
Acta Armamentarii ›› 2025, Vol. 46 ›› Issue (11): 250023-.doi: 10.12382/bgxb.2025.0023
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HE Yang*(
), LI Gang, JI Fengbiao, ZHOU Junpeng
Received:2025-01-07
Online:2025-11-27
Contact:
HE Yang
CLC Number:
HE Yang, LI Gang, JI Fengbiao, ZHOU Junpeng. Research on Intelligent Automobile Trajectory Tracking Control Method Based on VUFAMPC[J]. Acta Armamentarii, 2025, 46(11): 250023-.
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| 估计方法 及参考值 | 附着 系数 | 轮胎力 | | | RMSE | |
|---|---|---|---|---|---|---|
| SRCKF | 0.85 | FyfL | 6114 | 1868 | 9.59 | |
| FyfR | 5549 | 1719 | 9.83 | |||
| FyrL | 4031 | 1085 | 10.69 | |||
| FyrR | 3751 | 1032 | 11.24 | |||
| 0.85~0.45 | FyfL | 6062 | 1703 | 15.01 | ||
| FyfR | 5456 | 1704 | 15.26 | |||
| FyrL | 4095 | 1085 | 17.23 | |||
| FyrR | 3944 | 1071 | 17.41 | |||
| ST-SRCKF | 0.85 | FyfL | 5973 | 1856 | 4.50 | |
| FyfR | 5419 | 1737 | 4.81 | |||
| FyrL | 4095 | 1084 | 4.53 | |||
| FyrR | 3715 | 1069 | 4.87 | |||
| 0.85~0.45 | FyfL | 5906 | 1784 | 6.03 | ||
| FyfR | 5343 | 1715 | 6.16 | |||
| FyrL | 3962 | 1104 | 6.33 | |||
| FyrR | 3623 | 1053 | 6.46 | |||
| 参考值 | FyfL | 5825 | 1831 | |||
| FyfR | 5337 | 1765 | ||||
| FyrL | 4073 | 1001 | ||||
| FyrR | 3717 | 1046 | ||||
Table 1 Statistical values of tire lateral force estimation
| 估计方法 及参考值 | 附着 系数 | 轮胎力 | | | RMSE | |
|---|---|---|---|---|---|---|
| SRCKF | 0.85 | FyfL | 6114 | 1868 | 9.59 | |
| FyfR | 5549 | 1719 | 9.83 | |||
| FyrL | 4031 | 1085 | 10.69 | |||
| FyrR | 3751 | 1032 | 11.24 | |||
| 0.85~0.45 | FyfL | 6062 | 1703 | 15.01 | ||
| FyfR | 5456 | 1704 | 15.26 | |||
| FyrL | 4095 | 1085 | 17.23 | |||
| FyrR | 3944 | 1071 | 17.41 | |||
| ST-SRCKF | 0.85 | FyfL | 5973 | 1856 | 4.50 | |
| FyfR | 5419 | 1737 | 4.81 | |||
| FyrL | 4095 | 1084 | 4.53 | |||
| FyrR | 3715 | 1069 | 4.87 | |||
| 0.85~0.45 | FyfL | 5906 | 1784 | 6.03 | ||
| FyfR | 5343 | 1715 | 6.16 | |||
| FyrL | 3962 | 1104 | 6.33 | |||
| FyrR | 3623 | 1053 | 6.46 | |||
| 参考值 | FyfL | 5825 | 1831 | |||
| FyfR | 5337 | 1765 | ||||
| FyrL | 4073 | 1001 | ||||
| FyrR | 3717 | 1046 | ||||
| dey | ey | |||||||
|---|---|---|---|---|---|---|---|---|
| 正 | 负 | |||||||
| 正 | ψ<ψref | ey ↑ | τQ ↑ | τR↑ | ψ>ψref | ey ↓ | τQ ↑ | τR ↓ |
| 负 | ψ<ψref | ey ↓ | τQ↑ | τR↓ | ψ>ψref | ey ↑ | τQ↑ | τR ↑ |
Table 2 Input and output relationship list
| dey | ey | |||||||
|---|---|---|---|---|---|---|---|---|
| 正 | 负 | |||||||
| 正 | ψ<ψref | ey ↑ | τQ ↑ | τR↑ | ψ>ψref | ey ↓ | τQ ↑ | τR ↓ |
| 负 | ψ<ψref | ey ↓ | τQ↑ | τR↓ | ψ>ψref | ey ↑ | τQ↑ | τR ↑ |
| τQ/τR | ey | |||||||
