A vehicle platoon cooperative prediction control method in a curved road scene

Abstract

This invention discloses a vehicle queuing cooperative predictive control method for curved road scenarios. This method ensures that each following vehicle in the queuing maintains a constant speed and a constant inter-vehicle travel path length on curved roads. The method assumes a unidirectional communication topology between vehicles, meaning vehicle state information is transmitted only from the vehicle in front to the vehicle behind. Using the delayed trajectory of the preceding vehicle as a reference trajectory, a local MPC optimization problem is established for each following vehicle. The control input for each following vehicle is obtained by solving this local MPC optimization problem online, ensuring that each following vehicle in the queuing maintains a constant speed and a constant inter-vehicle travel path length on curved roads, avoiding the need for road information or pre-set travel trajectories. Even with a unidirectional communication topology containing a directed spanning tree, this method enables a closed-loop queuing control system to achieve stable driving at the desired speed and desired inter-vehicle travel path length on curved roads.

Description

Technical Field

[0001] This invention relates to the field of intelligent transportation technology, specifically a cooperative control method for vehicle platoons on curved roads based on distributed model predictive control (DMPC), which enables each following vehicle in the platoon to maintain a constant speed and a constant travel path length on curved roads, thereby achieving efficient and orderly driving. Background Technology

[0002] In recent years, research in the field of intelligent transportation has attracted widespread attention. Vehicle platooning control, as a fundamental issue in vehicle-road cooperative applications, can effectively improve road safety, alleviate traffic congestion, and reduce vehicle fuel consumption. Therefore, vehicle platooning control has significant research importance and application value.

[0003] Currently, most research on vehicle platooning control focuses on longitudinal control, covering the design of longitudinal controllers and related stability analyses. This part of the research only considers simplified vehicle kinematic models and does not involve lateral vehicle control. However, in curve scenarios, more complex vehicle dynamic models and their coordinated longitudinal and lateral control need to be considered. Research on single-vehicle control in curve scenarios is mainly divided into two parts: trajectory planning and tracking control. That is, first, the optimal reference trajectory is planned, and then the vehicle is tracked based on the reference trajectory. Extending from single-vehicle control in curves to vehicle platooning control, most studies only consider a single forward-following (PF) communication topology, while vehicle platooning control is mainly achieved through decoupled longitudinal and lateral control coordination.

[0004] Existing technical literature [1] ([1] G. Nie, X. Bo, H. Lu, and Y. Tian, ​​“Acooperative lane change approach for heterogeneous platoons under different communication topologies,” IET Intelligent Transport Systems, vol.16, no.1,pp.53-70, 2022.) proposes a platoon cooperative lane change strategy when there is a slow-moving obstacle ahead, including trajectory planning and cooperative control, to achieve simultaneous lane change of all vehicles under the premise of ensuring asymptotic stability.

[0005] The existing technical literature [2] ([2] S. Wei, Y. Zou, X. Zhang, T. Zhang and X. Li, “An integrated longitudinal and lateral vehicle following control system with radar and vehicle-to-vehicle communication,” IEEE Transactions on Vehicular Technology, vol.68, no.2, pp.1116-1127, Feb.2019.) introduces a forward vehicle following (PF) control framework that utilizes onboard radar sensors and V2V communication. It designs a vehicle controller with longitudinal and lateral decoupling and adopts longitudinal PID control and lateral MPC control to enable the vehicle to follow stably in both longitudinal and lateral directions.

[0006] Existing technical literature [3] ([3] A. Bayuwindra, J. Ploeg, E. Lefeber and H. Nijmeijer, “Combined longitudinal and lateral control of car-like vehicleplatooning with extended look-ahead,” IEEE Transactions on Control Systems Technology, vol.28, no.3, pp.790-803, May.2020.) designed a vehicle tracking control system based on forward following (PF) with longitudinal and lateral coupling, and adopted a consistency control method to realize vehicle following on curved roads.

