In the field of robotics, legged locomotion systems have garnered significant attention due to their superior adaptability in unstructured environments compared to wheeled or tracked counterparts. As a researcher engaged in this domain, I have focused on designing a bionic robot that addresses common limitations such as high power consumption, complex control, and cost inefficiency. This paper presents the development of a novel eight-legged walking bionic robot, emphasizing its mechanical design, kinematic analysis, optimization, and functional capabilities. The bionic robot features a compact structure with only one drive motor per leg pair, simplifying control while enhancing mobility, climbing ability, and turning flexibility. Through virtual prototyping and physical prototype testing, this bionic robot demonstrates robust performance in various terrains, making it suitable for applications like disaster relief and military logistics.
The inspiration for this bionic robot stems from biological locomotion observed in multi-legged organisms, which exhibit stability and adaptability. Traditional walking robots often require multiple actuators per leg, leading to intricate coordination challenges. In contrast, our eight-legged bionic robot employs a simplified linkage mechanism that reduces the number of motors to four for the entire system. Each pair of legs shares a single drive motor, which transmits motion via gears to a rotating disk connected to eccentric shafts on the legs. This design mimics natural stepping patterns while minimizing energy consumption. The overall dimensions of the bionic robot are approximately 1200 mm in length, 780 mm in width, and 870 mm in height, ensuring a balance between size and functionality. By adjusting phase differences between motor inputs, the bionic robot can perform straight-line movement or turning maneuvers, including zero-radius turns, which are critical for navigation in confined spaces.
To analyze the motion of this bionic robot, we begin with the kinematic modeling of its leg mechanism. The leg is composed of a multi-linkage system similar to a Stephenson six-bar chain, as shown in the schematic. Using the D-H homogeneous coordinate transformation matrix, we derive the trajectory of the leg’s endpoint (point D) along the path O → A → B → C → D. The position vector of point D can be expressed in terms of link lengths and joint angles. Let us define the coordinates and parameters: OA, AB, BC, CD represent link lengths, while θ1, θ2, θ3 denote the rotational angles at joints. The transformation matrices are multiplied sequentially to obtain the endpoint equation:
$$
\begin{bmatrix}
X_D \\
Y_D \\
1
\end{bmatrix}
=
\begin{bmatrix}
1 & 0 & OA \\
0 & 1 & 0 \\
0 & 0 & 1
\end{bmatrix}
\cdot
\begin{bmatrix}
\cos \theta_1 & -\sin \theta_1 & 0 \\
\sin \theta_1 & \cos \theta_1 & 0 \\
0 & 0 & 1
\end{bmatrix}
\cdot
\begin{bmatrix}
1 & 0 & AB \\
0 & 1 & 0 \\
0 & 0 & 1
\end{bmatrix}
\cdot
\begin{bmatrix}
\cos \theta_2 & -\sin \theta_2 & 0 \\
\sin \theta_2 & \cos \theta_2 & 0 \\
0 & 0 & 1
\end{bmatrix}
\cdot
\begin{bmatrix}
1 & 0 & BC \\
0 & 1 & 0 \\
0 & 0 & 1
\end{bmatrix}
\cdot
\begin{bmatrix}
\cos \theta_3 & -\sin \theta_3 & 0 \\
\sin \theta_3 & \cos \theta_3 & 0 \\
0 & 0 & 1
\end{bmatrix}
\cdot
\begin{bmatrix}
CD \\
0 \\
1
\end{bmatrix}
$$
Where the angles are computed based on geometric constraints. For instance, θ1 involves inverse trigonometric functions of link lengths and angles such as ∠FOA. The detailed expressions are:
$$
\theta_1 = 180^\circ – \arccos\left( \frac{OF^2 + OA^2 – 2 \cdot OF \cdot OA \cdot \cos(\angle FOA) + EA^2 – EF^2}{2 \cdot EA \cdot \sqrt{OF^2 + OA^2 – 2 \cdot OF \cdot OA \cdot \cos(\angle FOA)}} \right) + \arcsin\left( \frac{OF}{FA} \sin(\angle FOA) \right) – \angle EAB
$$
$$
\theta_2 = -360^\circ + \arccos\left( \frac{OF^2 + OA^2 – 2 \cdot OF \cdot OA \cdot \cos(\angle FOA) + GA^2 – FG^2}{2 \cdot GA \cdot \sqrt{OF^2 + OA^2 – 2 \cdot OF \cdot OA \cdot \cos(\angle FOA)}} \right) + \arccos\left( \frac{OF^2 + OA^2 – 2 \cdot OF \cdot OA \cdot \cos(\angle FOA) + EA^2 – EF^2}{2 \cdot EA \cdot \sqrt{OF^2 + OA^2 – 2 \cdot OF \cdot OA \cdot \cos(\angle FOA)}} \right) + \angle EAB
$$
$$
\theta_3 = 180^\circ + \angle GCD – \arccos\left( \frac{OF^2 + OA^2 – 2 \cdot OF \cdot OA \cdot \cos(\angle FOA) + GA^2 – FG^2}{2 \cdot GA \cdot \sqrt{OF^2 + OA^2 – 2 \cdot OF \cdot OA \cdot \cos(\angle FOA)}} \right) – \arccos\left( \frac{OF^2 + OA^2 – 2 \cdot OF \cdot OA \cdot \cos(\angle FOA) + EA^2 – EF^2}{2 \cdot EA \cdot \sqrt{OF^2 + OA^2 – 2 \cdot OF \cdot OA \cdot \cos(\angle FOA)}} \right) – \angle EAB
$$
These equations form the basis for optimizing the leg mechanism to maximize performance metrics such as stride height and stability. The trajectory of point D is crucial for obstacle clearance and smooth locomotion, making kinematic analysis essential for this bionic robot.
