## 4 Simulation and Experiment
### Experimental Verification of Model  
An experiment was used to verify the effect of the pressing component and the simulation method on the dynamics of the FPTLIR landing. The experimental frame was built as shown in Figure 16. The following parameters were used for the experiment. (1) The type of the PTL was LGJ-95/55, and the span was 10 m. It had a diameter of 16 mm,  
Figure 15: The Z-displacement t and attitude changes of FPTLIRs with different masses during landing at the midpoint of the PTL: (**a**) Z-displacement; (**b**) pitch angle; (**c**) roll angle; (**d**) yaw angle. a linear density of 707 kg/km, and an elastic modulus of 105 GPa. (2) A lifting platform was installed at the left end of the frame to adjust the slope of the PTL. (3) The 3D tilt sensor (MPU6050) was used to collect the FPTLIR's attitude information. (4) The position of FPTLIR was measured by an IMU. (5) The FSR used was the IMS003-C10A-50, which was attached to the surface of the travelling wheel to monitor changes in contact force. It was embedded beneath the wheel surface material, with a total of six units installed to ensure that contact force could still be accurately measured even in cases of slippage at the contact points. (6) The PC was used to communicate with the STM32 and FSR data acquisition card for FSR to collect experimental data. The parameters were set in MATLAB to match those used in the experiment. The simulation was run for 40 s with a convergence criterion of \(1\times 10^{-3}\). A total of 20 nodes were set up for the simulation. The comparison between experimental and simulation results demonstrates that the simulation model exhibits strong fitting capability to the experimental data (Figure 17). For Z-displacement, the experimental initial amplitude was \(\pm\)0.1 m, while the simulation result was also \(\pm\)0.1 m, and both showed a damped oscillation pattern. The pitch angle had an experimental initial amplitude of \(\pm\)0.5\({}^{\circ}\), while the simulation was \(\pm\)0.3\({}^{\circ}\), with slight fluctuations persisting after stabilization. The roll angle's initial amplitude was \(\pm\)2.5\({}^{\circ}\) in both the experiment and simulation, but the simulation decayed more slowly, stabilizing around 15 s with a smoother trend, whereas high-frequency vibrations persisted up to 20 s in the experiment. For the yaw angle, the experimental results oscillated near 0\({}^{\circ}\) before stabilizing around that value, while the simulation stabilized near 0\({}^{\circ}\). The stabilization trends were similar. Regarding contact force in Figure 18, the force value rose rapidly in the initial stage, with the experiment peaking at 400 N around 5 s, stabilizing at approximately 380 N. The simulation displayed a similar trend but with smoother results. However, experimental data showed oscillations after 5 s, likely due to changes in the contact area caused by FPTLIR attitude adjustments. The comparison of experimental and simulation data through the calculation of mean relative error (MRE) is shown in Table 3.  
Overall, the simulation model effectively captures the system's dynamic trends and aligns well with experimental results. The MRE of the Z-displacement, contact force, and roll angle is relatively small, with values of 0.004, 0.044, and 0.079, respectively. The discrepancies, primarily in amplitude and stabilization time, are likely due to external disturbances in the experimental system or simplifications in the simulation model. The relatively larger MRE in the roll angle and yaw angle was attributed to their smaller fluctuation ranges and relatively higher susceptibility to interference. Nevertheless, the simulation model reproduces the key dynamic characteristics of the contact force, Z  
Figure 16: Experiment of the FPTLIR walking along the PTL. displacement, and angles, demonstrating a high reliability in predicting system dynamics under ideal conditions.