In the realm of robotics, the demand for versatile mobile platforms capable of operating in extreme, unstructured environments has never been greater. We, as researchers in the field, recognize the limitations of conventional mobile robots—wheeled, tracked, and legged—when faced with complex terrains such as disaster zones, archaeological sites, or extraterrestrial landscapes. Wheeled robots offer speed and efficiency on flat surfaces but falter on rough ground; tracked robots provide better traction on soft or uneven terrain but are bulky, slow, and noisy; legged bionic robots, inspired by biological organisms like insects, excel in obstacle negotiation and adaptability due to their discrete foothold selection, yet they can be complex to control and slower in open areas. To bridge these gaps, we propose an innovative hybrid solution: a wheel-legged bionic robot that seamlessly transitions between six-legged walking and four-wheeled rolling modes. This design aims to combine the agility and terrain adaptability of a multi-legged bionic robot with the speed and efficiency of a wheeled system, making it ideal for applications in search-and-rescue, exploration, and military operations where environmental conditions are unpredictable and challenging.
Our journey begins with a thorough review of existing mobile robot architectures. Wheeled robots, such as those used in planetary rovers, rely on continuous ground contact and are optimal for surfaces with low roughness relative to wheel size. Their kinematics are straightforward, often modeled using simple equations of motion. For instance, the velocity of a wheeled robot can be expressed as $$v = r \cdot \omega$$, where \(r\) is the wheel radius and \(\omega\) is the angular velocity. However, on rugged terrain, these systems struggle with stability and obstacle clearance. Tracked robots, like those employed in bomb disposal, distribute weight over a larger area, reducing ground pressure, but their turning radius is large, and they can damage delicate surfaces. In contrast, legged bionic robots, particularly hexapods, mimic the locomotion of insects, offering superior stability through static walking gaits and the ability to traverse discontinuous paths. The redundancy in legs—often six or eight—provides fault tolerance; if one leg is damaged, the bionic robot can adjust its gait to continue moving. Yet, this comes at the cost of increased mechanical complexity and control challenges. Our design seeks to harness the strengths of both paradigms, creating a bionic robot that adapts on-the-fly to terrain changes.
The core innovation of our wheel-legged bionic robot lies in its mechanical architecture. We drew inspiration from insect morphology, specifically the walking legs of hexapods like beetles or cockroaches, which consist of multiple segments: coxa, trochanter, femur, tibia, and tarsus. In our bionic robot, we simplified this to three main segments per leg—coxa, femur, and tibia—connected by revolute joints to reduce complexity while preserving functionality. Each leg features three degrees of freedom (DOF): a yaw joint at the coxa (connecting to the torso), a pitch joint at the hip (between coxa and femur), and a pitch joint at the knee (between femur and tibia). The torso is hexagonal, allowing symmetric leg placement and enabling omnidirectional movement, including zero-radius turns. This configuration provides the bionic robot with six legs, each with 3 DOF, resulting in 18 actuated joints. Using the Kutzbach-Grübler formula for spatial mechanisms, we calculate the total DOF of the bionic robot as: $$F = 6(n – g – 1) + \sum_{i=1}^{g} f_i$$ where \(n\) is the number of links, \(g\) is the number of joints, and \(f_i\) is the DOF of the \(i\)-th joint. For our bionic robot, with 20 links and 24 joints (18 revolute joints and 6 spherical joints at the feet), the DOF is: $$F = 6(20 – 24 – 1) + (18 \cdot 1 + 6 \cdot 3) = 6$$ This indicates a six-DOF parallel mechanism with redundancy, which enhances dexterity and avoids singularities.
