Presentation from NORTHMOST - a new biannual series of meetings on the topic of mathematical modelling in transport. Hosted at its.leeds.ac.uk, NORTHMOST 01 focussed on academic research, to encourage networking and collaboration between academics interested in the methodological development of mathematical modelling applied to transport. The focus of the meetings will alternate; NORTHMOST 02 - planned for Spring 2017 - will be led by practitioners who are modelling experts. Practitioners will give presentations, with academic researchers in the audience. In addition to giving a forum for expert practitioners to meet and share best practice, a key aim of the series is to close the gap between research and practice, establishing a feedback loop to communicate the needs of practitioners to those working in university research.

1. Agent-based car-following model for
heterogeneities of platoon driving with
V2V communication
Dong Ngoduy and Tony Jia
EPSRC career acceleration fellowship EP/J002186/1
(2011-2016)

2. Outline
• Background and car-following modeling approach
• Heterogeneous platoon dynamics (e.g. instabilities)
Realistic inter-vehicle communication with
heterogeneous transmission delay and packet loss [1][2]
Heterogeneous platoon operations with Human-driven
vehicles and CA vehicles [3]
1
[1] Jia and Ngoduy (2016a). "Platoon based cooperative driving model with consideration of realistic inter-
vehicle communication." Trans. Res. Part C 68 (2016): 245-264.
[2] Jia and Ngoduy (2016b). "Enhanced cooperative car-following traffic model with the combination of V2V
and V2I communication." Trans. Res. Part B 90 (2016): 172-191.
[3] Jia and Ngoduy (2016c). "Agent-based multiclass model and control of heterogeneous platoon with inter-
vehicle communication." Trans. Res. Part B, to appear.

3. Motivation for ICT
• Traffic congestion
More than 1 billion registered
motor vehicles in the world; and it
is expected that the number will be
doubled within the next 10 to 20
years.
• Vehicle emissions
Contribution to air pollution and
are a major ingredient in the
creation of haze in some large
cities.
2

4. Platoon-based Driving
• Platoon-based driving: With the help of inter-vehicle communication, a vehicle can timely
obtain information from neighbouring vehicles, then adopt a suitable control law to achieve
certain objective, e.g., maintaining a constant inter-vehicle spacing.
• Features:
 Within a platoon, one leader and several members following the leader
 All members following the driving behavior of leader
 Constant intra-platoon spacing and the same speed as the leader
• Benefits:
 Increase traffic flow throughput
 Reduce fuel consumption
 …
3
Platoon drivingPlatoon driving
Direction
Individual driving
Individual driving

5. Platoon driving with V2V communication
• Physical layer describes the
platoon dynamics under the
constraints of traffic environment.
• Cyber (networking) layer
describes the behaviours of
vehicular networks formed by
vehicles with communication
capability.
• Tight coupling between platoon-
dynamics and vehicular
networking.
4
Vehicular cyber-physical system [Jia et al.]
Jia et al. (2015) "A survey on platoon-based vehicular cyber-physical systems." IEEE Communications Surveys &
Tutorials 18, no. 1 : 263-284.

6. Car-following models
To describe “car-following” behaviour: a driver follows the (direct) leading
vehicle by judging:
• Space headway
• Relative speed

7. Agent-based model for CA vehicle
• Four components
Vehicle dynamics which inherently characterize vehicle’s behaviour stemming
from manufacture, e.g., actuator lag;
Information type: the information to be exchanged among vehicles, e.g., the
position and velocity of a vehicle;
Communication topology describing the connectivity structure of vehicular
networks, such as predecessor-follower, leader-follower, bidirectional, etc.;
Control law such as consensus control, etc., to be implemented on each
vehicle in order to define the car-following rule in the connected traffic flow
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8. Agent-based car-following model
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 𝑁𝑖 (t) denotes the neighbour set of vehicle i.
 Γ𝑙(.) describes the corresponding control algorithm for the
dynamics of the considered vehicle under the V2V communication.
• Communication topology among platoon members is represented
as a directed graph G=(V,E,A).
 V= 1,2,...,n is the set of vehicles
 E ⊆V ×V is the set of edges (communication links)
 A is an adjacency matrix with nonnegative elements which
represents the communication link between vehicle i and j. (𝑎𝑖𝑗=1
in the presence of a communication link from j to i, otherwise 𝑎𝑖𝑗= 0)
• Car-following model

9. System verification
8
• System specification
 IEEE 802.11p as the V2V communication protocols support information
exchange between CA vehicles.
All CA vehicles within the same platoon can connect with each other
Constant headway spacing strategy
Consensus control algorithm is adopted for CA vehicles.
• Platoon stability:the state errors between the leader and its
members are bounded

10. Consensus control
• Vehicle platooning can be formulated as a typical consensus problem,
i.e. state errors between followers and leader being convergence to
zero/bounded value [Fax et al.]
• Time-varying communication topology and heterogeneous
uncertainties (communication delays, packet loss, and transmission
errors) require a more generic communication structures suitable for
V2V communication description.
9
Fax et al. (2004) "Information flow and cooperative control of vehicle formations." IEEE transactions
on automatic control 49.9 : 1465-1476.

