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摘要: 目前常用于無人駕駛車輛路徑跟蹤控制的有模型控制方法有兩類，一類是基于全局模型的控制方法，另一類是基于局部模型的控制方法。基于全局模型的路徑跟蹤控制中無人駕駛車輛的縱向速度與全局坐標系中的橫向、縱向位移誤差之間存在隨航向角變化的耦合關系，這種耦合關系使得控制器無法將縱向速度作為控制輸入來提高路徑跟蹤控制的精確性。基于局部模型的路徑跟蹤控制器通常采用誤差模型作為參考模型，這種模型使得控制器在參考路徑曲率變化幅度較大時精確性較低。針對前述問題，基于非線性模型預測控制滾動優化的原理，提出一種基于時變局部模型的無人駕駛車輛路徑跟蹤控制方法，并在低速高附著路面、低速低附著路面和高速低附著路面等工況下進行仿真驗證。在仿真結果中，相比于基于全局模型的路徑跟蹤控制器、基于局部模型的路徑跟蹤控制器以及Stanley路徑跟蹤控制器，基于時變局部模型的路徑跟蹤控制器精確性更高，其位移誤差絕對值不超過0.3342 m，航向誤差絕對值不超過0.0913 rad。Abstract: The development of unmanned vehicles has been extremely rapid in recent years. Unmanned vehicles require path tracking control. Based on mature mathematical modeling methods for unmanned vehicles, path tracking control research using model-based control methods, such as feedback linearization control, optimal control, and model predictive control, is very common. Currently, two types of model-based control methods are commonly used in the path tracking control of unmanned vehicles: based on global and local models. The path tracking control based on the global model has a coupling relationship between the longitudinal speed of the unmanned vehicle and the lateral displacement error and longitudinal displacement error in the global coordinate system. Furthermore, this coupling relationship varies with the heading angle, making the controller unable to take the longitudinal speed as a control input to improve the accuracy of path tracking control. Path tracking controllers based on local models usually use errors as reference models, making the controller less accurate when the curvature of the reference path greatly varies. To address the above issue, an unmanned vehicle path tracking control method based on a time-varying local model is proposed considering the principle of rolling optimization of nonlinear model predictive control. Specifically, a time-varying local coordinate system is first established based on the time-varying pose of the vehicle. Then, a reference path in front of the vehicle is entered into this local coordinate system. The model-based iterative prediction is completed in this local coordinate system, and finally, the control is achieved using the optimization solution. The proposed control method is verified by co-simulation using MATLAB and CarSim. The simulation conditions include low-speed and high-adhesion road conditions, low-speed and low-adhesion road conditions, and high-speed low-adhesion road conditions. The simulation results show that the path tracking controller based on the time-varying local model outperforms the path tracking controller based on the global model, the path tracking controller based on the local model, and the Stanley path tracking controller. The maximum absolute value of the displacement error of the proposed controller does not exceed 0.3342 m under all simulation conditions, and the maximum absolute value of the heading error does not exceed 0.0913 rad. Moreover, the proposed controller can still complete the path tracking in situations where other controllers fail, such as high-speed and low-adhesion road conditions.
