Research on Trajectory Tracking Control of Autonomous Vehicle Based on MPC with Variable Predictive Horizon
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摘要: 为了保证自动驾驶汽车轨迹跟踪的精度及行驶过程中的稳定性，提出一种基于车辆横向稳定状态在线识别和模糊算法的变预测时域模型预测控制(MPC)方法。针对车辆稳定状态的在线识别，采用k-means聚类算法对车辆行驶状态参数进行聚类分析，得到聚类质心，通过在线对比当前车辆状态量与不同聚类质心之间的欧氏距离获取车辆的实时安全等级。同时计算出当前车辆的轨迹跟踪横向偏移量，以这二者为输入，通过模糊控制算法在线计算出预测时域的变化量并输出给MPC控制器实现预测时域的自适应调整，最后求解出自动驾驶车辆跟踪轨迹的最优的控制序列，以达到在保持车辆稳定的前提下实现高精度轨迹跟踪控制的目的。CarSim/Simulink联合仿真结果表明，改进后的变预测时域MPC算法在提高自动驾驶汽车轨迹跟踪精度及横向稳定性方面的表现优于传统MPC控制器。
为了保证自动驾驶汽车轨迹跟踪的精度及行驶过程中的稳定性，提出一种基于车辆横向稳定状态在线识别和模糊算法的变预测时域模型预测控制(MPC)方法。针对车辆稳定状态的在线识别，采用k-means聚类算法对车辆行驶状态参数进行聚类分析，得到聚类质心，通过在线对比当前车辆状态量与不同聚类质心之间的欧氏距离获取车辆的实时安全等级。同时计算出当前车辆的轨迹跟踪横向偏移量，以这二者为输入，通过模糊控制算法在线计算出预测时域的变化量并输出给MPC控制器实现预测时域的自适应调整，最后求解出自动驾驶车辆跟踪轨迹的最优的控制序列，以达到在保持车辆稳定的前提下实现高精度轨迹跟踪控制的目的。CarSim/Simulink联合仿真结果表明，改进后的变预测时域MPC算法在提高自动驾驶汽车轨迹跟踪精度及横向稳定性方面的表现优于传统MPC控制器。
Abstract: In order to ensure the trajectory tracking accuracy and driving stability of autonomous vehicles, a model predictive control with variable predictive horizon method was proposed based on on-line identification of vehicle lateral stability state and fuzzy algorithm. Aiming at the online recognition of vehicle stable state, k-means clustering algorithm was used to cluster the parameters of vehicle driving state and obtain the cluster centroid. The real-time safety level of vehicle was obtained by comparing the Euclidean distance between the current vehicle state quantity and different cluster centroids online. At the same time, the lateral offset of the current vehicle track tracking is calculated. With the two as inputs, the variation of prediction time domain is calculated online by fuzzy algorithm and output to MPC controller to realize adaptive adjustment of prediction time domain. Finally, the optimal control sequence of the track tracking of the autonomous vehicle is solved to achieve the goal of high precision trajectory tracking control under the premise of maintaining vehicle stability. The results of CarSim/Simulink co-simulation show that the improved MPC algorithm is superior to the traditional MPC controller in improving the trajectory tracking accuracy and lateral stability of autonomous vehicles.-
Key words:
- automatic drive /
- trajectory tracking /
- k-means algorithm /
- fuzzy algorithm /
- model predictive control
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表 1 车辆具体参数
参数 数值 簧上质量ms/kg 1 723 绕x轴转动量Ix/(kg·m2) 1 243.1 绕y轴转动量Iy/(kg·m2) 4 331.6 绕z轴转动惯量Iz/(kg·m2) 4 175 质心高度h/mm 460 前轮距质心距离lf/mm 1 232 后轮距质心距离lr/mm
轮距d/mm1 468
310
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表 2 聚类质心及对应危险等级
危险等级 $ {v_y}/({\text{km/h}}) $ $ {A_y}/({{\rm{m/}}}{{{\rm{s}}}^{\bf{2}}}) $ $ \dot \varphi /(\deg /{{\rm{s}}}) $ $ Roll/(°) $ $ A{V_x}/[(°)/{{\rm{s}}}] $ $ \beta /(°) $ $ \dot \beta /[(°)/{{\rm{s}}}] $ R1 R2 1 0.053 4 0.023 7 0.568 1 0.146 3 0.481 3 0.033 4 0.084 4 0.065 3 0.064 9 2 0.696 4 0.185 0 3.660 9 1.588 7 3.857 8 0.428 9 1.728 6 0.063 4 0.060 4 3 1.059 0 0.378 8 9.286 5 2.358 6 2.257 2 0.663 7 0.696 0 0.067 9 0.051 0 4 1.139 6 0.369 5 11.864 3 1.571 0 2.999 7 0.677 0 4.188 4 0.043 5 0.062 4 5 2.422 8 0.675 9 18.767 9 4.013 9 12.047 0 1.538 2 2.029 0 0.041 6 0.117 2
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表 3 量化因子
变量 L ey ΔNP 基本论域 [1, 5] [0, 2] [−10, 10] 模糊论域 [−4, 4] [−4, 4] [−10, 10] 量化因子 2 4 1
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表 4 模糊规则表
ΔNP 危险等级L NB NS ZO PM PB 横向偏差ey NB ZO ZO PS PB PB NM NS ZO ZO PM PB NS NS NS NS PM PB ZO NM NS NS PS PB PS NM NM NM PS PB PM NB NB NM NS PB PB PB PB PB PB PB
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表 5 仿真结果及对比
仿真工况 Vx=54 km/h
μ=0.9Vx=30 km/h
μ=0.4Vx=80 km/h
μ=0.9评价系数 WY Wφ WY Wφ WY Wφ NP=20 0.075 5 0.014 8 0.318 8 0.038 1 0.493 1 0.034 6 变预测时域MPC 0.058 1 0.013 3 0.290 4 0.037 3 0.406 8 0.030 7 提升比例(%) 23.0 10.1 8.91 2.1 17.9 11.3
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表 6 变预测时域MPC算法求解时间及方差
仿真工况 Vx=54 km/h
μ=0.9Vx=30 km/h
μ=0.4Vx=80 km/h
μ=0.9平均求解时间/ms 2.799 2 2.554 4 2.604 9 方差/ms 0.044 7 0.046 8 0.050 3
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