In the field of robotics, the development of bionic robots that mimic biological systems has gained significant attention due to their potential for enhanced adaptability and efficiency in complex environments. Among these, amphibious creatures like frogs exhibit remarkable swimming and jumping capabilities, making them ideal models for bionic robot design. This work focuses on the creation of a frog-inspired bionic robot driven by dielectric elastomer (DE) actuators, aiming to achieve miniaturization, flexibility, and high performance underwater. The bionic robot leverages the advantages of soft materials, specifically DE, which offers large strain capabilities, rapid response, and high energy density, closely mimicking natural muscle behavior. Here, I present a comprehensive study on the design, fabrication, testing, and analysis of this bionic robot, emphasizing its swimming mechanics, efficiency, and comparison with biological systems.
The inspiration for this bionic robot stems from the frog’s propulsion mechanism, which involves coordinated leg movements to generate thrust while minimizing drag. Frogs use a kick-and-glide motion, where their legs extend backward to push water and then retract to reduce resistance. This bio-inspired approach is integrated into the bionic robot through soft DE actuators that simulate muscular contractions. DE materials, such as acrylic elastomers, can achieve strains up to 380%, with energy conversion efficiencies reaching 80% and volume energy densities of 3.4 J/cm³, making them superior to other soft actuators like shape memory alloys or ionic gels. The goal of this bionic robot is to replicate frog-like swimming in a compact, lightweight form, enhancing environmental adaptability for applications in underwater exploration, surveillance, and environmental monitoring.
To design the bionic robot, I first analyzed the biomechanics of frog swimming, focusing on leg trajectory and force generation. The bionic robot consists of a main body fabricated from polylactic acid (PLA) via 3D printing, measuring 100 mm in length, 240 mm in width, and 70 mm in height. This compact size facilitates agile movements. The legs are constructed using a combination of DE membranes (VHB4910 from 3M) as artificial muscles, polyethylene terephthalate (PET) films for structural support, and acrylic plates for rigid foot components. The DE actuators serve as the core driving elements, enabling bending motions that mimic frog leg extensions and contractions. The design incorporates four adaptive legs, each with two segments: a proximal segment (first section) and a distal segment (second section) connected by a flexible joint. This configuration allows the bionic robot to adjust its leg area during swimming, increasing thrust during power strokes and reducing drag during recovery strokes.
The fabrication process for this bionic robot involves several precise steps to ensure optimal performance. Initially, acrylic plates (2 mm thick) are cut into small pieces to form the rigid parts of the adaptive feet. These are attached to a main PET frame (0.188 mm thick) using adhesive, with connecting PET strips (0.038 mm thick) providing flexibility. Next, DE membranes are pre-stretched biaxially to 540% × 540% to enhance their actuation range. Carbon grease electrodes are applied on both sides of the DE membranes to facilitate electrical conductivity. The prepared DE membranes are then sandwiched between the main PET frame and reinforcing PET ribs (0.25 mm thick), forming the actuator assembly. Under the elastic force of the pre-stretched membrane, the actuator naturally bends into a curved shape. Each leg is assembled by bonding the actuator to the foot structure, and four such legs are integrated into the PLA body at predefined slots. Electrical connections are made using insulated wires, with water serving as the ground electrode to complete the circuit. This bionic robot design emphasizes simplicity, with a total mass of approximately 50 grams, ensuring buoyancy and maneuverability underwater.
The actuation principle of the bionic robot relies on the Maxwell stress induced in DE materials when a voltage is applied. The DE actuator behaves as a capacitive element, where the Maxwell stress ($\sigma_z$) causes deformation according to the formula:
$$\sigma_z = \epsilon_0 \epsilon_r \left( \frac{U}{d} \right)^2$$
where $\epsilon_0$ is the vacuum permittivity (approximately $8.85 \times 10^{-12}$ F/m), $\epsilon_r$ is the relative permittivity of the DE material (around 4 for VHB4910), $U$ is the applied voltage, and $d$ is the thickness of the DE membrane. When voltage is applied, charges accumulate on the electrodes, generating Maxwell stress that compresses the DE membrane, leading to contraction and bending of the actuator. This mimics the contraction of frog muscles during swimming. In the bionic robot, cyclic voltage signals drive the legs to oscillate, producing a rhythmic motion similar to frog kicks. Finite element simulations using the Yeoh hyperelastic model confirm the deformation behavior, showing that without voltage, the actuator remains bent due to elastic forces, while with voltage, it straightens to reduce the bending angle, enabling propulsion.