11. Heterogeneities of vehicle platooning
• V2V communication: packet loss and probabilistic transmission delay
among V2V communication (due to the performance of IEEE802.11P)
• Composition structure: penetration of CA/human-driven vehicle,
relative order of the vehicle types in the platoon.
10

12. Impact of heterogeneity of realistic V2V
communication (transmission delay)
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13. Consensus control algorithms
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 𝜏𝑗is the time-varying communication delays from vehicle j to other members
 The first and second lines of Eq. (8) represent the vehicle’s position and velocity
difference between itself and platoon members, respectively
 The third and fourth lines of Eq. (8) represent the vehicle’s position and velocity
difference between itself and the platoon leader, respectively

14. System dynamics
13
• Let
We have
• The system equation:
where

15. Solution to the equation
• Using the Leibniz–Newton and based on Lyapunov stability condition,
the maximum delay can be estimated.
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• Bounded state error depends on
system parameters, such as
platoon size, beacon delivery
ratio, and acceleration
perturbation magnitude.

16. Simulation scenarios
• (1) a single large perturbation wherein the leader first decelerates
from 25 m/s to 5m/s, then maintains this speed for a period of time,
and finally accelerates to the original speed 25 m/s.(to mimic traffic
emergency like collision avoidance)
• (2) the continuous small perturbations wherein the leader
experiences a sinusoidal disturbance in speed. (to mimic common
traffic disturbance caused by abnormal driving behaviour)
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17. 16

18. 17

19. Conclusions
• The state (position and velocity) errors between the platoon
members and the leader can converge within a certain bound.
• The bounded values are determined by the system parameters, such
as platoon size, beacon delivery ratio, and acceleration perturbation
magnitude.
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20. Heterogeneous platoon with CA vehicles
and human-driven vehicles
(penetration and position order)
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21. Functions of CA/human-driven vehicle
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22. Heterogeneous platoon with CA
and human-driven vehicle
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Human-driven member
V2V communication
0
CA member
Moving
direction
CA leader
On-board sensing Human sensing
1234567
Example of communication topology for a heterogeneous platoon.

23. Modelling CA and human-driven vehicle
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• Car-following model for human-driven vehicle (i.e. IDM of Treiber et al.)
• Car-following model for CA vehicle (same as before…)

24. System dynamics
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Linearization of the “multi-class” system around the state errors:
Where

25. Modelling position order of vehicles
• Bitmap matrix : defining the number and the relative
position/order of CA vehicles in the platoon
• General format of adjacency matrix of heterogeneous platoon (star)
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26. Communication topologies
• The interplay between CA vehicles and the human-driven is described
via the structure of adjacency matrix A which is decided not only by
the CA vehicles’ penetration but also the relative order.
• Larger algebraic connectivity can lead to faster convergence of the
system. Hence, the system performance could be potentially
improved by adjusting the composition structure of the
heterogeneous platoon.
25

27. Solution to the equation
• Using the Leibniz–Newton and based on Lyapunov stability condition.
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• Bounded state error depends on
perception delay caused by human-
driven vehicles, as well as the number
(penetration) of the CA vehicles.
• Convergence rate determined by
not only the CA vehicles' penetration
but also their order/position in the
platoon

28. Simulation scenarios
• an initial phase during which all following vehicles launch from
predefined positions to finally cooperatively drive at the same
constant speed 25m/s regulated by the leader (essentially to mimic a
sharp perturbation).
• a continuous small perturbation wherein the leader experiences
a sinusoidal disturbance in speed (to mimic common traffic
disturbance caused by an abnormal driving behaviour)
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Human-driven member
V2V communication
0
CA member
Moving
direction
CA leader
On-board sensing Human sensing
1234567

29. Simulation Results
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Platoon performance with different penetration of human-driven vehicles
(initial stage with fixed position error (top) and continuous perturbations stage (bottom))

30. Simulation Results(cont’d.)
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Communication topologies in 4 different order
of human-driven vehicles

31. Simulation Results(cont’d.)
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Acceleration of the last vehicle at both initial and perturbation
stage with different human-driven penetrations

32. Conclusions
• The system transient-state performance is mainly determined by not
only the CA vehicles' penetration but also their order/position in the
platoon. Furthermore, the convergence rate can be improved by
optimizing the algebraic connectivity of the communication, which is
related to the communication topology of matrix A.
• For a given heterogeneous platoon driving with forward V2V
communication topology, the optimal composition structure is all
human-driven vehicles following all CA vehicle in the platoon.
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33. Thanks
Q&A
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