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摘要: 與行駛速度較高的其他無人駕駛工況相比, 自動泊車時參考路徑的曲率較大, 因此車輛轉向輪轉角速度的限制等系統約束條件會嚴重影響自動泊車路徑跟蹤控制器的性能. 為了解決這一問題, 提出了基于非線性模型預測控制的自動泊車路徑跟蹤控制器, 并在MATLAB/Simulink和PreScan聯合仿真環境中將該控制器與基于線性時變模型預測控制的控制器進行了對比. 仿真結果表明非線性模型預測控制器可以實現多約束條件下的自動泊車, 泊車完成后車輛航向與車位中線的夾角為0.0189 rad, 車輛后橋中點與車位中線的距離為0.1045 m, 僅為車身寬度的5.56%. 相比線性時變模型預測控制器, 非線性模型預測控制器具有泊車精度更高、安全裕度更大、泊車耗時更少等優勢. 在實時性方面, 該控制器也能夠滿足自動泊車的需求.Abstract: In megacities, the number of vehicles has rapidly grown. Automatic parking, a special type of unmanned driving, has become an important technology to ease parking difficulties. Path tracking is also a core part of automatic parking. However, during automatic parking, the curvature of the reference path is very large. This poses a challenge in automatic parking and is different from that in high-speed unmanned driving. When the curvature of the reference path is large, the constraints of the system severely restrain the path tracking performance. These constraints include the limit of the steering wheel angle speed. Applying model predictive control is a good way to handle multiple constraints. Recently, a path tracking controller for automatic parking based on linear time-varying model predictive control has been reported. However, for automatic parking, the accuracy of the linearized prediction model is still insufficient. To solve this problem, a path tracking controller based on nonlinear model predictive control was proposed in this paper. This controller was compared with the controller based on linear time-varying model predictive control. The simulation environment is a combination of MATLAB/Simulink and PreScan. The simulation results show that the proposed controller could complete automatic parking with multiple constraints. After the parking was completed, the angle between the vehicle heading and the center line of the parking space was 0.0189 rad. The distance between the midpoint of the rear axle of the vehicle and the center line of the parking space was 0.1045 m. This distance was only 5.56% of the width of the vehicle body. Compared with the controller based on linear time-varying model predictive control, the proposed controller for automatic parking exhibited a higher parking precision, larger safety margin, and less parking time. In terms of real-time performance, the proposed controller could also meet the requirements for automatic parking.
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Key words:
- vehicle /
- automatic parking /
- path tracking /
- motion control /
- nonlinear model predictive control
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圖 4 第一組仿真軌跡.(a)非線性模型預測控制軌跡; (b)線性時變模型預測控制軌跡
Figure 4. Trajectory of the first set of simulation: (a) trajectory of NMPC; (b) trajectory of LTV-MPC
圖 5 第一組仿真控制輸入.(a)縱向速度; (b)轉向輪轉角
Figure 5. Control input of the first set of simulation: (a) longitudinal velocity; (b) angle of steering wheel
圖 6 第一組仿真誤差.(a)橫向誤差; (b)航向誤差
Figure 6. Error of the first set of simulation: (a) displacement error; (b) heading error
圖 8 第二組仿真軌跡.(a)非線性模型預測控制軌跡; (b)改進后非線性模型預測控制軌跡
Figure 8. Trajectory of the second set of simulation: (a) trajectory of NMPC; (b) trajectory of improved NMPC
圖 9 第二組仿真控制輸入. (a)縱向速度; (b)轉向輪轉角
Figure 9. Control input of the second set of simulation: (a) longitudinal velocity; (b) angle of steering wheel
圖 10 第二組仿真誤差. (a)橫向誤差; (b)航向誤差
Figure 10. Error of the second set of simulation: (a) displacement error; (b) heading error
表 1 控制器參數
Table 1. Parameters of controllers
模型 Q1 Q2 Q3 Q4 NMPC $\left[\begin{array}{ccc}1000 & 0 & 0 \\ 0 & 1000 & 0 \\ 0 & 0 & 30000\end{array}\right]$ $\left[\begin{array}{cc}50 & 0 \\ 0 & 50\end{array}\right]$ 50 10 LTV-MPC $\left[\begin{array}{ccc}1000 & 0 & 0 \\ 0 & 1000 & 0 \\ 0 & 0 & 30000\end{array}\right]$ $\left[\begin{array}{cc}50 & 0 \\ 0 & 50\end{array}\right]$ 50 10 
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