5. Simulation results

In this section, two sets of simulation results are used to verify the effectiveness of proposed trajectory planner and controller in both highway and off-road scenarios. The simulation parameters are shown in Table 1.

In the first set of simulations, the controlled vehicle is overtaking the vehicle ahead in the same lane in the highway scenario. A slow vehicle (with the velocity of


Table 1. The simulation parameters [18].

## Path Planning for Autonomous Vehicle in Off-Road Scenario DOI: http://dx.doi.org/10.5772/intechopen.85384

After the individual tyre forces have been optimised and allocated in (42), the controlled values of individual steering and driving actuators can be mapped from

> <sup>δ</sup>fl <sup>¼</sup> Fsfl C<sup>α</sup> þ lfr vx

<sup>δ</sup>fr <sup>¼</sup> Fsfr C<sup>α</sup> þ lfr vx

<sup>δ</sup>rl <sup>¼</sup> Fsrl C<sup>α</sup>

<sup>δ</sup>rr <sup>¼</sup> Fsrr C<sup>α</sup>

This controlled actuator values can be input into actual electric vehicle to

In this section, two sets of simulation results are used to verify the effectiveness of proposed trajectory planner and controller in both highway and off-road scenar-

In the first set of simulations, the controlled vehicle is overtaking the vehicle ahead in the same lane in the highway scenario. A slow vehicle (with the velocity of

Symbol Definition Values m Mass 1298.9 kg lf Distance of CG from the front axle 1.3 m lr Distance of CG from the rear axle 1.5 m bf Front track width 1.6 m br Rear track width 1.6 m Cs Longitudinal stiffness of the tyre 50,000 N/unit slip C<sup>α</sup> Cornering stiffness of the tyre 30,000 N/unit slip Iz Vehicle moment of inertial about yaw axle 3900 kgm2 Ix Vehicle moment of inertial about longitudinal axle 765 kgm<sup>2</sup> Iy Vehicle moment of inertial about lateral axle 3477 kgm2 R<sup>ω</sup> Wheel radius 0.3 m I<sup>ω</sup> Wheel moment of inertial 4 kgm2 e The distance between the vehicle roll centre and CG 0.4 m h Height of the vehicle centre of gravity 0.533 m K<sup>ϕ</sup> The stiffness of roll axis 89,000

� lrr vx

� lrr vx

Ti ¼ FtiR<sup>ω</sup> (53)

(54)

(55)

(56)

(57)

the individual tyre force according to the following equations:

Path Planning for Autonomous Vehicles - Ensuring Reliable Driverless Navigation…

achieve desired vehicle trajectory.

ios. The simulation parameters are shown in Table 1.

5. Simulation results

Table 1.

40

The simulation parameters [18].

15 m/s) is moving 100 metres ahead of the controlled vehicle (with the velocity of 20 m/s). In order to overtake the slow vehicle, the controlled vehicle first decelerates from 20 m/s into 15 m/s and then makes the lane change to the right lane. After that, the controlled vehicle accelerates from 15 m/s into 20 m/s to go ahead of the overtaken vehicle. Finally, the controlled vehicle goes back to the left lane. The details of this scenario are described in Figure 3(a), and the whole global desired path can be divided by 5 sections. For the purpose of comparison, the control performance of the potential field method based on [26] is also presented here. Furthermore, in order to show the advantage of 4WIS-4WID vehicle model, the proposed trajectory planning and control performance based on two-wheel model is presented and compared.

In Figure 3(b), the moving trajectory of the overtaking vehicle controlled by both the potential field method and the proposed method based on two-wheel model and 4WIS-4WID model is compared. The proposed method based on twowheel model and 4WIS-4WID model shows good control performance, and the controlled vehicle is moving within the road boundary. Figure 3(c) shows that the overtaking vehicle and overtaken vehicle maintain the safety distance to avoid collision. Figure 4 demonstrates that the potential field method shows big lateral tracking error compared with the proposed methods based on two-wheel model and four-wheel model, while the longitudinal tracking error of potential filed method is smaller than the proposed method. Since the lateral tracking error is more important than longitudinal tracking error on highway overtaking scenario, the proposed method has better overall tracking performance than potential field method. It is also noted that the tracking error of proposed method based on two-wheel model is larger than four-wheel model, especially for the tracking error of the lateral position. This shows the advantages of 4WIS-4WID model.

In Figures 5(a) and 5(b), the longitudinal velocity and lateral velocity in the global coordinate system for both the potential field method and the proposed trajectory planning method are presented. Vxd1, Vxd2, Vxd3, Vxd<sup>4</sup> and Vxd<sup>5</sup> are desired longitudinal velocities on each section of road, while Vyd1, Vyd2, Vyd3, Vyd<sup>4</sup> and Vyd<sup>5</sup> are desired lateral velocities on each section of road. The potential field method can only roughly achieve the desired longitudinal velocity and lateral velocity, while the proposed method can accurately achieve desired values. This proves that the proposed method can not only achieve the desired ending positions but also achieve the desired ending velocities. Figure 5(c) and Figure 5(d) present the vehicle yaw rate and body side-slip angle responses, which proves that the proposed trajectory planning method can achieve much better handling and stability performance compared with potential field method.

