An overview of vehicular platoon control under the four-component framework

Abstract

The platooning of autonomous ground vehicles has potential to largely benefit the road traffic, including enhancing highway safety, improving traffic utility and reducing fuel consumption. The main goal of platoon control is to ensure all the vehicles in the same group to move at consensual speed while maintaining desired spaces between adjacent vehicles. This paper presents an overview of vehicular platoon control techniques from networked control perspective, which naturally decomposes a platoon into four interrelated components, i.e., 1) node dynamics (ND), 2) information flow topology (IFT), 3) distributed controller (DC) and, 4) geometry formation (GF). Under the four-component framework, existing literature are categorized and analyzed according to their technical features. Three main performance metrics, i.e. string stability, stability margin and coherence behavior, are also discussed.

Full text


Abstract— The platooning of autonomous ground vehicles
has potential to largely benefit the road traffic, including
enhancing highway safety, improving traffic utility and
reducing fuel consumption. The main goal of platoon control is
to ensure all the vehicles in the same group to move at
consensual speed while maintaining desired spaces between
adjacent vehicles. This paper presents an overview of vehicular
platoon control techniques from networked control perspective,
which naturally decomposes a platoon into four interrelated
components, i.e., 1) node dynamics (ND), 2) information flow
topology (IFT), 3) distributed controller (DC) and, 4) geometry
formation (GF). Under the four-component framework, existing
literature are categorized and analyzed according to their
technical features. Three main performance metrics, i.e. string
stability, stability margin and coherence behavior, are also
discussed.
I. INTRODUCTION
The platooning of autonomous vehicles on highway have
attracted extensive interests due to its potential to largely
benefit road traffic, e.g. enhancing highway safety, improving
traffic utility and reducing fuel consumption [1]. The control
of autonomous platoon aims to ensure all the vehicles in the
same group to move at consensual speed while maintaining
the desired spaces between adjacent vehicles [4].
The earliest implementation can date back to the PATH
program during the last eighties in California, in which many
fundamental topics were studied, including major goal of
platooning, division of control tasks, layout of control
architecture, technologies for sensing, actuation and
communication, as well as control laws for headway control,
etc. [2]-[6]. Since then, many issues on platoon control have
been discussed and addressed, such as the selection of spacing
policies [7]-[9], how to consider powertrain dynamics [10],
homogeneity and heterogeneity [11]-[14] etc. Advanced
control methods were also introduced into platoon control to
achieve better performances. For instance, Barooah et al.
(2009) introduced a mistuning-based control method to
improve the stability margin of vehicular platoon [16].
Dunbar and Derek (2012) proposed a distributed receding
The first two authors, S Eben Li and Y. Zheng, are equally contributed to
the research. Supported by NSF of China (51205228), Tsinghua University
Initiative Scientific Research Program (2012THZ0), and Chinese 863 Project
(2012AA111901).
Shengbo Eben Li, Yang Zheng, Keqiang Li, and Jianqiang Wang are with
The State Key Lab of Automotive Safety and Energy, Dept. of Automotive
Eng., Tsinghua University, Beijing 100084, China. (e-mail:
lisb04@gmail.com, zhengy093@gmail.com, likq@tsinghua.edu.cn,
wjqlws@tsinghua.edu.cn). *Corresponding author.
horizon controller and derived the sufficient conditions to
ensure string stability [18]. Ploeg et.al. (2014) developed a

