Author Contributions
Conceptualization, H.H.; methodology, H.H.; software, H.H.; validation, H.H.; formal analysis, B.L. and S.B.; investigation, H.H.; resources, H.H., B.L. and S.B.; data curation, H.H.; writing—original draft preparation, H.H., D.Z. and X.Z.; writing—review and editing, H.H., Q.Z. and B.L.; visualization, H.H.; supervision, X.H., B.L. and S.B.; project administration, B.L. and S.B.; funding acquisition, not applicable. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Vehicle two-degree-of-freedom dynamics model.
Figure 1.
Vehicle two-degree-of-freedom dynamics model.
Figure 2.
Steady-state transverse pendulum angle single-point preview model.
Figure 2.
Steady-state transverse pendulum angle single-point preview model.
Figure 3.
Controller design diagram.
Figure 3.
Controller design diagram.
Figure 4.
Sliding mode control systems based on low-pass filters.
Figure 4.
Sliding mode control systems based on low-pass filters.
Figure 5.
The steering wheel angle with and without filtering at RAC = 0.9 and VS = 10 m/s.
Figure 5.
The steering wheel angle with and without filtering at RAC = 0.9 and VS = 10 m/s.
Figure 6.
The steering wheel angle with and without filtering at RAC = 0.9 and VS = 20 m/s.
Figure 6.
The steering wheel angle with and without filtering at RAC = 0.9 and VS = 20 m/s.
Figure 7.
The steering wheel angle with and without filtering at RAC = 0.5 and VS = 10 m/s.
Figure 7.
The steering wheel angle with and without filtering at RAC = 0.5 and VS = 10 m/s.
Figure 8.
The steering wheel angle with and without filtering at RAC = 0.5 and VS = 20 m/s.
Figure 8.
The steering wheel angle with and without filtering at RAC = 0.5 and VS = 20 m/s.
Figure 9.
Carsim–Simulink Joint Simulation Model.
Figure 9.
Carsim–Simulink Joint Simulation Model.
Figure 10.
Double-shift line test road diagram.
Figure 10.
Double-shift line test road diagram.
Figure 11.
Comparison of trajectories and tracking error for different speeds of adaptive preview time.
Figure 11.
Comparison of trajectories and tracking error for different speeds of adaptive preview time.
Figure 12.
Comparison of trajectories and tracking error with different preview times at 5 m/s.
Figure 12.
Comparison of trajectories and tracking error with different preview times at 5 m/s.
Figure 13.
Comparison of trajectories and tracking error with different preview times at 10 m/s.
Figure 13.
Comparison of trajectories and tracking error with different preview times at 10 m/s.
Figure 14.
Comparison of trajectories and tracking error with different preview times at 15 m/s.
Figure 14.
Comparison of trajectories and tracking error with different preview times at 15 m/s.
Figure 15.
Comparison of trajectories and tracking error with different preview times at 20 m/s.
Figure 15.
Comparison of trajectories and tracking error with different preview times at 20 m/s.
Figure 16.
Comparison of trajectories and tracking error with different preview times at 25 m/s.
Figure 16.
Comparison of trajectories and tracking error with different preview times at 25 m/s.
Figure 17.
Comparison of trajectories and tracking error with different preview times at 30 m/s.
Figure 17.
Comparison of trajectories and tracking error with different preview times at 30 m/s.
Figure 18.
Comparison of trajectories and tracking error for different speeds of adaptive preview time.
Figure 18.
Comparison of trajectories and tracking error for different speeds of adaptive preview time.
Figure 19.
Comparison of trajectories and tracking error with different preview times at 5 m/s.
Figure 19.
Comparison of trajectories and tracking error with different preview times at 5 m/s.
Figure 20.
Comparison of trajectories and tracking error with different preview times at 10 m/s.
Figure 20.
Comparison of trajectories and tracking error with different preview times at 10 m/s.
Figure 21.
Comparison of trajectories and tracking error with different preview times at 15 m/s.
Figure 21.
Comparison of trajectories and tracking error with different preview times at 15 m/s.
Figure 22.
Comparison of trajectories and tracking error with different preview times at 20 m/s.
Figure 22.
Comparison of trajectories and tracking error with different preview times at 20 m/s.
Figure 23.
Structural diagram of the PP algorithm, where δ is front wheel steering angle; L is wheelbase of vehicle; ld is preview distance; draw the circle using the preview distance as the chord length of the circle, and R is the radius of the circle; the circle intersects the trajectory at point C; α is the angle of the chord to the vehicle body.
Figure 23.
Structural diagram of the PP algorithm, where δ is front wheel steering angle; L is wheelbase of vehicle; ld is preview distance; draw the circle using the preview distance as the chord length of the circle, and R is the radius of the circle; the circle intersects the trajectory at point C; α is the angle of the chord to the vehicle body.
