# Trajectory Tracking Control Strategy of 20-Ton Heavy-Duty AGV Considering Load Transfer
## 3 Load Transfer Analysis
### Longitudinal Load Transfer Analysis  
When the vehicle starts, brakes, runs on a ramp or accelerates or decelerates in a straight line, or when there are pits and speed bumps on the pavement surface, under the action of inertial force, the load on the vehicle is transferred before and after, that is, the longitudinal load transfer, which causes the vertical load of the front and rear wheels to change, ranging in size (does not cause the load of the left and right wheels to vary). When the wheel load on one side is low, and the driving torque is large, the wheel slips due to the high wheel adhesion rate. In order to avoid this phenomenon, it is necessary to design a torque distribution controller to redistribute the driving torque of the front and rear motors.  
The longitudinal load transfer can be determined by analyzing the vertical reaction force acting on the AGV wheel on the ground. In order to facilitate the analysis of the vertical reaction force of the front and rear wheels, the rotational inertia resistance moment and the rolling resistance moment are ignored. Due to the low speed, the air lift is ignored. When analyzing the longitudinal load transfer, the heavy-duty AGV is simplified to the model shown in Figure 6. In the figure, \(Gs\) is the total gravity of the vehicle, \(\alpha\) is the slope angle of the pavement, \(h_{g}\) is the centroid height of the vehicle, \(l_{f}\) and \(l_{r}\) are the distances from the front axle and the rear axle to the center of mass of the vehicle, \(1\) is the wheelbase of the vehicle, \(F_{\vec{z}}\) and \(F_{zr}\) are the normal reaction forces acting on the front and rear wheels of the vehicle.  
The torque of each force acting on the vehicle to the center of the contact surface between the front and rear wheels and the pavement can be obtained:  
\[F_{zf}=G_{s}(\frac{l_{f}}{l_{f}+l_{r}}\cos\alpha-\frac{h_{g}}{l_{f}+l_{r}}\sin \alpha)-F_{ax}\frac{h_{g}}{l_{f}+l_{r}} \tag{25}\]  
\[F_{zr}=G_{s}(\frac{l_{r}}{l_{f}+l_{r}}\cos\alpha+\frac{h_{g}}{l_{f}+l_{r}}\sin \alpha)+F_{ax}\frac{h_{g}}{l_{f}+l_{r}} \tag{26}\]  
The normal reaction force acting on each wheel can be obtained by the simultaneous (18)-(21), (25) and (26):  
\[F_{zfl}=\frac{G_{s}}{2}(\frac{l_{f}}{l_{f}+l_{r}}\cos\alpha-\frac{h_{g}}{l_{f} +l_{r}}\sin\alpha)-\frac{F_{ax}}{2}\frac{h_{g}}{l_{f}+l_{r}}+\Delta F_{zfl} \tag{27}\]  
\[F_{zfr}=\frac{G_{s}}{2}(\frac{l_{f}}{l_{f}+l_{r}}\cos\alpha-\frac{h_{g}}{l_{f} +l_{r}}\sin\alpha)-\frac{F_{ax}}{2}\frac{h_{g}}{l_{f}+l_{r}}+\Delta F_{zfr} \tag{28}\]  
\[F_{zrt}=\frac{G_{s}}{2}(\frac{l_{r}}{l_{f}+l_{r}}\cos\alpha+\frac{h_{g}}{l_{f} +l_{r}}\sin\alpha)+\frac{F_{ax}}{2}\frac{h_{g}}{l_{f}+l_{r}}+\Delta F_{zrl} \tag{29}\]  
Figure 6: Simplified model of AGV during longitudinal load transfer.  
\[F_{zrr}=\frac{G_{s}}{2}(\frac{l_{r}}{l_{f}+l_{r}}\cos\alpha+\frac{h_{g}}{l_{f}+l_{r} }\sin\alpha)+\frac{F_{ax}}{2}\frac{h_{g}}{l_{f}+l_{r}}+\Delta F_{zrr} \tag{30}\]  
From (27)-(30), it can be seen that the normal reaction force on each wheel is related to the parameters such as the vertical reaction force variation in the wheel \(\Delta F_{z\!f\!f}\), \(\Delta F_{z\!f\!f}\), \(\Delta F_{z\!r\!f}\), \(\Delta F_{z\!rr}\); the total gravity of the vehicle \(G_{s}\); the slope angle of the pavement \(\alpha\); and the centroid height of the vehicle \(h_{g}\), and has a high nonlinear relationship with the slope angle of the pavement \(\alpha\). Based on the vertical load of each wheel calculated by Formulas (27)-(30), the subsequent torque distribution control strategy can be designed.