Open access peer-reviewed chapter

Path Planning for Autonomous Vehicle in Off-Road Scenario

By Boyuan Li, Haiping Du and Bangji Zhang

Submitted: September 12th 2018Reviewed: February 22nd 2019Published: April 2nd 2019

DOI: 10.5772/intechopen.85384

Downloaded: 367

Abstract

The road topography information, such as bank angle and road slope, can significantly affect the trajectory tracking performance of the autonomous vehicle, so this information needs to be considered in the trajectory planning and tracking control for off-road autonomous vehicle. In this chapter, a two-level real-time dynamically integrated spatiotemporal-based trajectory planning and control method for off-road autonomous vehicle is proposed. In the upper-level trajectory planner, the most suitable time-parameterised trajectory with the minimum values of road slope and bank angle can be selected from a set of candidate trajectories. In the lower-level trajectory tracking controller, the sliding-mode control (SMC) technique is applied to control the vehicle and achieve the desired trajectory. Finally, simulation results are presented to verify the proposed integrated trajectory planning and control method and prove that the proposed integrated method has better overall tracking control and dynamics control performance than the conventional method both in the highway scenario and off-road scenario. Furthermore, the four-wheel-independent-steering (4WIS) and four-wheel-independent-driving (4WID) vehicle shows better tracking control performance than vehicle based on two-wheel model.

Keywords

  • trajectory planning
  • trajectory tracking control
  • off-road vehicle
  • vehicle dynamics
  • optimisation

1. Introduction

Nowadays, the off-road autonomous ground vehicle has been widely applied in various industries, such as military [1, 2] and space applications [3, 4]. Furthermore, this kind of vehicle also received focused attention in mining [5], agriculture and forestry sectors [6].

In order to improve the stability and safety of off-road autonomous vehicles, the path planning of these vehicles should be considered as the priority of current research. The path planning of autonomous vehicle includes two stages: the trajectory planning in the upper-level and trajectory tracking control in the lower-level. The upper-level trajectory planner considers the surrounding environment information according to the various sensors and selects the best desired trajectory, while the lower-level trajectory tracking controller controls the steering and driving actuators to achieve the desired trajectory.

In the current literature, the path planning of autonomous vehicle has attracted focused attention. Particularly, the spatial-based path planning methods are widely applied, but the time parameter is not considered [7]. For example, for the direct tracking method, the steering system is controlled to follow the pre-planned spatial-based desired path exactly at every time step [8, 9]. In the potential field method proposed in [10], the desired path is planned within a potential field with a tracking error tolerance along the road centreline. In this way, the autonomous vehicle does not need to strictly follow the road centreline, and smaller steering control effort is required compared with the direct tracking method. The spatiotemporal-based trajectory planning concept, on the other hand, considers the kinematic constraints and generates time-parameterised trajectories. Several typical spatiotemporal-based trajectory planning methods, such as the methods proposed in [11, 12, 13], aim to find the best suitable time-parameterised trajectory connecting the initial vehicle states with exactly defined goal states. These methods rely on discrete geometric structure, such as the rapidly exploring random trees (RRT) [14] and state lattice [13]. However, the generation of candidate trajectories requires large computational work. When the surrounding environment is unconstructed and complex, these methods may not be computational efficient. In [15, 16], the proposed trajectory planning strategies utilise ‘deliberated multiple final states’ method. This method deliberately generates multiple alternative final states which can respond to traffic changes very fast. In study [17], based on the concept of ‘deliberated multiple final states’, the combined trajectory planning of the longitudinal and lateral motion of autonomous vehicle are proposed, and the ‘deliberated multiple final states’ are described as the offset error values from the target reference final states. The most suitable trajectory which satisfies the initial and ending states with certain terminal time can be selected from candidate trajectory set, and the kinematic constraints are satisfied.

