Figure 2.PID feed-forward control
2.2 PP algorithm
PP algorithm is a more reliable path tracking control algorithm, Figure 3 shows the geometric relationship schematic diagram of PP algorithm, its principle is to control the vehicle turning radius R, so that the vehicle rear axle center point along the arc to reach the reference path target point (gx, gy) with forward-looking distance l, and then based on Ackermann steering model to calculate the required front wheel turning angle δ for control [29]. This control method has simple control and better robustness, even if large lateral errors and curvature changes occur in the tracking process still achieve better tracking results [30].
Previous studies have shown that the PP-based algorithm or the improved PP algorithm can effectively achieve path tracking under low-speed conditions. For example, literature [31] designed a path tracking controller based on PP algorithm, verified the effectiveness of the controller in tracking under low-speed conditions, and proved that the algorithm leads to complete loss of vehicle stability under high-speed conditions.Yang et al. proposed an improved PP tracking algorithm based on the optimal target point based on the problem of forward distance calculation, which finds the optimal target point by simulating the driver’s forward behavior, and compared with traditional PP algorithm, the tracking error is reduced by more than 20% [32].
The PP algorithm or the improved PP algorithm also has more applications in the path tracking control of parking and farm scenarios. For example, Yu et al. implemented path tracking in a parking scenario based on the PP algorithm, and the results showed that the algorithm met the requirements of smoothness, ride comfort, and safety through the continuous transformation of the steering wheel angle [33].Zhang et al. designed a path tracking algorithm for autonomous navigation of agricultural machines using PP and fuzzy control algorithms [34], and Wang et al. designed a PP model for agricultural applications by adding the heading error rate PP model for agricultural applications, and both showed good tracking accuracy and convergence of the improved algorithm through testing [35].
However, the tracking performance of the PP algorithm depends on the choice of the forward-looking distance, which is difficult to obtain the optimal value, and the tracking performance deteriorates due to the large difference between the system model and the actual vehicle characteristics under high-speed conditions, so the PP algorithm is generally suitable for path tracking control under low speed and small lateral acceleration.