Figures (15)  Tables (6)

    • Figure 1. 

      Variation of curvature and torsion in Euclidean three-dimensional space.

    • Figure 2. 

      Proposed pipeline for this study.

    • Figure 3. 

      Illustration of the vehicle used in this study.

    • Figure 4. 

      Lane marker detection system. (a) Center line. (b) Angle DSL: Distance between the Sensor to the Left Line DRS: Distance between the Sensor to the Right Line α: the drift angle between sensor heading direction (= vehicle heading).

    • Figure 5. 

      LKAS controller with the visual features connections.

    • Figure 6. 

      Control system of infrastructure, actors, and sensors in MATLAB/Simulink.

    • Figure 7. 

      Diagram of horizontal and vertical curve parameters.

    • Figure 8. 

      Experimental process.

    • Figure 9. 

      Data visualization in Prescan. (a) Av speed and acceleration profile. (b) Camera sensor output. (c) Lane keeping assistant GUI. (d) Car to lane distance error. (e) Filtered image output.

    • Figure 10. 

      GBDT model overall framework.

    • Figure 11. 

      Feature important score contribution ranking.

    • Figure 12. 

      SHAP value (the positive and negative influence of each variable under the value frame).

    • Figure 13. 

      Lane variable SHAP value mapping.

    • Figure 14. 

      SHAP value mapping value when SC300 is a single variable (SC300 is m−1).

    • Figure 15. 

      The mapping relationship between SHAP value when SC100 is a single variable (SC100 is m−1).

    • BlockDescription
      Simulation informationContaining all the simulation data
      ACTORThe vehicle used on the simulation senario
      SELFContaining data of all the object
      Trajectory (TRACK)Containing all trajectories that the actor does in the simulation scenario
      CameraViews of the scenario
      TISTechnology Independent Sensor
      PreScan sensor simulationOnce the simulation starts, the actuator blocks and sensors blocks are initialized directly or indirectly from the data models that come with the experiment
      Lane Marker sensorProvides information about the lane lines present on the road.

      Table 1. 

      Description of the components involved in the simulation scenario.

    • Intersection
      Point      		AVs speed
      Range (km/h)      		Radius
      (m)      		Transition curve
      length (m)      		Slopes
      rank (%)
      JD1


      40−100      		8001052−1.5
      JD28001050.5−2.85
      JD33101603−2.5
      JD43101600−2.26
      JD53751452.32−4
      JD61,10001.2−2.01
      JD75,9000−0.8 − −4
      JD8600115−2

      Table 2. 

      Experiment road geometric design parameters.

    • Horizontal alignmentVertical alignmentSpace combination alignmentCode
      name
      TangentSlopeTangent + slopeTT
      Vertical curveTangent + vertical curveTV
      Horizontal curveSlopeHorizontal curve + slopeCT
      Vertical curveHorizontal curve + vertical curveCV
      Spiral curveSlopeSpiral curve + slopeST
      Vertical curveSpiral curve + vertical curveSV

      Table 3. 

      Experiment road segment division.