∞
control method, in which the string stability was
explicitly satisfied [20]. More recently, some demos of
platoon control have been performed in the real world,
including the GCDC in the Netherlands [19], SARTRE in
Europe [21], and Energy-ITS in Japan [22], etc.
The earlier platoon often only relies on radar-based sensing
systems, in which the type of information exchange
topologies is quite limited [23]. The rapid deployment of
vehicle-to-vehicle (V2V) communications, such as DSRC
and VANET [24], however, can generate a more variety of
topologies for platoons, e.g. two-predecessor following type
and multiple-predecessor following type [23][25]. New
challenges naturally arise due to the variety of topologies, in
particular when considering the time delay, packet loss, and
quantization error in the communications. In such cases, it is
more preferable to view the vehicular platoon as a network of
dynamical systems, and to employ networked control
perspective to design the distributed controllers. For example,
Oncu et al. (2014) investigated the effect of network-induced
constant delay and sampling-hold process on string stability
from the networked control perspective [27]. Bernardo et al.
(2014) proposed a method to analyze the platooning problem
from the viewpoint of consensus control of a dynamic
network, and proved the stability of platoon in the presence of
time delay [29]. Wang et al. (2014) introduced a weighted
and constrained consensus seeking framework to study the
influence of time-varying network structures on the platoon
dynamics by using a discrete-time Markov chain [28].
From networked control perspective, a vehicular platoon is
actually one dimensional network of dynamical systems, in
which the vehicles only use their neighborhood information
for controller design but need to achieve the global
coordination. The perspective naturally decomposes a
platoon system into four interrelated components, i.e., node
dynamics (ND), information flow topology (IFT), distributed
controller (DC), and formation geometry (FG) [28]-[30]. This
decomposition is able to provide a unified four-component
framework to analyze, design and synthesize vehicular
platoon, as well as further on-road implementation [31]-[34].
Under the four-component framework, this paper summarizes
the existing platoon control outcomes by literature
categorization and technical analyses. Moreover, this paper
also reviews the techniques dealing with three major
performance metrics, i.e. string stability, stability margin and
coherence behavior. The remainder of this paper is as follows:
Section II introduces the four-component framework of a
platoon system; Section III reviews the mainstream
An Overview of Vehicular Platoon Control under the Four-Component
Framework
Shengbo Eben Li, Member, IEEE, Yang Zheng, Keqiang Li*, and Jianqiang Wang
2015 IEEE Intelligent Vehicles Symposium (IV)
June 28 - July 1, 2015. COEX, Seoul, Korea
978-1-4673-7265-7/15/$31.00 ©2015 IEEE 286

techniques by each component, followed by a brief of
performance metrics in Section IV. Section V concludes this
paper.
II. INTRODUCTION TO FOUR-COMPONENT FRAMEWORK
This paper considers a platoon on a flat road (see Fig. 1),
which aims to move at consensual speed while maintaining
desired space among vehicles. The platoon has a leading
vehicle (LV, indexed by) and other following vehicles (FVs,
indexed from  to). As demonstrated in Fig. 1, the platoon
system can be viewed as a combination of four main
components: 1) node dynamics; 2) information flow topology;
3) distributed controller, and 4) formation geometry. The
four-component framework of a platoon is demonstrated in
Fig. 1, which includes:
1) Node dynamics (ND), which describes the behavior of
each involved vehicle;
2) Information flow topology (IFT), which defines how the
nodes exchange information with each other;
3) Distributed controller (DC), which implements the
feedback control only using neighboring information;
4) Formation geometry (FG), which dictates the desired
inter-vehicle distance when platooning.
v
0
t
Information Flow TopologyDistributed Controller
......
LV
01node iN
i-1
d
r
d
des
Controller C
i
C
i-1
u
i
C
1
u
1
C
N
u
N
Formation Geometry
u
i-1
Node Dynamics
Fig. 1 Four major components of a platoon : 1) node dynamics, 2)
information flow topology, 3) distributed controller, 4) geometry
formation; where 

is the actual relative distance,

is the desired
distance, 

is the the contol signal for i-th vehicle, and C denotes the
controller.
The internal stability should be ensured for all platoons. A
platoon is said to be internally stable if and only if the
closed-loop system has eigenvalues with strictly negative real
parts [32]. Besides internal stability, the most concerned
performance metrics for a platoon are 1) string stability; 2)
stability margin, and 3) coherence behavior:
Definition 1 (String Stability). A platoon is said to be
string stable if and only if the disturbances are not amplified
when propagating downstream along the vehicle string
[11][35][41];
Definition 2 (Stability Margin). The stability margin of a
platoon is defined as the absolute value of the real part of the
least stable eigenvalue, which characterizes the convergence
speed of initial errors [32][33];
Definition 3 (Coherence Behavior). The coherence
behavior is quantified as the 

