Research on Cooperative Control of Multiple Intelligent Networked Vehicles Based on the Improved Leader–Follower Method

Abstract

In order to study the group cooperative control method of multiple intelligent networked vehicles, the multiple intelligent networked vehicles can move in the form of a fleet. Based on the leader–follower method, the paper optimizes the control effect of the leader–follower method by solving the error transmission phenomenon in the leader–follower method. In this paper, the modeling of the multiple intelligent connected vehicle adopts the vehicle dynamics model and the Magic Formula/Swift Magic tire model, and adopts the model predictive control (MPC) dynamics trajectory tracking controller for control. Through the CarSim–Simulink multi-vehicle dynamics co-simulation platform established in this paper, the group cooperative control experiments of multiple intelligent networked vehicles under different working conditions were carried out for simulation verification. The analysis results show that the maximum average error of the proposed method decreases from 8.802 to 0.094 in the case of straight line and 0.669 to 0.379 in the case of curve tracking, which proves that the method can effectively reduce the transmission of errors.

1. Introduction

The research on cooperative control of multi-intelligent connected vehicles originates from the study of cooperative control problems in multi-agent systems (multi-agent system: MAS) [1]. Its main objective is to achieve coordinated control between multiple intelligent networked vehicles by adapting and adjusting their own driving states in specific road situations in order to maintain relative stability in terms of position and velocity with other intelligent networked vehicles [2,3].

The advantages of cooperative control in multi-intelligent connected vehicles are as follows:

(1)

Increased road capacity: Smaller vehicle spacing greatly enhances the road's capacity [4,5].

(2)

Improved safety: Through vehicle-to-vehicle communication, inter-vehicle communication, and high-precision sensors, multi-vehicle cooperative control makes the driving process safer. It not only reduces traffic accidents caused by human errors but also provides greater safety and efficiency compared with stand-alone autonomous driving technologies that rely heavily on sensor performance [6,7].

(3)

Enhanced comfort: This offers a higher level of comfort compared with traditional vehicles [8].

Different formation control methods have their own advantages and disadvantages. The control of vehicle formation is mainly based on the virtual structure method [9,10], behavior-based method [11,12], leader–follower method [13,14,15,16], path-tracking-based method [17,18], artificial potential field method [19,20], graph theory method [21,22], etc. The leader–follower method is one of the most mature formation control methods at present [23,24].

However, there are two main disadvantages of vehicle cooperative control. These are as follows:

(1)

High requirements for the quality of communication between vehicles: Wireless communication between vehicles and between vehicles and objects inevitably introduces network defects. Problems such as communication delay, packet loss, interruption, and sampling interval make the security and stability of the entire vehicle queue system unguaranteed.

(2)

Cost and energy consumption: Vehicle platooning control requires hardware support such as high-precision sensors, computing units, and communication equipment, which increases the cost and energy consumption of the vehicle. In addition, because vehicles within a formation need to communicate and coordinate in real time, it also increases energy consumption and communication costs.

In order to improve the stability of the vehicle formation, Wi H. improves the longitudinal control of communication delay through the distributed model predictive control (DMPC) vehicle queue control system algorithm, which effectively solves the delay problem [25]; Zou C. proposed an event-driven information interaction method for an intelligent grid-connected vehicle queuing system, which solved the problems of packet loss in vehicle formation communication and improved the stability of the queue [26]. Li Y. et al. used the LaSallede invariant principle and Lyapunov's theorem to rigorously analyze the finite-time stability and consistency of the proposed control protocol, and proposed a control strategy for intelligent network vehicle queues based on nonlinear consensus under different communication topologies [27]. Based on the Markov jump system, Zhao H. designed the controller of the vehicle formation and studied the string stability of the vehicle queuing system under the influence of the switching topology [28]. In order to improve the transient stability performance of vehicle formation, Dai S. et al. [29] studied the formation tracking control problem of under-driven ground vehicles and proposed a lateral function control method to overcome the difficulties caused by non-diagonal system matrix and under-drive. Han S. [30] presents a control strategy consisting of speed and yaw rate controllers, which can be effectively implemented for real vehicles navigating diverse paths at high speeds. In order to ensure the safety of the workshop, Tabasso C. [31] proposed a multi-vehicle cooperative task coordination and collision avoidance control framework based on the speed regulation method to ensure the avoidance of non-cooperative moving obstacles. Zhigang L. [32] uses regression methods, adaptive neural networks, and dynamic surface control techniques, which rely entirely on the pilot's position and do not require any prior knowledge. The above literature considers improvements to the stability of vehicle formation under the communication delay between vehicles.