Motivated by the widely application of the off-road autonomous vehicle in various industries and based on above research studies on path planning, this chapter proposed a two-level real-time dynamically integrated spatiotemporal-based trajectory planning and control method by considering the off-road scenario. The major innovative part of this chapter is the development of the spatiotemporal-based trajectory planning method and considering the off-road topography information in trajectory planning. In the upper-level trajectory planner, a number of candidate spatiotemporal-based trajectories with various terminal times and state-ending conditions are generated. These candidate trajectories also include the road topography information—the bank angle and road slope. The best suitable trajectory can be selected from these candidate trajectories based on the optimised cost function which is used to minimise the tracking error, terminal time spent and the effect of road topography on the vehicle. After that, trajectory tracking controller in the lower-level is proposed based on the sliding-mode technique and vehicle dynamics model in order to track the selected best suitable trajectory. In addition, the vehicle dynamics model of this chapter is based on a four-wheel-independent-steering (4WIS) and four-wheel-independent-driving (4WID) electric vehicle. Due to a large number of available control actuators, the 4WIS-4WID electric vehicle shows advantages over the traditional vehicle. This chapter also discusses the advantage of 4WIS-4WID electric vehicle on trajectory planning and trajectory tracking control over traditional two-wheel vehicle.

In this chapter, Section 2 first discusses the vehicle dynamics model based on 4WIS-4WID electric vehicle. Then Section 3 describes the upper-level trajectory planner, and Section 4 shows the lower-level trajectory tracking control. After that, Section 5 presents the simulation results to verify the proposed trajectory planning and control method. Finally, the conclusion is given in Section 6.

2. Vehicle dynamics modelling

In this section, a 4WIS-4WID vehicle model is utilised first to describe the dynamic motion of an off-road autonomous vehicle [18]. The information of road slope and bank angle is included in the vehicle longitudinal and lateral dynamics equations. Furthermore, vehicle roll dynamics equation and pitch dynamics equation are included in the dynamics model to better present the effect of bank angle and road slope on the vehicle dynamics. The vector diagram of vehicle dynamics model is presented in Figure 1.

Figure 1.

The vector diagram of 4WIS-4WID vehicle dynamics model.

The equations of motion of this model are described as follows:

Longitudinal motion:

mv̇x=mvyr+Fxfl+Fxfr+Fxrl+Fxrr+mgsinθsE1

Lateral motion:

mv̇y=mvxr+Fyfl+Fyfr+Fyrl+Fyrr+mgsinθbE2

Yaw motion:

Izṙ=lfFyfl+FyfrlrFyrl+Fyrr+bf2FxflFxfr+br2FxrlFxrrE3

Roll motion:

Ixϕ¨=merv̇ymervxr+mgersinϕKϕϕCϕϕ̇E4

Pitch motion:

Iyφ¨=mepv̇xmepvyr+mgepsinφKφφCφφ̇E5

where vx,vyandrare the vehicle longitudinal velocity, lateral velocity and yaw rate. θsshows the road slope, and θbrepresents the road bank angle. bfand brrepresent the front and rear track width. lfis the length of front wheel base, and lris the length of rear wheel base. Izrepresents the moment of yaw inertia, and mis vehicle mass. Fxfland Fxfrrepresent the longitudinal tyre force of front left and front right tyre, while Fxrland Fxrrpresent the longitudinal tyre force of rear left and rear right wheel.Fyfland Fyfrpresent the lateral tyre force of front left and front right tyre, while Fyrland Fyrrpresent the lateral tyre force of rear left and rear right wheel. ϕand φrepresent the vehicle roll angle and pitch angle, respectively.eris the distance from the vehicle centre of gravity (CG) to the roll centre, and epis the distance from the vehicle CG to the pitch motion centre. Kϕis the roll axis torsional stiffness, and Cϕis the roll axis torsional damping. Kφis the pitch axis torsional stiffness, and Cφis the pitch axis torsional damping.