To evaluate the performance of this bionic robot, I conducted extensive underwater experiments in a controlled tank environment. The bionic robot was powered by a signal generator connected to a high-voltage amplifier (TREK 10/10B), which converted low-voltage square waves into high-voltage pulses. The input signals varied in voltage (3 kV, 4 kV, 5 kV) and frequency (0.5 Hz to 2.0 Hz), with a fixed duty cycle of 60%. High-speed cameras recorded the swimming motions, allowing for trajectory analysis and parameter extraction. The bionic robot exhibited a clear swimming cycle: during the powered phase (voltage on), the first leg segment swings backward, and the second segment aligns with it due to hydrodynamic forces, maximizing the thrust area; during the recovery phase (voltage off), the legs retract quickly, minimizing drag by aligning with the flow direction. This adaptive mechanism is key to the bionic robot’s efficiency, as it dynamically adjusts leg configuration based on water resistance.
For motion trajectory planning, I established relative coordinate systems at four points on the bionic robot’s legs (labeled B, E, D, F). Using image processing, I extracted position data over time under different frequencies at 5 kV. The trajectories were fitted to mathematical models, revealing sinusoidal patterns that correspond to the leg oscillations. For instance, at 1.0 Hz frequency, the points followed periodic curves with amplitudes up to 0.018 m for lateral movements. The table below summarizes key trajectory parameters for the bionic robot at various frequencies:
| Frequency (Hz) | Voltage (kV) | Max Amplitude, $L_A$ (m) | Average Angular Velocity, $\omega$ (rad/s) |
|---|---|---|---|
| 0.5 | 5 | 0.020 | 0.7418 |
| 1.0 | 5 | 0.018 | 1.4835 |
| 1.5 | 5 | 0.014 | 2.0060 |
| 2.0 | 5 | 0.013 | 2.5000 |
These trajectories demonstrate that the bionic robot’s leg movements are consistent and controllable, enabling precise swimming maneuvers. The bionic robot achieved a maximum swimming speed of 132 mm/s at 5 kV and 2.0 Hz, corresponding to a body-length-specific speed of 1.32 (speed divided by body length of 100 mm). This performance highlights the bionic robot’s agility, surpassing many existing soft robots. For comparison, other DE-driven bionic robots reported speeds of 19 mm/s to 135 mm/s, but with lower body-length ratios. The thrust force was measured using a force sensor (FUTEK LSB200) attached to the bionic robot, with values ranging from 0.05 N to 0.15 N depending on voltage and frequency. The relationship between speed, thrust, and input parameters is encapsulated in the following equations, derived from hydrodynamic principles:
$$v = k_1 \cdot U \cdot f \cdot \sin(2\pi f t)$$
$$F_T = k_2 \cdot \rho_f \cdot A \cdot v^2$$
where $v$ is the swimming speed, $U$ is voltage, $f$ is frequency, $F_T$ is thrust force, $\rho_f$ is water density (1000 kg/m³), $A$ is the effective leg area, and $k_1$, $k_2$ are constants determined empirically for this bionic robot. The data shows that higher voltages increase actuator deformation and speed, while higher frequencies reduce the oscillation amplitude but can enhance speed due to faster cycles.
The bionic robot’s underwater motion characteristics are analyzed using dimensionless numbers to compare with biological systems. The Reynolds number ($Re$), Strouhal number ($St$), and swimming number ($Sw$) are calculated as follows:
$$Re = \frac{v L \rho_f}{\mu}, \quad St = \frac{2 L_A f}{v}, \quad Sw = \frac{2 L_A \omega L \rho_f}{\mu}$$
where $L$ is the body length (0.1 m), $\mu$ is the dynamic viscosity of water (0.11 Pa·s), and other parameters as defined earlier. For the bionic robot at optimal conditions (5 kV, 2.0 Hz), $Re \approx 30,360$, $St \approx 0.3939$, and $Sw \approx 14,950$. These values fall within the ranges observed for real amphibians ($Re: 1.1 \times 10^3$ to $1 \times 10^5$, $Sw: 1.0 \times 10^4$ to $1.2 \times 10^5$), and the Strouhal number is close to that of efficient swimmers like fish (0.25–0.40). This indicates that the bionic robot emulates natural swimming dynamics effectively, with motion characteristics akin to living organisms. The table below compares the bionic robot with other aquatic creatures and robots:
| System | Reynolds Number ($Re$) | Strouhal Number ($St$) | Swimming Number ($Sw$) |
|---|---|---|---|
| Frog (biological) | ~10,000–50,000 | ~0.30–0.40 | ~20,000–100,000 |
| Fish (biological) | ~1,000–100,000 | 0.25–0.40 | ~10,000–50,000 |
| DE Bionic Robot (this work) | 30,360 | 0.3939 | 14,950 |
| Other Soft Robots | ~5,000–20,000 | 0.14–0.77 | ~5,000–15,000 |
This comparison underscores the bionic robot’s bio-inspired design success, as it operates in a regime similar to natural swimmers, enhancing its environmental integration and efficiency.
