Lane offset behavior and free driving trajectory model of hairpin curves of mountain roads
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摘要: 为揭示山区公路回头曲线路段的车道偏移行为和轨迹特征，建立了自由行驶轨迹模型；在一条山区复杂线形公路上开展了实车驾驶试验，使用高精度车载设备收集自然驾驶状态下的车辆行驶轨迹、速度和偏移数据；基于轨迹相对位置曲线定义了回头曲线路段左右转车辆的自由行驶轨迹模式；以曲线转角180°为界，建立了回头曲线路段车辆相对位置拟合模型，设计了基于偏移量的自由行驶轨迹计算方法，并以其他道路的回头曲线作为算例进行模型验证。研究结果表明：回头曲线左转车辆呈现出4种轨迹模式，右转车辆呈现出3种轨迹模式；车辆轨迹在回头曲线的入弯、弯中和出弯阶段均出现了较大的偏移，偏移量大于40%，此时车身侵占对向车道，不同的轨迹模式具有不同的偏移特征；不同位置所对应的速度与偏移量的分布较离散，当速度折减小于6.5 km·h-1时，驾驶人可以通过占用对向车道来降低回头曲线行驶时的速度折损；基于横向偏移量建立的不同曲线转角下的轨迹拟合模型中，当回头曲线转角约为180°时，拟合模型的精度最大，左转拟合精度介于0.90~0.97，右转拟合精度介于0.65~0.97；当回头曲线转角大于180°时，拟合模型最大拟合精度0.97发生在右转，当回头曲线转角小于180°时，拟合模型最大拟合精度0.89发生在左转。可见，本文建立的轨迹模型具有较强的适用性，可为山区公路回头曲线的行驶轨迹预测提供手段和方法。Abstract: A free driving track model was built to reveal the behavior of lane offset and the characteristics of vehicle tracks in hairpin curves of mountain roads. A real vehicle driving test was carried out on a complex mountainous linear road, and high-precision onboard equipment was used to collect vehicle track, speed, and offset data under natural driving conditions. By the relative position curves of the tracks, the free driving track patterns of left- and right-turning vehicles in the hairpin curves were defined. With the curve angle of 180° as the boundary, the fitting model of the relative position of a vehicle in a hairpin curve was constructed, and the calculation method of the free driving track based on the offset was designed. The model was verified by the examples of hairpin curves on other roads. Research results show that the left-turning vehicles in the hairpin curves have four track patterns, while the right-turning vehicles have three track patterns. The vehicle track has large offsets in the entrance, middle part, and exit of the hairpin curves, with an offset of more than 40%. As the opposite lane is occupied by vehicles, different offset features are presented for different track patterns. The distributions of speed and offset corresponding to different positions are discrete, and when the speed compensation is less than 6.5 km·h-1, the driver can reduce speed loss in the hairpin curve by occupying the opposite lane. Among the track fitting models built on the basis of the lateral offset under different curve angles, the highest accuracy of the models can be achieved when the hairpin curve angle is about 180°, with the fitting precision for left-turning vehicles between 0.90-0.97 and that for right-turning vehicles between 0.65-0.97. When the hairpin curve angle is greater than 180°, the maximum fitting precision of the fitting models is 0.97, and can be observed in the case of right-turning vehicles. When the hairpin curve angle is less than 180°, the maximum fitting precision of the fitting models is 0.89, and can be observed in the left-turning case. Therefore, the proposed track model has strong applicability and can provide means and method for driving track prediction in hairpin curves of mountain roads.