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Key words:
- unmanned driving /
- vehicle /
- path tracking /
- local coordinate system /
- model /
- predictive control
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圖 3 低速高附著路面仿真軌跡. (a)參考路徑; (b)提出的控制器; (c)基于全局模型的控制器; (d)基于局部模型的控制器; (e)Stanley控制器; (f)無約束的Stanley控制器
Figure 3. Low-speed and high-adhesion road simulation trajectory: (a) reference path; (b) proposed controller; (c) controller based global model; (d) controller based on local model; (e) Stanley controller; (f) Stanley controller without constraints
圖 4 低速高附著路面仿真位移誤差. (a) PC、GC和SC-C的位移誤差; (b) LC和SC的位移誤差
Figure 4. Displacement error of the low-speed and high-adhesion road simulation: (a) displacement error of PC, GC, and SC-C; (b) displacement error of LC and SC
圖 5 低速高附著路面仿真航向誤差. (a) PC、GC和SC-C的航向誤差; (b) LC和SC的航向誤差
Figure 5. Heading error of the low-speed and high-adhesion road simulation: (a) heading error of PC, GC, and SC-C; (b) heading error of LC and SC
圖 6 低速高附著路面仿真橫向速度. (a) PC、GC和LC的橫向速度; (b) SC和SC-C的橫向速度
Figure 6. Lateral speed of the low-speed and high-adhesion road simulation: (a) lateral speed of PC, GC, and LC; (b) lateral speed of SC and SC-C
圖 7 低速高附著路面仿真控制器輸出前輪轉角. (a) PC、GC和LC的前輪轉角; (b) SC和SC-C的前輪轉角
Figure 7. Front wheel angle output by the controller of the low-speed and high-adhesion road simulation: (a) front wheel angle of PC, GC, and LC; (b) front wheel angle of SC and SC-C
圖 8 Stanley控制器輸出的前輪轉角和執行器執行的前輪轉角
Figure 8. Front wheel angle output by the Stanley controller and the front wheel angle act by the actuator
圖 9 低速高附著路面仿真控制器輸出縱向速度
Figure 9. Longitudinal speed output by the controller of the low-speed and high-adhesion road simulation
圖 10 低速高附著路面仿真時間成本
Figure 10. Time cost of the low-speed and high-adhesion road simulation
圖 11 低速低附著路面仿真位移誤差和航向誤差. (a)位移誤差; (b)航向誤差
Figure 11. Displacement and heading errors of the low-speed and low-adhesion road simulation: (a) displacement error; (b) heading error
圖 12 低速低附著路面仿真控制器輸出前輪轉角和縱向速度. (a)前輪轉角; (b)縱向速度
Figure 12. Front wheel angle and longitudinal speed output by the controller of the low-speed and low-adhesion road simulation: (a) front wheel angle; (b) longitudinal speed
圖 13 低速低附著路面仿真橫向速度
Figure 13. Lateral speed of the low-speed and low-adhesion road simulation
圖 14 高速低附著路面仿真位移誤差和航向誤差. (a)位移誤差; (b)航向誤差
Figure 14. Displacement and heading errors of the high-speed low-adhesion road simulation: (a) displacement error; (b) heading error
圖 15 高速低附著路面仿真控制器輸出前輪轉角和縱向速度. (a)前輪轉角; (b)縱向速度
Figure 15. Front wheel angle and longitudinal speed output by the controller of the high-speed low-adhesion road simulation: (a) front wheel angle; (b) longitudinal speed
圖 16 高速低附著路面仿真橫向速度
Figure 16. Lateral speed of the high-speed low-adhesion road simulation
表 1 控制器權重系數
Table 1. Weight coefficient of controllers
Controllers ${ {\boldsymbol{Q} }_1}$ ${ {\boldsymbol{Q} }_2}$ ${ {\boldsymbol{Q} }_3}$ Proposed controller $\left[ {\begin{array}{*{20}{l}} 1&{}&{} \\ {}&{10}&{} \\ {}&{}&1 \end{array}} \right]$ $\left[ {10} \right]$ $\left[ {\begin{array}{*{20}{c}} 1&{} \\ {}&1 \end{array}} \right]$ Controller based on the global model $\left[ {\begin{array}{*{20}{l}} {10}&{}&{} \\ {}&{10}&{} \\ {}&{}&1 \end{array}} \right]$ $\left[ {10} \right]$ $\left[ {\begin{array}{*{20}{c}} 1&{} \\ {}&1 \end{array}} \right]$ Controller based on the local model $\left[ {\begin{array}{*{20}{l}} 1&{}&{} \\ {}&{10}&{} \\ {}&{}&1 \end{array}} \right]$ $\left[ {10} \right]$ $\left[ {\begin{array}{*{20}{c}} 1&{} \\ {}&1 \end{array}} \right]$ 
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表 2 無人駕駛車輛模型參數
Table 2. Parameters of unmanned vehicle model
Symbol Value $ {L_{\text{f}}} $/m 1.04 $ {L_{\text{r}}} $/m 1.56 m/kg 1230 $ {I_z} $/(kg?m?2) 1343.1
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表 3 魔術公式輪胎模型參數
Table 3. Parameters of the magic formula tire model
Symbol Value Symbol Value ${a_0}$ 1.415 ${a_4}$ 2.688×104 ${a_1}$ ?1.149×10?5 ${a_5}$ 0 ${a_2}$ 1.032 ${a_6}$ ?1.236×10?7 ${a_3}$ 3.423×103 ${a_7}$ ?0.1844
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