Intelligent vehicle trajectory tracking control algorithm based on recursive least square
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摘要: 提出一种实时估计轮胎侧偏刚度的自适应横向最优跟踪控制算法. 路面附着系数的改变使得轮胎侧向力的近似线性区间发生改变，线性近似得到的轮胎侧偏刚度将不再可靠. 基于递归最小二乘算法，以轮胎侧偏角和侧向力作为输入，实时在线估计轮胎的侧偏刚度，进而提出自适应线性二次型调节器（Adaptive Linear Quadratic Regulator，ALQR）控制器. 在Matlab/Simulink和Carsim联合仿真平台上对其有效性和稳健性进行验证. 结果表明，在多种路面附着条件和不同车速下，所设计的控制算法的性能均优于传统线性二次型调节器（Linear Quadratic Regulator，LQR）控制算法，最大横向位置误差和横摆角误差分别降低81.5%和73.0%. 通过实车测试，算法的实际应用性和有效性得到实证，最大轨迹跟踪误差仅为0.56 m.Abstract: A novel adaptive lateral optimal tracking control algorithm for real-time estimation of tire lateral stiffness was proposed. The approximate linear range of tire lateral forces were altered with variation in road surface adhesion coefficients, rendering tire lateral stiffness estimations based on linear approximations unreliable. Utilizing the recursive least squares algorithm and taking tire slip angle and lateral force as inputs, the tire's lateral stiffness was estimated in real time and an adaptive linear quadratic regulator (ALQR) controller was developed. The effectiveness and robustness of the algorithm were validated on a joint simulation platform combining Matlab/Simulink and Carsim. The results demonstrated that under various road surface adhesion conditions and at different vehicle speeds, the performance of the designed control algorithm consistently surpassed that of the traditional linear quadratic regulator (LQR) control algorithm. Specifically, the maximum lateral position error and yaw angle error were reduced by 81.5% and 73.0%, respectively. Real-vehicle tests empirically validated the practical applicability and effectiveness of the algorithm, with the maximum trajectory tracking error being only 0.56 m.
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Key words:
- recursive least squares /
- track tracking /
- optimum control /
- adaptive control
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图 3 不同附着系数下侧偏角与侧向力的关系
Figure 3. Relationship between lateral deflection angle and lateral force under different adhesion coefficients
图 5 高附着工况72 km/h控制效果对比
Figure 5. Comparison of 72 km/h control effect under high adhesion condition
图 6 低附着工况90 km/h控制效果对比
Figure 6. Comparison of 90 km/h control effect under low adhesion condition
表 1 整车参数
Table 1. Vehicle parameters
参数 数值 整车质量m/kg
轴距l/m
汽车的转动惯量Iz/（ kg∙m2）
质心到前轴的距离a/m
质心到后轴的距离b/m1865
2.7
4175
1.232
1.468
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表 2 车速72 km/h跟踪误差
Table 2. Vehicle speed 72 km/h tracking error
控制器 峰值横向位置
误差/m峰值横摆角
误差/（°）ALQR 0.0517 0.2235 LQR 0.0559 0.2340 误差降低/% 7.5 4.5
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表 3 低附着工况跟踪误差
Table 3. Tracking error under low adhesion condition
控制器 峰值横向位置
误差/m峰值横摆角
误差/（°）ALQR 0.5045 1.9675 LQR 2.7265 7.2911 误差降低/% 81.5 73.0
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