|---|---|---|---|---|---|---|---|---|
| NB | NM | NS | ZO | PS | PM | PB | ||
| dey | NB | PB/PB | PM/PB | PS/PB | ZO/PB | PS/PB | PM/PB | PB/PB |
| NM | PB/PM | PM/PM | PS/PM | ZO/PM | PS/PM | PM/PM | PB/PM | |
| NS | PB/PS | PM/PS | PS/PS | ZO/PS | PS/PS | PM/PS | PB/PS | |
| ZO | PB/PS | PM/PS | PS/ZO | ZO/ZO | PS/ZO | PM/PS | PB/PS | |
| PS | PB/PS | PM/PS | PS/PS | ZO/PS | PS/PS | PM/PS | PB/PS | |
| PM | PB/PM | PM/PM | PS/PM | ZO/PM | PS/PM | PM/PM | PB/PM | |
| PB | PB/PB | PM/PB | PS/PB | ZO/PB | PS/PB | PM/PB | PB/PB | |
Table 3 Fuzzy rules
| τQ/τR | ey | |||||||
|---|---|---|---|---|---|---|---|---|
| NB | NM | NS | ZO | PS | PM | PB | ||
| dey | NB | PB/PB | PM/PB | PS/PB | ZO/PB | PS/PB | PM/PB | PB/PB |
| NM | PB/PM | PM/PM | PS/PM | ZO/PM | PS/PM | PM/PM | PB/PM | |
| NS | PB/PS | PM/PS | PS/PS | ZO/PS | PS/PS | PM/PS | PB/PS | |
| ZO | PB/PS | PM/PS | PS/ZO | ZO/ZO | PS/ZO | PM/PS | PB/PS | |
| PS | PB/PS | PM/PS | PS/PS | ZO/PS | PS/PS | PM/PS | PB/PS | |
| PM | PB/PM | PM/PM | PS/PM | ZO/PM | PS/PM | PM/PM | PB/PM | |
| PB | PB/PB | PM/PB | PS/PB | ZO/PB | PS/PB | PM/PB | PB/PB | |
| 长×宽×高/m 4.78×1.87×1.46 | m/kg 1420 | Ix/(kg·m-2) 635.3 | Iy/(kg·m-2) 1837.8 | Iz/(kg·m-2) 2273.1 | lf/m 1.22 | lr/m 1.58 |
|---|---|---|---|---|---|---|
| Tf/m | Tr/m | h/m | Cxlf、Cxlr/(105N·m-1) | 轮胎规格 | s | Re/mm |
| 1.68 | 1.69 | 0.55 | 8.5 | 215/55 R17 | 0.2 | 334.15 |
Table 4 Related parameters of automobile
| 长×宽×高/m 4.78×1.87×1.46 | m/kg 1420 | Ix/(kg·m-2) 635.3 | Iy/(kg·m-2) 1837.8 | Iz/(kg·m-2) 2273.1 | lf/m 1.22 | lr/m 1.58 |
|---|---|---|---|---|---|---|
| Tf/m | Tr/m | h/m | Cxlf、Cxlr/(105N·m-1) | 轮胎规格 | s | Re/mm |
| 1.68 | 1.69 | 0.55 | 8.5 | 215/55 R17 | 0.2 | 334.15 |
| Ts/s 0.05 | T/s 0.1 | Nc/s 15 | Np/s 30 | αf,r/(°) (-6,6) | Δu/(°) [-0.015,0.015] | β [0,1] | ε 10 |
|---|---|---|---|---|---|---|---|
| γ | υ | Ej | Uj | ρ | δ/(°) | τQ | τR |
| 0.98 | 1.5 | [-3,3] | [0,1] | 1 000 | [-30,30] | (0,1] | (0,1] |
Table 5 Controller parameters
| Ts/s 0.05 | T/s 0.1 | Nc/s 15 | Np/s 30 | αf,r/(°) (-6,6) | Δu/(°) [-0.015,0.015] | β [0,1] | ε 10 |
|---|---|---|---|---|---|---|---|
| γ | υ | Ej | Uj | ρ | δ/(°) | τQ | τR |
| 0.98 | 1.5 | [-3,3] | [0,1] | 1 000 | [-30,30] | (0,1] | (0,1] |
| 参数 | FMPC | AMPC | VUFAMPC | 优化量% | |
|---|---|---|---|---|---|
| VUFAMPC/ FMPC | VUFAMPC/ AMPC | ||||
| 超调量/% | 15.20 | 22.90 | 4.10 | 11.1 | 18.8 |
| 上升时间/s | 0.38 | 0.43 | 0.33 | 13.2 | 23.3 |
| 峰值时间/s | 0.82 | 0.95 | 0.64 | 21.9 | 32.6 |
| 过渡时间/s | 1.18 | 1.96 | 0.63 | 46.6 | 67.9 |
Table 6 Statistical values
| 参数 | FMPC | AMPC | VUFAMPC | 优化量% | |