In the second set of simulations, the autonomous vehicle is assumed to move in the off-road scenario, and the road topography should be considered. Figure 6 presents the scenario in the second set of simulations: in a particular section of the road, the vehicle start position is (0, 0) and the target ending position is constrained by a certain boundary (90–110, 20–30); the initial and ending longitudinal velocity is 5 m/s, and the initial and ending lateral velocity is 0 and 3 m/s, respectively. The bank angle and road slope of this section of road is shown in Figure 7. The trajectory planner proposed in Eq. (26) will choose the best suitable ending position and vehicle trajectory by considering the road topography information (minimising the bank angle and road slope). The vehicle dynamics response of the trajectory planner which has not considered the road topography information proposed in Eq. (23) is also shown and compared. It is noted that trajectory planner without considering road topography is briefly called 'trajectory planner 1' and trajectory planner considering road topography is briefly called 'trajectory planner 4'. Figure 8 compares

#### Figure 3.

(a) Vehicle overtaking scenario in the first set of simulations (unit: m). (b) The vehicle trajectory in the global coordinate system. (c) The relative distance between the overtaking vehicle and overtaken vehicle [21].

the bank angle and road slope of the desired trajectories planned by trajectory planner 1 and trajectory planner 4 and proves that the trajectory planner 4 can generate the trajectory with smaller bank angle and road slope. Figure 9 shows the

Path Planning for Autonomous Vehicle in Off-Road Scenario

DOI: http://dx.doi.org/10.5772/intechopen.85384

The tracking errors of vehicle trajectory in the first set of simulations: (a) longitudinal position and (b) lateral

Figure 4.

43

position [21].

trajectory tracking performance when trajectory planner 4 applied is much improved compared with trajectory planner 1. Figure 10 shows the dynamics responses between trajectory planner 1 and trajectory planner 4. Figure 10(a) suggests that the undesired lateral velocity is reduced a lot when trajectory planner 4 has been applied. Figure 10(b) and Figure 10(c) prove that the autonomous

Figure 4.

The tracking errors of vehicle trajectory in the first set of simulations: (a) longitudinal position and (b) lateral position [21].

the bank angle and road slope of the desired trajectories planned by trajectory planner 1 and trajectory planner 4 and proves that the trajectory planner 4 can generate the trajectory with smaller bank angle and road slope. Figure 9 shows the trajectory tracking performance when trajectory planner 4 applied is much improved compared with trajectory planner 1. Figure 10 shows the dynamics responses between trajectory planner 1 and trajectory planner 4. Figure 10(a) suggests that the undesired lateral velocity is reduced a lot when trajectory planner 4 has been applied. Figure 10(b) and Figure 10(c) prove that the autonomous

Figure 3.

42

(a) Vehicle overtaking scenario in the first set of simulations (unit: m). (b) The vehicle trajectory in the global coordinate system. (c) The relative distance between the overtaking vehicle and overtaken vehicle [21].

Path Planning for Autonomous Vehicles - Ensuring Reliable Driverless Navigation…

Figure 6.

Figure 7.

45

set of simulations.

The vehicle off-road scenario in the second set of simulations (unit: mm).

Path Planning for Autonomous Vehicle in Off-Road Scenario

DOI: http://dx.doi.org/10.5772/intechopen.85384

The vehicle (a) road slope and (b) bank angle of the one particular section of uneven road surface in the second

#### Figure 5.

The vehicle state in the first set of simulations: (a) longitudinal velocity in the global coordinate system, (b) lateral velocity in the global coordinate system, (c) yaw rate and (d) body slip angle [21].

Figure 6. The vehicle off-road scenario in the second set of simulations (unit: mm).

Figure 7.

The vehicle (a) road slope and (b) bank angle of the one particular section of uneven road surface in the second set of simulations.

Figure 5.

44

The vehicle state in the first set of simulations: (a) longitudinal velocity in the global coordinate system, (b) lateral velocity in the global coordinate system, (c) yaw rate and (d) body slip angle [21].

Path Planning for Autonomous Vehicles - Ensuring Reliable Driverless Navigation…

Figure 8. The actual (a) bank angle and (b) road slope in the second set of simulations.

vehicle has smoother roll angle and pitch angle response when trajectory planner 4 is applied since the road bank angle and road slope is minimised compared with the

Vehicle dynamics responses in the second set of simulations: (a) lateral velocity, (b) roll angle and (c) pitch

situation when trajectory planner 1 is applied.

Path Planning for Autonomous Vehicle in Off-Road Scenario

DOI: http://dx.doi.org/10.5772/intechopen.85384

Figure 10.

angle.

47

Figure 9. The desired trajectory tracking performance in the second set of simulations.

Path Planning for Autonomous Vehicle in Off-Road Scenario DOI: http://dx.doi.org/10.5772/intechopen.85384

Figure 8.

Figure 9.

46

The actual (a) bank angle and (b) road slope in the second set of simulations.

Path Planning for Autonomous Vehicles - Ensuring Reliable Driverless Navigation…

The desired trajectory tracking performance in the second set of simulations.

Vehicle dynamics responses in the second set of simulations: (a) lateral velocity, (b) roll angle and (c) pitch angle.

vehicle has smoother roll angle and pitch angle response when trajectory planner 4 is applied since the road bank angle and road slope is minimised compared with the situation when trajectory planner 1 is applied.
