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Vehicle System Dynamics
International Journal of Vehicle Mechanics and Mobility
ISSN: 0042-3114 (Print) 1744-5159 (Online) Journal homepage: http://www.tandfonline.com/loi/nvsd20
Emergency steering control of autonomous vehicle
for collision avoidance and stabilisation
Xiangkun He, Yulong Liu, Chen Lv, Xuewu Ji & Yahui Liu
To cite this article: Xiangkun He, Yulong Liu, Chen Lv, Xuewu Ji & Yahui Liu (2018): Emergency
steering control of autonomous vehicle for collision avoidance and stabilisation, Vehicle System
Dynamics, DOI: 10.1080/00423114.2018.1537494
To link to this article: https://doi.org/10.1080/00423114.2018.1537494
Published online: 01 Nov 2018.
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VEHICLE SYSTEM DYNAMICS
https://doi.org/10.1080/00423114.2018.1537494
Emergency steering control of autonomous vehicle for
collision avoidance and stabilisation
Xiangkun Hea, Yulong Liua, Chen Lvb,XuewuJi
aand Yahui Liua
aThe State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing, People’s Republic
of China; bThe School of Mechanical and Aerospace Engineering and the School of Electrical and Electronic
Engineering, Nanyang Technological University, Singapore, Singapore
ABSTRACT
Collision avoidance and stabilisation are two of the most crucial
concerns when an autonomous vehicle finds itself in emergency sit-
uations, which usually occur in a short time horizon and require
large actuator inputs, together with highly nonlinear tyre cornering
response. In order to avoid collision while stabilising autonomous
vehicle under dynamic driving situations at handling limits, this
paper proposes a novel emergency steering control strategy based
on hierarchical control architecture consisting of decision-making
layer and motion control layer. In decision-making layer, a dynamic
threat assessment model continuously evaluates the risk associated
with collision and destabilisation, and a path planner based on kine-
matics and dynamics of vehicle system determines a collision-free
path when it suddenly encounters emergency scenarios. In motion
control layer, a lateral motion controller considering nonlinearity
of tyre cornering response and unknown external disturbance is
designed using tyre lateral force estimation-based backstepping
sliding-mode control to track a collision-free path, and to ensure
the robustness and stability of the closed-loop system. Both simula-
tion and experiment results show that the proposed control scheme
can effectively perform an emergency collision avoidance manoeu-
vre while maintaining the stability of autonomous vehicle in different
running conditions.
ARTICLE HISTORY
Received 5 February 2018
Revised 28 September 2018
Accepted 2 October 2018
KEYWORDS
Autonomous vehicle;
emergency steering control;
collision avoidance; vehicle
dynamics; driving limits
1. Introduction
Motor vehicles have become an indispensable means of transportation in the present-day
world, but the mobility brought by vehicles comes at a price [1–3]. In 2015, about 1.3 mil-
lion people around the world were killed in trac accidents, ranking tenth on the World
Health Organisation’s list of top causes of death [4]. Ninety-three per cent of the motor
vehicle trac crashes can be traced to human error [5]. With the rapid development of
articial intelligence and automobile technology, autonomous vehicle is expected to take
more burden and stress from human driver, thus enhancing safety and reducing driver’s
CONTACT Yahui Liu liuyahui@tsinghua.edu.cn; Xuewu Ji jixw@mail.tsinghua.edu.cn
© 2018 Informa UK Limited, trading as Taylor & FrancisGroup
2X. HE ET AL.
workload, etc [6–8]. Autonomous vehicle is a product of multi-disciplinary knowledge and
theories, in which environmentrecognition system, decision-making system, motion con-
trol system are the three main components of the software system [9,10]. Many researchers
have reported the progress made on overall architecture and feasibility of autonomous vehi-
cle technology [11–14]. This paper mainly focuses on the decision-making and motion
control of autonomous vehicle.
Accident analysis shows that collision accounts for 97.8% of all trac accidents [15].
There are two main reasons for them. First, misjudgment of vehicle travelling risk by
driver. Second, driver’s operational error or delayed reaction. Therefore, collision avoid-
ance technology for autonomous vehicle has become a hot topic for researchers. A collision
avoidance strategy for autonomous vehicle was proposed using hierarchical frameworks, in
which a high-level MPC algorithm communicates collision-free paths to a low-level MPC
algorithm responsible for path tracking [16]. A collision avoidance system for autonomous
vehicle was developed using a motion planner and MPC-based active vehicle steering
and active wheel torque control [17]. An additional feature of an MPC-based strategy for
collision avoidance is that it continuously optimises the performance index by receiving
information about vehicle position, heading angle and obstacles in the environment [18]. A
rear-end collision avoidance system of autonomous vehicle was designed using hierarchical
scheme consisting of linear threat assessment, projected escape path planning with non-
zero initial condition, reference path generator and linear state feedback controller [19].
