## 3 Results and Discussion
### Feasibility and Necessity of Equivalent Steering Angle Prediction  
In the experiment, in two environments of cement ground and paddy field, the paddy field management machine collected the test data at two traveling speeds of 25 cm/s and 50 cm/s, and the steering control angle was divided into three cases: 0\({}^{\circ}\), \(-\)10\({}^{\circ}\), and +10\({}^{\circ}\). According to the collected data, the least squares circle fitting method was used to fit and analyze the driving trajectory in the environment of matlab2019a to verify the feasibility and effectiveness of the equivalent steering angle prediction. A fitted track for cement ground is shown in Figure 6. The red part in the figure is the actual driving displacement of the paddy field management machine, while the gray part is the trajectory fitting circle. Modes 1, 3, and 5 are 0\({}^{\circ}\), \(-\)10\({}^{\circ}\) and +10\({}^{\circ}\) steering angles at a speed of 25 cm/s. Likewise, modes 2, 4, and 6 were performed at a speed of 50 cm/s.  
When analyzing Figure 6, it can be seen that when the steering angle of the stable steering wheel is changed, the trajectory can be fitted to a closed circle, and the steering 3 angle of the front wheel obtained after fitting deviated from the steering angle of the set control. When this is 0\({}^{\circ}\), the corresponding deviations of steering angles were \(-\)0.5\({}^{\circ}\) and  
Figure 5: Test environments ((**Left**), cement ground; (**Right**), subsiding paddy field).  
Figure 6: Fitting circle diagram of a track on cement ground.  
0.1\({}^{\circ}\); for the corresponding deviation of \(-\)10\({}^{\circ}\), the steering angles were \(-\)2.5\({}^{\circ}\) and \(-\)0.3\({}^{\circ}\); and, when the corresponding deviation is 10\({}^{\circ}\), the steering angles were \(-\)0.2\({}^{\circ}\) and 0.9\({}^{\circ}\). The subsiding paddy field's (mode 1 to 6) driving data fitting circles are shown in Figure 7.  
From Figure 7, it can be seen that when the steering angle of the stable steering wheel changed, the trajectory line could be fitted to a closed circle, and the front wheel steering angle obtained after fitting deviated from the steering angle set control. For 0\({}^{\circ}\), the corresponding deviations of steering angles were 1.2\({}^{\circ}\) and 1.7\({}^{\circ}\); at the corresponding deviation of \(-\)10\({}^{\circ}\), the steering angles were 0.3\({}^{\circ}\) and \(-\)0.3\({}^{\circ}\); and, with the corresponding deviation of 10\({}^{\circ}\), the steering angles were 3\({}^{\circ}\) and 8.1\({}^{\circ}\). Based on the overall analysis of Figures 6 and 7, combined with our analysis of the raw data, the following conclusions can be drawn:  
1. In terms of the asymmetric oscillations between the left and right steering wheels, the frequency and amplitude of the steering oscillations conformed to a normal distribution and could form a fitting circle, which proves the feasibility of the equivalent steering angle prediction.
2. When affected by ground resistance, there was a certain control deviation from the preset steering angle control of the hydraulic steering motor. The effectiveness of the left and right steering wheel controls differed, resulting in a difference between the target control angles of the left and right steering wheels, indicating that prediction of the equivalent steering angle of the machinery is necessary.