# Design and Mechanical Behavior Research of Highway Guardrail Patrol Robot
## 4 Dynamic Simulation of Guardrail Inspection Robot  
### Barrier-Free Guardrail Section  
The movement of the robot along the barrier-free section is relatively straightforward, consisting of two parts: movement on a straight section and movement on a small-curvature curved section. For the small-curvature curved sections, guardrails are typically treated using compression bending, allowing the two sections to be combined. The robot is set to travel back and forth along the combined guardrail section once, with a one-way travel time of 17 s and a total duration of 34 s.  
The simulation results, as illustrated in Figure 5, show the vertical position changes of the robot during its operation in the barrier-free section. It is evident that the robot's vertical position is not stable or constant, but fluctuates continuously during operation. This occurs because the spring constraint is not entirely rigid. Additionally, the curve is largely symmetrical, indicating minimal differences in stability between the robot's forward and backward (return) movements along the same guardrail section.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**(Unit N/mm)** & \(\mathbf{k_{1}}\) & \(\mathbf{k_{2}}\) \\ \hline Group 1 & 2 & 0.1 \\ Group 2 & 2 & 0.3 \\ Group 3 & 2 & 0.5 \\ Group 4 & 2.2 & 0.5 \\ Group 5 & 2.4 & 0.5 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Parameters of each group of spring stiffness.  
Figure 4: Diagram of impact of different parameters on obstacle crossing. (**a**) The impact of adhesion coefficient on obstacle-crossing. (**b**) The impact of spring stiffness on obstacle-crossing.  
When the stiffness \(k_{1}\) of the active wheel side spring and the stiffness \(k_{2}\) of the passive wheel side spring are set to the values of Group 2, Group 3, and Group 4, the robot runs the most smoothly. On the small-curvature bending guardrail section, the robot experiences a downward movement due to the compression of the load-bearing wheel and the bending guardrail, but it automatically adjusts after returning. When set to Group 1, the robot experienced a slight drop at 12 s, but overall, the stability was within an acceptable range. When \(k_{1}\) and \(k_{2}\) are set to 2.4 and 0.5, the robot experiences a significant drop at 7-8 s, and the stop of the fall is due to the limiting effect of the single edge of the auxiliary wheel. This occurs because the robot is driven on one side, and the excessively high spring stiffness on the active wheel side exerts a stronger force on the guardrail than the overall structure on the passive wheel side. As a result, the robot cannot automatically adjust to a neutral position and instead becomes supported by the active wheel side, causing displacement.  
In the theoretical analysis, to simplify the mathematical model, the friction coefficient \(\mu_{1}\) between the auxiliary wheels and the guardrail, as well as the friction coefficient \(\mu\) between the non-driving rubber-coated wheels and the guardrail, are neglected. Additionally, when analyzing the detachment conditions of the robot on the guardrail, the robot's mass distribution is idealized as a planar problem, with the center of gravity approximated at the centroid of the active and driven axes. While the simulation environment is closer to real-world conditions, setting a higher stiffness \(k_{1}\) for the active wheel side spring, though theoretically beneficial for the obstacle crossing, can lead to excessive force on the active wheel side in a three-dimensional environment. This makes it difficult for the robot to adapt to guardrail variations, increasing the risk of derailment. Consequently, the analysis of the spring stiffness setting for Group 5 is excluded in the following discussion.