# Trajectory Tracking Control Strategy of 20-Ton Heavy-Duty AGV Considering Load Transfer
## 4 Design of Trajectory Tracking Control Strategy Considering Load Transfer
### Torque Adaptive Distribution Longitudinal Load Transfer Control Strategy  
The longitudinal load transfer control strategy of torque adaptive distribution is composed of a PID speed controller and torque distribution controller. The PID speed controller realizes the tracking of the speed output by the improved MPC controller, and the output is the total driving torque \(T_{d}\) of the vehicle. The total driving torque is distributed to the front and rear motors through the torque distribution module and finally acts on the dynamic model of the vehicle. The structure diagram of the longitudinal load transfer control strategy with adaptive torque distribution is shown in Figure 8.  
The driving torque \(T_{d}\) formula calculated by the PID speed controller at time \(t\) is:  
\[T_{d}=K_{P}e(t)+K_{I}\int e(t)dt+K_{D}\frac{de(t)}{dt} \tag{43}\]  
\[e(t)=V_{0}(t)-V(t) \tag{44}\]  
where \(V_{0}(t)\) is the expected speed of MPC output at time \(t\); \(V(t)\) is the actual speed of the vehicle at time \(t\); \(K_{p}\), \(K_{I}\), and \(K_{D}\) are the proportional coefficient, integral coefficient, and differential coefficient, respectively, and their specific values of 10,000, 8000, and 0.1 are obtained through continuous trial and adjustment during the simulation process; and \(e(t)\) is the difference between the expected speed and the actual speed at time \(t\).  
Figure 8: Structure diagram of torque adaptive distribution control strategy.  
In order to adapt to the situation of load transfer before and after AGV operation, it is necessary to adaptively allocate the driving torque to prevent the wheel adhesion rate on one side from being large due to the unequal vertical load on the front and rear wheels, thus reducing the driving stability of AGV. The commonly used methods of torque distribution controller include the average distribution method [35], the proportional distribution method according to the vertical load of the wheel [36], and the quadratic programming method with the goal of economy or stability [37]. In this paper, the proportional distribution method of the vertical load of the wheel is used to distribute the torque based on the vertical load of each wheel calculated by (27) to (30).  
\[T_{df}=\frac{F_{Zf{f}}+F_{z{f}r}}{F_{Z{f}l}+F_{z{f}r}+F_{z{r}l}+F_{z{r}r}}T_{d} \tag{45}\]  
\[T_{dr}=\frac{F_{z{r}l}+F_{z{r}r}}{F_{z{f}l}+F_{z{f}r}+F_{z{r}l}+F_{z{r}r}}T_{d} \tag{46}\]  
In order to prevent the driving force of the vehicle from exceeding the pavement adhesion limit, the maximum driving torque constraint of the front and rear wheels is set as follows:  
\[T_{df}\leq\mu\text{min}(F_{z{f}l},F_{z{f}r}) \tag{47}\]  
\[T_{dr}\leq\mu\text{min}(F_{z{r}l},F_{z{r}r}) \tag{48}\]  
where \(\mu\) is the pavement adhesion coefficient.  
At this point, the design of the trajectory tracking control strategy for heavy-duty AGV considering load transfer is completed. The IMPC controller is used for lateral load transfer control. The improvements are in the design of the prediction model and objective function. By predicting the related items of pose error and acceleration, the objective function, which considers tracking error and lateral load transfer, is designed. The longitudinal load transfer control adopts the driving torque proportional distribution controller.