# Trajectory Tracking Control Strategy of 20-Ton Heavy-Duty AGV Considering Load Transfer
## 2 Establishment of Heavy-Duty AGV Vehicle Model
### Three-Degree-of-Freedom Vehicle Kinematics Model  
The steering modes of heavy-duty AGV mainly include four-wheel independent drive, four-wheel independent steer (4 WID/4 WIS) type [30], differential wheel type [31], Mecanum wheel type [32], single Ackerman steering type [33], and double Ackerman steering type. Although the 4 WID/4 WIS is flexible and changeable, the cost of the 4 WID/4 WIS is high, and the requirements for the motor and control accuracy are high. The differential wheel steering structure is relatively simple, and the cost is relatively low, but the requirements for ground flatness are harsh, and the load is light. Mecanum wheel steering is more flexible and can achieve movement in all directions, but the ground flatness requirements are higher, and the price is high; although the structure of the single Ackerman steering is simple, the flexibility is poor because there is only one steering shaft. Double Ackerman steering has higher flexibility, a smaller steering radius, and better driving stability, which is suitable for complex environments with changeable pavements. To sum up, the heavy-duty AGV designed in this paper is used in the scene where the outdoor factory pavement is changeable and has certain flexibility and stability requirements, so the double Ackerman steering is selected. A front and rear dual-motor drive configuration is adopted, with permanent magnet synchronous motors selected as the drive motors. Considering the operating conditions and design requirements of the heavy-duty AGV during operation, the power of a single-drive motor is calculated. The finally selected motor has a rated power of 75 kW, a rated torque of 477 N\(\cdot\)m, and a rated speed of 1500 r/min. The double Ackerman steering geometric model is shown in Figure 2. It mainly includes the front and rear wheels and the steering center, in which the steering wheels  
Figure 1: Three-dimensional model of heavy-duty AGV: 1—Drive module; 2—Control module; 3—Power module; 4—Lift module; 5—Ladar. on both sides are connected by the steering axle. When the model is established, the main parameters considered are the front and rear left and right wheel angles \(\delta_{fl}\), \(\delta_{fr}\), \(\delta_{rl}\), \(\delta_{rr}\), which are simplified to the equivalent front and rear wheel angles \(\delta_{f}\), \(\delta_{r}\); wheel track \(W\); wheelbase \(l\); the longitudinal distance \(l_{1}\) and \(l_{2}\) from the steering center to the front and rear axles; and the vertical distance \(R\) from the steering center to the center of the car body. \(CE\) is the steering center of AGV. From Figure 2, the relationship between the rotation angles \(\delta_{fl}\), \(\delta_{fr}\), \(\delta_{rt}\), \(\delta_{rr}\) of each wheel and the rotation angles \(\delta_{f}\), \(\delta_{r}\) of the front and rear wheels after cycling can be obtained as follows:  
\[\delta_{fl}=\arctan\frac{2l_{1}}{2R-W} \tag{1}\]  
\[\delta_{fr}=\arctan\frac{2l_{1}}{2R+W} \tag{2}\]  
\[\delta_{rf}=\arctan\frac{-2l_{2}}{2R-W} \tag{3}\]  
\[\delta_{rr}=\arctan\frac{-2l_{2}}{2R+W} \tag{4}\]  
where \(R=\frac{l_{1}}{\tan\delta_{f}}\), \(l_{1}=\frac{l\cdot\tan\delta_{f}}{\tan\delta_{f}-\tan\delta_{r}}\), \(l_{2}=\frac{-l\cdot\tan\delta_{r}}{\tan\delta_{f}-\tan\delta_{r}}\)  
The relationship between \(\delta_{f}\) and \(\delta_{r}\) is  
\[\frac{\tan\delta_{f}}{\tan\delta_{r}}=\frac{l_{1}}{l_{1}-l} \tag{5}\]  
From (1)-(4), the relationship between the steering wheel angles on both sides can be obtained:  
\[\cot\delta_{fr}-\cot\delta_{fl}=\frac{W}{l_{1}} \tag{6}\]  
\[\cot\delta_{rf}-\cot\delta_{rr}=\frac{W}{l_{2}} \tag{7}\]  
From (6) and (7), it can be seen that when the wheel track \(W\) is determined, the size of \(l_{1}\) and \(l_{2}\) is related to the wheel rotation angle \(\delta_{fl}\), \(\delta_{fr}\), \(\delta_{rl}\), and \(\delta_{rr}\). The wheels on both sides are connected by the steering bridge.