norm of the closed-loop
system [51], which is a scalar index that captures the
robustness of a platoon subject to exogenous disturbances.
Each component in Fig. 1 has significant influence on the
performance metrics of a platoon. The categorization result of
existing literature is shown in TABLE I.
III. LITERATURE REVIEW ON EACH COMPONENT
A. Node Dynamics (ND)
Most research on platoon control only gives emphasis on
the dynamical behaviors of ND in longitudinal direction.
Only a few studies discuss the integrated longitudinal and
lateral control [56][57]. The later control usually adopted the
bicycle model, see [56][57] for details. This paper only
reviews the modeling of ND in longitudinal direction.
The vehicle longitudinal dynamics are inherently nonlinear,
which is composed of engine, drive line, brake system,
aerodynamics drag, tire friction, rolling resistance,
gravitational force, etc. [4][18]. Some studies directly use
nonlinear models for platoon control, see [18][35][43] and
[56] for examples,. The asymptotic stability and string
stability can be guaranteed by carefully selecting the control
parameters, but explicit performance limits are rather difficult
to analyze with given spacing policy and communication
topology. Actually, linear models are more frequently used
for tractable issues. The commonly used models include 1)
single integrator model, 2) second-order model (including
double-integrator model), 3) third-order model, and 4)
single-input-single-out (SISO) model (see TABLE I. for
details).
The single integrator model is the simplest case, which
takes the vehicle speed as control input and position as the
exclusive state. This can significantly simplify the theoretical
analysis on controller design. For instance, the structured
optimal control of platoon can be transformed into a convex
optimization problem under single integrator assumption, but
quite challenging for other models[49][51]. However, besides
largely depart from actually vehicle dynamics, the single
integrator model fails to reproduce the slinky-type effects or
string instability [44]. An improvement is to assume ND as a
point mass, resulting in the double-integrator model [15][16]
[44], or even to consider a platoon as a mass-spring-damper
system, resulting in the second-order linear model
[69][72][73]. The two models both use acceleration as control
input. Many important theoretical results, like decentralized
optimal control [49], stability margin scaling trend
[16][32][33][47][48], and coherence behavior [66], rely on
the assumption of second-order dynamics. This assumption
still does not catch many features of vehicle dynamics, e.g.
inertial delay in powertrain dynamics, and might lead to
instability in real world [10][17][19][20]. One modeling trend
for ND is to further increase one state and yield so-called
third-order model. The increased state is often used to
approximate the input/output behaviors of powertrain, which
equivalently degrades the control input to engine torque
and/or braking torque [8][10][14][17][20]. Now the majority
of approximation use either feedback linearization technique
[3][10][17][23] or lower-layer control technique [2][4][56].
The last, but not the least, model is the SISO model, which is
often used to analyze string stability from frequency domain.
The pioneer work on this model started from Seiler, Pant, and
Hedrick [41], and later widely employed in many other
studies, e.g. [12][59][64] and [65].
287

TABLE I. CATEGORIZATION OF PLATOON CONTROL
Node Dynamics (ND)
Single-integrator
Second-order model
Third-order model
SISO model
Nonlinear model
[49][50][51][52][53]
[13][15][16][28][29][32][33][44][46][47][48
][49][61][62][63][66][69][72][73]
[3][5][6][8][9][10][11][14][15][17][19][20][23][26]
[27][30][31][34][36][42][45][58][67][68][70][71]
[12][41][59][64][
65]
[18][35][43][54][
56][60]
Homogeneous
Heterogeneous
[3][5][6][8][10][15][16][20][23][28][30][31][32][33][34][41][42][46][48][49][50][51][52][53]
[58][59][61][62][63][65][66][69][70][73]
[9][10][11][12][13][14][17][18][19][26][27][29][35][36][43][44][45][4
7][54][56][60][64][67][68] [71][72]
Information Flow Topology (IFT)
PF
PFL
BD
BDL
TPF
[3][8][9][10][11][15][19][20][23][27][30][36][41
][42][45][46][48][54][58][61][65][70][71][73]
[5][6][11][14][17][18][23][26]
[30][35][41][56][58][67][69]
[12][13][16][23][30][32][33][34][41][43
][47][48][49][59][60][64][68][72][73]
[12][23][30][34]
[20][23][30]
[58]
TPFL
Undirected
Limited Range
General Topologies
[23][30]
[23][30][31][34][44][62]
[64][66]
[23][28][29][30][32][50][51][52][53][63]
Distributed Controller (DC)
Linear Controller
Optimal Controller