The research on the control algorithm mainly focuses on solving the problem of formation and rapid and stable formation and does not study the actual route of the vehicle following the vehicle during driving.

In reality, the vehicle formation in the pilot follower mode only relies on the information of the pilot vehicle to drive under high-speed driving conditions, and the information transmission between the following vehicle and the pilot vehicle lags behind, resulting in the deviation of the actual following trajectory and theory. Furthermore, once the pilot vehicle and the following vehicle are interfered with by the outside world, the stability of the vehicle formation will be seriously affected, and even traffic accidents will occur. By transmitting the following trajectory required by the pilot vehicle to the following vehicle in advance, the following vehicle corrects the deviation between the actual following trajectory and the theoretical following trajectory, and the corrected trajectory is used as the practical following trajectory. In this way, when the pilot vehicle is disturbed or the movement trajectory changes too much, the error can be reduced so as to improve the stability of the formation.

In this paper, the leader–follower method is studied, aiming at the shortcomings of error transmission, and an improvement is made. This method relies on the state of the following vehicle itself to optimize the following route and realize the stability of the formation mode of the pilot following method.

2. Technical Background

2.1. The Traditional Leader–Follower Methods

The leader–follower method is the most widely used method in formation control. Its working principle is to determine one or more individuals to be the leader in the formation to be controlled. The unselected individuals follow the leader and follow according to the designed rules. The following rules can be designed to achieve the effect of the whole formation [33].

The core of the pilot following method is that, under the premise that the movement trajectory and state of the selected navigator have been obtained, the movement trajectory of the follower is deduced according to the rules between the navigator and the follower that have been set, which is essentially the tracking control problem of the follower, and then the control law of the follower is designed to simplify the formation control problem.

Desai et al. designed a feedback linearization control method for the pilot following method, which has the two following rules, $l-l$ [34] & $l-\varphi$ [35]:

(1)

$l-l$: Applied between three individuals. Sets two leaders and a follower and sets a fixed distance between the follower and the leader.

(2)

$l-\varphi$: More advanced and sets the relative distance and relative bearing of the follower and the leader. According to the Lyapunov theory, Mastellone S et al. stipulated the movement rules for the individual in the formation, and then extended them to all the formation by combining the pilot following method [36].

The disadvantage is that there will be errors in the process of transmission. If the leader is affected by the outside world, the error of the control system will be large.

The traditional pilot following method selected in this section is the most representative $l-\varphi$ type pilot following method, and the characteristic of the algorithm is that only one pilot vehicle is required as the target tracking vehicle of the following vehicle. The target position of the following vehicle is determined by the position of the pilot vehicle, the relative distance between the two vehicles, the angle between the connection of the two vehicles and the driving direction of the pilot vehicle, and then the following vehicle reaches the target position by relying on a specific control algorithm. One of the most used control algorithms is PID control [14]. The model is shown in Figure 1.

