Amphibious bionic robots represent a significant frontier in unmanned systems, designed to operate seamlessly across aquatic and terrestrial domains. Their potential applications span critical areas such as disaster response, environmental monitoring, underwater infrastructure inspection, and resource exploration in coastal and littoral zones. A primary challenge in the development of these versatile machines is the transition from water to land, often requiring navigation over complex and unstructured terrain like rocky shores, steep embankments, or artificial obstacles. This paper addresses this challenge by proposing a novel wheel-fin compound amphibious bionic robot equipped with a self-adaptive obstacle-climbing mechanism. The integration of a bio-inspired undulating fin for efficient underwater propulsion and a uniquely designed terrestrial drive system aims to create a platform with superior mobility in both environments.
The core innovation of this amphibious bionic robot lies in its adaptive wheel mechanism, which enables autonomous climbing over vertical obstacles without requiring complex sensing or control algorithms for the climbing action itself. The mechanical intelligence embedded within the wheel’s planetary gear system allows it to reconfigure its posture upon encountering an obstacle, lifting the main body over the hurdle. The following sections detail the mechanical design, establish a kinematic and dynamic model for the critical climbing phase, optimize the structural and operational parameters to minimize required torque, and validate the design through simulation and physical experimentation.
Mechanical Design of the Adaptive Wheel-Fin Compound Bionic Robot
The proposed amphibious bionic robot synthesizes two efficient locomotion principles. For underwater propulsion, a long undulating fin, inspired by the locomotion of gymnotiform fish like the black ghost knife fish, is mounted along the ventral side of the main body. This fin generates thrust through the propagation of a traveling wave, offering high efficiency, maneuverability, and low acoustic signature. For attitude control in water, two auxiliary thrusters are mounted at the front of the hull.
The terrestrial locomotion system is centered on a pair of self-adaptive obstacle-climbing wheels. The internal structure of each wheel, as shown in the conceptual diagram, consists of two main subsystems:
- A Two-Stage Fixed-Axis Gear Train: This system provides speed reduction and torque amplification from the drive motor.
- A Two-Degree-of-Freedom Planetary Gear System: This is the core of the adaptive mechanism. It comprises a central sun gear (driven by the fixed-axis train), two planetary transmission gears, and the paddle wheel (acting as a planet carrier with an integrated gear). The entire planetary carrier, or “rocking arm,” can rotate freely about the sun gear’s axis.
During normal ground traversal on flat terrain, the paddle wheels rotate, driving the bionic robot forward. The planetary system remains static relative to the main chassis, behaving like a fixed-axle drive. When a paddle wheel contacts a vertical obstacle and its rotation is impeded, the resulting reaction torque causes the entire planetary rocking arm to flip upwards. This motion pushes the main body of the bionic robot forward and upward. As the arm continues to rotate, the paddle wheel engages the top surface of the obstacle, providing traction to pull the robot’s center of mass over the ledge. This process is entirely passive and self-triggered by the interaction with the obstacle.
Kinematic and Dynamic Modeling of the Critical Climbing State
To analyze and optimize the climbing performance of the amphibious bionic robot, a model for the critical instant of obstacle negotiation is developed. This state occurs when the robot’s center of mass is directly above the edge of the obstacle, representing the point of maximum required driving torque.
We define three coordinate systems: the world frame \(\{x_0, O_0, y_0\}\), the robot body frame \(\{x_1, O_1, y_1\}\) attached to the rear chassis, and the rocking arm frame \(\{x_2, O_2, y_2\}\). Let \(m_1\) and \(m_2\) be the masses of the rear chassis and a single rocking arm assembly (including its paddle wheel), respectively. The total mass is \(m = m_1 + 2m_2\). Key geometric parameters are:
- \(l_1\): Distance from the robot’s rear pivot point \(O_1\) to the rocking arm pivot \(O_2\).
- \(R\): Length of the rocking arm (distance from \(O_2\) to the paddle wheel axle).
- \(r\): Radius of the paddle wheel.
- \(L_{c1}\): Distance from \(O_1\) to the center of mass of the rear chassis.