controller
SMC
MPC
[3][6][9][11][12][13][16][19][23][27][28][29][30][31][32][33][34][36][41][42][44][46
][47][48][50][52][53][58][59][60][61][62][64][65][66][68][69][70][71][72][73]
[15][17][49]
[51][54][63]
[14][26][20][67]
[5][8][10]
[35][43][56]
[18][19][45]
Formation Geometry (FG)
CD
CTH
NLD
[3][5][6][9][11][12][13][14][16][17][18][23][26][28][30][31][32][33][34][35][41][43][44][46
][47][48][49][50][51][52][53][55][56][58][59][61][62][63][64][66][67][68][69][72][73]
[9][10][15][19][20][27][29][36][42][45][54][6
0][64][65][71][73]
[8][70]
Performance Metric
String Stability
Stability Margin
Coherence Behavior
[3][5][6][8][9][10][11][12][14][15][17][18][19][20][26][27][35][36][41][42][43][
44][45][46][54][56][58][59][60][61][62][64][65][67][68][69][70][71][72][73]
[13][16][23][28][29][30][31][32][33][34][47][48]
[63]
[16][49][50][51]
[52][53][66]
An important terminology for ND is homogeneity. A
platoon is said to be “homogeneous” if all nodes have
identical dynamics; otherwise, it is called to be
“heterogeneous”. The homogeneous assumption can simplify
the theoretical analysis of platoon control (see [20][23][32]
and [41] for examples), while the heterogeneous assumption
is more aligned with the reality (see [9]-[12] and [17] for
examples).
( b )
...
( a )
...
( d )
...
( e )
...
( f )
...
...
( c )
Fig. 2 Typical IFTs for Platoon. (a) PF; (b) PLF; (c) BD; (d) BDL; (e) TPF; (f)
TPLF
B. Information Flow Topology (IFT)
The IFT applied in a platoon is closely related to the way a
vehicle acquires the information of its surrounding vehicles.
The IFT describes the information used by each local
controller and has significant influence on the collective
behaviors of the platoon, e.g. string stability [41], stability
margin [30][32] and coherence behavior [49][56] etc.
Early-stage platoons are mainly radar-based, which means
that a vehicle can only obtain the information of its nearest
neighbors, i.e. front and back. Under this sensing system,
IFTs are the predecessor following (PF) and bidirectional
(BD) topologies (see TABLE I. for details). Nowadays, as the
rapid deployment of vehicle-to-vehicle (V2V)
communications, such as DSRC and VANET, various IFTs
are emerging, including predecessor-following leader (PFL)
type, two predecessor-following (TPF) type, two
predecessor-following leader (TPFL) type, undirected, and
other limited communication range topologies (see TABLE I.
for details). Fig. 2 demonstrates some of these topologies.
Note that TABLE I. is only based on the connection
characteristics without consideration of the communication
characteristics such as quantization, data dropout and time
delay.
No matter what kind of topology is employed, internal
stability must be guaranteed in a platoon. Two main
approaches have been proposed to ensure the internal stability:
1) global approach, e.g. [14] and [67], and 2) local approach,
e.g. [8][10][20] and [27]. The first approach is to
straightforwardly take the overall platoon as a structured
system and then design a centralized controller, for which IFT
becomes less important to controller design. For example, the
linear matrix inequality (LMI) was obtained based on the
global platoon dynamics to guarantee internal stability in [14]
and [67]. One major drawback for this approach is that the
computation efficiency quickly worsens with increasing
platoon size. Therefore, most studies decomposed a platoon
into sub-systems and tried to use decentralized control
methods, leading to the second approach. For instance, under
PF topology, a platoon can be naturally viewed as
unidirectional cascade systems, which only needs to study
any two successive vehicles to guarantee stability, e.g.
[8][10][20][27] and [36]. Besides, the inclusion principle was
used to decompose such kind of platoon into locally
288