The position of the leader car is $C_1$, coordinates are $(x_1,y_1)$, and the yaw angle is ${\theta }_1$. The position of the leader car is $C_2$, coordinates are $(x_2,y_2)$, and the yaw angle is ${\theta }_2$.$l$ is the distance between the leader car and follower car. $\varphi$ is the relative angle between the connection between the car in front and the car behind and the direction the car in front is traveling. The position relationship between the two vehicles is described as follows:

$$\left\{\begin{array}{c}{x}_r=x_1+l\mathit{cos}(\varphi +{\theta }_1)\\ y_r=y_1+l\mathit{sin}(\varphi +{\theta }_1)\end{array}\right.$$

(1)

The derivative with respect to (1) obtains the following equation:

$$\left\{\begin{array}{c}{\dot{x}}_r={\dot{x}}_1+\dot{l}\mathit{cos}(\varphi +{\theta }_1)-l(\dot{\varphi }+{\dot{\theta }}_1)\mathit{sin}(\varphi +{\theta }_1)\\ {\dot{y}}_r={\dot{y}}_1+\dot{l}\mathit{sin}(\varphi +{\theta }_1)+l(\dot{\varphi }+{\dot{\theta }}_1)\mathit{cos}(\varphi +{\theta }_1)\end{array}\right.$$

(2)

Considering (1) and (2) together, we can define the expected motion state of the following car:

$$\left\{\begin{array}{l}{v}_r={\dot{x}}_2\mathit{cos}{\theta }_2+{\dot{y}}_2\mathit{sin}{\theta }_2\\ v_s={\dot{y}}_2\mathit{cos}{\theta }_2+{\dot{x}}_2\mathit{sin}{\theta }_2\\ {\omega }_r=v_{sr}/L\end{array}\right.$$

(3)

$v_r$ is the expected forward speed of the follower car,$v_s$ is the expected lateral velocity of the car,${\omega }_r$ is the expected yaw angular velocity,$x_r,y_r$ is the expected horizontal and vertical of the car, and ${\alpha }_r$ is the expected yaw angle.

At present, the traditional navigation tracking method has the following problems:

(1)

Constrained by the accuracy of models and the selection of parameters, navigation tracking methods often heavily rely on these system components. However, any inaccuracies in the models or improper parameter selection can significantly impact control performance. Traditional approaches lack adaptability and robustness when faced with uncertainty.

(2)

Dealing with obstacle avoidance is challenging: Traditional navigation tracking methods often treat the target path as an ideal trajectory and rarely consider the issue of obstacle avoidance in real-world scenarios. In the presence of dynamic obstacles or complex environments, traditional methods may struggle to achieve effective path planning and obstacle avoidance control.

(3)

High demands on perception and localization systems: Traditional navigation tracking methods typically rely on accurate perception and localization systems to obtain target position and orientation information. In complex environments or in the presence of sensor failures, tracking performance can deteriorate.

2.2. Model Predictive Control (MPC)

In order to reasonably control the trajectory tracking of driverless vehicles, it is necessary to consider various physical constraints when the vehicle is driving, including hard constraints on the mechanical side and soft constraints on the control performance. By virtue of its own characteristics, MPC can better solve this kind of constrained problem.

The improved pilot following method proposed in this paper will be controlled by the MPC dynamic trajectory tracking controller previously proposed by the authors [37]. The following three aspects are introduced, including the establishment of the linear error model, the selection of the objective function, and the design of the constraints.

2.2.1. Linearity Error Modeling

The input to the system is $u(v,\delta )$, and the state amount is $X(x,y,\phi )$. The system is represented as:

$$\dot{X}=f(X,u)$$

(4)

where $\dot{X}$ is the motion state response; $v$ is the speed at which the vehicle travels; $\delta$ the front wheel corner; $x$ is the abscissa of the vehicle; $y$ is the ordinate of the vehicle; $\phi$ is the angle between the direction of motion of the vehicle and the abscissa.