The tyre side force Fsiand traction or brake force Ftican be transferred to the longitudinal force Fxiand the lateral tyre force Fyias follows:

Fxi=FticosδiFsisinδiFyi=Ftisinδi+FsicosδiE6

where i=fl,fr,rlandrr, which represents the front left wheel, front right wheel, rear left wheel and rear right wheel.

The non-linear Dugoff tyre model is used in this chapter [19], and tyre traction or brake force and side force of each wheel are described by:

Tyre side force:

Fsi=Cαtanαi1sifλiE7

Tyre traction or brake force:

Fti=Cssi1sifλiE8

λiin Eqs. (7) and (8) can be determined by the following equation:

λi=μFzi1εruisi2+tan2αi1si2Cs2si2+Cα2tan2αiE9

fλiin Eqs. (7) and (8) can be determined by the following equation:

fλi=λi2λiλi<11λi>1E10

where Cαrepresents the lateral cornering stiffness and Csis the longitudinal cornering stiffness. The tyre-road friction coefficient can be represented as μ, and Fzirepresents the individual wheel vertical load. αirepresents the lateral side-slip angle, and siis the longitudinal slip ratio. uirepresents the vehicle longitudinal velocity in the individual wheel plane. εris the road adhesive reduction factor, which is a constant value.

The following equation shows the wheel rotation dynamics:

Iωω̇i=RωFti+TiE11

where ωipresents the wheel angular velocity of each wheel and Tipresents the traction or brake torque of each wheel. Rωis the wheel radius, and Iωis the wheel moment of inertial.

The load transfer model is considered here by adding the roll and pitch motion to better present the effect of road slope and bank angle on the vehicle vertical load distribution [20]. The vertical load of individual wheel can be presented by the following equations by including the load transfer model:

Fzfl=mlf+lr12glr12v̇xh+lrbfv̇yhgersinϕ+12gepsinφlf+lr2E12
Fzfr=mlf+lr12glr12v̇xhlrbfv̇yhgersinϕ+12gepsinφlf+lr2E13
Fzrl=mlf+lr12glf+12v̇xh+lfbrv̇yhgersinϕ12gepsinφlf+lr2E14
Fzrl=mlf+lr12glf+12v̇xhlfbrv̇yhgersinϕ12gepsinφlf+lr2E15

where his the height of the vehicle CG above the ground.

3. Upper-level trajectory planner

Figure 2 presents the whole structure of the proposed integrated trajectory planning and control method, which mainly includes the upper-level trajectory planner, the lower-level trajectory controller and the vehicle dynamics model [21].

Figure 2.

The whole structure of the proposed integrated trajectory planning and control method.

At the beginning, it is assumed that a behaviour layer planner exists and can determine the rough global reference path according to the digital map. This behaviour layer planner consists of a number of modules, such as digital map, perception and localisation system and behaviour level path planner [22]. The digital map provides real-time traffic information, and the real-time vehicle position on the digital map can be determined by the perception and localization system (such as the GPS combined with IMU and wheel encoder). When digital map and vehicle’s real-time position on the digital map are available, the behaviour planner can make deliberate manoeuvre task decisions, such as lane following, lane changing, vehicle following and overtaking, in complex street-driving scenario. Based on the manoeuvre task decisions, the global route planner in the behaviour planner can compute the rough reference path. This is a reasonable assumption because many studies in the literature have determined the rough reference path by behaviour level task planner based on digital map [22, 23, 24].

In the upper-level trajectory planner, according to the rough desired path determined by the behaviour planner, the desired vehicle initial and ending states of each section of the road along the rough reference path can be assumed to be known in advance.