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Key words:
- traffic safety /
- mountain road /
- hairpin curve /
- lane offset /
- track prediction /
- track model
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图 4 回头曲线路段的轨迹横向位置和车道偏移
Figure 4. Trajectory lateral positions and lane offsets at hairpin curve section
图 6 左转回头曲线的车辆横向相对位置和车道偏移
Figure 6. Vehicle lateral relative positions and lane offsets in left-hand hairpin curves
图 7 右转回头曲线的车辆横向相对位置和车道偏移
Figure 7. Vehicle lateral relative positions and lane offsets in right-hand hairpin curves
图 11 轨迹偏移量-速度-入弯距离三维散点分布
Figure 11. Three dimensional scatter distributions of travel trajectory offset-driving speed-travelling distance
图 12 车辆横向相对位置-速度折损散点分布
Figure 12. Scatter distributions of vehicle ralative lateral position-speed reduction
图 13 回头曲线路段自由行驶轨迹计算步骤
Figure 13. Calculation steps of free driving trajectories at hairpin curves sections
图 14 大头线B1的行驶轨迹预测结果
Figure 14. Prediction results of driving trajectory of big head curve B1
图 15 平头线B2的行驶轨迹预测结果
Figure 15. Prediction results of driving trajectory of flat head curve B2
图 16 小头线B3的行驶轨迹预测结果
Figure 16. Prediction results of driving trajectory of small head cruve B3
表 1 曲线参数与轨迹模式
Table 1. Curve parameters and track modes
曲线类别 大头线 平头线 小头线 曲线序号 C1 C6 C9 C11 C2 C3 C10 C4 C5 C7 C8 曲线转角/(°) 192.7 190.6 186.6 194.6 186.2 180.1 180.5 169.5 159.4 150.6 172.6 半径/m 20.16 20.86 20.30 20.35 20.23 20.08 20.33 20.03 22.43 22.32 20.26 弯前直线坡度/(°) 3.0 2.8 6.5 6.9 7.0 9.0 7.2 9.0 9.0 9.0 9.0 弯道内坡度/(°) 3.0 2.8 3.0 3.0 3.0 3.0 3.0 3.0 2.7 3.0 3.0 弯后直线坡度/(°) 9.0 9.0 9.0 8.5 9.0 9.0 9.0 9.0 5.5 9.0 7.5 弯道长度/m 125 110 125 150 160 135 115 125 125 175 145 左转偏移模式 ⅠL ⅡL ⅢL ⅢL ⅡL ⅣL ⅡL ⅡL ⅢL ⅢL ⅡL 右转偏移模式 ⅠR ⅡR ⅠR ⅠR ⅡR ⅢR ⅡR ⅡR ⅠR ⅠR ⅡR 
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表 2 大头线的轨迹偏移模型系数
Table 2. Coefficients of track offset model for big head curve
模式 A B C D R2 ⅠL 44.89 0.50 -19.00 0.10 0.73 ⅡL 2.80 0.48 7.60 -8.00 0.94 ⅢL 21.76 0.46 -5.76 2.00 0.55 ⅠR 59.93 -0.19 -6.15 4.00 0.81 ⅡR 38.23 -0.79 13.74 -4.00 0.97
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表 3 平头线的轨迹偏移模型系数
Table 3. Coefficients of track offset model for flat head curve
模式 A B C D R2 ⅡL 14.79 0.25 3.37 -2.00 0.90 ⅡL 9.85 0.27 9.19 -7.00 0.97 ⅣL 25.17 0.26 7.68 -9.00 0.94 ⅡR 26.02 -0.65 13.34 -5.00 0.81 ⅢR 55.45 -0.87 0.99 -3.00 0.65
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表 4 小头线的轨迹偏移模型系数
Table 4. Coefficients of track offset model for small head curve
模式 A B C D R2 ⅡL 18.30 0.13 5.56 -3.00 0.89 ⅢL 22.17 0.35 -3.38 1.00 0.40 ⅠR 54.06 -0.18 -2.79 2.00 0.71 ⅡR 27.82 -0.60 12.69 -5.00 0.70
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表 5 回头曲线参数
Table 5. Linear parameters of hairpin curves
序号 半径/m 转角/(°) 类别 回旋线长度/m 平曲线长度/m B1 15.41 200.90 大头线 25.00 79.20 B2 15.10 185.78 平头线 25.00 74.11 B3 15.00 162.21 小头线 0.00 42.47
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表 6 特征断面的偏移量
Table 6. Offsets of feature sections
% 弯道类别 大头线B1 平头线B2 小头线B3 模式 ⅠL ⅡL ⅢL ⅠR ⅡR ⅡL ⅣL ⅡR ⅢR ⅡL ⅢL ⅠR ⅡR 断面1 44.88 2.80 21.76 59.93 38.23 9.85 25.17 26.02 55.45 18.30 22.17 54.06 27.82 断面2 48.43 10.14 26.79 57.23 31.29 20.08 33.97 19.32 44.99 22.89 27.90 49.50 20.50 断面3 42.02 27.59 31.94 47.03 25.50 36.33 45.15 18.12 35.01 30.48 31.40 43.68 20.92 断面4 33.54 37.14 32.08 39.55 27.95 43.91 48.62 21.30 33.21 40.22 33.22 37.17 27.18 断面5 23.18 45.04 32.58 32.41 33.46 51.05 49.81 25.99 33.05 50.01 33.66 31.46 36.60 断面6 8.07 48.90 30.67 21.87 48.59 58.94 40.09 38.45 36.20 57.72 33.30 27.84 45.79 断面7 4.39 45.49 29.67 18.43 58.18 57.59 24.61 50.20 41.38 62.20 32.76 26.85 52.29
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