## 5 Simulation and Numerical Calculation  
Based on the analysis and our task requirements, we have carefully designed and developed a robot for urban environments. To gain a better understanding of the robot's performance, we have listed its relevant parameters in Table 1. The robot we have manufactured is shown in the following, Figure 12. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Parameters** & **Value** & **Unit** \\ \hline Front swing arm mass & \(m_{1}\) & 1.02 & kg \\ Rear swing arm mass & \(m_{2}\) & 1.02 & kg \\ Intermediate body mass & \(M\) & 16.05 & kg \\ Length of front swing arm & \(L_{1}\) & 200 & mm \\ Rear swing arm length & \(L_{2}\) & 200 & mm \\ Length of main body & \(L\) & 520 & mm \\ Distance from sidetrack to centerline & \(b\) & 568 & mm \\ Distance of main body center of mass from point \(o\) & \(l\) & 314.42 & mm \\ Angle between the center of mass of main body & \(\alpha\) & 13.96 & \({}^{\circ}\) \\ and \(x\)-axis & \(a_{2}\) & 65.62 & mm \\ Distance from the center of mass of the swing leg to \(o\) & \(a_{2}\) & 65.62 & mm \\ Wheel radius & \(R\) & 91 & mm \\ Active pulley radius & \(R_{1}\) & 78 & mm \\ Slave pulley radius & \(R_{2}\) & 48 & mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Robot construction parameters. Figure 11: Schematic diagram of lateral slope climbing. Substitute the parameters of the robot into Equations (4)-(19). After calculation, for the robot climbing low steps, it reaches the maximum height of climbing \(h_{max}=206.65\) mm when \(\theta_{1}=13.49^{\circ}\). As for climbing high steps, the maximum height of the robot climbing high step is \(h_{max}=542.47\) mm. For the height of the robot platform overturning, the maximum overturning height is \(H_{max}=505.3\) mm. Thus, the robot's maximum step climbing height is 505.3 mm. When the height is below 206.65 mm, the robot adopts the first gait to improve climbing efficiency. For heights exceeding 206.65 mm, the second gait is used to maximize the climbing ability. Figure 13a shows the curve of the swing arm track's effective radius \(R_{e}\) and step height \(h\), when the robot climbs a low step. The intersection of the two curves is the maximum height the robot can climb under a low step. Figure 13b shows the surface plot of the swing arm's effective radius \(R_{e}\) and step height \(h\), when the robot climbs a high step. The highest point on the intersection line of the two surfaces is the maximum height that the robot can climb under the high step. Figure 13c shows the surface plot of the relationship between the overturning height of the robot and the angle of the swing arm track. The highest point on the surface corresponds to the maximum height that the robot can overturn. The virtual prototype of the wheel-tracked robot and the obstacle model were created in the three-dimensional modeling software Unigraphics NX 8.0 and imported into ADAMS. The four main wheels of the robot and the ground were set as the contact collision type, and the dynamic friction and static friction coefficients were redefined so that the robot wheels can contact the road and generate sufficient friction for movement. This allowed for the robot model movement on the road. The initial simulation settings and obstacle parameter settings are listed in Table 2.  
Figure 12: The robot for urban environments. Figure 13: _Cont._  
The linear motion speed curve of the robot is shown in Figure 14. The model of the robot undergoes a linear acceleration process within 0.4 s after startup. The model can fully drive into the simulated road surface after 1.2 s of trial calculation because of the non-excitation road surface at the beginning of driving. After approximately 0.41 s, the robot mobile reaches its maximum motion speed and enters a uniform linear motion state. The robot ultimately meets the preset requirement of 1 m/s.