    • Road segmentCurvature k calculation formulaTorsion $ \tau $ calculation formula
      TT00
      TV$ \begin{array}{c}\dfrac{1}{{R}_{v}{\left(1+{\left(\dfrac{\left(l+{l}_{b}\right)}{{R}_{v}}+{i}_{1}\right)}^{2}\right)}^{\frac{3}{2}}}\\ \dfrac{\left({l}_{s}+{l}_{a}\right)}{{A}^{2}\left(1+{i}_{1}^{2}\right)}\end{array} $0
      ST$ \dfrac{\left({l}_{s}+{l}_{a}\right)}{{A}^{2}\left(1+{i}_{1}^{2}\right)} $$ \dfrac{{i}_{1}\left({l}_{s}+{l}_{a}\right)}{{A}^{2}\left(1+{i}_{1}^{2}\right)} $
      SV$ \dfrac{{\left(\dfrac{1}{{R}_{v}^{2}}+{\left(\dfrac{\left({l}_{s}+{l}_{a}\right)}{{A}^{2}}\right)}^{2}\left({\left(\dfrac{\left(l+{l}_{b}\right)}{{R}_{v}}+{i}_{1}\right)}^{2}+1\right)\right)}^{\frac{1}{2}}}{{\left(1+{\left(\dfrac{\left(l+{l}_{b}\right)}{{R}_{v}}+{i}_{1}\right)}^{2}\right)}^{\frac{3}{2}}} $$ \dfrac{{\left(\dfrac{\left({l}_{s}+{l}_{a}\right)}{{A}^{2}}\right)}^{3}\left(\dfrac{\left(l+{l}_{b}\right)}{{R}_{v}}+{i}_{1}\right)-\dfrac{1}{{A}^{2}{R}_{v}}}{\dfrac{1}{{R}_{v}^{2}}+{\left(\dfrac{\left({l}_{s}+{l}_{a}\right)}{{A}^{2}}\right)}^{2}\left({\left(\dfrac{\left(l+{l}_{b}\right)}{{R}_{v}}+{i}_{1}\right)}^{2}+1\right)} $
      CT$ \dfrac{1}{{R}_{h}\left(1+{i}_{1}^{2}\right)} $$ \dfrac{{i}_{1}}{{R}_{h}\left(1+{i}_{1}^{2}\right)} $
      CV$ \dfrac{{\left(\dfrac{1}{{R}_{v}{}^{2}}+\dfrac{1}{{R}_{h}{}^{2}}\left({\left(\dfrac{\left(l+{l}_{b}\right)}{{R}_{v}}+{i}_{1}\right)}^{2}+1\right)\right)}^{\frac{1}{2}}}{{\left(1+{\left(\dfrac{\left(l+{l}_{b}\right)}{{R}_{v}}+{i}_{1}\right)}^{2}\right)}^{\frac{3}{2}}} $$ \dfrac{\left(\dfrac{\left(l+{l}_{b}\right)}{{R}_{v}}+{i}_{1}\right)\dfrac{1}{{R}_{h}{}^{3}}}{\dfrac{1}{{R}_{v}^{2}}+\dfrac{1}{{R}_{h}^{2}}\left({\left(\dfrac{\left(l+{l}_{b}\right)}{{R}_{v}}+{i}_{1}\right)}^{2}+1\right)} $

      Table 4. 

      Curvature and torsion calculation formula.

    • No.Parameters (independent variables)Symbol definition
      1LaneL
      2SlopeS
      3Direction (left turn, right turn)D
      4Upstream 300 m average spatial curvatureSC300
      5Upstream 300 m spatial curvature composite indexXsc300
      6Upstream 300 m average spatial torsionST300
      7Upstream 300 m spatial torsion composite indexXst300
      8Upstream 100 m average spatial curvatureSC100
      9Upstream 100 m spatial curvature composite indexXsc300
      10Upstream 100 m average spatial torsionST100
      11Upstream 100 m spatial torsion composite indexXst100
      12Maximum sudden change in spatial curvature nearest to the road sectionSCM
      13Maximum sudden change in spatial torsion nearest to the road sectionSTM
      14Spatial curvature in the sectionSCS
      15Curvature difference of adjacent road sectionSCS-AD
      16Average curvature difference of adjacent road sectionSCS-A
      17Spatial curvature torsionSCT
      18Torsion difference of adjacent road sectionSTS-AD
      19Average torsion difference of adjacent road sectionSTS-A

      Table 5. 

      Space alignment parameters index.

    • Spatial parametersAutonomous vehicleConventional vehicle
      Upstream 300 m average spatial curvature (SC300)10% of the impact.
      When SC300 is higher, it has a positive impact on TD.
      When the AV is driving on the downhill road section, the TD is not affected.
      		17% of the impact factors.
      When SC300 is higher, the TD is significantly affected, and the larger SC300 is the more restrained the TD on the downhill section


      Upstream 100 m average spatial curvature (SC100)      		8% of the impact factors.
      Has a positive and negative impact on the TD.
      Increasing his value does not have a significant impact on the TD due to the AV's rapid reaction time.
      		10.9% of the impact factors
      The values remain between positive and negative.
      SC100 has no direct impact on the deviation of the driving trajectory. Due to the lack of time for the driver to adjust the vehicle during the upstream 100, the deviation value of the driving trajectory when the vehicle is in the corresponding section remains the same
      Lane7% of the impact factors.
      The AV's TD is positively affected when it is driving in the inner lane and negatively affected when it is driving in the outer lane.
      When AV is making a left turn, it tends to shift outward.      		12.2% of the impact factors.
      When considering the interaction with SC300, the larger the SC300 in the left-turn section, the more restrained the deviation of the driving trajectory.
      A serious left deviation occurs When a conventional vehicle is making a left turn.

      Table 6. 

      AVs and conventional TD behavior comparaison.