Robustness against main lane vehicles moving with xed speed

In this section, merging with two sets of initial conditions is simulated. In the rst case the initial conditions motivate collision between the main lane vehicle and the merging vehicle.

But the initial positions of the two vehicles are rather far from the merging point. Therefore, the time that could be used to adjust the motion of the vehicles is comparatively long. In the second case, the initial conditions also motivate collision between the two vehicles, and the initial positions are quite near to the merging point. Therefore, the time could be used to adjust the motion of the vehicles is rather shorter. In both the situations the main lane vehicle are set to move with constant speed v2x = 16.7 m/s during the merging maneuver.

The initial conditions and simulation results are shown as follows:

Collision case with initial positions far from the merging point

In this simulation, the initial conditions are set as follow: x_1x=0m,x_2x=0m,v_1x=16.7m/s, v_2x=16.7m/s. As shown: x_1x=x_2x,v_1x=v_2x=v_d. If vehicle1 does not adjust its speed accord-ing to the motion of the motion of Vehcile2, these two vehicles would collide with each other.

The simulation results are shown in Fig. 7.2.1 and Fig. 7.2.2. Fig. 7.2.1 shows the trajectories of the vehicles. Fig. 7.2.2 shows the time history of the variables during merging. As shown

Figure 7.2.1: Moving trajectories of the merging vehicle and the main lane in the relaxed collision case.

in these two gures, the merging conducted successfully even the main lane vehicle did not move in the predicted optimal way and the initial condition motivate collision. As shown in Fig. 7.2.1, the merging vehicle slowed down to keep relative distance and merged to the behind of the main lane vehicle. Acceleration constraints were kept and relative distance was kept above 0. b also changed a lot during merging, and as a result, the merging vehicle moved near the upper range of the available moving area to keep relative distance. This also show the necessity of adjustable merging trajectory and optimal of merging point. It can be known from Fig. 7.2.2 that the actual value ofa2x is a little dierent from the optimal value.

Compared with Fig. 6.2.8 and Fig. 6.2.9, it can be known that the motion of Vehicle1 is also

Figure 7.2.2: Time history of variables during merging in the relaxed collision case.

a little dierent in this simulation. From the variation of v_1x in Fig. 6.2.9 and Fig. 7.2.1, it can be known that the minimum value ofv_1x in Fig. 7.2.1 is smaller than that in Fig. 6.2.9.

Since Vehicle2 did not decelerated cooperatively, Vehicle1 had to decelerate more severely to keep relative distance with Vehicle2. This phenomenon shows the robustness of the proposed method against the non optimal motion of the main lane vehicle.

In this case, the initial positions of the vehicles are rather far from the merging intersec-tion, the point with the coordinate (159.8, 0). As a result, it is comparatively easy to be adjusted motion of the merging vehicle according to the unexpected motion of the main lane vehicle to convert the collision case to a successful merging. That is also why this case is

named as the relaxed collision case. However, in actual implementation, it would be dicult to obtain the position and speeds of a main lane vehicle when it is far from the merging vehicle. Therefore, in the next case, the robustness of the proposed method is investigated in the case when the initial positions are rather near to the merging point.

Collision case with initial positions near the merging point

To investigate the eectiveness of the proposed method when the initial condition make it very dicult to merge successfully, the initial conditions are set as: x_1x=75.0m,x_2x=75.0m, v_1x=16.7 m/s, v_2x=16.7 m/s, a_2x=0. Also in this case x_1x=x_2x, v_1x=v_2x=v_d. Therefore without adjustment of the motions, the merging vehicle and the main lane vehicle would collide with each other. The simulation results shown in Fig. 7.2.3 and Fig. 7.2.4 represent that the merging maneuver conducted successfully.

Figure 7.2.3: Moving trajectories of the merging vehicle and the main lane in the intense collision case.

Although the main lane vehicle did not move cooperatively and the time can be used to adjust vehicle motion is quite short, the merging vehicle also slowed down and merged to the behind of the main lane vehicle. During this merging the relative distance were kept appropriate, and accelerations were all kept in the specied range. The merging path was adjusted by varyingb. As a result the merging vehicle moved near the range of the available

Figure 7.2.4: Time history of variables during merging in the intense collision case.

moving area and merged successfully at last. Therefore the proposed method is also eective in this case despite the main lane vehicle did not move in the optimal way. Fig. 7.2.4 shows that the actual value of a_2x is also dierent from the optimal value of it. a_1x changed more severely than in the last case, and the minimum value of v_1x is smaller than the last case.

Since the available adjusting time is shorter than the relaxed collision case, it is reasonable for Vehicle1 to move in such away.

As a result, it is concluded that the proposed method is robust against the discrepancy between the optimal motion and uniform motion of the main lane vehicle in this case.

7.2.2 Robustness against main lane vehicles moving with xed