[0007] The existing technical literature [4] ([4] L. Xu, W. Zhuang, G. Yin, C. Bian and H. Wu, “Modeling and robust control of heterogeneous vehicle platoons on curved roads subject to disturbances and delays,” IEEE Transactions on Vehicular Technology, vol.68, no.12, pp.11551-11564, Dec.2019.) proposes a lateral and longitudinal decoupled platoon control framework for different vehicles on curved roads with different slopes, aerodynamic drag and wireless communication delays. It adopts a robust control method and achieves stable platoon driving on curved roads by acquiring road information.

[0008] In summary, current research on platoon control on curved roads largely requires known road information and has not yet considered lateral and longitudinal coupling control under general communication topologies. This invention addresses the cooperative control problem of vehicle platoons on curved roads by proposing a distributed model predictive control (DMPC) method. This method assumes that the communication topology between vehicles is unidirectional, meaning vehicle state information is only transmitted from the vehicle in front to the vehicle behind. Using the delayed trajectory of the preceding vehicle as a reference trajectory, a local MPC optimization problem is established for each following vehicle. By solving this local MPC optimization problem online, the control input for each following vehicle is obtained, ensuring that each following vehicle in the platoon maintains a constant speed and a constant inter-vehicle travel path length on curved roads, avoiding the need for road information or pre-set travel trajectories. Further simulation experiments verify the feasibility of the proposed DMPC optimization problem. Furthermore, even with a unidirectional communication topology containing a directed spanning tree, this closed-loop platoon control system achieves stable operation on curved roads with the desired speed and desired inter-vehicle travel path length. Summary of the Invention

[0009] The purpose of this invention is to provide a distributed model predictive control (DMPC) method for cooperative driving of vehicle platoons on curved roads. This method, designed for vehicle platoons on curved roads, achieves cooperative driving of the platoon on curved sections by relying on the delayed trajectory information of the preceding vehicle, without requiring external reference trajectories or global road information. This ensures that each following vehicle in the platoon maintains a constant speed and a constant inter-vehicle travel path length on the curved road. This DMPC method uses the delayed trajectory of the preceding vehicle as a reference trajectory, avoiding the need for road information or pre-set travel trajectories. Simulation experiments then verify the feasibility of the proposed DMPC optimization problem and the effectiveness of the closed-loop platoon control system in cooperative driving scenarios on curved roads.

[0010] To achieve the above objectives, the present invention provides the following technical solution:

[0011] A cooperative control method for vehicle platooning on curved roads based on distributed model predictive control (DMPC) is characterized by the following steps:

[0012] Step 1: Define the communication topology of the vehicle queue

[0013] Create a A queue of vehicles, with index . The vehicle was traveling on a winding road. The vehicle representing the leader travels forward at a constant longitudinal speed, using... Indicates. The remaining indexes of following vehicles are from arrive Each vehicle receives status information from other vehicles according to the corresponding communication topology, such as... Figure 1 As shown.

[0014] The communication topology of the vehicle queue is represented by a directed graph. To model, its node set edge set Adjacency matrix Indicates from node To the node There exists a directional edge representing a vehicle. Received vehicle Information. Represented as:

[0015] when At that time, the vehicle It is a vehicle The neighbor, then the vehicle The neighbor set is represented as

[0016]

[0017] If there exists a root node such that any other node in the directed graph can be reached through at least one path originating from the root node, then the directed graph G is said to contain a directed spanning tree.

[0018] Suppose that the communication topology G of the vehicle platoon contains a directed spanning tree and is unidirectional, meaning that information is only transmitted from the vehicle in front to the vehicle behind. Common unidirectional communication topologies include lead-vehicle following (PF) topology, lead-leader following (PLF) topology, and two-leader following (TPF) topology, such as... Figure 2 As shown.

