## 4 Motion Simulation and Experiment of the Lunar Exploration Hexapod Robot
### Kinematic Simulation Analysis of the Lunar Exploration Hexapod Robot  
#### 4.2.1 Straight Forward Gait and Inverted Gait Planning  
The walking of the hexapod robot is a cyclical variation process, with each leg having two states: a swing phase and a support phase. The swing phase is the process where a single leg gradually lifts from the supporting state to the preset highest joint position and then gradually lands, completing the positional movement. Subsequently, the legs of the robot support the ground, and the swinging process of the hip joint is called the support phase [27; 28; 29]. The motion gait of the hexapod robot can be classified into tripod gait, quadruped gait, adaptive gait, etc., depending on the number of legs in the support phase. Among them, the tripod gait is the most common gait for hexapod robots. The legs are divided into two groups, and each group moves alternately to maintain the stability of the robot. The tripod gait can be optimized by adjusting gait parameters and changing step \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Setpoint** \\ \hline Contact Type & entity \\ Stiffness & 100.0 (N.mm) \\ Force Exponent & 2.2 \\ Damping & 10.0 (Ns/mm) \\ Penetration Depth & 0.1 (mm) \\ Coulomb Friction & On \\ Static Coefficient & 0.75 \\ Dynamic Coefficient & 0.75 \\ Station Transition Vel. & 100.0 (mm/s) \\ Friction Transition Vel. & 100.0 (mm/s) \\ Parameter & Setpoint \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Contact force parameter settings. Figure 7: Sketch of the overall structure of the lunar exploration hexapod robot. frequencies to adapt to different environmental conditions. The quadruped gait involves four legs supporting the robot during movement, offering higher stability and adaptability compared to the tripod gait but at a slower speed. Adaptive gait is primarily achieved by the robot's own sensors obtaining environmental information and then adjusting the corresponding gait through the control system to adapt to different terrains, which involves relatively complex control [30; 31; 32]. This paper employs the tripod gait for simulating the straight-line motion of the lunar exploration hexapod robot. The traditional tripod gait is illustrated in Figure 8. Firstly, the six legs are numbered and divided into two groups, with legs 1, 3 and 5 forming the first group and legs 2, 4 and 6 forming the second group. The vertical arrows indicate the forward direction of the robot. At t = 0, all six legs support the robot, as shown in Figure 8a. Subsequently, the first group of legs lifts and swings forward within 1 s, while the second group of legs supports the robot, as shown in Figure 8b. After 1 s, the second group of legs lifts and swings forward, while the first group of legs supports the robot, and their hip joints swing backward, as shown in Figure 8c. Figure 8d-f illustrate the alternating movement of the two groups of legs during the robot's forward motion. The robot's straight-line motion is completed through the periodic cycle of these two movements. Figure 9 depicts the temporal changes in the states of the robot's six legs, where white represents the swinging phase and black represents the supporting phase. Figure 8: Conventional gait diagram of the lunar exploration hexapod robot: (**a**) robot initial state; (**b**) robot morphology at 1 s; (**c**) robot morphology at 2 s; (**d**) robot morphology at 3 s; (**e**) robot morphology at 4 s; (**f**) robot morphology at 5 s.  
To address the issues of slow robot movement and joint tremors, this paper proposes an \"inverted gait\" motion mode based on the tripod gait, as shown in Figure 10. At t = 0, all six legs of the robot are supporting the ground, as illustrated in Figure 10a. Subsequently, within 0.5 s, the second group of legs lifts and swings slightly backward, while the first group of legs supports the robot. The robot presents an inverted starting posture, as shown in Figure 10b.