The realm of bionic robotics draws profound inspiration from nature’s masterpieces. By studying the unique locomotion strategies of biological organisms, researchers aim to engineer robotic systems with unprecedented adaptability across diverse environments—land, air, and water. This pursuit drives significant progress in robotics. My work is inspired by a remarkable creature: the basilisk lizard, renowned for its ability to sprint across water surfaces at high speeds. This thesis documents my investigation into the lizard’s water-running mechanics and the subsequent design, analysis, and experimental validation of a novel bionic bipedal robot capable of dynamic locomotion on water, offering a new paradigm for environmental adaptation.
Unlike small insects like water striders that rely on surface tension, the basilisk lizard, weighing up to 200 grams, utilizes a dynamic slapping and stroking action with its feet. This high-frequency movement (5-10 Hz) generates transient air cavities beneath its feet, providing the necessary vertical support and horizontal thrust. The core challenge in building a bionic robot lies in replicating this high-dynamic motion with a lightweight, efficient, and stable mechanical system.
Decoding the Basilisk’s Gait: Mechanism and Kinematics
The lizard’s water-running stride can be dissected into three distinct phases: slap, stroke, and recovery. A detailed analysis of these phases provides the foundational principles for the bionic robot’s design.
In the slap phase, the foot impacts the water almost vertically at high speed, creating an initial air cavity and generating a large impulsive vertical force. The maximum impulse $I_{slap}$ during this phase can be modeled as:
$$I_{slap} = k_A \rho A_e v_{slap}^{2/3}$$
where $k_A$ is a shape-dependent coefficient, $\rho$ is water density, $A_e$ is the effective foot area, and $v_{slap}$ is the foot’s impact velocity.
The subsequent stroke phase involves the leg sweeping backward. The foot, now more horizontal, expands the air cavity and primarily generates forward thrust. The force $F_{stroke}$ during this phase combines inertial and drag components:
$$F_{stroke} = \frac{1}{2} C_d \rho S v_{stroke}^2 + \rho g h S$$
Here, $C_d$ is a drag coefficient, $S$ is the wetted area, $v_{stroke}$ is the foot’s velocity, $g$ is gravity, and $h$ is the submersion depth.
Finally, the recovery phase involves lifting the foot out of the water before the air cavity collapses and resetting its position for the next stride. This phase contributes minimal propulsive force.
To guide the bionic robot’s mechanism design, I analyzed the planar motion of the lizard’s leg. The trajectory of the ankle joint is particularly critical. By fitting empirical data from biological studies, the ankle’s periodic motion in the sagittal plane can be described by Fourier series:
$$x(t) = a_{x0} + a_{x1}\cos(\omega_x t) + b_{x1}\sin(\omega_x t)$$
$$y(t) = a_{y0} + a_{y1}\cos(\omega_y t) + b_{y1}\sin(\omega_y t) + a_{y2}\cos(2\omega_y t) + b_{y2}\sin(2\omega_y t)$$
The fitted parameters are summarized below:
| Parameter | Value | Parameter | Value |
|---|---|---|---|
| $a_{x0}$ | -4.256 | $a_{y0}$ | -2.927 |
| $a_{x1}$ | -3.586 | $a_{y1}$ | 0.750 |
| $b_{x1}$ | 1.438 | $b_{y1}$ | -3.236 |
| $\omega_x$ | 0.987 | $a_{y2}$ | 0.136 |
| – | – | $b_{y2}$ | 0.445 |
| – | – | $\omega_y$ | 0.985 |
Simultaneously, the orientation of the footpad changes significantly during slap and stroke, which is essential for effective force generation.
Mechanism Synthesis for Bipedal Water-Walking
The primary design goal was to create a single-DOF (Degree of Freedom) mechanism that could accurately replicate the ankle trajectory and foot orientation of the basilisk lizard while being lightweight and suitable for high-speed operation. A novel six-bar linkage, evolved from a swinging guide-bar mechanism, was conceived.
The mechanism consists of a driving crank, a swinging guide tube, a rocker arm, a rear support link, and the foot link. Its unique geometry converts the crank’s rotation into a compound motion of the foot: a fast vertical slap, a posterior stroke, and a recovery arc. The two leg mechanisms are driven 180° out of phase by the same motor via a gear train, ensuring continuous alternating support. The kinematics of this bionic robot mechanism are governed by the following vector relations, where $l_i$ represent link lengths and $\theta$ is the crank angle:
Position of the ankle joint (Point A):
$$
\begin{bmatrix} x_A \\ y_A \end{bmatrix} = \begin{bmatrix} l_0 \cos\gamma_1 + l_p \cos\varphi \\ l_0 \sin\gamma_1 + l_p \sin\varphi \end{bmatrix}
$$
where $l_p = \sqrt{l_0^2 + l_1^2 – 2 l_0 l_1 \cos(\theta – \gamma_1)}$ and $\varphi = \arctan\left(\frac{l_0 \sin\gamma_1 – l_1 \sin\theta}{l_0 \cos\gamma_1 – l_1 \cos\theta}\right)$.
The foot orientation angle $\beta$ is constrained by a secondary four-bar loop (B-G-F-A), ensuring a specific pitch profile during the stride.
