen 428, The robot’s TDS module (mean 404.91 ± standard deviation (SD)) 0.97. Row 5: No. sample 5, TDS pen 621, The robot’s TDS module (mean 566.22 ± standard deviation (SD)) 1.42. Row 6: No. sample 6, TDS pen 744, The robot’s TDS module (mean 649.38 ± standard deviation (SD)) 4.23.

Figure 11.

Illustration of the fabricated propulsive module.

Figure 11. Long description

A diagram of a fabricated propulsive module with labeled components. The diagram includes a driven gear, fin tip base, solid bronze flanged bushings, slide pin on gear, permanent magnet coupling, driving gear, and frame fixing bars. The driven gear is located at the top left, while the fin tip base is positioned centrally. Solid bronze flanged bushings are distributed along the central axis. The slide pin on gear is situated near the driven gear. The permanent magnet coupling is located at the bottom left, adjacent to the active bear. Frame fixing bars are positioned at the bottom right, supporting the structure.

To prevent water ingress into the robot’s body while ensuring the transmission of rotational motion from the motor to the propulsion module, a magnetic coupling design was implemented. Each side of the coupling utilized ten $10 \times 5 \times 3 \text{ mm}^3$ permanent magnets arranged in an alternating polarity fan configuration to enhance coupling strength [Reference Shin, Choi, Jang and Lim39]. The water-sealing partition between the two coupling halves was constructed from 0.2 mm thick stainless steel. For the propulsion system, a BLDC M2006 motor and a C610 RobotMaster controller were employed due to their compact size and high torque output. The robot was equipped with an Arduino M0 mini microcontroller, a Gravity-Analog water pressure sensor, a 10 DOF IMU sensor (Waveshare), and an INA226 voltage, current, and power consumption sensor. Additionally, the robot incorporated a LoRa Lora HAT SX126X 443 MHz wireless communication module. This module was selected for its long-range transmission capabilities and superior data transfer efficiency from aquatic to aerial environments, facilitated by an antenna, compared to high-frequency RF alternatives.

To achieve a neutral buoyancy state, counterweights were added through an iterative, step-by-step process. The horizontal balance (the alignment of the Center of Mass (CoM) and CoB) was then refined by adjusting the positions of these weights. Specifically, the robot was equipped with a dedicated CoM adjustment module featuring small counterweights, allowing for precise and convenient post-assembly tuning (see Figure 6).

Subsequently, additional components were fabricated via FDM 3D printing, with the two halves of the shell constituting the largest PETG-printed parts. To enhance their structural integrity, these shell components were externally laminated with a carbon fiber fabric layer through a vacuum-assisted epoxy bonding process. Meanwhile, to facilitate smooth fin tip motion, the fin membrane was fabricated from approximately 0.1-mm-thick polyvinyl chloride (PVC) sheets. The resulting four distinct fin configurations, corresponding to the four phase-difference scenarios, are illustrated in Figure 12.

Furthermore, to monitor environmental parameters, a DS18B20 temperature sensor is mounted on the underside of the robot’s rear body. The external module comprises an analog turbidity sensor, an analog TDS sensor (DFRobot), a VL53L0X laser rangefinder, and an MPS20N0040D-S pressure sensor. This module is mechanically and electrically integrated with the main robotic fuselage to facilitate both environmental data acquisition and water sampling pump actuation. Notably, the ranging performance of the laser sensor undergoes significant attenuation underwater, demonstrating a high susceptibility to water turbidity. Figure 13 illustrates the complete experimental setup.

During the sensor calibration process for TDS and turbidity, the scaling coefficients for both sensors were configured based on the manufacturer reference source codes. The accuracy of the TDS sensor was subsequently validated against a commercial reference device (Xiaomi TDS pen, model: XMTDS01YM) using six distinct water samples. The validation results, summarized in Table I, demonstrate acceptable agreement with the reference device. Regarding the turbidity sensor, due to the unavailability of an industrial-grade turbidimeter for direct cross-referencing, the system relied solely on the manufacturer’s protocol and a pure water baseline. Consequently, the turbidity and TDS measurements in this study are utilized primarily to evaluate relative environmental trends rather than absolute values.

Figure 12.

Four types of ribbon fins corresponding to the four distinct phases of fin kinematics used in the experiments.

Figure 13.

Experimental illustration of the robotic fish with the expansive measuring device.

To regulate the speed of the motor $K$ to the desired value (where the subscript $K \in \{L, R\}$ represents the left or right side, respectively), a discrete-time PID control law is applied. The control current applied to the motors through the C610 driver at the $j$ -th time step is expressed as follows:

(29) \begin{equation} I_K(\,j)=K_pe_K(\,j)+K_i ei_K(\,j)+K_ded_K(\,j), \end{equation}

where $K_p$ , $K_i$ , and $K_d$ represent the proportional, integral, and derivative gains of the motor controllers, respectively (with the sampling time of 0.01 s implicitly integrated into $K_i$ and $K_d$ ). The terms $e_K$ , $ei_K$ , and $ed_K$ denote the tracking error, the accumulated error, and the error derivative of the motor $K$ , which are defined as follows:

(30) \begin{equation} \begin{cases}e_K(\,j) = n^m_{dK}(\,j) - n^m_{K}(\,j), \\ ei_K(\,j) = ei_K(\,j-1) + e_K(\,j), \\ ed_K(\,j) = e_K(\,j) - e_K(\,j-1), \end{cases} \end{equation}

where $n^m_{dK}(\,j)$ and $n^m_{K}(\,j)$ are the desired and actual speeds of the motor $K$ at time step $j$ , respectively.

To ensure computational efficiency for the PID controller, which is configured with gains of $K_p = 0.55$ , $K_i = 0.12$ , and $K_d = 0.005$ , while maintaining reliable data transmission via the LoRa module (9600 baud), the experimental protocol specified a speed error sampling interval of 0.1 s, with each trial replicated three times. Detailed experimental results are discussed comprehensively in the subsequent section.

Figure 14.

Mean speed error response of the M2006 motors.

An artificial rectangular water tank, INTEX 2282L ( $2.60\text{ m} \times 1.60\text{ m} \times 0.65\text{ m}$ ), was utilized to test the swimming performance of the robot. A high-speed digital camera, Casio Exilim EX-ZR1000, was employed to capture the robot’s movements in pixel coordinates at a speed of 30 frames/second (see Figure 13). Initially, the camera was calibrated using an $8 \times 7$ checkerboard (with a grid size of $0.05\text{ m} \times 0.05\text{ m}$ ) to determine the intrinsic parameters and distortion coefficients. The recorded video was processed to identify the coordinates of red and blue marker points, which were subsequently converted to a millimeter-based coordinate system. The distance between the two identified points on the robot’s body in the millimeter coordinate system was recalculated to verify the accuracy of the transformation from pixel to real-world coordinates, minimizing errors. Finally, the robot’s center point coordinates, velocity, orientation, and turning radius were computed in the millimeter coordinate system. To mitigate random errors and ensure repeatability for each scenario, three independent trials were conducted for straight swimming and six for turning maneuvers (three each for left and right). Similarly, to reduce the effects of disturbances introduced during the image acquisition process, a 5-point moving average filter was applied to the post-processed motion data. This filter had a negligible impact on the analysis of dynamic swimming behaviors, as the resulting time lag of approximately 0.17 s is considered insignificant for offline evaluation.