# Trajectory Tracking Control Strategy of 20-Ton Heavy-Duty AGV Considering Load Transfer
## 3 Load Transfer Analysis
### Lateral Load Transfer Analysis  
When turning, the AGV's own load and cargo load transfers from the inner wheel to the outer wheel; that is, the lateral load transfer occurs. When the vehicle speed is large, the lateral load transfer is easy to cause the vehicle to roll over [34]. The heavy-duty AGV travels at a small speed and has a large load. Although the load transfer effect does not cause the vehicle to roll over, it causes uneven wheel load on both sides, resulting in changes in the friction between the AGV wheel and the pavement surface. In this paper, the power of the drive motor is almost evenly distributed to the wheels on both sides through the differential, which easily causes the torque of the inner wheel to be too large and the torque of the outer wheel to be insufficient. If the torque output of the motor is increased, it may cause the inner wheel to slip, or the drive motor is overloaded, which reduces the service life of the wheel. In order to avoid large lateral load transfer during vehicle motion, it is necessary to design a controller to optimize the relevant variables. The vertical load acting on the wheel is equal to the vertical reaction force acting on the wheel by the ground. The lateral load transfer can be determined by analyzing the vertical reaction force acting on the AGV wheel by the ground. In order to facilitate the analysis of the vertical reaction force of the left and right wheels, the AGV is simplified to the model shown in Figure 5. The I-shaped frame shown in Figure 5a is supported by elastic elements on the front and rear axles, where \(G_{s}\) is the total gravity of AGV and cargo, \(P_{f}\) and \(P_{r}\) are the roll centers of front and rear suspensions. Figure 5b shows the lateral force distribution of the frame. The centrifugal force \(F_{ay}\) acting on the carriage is distributed to the roll center \(P_{f}\) and \(P_{r}\) of the front and rear suspensions according to the position of the vehicle center of mass, which is balanced by the lateral reaction forces \(F_{s\!f\!f}\) and \(F_{s\!r\!f}\) at the front and rear roll centers. Figure 5c,d are shown as the force diagram of the front and rear axles. In the analysis, the total gravity of the AGV and the cargo in the static state is separated from the vertical reaction force of the ground on the corresponding four wheels as an equilibrium force system. Figure 5: The simplified model of AGV during lateral load transfer is analyzed: (**a**) I-shaped frame force diagram; (**b**) lateral force balance diagram; (**c**) front axle force diagram; (**d**) rear shaft force diagram. In Figure 5b, \(F_{ssf}\) and \(F_{sgr}\) are the lateral reaction forces of the front and rear suspensions to balance the centrifugal force \(F_{ay}\). The following can be obtained:  
\[F_{ssf}=F_{ay}\frac{l_{r}}{l_{r}+l_{f}} \tag{15}\]  
\[F_{sgr}=F_{ay}\frac{l_{f}}{l_{r}+l_{f}} \tag{16}\]  
The torque of the front and rear suspensions relative to the front and rear roll centers is  
\[T_{ff}=K_{ff}f_{r} \tag{17}\]  
\[T_{fr}=K_{fr}f_{r} \tag{18}\]  
where \(K_{\phi}\) and \(K_{\phi r}\) are the roll angle stiffness of the front and rear suspensions, and \(\phi_{r}\) is the frame roll angle.