3.1 Generate the candidate trajectory set

In each section of road, when the initial states are assumed to be available, the multiple target ending states can be defined as a group of offset state values from the reference state values (such as longitudinal position, longitudinal velocity, lateral position and lateral velocity). The start state is assumed as d0ḋ0d¨0, and the desired ending state is assumed as d1ḋ1d¨1. d0is the initial vehicle position, and d1is a group of offset positions from reference ending position, and these offset positions are constrained within the road boundary. ḋ0and d¨0present the initial velocity and acceleration, while ḋ1and d¨1present the ending velocity and acceleration. For the purpose of the guarantee of the continuities of the planned trajectory between each section of the road, the initial state d0in current section of road should be the ending state of previous section.

In each section of the road, when the initial and ending state values are determined, the candidate trajectories with different ending conditions d1iand terminal time τjcan be generated [17], where i,jmeans that the number of i×jtrajectories will be generated by the trajectory planner. d1irepresents inumber of final positions and will close to the target ending position when d1id1. τjrepresents the jnumber of candidate terminal time. The optimisation algorithm presented in the later section will choose the best trajectory from these i×jtrajectories.

It can be assumed that the candidate vehicle trajectory dτin the optimisation of trajectory planning can be described by the following quintic state equations [17]:

For the position of candidate trajectory:

d1=c0+c1t+c2t2+c3t3+c4t4+c5t5E16

For the velocity of candidate trajectory:

ḋ1=c1+2c2t+3c3t2+4c4t3+5c5t4E17

For the acceleration of candidate trajectory:

d¨1=2c2+6c3t+12c4t2+20c5t3E18

with c0,c1,,c5Rand t0τ. τis the terminal time of the candidate trajectory and τ0T. Tis the longest time required to complete the motion.

Eqs. (16)(18) can be rewritten as the following equation:

ξtt=M1tc012+M2tc345E19

where M1t=1tt2012t002, M2t=t3t4t53t24t35t46t12t220t3and ξtt=d1tḋ1td¨1t.

The coefficients c012and c345of the quintic state trajectory in Eq. (19) can be calculated as follows:

c012=c0c1c2=M101ξ0E20
c345=c3c4c5=M2τ1ξtM1τc012E21

where M10=100010002and ξ0=d0ḋ0d¨0.

After the coefficients c012and c345are calculated, the vehicle trajectory can be described as d1tin Eq. (16). In this way, candiadate trajectories in this section of the road can be determined, and the best trajectory can be selected based on the proposed optimisation cost function in the next section.

3.2 Determine the optimisation cost function

After the candidate trajectories have been determined in each section of the road, the next step is to determine the cost function to select the best suitable trajectory. The optimisation cost function is designed as the following equation:

mind1,τJ1=kττ+kddrd1τ2E22

where this cost function has two optimization variables, the ending position d1and terminal time τ. This cost function also includes two terms, and kτand kdare the scaling factors of each term, which can be used to balance the term of total time cost and the term of offset error from the desired ending state. dris the reference vehicle ending state. drd1τpresents the offset error from the desired reference ending state. The selection of total time cost can greatly affect the vehicle trajectory tracking behaviour: with the small total time cost, the vehicle can reach the final states early, while large time cost will make the vehicle movement slow and stable with late arrival of final states.

Furthermore, the vehicle longitudinal or lateral jerk (presented as dτ) should be minimised to improve the smoothness of the trajectory. The total optimisation cost function J1of the trajectory planning can be augmented as:

mind1,τJ1=kJd1τ2+kττ+kddrd1τ2E23

where kJis the scaling factor of the term related to longitudinal or lateral jerk. It can be noted that the target final velocity ḋ1or acceleration d¨1can be used in (23) instead of d1if the final velocity or acceleration is required to be optimised.

In optimisation cost function (23), the road topography information, such as the road slope and bank angle, has not been considered. However, road topography will greatly affect the trajectory planning and vehicle dynamics performance in off-road scenario. The trajectory planning optimisation cost function should consider the additional optimisation control target of road topography by selecting the trajectory with the smaller road slope and bank angle. Furthermore, in order to prevent the abrupt change of road slope and bank angle, the change of the road slope and bank angle between current and previous time step should be minimised.

