基于非线性模型的农用车路径跟踪控制器设计与试验

为提高农用车辆路径跟踪性能,提出一种基于非线性模型预测的路径跟踪控制方法。该方法将路径跟踪问题转换为求解满足速度、转角约束的最优值问题。首先将农用车的非线性运动学模型进行离散化推出递推模型,作为控制器的预测方程;然后建立以农用车运动学模型控制量为状态量的目标函数,设计各个变量的约束条件,把预测方程代入目标函数将其转化为基于递推序列的二次规划法响应问题,在此基础上进行梯度计算解决非线性的约束优化;最后,利用实时反馈与滚动优化实现控制器的闭环校正;重复以上过程,完成预测控制。Matlab仿真结果表明:非线性模型预测控制器能够实现对所设计路径的有效跟踪。相对应的场地试验结果表明:试验小车以2 m/s的速度跟踪参考路径时,最大横向偏差为-4.28 cm;3 m/s跟踪参考路径时,最大纵向偏差为-6.61 cm,可以满足农用车辆对于路径跟踪的精度要求。与线性模型预测控制器的对比试验表明:以3 m/s的速度跟踪圆形路径时,设计的控制器跟踪横向偏差降低了36.8%,纵向偏差降低了32.98%。

Design and Test of Path Tracking Controller Based on Nonlinear Model Prediction

To improve the trajectory tracking performance of agricultural vehicles, a new path tracking control method based on the nonlinear model prediction was proposed. The path tracking problem was transformed into solving the trajectory planning and trajectory tracking control problems with satisfying speed and angle constraint. Firstly, the nonlinear kinematic model of agricultural vehicles was discretized, and the recursive model was derived as the predictive equation of the controller. Then the objective function which defined the system control quantities as the state quantities was set up. Finally, the prediction equation was brought into the objective function to transform the problem into a quadratic programming method based on the recursive sequence and the gradient computation was performed to solve the nonlinear constrained optimization. The closed-loop correction of controller was realized by real-time feedback and rolling optimization. Predictive control can be achieved by repeating the process. Matlab simulation results showed that the nonlinear model prediction controller can realize effective tracking and had strong robust stability. The comparison test with the linear model prediction controller indicated that with the control of the controller, the lateral deviation was reduced by 36.8% and the longitudinal deviation was reduced by 32.98% when the velocity was 3m/s and tracking path was circular. At the same time, the corresponding field test was carried out and the results showed that when the test car was tracking the reference path with the velocity of 2m/s, the maximum lateral deviation was -4.28cm and when the velocity was 3m/s, the maximum longitudinal deviation was -6.61cm.