In recent years, the development of specialized robots has gained significant attention, particularly in hazardous environments where human intervention is risky. As part of the growing field of China robot technology, wall-climbing robots have emerged as crucial tools for inspection and maintenance tasks. These robots are designed to operate on vertical surfaces, such as communication towers, which are common in infrastructure across China. Traditional robots often struggle with obstacles and complex transitions on these structures, leading to inefficiencies and limitations. To address these challenges, we present a novel bipedal wall-climbing robot with dual walking modes, enhancing adaptability and performance in demanding scenarios. This work focuses on the structural design, kinematic analysis, simulation, and prototype testing of the robot, contributing to the advancement of China robot capabilities in industrial applications.
The robot features a serial-link mechanism with four independent rotational joints, allowing for two distinct walking modes: flipping and striding. These modes enable the robot to navigate planar surfaces, overcome obstacles, and transition between surfaces of varying angles. The design incorporates electromagnetic adhesion feet, which provide secure attachment to steel surfaces without continuous power, ensuring safety during operations. In this paper, we detail the kinematic modeling using the Denavit-Hartenberg (D-H) method, derive the forward and inverse kinematics equations, and compute the velocity Jacobian matrix using differential transformations. Simulations conducted in MATLAB’s Robotics Toolbox validate the robot’s workspace and motion trajectories, while prototype experiments demonstrate its practical efficacy. The integration of these elements underscores the potential of China robot innovations to solve real-world problems in inspection and maintenance.
Structural Design and Walking Modes
The bipedal wall-climbing robot consists of two identical walking leg segments (A and B) connected by a central frame. Each leg segment includes an electromagnetic adhesion foot, a cross-rotation servo, and a flip servo. The central frame houses two flip servos that link the leg segments, forming a serial chain with four degrees of freedom. The cross-rotation servos allow 360° rotation, while the flip servos provide 270° motion, facilitating flexible posture adjustments and locomotion. The electromagnetic feet, with a diameter of 35 mm, are designed for small-space operations on truss structures, common in communication towers. This compact design is a key feature of China robot development, emphasizing adaptability and efficiency.
The robot operates in two primary walking modes: flipping mode and striding mode. In flipping mode, the cross-rotation servos remain stationary, and the flip servos drive the robot to perform rotational movements, enabling it to traverse planar surfaces, cross obstacles, and transition between surfaces at different angles. This mode is ideal for covering large distances in a single step, as the robot alternates adhesion between its feet. In striding mode, both cross-rotation and flip servos coordinate to lift and place the feet, allowing the robot to step over gaps or protrusions. This mode is particularly useful for navigating narrow spaces or overcoming localized obstacles, showcasing the versatility of China robot designs in complex environments.
To quantify the robot’s design parameters, we present a table summarizing key dimensions and joint ranges. These parameters are essential for kinematic analysis and simulation, reflecting the precision engineering typical of China robot projects.
| Parameter | Value |
|---|---|
| Leg Segment Length | 159.4 mm |
| Adhesion Foot Diameter | 35 mm |
| Cross-Rotation Servo Range | 360° |
| Flip Servo Range | 270° |
| Total Mass | 554 g |
| Payload Capacity | 120 g |
Kinematic Analysis
Kinematic analysis is fundamental for understanding the robot’s motion capabilities. We employ the standard D-H method to establish coordinate systems and derive the transformation matrices between joints. The robot’s serial chain consists of four links, with joint variables denoted as $\theta_i$ for $i = 1, 2, 3, 4$. The D-H parameters are listed in the following table, which includes link lengths, offsets, and twist angles. This approach is widely used in China robot research for its simplicity and accuracy in modeling robotic manipulators.