The assumption is made that the topography information along each candidate trajectory is already known through various sensors equipped in the intelligent vehicle system. In this chapter, the topography information at a specific point can be obtained from a lookup table. The average road slope θ¯sand bank angle θ¯balong one particular candidate trajectory could be calculated as the following equation:

θ¯s=i=1nθsxiyinE24
θ¯b=i=1nθbxiyinE25

where θsxiyiand θbxiyiare the road slope and bank angle at a specific point along the candidate trajectory. nis the total number of discrete points along this candidate trajectory.

After the road topography information is available, the road topography information can be included into the optimal cost function (23) as the following equation:

mind1,τJ1=kJ(d1(τ))2+kττ+kd(drd1(τ))2+ksθ¯s(d1(τ))+ksdθ¯̇s(d1(τ))+kbθ¯b(d1(τ))+kbdθ¯̇b(d1(τ))E26

where this cost function have four additional cost function terms compared with cost function (23). The terms ksθ¯sd1τand kbθ¯bd1τare designed to minimise the road slope and bank angle along the selected trajectory. ksdθ¯̇sdx,yτand kbdθ¯̇bdx,yτare designed to prevent the abrupt change of road slope and bank angle. ks,ksdand kb,kbdare scaling factors of each term.

When the optimisation values of ending position d1and terminal time τare determined based on (26), the desired best trajectory can be determined according to Eqs. (16)(18).

It is noted that the trajectory planning in this section can be divided as the longitudinal trajectory planning and lateral trajectory planning. Eqs. (16)(26) merely provide the common mathematical equations to generate the candidate trajectory set and determine the best suitable trajectory according to optimisation cost function. These mathematical equations are only corresponding to one section of road. The predefined global desired path can have a number of sections of road, and a number of the optimisation calculations are implemented successively. In the ideal condition, the more sections the desired global path is divided, the more accurate the optimisation results would be. However, a large number of the divided sections of road require intensive computing efforts, and the computational cost will increase a lot.

3.3 Map planned trajectory into vehicle dynamics control targets

After the desired trajectory is planned and determined while satisfying certain position constraints and velocity constraints, the next step is to map the desired trajectory into vehicle dynamics control targets: desired yaw angle and desired longitudinal velocity in the body-fixed coordinate system.

The desired yaw angle φdand longitudinal velocity vxdin the body-fixed coordinate system can be determined according to the following optimisation cost function:

minφd,vxdJ2=avxdkvxdbk2+bvxdtanφdkvydbk2+cφdkφdk12E27

where this cost function includes three terms, which are used to achieve the desired longitudinal velocity (the first term), desired lateral velocity (the second term) and avoid the abrupt change of the yaw angle between each time step and improve the smooth of the trajectory (the third term). a, band care scaling factors of each term.krepresents the time step tk, and k1represents the time step tk1. vxdband vydbrepresent the desired longitudinal velocity and lateral velocity in the body-fixed coordinate system, which can be calculated according to the desired longitudinal velocity vxdgand lateral velocity vydgin the global coordinate system:

vxdb=vxdgcosφ+vydgsinφE28
vydb=vxdgsinφvydgcosφE29

where the desired longitudinal velocity vxdgand lateral velocity vydgalong the desired trajectory in the global coordinate system can be determined according to Eqs. (17), (26).

After the desired longitudinal velocity and yaw angle in the vehicle body-fixed coordinate system are determined, the desired tyre forces and yaw moment to achieve these desired control targets can be calculated by the lower-level trajectory controller in the next section.

4. Lower-level trajectory tracking controller

In this section, the lower-level two-layer trajectory tracking controller is proposed to control the autonomous vehicle to follow the desired planned trajectory [21]. In the first layer, according to the desired longitudinal velocity, desired zero lateral velocity and desired yaw angle, the desired longitudinal force, lateral force and yaw moment in the vehicle body-fixed coordinate system can be calculated. In the second layer, the individual steering and driving actuators are optimised and controlled to achieve the desired longitudinal force, lateral force and yaw moment.