A shared control method of semiautonomous vehicle was proposed for obstacle avoid-
ance and stability control using two safe driving envelopes [20]. In this method, one of
the envelopes was dened by vehicle driving limits, and the other by spatial limitations
imposed by lane boundaries and obstacles. In addition, an MPC-based strategy deter-
minedateachtimestepwhetherthecurrentdriver’scommandallowedforasafevehicle
path within these two envelopes, intervening only when such a path did not exist. A dual-
envelop-oriented path-tracking scheme for autonomous vehicle was described in [21], in
which the shape of vehicle was considered as inner-envelop and the feasible road region
was described as outer-envelop. Then an implicit linear MPC algorithm was proposed to
design moving horizon path-tracking controller to handle dangerous scenarios that may
lead to collision or running out of road. A two-stage control approach was proposed for
autonomous vehicle obstacle avoidance in highway cruise conditions [22]. In this scheme,
an outer-loop nonlinear nonconvex model predictive control was adopted to generate the
collision-free path, and an inner-loop linear controller with preview information was used
to track collision-free trajectory. A collision avoidance system for autonomous vehicle
is developed, which mainly consisted of a path planner and a robust tracking controller
[23]. In this system, the path planner was designed based on polynomial parameterisa-
tion optimised by simulated annealing algorithm, and the robust tracking controller was
designed to resist external disturbances and follow planning path. A path-planning method
based on the theory of virtual potential eld and a path-tracking strategy using multi-
constrained MPC were proposed for autonomous vehicle, which seeks to minimise the
incidence for collision on roads [24]. An improved reinforcement learning algorithm was
applied to develop an obstacle avoidance control scheme so that autonomous vehicle could
execute continuous actions [25]. Moreover, the vehicle dynamics constraints and trac
rule constraints were added to the control strategy, which makes vehicle motion more
eective.
VEHICLE SYSTEM DYNAMICS 3
However, when autonomous vehicles leave research laboratory and enter public traf-
c,theymustbeabletodealwithemergencysituations,someofwhichmaynecessitate
manoeuverings, such as emergency collision avoidance, which happens in a short time
horizon and requires large actuator inputs, together with high yaw rates. Tyres will be
highly saturated and begin to sideslip. In this situation, the characteristics of tyre force
become highly nonlinear, making it dicult to stabilise the vehicle. Meanwhile, path
following can no longer be executed eectively, as this may jeopardise vehicle stability.
For these reasons, emergency collision avoidance technology of autonomous vehicle has
attracted wide attention from academia and industry in recent years. Biral et al. pro-
posed a four-wheel optimal steering control scheme of emergency collision avoidance
for semiautonomous vehicle based on optimal control, in order to fully exploit vehicle’s
manoeuvrability limits [26]. Seewald et al. proposed an emergency collision avoidance
strategy for semiautonomous vehicle by path planner using a 5th order polynomial and
nonlinear vehicle lateral controller [27,28]. Cao et al. designed a comprehensive architec-
ture of emergency collision avoidance system for autonomous vehicle, which integrated
adecision-makingmodule,apathplanningmodule,anMPC-basedlateralmotioncon-
trol module and a fuzzy logic-based longitudinal motion control module to deal with
potential hazards on road [29]. To deal with the coupled and nonlinear features of vision-
based autonomous vehicle under the conditions of emergency avoidance of obstacles, Guo
et al. developed a coordinated steering and braking control scheme based on nonlinear
backstepping control framework and adaptive fuzzy sliding-mode control technique [30].
Funke et al. proposed a control strategy that integrates path tracking, vehicle stabilisa-
tion and collision avoidance and mediates among these sometimes conicting objectives
by giving priority to emergency collision avoidance [31]. In addition, the framework was
implemented using a feedback-feedforward-based longitudinal motion controller and an
MPC-based lateral motion controller.
Although the above research achievements were successful to some extent, there is still
room for improvement and perfection. Firstly, most of the studies did not discuss threat
assessment associated with collision and destabilisation of autonomous vehicle. Secondly,
some researchers, in attempting to solve problems connected with emergency collision
avoidance for autonomous vehicle, tend to focus on obstacle avoidance technology within
or close to the linear region of tyres. Thirdly, due to the fact that tyre operating at or close to
its physical limits of friction exhibits highly nonlinear cornering response and the fact that
unknown external disturbances can be caused by changing driving conditions, most of the
control schemes mentioned above would be insucient to ensure path-tracking capability
and stability of autonomous vehicle in emergency collision avoidance.
Based on above analysis, it is necessary to investigate how to eectively conduct threat
assessment associated with collision and destabilisation, and to reduce the adverse eects of
nonlinearity of tyre cornering response and unknown external disturbance on emergency
collision avoidance for autonomous vehicle at or near the physical limits of tyre friction.
For threat assessment, compared with time to collision (TTC) scheme, dynamic safety dis-
tance model was found to be better at considering the risk of collision and destabilisation
for autonomous vehicle [19,28]. For tyre nonlinearity and unknown external disturbance,
the combined scheme of dynamic states estimation and nonlinear robust control could be
an eective solution. With higher lateral accelerations or lower road adhesion, the char-
acteristics of tyre force would become highly nonlinear or saturated, making it dicult to
4X. HE ET AL.
Figure 1. Architecture of emergency collision avoidance control scheme.
control the vehicle. Therefore, estimation of tyre lateral force can eectively compensate for
the nonlinearity and uncertainty of system, thus improving vehicle control performance at
or close to the driving limits. The backstepping sliding-mode control is a specic type of
robust control, which combines the merits of both backstepping control and sliding-mode
control, and has shown its eectiveness in dealing with multiple dynamics, nonlinearity
and uncertainty [32,33]. The central idea of backstepping sliding-mode control is that some
appropriate functions of state variables are selected recursively as pseudocontrol inputs for
lower dimension subsystems of the overall system [34]. Moreover, the Lyapunov function
is used to guarantee the asymptotic stability of each subsystem. Nevertheless, this type of
approach is designed on the basis of an assumed mathematical model, whose imperfections
can lead to the lowered performance of the controller. Hence, the need to design some kind
of compensator is clear.