decoupled subsystems, for which overlapping controller
could be designed [17]. This decomposing technique does not
suit for a platoon with BD topology because its spacing errors
propagate from both forward and backward directions. The
partial differential equation (PDE) technique were employed
to approximate the dynamics of platoons under BD topology
in [13][16][32][33] and [68], which avoided to analyze high
dimensional dynamics. For platoons under general topologies,
the matrix similarity transformation and factorization is an
important approach, which actually decompose the internal
stability into two components: 1) stability of information flow
for given IFT and 2) stability of individual vehicles for given
DC, see [23][30] and [55]. This method is only applicable for
homogeneous platoon.
C. Distributed Controller (DC)
The DC implements the feedback control using neighbor’s
information to achieve the global coordination of the platoon.
An unstructured DC is one that corresponds to complete
graph which requires communication between any pair of
vehicles. Many existing studies belong to structured control
law either in an explicit or implicit way, see [9][10][17] and
[49]. It is the structural property governed by IFT that brings
both the difficulties in controller design [49] and fundamental
limits in platoon performances [30][32][56].
The commonly used DC are linear for the purpose of
comprehensive results on theoretical analysis, and
convenience in hardware implementation [7][11][16][23].
The internal stability of linear controller largely depends on
the structure of IFT, which means linear DC design is often in
a case-by-case way. The stabilized region of linear control
gains is explicitly derived in [23] for a large amount of
topologies, and the string stability requirements for platoon
under PF topology are established in [10]. The optimization
methods, either numerical or analytical, were also proposed to
optimize the localized gains in [15][17] and [49]. There are
also some studies employing sliding model control (SMC) to
design string-stable platoon [5][8][10]. For SMC, the internal
stability and string stability of platoons have to be realized
through a posterior controller tuning.
There are two main drawbacks in the aforementioned
design methods, i.e. 1) unable to explicitly handle the string
stability, and 2) unable to handle the state or control
constraints. Recently, the 

controller synthesis is
proposed to include the string stability requirement as a priori
in the design specification [20]. In addition, model predictive
control (MPC) has been introduced into the platoon control to
forecast system dynamics, explicitly handling actuator/state
constraints by optimizing given objectives [18][19][45].
D. Formation Geometry (FG)
There are three major policies of FG for vehicular platoons:
1) constant distance (CD) policy, 2) constant time headway
(CTH) policy, and 3) nonlinear distance (NLD) policy [7][58].
For the CD policy, the desired distance between two
consecutive vehicles is independent of vehicle velocity,
which can lead to a very high traffic capacity. For the CTH
policy, the desired inter-vehicle range varies with vehicle
velocity, which accords with driver behaviors to some extent
but limits achievable traffic capacity. For the NLD policy, the
desired inter-vehicle is a nonlinear function of vehicle
velocity, which has the potential to improve both the traffic
flow stability and traffic capacity compared with CD and
CTH policies (see [8][70] for details).
IV. LITERATURE REVIEW ON PLATOON PERFORMANCE
Some practical benefits brought by platooning, such as
reducing fuel consumption and improving traffic efficiency,
are not covered in this paper. For these topics, interested
reader can refer to [37]-[40]. The major techniques for
internal stability are presented in Section II.A. Hence, this
section only focuses on string stability, stability margin and
coherence behaviors.
A. String Stability
Internal stability of a platoon in the Lyapunov sense does
not guarantee string stability. If not well designed, error
signals can amplify when propagating downstream the
vehicle string, which may result in rear-end collision [10][41].
This effect is called string instability, e.g. in [41] or slinky
effect, e.g. in [17].
The achievability of string stability has tight relationship
with FG and IFT employed in the platoon. Seiler et al. (2004)
showed that due to the complementary sensitivity integral
constraint, string stability cannot be guaranteed for any linear
identical controllers under PF topology and CD policy [41].
Barooah et al. (2005) further pointed out that for a
homogeneous platoon under BD topology, linear identical
controllers also suffered fundamental limitations on the string
stability due to amplified spacing errors and disturbances [59].
Middleton et al. (2010) extended the work in [41] by
considering heterogeneous ND, limited communication range,
non-zero time headway policy, and showed that both forward
communication range and small time headway cannot alter
the string instability [64]. Some solutions are proposed to
improve string stability, including:
a) Relaxing formation rigidity, i.e. introducing enough
time headway in the spacing policy (e.g. [9][10][15]), or
using nonlinear policy (e.g. [8][70] );
b) Using non-identical controller for different vehicle, (e.g.
[16][46]);
c) Extending the information flow by using more complex
IFT, e.g. broadcasting the leader’s information (e.g.
[11][17]). Note that that the analysis in [63] pointed out
the necessity to have some global information (e.g.
leader’s velocity) in DC to ensure string stability.
Recently, some advanced controllers have been proposed
to ensure string stability, including SMC [8][10], MPC
[18][19] and 