| Link i | $\theta_i$ | $d_i$ (mm) | $a_i$ (mm) | $\alpha_i$ (°) |
|---|---|---|---|---|
| 1 | $\theta_1$ | 27 | 0 | 90 |
| 2 | $\theta_2$ | 0 | 159.4 | 0 |
| 3 | $\theta_3$ | 0 | 0 | 90 |
| 4 | $\theta_4$ | 110.8 | 0 | 0 |
The homogeneous transformation matrix from frame {i-1} to frame {i} is given by:
$$^{i-1}T_i = \begin{bmatrix}
\cos\theta_i & -\sin\theta_i \cos\alpha_i & \sin\theta_i \sin\alpha_i & a_i \cos\theta_i \\
\sin\theta_i & \cos\theta_i \cos\alpha_i & -\cos\theta_i \sin\alpha_i & a_i \sin\theta_i \\
0 & \sin\alpha_i & \cos\alpha_i & d_i \\
0 & 0 & 0 & 1
\end{bmatrix}$$
For the robot, the overall transformation from the base frame {0} to the end-effector frame {4} is computed as $^0T_4 = ^0T_1 \cdot ^1T_2 \cdot ^2T_3 \cdot ^3T_4$. This matrix defines the position and orientation of the end-effector (foot B) relative to the base (foot A). The elements of $^0T_4$ are functions of the joint angles, enabling forward kinematics calculations. For instance, the position coordinates $(p_X, p_Y, p_Z)$ of the end-effector can be expressed as:
$$p_X = c_1 c_2 s_3 d_4 + c_1 s_2 c_3 d_4 + c_1 a_2 c_2$$
$$p_Y = s_1 c_2 s_3 d_4 + s_1 s_2 c_3 d_4 + s_1 a_2 c_2$$
$$p_Z = s_2 s_3 d_4 – c_2 c_3 d_4 + a_2 s_2 + d_1$$
where $c_i = \cos\theta_i$ and $s_i = \sin\theta_i$. These equations allow us to determine the end-effector’s position for any set of joint angles, a critical step in motion planning for China robot applications.
Inverse kinematics involves solving for the joint angles given the end-effector’s position and orientation. Using algebraic methods, we derive closed-form solutions for $\theta_1$, $\theta_2$, $\theta_3$, and $\theta_4$. For example, $\theta_1$ can be found as:
$$\theta_1 = \arctan2(p_Y, p_X)$$
Similarly, $\theta_2$ and $\theta_3$ are computed using trigonometric identities and separation of variables. The inverse kinematics solutions ensure that the robot can achieve desired poses, which is essential for trajectory planning in dynamic environments. This capability is a hallmark of advanced China robot systems, enabling precise control and adaptability.
Velocity Jacobian Matrix
The velocity Jacobian matrix relates the joint velocities to the end-effector’s linear and angular velocities. For a robot with $n$ joints, the Jacobian $J$ is a $6 \times n$ matrix. The first three rows correspond to linear velocity, and the last three to angular velocity. Using the differential transformation method, we compute the Jacobian columns for each joint. For joint $i$, the column vector $J_i$ is given by:
$$J_i = \begin{bmatrix}
(P_i \times n_i)_Z \\
(P_i \times o_i)_Z \\
(P_i \times a_i)_Z \\
n_{Zi} \\
o_{Zi} \\
a_{Zi}
\end{bmatrix} = \begin{bmatrix}
-P_{Yi} n_{Xi} + P_{Xi} n_{Yi} \\
-P_{Yi} o_{Xi} + P_{Xi} o_{Yi} \\
-P_{Yi} a_{Xi} + P_{Xi} a_{Yi} \\
n_{Zi} \\
o_{Zi} \\
a_{Zi}
\end{bmatrix}$$
where $n_i$, $o_i$, $a_i$, and $P_i$ are the orientation and position vectors from the transformation matrix $^iT_4$. The full Jacobian matrix for our robot is:
$$J = \begin{bmatrix}
J_1 & J_2 & J_3 & J_4
\end{bmatrix}$$
This matrix is crucial for analyzing singularities, optimizing trajectories, and ensuring stable motion. The derivation of the Jacobian underscores the mathematical rigor in China robot development, facilitating high-performance control systems.