Based on these considerations, for emergency scenarios on expressway, this paper
proposes a novel emergency steering control strategy which can maintain autonomous
vehicle’s stabilisation while avoiding collision in dynamic driving situations at handling
limits. A block diagram of architecture for the emergency steering control scheme is shown
in Figure 1, which consists of decision-making layer and motion control layer. In decision-
making layer, a dynamic threat assessment model continuously analyses the risk associated
with collision and destabilisation, and a path planner based on kinematics and dynamics
of vehicle system determines a collision-free path when vehicle suddenly enters emergency
situations. In motion control layer, a lateral motion controller considering nonlinearity of
tyre cornering response and unknown external disturbance is developed using tyre lat-
eral force estimation-based backstepping sliding-mode control to track the collision-free
path, and to guarantee the robustness and stability of the closed-loop system. Finally, a
Matlab/Simulink-CarSim co-simulation and a test in hardware-in-the-loop (HIL) system
were conducted to verify the eectiveness of the proposed control scheme.
This paper is organised as follows: in Section 2 the decision-making layer is designed,
including a dynamic threat assessment model and a path planner. In Section 3, the motion
VEHICLE SYSTEM DYNAMICS 5
control layer is illustrated. In Section 4 and Section 5, the simulation results and experiment
results are analysed. Finally, the conclusion of this paper is made in Section 6.
2. Decision-making layer design
Thedecision-makinglayerconsistsofadynamicthreatassessmentmodelandapathplan-
ner. The former continuously analyses the risk metricsassociatedwithcollisionanddesta-
bilisation. The latter, based on fth-order polynomial equation, calculates a collision-free
trajectory considering the constraints of kinematics and dynamics when an autonomous
vehicle encounters an emergency situation.
As shown in Figure 2, a single lane change manoeuvre is adopted to avoid collision. A
fth-order polynomial equation can be used to describe the path of lane change:
y=ATX,(1)
with
A=a0a1a2a3a4a5T,
X=1xx
2x3x4x5T,
where x,yare the longitudinal and lateral coordinates for the escape path, and an
(n=1,2, ...)ispolynomialcoecients.
The boundary restraint conditions of the fth-order polynomial are dened as:
⎧
⎪
⎨
⎪
⎩
y(x0)=0, y(xT)=yT
˙
y(x0)=0, ˙
y(xT)=0
K(x0)=0, K(xT)=0
,(2)
with
K=d2y/dx2
[1 +(dy/dx)2]3/2,
where x0and y0are longitudinal and lateral coordinates of vehicle centroid at the beginning
moment of collision avoidance manoeuvre respectively, and x0=0, xTand yTare longi-
tudinal and lateral terminal point coordinates for the collision-free trajectory respectively,
Kis the curvature of the path.
Figure 2. Illustration of the collision-free trajectory.
6X. HE ET AL.
Substitute Equation (1) into the boundary restraint conditions, the following relation
can be obtained:
BA =0yT0000
T,(3)
where
B=
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎣
1x0x2
0x3
0x4
0x5
0
1xTx2
Tx3
Tx4
Tx5
T
012x03x2
04x3
05x4
0
012xT3x2
T4x3
T5x4
T
00 2 6x012x2
020x3
0
00 2 6xT12x2
T20x3
T
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎦
.
with Equation (3), the coecients Acan be derived from:
A=00010
yT
x3
T
−15 yT
x4
T
6yT
x5
TT.(4)
Combining Equation (1) and Equation (4), the expression of collision-free trajectory can
be obtained:
y(x)=10yTx
xT3
−15yTx
xT4
+6yTx
xT5
.(5)
So far the path planning process has only considered kinematic constraint conditions.
However, in an emergency collision avoidance, tyre could be highly saturated and begin
to sideslip, which makes it dicult to stabilise the vehicle. Therefore, in the decision-
making layer, vehicle dynamics constraint conditions need to be taken into consideration,
and a dynamic threat assessment model has to be designed to continuously assess the risk
associated with collision and destabilisation.
The lateral acceleration at the barycentre of vehicle can be dened as:
ay=vxγ+˙vy,(6)
with
vy=vxtan(β),
where vxis longitudinal velocity, vyis lateral velocity, γis yaw rate of vehicle body, βis
sideslip angle of vehicle body.
By Equation (6), the lateral acceleration is described as:
ay=vxγ+˙vxtan(β) +vx˙
β
1+tan2(β) .(7)
The lateral acceleration must be bounded by tyre–road friction coecient, and then the
following relation can be given:
vxγ+ac≤μg,(8)
with
ac=˙vxtan(β) +vx˙
β
1+tan2(β) ,
where μis tyre–road friction coecient, gis gravitational acceleration.
VEHICLE SYSTEM DYNAMICS 7
Dene the following relation as:
ac=(1−k)μg,(9)
where k(0 <k<1) is dynamic factor.
Combining Equation (8) and Equation (9), the following relation can be obtained:
γ≤kμg
vx
. (10)
According to the kinematic principle, desired yaw rate can be given:
γd=Kvx. (11)
With Equation (2) and Equation (5), Equation (11) can be written as:
γd=
60yTx
x3
T
−180yTx2
x4
T
+120yTx3
x5
T
1+30yTx2
x3
T
−60yTx3
x4
T
+30yTx4
x5
T23
2
vx
=60yTU(U−1)(2U−1)
x2
T1+30yT
xT2U4(U−1)43
2
vx, (12)
where
U=x
xT
.
Considering that genetic algorithm has the ability to search a global optimal, and it can
solve any kind of continuous or discrete optimisation problem [35], this paper adopts the
optimisation scheme as shown in Figure 3.ThepopulationsizeNp, the chromosome length
Lc and the termination generation Gt are designed to be 100, 20 and 500, respectively. The
crossover probability Pc and the mutation probability Pm are selected to be 0.8 and 0.1,
respectively.
Figure 3. Illustration of the genetic algorithm scheme.
8X. HE ET AL.
As a result, when Uequals about 0.20, the equivalent maximum value of desired yaw
rate can be obtained:
γde_max =p1yT
x2
T1+p2y2
T
x2
T3
2
vx, (13)
where p1,p2are gain parameters, and the approximate values are 5.76 and 0.59, respectively.