|---|---|---|---|---|---|
| VUFAMPC/ FMPC | VUFAMPC/ AMPC | ||||
| 超调量/% | 15.20 | 22.90 | 4.10 | 11.1 | 18.8 |
| 上升时间/s | 0.38 | 0.43 | 0.33 | 13.2 | 23.3 |
| 峰值时间/s | 0.82 | 0.95 | 0.64 | 21.9 | 32.6 |
| 过渡时间/s | 1.18 | 1.96 | 0.63 | 46.6 | 67.9 |
| 工况 | | FMPC | VUFMPC /FMPC | AMPC/ FMPC/ VUFMPC | VUFAMPC/ FMPC/ VUFMPC/ AMPC |
|---|---|---|---|---|---|
| 90km/h μ=0.85 | 最大值 | 4.65 | 3.86 | 1.61 | 1.21 |
| 均值 | 0.65 | 0.41 | 0.25 | 0.18 | |
| RMSE | 1.201 | 0.876 | 0.451 | 0.368 | |
| 优化量/ % | 最大值 | 17.0 | 65.4/ 58.3 | 73.9/68.7/ 24.8 | |
| 均值 | 36.9 | 61.5/ 39 | 72.3/56.1/ 28 | ||
| 90km/h μ=0.45 | 最大值 | 7.67 | 4.98 | 3.64 | 1.54 |
| 均值 | 5.15 | 0.62 | 0.43 | 0.17 | |
| RMSE | 3.861 | 1.178 | 0.923 | 0.529 | |
| 优化量/ % | 最大值 | 35.1 | 52.5/ 26.9 | 79.9/69.1/ 57.7 | |
| 均值 | 87.9 | 91.7/ 30.6 | 96.7/72.6/ 60.5 |
Table 7 Statistical values of lateral trajectory tracking error
| 工况 | | FMPC | VUFMPC /FMPC | AMPC/ FMPC/ VUFMPC | VUFAMPC/ FMPC/ VUFMPC/ AMPC |
|---|---|---|---|---|---|
| 90km/h μ=0.85 | 最大值 | 4.65 | 3.86 | 1.61 | 1.21 |
| 均值 | 0.65 | 0.41 | 0.25 | 0.18 | |
| RMSE | 1.201 | 0.876 | 0.451 | 0.368 | |
| 优化量/ % | 最大值 | 17.0 | 65.4/ 58.3 | 73.9/68.7/ 24.8 | |
| 均值 | 36.9 | 61.5/ 39 | 72.3/56.1/ 28 | ||
| 90km/h μ=0.45 | 最大值 | 7.67 | 4.98 | 3.64 | 1.54 |
| 均值 | 5.15 | 0.62 | 0.43 | 0.17 | |
| RMSE | 3.861 | 1.178 | 0.923 | 0.529 | |
| 优化量/ % | 最大值 | 35.1 | 52.5/ 26.9 | 79.9/69.1/ 57.7 | |
| 均值 | 87.9 | 91.7/ 30.6 | 96.7/72.6/ 60.5 |
| 工况 | | FMPC | VUFMPC | AMPC/VUFMPC | VUFAMPC/VUFMPC/AMPC |
|---|---|---|---|---|---|
| 90km/h μ∈0.85~0.45 | 最大值 | 12.80 | 7.34 | 1.78 | 1.35 |
| 均值 | 5.04 | 1.70 | 0.61 | 0.22 | |
| RMSE | 6.72 | 2.809 | 0.710 | 0.405 | |
| 优化量/% | 最大值 | 75.7 | 81.6/24.2 | ||
| 均值 | 64.1 | 87.1/63.9 | |||
| 120km/h μ∈0.85~0.45 | 最大值 | 21.90 | 7.79 | 2.81 | 1.55 |
| 均值 | 3.93 | 1.88 | 0.34 | 0.18 | |
| RMSE | 7.077 | 3.061 | 0.786 | 0.415 | |
| 优化量/% | 最大值 | 63.9 | 80.1/44.8 | ||
| 均值 | 81.9 | 90.4/47.1 |
Table 8 Statistical values of lateral trajectory tracking errors(dockingroad)
| 工况 | | FMPC | VUFMPC | AMPC/VUFMPC | VUFAMPC/VUFMPC/AMPC |
|---|---|---|---|---|---|
| 90km/h μ∈0.85~0.45 | 最大值 | 12.80 | 7.34 | 1.78 | 1.35 |
| 均值 | 5.04 | 1.70 | 0.61 | 0.22 | |
| RMSE | 6.72 | 2.809 | 0.710 | 0.405 | |
| 优化量/% | 最大值 | 75.7 | 81.6/24.2 | ||
| 均值 | 64.1 | 87.1/63.9 | |||
| 120km/h μ∈0.85~0.45 | 最大值 | 21.90 | 7.79 | 2.81 | 1.55 |
| 均值 | 3.93 | 1.88 | 0.34 | 0.18 | |
| RMSE | 7.077 | 3.061 | 0.786 | 0.415 | |
| 优化量/% | 最大值 | 63.9 | 80.1/44.8 | ||
| 均值 | 81.9 | 90.4/47.1 |
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