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)

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]

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[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.

Motivation for ICT

• Traffic congestionMore 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.

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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 …

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Platoon drivingPlatoon driving

DirectionIndividual driving

Individual driving

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.

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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.

Car-following models

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

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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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

System verification

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• 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

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.

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Fax et al. (2004) "Information flow and cooperative control of vehicle formations." IEEE transactions on automatic control 49.9 : 1465-1476.

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.

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Impact of heterogeneity of realistic V2V communication (transmission delay)

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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

System dynamics

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• Let

We have

• The system equation:

where

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.

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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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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Heterogeneous platoon with CA vehicles and human-driven vehicles

(penetration and position order)

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Functions of CA/human-driven vehicle

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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

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Example of communication topology for a heterogeneous platoon.

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…)

System dynamics

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Linearization of the “multi-class” system around the state errors:

Where

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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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.

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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

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

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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))

Simulation Results(cont’d.)

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Communication topologies in 4 different order of human-driven vehicles

Simulation Results(cont’d.)

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Acceleration of the last vehicle at both initial and perturbation

stage with different human-driven penetrations

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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ThanksQ&A

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