Since the desired yaw rate must satisfy vehicle dynamics constraint conditions, the
following relation can be given:
|γde_max|≤kμg
vx
, (14)
Combining Equation (13) and Equation (14), the following relation can be obtained:
f(vx,k,μ,xT,yT)≤0, (15)
with
f=v2
x
kμg
p1yT
x2
T1+p2y2
T
x2
T3
2
−1,
where fis risk assessment function.
During collision avoidance, in order to more eectively assess risks and further explore
the limits of safe driving, real-time distance between following vehicle and lead vehicle
should be adopted.
Design the following relations as:
xT=nx
yT=my
, (16)
where n,mare positive proportional coecients.
The adopted emergency collision avoidance scheme is shown in Figure 4,wherexis
the vehicle-to-vehicle longitudinal distance from radar or camera, and yis lateral dis-
placement of following vehicle when driving distance is x, respectively. The assumption
that (x,y) is a point on the collision-free trajectory, and combining Equation (5) and
Equation (16), the following equation can be obtained:
m=n5
10n2−15n+6. (17)
Substitute Equation (16) and Equation (17) into the risk assessment function f,the
improved risk assessment function Eis derived:
E=v2
x
kμg
p1y
x2
1+p2y2
x2
n8
(10n2−15n+6)23
2
n3
10n2−15n+6−1. (18)
Let the improved risk assessment function Ebe zero, that is E=0. The longitudinal
distance between following vehicle and lead vehicle xand the positive proportional coef-
cient nare regarded as dependent variable and independent variable, respectively. Other
VEHICLE SYSTEM DYNAMICS 9
Figure 4. Illustration of emergency collision avoidance scheme.
Figure 5. Illustration of the critical dynamic factor at different vehicle-to-vehicle distance, different
velocity and different tyre–road friction coefficient.
termsinEquation(18)areregardedasconstants.Theminimumofxcan be obtained
when napproximately equals 2.2. In addition, by Equation (17), when nequals 2, mequals
2. Therefore, in order to simplify the design process, n=2 is selected in this section, and
Equation (18) can be written as:
E=1
2
v2
x
kμg
p1y
x2
1+p2y2
x2
3
2
−1. (19)
Let E=0, the critical dynamic factor is derived:
kc=1
2
v2
x
μg
p1y
x2
1+p2y2
x2
3
2
, (20)
The critical dynamic factor kccan predict and analyse the emergency degree of collision
avoidance process. Passenger vehicle width is about 1.8m, and safety margin of lateral dis-
placement is set to 0.4 m in this section, and yis designed to be 2.2 m. As shown in Figure
5,thecriticaldynamicfactorkcincreases with vx,withthedecreaseofxand μ.Moreover,
it can be seen that the kcon the domain (0.8, 1) increases sharply with the decrease of x
and the increase of vx.
10 X. HE ET AL.
Figure 6. Logic diagram of decision-making for emergency collision avoidance.
Figure 7. Observation for minimum lateral distance from lead vehicle during emergency collision
avoidance.
Therefore, Equation (20) is adopted as dynamic threat assessment model in this paper.
It can be seen from Figure 6that, when the kcis greater than threat threshold Th,anemer-
gency collision avoidance manoeuvre is triggered, else it is not activated. Considering that
the kcon the domain (0.8, 1) increases sharply with the decrease of xand the increase
of vx, and this work focuses on emergency collision avoidance situation, the This set
to 0.85.
In order to evaluate the eectiveness of the proposed emergency collision avoidance
scheme, minimum lateral distance from lead vehicle needs to be observed. As shown
in Figure 7,Gis barycentre of following vehicle, ψis the vehicle heading, D0is the
distancebetweenmiddlepointforthebackofleadvehicleandthemedialaxisoffol-
lowing vehicle, Wland Wfare lead vehicle width and following vehicle width respec-
tively. Therefore, in this paper, the minimum lateral distance from lead vehicle can be
described as:
DL=[yfcot(ψ) +xl0−xf]sin(ψ) −1
2(Wf+Wl), (21)
where (xf,yf) is the barycentric coordinate of following vehicle, (xl0,0) is middle point
coordinate for the back bumper of lead vehicle.
Because tyre–road information and vehicle states estimation schemes have already
been discussed in detail in [36–38], it is assumed that tyre–road friction coecient, vehi-
cle velocity and sideslip angle can be estimated directly, and other control data can be
measured by environment recognition system or sensing system.
VEHICLE SYSTEM DYNAMICS 11
3. Motion control layer design
Inthissection,thedesignoflateralmotioncontrollerisshown,whichadoptsatyrelateral
force estimation-based backstepping sliding-mode control strategy. To focus on the study
of emergency collision avoidance for autonomous vehicle, the control of actuator is not
discussed in this study.
3.1. System models for control design
To design control law, the system models are established in this section, which consist of
vehicle kinematics model and vehicle dynamics model.
3.1.1. Vehicle dynamics model
In designing vehicle steering controller, a widely used simplied vehicle model with
two-degrees-of-freedom (2DOF) is employed to capture the vehicle’s essential lateral
dynamics:
⎧
⎪
⎪
⎨
⎪
⎪
⎩
˙
β=(FL +FLfr)+(FLrl +FLrr )
mvx
−γ
˙γ=a(FL +FLfr)−b(FLrl +FLrr )
Jz
, (22)
where mis the vehicle total mass, Jzis yaw moment of inertia, aand bare distance
from the centre of gravity to front and rear-axle, respectively, FLf and FLr are tyre lat-
eral forces of front-axle and rear-axle, FL and FLfr aretyrelateralforcesontheleftand
right of front-axle, FLrl and FLrr are tyre lateral forces on the left and right of rear-axle,
respectively.