To enable wheeled locomotion, we integrated four omnidirectional wheels into the tibia segments of selected legs. Specifically, we chose four legs arranged diagonally on the hexagonal torso. By rotating the knee joints inward by 90 degrees, the omnidirectional wheels contact the ground, lifting the other two legs clear. This transforms the bionic robot from a six-legged walker into a four-wheeled roller. The omnidirectional wheels, driven by DC gear motors, allow holonomic movement—forward, backward, sideways, and rotation—providing high mobility on flat surfaces. A caster wheel at the chassis center offers additional support to distribute weight. The transition between modes is swift, taking approximately 3 seconds in our prototypes, making the bionic robot highly adaptable. Table 1 summarizes the key mechanical parameters of our bionic robot’s leg design, which were optimized through iterative simulation and testing.
| Segment | Length (mm) | Joint Type | Range of Motion (degrees) |
|---|---|---|---|
| Coxa (L1) | 50 | Yaw | -30 to 30 |
| Femur (L2) | 50 | Pitch | -45 to 60 |
| Tibia (L3) | 70 | Pitch | 45 to 90 |
The control system of our bionic robot is a hierarchical architecture split into upper and lower levels. The upper-level controller, typically a PC or embedded computer, handles high-level tasks such as gait planning, obstacle avoidance, and mode switching. It receives sensor data from the lower level, processes it using algorithms like inertial measurement unit (IMU) fusion for attitude estimation, and sends joint angle commands. The lower-level controller, based on an Arduino microcontroller, interfaces directly with actuators and sensors. It drives the 18 servo motors for leg joints in walking mode and the 4 DC motors for wheels in rolling mode, implementing closed-loop control for precise positioning. An IMU sensor, comprising three-axis accelerometers and gyroscopes, provides real-time orientation data, enabling the bionic robot to maintain balance and adjust its posture. The control logic for walking gaits, such as the tripod gait, is implemented in the upper level. In this gait, legs are grouped into two triads (e.g., legs 1, 3, 5 and 2, 4, 6) that alternate between swing and stance phases, ensuring that the center of mass remains within the support polygon for stability. The velocity profile for each joint can be modeled using sinusoidal functions: $$\theta(t) = \theta_0 + A \sin(2\pi f t + \phi)$$ where \(\theta_0\) is the initial angle, \(A\) is the amplitude, \(f\) is the frequency, and \(\phi\) is the phase shift. This allows smooth, energy-efficient motion for the bionic robot.
To evaluate the bionic robot’s capabilities, we conducted a detailed workspace analysis for a single leg. Using the Denavit-Hartenberg (D-H) convention, we established coordinate frames at each joint. The D-H parameters are listed in Table 2, which serve as the basis for forward kinematics calculations. These parameters define the transformations between successive links, crucial for determining the foot-tip position relative to the torso.
| Link | θ_i (degrees) | d_i (mm) | a_{i-1} (mm) | α_{i-1} (degrees) |
|---|---|---|---|---|
| 0-1 | θ1 | 0 | L1 = 50 | 90 |
| 1-2 | θ2 | 0 | L2 = 50 | 0 |
| 2-3 | θ3 | 0 | L3 = 70 | 0 |
The transformation matrix between link \(i-1\) and link \(i\) is given by: $$^{i-1}T_i = \begin{bmatrix} \cos\theta_i & -\sin\theta_i \cos\alpha_{i-1} & \sin\theta_i \sin\alpha_{i-1} & a_{i-1}\cos\theta_i \\ \sin\theta_i & \cos\theta_i \cos\alpha_{i-1} & -\cos\theta_i \sin\alpha_{i-1} & a_{i-1}\sin\theta_i \\ 0 & \sin\alpha_{i-1} & \cos\alpha_{i-1} & d_i \\ 0 & 0 & 0 & 1 \end{bmatrix}$$ By multiplying these matrices, we derive the forward kinematics for the leg: $$^0T_3 = ^0T_1 \cdot ^1T_2 \cdot ^2T_3 = \begin{bmatrix} n_x & o_x & a_x & p_x \\ n_y & o_y & a_y & p_y \\ n_z & o_z & a_z & p_z \\ 0 & 0 & 0 & 1 \end{bmatrix}$$ where the position vector \((p_x, p_y, p_z)\) of the foot-tip is: $$p_x = L_3(\cos\theta_1 \cos\theta_2 \cos\theta_3 – \cos\theta_1 \sin\theta_2 \sin\theta_3) + L_2 \cos\theta_1 \cos\theta_2 + L_1 \cos\theta_1$$ $$p_y = L_3(\sin\theta_1 \cos\theta_2 \cos\theta_3 – \sin\theta_1 \sin\theta_2 \sin\theta_3) + L_2 \sin\theta_1 \cos\theta_2 + L_1 \sin\theta_1$$ $$p_z = L_3(\sin\theta_2 \cos\theta_3 + \cos\theta_2 \sin\theta_3) + L_2 \sin\theta_2$$ Using these equations, we computed the workspace by varying θ1, θ2, and θ3 within their ranges. The results, plotted via MATLAB, show that the bionic robot’s leg can achieve a maximum stride length of approximately 150 mm in the Y-direction, a lateral span of 140 mm in the X-direction, and a lifting height of 110 mm in the Z-direction. This workspace analysis confirms that the bionic robot can step over obstacles up to 62 mm high, as validated in experiments.
