## 4 Experimental Results
### Experimental Results Discussion  
#### 4.2.1 Experiments in Straight Conditions  
The desired longitudinal velocity of the vehicle was set to vary between 0 and 5 km/h. Figure 8 shows the desired speed at different times. At the beginning of the time, the desired speed was set to 1.8 km/h, and then, at 2 s, the desired speed was set to 5 km/h. Figure 8 compares the response of the actual speed resulting from the three control methods. From 13 to 22 s, the desired longitudinal velocity was set to 3 km/h. After that, from 22 to 24 s, the desired speed was set to 0; from 24 to 34 s, the desired speed was set to \(-\)5 km/h; and from 34 to 42 s, the desired speed was set to \(-\)3 km/h, and then, it was set to 0 until the end. Here, a negative desired speed means an opposite motion direction relative to the starting desired motion direction. The locally magnified graph in Figure 8 shows the response of the actual velocity when the desired velocity was increased at 13 s. As mentioned above, the longitudinal velocity tracking accuracy of the three control methods is approximate in straight conditions. Figure 9 shows the yaw rate tracking performance of the three control methods, which is similar to in the above case. Figure 9 presents the yaw rate tracking performance. The tracking errors of the three controllers are very small and nearly the same. Figure 9-d present the torque on each wheel of the three controllers. The torques on each wheel with Ref2 and the proposed controller are nearly same, and are a little larger than those with Ref1.  
Figure 10a,b compare the responses to heading and heading error. However, while the yaw rate tracking accuracy is approximately the same for the three control methods in Figure 9, the heading and heading errors are different. Compared to at the starting point, from 0 to 25 s, the heading errors with the Ref1 and Ref2 controllers were almost same, and the maximums were about \(-\)0.94\({}^{\circ}\), but the maximum of the heading error with the proposed controller was about \(-\)0.8\({}^{\circ}\), which was the smallest among the three controllers. After 25 s, the heading errors with the Ref1 and the proposed controllers were almost same, and Ref2 had the largest among the three controllers. In other words, the proposed controller reduces the heading error in straight conditions. As a result, the proposed control method has better tracking performance when tracking straight conditions.  
Figure 8: Longitudinal velocity tracking.  
Figure 11 shows the response of the sideslip angle of the vehicle. When the platform was moving in straight conditions, the value of the sideslip angle was small with the three controllers. According to Figure 8, when the desired speed underwent a step-jump change, the motor torque of each wheel, heading, and sideslip angle of the platform underwent a jump change, as shown in Figures 9, 10a and 11. To depict the performance more directly, the phase planes of the sideslip angle vs. yaw rate are shown in Figure 12. It can be  
Figure 10: Comparison of heading and heading error with three controllers: (**a**) Comparison of heading; (**b**) Comparison of heading error.  
Figure 9: Comparison of yaw rate and the desired torque on each wheel with three controllers: (**a**) Comparison of yaw rate; (**b**) Torque on each wheel with Ref1 controller; (**c**) Torque on each wheel with Ref2 controller; (**d**) Torque on each wheel with the proposed controller.  
seen that the movement of the boundary of the vehicle motion states with the proposed controller is smaller than that with the other two controllers. This means that the proposed controller has better stability performance.