[0019] Step 2: Establish vehicle dynamics model

[0020] Step 2.1:

[0021] Vehicle construction exist Differential equations in a coordinate system are used to derive a vehicle dynamics model with three degrees of freedom (e.g., Figure 3 (as shown)

[0022]

[0023]

[0024]

[0025] Among them, subscript Representing the a car, and This refers to the front and rear tires, and in the formula above, they are related to... The relevant symbols all represent the forces exerted by the tires. They represent the first The resultant longitudinal force on the front and rear tires of a vehicle. They represent the first The resultant lateral force on the front and rear tires of a vehicle. Assuming the rear wheel steering angle is 0, this means the longitudinal and lateral forces on the tires are equal to the force acting on the center of the rear wheel. Based on the tire slip angle... (or Tire slip ratio (or ), road surface friction coefficient and vertical load The longitudinal and lateral forces of each front (or rear) wheel can be obtained. Due to the strong coupling between longitudinal and lateral tire forces, developing an accurate tire model is crucial. This invention uses the HB Pacejka tire model to describe the variation of tire forces. If the tire's sideslip angle is small, the sideslip force can be approximated as a linear function of the sideslip angle. Similarly, if the slip ratio is small, the longitudinal force can be approximated as a linear function of the slip ratio, thus obtaining the tire force model.

[0026] Based on the tire model, the magic formula, and the geodetic coordinate system transformation formula, the state-space equation of the complete vehicle dynamics model is expressed as:

[0027]

[0028] Define state variables Control input variables Its detailed form is as follows:

[0029]

[0030] State variables in equation (1.7) For the team, the first The longitudinal speed of the vehicle, For lateral velocity, Yaw rate, The yaw angle is an intermediate variable. Expressed as yaw rate for distinction and , and These are the geodetic coordinates after the vehicle body coordinates have been transformed. For rotational inertia, This is the distance from the center of the front wheel. The distance from the rear wheel to the center. For the stiffness of the front wheels, For the stiffness of the rear wheels, For the mass of the vehicle; control input variables and The first The steering angle and acceleration of a vehicle's wheels.

[0031] Step 2.2:

[0032] To convert differential equations into difference equations, the explicit Euler method is used.

[0033] First, we define an initial value problem for a first-order differential equation:

[0034]

[0035] The initial time, This is the initial state. It is a known function of time and state.

[0036] Replace the differential with the first-order positive difference quotient, that is, in the th order... time:

[0037]

[0038] Represents a discrete time interval.

[0039] Using the above difference quotient, this invention transforms the differential equation into an explicit difference equation:

[0040]

[0041] The above equation provides from arrive The recursive form, based on the initial values, allows for the sequential acquisition of numerical solutions for each step of the differential equation.

[0042] Step 2.3:

[0043] Next, the state-space equations of the vehicle dynamics model are transformed into discrete time intervals according to step 2.2. Difference equation:

[0044]

[0045] The discrete nonlinear model of the vehicle queue is obtained as follows:

[0046]

[0047] Output vector , where the matrix .

[0048] Step 3: Establish a local optimization problem based on tracking the delay trajectory of the preceding vehicle.

[0049] Step 3.1:

[0050] Before designing a local optimization problem, first use Represents the prediction time domain and makes the control time domain equal Then, the present invention defines the sequence of control inputs, states, and outputs in the predicted state and the ideal state within the prediction range.

[0051] The control input sequence under the prediction state is: The state sequence is The output sequence is ;

[0052] Under ideal conditions, the control input sequence is: The state sequence is The output sequence is .