- \(d_2\): Vertical offset of the rocking arm pivot from the bottom of the chassis.
- \(\alpha\): Pitch angle of the robot body.
- \(\beta\): Angle of the rocking arm relative to the robot body.
The transformation from the rocking arm frame to the robot body frame is given by:
$$
^1T_2 = \begin{bmatrix}
\cos\beta & -\sin\beta & 0 & l_1 \\
\sin\beta & \cos\beta & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1
\end{bmatrix}
$$
The position of the robot’s overall center of mass in the world frame, \(^0P = [P_x, P_y, P_z, 1]^T\), is crucial for stability analysis. Its coordinates can be derived through sequential transformations. For the critical climbing state against an obstacle of height \(H\), a geometric relation can be established:
$$
H = (L_x – L_y \tan\alpha)\sin\alpha + d_2\cos\alpha – \frac{d_2}{\cos\alpha}
$$
where \(L_x = \frac{m_1 L_{c1} + 2m_2 l_1}{m}\) and \(L_y = 0\) assuming lateral symmetry.
A static force and moment balance is performed for the critical state. The key forces involved are:
- \(F_{N1}\): Ground reaction force on the rear of the chassis.
- \(F_{N2}\): Vertical reaction force from the obstacle on one paddle wheel (two wheels total).
- \(N_2\): Normal force from the obstacle edge on the chassis.
- \(F_2\): Traction force generated by the rotating paddle wheel on the obstacle surface.
- \(f_{N2} = \mu F_{N2}\): Friction force at the paddle wheel-obstacle contact (\(\mu\) is the coefficient of friction).
The torque provided by the motor at the sun gear shaft of one rocking arm is denoted as \(T\). The torque at the paddle wheel axle is \(T_1\), related to \(T\) by the internal gear ratio \(i_{48}\) (where \(1/i_{48} > 1\) for torque amplification at the wheel).
Summing forces in the vertical and horizontal directions for the entire bionic robot yields:
$$
2F_{N2} + F_{N1} + N_2 \cos\alpha = m g
$$
$$
2(F_2 – \mu F_{N2}) – N_2 \sin\alpha = 0
$$
Taking moments about the rocking arm pivot \(O_2\) for the entire system and for the rocking arm itself, and considering the gear ratio, we can derive the fundamental equation relating the required motor torque \(T\) to the geometric and mass parameters, as well as the pose angles \(\alpha\) and \(\beta\). The combined equation is:
$$
2T(1 + i_{48}) + \left[ \frac{l_1 – (L_x – d_2 \tan\alpha) + R\cos\beta – r\sin\alpha}{l_1 \sin\alpha \sin\beta} \sin(\pi/2 + \alpha – \beta) – L_x + d_2 \tan\alpha \right] N_2 – 2(F_2 – \mu F_{N2})r – m_1g\left[(l_1 – L_{c1})\cos\alpha + R\sin(\pi/2 + \alpha – \beta)\right] – 2m_2g R \sin(\pi/2 + \alpha – \beta) = 0
$$
This equation, along with the force balance equations, allows for the solution of the required torque \(T\) given all other parameters.
Parameter Optimization for Minimum Climbing Torque
The goal of the optimization is to determine the optimal structural parameters \((R, l_1)\) and the operational pose angles \((\alpha, \beta)\) at the critical climbing state that minimize the required motor torque \(T\) for a given obstacle height \(H\). This ensures the amphibious bionic robot can climb the target obstacle with the most efficient use of actuator power, allowing for smaller, lighter motors and longer operation time.