controller [14][20][67]. Note that all of
them either employ CTH policy or use certain global
information.
B. Stability Margin
Stability margin is used to characterize the convergence
speed in a platoon [32][33]. Most of current research on
stability margin focus on the CD policy, which has revealed
that stability margin is a function of 1) platoon size (), 2)
ND, 3) IFT, 4) the DC structure [16][30]-[34].
289

By considering ND as a point mass, Barooah et.al (2009)
demonstrated that the stability margin approached zero as


 

 
under symmetric bidirectional control, and proved
that asymptotic behavior of stability margin could be
improved to 

 
 
by introducing small amounts of
“mistuning” [16]. This result was extended to linear
third-order dynamics, which covers the inertial delay of
powertrain dynamics [30]. Using partial differential equation
(PDE) approximation, Hao et al. (2011) showed that scaling
law of stability margin could be improved to  
 



under D-dimensional IFT [32]. Recently, it was proved that
employing asymmetric control, the stability margin could be
bounded away from zero, which was independent with the
platoon size  in [33]. From the perspective of topology
selection and control adjustment, Zheng et al. (2014) further
pointed out two basic methods to improve the stability margin
[34].
C. Coherence behavior
The coherence behavior is a scalar metric
adopting

-norm of the closed-loop system to character the
robustness of vehicular platoon driven by exogenous
disturbances, which captures the notion of coherence [53][66].
Bamieh et al. investigated the asymptotic scaling of upper
bounds on coherence behavior with respect to platoon size,
and indicated the IFT may play a more important role than
DC [66]. Several recent research used coherence behavior as
the cost function to optimize the local control gains, e.g. in
[49], and the communication structure of IFTs, e.g. in
[50][51][53] by using augmented Lagrangian approach and
alternative direction method of multipliers.
V. DISCUSSIONS
This paper presents a review on vehicular platoon control
from the perspective of networked control system. Although
some theoretical and/or experimental results have been
provided, there are still many open questions, especially
considering the emerging large-scaled applications of V2V
and V2I communication. Some of them are briefly discussed
here:
1) How to model, analyze and design vehicular platoon
control in a systematic way. The future challenge comes from
the nonlinearity of node dynamics, the variety of topologies,
and the low-cost demands of controllers. The communication
issues, e.g. data delay, quantization error and packet loss, also
pose significant challenge on platoon control technique. One
interesting question is how to optimize the design of
topologies and controllers considering both platoon
performances and communication issues.
2) How to balance various performances in a platoon,
including practical requirements from highway. The balance
of string stability, stability margin and coherence behavior is
attracting increasing interests now. Moreover, final goal of
platooning is to enhance highway safety, improve traffic
utility and reduce fuel consumption. How to consider
practical performance requirement is rather challenging for
platoon control. A comprehensive design framework is
needed to incorporate and balance multiple performance
metrics.
ACKNOWLEDGMENT
Special thanks should be given to Prof. Le-Yi Wang, Prof.
Hongwei Zhang, and Prof. Gang G. Yin in Wayne State
University, and Prof. Francesco Borrelli, Prof. J. Karl
Hedrick from University of California, Berkeley for their
valuable suggestions and comments.
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