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Connected and automated vehicle (CAV) has become an increasingly popular topic recently. As an application, Cooperative Adaptive Cruise Control (CACC) systems are of high interest, allowing CAVs to communicate with each other and coordinating their maneuvers to form platoons, where one vehicle follows another with a constant velocity and/or time headway. In this study, we propose a novel CACC system, where distributed consensus algorithm and protocol are designed for platoon formation, merging maneuvers, and splitting maneuvers. Predecessor following information flow topology is adopted for the system, where each vehicle only communicates with its following vehicle to reach consensus of the whole platoon, making the vehicle-to-vehicle (V2V) communication fast and accurate. Moreover, different from most studies assuming the type and dynamics of all the vehicles in a platoon to be homogenous, we take into account the length, location of GPS antenna on vehicle, and braking performance of different vehicles. A simulation study has been conducted under scenarios including normal platoon formation, platoon restoration from disturbances, and merging and splitting maneuvers. We have also carried out a sensitivity analysis on the distributed consensus algorithm, investigating the effect of the damping gain on convergence rate, driving comfort, and driving safety of the system.

Recently, the rapid development of our transportation systems has led to a worldwide economic prosperity, where transportation for both passengers and goods is much more convenient both domestically and internationally. The number of motor vehicles worldwide is estimated to be more than 1 billion now and will double again within one or two decades [

Significant efforts have been made around the world to address these transportation issues. Many propose simply expanding our existing transportation infrastructure to help solve these traffic-related problems. However, not only is this costly but also it has many negative social and environmental effects. As an alternative solution, the development of connected and automated vehicle (CAV) can help better manage traffic, thus improving traffic safety, mobility, and reliability without the cost of infrastructure build-out. One of the more promising CAV applications is Cooperative Adaptive Cruise Control (CACC), which extends Adaptive Cruise Control (ACC) with CAV technology (e.g., mainly via vehicle-to-vehicle (V2V) communication) [

The core of a CACC system is the vehicle-following control model, which depends on the vehicle information flow topology. The topology determines how all CAVs in a CACC system communicate with others, and it has been well studied by researchers. Zheng et al. [

Stability is a basic requirement to ensure the safety of a CACC system. The control system should be capable of dealing with various disturbances and uncertainties. Laumônier et al. [

Communication plays a crucial role in the formation of a CACC system. The United States Department of Transportation (USDOT) developed a Connected Vehicle Reference Implementation Architecture (CVRIA) to provide the communication framework for different applications, including V2V and Vehicle-to-Infrastructure (V2I) communications [

Essentially, the proposed system is different from a conventional Adaptive Cruise Control (ACC) system for the following reasons. (1) In the proposed system, although some forward ranging sensing techniques such as camera, radar, and lidar (Light Detection and Ranging) might be needed as supplementary methods, the core technique for CAVs to form platoon is V2V communication. CAVs send their absolute position and instantaneous velocity information measured by equipped sensors (e.g., high-precision GPS, inertial measurement unit, and on-board diagnostic system) to their followers by V2V communication. However, for a conventional ACC system, V2V communication is not enabled, where vehicles need to use their forward ranging sensing equipment to obtain predecessors’ information. (2) A conventional ACC system can only implement the function of vehicle following; however, the proposed CACC system allows individual vehicle to merge into the platoon by using V2V communication. “Ghost” vehicles are created as predecessors for following vehicles to follow; however, since they are virtual and only for V2V communication, it is impossible for forward ranging sensing techniques to sense them. (3) The measurement delay of forward ranging sensing techniques in a conventional ACC system is apparently different from the V2V communication delay of DSRC in the proposed system, which leads to different system behaviors in different scenarios, especially the one we talk about in Section

Despite the advantages of consensus-based platooning approach for the CACC system, several issues still need to be addressed to improve the reliability and practicality.

(a) The primary V2V communication method being used nowadays is DSRC, which normally has a 300-meter transmission range [

(b) Most existing CACC-related research has only considered vehicles in the system as homogenous point mass models. However, in reality, vehicles should be heterogeneous with different lengths and braking performances. Therefore, we take into account the vehicle length together with the position of GPS antenna on vehicle in this study. Moreover, according to different braking performances, we assign different braking factors to different types of vehicles in our system, allowing the intervehicle distances to be weighted based on these factors.

