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A third-order consensus approach is proposed for the vehicle platoon. For addressing the platoon problem, a realistic, third-order vehicle dynamics model is used, and the spacing policy and the vehicle acceleration error are embedded into the consensus protocol. A sufficient and necessary condition of asymptotically stability is obtained for the vehicle platooning system. Numerical simulations for several traffic scenarios are carried out. The results demonstrate the effectiveness and the robustness of the presented approach.

Traffic congestion is a serious problem and considerable challenge in many parts of the world. How to alleviate traffic congestion has attracted great concern in recent years. Platoon based cooperative driving is one of the promising approaches to improve traffic flow, enhance traffic capacity, and reduce fuel consumption (see [

This paper is concerned with the consensus control strategy for platooning of vehicles. Consensus control is an active research field in multivehicle cooperative control. The pioneering work has been reported by Fax and Murray [

di Bernardo et al. [

In [

Jia and Ngoduy [

In this paper, we propose a novel third-order consensus strategy for the vehicle platooning system. Comparing with the studies [

The rest of the paper is organized as follows. In Section

Suppose that the platoon consists of a leader vehicle (labeled with 0) and

We next recall some important lemmas and theorems used in studying the stability of the vehicle platoon system.

Let

Let

Let

For any

The cooperative driving strategy of the platoon is to make each member of the platoon follow the leader’s behavior and maintain the desired small intervehicle spacing. Consider a platoon consisting of

The consensus control goal of the platoon can be expressed as

To achieve the control goal that the platoon members follow the leader’s state, we design the following consensus control algorithm embedding the spacing policy information and the time-varying communication delays:

The algorithm (

According to (

To prove asymptotic stability of the closed-loop dynamics driven by the control action, we first define position, velocity, and acceleration errors with respect to the reference signals

Applying the Leibniz-Newton formula leads to

The matrix

Let

Let the matrix

Let

(Necessity). If

Consider system (

Choose appropriate control parameters based on Lemma

(Necessity). Notice that system (

We adopt PLEXE simulator [

Parameters for the traffic simulation and consensus control algorithm.

| | | |
---|---|---|---|

Vehicle length | 4 m | Maximum acceleration | 3 m^{2}/s |

Stable speed | 25 m/s | Maximum deceleration | 5 m^{2}/s |

Vehicle drivetrain | 0.5 s | Maximum velocity | 35 m/s |

Control parameters | | Standstill distance | 15 m |

if | |

We select a typical communication topology: the leader- and predecessor-following topology considering information from both the preceding vehicle and the leader (see Figure

The information flow topology used in simulations: leader- and predecessor-following topology.

We first consider the platoon composed of seven following vehicles and a leader initially starting from different positions with different speeds. It is assumed that there are no packet losses to avoid the effect of the communication on the system performance. Figure

Platoon performance for the initial scenario: (a) the position error

We consider a single large perturbation scenario similarly reported in [^{2}/s from 10 m/s to 25 m/s. The test is used to evaluate the ability of the approach in tracking the leader motion. The simulation results are shown in Figure

Platoon performance for a single large perturbation scenario: (a) the position error

To further verify the efficiency of the presented algorithm, we consider a periodic disturbance, where the following sinusoidal disturbance is added onto the leading vehicle speed:

Platoon performance for the sinusoidal disturbance scenario: (a) the relative position

We next study another kind of perturbation coming from security risks discussed by [

Platoon performance for the initial scenario under spoofing attack: (a) the position error

In this subsection, we study the performance of the proposed consensus algorithm for different platoon lengths. We consider the platoons with 4, 7, 10, 13, and 16 vehicles. Figure

Platoon performance in the presence of the initial scenario under different platoon lengths: (a) the position error

Figure

Platoon performance in the presence of the sinusoidal disturbance scenario under different platoon lengths: (a) speed; (b) acceleration.

In this paper, we have proposed a novel third-order consensus strategy for the vehicle platoon and have proven the asymptotically stability of the platooning algorithm in presence of time-varying delays. We have tested several traffic scenarios including the initial case, the large perturbation, the sinusoidal disturbance, and the perturbation coming from security risks. The simulation results illustrate the effectiveness of the approach and confirm the robustness of the proposed strategy in the presence of perturbations. In addition, the proposed consensus control approach shows the effectiveness for different platoon lengths. Future work will be devoted to investigating the effect of switching communication network topologies. Furthermore, more sophisticated spacing strategy should be introduced to determine the desired distance of vehicle. In addition, how to choose the optimal control parameter values will be studied in future work.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

This work was supported by the National Natural Science Foundation of China (no. 11772264).