# The Full-Field Path Tracking of Agricultural Machinery Based on PSO-Enhanced Fuzzy Standley Model
## 1 Introduction  
Intelligent agricultural machinery is a crucial support for unmanned farm and smart agriculture, where automatic navigation is the core technology and has been widely studied [1; 2]. During the special period of the outbreak of the new crown epidemic, the automatic navigation of agricultural machinery provides an important guarantee for agricultural production and food security. The path tracking of agricultural machinery controls the agricultural machinery driving along a predetermined trajectory autonomously, which is an important part of the unmanned autonomous operation of agricultural machinery in the farmland [3; 4]. The widely employed path tracking control methods for agricultural machinery include PID control, pure pursuit control, fuzzy control, neural network-based control and optimal control [5; 6; 7; 8; 9], to name a few. [PERSON] et al. [10] proposed a cascaded navigation control method for straight line path tracking, which separates the navigation control into path tracking control and steering control, and the standard deviation of the lateral error is 0.04 m. [PERSON] et al. [11] developed a path tracking controller by integrating an adaptive neural network estimator and a saturated auxiliary system, and compared it with the traditional methods. The controller reduces the tracking error by more than 28%. Amodel predictive control-based path following the controller was developed for high-speed vehicle path tracking in [12], where the fluctuation of longitudinal velocity is compensated in the predicted horizon to reduce the state prediction error. The experimental results indicate that the controller not only reduces the lateral and heading deviation effectively but also maintains the control stability under large vehicle maneuver. [PERSON] et al. [13] proposed an adaptive sliding mode control method based on non-time reference and RBF neural network to handle uncertain disturbances. The experiments demonstrate that the proposed method not only improves the path tracking performance but also eliminates the chattering phenomenon when the wheeled mobile robot suffers from uncertain disturbances. In order to overcome the disadvantages of pure pursuit in high-speed path tracking, a model predictive active yaw control implementation of pure pursuit path tracking was proposed in [14], which improves the tracking performance at high speeds by accommodating the vehicle's steady-state lateral dynamics. Most of the abovementioned adaptive path tracking algorithms improve the tracking precision or robustness with respect to disturbances at the cost of computational complexity, which hinders their application from real-time path tracking application. Stanley model (SM) is a nonlinear feedback function based on lateral tracking error, which generates the steer angle command by employing the relative geometric relationship between vehicle's pose and predefined trajectory. SM does not depend on the look-ahead distance as pure pursuit, and its lateral tracking error converges to zero exponentially [15]. The unmanned vehicle based on SM is the winner of DARPA's second unmanned vehicle challenge, whereas its application on the automatic navigation of agricultural machinery is rarely reported. The adaptive parameter tuning is an active research field for a geometric-based path tracking controller, and there is similar problem for SM especially when vehicle maneuver or road conditions vary from time to time. The look-ahead distance of pure pursuit is adjusted in [16] by using improved particle swarm optimization (PSO), which indicates when the speed of agricultural machinery is 0.7 m/s and the driving distance exceeds 5 m, the maximum lateral error is 0.02 m. [PERSON] et al. [17] utilized the multi-population genetic algorithm to optimize the parameters of SM controller, and results show that the path tracking performance is improved by 41.72% and 48.61% for two typical tractor turning methods (U and \(\Omega\) routes), compared with SM without optimization. [PERSON] et al.