(c) While the information flow topology and algorithm have been well studied, not many protocols have been developed to apply the theory to real-world transportation systems, especially for different traffic scenarios. In this study, we design protocols for the normal platoon formation scenario and merging and splitting scenario. Sensitivity analysis is also conducted to study the practical issues of the proposed CACC system, including the convergence rate of a platoon, the driving comfort for human passengers, and the driving safety of the whole system. By optimizing the damping gain value of our algorithm, the proposed system is supposed to be efficient, comfortable, and safe.

The remainder of this paper is organized as follows. Section

We represent the information flow topology of a distributed network of vehicles by using a directed graph

Before proceeding to designing our distributed consensus algorithm for the CACC system, we recall here some basic consensus algorithms which can be used to apply similar dynamics on the information states of vehicles. If the communication between vehicles in the distributed networks is continuous, then a differential equation can be used to model the information state update of each vehicle.

The single-integrator consensus algorithm [

Equation (

It shall be noted that since our study mainly focuses on communication topology and control algorithm of the system, we make some reasonable assumptions while modelling the general system to enable the theoretical analysis.

(a) All vehicles are CAVs with the ability to send and receive information among the same transmission range, and there is no vehicle actuator delay in the proposed system.

(b) Every vehicle in the proposed system is equipped with appropriate sensors (e.g., high-precision GPS, inertial measurement unit, and on-board diagnostic system) to measure its absolute position and instantaneous velocity, and the measurement is precise without noise.

(c) Vehicle types are assumed to be heterogeneous, with different vehicle length, location of GPS antenna on vehicle, and braking performance.

The objective of the distributed consensus-based CACC system is to use algorithms and protocols that ensure consensus of a platoon of vehicles. Toward this end, the meaning of consensus is twofold: one is the absolute position consensus, where one vehicle maintains a certain distance with its predecessor, and the other is the velocity consensus, where one vehicle maintains the same velocity with its predecessor. Taking into account second-order vehicle dynamics, we propose the distributed consensus algorithm for the CACC system, for

Positions of vehicles in the proposed system.

With (

As mentioned in Section

The braking performance of a vehicle can be affected by many factors, including the mass of the vehicle and the aerodynamics performance of the vehicle. We assign a braking factor

We assume that the vehicle in the proposed system receives its absolute position (location) information by the GPS antenna that is installed on a certain position of the vehicle’s roof. Both the length between antenna and the front bumper

Equation (

Considering different scenarios in our system, two protocols are designed in the following.

This protocol is designed for vehicles to form a platoon. For vehicle

(a) If yes, then vehicle

(b) If no, then vehicle

After the above procedure, vehicle

(a) For a following vehicle

(b) For a leading vehicle

Figure

Normal platoon formation protocol.

Normal platoon formation protocol addresses the longitudinal maneuvers, while merging and splitting maneuvers protocol is aimed at handling the lateral maneuvers (i.e., lane change). It is introduced in [

For the case where vehicle

Merging maneuvers protocol (assuming merging into the 2nd position).

The case where vehicle

We use MATLAB Simulink [

In the first scenario, we assume that there are four CAVs of different types (i.e., 2 sedans, 1 SUV, and 1 truck) driving at randomly varied velocities on the same lane of a highway. At a certain time (

Values of vehicle parameters.

Parameters | Vehicle 1 | Vehicle 2 | Vehicle 3 | Vehicle 4 | |||
---|---|---|---|---|---|---|---|

GPS antenna to front bumper |
3 m | 3 m | 3 m | 6 m | |||

GPS antenna to rear bumper |
2 m | 2 m | 2 m | 4 m | |||

Braking factor |
1 | 1 | 1.1 | 1.6 | |||

Initial velocity |
30 m/s | 33 m/s | 36 m/s | 39 m/s | |||

Desired velocity |
30 m/s | 30 m/s | 30 m/s | 30 m/s | |||

Initial time gap |
0.91 s | 1.11 s | 1.67 s | ||||

Initial weighted intervehicle distance |
30 m | 40 m | 65 m | ||||

Desired time gap |
0.43 s | 0.48 s | 0.69 s | ||||

Desired time headway |
0.6 s | 0.64 s | 0.86 s | ||||

Desired weighted intervehicle distance |
13 m | 14.3 m | 20.8 m | ||||

Desired unweighted intervehicle distance |
13 m | 13 m | 13 m |

As can be seen from Table

As a key parameter, the damping gain

Simulation results of normal platoon formation.