3.1.2. Vehicle kinematics model
To focus on path-tracking ability, the state variables of vehicle dynamics are transformed
into state variables relevant to the collision-free path. Generally, it is desirable to eliminate
both lateral error eand heading error ψ. But only one of them can be reduced with single
input steering angle δf.Inthispaper,theprojectederrorepisadoptedtocombinethelateral
error eand the heading error ψ. The vehicle kinematics model for the states in Figure 8
is given by:
⎧
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎩
˙
e=vxsin(ψ) +vycos(ψ)
˙
s=vxcos(ψ) −vysin(ψ)
ep=e+xpsin(ψ)
ψ =ψ−ψr
, (23)
where sis the distance along the reference path, ψris the heading of the reference path and
xpis the constant projected distance.
12 X. HE ET AL.
Figure 8. Vehicle system model used for motion control.
3.2. Realisation of tyre lateral force estimation-based backstepping sliding-mode
control scheme
According to small angle approximation for ψ ,andbydierentiatingepand ψ in
Equation (23), the following relations can be obtained:
⎧
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎩
˙
e=vy+vxψ
ep=e+xpψ
˙
ep=˙
e+xp˙
ψ
˙
ψ=γ−K˙
s
. (24)
In the case of relatively high lateral acceleration or low adhesion, the closed-loop steering
responsebecomesunderdamped,andtheresultwillbesignicantoscillationofyawrate
[39]. In order to eliminate the projected error and the oscillation of yaw rate, with Equation
(24), the following relations can be derived:
¨
ψ=˙γ−˙
K˙
s−K¨
s, (25)
¨
e=˙vy+˙vxψ +vx˙
ψ, (26)
¨
ep=˙vy+˙vxψ +vx(γ −K˙
s)+xp(˙γ−˙
K˙
s−K¨
s). (27)
Substitute Equation (22) into Equation (27), the following equation can be obtained:
¨
ep=˙vy+˙vxψ +vx(γ −K˙
s)+xpa(FL +FLfr)−b(FLrl +FLrr )
Jz
−˙
K˙
s−K¨
s.
(28)
In practical situation, measuring tyre lateral forces is dicult for technical, physical and
economic reasons. Therefore, these important data need to be observed or estimated. In
VEHICLE SYSTEM DYNAMICS 13
order to fully represent the tyre cornering characteristics, the following estimation method
ofnonlineartyrelateralforceisadopted:
ˆ
FL=ˆ
FL ˆ
FLfr
ˆ
FLrl ˆ
FLrr =μˆ
Cαfμˆ
Cfrαf
μˆ
Crlαrμˆ
Crrαr, (29)
where αfand αrare slip angles of front-axle tyres and rear-axle tyres, Cand Cfr are
tyre cornering stinesses on the left and right of front-axle, Crl and Crr aretyrecorner-
ing stinesses on the left and right of rear-axle respectively. In addition, using small angle
approximations, the tyre slip angles of front-axle and rear-axle can be described as:
⎧
⎪
⎪
⎨
⎪
⎪
⎩
αf=arctan vsin(β) +aγ
vcos(β) −δf≈β+aγ
vx−δf
αr=arctan vsin(β ) −bγ
vcos(β) ≈β−bγ
vx
, (30)
where δfis front wheel steering angle, vis the velocity of vehicle.
In order to fully represent the tyre cornering characteristics, the following Pacejka
nonlinear cornering stinesses are adopted [40]:
⎧
⎪
⎨
⎪
⎩
ˆ
C=Cf0sin 2arctanˆ
FZ
Zf0,ˆ
Cfr =Cf0sin 2arctanˆ
FZfr
Zf0
ˆ
Crl =Cr0sin 2arctanˆ
FZrl
Zr0,ˆ
Crr =Cr0sin 2arctanˆ
FZrr
Zr0 , (31)
where Cf0and Cr0are normal cornering stinesses of front-axle and rear-axle, Zf0and Zr0
are load factors of front-axle and rear-axle respectively.
Considering the longitudinal and lateral acceleration, the vertical load of each wheel can
be estimated by [41]:
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎩
ˆ
FZ =(gb
2−˙vxh
2−˙vybh
c+˙vx˙vyh2
gc )m
L
ˆ
FZfr =(gb
2−˙vxh
2+˙vybh
c−˙vx˙vyh2
gc )m
L
ˆ
FZrl =(ga
2+˙vxh
2−˙vyah
c−˙vx˙vyh2
gc )m
L
ˆ
FZrr =(ga
2+˙vxh
2+˙vyah
c+˙vx˙vyh2
gc )m
L
, (32)
where his the height of the centre of gravity, cis track width, Lis wheelbase.
Combining Equations (28), (29) and (30), the following relations can be obtained:
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎩
¨
ep=p1+p2+p3δf
p1=˙vy+˙vxψ +vx(γ −K˙
s)
p2=xpμa(vxβ+aγ)(ˆ
C+ˆ
Cfr)
vxJz
−μbαr(ˆ
Crl +ˆ
Crr)
Jz
−˙
K˙
s−K¨
s
p3=−xp
μa(ˆ
C+ˆ
Cfr)
Jz
. (33)
In order to take into account random road input’s inuence on lateral motion control per-
formance of autonomous vehicle, the equivalent random disturbance acting on front-axle
14 X. HE ET AL.
is dened as [42]:
dfe(·)=p3
de(·)
i, (34)
with
|dfe(·)|≤D,
where de(·) is equivalent random disturbance acting on steering actuator, iis steering ratio,
Disapositiveconstant.