For known reference trajectories, you can use the motion trajectory description of the reference vehicle. The reference quantity is denoted by r, and the system is denoted as:

$${\dot{X}}_r=f(X_r,u_r)$$

(5)

where $X_r=(x_r{y}_r{\phi }_r{)}^T;u_r=[u_r{\delta }_r{]}^T$; $X_r$ is the state of motion in the reference coordinate system; $u_r$ is the speed at which the vehicle travels in the reference coordinate system; ${\delta }_r$ is the angle of rotation of the front wheel in the reference coordinate system; $x_r$ is the abscissa of the vehicle in the reference coordinate system; $y_r$ is the ordinate of the vehicle in the reference coordinate system; ${\phi }_r$ is the angle between the direction of motion of the vehicle and the abscissa in the reference coordinate system.

Equation (4) is expanded by the Taylor series at the reference trajectory point and ignores the higher-order terms, and the following equation is obtained:

$$\dot{X}=f(X_r,u_r)+\partial f(X,u)/\partial X{|}_{\stackrel{X=X_r}{u=u_r}}(X-X_t)+\partial f(X,u)/\partial u{|}_{\stackrel{X=X_r}{u=u_r}}(u-u_r)$$

(6)

Subtracting Equation (6) from Equation (5) yields the following formula:

$$\dot{\widehat{X}}=\left[\begin{array}{c}\dot{x}-{\dot{x}}_r\\ \dot{y}-{\dot{y}}_r\\ \dot{\phi }-{\dot{\phi }}_r\end{array}\right]=\left[\begin{array}{ccc}0& 0& -{\upsilon }_{r}sin{\phi }_r\\ 0& 0& v_{r}sin{\phi }_r\\ 0& 0& 0\end{array}\right]\left[\begin{array}{c}x-{\chi }_r\\ y-y_r\\ \phi -{\phi }_r\end{array}\right]+\left[\begin{array}{cc}cos{\phi }_r& 0\\ sin{\phi }_r& 0\\ \frac{\mathit{tan}{\delta }_f}{l}& \frac{v_r}{l{cos}^2{\delta }_f}\end{array}\right]\left[\begin{array}{c}v-v_r\\ \delta -{\delta }_r\end{array}\right]$$

(7)

2.2.2. Design of Objective Functions

In order to make the driverless car track the set desired trajectory well, it is necessary to consider the optimization of the control quantity and the control of the deviation of the system state quantity. Consider the following objective function:

$$J\left(k\right)={\displaystyle {\sum }_{j=1}^N}{\tilde{X}}^T(k+j|k\left)Q\tilde{X}\right(k+j)+{\tilde{u}}^T(k+j-1\left)R\tilde{u}\right(k+j-1)$$

(8)

The objective function has the problem that it cannot avoid the abrupt change of the control quantity of the control system, which affects the continuity of the control quantity. Therefore, the soft constraint method [38] is used to improve the following:

$$J\left(k\right)={\sum }_{i=1}^{N_p}\parallel \eta (k+i|t)-{\eta }_{ref}(k+i\left|t\right){\parallel }_Q^2+{\sum }_{i=1}^{N_e-1}\parallel \Delta U(k+i|t){\parallel }_R^2+\rho {\epsilon }^2$$

(9)

where $N_p$ is the predicted time domain;$N_e$ is the control time domain.;$\rho$ is the weight factor;$\epsilon$ is the relaxation factor.

2.2.3. Design of Constraints

Considering the limit constraints of the control quantity and the constraints of the control increment in the control process, the expression form is as follows:

$$\begin{array}{c}{u}_{min}(t+k)⩽u(t+k)⩽u_{max}(t+k)\\ \Delta u_{min}(t+k)⩽\Delta u(t+k)⩽\Delta u_{max}(t+k)\\ k=\mathrm{0,1},2,\cdots ,N_c-1\end{array}$$

(10)

Because the variable to be solved is a control increment, only the form of control increment can appear in the constraints. This can be transformed to obtain the corresponding transformation matrix. It takes the form of the following equation:

$$U_{min}⩽A\Delta U_t+U_t⩽U_{max}$$

(11)

where $U_{min}$ and $U_{max}$ are the sets of the minimum and maximum values of the control quantity in the control time domain, respectively.