The optimization problem is formally stated as:
$$
\begin{aligned}
& \underset{\alpha, \beta, R, l_1}{\text{minimize}}
& & f(\alpha, \beta, R, l_1) = T \\
& \text{subject to}
& & g_1(\alpha, l_1) = H – \left[(L_x – d_2 \tan\alpha)\sin\alpha + d_2\cos\alpha – \frac{d_2}{\cos\alpha}\right] = 0 \\
&&& \frac{\pi}{12} \leq \alpha \leq \frac{2\pi}{9} \\
&&& \frac{4\pi}{45} \leq \beta \leq \frac{5\pi}{36} \\
&&& 100\ \text{mm} \leq R \leq 200\ \text{mm} \\
&&& 650\ \text{mm} \leq l_1 \leq 850\ \text{mm}
\end{aligned}
$$
The constraint \(g_1 = 0\) ensures the bionic robot’s geometry is compatible with the specified obstacle height \(H = 150\) mm. The bounds on \(\alpha\) and \(\beta\) are set based on practical mechanical limits and stability considerations. Parameter values are set as follows: \(m_1 = 5.0\ \text{kg}\), \(m_2 = 0.8\ \text{kg}\), \(r = 60\ \text{mm}\), \(d_2 = 40\ \text{mm}\), \(\mu = 0.8\), \(L_{c1} = 150\ \text{mm}\), and \(1/i_{48} = 3.8\).
A Genetic Algorithm (GA) was employed to solve this nonlinear constrained optimization problem due to its effectiveness in navigating complex, multi-modal design spaces. The results of the optimization are summarized in the table below, comparing them with a reasonable initial guess.
| Parameter | Initial Guess | Optimized Value | Unit | Change |
|---|---|---|---|---|
| Rocking Arm Angle, \(\beta\) | 20° | 25° | deg | +5° |
| Rocking Arm Length, \(R\) | 105 | 100 | mm | -5 mm |
| Pivot Distance, \(l_1\) | 770 | 678.8 | mm | -91.2 mm |
| Required Sun Gear Torque, \(T\) | 6871.8 | 6153.4 | N·mm | -718.4 N·mm (-10.5%) |
The optimization successfully reduced the required torque by over 10%, primarily by shortening the pivotal distance \(l_1\), which brings the system’s center of mass closer to the obstacle edge during the critical climb, reducing the moment arm. The increase in \(\beta\) also contributed to a more favorable force geometry. This torque reduction directly translates to lower power consumption and less demanding motor specifications for the amphibious bionic robot.
To contextualize the obstacle-climbing capability of our wheel-fin bionic robot, we compare its performance metric (obstacle height \(H\) relative to its own height \(h\)) with other amphibious robots reported in the literature. The ratio \(H/h\) indicates the relative climbing prowess of the machine.
| Robot Type | Robot Height, \(h\) (mm) | Climbed Obstacle Height, \(H\) (mm) | Relative Performance \(H/h\) |
|---|---|---|---|
| Proposed Wheel-Fin Bionic Robot | ~100 | 150 | 1.50 |
| Amphibious Crab Robot | 52 | 20 | 0.38 |
| Amphibious Spherical Robot | 180 | 50 | 0.28 |
| Six-Arc-Legged Amphibious Robot | 228 | 180 | 0.79 |
The proposed bionic robot demonstrates a superior relative climbing ability, capable of surmounting vertical obstacles 1.5 times its own height. This highlights the effectiveness of the self-adaptive wheel mechanism in enhancing the terrestrial mobility of this amphibious platform.
Sensitivity analysis provides further insight. The plot of minimum required torque \(T_{min}\) versus the rocking arm angle \(\beta\) confirms the optimum found by the GA at \(\beta = 25°\). Furthermore, analyzing \(T\) versus the body pitch angle \(\alpha\) for different fixed \(\beta\) values shows that the required torque generally has a concave relationship with \(\alpha\), with a distinct minimum for each \(\beta\). The forces \(F_{N1}\), \(N_2\), and \(F_2\) also vary significantly with both \(\alpha\) and \(\beta\), illustrating the complex interplay of forces during the climb.
Dynamic Simulation of Locomotion and Climbing
A multi-body dynamics simulation was conducted using Adams software to validate the kinematic and dynamic behavior of the optimized amphibious bionic robot design. The simulation scenario involved the robot traversing flat ground, climbing a 150 mm vertical obstacle, and subsequently ascending a 15° slope. The drive motors were modeled with a constant angular velocity input of 500°/s.