In addition to kinematics, we considered dynamics to optimize the bionic robot’s performance. The Lagrangian formulation can be applied to derive equations of motion for each leg: $$L = K – U$$ where \(K\) is the kinetic energy and \(U\) is the potential energy. For a link with mass \(m_i\) and inertia tensor \(I_i\), the kinetic energy is: $$K = \frac{1}{2} m_i v_i^T v_i + \frac{1}{2} \omega_i^T I_i \omega_i$$ and potential energy is \(U = m_i g h_i\), with \(g\) as gravity and \(h_i\) as height. The joint torques τ can be computed using: $$\tau = \frac{d}{dt} \left( \frac{\partial L}{\partial \dot{q}} \right) – \frac{\partial L}{\partial q}$$ where \(q\) are the joint angles. This dynamic model helps in selecting appropriate actuators—servo motors with sufficient torque for the legs and DC motors for the wheels—ensuring the bionic robot can carry payloads up to 2 kg without compromising agility.
We fabricated a physical prototype of the bionic robot using 3D-printed components for the legs and torso, coupled with metal joints for durability. The control system was implemented with an Arduino Mega 2560 and an MPU-6050 IMU sensor. Experiments focused on three aspects: mode transition, walking gait execution, and obstacle negotiation. For mode transition, we commanded the bionic robot to switch from six-legged to four-wheeled configuration; the process completed within 3 seconds, demonstrating rapid adaptability. In walking mode, we programmed the tripod gait, where legs 1, 3, and 5 moved in synchrony with legs 2, 4, and 6 alternately. The bionic robot achieved a walking speed of 0.1 m/s on flat ground, with stable posture maintained by the IMU feedback. For obstacle tests, we placed a 62 mm high wooden block; the bionic robot successfully traversed it by lifting its legs to clear the height, as predicted by the workspace analysis. Table 3 summarizes key performance metrics from these experiments, highlighting the bionic robot’s versatility.
| Metric | Value | Conditions |
|---|---|---|
| Mode Transition Time | 3 seconds | From six-legged to four-wheeled |
| Walking Speed | 0.1 m/s | Tripod gait on flat surface |
| Maximum Obstacle Height | 62 mm | Wooden block, walking mode |
| Wheeled Speed | 0.5 m/s | Omnidirectional movement |
| Power Consumption | 15 W (walking), 10 W (wheels) | At nominal load |
Further analysis involved comparing our bionic robot with existing mobile platforms. We developed a quantitative assessment based on criteria such as terrain adaptability, speed, energy efficiency, and mechanical complexity. Using a scoring system from 1 (poor) to 5 (excellent), we evaluated wheeled, tracked, legged, and our hybrid bionic robot. The results, shown in Table 4, underscore the advantages of our design: it scores high in adaptability and speed, balancing the trade-offs inherent in single-mode robots. This hybrid approach makes the bionic robot suitable for missions where terrain varies from smooth floors to rocky outcrops.
| Robot Type | Terrain Adaptability | Speed | Energy Efficiency | Complexity | Overall Score |
|---|---|---|---|---|---|
| Wheeled | 2 | 5 | 4 | 2 | 3.25 |
| Tracked | 3 | 3 | 3 | 3 | 3.00 |
| Legged (Hexapod) | 5 | 2 | 2 | 4 | 3.25 |
| Our Bionic Robot | 4 | 4 | 3 | 3 | 3.50 |
From a control perspective, we implemented a state machine to manage the bionic robot’s behaviors. The states include “Idle,” “Walk,” “Roll,” and “Transition,” with triggers based on sensor input or external commands. For instance, if an ultrasonic sensor detects a large obstacle, the bionic robot might switch from rolling to walking mode to climb over it. The control algorithm uses PID controllers for joint positioning: $$u(t) = K_p e(t) + K_i \int_0^t e(\tau) d\tau + K_d \frac{de(t)}{dt}$$ where \(e(t)\) is the error between desired and actual joint angles, and \(K_p\), \(K_i\), \(K_d\) are tuned gains. This ensures precise movements for the bionic robot, whether navigating tight spaces or crossing rough terrain.