Next, we focus on optimizing the leg mechanism using virtual prototyping technology. The goal is to enhance the bionic robot’s ability to traverse uneven terrain by maximizing the vertical displacement (Y-direction) of the leg endpoint. We define design variables corresponding to the coordinates of key points in the linkage, such as POINT_A, POINT_B, etc. The objective function is:
$$
F_Y = \max(Y_D)
$$
Subject to constraints that ensure physical feasibility, including positive link lengths and geometric compatibility:
$$
OF, OA, AB, AE, FE, FG > 0
$$
$$
AG, BC, GD, CD, EB, CG > 0
$$
$$
AB = CG
$$
$$
AG = BC
$$
We perform a design sensitivity analysis to identify variables that significantly influence the objective function. The sensitivity coefficient \( S_n \) for each variable is calculated as:
$$
S_n = \frac{1}{2} \left( \frac{Q_{n+1} – Q_n}{V_{n+1} – V_n} + \frac{Q_n – Q_{n-1}}{V_n – V_{n-1}} \right)
$$
Where \( Q_n \) is the objective function value and \( V_n \) is the design variable value at the n-th analysis. The results are summarized in the following table, which highlights variables with high sensitivity:
| Design Variable | Point | Coordinate Direction | Sensitivity to \( F_Y \) |
|---|---|---|---|
| DV_1 | POINT_A | X | -3.9 |
| DV_2 | POINT_B | X | 1.2 |
| DV_3 | POINT_B | Y | 1.2 |
| DV_4 | POINT_C | X | -1.4 |
| DV_5 | POINT_C | Y | -1.1 |
| DV_6 | POINT_D | X | -0.7 |
| DV_7 | POINT_D | Y | 0.7 |
| DV_8 | POINT_E | X | 0.7 |
| DV_9 | POINT_E | Y | -0.3 |
| DV_10 | POINT_F | Y | -3.8 |
| DV_11 | POINT_G | X | 2.9 |
| DV_12 | POINT_G | Y | 2.3 |
Based on the sensitivity analysis, we select the most influential variables (DV_1, DV_10, DV_11, DV_12) for optimization. The optimization process adjusts these variables to improve \( F_Y \). The comparison before and after optimization is shown in the following table:
| Parameter | Before Optimization | After Optimization |
|---|---|---|
| \( F_Y \) (mm) | -571.5 | -545.0 |
| DV_1 (mm) | 300 | 297 |
| DV_2 (mm) | -85.5 | -86.355 |
| DV_3 (mm) | 380 | 383.8 |
| DV_4 (mm) | -240 | -237.6 |
The optimized leg mechanism exhibits a 26.5 mm increase in maximum vertical displacement, enhancing the bionic robot’s obstacle-crossing capability. The time-displacement curves in the Y-direction before and after optimization demonstrate a smoother and more elevated trajectory, crucial for stable gait generation. This optimization directly contributes to the bionic robot’s performance in rough terrains.
With the optimized design, we proceed to functional analysis through simulations in a virtual environment. The bionic robot’s total mass is set to 20 kg, with friction coefficients of 0.3 (static) and 0.1 (kinetic) between the feet and ground. The average acceleration during motion is 9 m/s², resulting in gravitational force of 196 N, static friction of 58.8 N, kinetic friction of 19.6 N, and inertial force of 180 N. Each of the four drive motors has a maximum load torque of 50 N·m. We evaluate three key functionalities: gradeability, uneven terrain traversal, and turning gait planning.