The objective function is converted to a standard quadratic form and the constraints are taken into account:

$$\begin{gathered} J\left(\xi \right(t),u(t-1),\Delta U(t\left)\right)=[\Delta U(t\left)\stackrel{T}{,}\epsilon \right]\stackrel{T}{H_t}[\Delta U(t\left)\stackrel{T}{,}\epsilon \right]+G_t[\Delta U(t\left)\stackrel{T}{,}\epsilon \right] \\ s.t.\Delta U_{min}⩽\Delta U_t⩽\Delta U_{max} \\ {U}_{min}⩽A\Delta U_t+U_t⩽U_{max} \end{gathered}$$

(12)

3. The Improved Leader–Follower Method

As mentioned above, the traditional leader–follower method has the problem of error transmission, especially when the leader–follower is disturbed.

To this end, this paper proposes an improved leader–follower method, the essence of which is to transfer the trajectory that the leader needs to track to all followers, so that the trajectory can be used as the bottom tracking track of each follower, and the process is as follows:

(1)

Solve the error between the actual trajectory of the pilot vehicle and the target trajectory.

(2)

Optimize the tracking trajectory according to the trajectory error, and pass the optimized trajectory to the following vehicle, and the following vehicle drives with the optimized following trajectory.

(3)

Solve the error between the optimized target trajectory and the actual trajectory of the first following vehicle and the second following vehicle to optimize its own tracking trajectory.

(4)

Repeat step 3 for the rest of the following vehicles.

In this way, when the leader is disturbed or the movement state changes too much, each follower will track with the bottom tracking track as the target track. The schematic diagram of the improved pilot tracking method is shown in Figure 2 below.

Among them, the obviously wrong data caused by vibration or noise are constrained and filtered within a numerical range obtained through experiments. If there are too many wrong data, the last optimized trajectory or the initial target trajectory will be used as the tracking trajectory.

This is reflected in the comparison between the first car and the target trajectory. To obtain the error, discard the error exceeding a certain value and replace it with the target trajectory, the optimized trajectory as the target trajectory of the next car, and so on.

The traditional model based on time-varying relative distance and time-varying relative angle is transformed into the constraint of the algorithm, so as to further improve the stability of the algorithm.

4. The Simulation Results

In order to verify the formation control effect of the optimized pilot following method proposed in this paper, and make a comparative analysis with the traditional pilot following method, it is verified whether the error transmission phenomenon of the traditional pilot following method is optimized.

In this chapter, simulation tests of different road conditions are carried out on the CarSim–Simulink co-simulation platform, and the maximum lateral tracking error and average lateral tracking error of different algorithms are compared.

The software versions used in this article are CarSim 2016.1 (MCS, Nanuet, NY, USA) and Matlab 2016 (MathWorks, Natick, MA, USA). CarSim serves as a platform for vehicle models, road models, 3D simulations, and data post-processing, and Simulink serves as a platform for trajectory tracking control and crowd collaborative control algorithms. There is a certain difference between the cooperative control of multiple vehicles studied in this paper and the co-simulation platform construction of a single vehicle. In the setting of the CarSim input and output interface, you need to define the vehicle DLL file of the vehicle, distinguish it from the file of the first vehicle, and keep the number of experimental vehicles in the simulation consistent with the number of vehicle DLL files. After sending to Simulink, it is necessary to manually configure different CarSim vehicle models to distinguish the information of different experimental vehicles, so as to better design and develop subsequent control algorithms and avoid mutual influence between different vehicle models.

In order to verify the simplification and reasonability of the vehicle model in this paper, the real vehicle model in CARSIM can be used to set each parameter of the vehicle, including tire parameters.

Table 1. Vehicle and tire parameters.