The simulation results captured the dynamic response of the bionic robot. The displacement and velocity profiles show characteristic fluctuations during the obstacle-climbing phase (Stages II-IV). These fluctuations correspond to the sequential events of rear wheel lift-off, chassis translation, and front wheel engagement with the obstacle top. A brief period of reduced velocity indicates wheel slip or the overcoming of a potential energy barrier. Stable motion is recovered once on the obstacle and during slope climbing.
| Stage | Event Description | Duration (s) | Rocking Arm Rotation, \(\theta\) | Characteristic |
|---|---|---|---|---|
| I | Flat ground acceleration | 0-2 | 0° to ~30° | Steady increase in velocity. |
| II | Initial contact & rear lift-off | ~2-4 | ~30° to 90° | Velocity dip; rear contact force drops to zero. |
| III | Chassis climb & front engagement | ~4-6 | ~90° to 160° | Front wheel torque peaks; center of mass passes obstacle edge. |
| IV | Traversal of obstacle top | ~6-8 | ~160° to 190° | Stabilization of forces and velocity. |
| V | Slope ascent | >8 | >190° | Constant velocity under gravitational load. |
The torque on the sun gear shaft \(T\) was plotted against the rocking arm rotation angle \(\theta\). The profile shows a sharp initial rise as the wheel contacts the obstacle, followed by a decrease as the arm passes the 90° position (reducing the load moment arm), and a final increase as the arm works to pull the chassis fully onto the obstacle. The peak simulated torque aligns with the order of magnitude predicted by the static model for the critical state, validating the model’s usefulness for motor sizing. The contact forces between the wheels/ball casters and the ground clearly trace the transition of support from the rear to the front of the bionic robot during the climb.
Prototype Development and Experimental Validation
Based on the optimized design, a functional prototype of the amphibious bionic robot was constructed. For the terrestrial drive system, geared DC motors with a rated stall torque of 5 N·m and a continuous torque of 2.8 N·m at 500 rpm were selected, providing sufficient margin over the calculated required torque of approximately 6.2 N·m for the critical climb.
Experiments with the physical prototype successfully demonstrated the self-adaptive climbing capability. The robot reliably climbed a 150 mm vertical obstacle and navigated standard staircases. The sequence of motions—contact, rocking arm flip, chassis lift, and traversal—occurred autonomously as designed, confirming the mechanical intelligence of the system. The bionic robot exhibited stable and repeatable climbing performance.
To verify the aquatic propulsion capability, a separate test platform for the undulating fin was built. Experiments measured the forward swimming speed against the actuation frequency of the fin. The results showed a linear relationship, with a speed of approximately 300 mm/s achieved at a driving frequency of 2 Hz. This confirms that the bionic robot possesses competent underwater mobility to complement its advanced terrestrial climbing skills.
Conclusion
This paper presented the design, optimization, and validation of a novel wheel-fin compound amphibious bionic robot featuring a passive self-adaptive obstacle-climbing mechanism. The key contributions are:
- Integrated Design: The fusion of an undulating fin for efficient underwater propulsion and an adaptive wheel for robust terrestrial mobility, including obstacle climbing, creates a versatile amphibious platform.
- Mechanical Intelligence: The planetary gear-based wheel design enables autonomous reconfiguration and climbing upon obstacle contact, simplifying control requirements for a critical mobility function.
- Model-Based Optimization: A static force and moment model for the critical climbing state was developed and used within a Genetic Algorithm framework to optimize structural parameters (\(l_1, R\)) and operational angles (\(\alpha, \beta\)), minimizing the required motor torque by 10.5%.
- Superior Climbing Performance: The optimized bionic robot achieves a relative climbing performance (\(H/h = 1.5\)) that exceeds that of several other amphibious robot designs, highlighting the effectiveness of the proposed mechanism.
- Experimental Verification: Both dynamic simulation and physical prototype testing confirmed the feasibility and performance of the design. The robot successfully climbed 150 mm obstacles and stairs, while the fin propulsion system provided effective underwater thrust.
The proposed amphibious bionic robot represents a significant step towards creating highly mobile unmanned systems capable of operating in the most challenging transition zones between water and land. Future work will focus on integrating and testing the complete hybrid system in aquatic-terrestrial transition scenarios, refining waterproofing, and implementing higher-level navigation and control algorithms for fully autonomous missions.