[0053] Step 3.2:

[0054] set up Indicates vehicle Future time step The predictive control input will be at the current time step. The following is determined. Given a control input sequence. Current state Then the predicted state and output are in Place, Use respectively and This can be calculated iteratively using the following formula:

[0055]

[0056] Step 3.3:

[0057] To achieve the desired uniform longitudinal speed for each vehicle on curved roads and the expected driving path length The control objective, ideally, is that each vehicle in the queue follows the delayed trajectory of the leading vehicle, and the delay time of any vehicle is... yes Based on this idea, each vehicle is defined. :

[0058]

[0059] Then for each car Propose an optimization problem :

[0060]

[0061]

[0062]

[0063] In optimizing the problem In equation (1.16), the feasible range of wheel steering angle is constrained. Let represent the minimum and maximum angle ranges of the wheel, respectively. Equation (1.17) guarantees the terminal output of each vehicle. The terminal constraint is equal to the average historical terminal output of its neighboring vehicles.

[0064] Step 4: Propose a distributed model predictive control algorithm for vehicle queuing on curved roads.

[0065] Based on the local optimization problem, this invention proposes a distributed model predictive tracking control algorithm for vehicle platoons, namely the delayed trajectory tracking method. This method uses the average of the delayed trajectories of adjacent vehicles and the control input as a reference, avoiding the requirement for road information and preset (or estimated) driving trajectories, thus enabling cooperative driving on curved roads. The DMPC algorithm is shown below.

[0066] Step 4.1:

[0067] Initialize the initial state of each vehicle using the Simulink system controller. ;

[0068] set up Assume that each vehicle stores information about its neighboring vehicles. Historical and current output and input information:

[0069] ;

[0070] Step 4.2:

[0071] from Start traversing to , from Start traversing to vehicles The loop begins;

[0072] By solving local optimization problems ,vehicle Obtain the control input prediction sequence for the current time step:

[0073] , ;

[0074] vehicle The first item As the actual control input for the current time step, i.e. ;

[0075] Step 4.3:

[0076] vehicle Based on the actual control input at the current time step Update the state parameters of the nonlinear dynamic model for the next step. :

[0077]

[0078] Step 4.4:

[0079] vehicle transmission and Receive and store the state sequences and control inputs of neighboring vehicles: , , ;

[0080] Step 4.5:

[0081] Update status at the next time step With output The process continues until the loop stops, storing the state sequence and output sequence in the working area; thus, distributed model predictive control for cooperative driving of vehicle platoons on curved roads is realized.

[0082] Compared with existing technologies, this invention does not require external reference trajectories or global road information. It relies on the delayed trajectory information of the preceding vehicle to achieve cooperative driving of the vehicle platoon on curved road sections, thus avoiding the need for road information or pre-set driving trajectories. Secondly, this invention uses the delayed trajectory of the preceding vehicle as a reference trajectory to establish a local MPC optimization problem for each following vehicle. In the case of a unidirectional communication topology containing a directed spanning tree, the control input of each following vehicle is obtained by solving this local MPC optimization problem online in a lateral and longitudinal coupling control manner. This enables each following vehicle in the platoon to maintain a constant speed and a constant inter-vehicle travel path length on curved roads, achieving stable driving on curved roads at the desired speed and desired inter-vehicle travel path length. This fills the gap in the research methods for cooperative driving of platoons on curved roads in the field of vehicle lateral and longitudinal coupling control. Attached Figure Description

[0083] Figure 1 This is a diagram of a vehicle queue model.

[0084] Figure 2 This is a topology diagram of a one-way vehicle queue.

[0085] Figure 3 This is a diagram of a three-degree-of-freedom vehicle dynamics model.

[0086] Figure 4 The images show two urban traffic scenarios. (a) Scenario 1: Urban road section; (b) Scenario 2: Expressway exit ramp section.

[0087] Figure 5 This is the trajectory map of the convoy in Scene 1.

[0088] Figure 6 For the convoy in Scene 1 , , and picture.

[0089] Figure 7 For the convoy in Scene 1 and picture.

[0090] Figure 8 For the convoy in Scene 1 , , and picture.

[0091] Figure 9 This is the trajectory map of the convoy in Scenario 2.

[0092] Figure 10 For the convoy in Scene 2 , , and picture.