Figure 24.
Comparison experiments between PP and SMC algorithms at different speeds.
Figure 24.
Comparison experiments between PP and SMC algorithms at different speeds.
Table 1.
Parameters of sliding mode controller.
Table 1.
Parameters of sliding mode controller.
Parameters | Value | Unit |
---|
T | 0.5 (coefficient road adhesion is 0.9) | s |
0.7 (coefficient road adhesion is 0.5) | s |
λ | 60 | - |
η | 10 | - |
Φ1 | 300 | - |
Φ2 | 200 | - |
ξ | 1800 | - |
Table 2.
Carsim import/export channels.
Table 2.
Carsim import/export channels.
Parameters | Import/Export Channels | Unit |
---|
Lead distance to drive model path | IMP_LX_SEN_1 | m |
Steering wheel angle | IMP_STEER_SW | deg |
Lateral distance to target preview point 2 | L_Drv_2 | m |
Longitudinal speed | Vx_SM | km/h |
Yaw rate of vehicle | AV_Y | deg/s |
Slip angle of vehicle | Beta | deg |
Lateral distance to target preview point 1 | L_Drv_1 | m |
Table 3.
Parameters of vehicle.
Table 3.
Parameters of vehicle.
Parameters | Value | Unit |
---|
m | 1820 | kg |
Iz | 1523 | kg·m−2 |
Cf | 108,861 | N·rad−1 |
Cr | 108,861 | N·rad−1 |
isw | 19.562 | - |
Table 4.
Double-shift line road centerline discrete point table.
Table 4.
Double-shift line road centerline discrete point table.
X (m) | Y (m) | Station (m) | X (m) | Y (m) | Station (m) |
---|
0 | 0 | 0 | 95 | 3.4 | 90.291 |
65 | 0 | 65 | 120 | 3.4 | 95.292 |
70 | 0.1 | 70.001 | 125 | 3.3 | 125.296 |
75 | 0.7 | 75.037 | 130 | 2.4 | 130.377 |
80 | 1.8 | 80.156 | 135 | 1.1 | 135.543 |
85 | 2.8 | 85.255 | 140 | 0.2 | 145.627 |
90 | 3.4 | 90.291 | 200 | 0 | 200.627 |
Table 5.
Maximum and minimum offsets for different preview time and different speed for road segment three.
Table 5.
Maximum and minimum offsets for different preview time and different speed for road segment three.
Speed (m/s) | Adaptive Preview Time (m) | 0.5 s Preview Time (m) | 0.8 s Preview Time (m) | 1.2 s Preview Time (m) |
---|
Maximum Offset | Minimum Offset | Maximum Offset | Minimum Offset | Maximum Offset | Minimum Offset | Maximum Offset | Minimum Offset |
---|
5 | 0.0307 | −0.0186 | 0.0307 | −0.0191 | 0.0302 | −0.0298 | 0.0354 | −0.0570 |
10 | 0.0296 | −0.0470 | 0.0296 | −0.0309 | 0.0350 | −0.1281 | 0.0310 | −0.2718 |
15 | 0.0294 | −0.0942 | 0.0278 | −0.1182 | 0.0170 | −0.2640 | −0.0815 | −0.4975 |
20 | 0.0242 | −0.1570 | 0.0152 | −0.2028 | −0.0540 | −0.4232 | −0.2942 | −0.8555 |
25 | −0.0154 | −0.2517 | −0.0172 | −0.2769 | −0.1719 | −0.6516 | −0.5247 | −1.1763 |
30 | 0.2825 | −0.4226 | −0.0937 | −0.4095 | −0.3068 | −0.8712 | −0.7394 | −1.4423 |
Table 6.
Maximum offsets and minimum offsets for different preview times and different speeds for road segment three.
Table 6.
Maximum offsets and minimum offsets for different preview times and different speeds for road segment three.
Speed (m/s) | Adaptive Preview Time (m) | 0.5 s Preview Time (m) | 0.8 s Preview Time (m) | 1.2 s Preview Time (m) |
---|
Maximum Offset | Minimum Offset | Maximum Offset | Minimum Offset | Maximum Offset | Minimum Offset | Maximum Offset | Minimum Offset |
---|
5 | 0.0307 | −0.0186 | 0.0307 | −0.0191 | 0.0302 | −0.0298 | 0.0354 | −0.0570 |
10 | 0.0296 | −0.0470 | 0.0296 | −0.0309 | 0.0350 | −0.1281 | 0.0310 | −0.2718 |
15 | 0.0294 | −0.0942 | 0.0278 | −0.1182 | 0.0170 | −0.2640 | −0.0815 | −0.4975 |
20 | 0.0242 | −0.1570 | 0.0152 | −0.2028 | −0.0540 | −0.4232 | −0.2942 | −0.8555 |