Figure

In this scenario, a simulation test is conducted to demonstrate the string stability of our CACC system, where the distributed consensus algorithm has the capability of attenuating the impact of sudden disturbances. In the platoon mode of our distributed consensus-based CACC system, if one vehicle (e.g., leading vehicle) suddenly brakes and reduces its velocity due to emergency, then the following vehicles will decelerate accordingly to maintain certain weighted intervehicle distances.

For example, we assume that all the parameters remain the same as the first scenario. At time

The simulation results of sudden brake are shown in Figures

Simulation results of platoon restoration from disturbances.

The velocity of vehicles in platoon is shown in Figure

Figure

In this scenario, we show the effects when the proposed distributed consensus algorithm is performed together with the merging and splitting maneuvers protocol as presented in Section

For merging maneuvers, assume that, at time

Simulation results of merging and splitting maneuvers.

It can be observed from Figure

For splitting maneuvers, assume that, at time

The second vehicle of the platoon switches off the platoon mode and drives away (constantly accelerates from 30 m/s to 35 m/s) from platoon at time

Therefore, the simulation results of the third scenario show that our distributed consensus-based CACC system is capable of carrying out merging and splitting maneuvers.

In this section, a sensitivity analysis is conducted to study how the uncertainty in the damping gain

This sensitivity analysis is based on the normal platoon formation scenario, where the information flow topology

Information flow topology of normal platoon formation scenario.

The adjacency matrix then can be defined as

Recall that, in (

The convergence rate of the proposed distributed consensus algorithm will affect the time required for our CACC system to reach the steady state. The faster the convergence rate is, the less time will be consumed and thus the higher efficiency of our CACC system is.

In this case, we study the convergence rate of our system without communication delay for the sake of brevity. Define

The way to find the eigenvalues of

As aforementioned,

By comparing (

Therefore, the eigenvalues of

The convergence rate is an exponential decay term known as

Since

Therefore, the maximum convergence rate is achieved as

Noting that the Laplacian matrix

In this part, we analyze the effect of ^{2} and ±10 m/s^{3} for acceleration and jerk separately will be comfortable for human passengers. We measure the values of

Parameters of this analysis are set in Table

Values of vehicle parameters.

Parameters | Vehicle 1 | Vehicle 2 |
---|---|---|

GPS antenna to front bumper |
3 m | 3 m |

GPS antenna to rear bumper |
2 m | 2 m |

Braking factor |
1 | 1 |

Initial velocity |
30 m/s | 33 m/s |

Desired velocity |
30 m/s | 30 m/s |

Initial weighted intervehicle distance |
30 m | |

Desired weighted intervehicle distance |
13 m |

Driving comfort analysis.

In this part, we analyze the effect of

We first analyze how the changes of

Driving safety analysis related to initial weighted intervehicle distance.

As shown in the result, the areas indicating

We also analyze how the changes of

Driving safety analysis related to initial velocity difference.

As shown in the figures, collision only happens in the areas where

By analyzing the results of driving safety analysis, we know that the preliminary value of

In this study, we have proposed a novel CACC system based on a distributed consensus algorithm, which takes into account the unavoidable time-varying communication delay, as well as the length, GPS antenna’s location, and braking ability of different vehicles. We have also developed distributed consensus protocol, allowing our CACC system to process the algorithm to implement the function of forming a platoon, merging, and splitting. The algorithm and protocol have been implemented in MATLAB Simulink and the system is shown to have the ability to be restored from a variety of disturbances and carry out merging and splitting maneuvers. In addition, a sensitivity analysis was performed on the algorithm, indicating that the distributed consensus algorithm reaches the maximum convergence rate when

It should be pointed out that although the system level (cyberspace) of vehicles has been taken into account in this study, the actual vehicle dynamics model (physical space) has been neglected. Combination of the cyberspace and the physical space may be a future goal of this study. Also, as discussed in Section

Given the proposed distributed consensus algorithm (see (

The Newton-Leibniz formula can be introduced as

Then the following lemmas can be proposed to study the convergence of our distributed consensus algorithm (see (

Matrix

Let matrix

Given by Lemma

Given Lemmas

If there exists a directed spanning tree in the platoon information flow topology

Since matrix

Take derivative of

Based on Lemma 3, define

Therefore, if the value of

Writing the distributed consensus algorithm (see (

The authors declare that there are no conflicts of interest regarding the publication of this paper.