基于ARMAX-KF与速度补偿的拖拉机无前轮传感器转角估计方法

Steering Angle Estimation Method for Tractors without Angle Sensor Using ARMAX-KF and Speed Compensation

摘要:

为了解决传统农机导航系统中前轮转角测量传感器不易安装、维护困难以及转角估计不准确等问题，本文提出了一种基于受控自回归滑动平均模型和卡尔曼滤波器的组合模型(Auto-regressive moving average with exogenous input-Kalman filter,ARMAX-KF)与速度补偿的拖拉机无前轮传感器转角估计方法。首先，利用Hammerstein非线性系统对拖拉机的转向系统建模，并采用递归最小二乘法(Recursive least squares method，RLS)将其辨识为ARMAX模型；其次，对后轮轴中心接地点速度进行杆臂误差补偿；最后，提出了ARMAX-KF方法，利用卡尔曼滤波器的校正特性，以拖拉机的运动学转角作为观测值，修正ARMAX模型预测的转角速度积分值，从而估计拖拉机的前轮转角。在速度杆臂补偿测量方法试验验证中，补偿后运动学转角平均绝对误差为1.110°，标准差为1.727°，相比补偿前分别减少61.13%和31.55%；在动态转角试验中，ARMAX模型预测的转角速度标准差为2.439(°)/s，相比采用固定传动比方法误差减少56.58%；采用基于ARMAX-KF的前轮转角估计绝对平均误差为0.649°，标准差为0.371°，相比采用固定传动比和卡尔曼滤波器的方法分别减少56.9%和78.82%；在直线导航跟踪试验中，采用基于ARMAX-KF的前轮转角估计标准差为0.649°，本文提出的方法提高了转角估计精度和农机导航作业质量。

Abstract:

To address the complicated installation and maintenance of the steering angle sensor and inaccurate angle estimation in traditional agricultural machinery navigation systems, the ARMAX-KF method and vehicle speed compensation were proposed to estimate the steering angle of tractors without steering angle sensors. Initially, the Hammerstein nonlinear system was used to model the tractor’s steering system, followed by identification using the RLS method as an ARMAX model. Subsequently, a method was proposed to obtain the velocity of the rear axle center point through speed lever arm compensation. Finally, ARMAX-KF was designed to estimate the steering angle, utilizing the correcting characteristics of the Kalman filter, using the tractor’s kinematic steering angle as the observation value to correct the integrated angle velocity predicted by the ARMAX model, thus estimating the steering angle of the tractor. The method of measuring speed for speed lever arm compensation achieved the average absolute error of the compensated kinematics steering angle of 1.110°, with a standard deviation of 1.727°, reducing the error by 61.13% and 31.55% compared with the values obtained before compensation. In the dynamic angle test, the standard deviation of the angle velocity predicted by the ARMAX model was 2.439(°)/s, reducing the error by 56.58% compared with the method using a fixed transmission ratio. The absolute average error of the steering angle estimation based on ARMAX-KF was 0.649°, with a standard deviation of 0.371°, reducing the error by 56.9% and 78.82%, respectively, compared with the methods using a fixed transmission ratio and the Kalman filter. In the straight-line navigation tracking test, the steering angle estimation standard deviation based on ARMAX-KF was 0.649°. The proposed method improved the accuracy of angle estimation and enhanced the quality of agricultural machinery navigation.