4.1 Trajectory tracking controller in the first layer

First, the error dynamics equation of vehicle trajectory tracking including the longitudinal velocity error, lateral velocity error and yaw angle error is presented to calculate the feedback tyre force and moment, which can be presented by the following equation based on [25]:

vy=vxsinφ+vycosφvydE30
vx=vxcosφvysinφvxdE31
φ=φactφdE32

where φactis the actual measurement yaw angle. vxand vyare actual measurement feedback longitudinal and lateral velocity. vxand vyare longitudinal velocity error and lateral velocity error, respectively. In order to improve the vehicle stability, the desired lateral velocity vydis assumed as zero value.

The feedback tyre force and moment can be determined according to the tracking error dynamics in Eqs. (30–32):

Fx,feedback=K1vxE33
Fy,feedback=K2pvyK2dv̇yE34
Mz,feedback=K3pφK3dφ̇E35

where K1,K2p,K2d,K3pandK3drepresent feedback control gains.

The feedforward tyre force and moment can be calculated as:

Fx,forward=mv̇xdmvyφ̇dE36
Fy,forward=mvxdφ̇d+mvxφ̇dE37
Mz,forward=Izφ¨dE38

The vehicle total desired longitudinal force Fx,total, lateral force Fy,totaland yaw moment Mz,totalcan be determined by adding up feedforward and feedback terms:

Fx,total=mv̇xdmvyφ̇dK1vxE39
Fy,total=mvxdφ̇d+mvxφ̇dK2pvyK2dv̇yE40
Mz,total=Izφ¨dK3pφK3dφ̇E41

4.2 Trajectory controller in the second layer

In this section, the individual steering and driving control actuators are allocated and controlled to achieve the desired total longitudinal tyre force, the desired total lateral tyre force and desired yaw moment determined in the first layer of trajectory controller. First the individual tyre forces are optimal allocated by the optimisation cost function, and then the allocated tyre forces can be mapped into the individual steering and driving control actuators.

The mathematical equation of cost function of this control allocation and optimisation problem can be shown as follows:

minFti,FsiJ3=Ftfl2+Fsfl2μ2Fzfl2+Ftfr2+Fsfr2μ2Fzfr2+Ftrl2+Fsrl2μ2Fzrl2+Ftrr2+Fsrr2μ2Fzrr2E42

with the constraints of:

BxF=Fx,totalE43
ByF=Fy,totalE44
BrF=Mz,totalE45

where F=FtflFtfrFtrlFtrrFsflFsfrFsrlFsrrT,Bx=cosδflcosδfrcosδrlcosδrrsinδflsinδfrsinδrlsinδrr.

By=sinδflsinδfrsinδrlsinδrrcosδflcosδfrcosδrlcosδrr

Br=lfsinδfl+0.5bfcosδfllfsinδfr0.5bfcosδfr
lrsinδrl+0.5brcosδrllrsinδrr0.5brcosδrr
lfcosδfl0.5bfsinδfllfcosδfr+0.5brsinδfr
lrcosδrl0.5brsinδrllrcosδrr+0.5brsinδrr
Fti2+Fsi2μFzi2E46

where the optimisation variables of this cost function are individual tyre forces Fti, and Fsi. Fx,total,Fy,totalandMz,totalare the desired total longitudinal tyre force, lateral tyre force and yaw moment determined in the first layer controller. The effect of tyre friction circle is considered in (46). The constraints (43), (44) and (45) are used to achieve the desired total longitudinal tyre force, lateral tyre force and yaw moment. In order to overcome the model error due to the non-linear characteristic of the vehicle dynamics model, the sliding-mode controller (SMC) is applied and included in constraints (43), (44) and (45) to accurately track the desired total tyre forces and yaw moment. After applying the SMC control law, the following equations are proposed to replace the constraints (43), (44), (45):