Parameter	Value	Parameter	Value
Sprung mass	1723 kg	The most powerful	125 kw
The moment of inertia	1243 kg/${\mathrm{m}}^2$	Reference vertical force	6500 N
Pitch moment of inertia	4331 kg/${\mathrm{m}}^2$	Spring stiffness	268 N/mm
Deflection of inertia	4175 kg/${\mathrm{m}}^2$	The tire width	215 mm
The wheelbase	2700 mm	Flat is better than	55%
Distance from center of mass to front axis	1232 mm	Tire structure	Radial tire
Distance from center of mass to rear axis	1468 mm	Wheel size	17 inch
A half wheel track	325 mm

lists the vehicle parameters selected in this document.

4.1. Straight Line Condition

Figure 3 shows the trajectory map obtained by sampling the formation tracking control of four intelligent networked vehicles using the traditional pilot following method. The X and Y axes in the figure correspond to the lateral movement of the vehicle and the distance of longitudinal movement, respectively. It can be seen from the trajectory diagram that the traditional pilot following method has obvious tracking error without optimization, and the tracking error will also increase significantly with each additional car in the fleet, and the error of the driving trajectory of the upper car is transmitted to the next vehicle. Specific data are shown in

Table 2. Tracking error of traditional pilot following method under linear condition.

	Leader	Follower 1	Follower 2	Follower 3
Maximum lateral tracking error	0.865 m	1.715 m	2.633 m	3.533 m
Horizontal tracking average error	0.146 m	0.296 m	0.469 m	0.669 m

.

As can be seen from the data in Table 2, under straight working conditions, the maximum lateral tracking error of each follower for the pilot car gradually increases, and the average lateral tracking error also presents an increasing trend.

It can be seen that when the number of vehicles in the convoy reaches a certain number, the error transmission problem of the traditional piloting and following method will lead to the chaos of the whole convoy and thus become ineffective.

Figure 4 is the multi-vehicle state diagram of the traditional pilot following method. It can be seen from the figure that, starting from the following vehicle 2, various parameters fluctuate significantly, and the fluctuation value reaches the maximum within the constraint range, which has a huge impact on the driving stability of the vehicle.

Figure 5 shows the improved leader–follower method for group cooperative tracking of multiple intelligently connected vehicles in a straight line. It can be seen from the picture that the error transmission phenomenon in the previous section has been eliminated.

In addition, the following trajectory of car 1, car 2, and car 3 is kept within a certain range around the following trajectory of the pilot car and tends to be closer to the target trajectory. The specific data are shown in

Table 3. Tracking error of improved pilot following method under linear condition.

	Leader	Follower 1	Follower 2	Follower 3
Maximum lateral tracking error	0.022 m	0.455 m	0.482 m	0.478 m
Horizontal tracking average error	0.001 m	0.085 m	0.057 m	0.094 m

below.

As can be seen from the data in Table 3, the maximum lateral tracking error of following car 3 is reduced compared with that of following car 2, and the maximum lateral tracking error of following car 1, following car 2, and following car 3 is maintained within a certain range without large fluctuations.

The average error of lateral tracking is also maintained within a very small numerical range.

Figure 6 shows the variation of each parameter with time in the straight working condition when four intelligent networked vehicles are driving in formation.

As can be seen from the picture, compared with the traditional leader–follower method, the improved leader–follower method has better stability of each parameter in the multi-vehicle cooperative following. In particular, the stability of the following cars 2 and 3 can be maintained within a small range, although there are fluctuations.

4.2. Bend Road Conditions

Figure 7 shows the trajectory diagram obtained by the formation tracking control of four intelligent networked vehicles under the traditional pilot following method in the case of curves. It can be seen from the trajectory diagram that the traditional pilot following method in the case of curves has a more obvious tracking error than in the case of straight lines, and the specific data are shown in

Table 4. Tracking error of traditional pilot following method in curve condition.

	Leader	Follower 1	Follower 2	Follower 3
Maximum lateral tracking error	1.746 m	34.985 m	61.277 m	80.313 m
Horizontal tracking average error	4.366 m	7.633 m	8.802 m	7.105 m

below.