Hence, under equivalent random disturbance, Equation (33) can be written as:
¨
ep=p1+p2+p3δf+de(·)
i
=p1+p2+p3δf+dfe(·). (35)
In addition, for the design of the proposed control scheme, the nonlinear vehicle-road
system with the disturbance can be transformed into the following form:
˙
x1=x2
˙
x2=p1+p2+p3δf+dfe(·), (36)
where x1=ep.
In the following part, the design procedure of backstepping sliding-mode control
approach for system (36) is given.
Step 1. With Equation (36), the tracking error e1and its corresponding rst order
derivative are dened as:
⎧
⎪
⎨
⎪
⎩
xd=0
e1=x1−xd=x1
˙
e1=˙
x1−˙
xd=x2
, (37)
where xdis the desired value.
To make the tracking error e1converge to zero, select Lyapunov function as:
L1=1
2e2
1. (38)
Hence, the dierentiation of Equation (38) is derived:
˙
L1=e1˙
e1. (39)
In order to realise ˙
L1≤0, the sliding-mode surface function is dened as:
sf=x2+c1x1
=˙
e1+c1e1, (40)
where c1is a strictly positive gain parameter.
VEHICLE SYSTEM DYNAMICS 15
With Equation (40), Equation (39) can be described as:
˙
L1=e1sf−c1e2
1. (41)
If sf=0, then ˙
L1≤0. Hence, in order to meet the Lyapunov stability theory, the design of
next step is required.
Step 2. Design Lyapunov function as:
L2=L1+1
2s2
f. (42)
Combining Equation (36) and Equation (40), the dierentiation of the sliding-mode
surface function can be written as:
˙
sf=˙
x2+c1˙
x1
=p1+p2+p3δf+dfe(·)+c1˙
e1. (43)
Therefore, the derivative of L2becomes:
˙
L2=˙
L1+sf˙
sf
=e1sf−c1e2
1+sf[p1+p2+p3δf+dfe(·)+c1˙
e1]. (44)
In order to achieve ˙
L2≤0, a stabilising control law is designed:
δf=−
p1+p2+c2sf+e1+c1˙
e1+ηtanh(sf)
p3
, (45)
where c2and ηare the strictly positive gain parameters.
Substitute Equation (45) into Equation (44), with Equation (34) and according to
Appendix A in [42], the following relation can be derived:
˙
L2=−c1e2
1−c2s2
f−ηsftanh(sf)+sfdfe(·)
≤−c1e2
1−c2s2
f−ηsftanh(sf)+|sfdfe (·)|
=−c1e2
1−c2s2
f−ηsftanh(sf)+|dfe (·)|·|sf|
≤−c1e2
1−c2s2
f−ηsftanh(sf)+D|sf|. (46)
The η(or c1,orc2) can be designed, for instance, the following relation:
ηD. (47)
Therefore, the following relation can be obtained:
˙
L2≤−c1e2
1−c2s2
f−ηsftanh(sf)+D|sf|≤0. (48)
Accordingly, x1→0, x2→0andsf→0ast→∞, in which case the closed-loop system
is globally asymptotically stable.
With Equation (45), the control input for steering actuator can be obtained:
δsc =iδf. (49)
The numerical values of main parameters for the lateral motion controller are given in
Table 1.
16 X. HE ET AL.
Tab le 1. The main parameters of the controller.
Symbol Parameters Value Units
aDistance from front-axle to gravity centre 1.192 m
bDistance from rear-axle to gravity centre 1.598 m
cTrack width 1.565 m
hHeight of gravity centre 0.506 m
xpProjected distance 10 m
mVehicle mass 1528.13 kg
JzYaw inertia 2280 kg m2
Cf0Normal cornering stiffness of front-axle 23,000 N/rad
Cr0Normal cornering stiffness of rear-axle 38,000 N/rad
Zf0Load factor of front-axle 6000 N
Zr0Load factor of rear-axle 6500 N
ηStrictly positive gain parameter 1 null
c1Strictly positive gain parameter 20 null
c2Strictly positive gain parameter 20 null
iSteering ratio 18.5 null
4. Simulation and discussions
In our previous work [42,43], the experimental verication of vehicle model was imple-
mented to obtain an accurate simulation model, and the parameters of the vehicle model
were given. In this section, two simulation cases are presented to verify the eectiveness
of the proposed emergency steering control strategy for autonomous vehicle. The co-
simulations are conducted based on Matlab/Simulink – CarSim with a high-delity and
full-vehicle model.
4.1. Test on a low adhesion-coecient road (µ=0.3)
Considering that the vehicle can easily become unstable when it makes a sharp turn on a
low adhesion road, an emergency collision avoidance manoeuvre is conducted on an ice
snow covered pavement with road adhesion coecient μ=0.3 and velocity v=54 km/h
to verify the eectiveness of the emergency steering control scheme for autonomous
vehicle.
As shown in Figure 9(e), the peak lateral accelerations of vehicle controlled by a sliding-
mode control strategy (SMC) based on nominal model [44], by the proposed solutions
without de(·)andwithde(·) are about 2.57 –2.45 and –2.47m/s2,respectively.Hence,
it can be inferred that, during the emergency collision avoidance, the tyres of vehicle
using the dierent methods run in the situation which is very close to tyre–road friction
limit (μg).
The results in Figure 9(a) show that, compared with the SMC strategy, the proposed
solutions without de(·)andwithde(·), both show superior performance in tracking
collision-free trajectory. It can be found from Figure 9(b) that, peak values of lateral
trajectory tracking error of vehicle controlled by the SMC scheme, by the proposed solu-
tions without de(·)andwithde(·) are about –0.19, –0.07 and –0.07m, respectively. Figure
9(c) shows the peak values of heading error for vehicle controlled by the SMC strategy,
by the proposed solutions without de(·)andwithde(·) are about 1.81°, 0.44° and 0.52°,
respectively.
