CHAPTER I Introduction
6.3 Analysis of the Eectiveness of the Proposed Method
6.3.2 Eectiveness of the acceleration-lane-shaped available moving areaarea
Figure 6.3.9: Time histories of main variables during merging in Case3.
6.3.2 Eectiveness of the acceleration-lane-shaped available moving
relative distance are set as ar12=7.0, br12=7.0. According the width of the merging lane the upper and lower bounds of variable b are set as: −bmin=bmax=2.04. The values of the other road shape parameters are the same as described in the former section. The resultant model of the road are as Fig. 6.3.10 Ts=18 s, the prediction horizon T=2 s, h=0.01 s. To make
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0 5 10 15
l33 l12
Y
l22 Vehicle1
Vehicle2
X Figure 6.3.10: Model of the helicopter-shot merging scene
the merging results as realistic as possible, ω12, ωlb, ωrb, ωv1, ωv2, ωa1, ωa2, and ωab were set appropriately as follows: ω12=10.0,ωlb=0.01, ωrb=0.011, ωv1=0.02, ωv2=0.02,ωa1=0.12, ωa2=0.1205, ωab=0.01. In the resultant trajectories, to make it easy to compare the relative distances of the two vehicles and easy to recognize the position of them, instead of every sampling time,t=nh,(n=0,1,2,· · · , Ts/h), only the positions of the two vehicles at the time t0=0 s,t1=2s,t2=4 s,t3=6 s,t4=8 s,t5=10s,t6=12s,t7=14s,t8=16s,t9=18s are shown.
To make sure the road shape are appropriately approximated, a1y is derived by calculating the second time derivative of (7.1.4) along the trajectories of (7.1.1).
Case1: Reproduction of actual merging
To represent the cases in which the main lane vehicle would slow down a little to let the merging vehicle merge in more easily, the initial conditions were set to be the same with that of the helicopter-shot typical merging scene as follows: x1x=59.0 m, x2x=0 m, b=0 m,v1x=9.9m/s,v2x=20.0m/s, vb=0m/s. Fig. 6.3.12 shows the merging trajectory, and
Fig. 6.3.13 shows the variation of the variables in the simulation. To prove that the merging results are realistic, Fig. 6.3.11 shows the helicopter-shot merging trajectory. Fig. 6.3.11 shows that Vehicle2 slowed down a little to let Vehicle1 merge in. Therefore the helicopter-shot merging can be considered as an example of the cooperative driving phenomenon.
Figure 6.3.11: Helicopter-shot merging trajectory
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20Y t0
t9 t8
t7 t6
t5 t3
t2 t1
t4
t0 t1 t2 t3
t4
t6 t7
t5 t8 t9
X Figure 6.3.12: Simulation merging trajectory of Case 1
Fig. 6.3.12 shows that Vehicle1 merged to the front of Vehicle2 with appropriate relative distance successfully. The First diagram in Fig. 6.3.13 shows the variation of the velocities which proves that the two vehicles have appropriate nal speeds. The second and the third diagrams show the variation of the accelerations of the two vehicles. The second diagram shows that Vehicle2 decelerated to let the merging vehicle merge in, while Vehicle1 acceler-ated to merge successfully. Furthermore, accelerations and decelerations were always kept below the specied appropriate value3.0m/s2. Moreover, the variation of its acceleration is more severe than the main lane vehicle. This phenomenon is consistent with the logic of the
Figure 6.3.13: Variation of variables in Case 1
cooperative driving behavior. The third diagram shows that the acceleration of Vehicle1 in the Y-axis direction is also appropriate. The fourth diagram shows that the variation ofb is not very large in this case which means the merging trajectory did not translate very much.
This is consistent with the result shown in Fig. 6.3.12. The fth diagram shows that during merging the two vehicles kept an appropriate distance. Therefore it is concluded that the proposed method can work well without severe translation of the merging trajectory of the merging vehicle, by making use of the cooperative driving behavior.
Case 2: Merging vehicle should become leading vehicle
The initial conditions of the two vehicles were set as: x1x=59.0 m,x2x=59.0 m,b=0 m, v1x=9.9m/s, v2x=20.0m/s, vb=0m/s, accelerations are all 0 m/s2. This case represents the cases in which the merging vehicle goes to the behind of the main lane vehicle. Obviously, x1x=x2x,v1x<v2x,a1x=a2x, normal drivers will merge to the behind of the main lane vehicle,
to avoid excessive accelerations and risks in merging.
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t2 t3 t4
t0 t1 t3 t4
t2 t1 t0
t5
t5 t6
t6 t7 X
t8
t7 t9
Figure 6.3.14: Simulation merging trajectory of Case 2
Figure 6.3.15: Variation of variables in Case 2
Fig. 6.3.14 and Fig. 6.3.15 show the simulation results. Just as in actual cases, Vehicle1 merged to the behind of Vehicle2, and kept an appropriate distance r with Vehicle2, as shown in Fig. 6.3.15. Accelerations are always below 3.0 m/s2 as well. The variation of the acceleration of the merging vehicle is also more severe than that of the main lane vehicle.
The variation of b is also not very large in this case. So the proposed method can also generate realistic merging path without severe translation of the merging trajectory.
Case3: Initial condition motivate collision between vehicles
In this case the performance of the proposed method in the case when without con-trol the two vehicles will collide with each other is investigated. The initial conditions are as follows: x1x=59.0 m, x2x=59.0 m, b=0 m, v1x=16.0 m/s, v2x=16.0 m/s, vb=0 m/s, a1x=a2x=ab=0 m/s2. Since x1x=x2x, v1x=v2x, a1x=a2x, without control the motions of the two vehicles in the X-axis direction would be the same, thus they would collide. While the simulation results show that with the proposed method the merging maneuver conducted appropriately.
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X
Y t0
t7 t4
t3 t1
t2
t0 t1 t2
t3
t4 t5 t5 t6 t6 t7 t8
Figure 6.3.16: Simulation merging trajectory of Case 3
Figure 6.3.17: Zoomed simulation merging trajectory of Case 3
The simulation results are shown in Fig. 6.3.16, Fig. 6.3.17, and Fig. 6.3.18. As a result of the rst term of the penalty function, Vehicle1 decelerated a little and Vehicle2 accelerated
Figure 6.3.18: Variation of variables in Case 3
cooperatively. Therefore the relative distance of the two vehicles in the X-axis increased from 0 little by little. This prevented collision and the merging became a reasonable one.
After merging Vehicle1 ran behind Vehicle2, and the relative distance is kept above 7.0 m.
Accelerations were always kept below3.0m/s2. The variation of the acceleration of Vehicle1 was also more severe than that of Vehicle2. The variation of b was obviously shown in Fig. 6.3.18, and the translation of the merging trajectory was also visible in Fig. 6.3.17 which is the zoomed merging trajectory. The normal width of a lane on highway is 3.5 m in Japan. Therefore the upper boundary of the main lane would be the line y = 1.75. The merging trajectory moved to the right of the centerline by 7.7 m when Vehicle1 enter the acceleration lane. This shows that the merging point is optimized to some extent.
However, the merging vehicle departed froml33, the centerline of the merging lane, before it enter the acceleration lane. This is unreasonable, because in actual situation this would make the driver feel unsafe. This phenomenon show the eectiveness of the
acceleration-lane-shaped available moving area.