It can be seen from Table 4 that a large error has appeared since the first following car, and the error shows an increasing trend.

The disadvantages of the traditional leader–follower method are exposed, which has a great impact on the safety of driving.

Figure 8 is the multi-vehicle state diagram of the traditional leader–follower method in the case of curves. It can be seen from the figure that, starting from the following vehicle 2, various parameters fluctuate significantly, and the fluctuation value also presents the phenomenon of error transmission, which has a huge impact on the driving stability of the vehicle.

Figure 9 shows the improved leader–follower method for group cooperative tracking of multiple intelligent networked vehicles in the case of curves. It can be seen from the picture that the error transmission phenomenon in the previous section has been eliminated.

In addition, the following trajectory of car 1, car 2, and car 3 is kept within a certain range around the following trajectory of the pilot car and tends to be closer to the target trajectory. The specific data are shown in

Table 5. Tracking error of improved pilot following method in curve condition.

	Leader	Follower 1	Follower 2	Follower 3
Maximum lateral tracking error	0.157 m	1.835 m	1.878 m	1.899 m
Horizontal tracking average error	0.085 m	0.379 m	0.359 m	0.324 m

below.

As can be seen from the data in Table 5, the maximum lateral tracking error of following car 3 is reduced compared with that of following car 2, and the maximum lateral tracking error of following car 1, following car 2, and following car 3 is maintained within a certain range without large fluctuations.

The average error of lateral tracking is also maintained within a very small numerical range.

As shown in Figure 10 below, when four intelligent networked vehicles are driving in formation, the variation of each parameter with time in the bend condition is shown.

As can be seen from the picture, compared with the traditional leader–follower method, the improved leader–follower method has better stability of each parameter in the multi-vehicle cooperative following. In particular, the stability of following car 2 and following car 3 can be maintained within a small range despite fluctuations.

5. Conclusions and Future Research Directions

In vehicle formation control, the traditional pilot following method only relies on the relative position of the vehicle in front and the following vehicle to control the following path of the vehicle. When the following vehicle is disturbed, the movement trajectory of the vehicle cannot be adjusted in time, and there is a serious error in the following trajectory, and when the number of following vehicles increases, this error will increase again. By following the actual trajectory of the vehicle and the error between the theoretical trajectory, the vehicle running path can be optimized, and the stability between vehicle formations can be improved.

Based on the CarSim–Simulink co-simulation platform, two test scenarios of main road conditions are set up in this paper, namely, straight line and curved path.

Firstly, in the simulation of the traditional pilot following method, the tracking error of the traditional method increases with the increase in the number of follow-up vehicles, regardless of whether it is a straight line or a curve. Especially in the curve condition, the maximum lateral tracking average error of the following vehicle is 8.802, and the draw error of the straight line is 0.669, which shows that the error transmission characteristics of the traditional pilot following method are very obvious. Secondly, the simulation results of the improved pilot following method proposed in this paper show that the maximum average error of lateral tracking is 0.094 in the straight case and 0.379 in the curve case. The data show that the improved pilot following method effectively prevents the further transmission and expansion of the error and compares the actual driving trajectory of each vehicle with the target trajectory, and the error is very stable, which eliminates the error transmission problem of the traditional pilot following method.

Although this study has achieved certain results, there are still some shortcomings that need further improvement. They are as follows:

(1)

This study did not consider the issue of vehicle-to-vehicle communication, and further research is needed to address communication delays and failures between vehicles, for example, the influence of inter-vehicle networking, sensor transmission delay, and communication packet loss on the dynamic stability of vehicle queues.

(2)

This study only conducted vehicle dynamic performance simulations using the CarSim vehicle dynamics software and did not perform hardware-in-the-loop or on-road testing, which introduces a certain gap compared with actual on-road tests. Conducting experiments on real vehicles in future research would be beneficial for addressing the issues studied in this paper in a more practical manner and further advancing its applicability.