We also explored energy optimization strategies for the bionic robot. In walking mode, the tripod gait minimizes energy by keeping three legs grounded at all times, reducing the torque required for support. The mechanical design leverages lightweight materials, with the total mass of the bionic robot at 3.5 kg. The power system uses lithium-polymer batteries, providing up to 2 hours of operation in mixed mode. To quantify energy use, we modeled the power consumption \(P\) as: $$P = \sum_{i=1}^{18} \tau_i \dot{\theta}_i + \sum_{j=1}^{4} V_j I_j$$ where \(\tau_i\) and \(\dot{\theta}_i\) are torque and angular velocity of leg joints, and \(V_j\) and \(I_j\) are voltage and current of wheel motors. In experiments, the bionic robot consumed 15 W while walking and 10 W while rolling, indicating that wheeled mode is more efficient for flat terrain, as expected.
Looking ahead, we identify several areas for improvement. First, the bionic robot’s walking speed could be increased by optimizing gait parameters using genetic algorithms or reinforcement learning. Second, adding more sensors—such as LIDAR or cameras—would enhance autonomous navigation capabilities, allowing the bionic robot to map environments and plan paths in real-time. Third, we plan to investigate dynamic gaits, like running or jumping, to further expand the bionic robot’s mobility. Finally, material advancements could reduce weight and increase durability, making the bionic robot suitable for harsher conditions.
In conclusion, our wheel-legged bionic robot represents a significant step forward in mobile robotics. By fusing the benefits of legged and wheeled locomotion, it achieves remarkable adaptability across diverse terrains. The mechanical design, inspired by insect anatomy, provides robustness and flexibility, while the control system ensures smooth operation and mode transitions. Workspace analysis and experimental validation confirm that the bionic robot can negotiate obstacles and move efficiently. As robotics technology evolves, hybrid platforms like this bionic robot will play a crucial role in extending human reach into challenging environments, from deep-sea exploration to extraterrestrial colonization. We are confident that continued research will refine this bionic robot, unlocking new possibilities for autonomous systems in the years to come.
To further illustrate the mathematical foundations, consider the inverse kinematics problem for the bionic robot’s leg: given a desired foot position \((p_x, p_y, p_z)\), we solve for joint angles \(\theta_1, \theta_2, \theta_3\). From the forward kinematics equations, we can derive: $$\theta_1 = \arctan2(p_y, p_x)$$ Then, let \(r = \sqrt{p_x^2 + p_y^2} – L_1\) and \(z = p_z\), we have: $$r = L_2 \cos\theta_2 + L_3 \cos(\theta_2 + \theta_3)$$ $$z = L_2 \sin\theta_2 + L_3 \sin(\theta_2 + \theta_3)$$ Squaring and adding these equations: $$r^2 + z^2 = L_2^2 + L_3^2 + 2L_2L_3 \cos\theta_3$$ Thus, $$\theta_3 = \arccos\left( \frac{r^2 + z^2 – L_2^2 – L_3^2}{2L_2L_3} \right)$$ Finally, \(\theta_2\) can be found using: $$\theta_2 = \arctan2(z, r) – \arctan2(L_3 \sin\theta_3, L_2 + L_3 \cos\theta_3)$$ These equations enable precise foot placement for the bionic robot, essential for stepping over gaps or climbing stairs.
In summary, the development of this wheel-legged bionic robot involved interdisciplinary efforts in mechanical engineering, control theory, and computer science. The bionic robot’s ability to switch modes on-demand makes it a versatile tool for real-world applications. As we continue to enhance its capabilities, we envision a future where bionic robots like this one operate alongside humans, performing tasks that are too dangerous or inaccessible. The journey of innovation in bionic robotics is ongoing, and we are excited to contribute to this dynamic field.