# A Review of Foot-Terrain Interaction Mechanics for Heavy-Duty Legged Robots
## 2 Supporting Feet of Heavy-Duty Legged Robots
### Spherical Supporting Foot Configurations
Hemispherical Supporting Foot Configurations  
The SILO6 robot [54] is a hexapod robot system used for humanitarian demining missions. According to the static stability design, a triangular gait is adopted to achieve the maximum speed of the robot. The foot is fixed to the hemisphere of the ankle, with a simple structure and good performance on the hard terrain. But increasing the radius of the ball on the loose terrain will reduce the sinking amount. At the same time, on hard terrain, the radius of the ball is too large to make it attempt to rotate, changing the positions of the foot's support. The SILO-6 robot is shown in Figure 14a. The SDU Hex electric hexapod robot [55] designed by researchers from Shandong University in 2021 can achieve leg arm reuse and strong operation. The structure of the entire SDU Hex robot is shown in Figure 14b. The feet adopt hemispherical structures. And the feet are equipped with a high adhesion damping rubber pattern and air chamber, reducing the impact force during the interaction between the foot and the terrain. The hemispherical feet and spherical feet have the same contact methods with the terrain, both of which are point contact. Therefore, the mechanical models of the two above can be generalized and will not be explained in detail here. Square Supporting Foot Configurations  
The Hydraulic Landmaster robot is a large hexapod robot that works on steep forest terrain, as shown in Figure 15. The weight of the robot is 3950 kg, with a rated load of 1000 kg. The size is 3.6 m \(\times\) 2.3 m \(\times\) 2.6 m, with a maximum height of 4.5 m, and a maximum height of 1.7 m when passing through obstacles. Electric Landmaster 3 is the previous generation of Hydraulic Landmaster. The electric Landmaster 3 robot has a weight of 82 kg and a rated load of 30 kg. Both robots have the same model structure with principle, and both have significant heavy-duty capacity. Square feet are used at the feet of robots [1]. Figure 14: Robots of SILO-6 and SDU Hex: (**a**) SILO-6 [54]; (**b**) SDU Hex [55]. The Petman robot [56] developed in the United States is a humanoid bipedal robot, as shown in Figure 16a. The maximum speed can reach 7.2 km/h. The robot's use of Big Dog's leg structure and electronic equipment enables faster design and testing experiments. When pushing moderately from the side while walking, it can restore its balance. Square feet are used at the feet. Another humanoid bipedal robot Altas [57] also adopts square foot structures, as shown in Figure 16b. The advantages of square configuration are that the design is relatively simple, and no spiral structure design is required. The disadvantage is that it cannot adapt to more complex terrain. The rectangular foot-terrain mechanics models can be obtained by multiplying the average stress distribution with the plantar area. The rectangular foot-terrain mechanics models can be given in Equation (4). Then  
\[\left\{ \begin{array}{l}F_{\text{N}}(t)=\big{(}k_{c}\cdot a+k_{\varphi}\cdot a \cdot b\big{)}\delta^{n}\\ F_{\text{T}}(t)=a\cdot b\cdot c+F_{\text{N}}(t)\cdot\text{tan}\,\varphi\end{array} \right. \tag{4}\]  
where \(a\), \(b\), and \(c\) are the dimensions of the long side, wide side, and high side of the rectangular foot, respectively. Special Supporting Foot Configurations  
Charlie is a quadruped robot designed based on primitive humans. The feet of the front legs adopt curved structures [58; 59]. The quadruped forward movement of the robot  
Figure 16: Robots of Petman and Altas: (**a**) Petman [56]; (**b**) Altas [57]. Figure 15: Hydraulic Landmaster robot [1]. can be achieved. The Charlie robot can walk upright with both feet. The quadruped and bipedal walking postures are, respectively, shown in Figure 17a,b. In the 1960s, General Electric designed a quadruped walking truck for the US Army, as shown in Figure 18. The shape of the foot is curved [60]. The advantages of curved feet are that they have simpler structures and a lighter weight. Their disadvantage is that they cannot carry a larger mass.