Simulation Studies
We conducted simulations using MATLAB’s Robotics Toolbox to validate the kinematic model and explore the robot’s workspace. The robot model was built based on the D-H parameters, and Monte Carlo methods were employed to generate the reachable workspace. The joint angle ranges were set as $\theta_1 \in [-180^\circ, 180^\circ]$, $\theta_2 \in [-10^\circ, 190^\circ]$, $\theta_3 \in [-10^\circ, 190^\circ]$, and $\theta_4 \in [-180^\circ, 180^\circ]$. The resulting workspace plots show the volume accessible by the end-effector, demonstrating the robot’s ability to cover significant areas on vertical surfaces. This simulation approach is commonly used in China robot research to verify design feasibility before physical implementation.
For the flipping mode, we simulated a single-step trajectory from point $P_1$ to $P_2$, with coordinates $P_1 = (0.159, 0, 0)$ m and $P_2 = (-0.159, 0, 0)$ m. The joint angles for these points are $q_1 = [0, 0, 0, 0]$ and $q_2 = [0, 180^\circ, 180^\circ, 0]$, respectively. Using fifth-order polynomial interpolation, we generated smooth trajectories for the joint variables, ensuring continuous motion. The trajectory plots in Cartesian space confirm that the robot maintains proper adhesion orientation during movement, a key requirement for reliable operation.
In striding mode, the trajectory involves points $P_3 = (0.113, 0.113, 0)$ m, $P_4 = (0, 0.224, 0.224)$ m, and $P_5 = (-0.113, 0.113, 0)$ m. The corresponding joint angles are $q_3 = [45^\circ, 0, 0, 0]$, $q_4 = [90^\circ, 45^\circ, 45^\circ, 0]$, and $q_5 = [135^\circ, 0, 0, 0]$. The simulation shows that the robot can step over obstacles up to 82.7 mm wide, highlighting its versatility. These results align with the goals of China robot projects to enhance obstacle negotiation in complex environments.
| Walking Mode | Step Distance (mm) | Max Obstacle Height (mm) | Key Joint Angles |
|---|---|---|---|
| Flipping | 318 | 95.8 | $\theta_2, \theta_3 = 180^\circ$ |
| Striding | 226 | 82.7 | $\theta_1, \theta_2, \theta_3$ varied |
Prototype Testing and Experimental Results
We fabricated a prototype using PLA 3D printing and integrated an Arduino-based control system. The robot was tested on simulated communication tower structures to evaluate its walking and obstacle-crossing capabilities. In flipping mode, the robot successfully traversed planar surfaces and transitioned between surfaces at 60° angles. It also overcame obstacles up to 60 mm wide and 16.5 mm high without slippage. In striding mode, the robot navigated bolt connections and V-shaped trusses, demonstrating effective gap crossing. These experiments validate the robot’s design and kinematics, showcasing the practical benefits of China robot technology in real-world inspections.
Further tests on actual communication towers involved crossing bolt connections with 70 mm gaps and 55 mm heights. The robot used both walking modes to adapt to different scenarios, such as horizontal-to-vertical transitions and inverted surfaces. The adhesion system remained secure throughout, ensuring stability. The following table summarizes key performance metrics from the tests, emphasizing the robot’s reliability as a China robot solution for tower inspection.
| Test Scenario | Walking Mode | Success Rate | Max Obstacle Handled |
|---|---|---|---|
| Planar Surface | Flipping | 100% | 16.5 mm height |
| Surface Transition | Flipping | 100% | 60° angle |
| Bolt Connection | Striding | 95% | 70 mm gap |
| V-Truss | Striding | 90% | 50 mm height |
Conclusion and Future Work
In this work, we designed and analyzed a bipedal wall-climbing robot with dual walking modes, addressing challenges in communication tower inspection. The kinematic analysis using D-H parameters and Jacobian matrices provides a foundation for motion planning and control. Simulations in MATLAB confirmed the robot’s workspace and trajectory capabilities, while prototype tests demonstrated practical effectiveness in overcoming obstacles and transitioning between surfaces. This research contributes to the evolution of China robot technology, offering a scalable solution for hazardous environment operations.
For future improvements, we plan to enhance the adhesion system for varied surface textures and curvatures. Additionally, implementing wireless communication and power systems will eliminate tethering constraints, increasing mobility. These advancements will further solidify the role of China robot innovations in industrial automation and inspection tasks, pushing the boundaries of robotic adaptability and performance.