BxF=Fx,totalKs1sgnS1E47
ByF=Fy,totalKs2sgnS2E48
BrF=Mz,totalKs3sgnS3E49

where Ks1,Ks2and Ks3are positive control gains of SMC. The sliding surface S1,S2and S3in Eqs. (47)(49) can be presented as follows:

S1=BxFFx,totalE50
S2=ByFFy,totalE51
S3=BrFMz,totalE52

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 the individual tyre force according to the following equations:

Ti=FtiRωE53
δfl=FsflCα+lfrvxE54
δfr=FsfrCα+lfrvxE55
δrl=FsrlCαlrrvxE56
δrr=FsrrCαlrrvxE57

This controlled actuator values can be input into actual electric vehicle to achieve desired vehicle trajectory.

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.

SymbolDefinitionValues
mMass1298.9 kg
lfDistance of CG from the front axle1.3 m
lrDistance of CG from the rear axle1.5 m
bfFront track width1.6 m
brRear track width1.6 m
CsLongitudinal stiffness of the tyre50,000 N/unit slip
CαCornering stiffness of the tyre30,000 N/unit slip
IzVehicle moment of inertial about yaw axle3900 kgm2
IxVehicle moment of inertial about longitudinal axle765 kgm2
IyVehicle moment of inertial about lateral axle3477 kgm2
RωWheel radius0.3 m
IωWheel moment of inertial4 kgm2
eThe distance between the vehicle roll centre and CG0.4 m
hHeight of the vehicle centre of gravity0.533 m
KϕThe stiffness of roll axis89,000

Table 1.

The simulation parameters [18].

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 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.

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].

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 two-wheel 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.

Figure 4.

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

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, Vxd4andVxd5are desired longitudinal velocities on each section of road, while Vyd1, Vyd2, Vyd3,Vyd4andVyd5are 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.

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].

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 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 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.

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 8.

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

Figure 9.

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

Figure 10.

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

6. Conclusion

In this chapter, a dynamically integrated spatiotemporal-based trajectory planning and control method for the off-road autonomous vehicles is proposed. The upper-level trajectory planner can select the best time-parameterised trajectory among a group of the candidate trajectories by considering the road topography information. Then, the lower-level trajectory controller can control the motion of the vehicle and achieve the desired trajectory.

Simulation results have proved that the proposed trajectory planning and control method can successfully control the motion of autonomous vehicles and achieve the spatiotemporal-based desired trajectory while satisfying the target ending position and velocity. In the highway scenario, the proposed method has better overall position tracking control performance and can better achieve the desired longitudinal and lateral velocity compared with the conventional potential field method. In addition, the 4WIS-4WID vehicle shows better tracking control performance than traditional vehicle based on two-wheel model.

In the off-road scenario, the proposed trajectory planning method can successfully find a specific trajectory which can avoid the peak values of bank angle and road slope. Simulation results prove that the proposed trajectory planner when considering the road topography information can generate the trajectory with much smaller bank angle and road slope compared with trajectory generated by traditional trajectory planner. The actual trajectory tracking performance, roll stability and pitch stability performance can be improved by using the proposed trajectory planning method to minimise the effect of road topography on vehicle dynamics.

Conflict of interest

We declare that there is no conflict of interest in this chapter.

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Boyuan Li, Haiping Du and Bangji Zhang (April 2nd 2019). Path Planning for Autonomous Vehicle in Off-Road Scenario, Path Planning for Autonomous Vehicles - Ensuring Reliable Driverless Navigation and Control Maneuver, Umar Zakir Abdul Hamid, Volkan Sezer, Bin Li, Yanjun Huang and Muhammad Aizzat Zakaria, IntechOpen, DOI: 10.5772/intechopen.85384. Available from:

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