First, for gradeability analysis, we simulate the bionic robot on slopes of varying inclines to determine the maximum climbable angle. The bionic robot’s center of mass displacement in the Y-direction is measured over time. The results indicate that for slopes up to 10°, the displacement curves are similar, with minor deviations due to gravitational effects. Beyond 11°, the time required to ascend increases significantly, and at 12.45°, the bionic robot fails to climb within a reasonable duration. Thus, the optimal operating slope for this bionic robot is 11° or less. The mathematical relation for the climbing force balance involves:
$$
F_{\text{climb}} = mg \sin(\theta) + F_{\text{friction}}
$$
Where \( m \) is mass, \( g \) is gravity, and \( \theta \) is slope angle. The bionic robot’s motors must provide sufficient torque to overcome this force, which is validated in simulations.
Second, for uneven terrain traversal, we model a non-flat surface with peak-to-valley differences of 70 mm and an approximate slope of 8.2°. The bionic robot’s stability is assessed by monitoring displacements in Y and Z directions. The Y-direction displacement shows minimal fluctuations, indicating steady progression, while the Z-direction displacement varies by about 20 mm, which is negligible relative to the bionic robot’s size. This confirms the bionic robot’s adaptability to irregular surfaces, a critical feature for real-world applications. The root mean square (RMS) of displacement errors can be computed as:
$$
\text{RMS} = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (y_i – \bar{y})^2}
$$
Where \( y_i \) are displacement samples and \( \bar{y} \) is the mean. In our simulations, RMS values remain low, underscoring stability.
Third, for turning gait planning, we implement differential speeds for the outer motor pairs. Let \( \omega_1 \) be the angular velocity of the inner pair and \( \omega_2 \) for the outer pair. The turning radius \( R \) is inversely proportional to the speed difference:
$$
R \propto \frac{1}{|\omega_2 – \omega_1|}
$$
By adjusting \( \omega_1 \) and \( \omega_2 \), the bionic robot achieves turning radii from large curves to zero-radius turns. Trajectory plots show smooth arcs with minimal body sway, enabling agile navigation. This flexibility is a hallmark of this bionic robot, setting it apart from conventional designs.
Following successful simulations, we develop a physical prototype of the bionic robot to validate theoretical findings. The prototype’s mechanical components are fabricated from aluminum using wire-cut machining, ensuring lightweight yet durable construction. The control system integrates an ATM32 mainboard, motor drivers, ultrasonic distance sensors, voltage regulators, and lithium battery packs. This hardware setup enables autonomous operation and real-time feedback for the bionic robot.
Experimental tests are conducted in various environments. On unstructured terrain like pebble-covered ground, the bionic robot demonstrates effective obstacle negotiation and stable gait patterns. Zero-radius turning tests confirm the bionic robot’s ability to pivot seamlessly, enhancing maneuverability in tight spaces. Gradeability tests on slopes around 10° reveal satisfactory performance, though further optimization is needed for steeper inclines. These experiments collectively verify the bionic robot’s robustness and practicality.
In conclusion, this eight-legged walking bionic robot offers significant advantages over traditional robots. Its simplified control scheme, achieved through shared motors and phase modulation, reduces complexity and cost. The optimized leg mechanism enhances vertical displacement, improving obstacle clearance. Functional analyses prove its competence on slopes up to 11°, uneven surfaces, and versatile turning capabilities. The physical prototype corroborates simulation results, though areas like joint coupling and energy efficiency warrant future refinement. Overall, this bionic robot represents a step forward in legged robotics, with potential applications in search-and-rescue, exploration, and industrial logistics. The iterative design process, combining virtual prototyping and real-world testing, underscores the value of integrated engineering approaches for advancing bionic robot technology.
Looking ahead, we plan to explore dynamic gait optimization using machine learning algorithms to further enhance the bionic robot’s adaptability. Additionally, incorporating sensor fusion for environment perception could enable autonomous decision-making in complex scenarios. The bionic robot platform will serve as a testbed for studying bio-inspired locomotion principles, contributing to the broader field of robotics. As we continue to refine this bionic robot, we aim to push the boundaries of what legged machines can achieve in unstructured environments, ultimately creating more resilient and intelligent systems.
Throughout this development, the keyword “bionic robot” has been emphasized to highlight the bio-inspired nature of the design. This bionic robot not only mimics biological forms but also integrates engineering innovations to overcome practical challenges. By leveraging kinematics, optimization, and simulation, we have created a bionic robot that balances performance and simplicity. Future iterations of this bionic robot will incorporate advanced materials and control strategies, paving the way for next-generation walking machines. The journey of developing this bionic robot underscores the interdisciplinary effort required to bridge biology and engineering, resulting in a versatile and efficient platform for various applications.