VEHICLE SYSTEM DYNAMICS 17
Figure 9. The results of emergency collision avoidance manoeuvre on an ice snow covered pavement
(µ=0.3). (a) Global trajectory of the path following, (b) path-tracking error, (c) heading error, (d) obser-
vation of minimum lateral distance from lead vehicle, (e) vehicle lateral acceleration, (f) vehicle yaw rate,
(g) vehicle sideslip angle, (h) tyre lateral forces from Carsimand estimated tyre lateral forces for front-axle
and rear-axle, (i) control input of steering actuator and equivalent random disturbance, (j) angle rate of
steering actuator.
18 X. HE ET AL.
It can be seen from Figure 9(d) that, after the vehicle-to-vehicle longitudinal distance is
equal to zero, the minimum lateral distances from lead vehicle DLby the SMC strategy, by
the proposed solutions without de(·)andwithde(·) are about 0.54, 0.60 and 0.60 m, respec-
tively. Hence, the vehicle controlled by any of the three schemes can avoid collision. In the
case of low adhesion coecient, the closed-loop steering response becomes underdamped,
which results in some oscillation in vehicle lateral motion.
Figure 9(e–g) illustrate that, compared with the SMC strategy, the proposed solu-
tion shows more satisfactory dynamics control performance during emergency collision
avoidance. As shown in Figure 9(a–g), the proposed solution can eectively resist against
unknown external disturbance. In Figure 9(h), it can easily be found that, the estimated tyre
lateral forces can converge consistently to the tyre lateral forces from Carsim. As shown in
Figure 9(i), the peak values of steering angle in the proposed solutions without de(·)and
with de(·) are smaller than that of the SMC strategy, and the peak value of the disturbance
is about 16.76° which is roughly a quarter of the peak steering angle controlled by the pro-
posed scheme. It can also be found from Figure 9(j) that, the steering angle rate controlled
by the proposed scheme has faster convergence than that of the SMC strategy.
4.2. Test on a high adhesion-coecient road (µ=1.0)
In order to further evaluate the performance of the proposed control method, an emer-
gency collision avoidance manoeuvre is conducted on a dry asphalt pavement with road
adhesion coecient μ=1.0 and velocity v=90 km/h.
The results in Figure 10(e) show that the peak lateral accelerations of vehicle controlled
by the SMC strategy, by the proposed solutions without de(·)andwithde(·) are about 7.76,
–7.76 and –7.70 m/s2,respectively.Meanwhile,itcanalsobeseenfromFigure10(g) that,
thetyresarehighlysaturated.Hence,itcanbeinferredthat,duringemergencycollision
avoidance,thetyresofvehicleusingthedierentmethodsworkintheirnonlinearregion,
and the autonomous vehicle operates at or close to its driving limits.
In Figure 10(a), it can easily be seen that, compared with the SMC strategy, the proposed
solutions without de(·)andwithde(·), both exhibit satisfactory performance in tracking
collision-free trajectory. As shown in Figure 10(b), peak values of lateral trajectory track-
ing error of vehicle controlled by the SMC strategy, by the proposed solutions without
de(·)andwithde(·) are about –0.86, 0.49 and 0.49 m, respectively. Figure 10(c) shows the
peak values of heading error for vehicle controlled by the SMC strategy, by the proposed
solutions without de(·)andwithde(·) are about 4.95°, –2.87° and 2.86°, respectively.
It can be found from Figure 10(d) that, after the vehicle-to-vehicle longitudinal dis-
tance is equal to zero, the minimum lateral distances from lead vehicle DLby the SMC
strategy, by the proposed solutions without de(·)andwithde(·) are about –0.48, 0.10 and
0.10 m, respectively. Therefore, the vehicle controlled by the SMC strategy cannot avoid
collision on a high adhesion road, and the vehicle controlled by the proposed scheme eec-
tively avoids collision. It can also be seen from Figure 10(d) that, there appears to be some
second order oscillation in the steering response bringing DLquite close to zero. This is
because in the case of high lateral acceleration, the closed-loop steering response becomes
underdamped, which results in some oscillation in vehicle lateral motion.
As shown in Figure 10(e–g), compared with the SMC strategy, the proposed solu-
tion shows more superior dynamics control performance during emergency collision
VEHICLE SYSTEM DYNAMICS 19
Figure 10. The results of emergency collision avoidance manoeuvre on a dry asphalt pavement
(µ=1.0). (a) Global trajectory of the path following, (b) path-tracking error, (c) heading error, (d) obser-
vation of minimum lateral distance from lead vehicle, (e) vehicle lateral acceleration, (f) vehicle yaw rate,
(g) vehicle sideslip angle, (h) tyre lateral forces from Carsimand estimated tyre lateral forces for front-axle
and rear-axle, (i) control input of steering actuator and equivalent random disturbance, (j) angle rate of
steering actuator.
20 X. HE ET AL.
Figure 11. The HIL system for autonomous driving experiment.
Figure 12. Diagram of architecture for the HIL system.
avoidance. As shown in Figure 10(a–g), the proposed solution can eectively resist against
unknown external disturbance. In Figure 10(h), it can be found that the estimated tyre lat-
eral forces can converge consistently to the tyre lateral forces from Carsim. As shown in
Figure 10(i), the steering angle in the proposed solutions without de(·)andwithde(·)are
feweroscillationsthanthatoftheSMCstrategy,andthepeakvalueofthedisturbanceis
about –41.30° which is roughly a quarter of the peak steering angle controlled by the pro-
posedsolution.ItcanalsobeseenfromFigure10(j) that, the steering angle rate controlled
by the proposed scheme has faster convergence than that of the SMC strategy.
