## 3 Methods
### Terrain Recognition and Stability Analysis
#### 3.3.2 Stability Analysis  
In the static simulation, it was determined that the robot is made of stainless steel with a density of 7930 kg/m\({}^{3}\), and the rubber density of the tire is 1200 kg/m\({}^{3}\). Through the statistics of the 3D digital model with a 1:1 ratio with the real object, it is known that the mass of the truss composed of non-standard stainless steel parts is 35.3 kg, the mass of the 4 wheels is 10 kg, and the total mass of the 2 hip joints, 2 knee joints, and 2 ankle joints is 36.4 kg. The total mass of the wheeled robot is 81.7 kg, and its center of gravity coordinates are (0,0,0). Based on this, the theoretical analysis of the robot's driving stability on flat ground and slopes is carried out. The C++ programming language was used, and the UG10.0 (Unigraphics NX) 3D digital model design software was used to design the robot in 1:1 size. The ANSYS Workbench2021R2 simulation software was used to construct the finite element space of the digital model. Straight-line driving stability means that the tires do not slip during straight driving, and the condition is that the tire adhesion force is not less than the driving force \(F_{t}\) generated by the ankle joint motor. The driving force is the resultant force in the horizontal direction from the ground resistance \(F_{f}\), air resistance \(F_{w}\) and acceleration resistance \(F_{j}\) during tire rolling. As shown in Figure 8a, the relationship is shown in the following formula. \[ \begin{split} F_{t}=F_{f}+F_{w}+F_{j}\leq F_{\mu}\\ fmg+\frac{1}{2}C_{D}A\rho v^{2}+ma\leq\mu mg\end{split}  \tag{17}\]  
In the formula, \(f\) is the rolling damping coefficient, \(g\) is the acceleration of gravity, \(C_{D}\) is the air damping coefficient, \(\rho\) is the air density, \(A\) is the windward area, \(v\) is the relative speed of the robot and the air, \(m\) is the mass of the robot, \(a\) is the acceleration, and \(\mu\) is the adhesion coefficient between the tire and the road. Under normal circumstances \(C_{D}\), \(\rho\), \(g\), \(A\) and \(m\) remain unchanged, so the instantaneous acceleration \(a\) when the robot travels horizontally and straight mainly depends on the adhesion coefficient \(\mu\) and the rolling damping coefficient \(f\). That is, the constraint condition for the wheel-footed robot to run straight on flat ground without slipping is:  
Figure 7: Different ground terrain datasets. (From (**a**)–(**h**): soil, pebble, sand, cement, grass, asphalt, brick, wood_chips). \[a\leq\frac{\mu mg-fmg-1/2C_{D}A\rho v^{2}}{m} \tag{18}\]  
In the above formula, \(C_{D}\) is 0.3, air density \(\rho\) is 1.29 kg/m\({}^{3}\), gravity acceleration \(g=9.80\) m/s\({}^{2}\), robot windward area \(A=0.45\) m\({}^{2}\), and mass \(m\) is 81.7 kg. On cement floors, bricks and asphalt roads, the adhesion coefficient \(\mu\) between the rubber tire and the ground should be 0.7, the rolling damping coefficient \(f\) should be 0.4, and the maximum straight speed is designed according to 10 m/s. Then, the acceleration \(a\leq 2.83\) m/s\({}^{2}\) during the straight movement of the wheel-footed robot, otherwise slipping may occur. On grass, sand, soil, gravel and wood chips roads, the adhesion coefficient \(\mu\) between the rubber tire and the ground should be 0.6, the rolling damping coefficient \(f\) should be 0.5, and the maximum straight speed is designed according to 6 m/s. Then the acceleration \(a\leq 0.94\) m/s\({}^{2}\) during the straight movement of the wheel-footed robot, otherwise it may slip. As shown in Figure 7(b). The distance between the grounding points \(O_{1}\) and \(O_{2}\) of the two wheels of the robot is \(L\).