Using the biological trajectory as a target, I performed a dimensional optimization to minimize the error between the desired and generated ankle paths and foot angles. The optimal geometric parameters for the bionic robot are listed below:
| Link | Parameter | Optimized Value |
|---|---|---|
| Fixed Link | $l_0$ | 58.21 mm |
| Crank | $l_1$ | 35.84 mm |
| Guide Tube | $l_2$ | 62.32 mm |
| Rocker Arm | $l_3$ | 31.58 mm |
| Support Link | $l_4$ | 88.16 mm |
| Foot Rear | $l_5$ | 42.47 mm |
| Footpad | $l_6$ | 50.00 mm |
| Angle | $\gamma_2$ | 20.75° |
Dynamics and Fluid-Structure Interaction Analysis
The dynamic performance of the bionic robot is crucial for stable water-running. Using Lagrangian dynamics, the required drive torque $M$ for a given gait frequency $f$ can be derived. The equation of motion is:
$$M – T_f = \frac{d}{dt}\left(\frac{\partial E_k}{\partial \dot{\theta}}\right) – \frac{\partial E_k}{\partial \theta}$$
where $E_k = \sum \frac{1}{2} m_i \mathbf{v}_i^2 + \sum \frac{1}{2} I_i \omega_i^2$ is the system’s kinetic energy, and $T_f$ is the torque due to hydrodynamic force $F_w$ on the foot. Analysis indicated that to support a robot mass of ~180g, a stepping frequency of at least 5.8 Hz is theoretically required, with the drive torque increasing proportionally to the square of the frequency.
To validate the foot-water interaction, I conducted a two-phase (water-air) fluid dynamics simulation using the COMSOL Multiphysics® software with a level-set method. A simplified 2D model of the foot underwent the prescribed slapping and stroking motion. The simulation vividly captured the formation, expansion, and collapse of the air cavity, confirming the core principle exploited by the bionic robot. The resulting vertical force on a single foot peaked at approximately 8.7 N during the slap, closely matching theoretical predictions and demonstrating the feasibility of generating sufficient lift.
Prototype Development and System Integration
Translating the design into a functional bionic robot required careful selection of components and materials to achieve a high strength-to-weight ratio.
Mechanical System: The chassis and links were fabricated from 1.5mm carbon fiber sheets and rods, offering exceptional stiffness and lightness. Custom joints and connectors were 3D-printed using a strong, lightweight resin. A high-RPM brushless DC motor (T-Motor AT2308) coupled with a custom two-stage 10:1 reduction gearbox provides the necessary torque and speed to drive both leg mechanisms.
Control System: For dynamic stability, an active balance control system was implemented. An Arduino Nano serves as the central processor. It reads the robot’s roll angle and angular velocity from a JY-901 attitude sensor. Simultaneously, a PQY13 magnetic encoder monitors the crank shaft position to determine the phase of each leg’s gait. A PID controller adjusts the motor’s PWM signal in real-time based on the tilt error $e(t)$:
$$u(t) = K_p e(t) + K_i \int e(t) dt + K_d \frac{de(t)}{dt}$$
This allows the system to momentarily vary the driving speed of the legs to apply corrective lateral forces, forming a closed-loop balance control system. The final prototype weighs 156 grams.
Experimental Validation and Results
I conducted a series of experiments to validate the bionic robot’s water-walking capabilities.
1. Cavity Formation Visualization: High-speed video confirmed that at a stepping frequency of 6.8 Hz, a clear air cavity forms and persists during the slap and stroke phases, replicating the lizard’s key mechanism. At lower frequencies (3.7 Hz), the cavity was less stable and collapsed prematurely.
2. Three-Axis Force Measurement: Using a force sensor, I measured the interaction forces between the robot and the water. At 6.8 Hz, the peak vertical force reached 3.84 N (2.4 times the robot’s weight), and the peak forward thrust was 1.99 N. The force profiles confirmed the theoretical models, with vertical support present for over 95% of the stride cycle.
| Motion Frequency | Peak Vertical Force | Peak Forward Thrust | Avg. Forward Speed |
|---|---|---|---|
| 3.7 Hz | 2.32 N | ~0.6 N | Low |
| 6.8 Hz | 3.84 N | 1.99 N | 0.3 – 0.8 m/s |
3. Displacement Measurement: With the robot mounted on low-friction vertical and horizontal slides, magnetic scales recorded its motion. The data showed a periodic hopping motion (2.7 mm ascent per step) and sustained forward propulsion, empirically proving its ability to generate lift and thrust.
4. Balance Control Test: The PID control system was successfully tested. The motor drive signal responded promptly (< 0.05s) to induced roll angles, modulating the thrust of each leg appropriately to enact a corrective rolling moment, confirming the control loop’s effectiveness.
Conclusion and Outlook
This research successfully demonstrates the feasibility of a bionic bipedal robot based on the basilisk lizard’s water-running principle. Through mechanistic analysis, innovative linkage design, dynamic simulation, and systematic prototyping, I developed a functional robot that can generate lift and thrust via dynamic foot-water interaction. Experiments validated the formation of supporting air cavities and the robot’s ability to propel itself on the water surface under partial constraints. The implemented balance control system lays the groundwork for fully autonomous, stable locomotion.
Future work will focus on achieving untethered, free-running water-walking by further optimizing the power-to-weight ratio, refining footpad geometry for enhanced lateral stability, and implementing more advanced adaptive control algorithms. This bionic robot platform opens new avenues for exploration in amphibious robotics, with potential applications in environmental monitoring, search and rescue, and reconnaissance in complex wetland terrains.