5. Experiment results with HIL system
An HIL experiment is conducted to test the real-time performance of the proposed
emergency steering control method for autonomous vehicle. Figure 11 shows the testing
facilities, which consists mainly of a DS1501 MicroAutoBox from dSPACE, a Freescale G36
actuator driver, a steer-by-wire system, a EXLAR electric servo cylinder for steering resis-
tance loading, a BOSCH steering angular sensor, a NI®PXI hardware, a monitor, a power
supply, a terminal block, two host PCs and two displays.
Figure 12 illustrates the implementation architecture of the HIL system, in which
vehicle-road system model of CarSim platform is encoded into NI®PXI hardware. After
obtaining the vehicle motion states from NI®PXI hardware, the proposed strategy, which
VEHICLE SYSTEM DYNAMICS 21
Figure 13. The experiment results of emergency collision avoidance manoeuvre on an ice snow cov-
ered pavement (µ=0.3). (a) path-tracking error, (b) heading error, (c) observation of minimum lateral
distance from lead vehicle, (d) vehicle lateral acceleration, (e) vehicle yaw rate, (f) vehicle sideslip angle,
(g) output of steer-by-wire system and equivalent random disturbance, (h) tyre lateral forces from Carsim
and estimated tyre lateral forces for front-axle and rear-axle.
22 X. HE ET AL.
is implemented in the MicroAutoBox, calculates the steering angle command of the steer-
by-wire system. Then the angle command is sent to the actuator driver to operate the
steer-by-wire system, and the angular sensor feeds the values of corresponding steering
column angle and angular speed back to nonlinear vehicle model of CarSim platform. The
steering resistance torque, which is obtained from CarSim platform, acts on the rack of
thesteer-by-wiresystembytheEXLARelectricservocylinder.Thesamplingrateofthe
experiments is 100 Hz.
In the HIL system, an emergency collision avoidance manoeuvre is performed on a low
adhesion-coecient road with friction coefcient μ=0.3 and velocity v=54 km/h. The
test results are shown in Figure 13.Itcanbeseenthattheresultsaresimilartobutnot
exactly the same as those given by CarSim-Simulink co-simulation. This is mainly because
of communication delay and real characteristics of the electro-mechanical system.
The results in Figure 13(d) show that the peak lateral accelerations of vehicle controlled
by the SMC strategy, by the proposed solutions without de(·)andwithde(·)areabout–
2.63, –2.32 and 2.18 m/s2, respectively. Hence, it can be inferred that, during the emergency
collision avoidance, the vehicle controlled by any of these methods operates in the situation
which is very close to the tyre–road friction limit (μg).
As shown in Figure 13(a), peak values of lateral path-tracking error of vehicle controlled
by the SMC strategy, by the proposed solutions without de(·)andwithde(·)areabout–
0.39, –0.13 and 0.16 m, respectively. Figure 13(b) shows the peak values of heading error
for vehicle controlled by the SMC strategy, by the proposed solutions without de(·)and
with de(·) are about 3.25°, 0.58° and 0.95°, respectively.
It can be seen from Figure 13(c) that, after the vehicle-to-vehicle longitudinal dis-
tance is equal to zero, the minimum lateral distances from lead vehicle DLby the SMC
strategy, by the proposed solutions without de(·)andwithde(·) are about 0.30, 0.54 and
0.51 m, respectively. Therefore, the vehicle controlled by any of the three schemes can avoid
collision.
Figure 13(d–f) illustrate that, compared with the SMC strategy, the proposed solution
shows more superior dynamics control performance during emergency collision avoid-
ance. As shown in Figure 13(a–f), the proposed solution can eectively resist against
unknown external disturbance. As shown in Figure 13(g), the peak values of steering angle
in the proposed solutions without de(·)andwithde(·) are smaller than that of the SMC
strategy, and the peak value of the disturbance is about 16.76° which is roughly a quarter
of the peak steering angle controlled by the proposed method.
As shown in Figure 13(h), the estimated tyre lateral force of rear-axle can accept-
ably converge to the tyre lateral force from Carsim, and there is a signicant mismatch
between the estimated tyre lateral force of front-axle and the tyre lateral force from Carsim.
However, according to above analysis, the proposed solution shows good lateral motion
control performance, that is, the proposed method exhibits superior robustness to model
mismatch.
6. Conclusion
In this paper, a novel emergency steering control strategy is proposed to realise colli-
sion avoidance and ensure the stability of autonomous vehicle at the same time under
dynamic driving situations at handling limits. The proposed scheme adopts a hierarchical
VEHICLE SYSTEM DYNAMICS 23
control architecture consisting of two layers. In the decision-making layer, a dynamic
threat assessment model continuously evaluates the risk associated with collision and
destabilisation, and a path planner based on kinematics and dynamics of vehicle sys-
tem determines a collision-free path when it suddenly enters emergency situations. In
themotioncontrollayer,alateralmotioncontrollerconsideringnonlineartyrecorner-
ing response and unknown external disturbance is developed using tyre lateral force
estimation-based backstepping sliding-mode control approach.
The results of co-simulation and experiment in HIL system show that, in dierent run-
ning conditions, both the proposed schemes without de(·)andwithde(·)canprovide
sucient collision avoidance capability as well as yaw stability for autonomous vehicle at or
close to the driving limits. Compared with the SMC scheme, the proposed strategy shows
superior lateral motion control. In addition, the proposed scheme exhibits satisfactory
robustness to unknown external disturbances in emergency collision avoidance.
In future work, behaviour decision-making considering steering and braking will be
investigated to avoid collision while maintaining stabilisation of autonomous vehicle in
emergency situations.
Disclosure statement
No potential conict of interest was reported by the authors.
Funding
This work was supported by the National Natural Science Foundation of China [grant numbers
U1664263, 51875302], the Independent Research Program of Tsinghua University [grant number
2015Z09006].
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