To optimize the bionic robot’s performance, I developed a propulsion efficiency model that accounts for energy input and output. The input power ($P_i$) is derived from the electrical energy supplied to the DE actuators, treating them as capacitors. The capacitance ($C_a$) of the DE actuator at maximum deformation is given by:
$$C_a = \frac{\epsilon S}{d}$$
where $S$ is the area of the DE membrane under actuation. The input power can be expressed as:
$$P_i = C_a U^2 f K$$
with $K$ as the duty cycle (0.6). The output power ($P_o$) is the mechanical power used for swimming:
$$P_o = v F_T$$
where $v$ is the average speed and $F_T$ is the thrust force. The propulsion efficiency ($\eta$) is then:
$$\eta = \frac{P_o}{P_i}$$
Experimental measurements of $C_a$, $U$, $f$, $v$, and $F_T$ allow efficiency calculation. For instance, at 5 kV and 0.5 Hz, $C_a$ is approximately 2.45 nF (from area and thickness data), yielding $\eta$ up to 25.5%. The efficiency varies with operating conditions, as shown in the table below for the bionic robot:
| Voltage (kV) | Frequency (Hz) | Input Power, $P_i$ (mW) | Output Power, $P_o$ (mW) | Efficiency, $\eta$ (%) |
|---|---|---|---|---|
| 3 | 0.5 | 12.3 | 2.5 | 20.3 |
| 3 | 1.0 | 24.6 | 4.8 | 19.5 |
| 3 | 1.5 | 36.9 | 7.1 | 19.2 |
| 3 | 2.0 | 49.2 | 10.0 | 20.3 |
| 4 | 0.5 | 28.1 | 7.2 | 25.6 |
| 4 | 1.0 | 56.2 | 13.5 | 24.0 |
| 4 | 1.5 | 84.3 | 19.8 | 23.5 |
| 4 | 2.0 | 112.4 | 26.0 | 23.1 |
| 5 | 0.5 | 52.5 | 13.4 | 25.5 |
| 5 | 1.0 | 105.0 | 24.9 | 23.7 |
| 5 | 1.5 | 157.5 | 35.5 | 22.5 |
| 5 | 2.0 | 210.0 | 46.2 | 22.0 |
The efficiency peaks at lower frequencies and higher voltages, as larger leg strokes generate more thrust per cycle. This model guides the optimization of the bionic robot for specific tasks, such as endurance swimming or high-speed bursts. Compared to other DE-driven bionic robots, which report efficiencies around 10-15%, this bionic robot demonstrates superior energy utilization, thanks to its adaptive leg design and precise control.
The bionic robot’s design also incorporates fault tolerance and scalability. The soft materials allow it to withstand impacts and deformations without damage, making it suitable for rough underwater environments. Future iterations of the bionic robot could include sensors for autonomous navigation, such as pressure sensors for depth control or cameras for vision-based guidance. Additionally, the bionic robot can be scaled down for micro-robotics applications or up for larger payloads, demonstrating the versatility of DE-based actuation. The use of bio-inspired control algorithms, mimicking frog neural systems, could further enhance the bionic robot’s adaptability, enabling complex behaviors like obstacle avoidance or cooperative swimming in swarms.
In conclusion, this work presents a comprehensive approach to designing and analyzing a frog-inspired bionic robot using dielectric elastomer actuators. The bionic robot achieves high swimming speeds (up to 132 mm/s) and efficiency (up to 25.5%) through bio-mimetic leg mechanisms and optimized control parameters. Its motion characteristics, quantified by dimensionless numbers, align closely with biological amphibians, validating its bio-inspired design. The propulsion efficiency model provides a framework for performance optimization, highlighting the trade-offs between voltage, frequency, and speed. This bionic robot represents a significant step toward agile, adaptable soft robots for underwater exploration, with potential extensions to other bio-inspired systems. Future work will focus on integrating smart materials for self-sensing, improving energy autonomy with embedded power sources, and exploring amphibious capabilities for land-water transitions. The success of this bionic robot underscores the promise of combining soft robotics with biological principles to create next-generation machines that seamlessly interact with natural environments.