[0093] Figure 11 For the convoy in Scene 2 and picture.

[0094] Figure 12 For the convoy in Scene 2 , , and picture. Detailed Implementation

[0095] The present invention will now be further described in conjunction with implementation examples and accompanying drawings:

[0096] Simulations were performed using MATLAB / Simulink. The Driving Scenario Designer (DSD) was used to construct the scenario, pre-set reference trajectories, and design the leading vehicle controller. A platoon of five vehicles in a PLF topology was designed for simulation experiments. Except for the lead vehicle, all vehicles in the platoon were isomorphic, with the following vehicle parameters: ; ; ; ; ; .

[0097] like Figure 4 As shown, this invention was tested in two different urban traffic scenarios. In scenario 1, the convoy operated in an urban road environment, while in scenario 2, the convoy operated on a section of a highway exit ramp. First, the positions of the five vehicles and the driving route of the leading vehicle were established in the DSD (Distributed Scenarios Data Model), and then the data was stored in the Matlab workspace. Using Simulink, the Matlab workspace data was combined with the ADT (Automatic Trajectory Controller) module data to construct and display the trajectory tracking controller for the leading vehicle.

[0098] The total simulation time is denoted as , each time step The desired longitudinal velocities for scenarios 1 and 2 are set as follows: and In scenarios 1 and 2, the desired inter-vehicle travel path lengths are set as follows: and Then calculate. Predicting the time domain Set as Obviously satisfied Furthermore, all of them matrix and Set as:

[0099]

[0100]

[0101] After the simulation code runs, it saves the fleet trajectory, vehicle status, and the results of their control inputs.

[0102] Figure 5 - 12 represents the experimental results, where the thin red line indicates the state of the leading vehicle, and subsequent vehicles are represented by red, blue, green, and magenta lines, respectively. The state error curve is obtained by comparing the state information sequence using the following formula. Where... , , , and Each vehicle represents , , , and error.

[0103]

[0104] Experimental results show that:

[0105] Scene 1: City Road

[0106] For urban road scenarios, this invention first plots the trajectories of all vehicles in the queue in a geodetic coordinate system, such as... Figure 5 As shown, it clearly demonstrates that the vehicle trajectories converge to an overlapping path. Furthermore, to verify whether the vehicle platoon has reached the required inter-vehicle travel path length, this invention plots the trajectories of all vehicles in the platoon, along with the corresponding errors for all following vehicles, as shown... Figure 6 The results showed that... From the maximum value Gradually converged to The average error Stay Within, gradually converged to .

[0107] Furthermore, the present invention in Figure 7 The image shows the longitudinal velocities of all vehicles in the queue. The trajectory and the corresponding errors of all following vehicles. It is easy to observe that subsequent vehicles in the convoy started at different initial speeds, but successfully tracked the leading vehicle. The expected speed. Correspondingly, Figure 8 The yaw angles of all vehicles in the convoy are given. and yaw angle The trajectory, and the corresponding errors of all following vehicles. and It can be seen that all the following vehicles and They all gradually converge to 0.

[0108] Scene 2: Highway exit ramp

[0109] In the scenario of a highway exit ramp, this invention first plots the trajectories of all vehicles in the queue in a geodetic coordinate system, such as... Figure 9 As shown, it clearly demonstrates that the vehicle trajectories converge to an overlapping path. Furthermore, to verify whether the vehicle platoon has reached the required inter-vehicle travel path length, this invention plots the trajectories of all vehicles in the platoon, along with the corresponding errors for all following vehicles, as shown... Figure 10 The results showed that... From the maximum value Gradually converged to The average error Stay Within, gradually converged to .

[0110] Furthermore, the present invention in Figure 11 The image shows the longitudinal velocities of all vehicles in the queue. The trajectory and the corresponding errors of all following vehicles. It is easy to observe that the subsequent vehicles in the queue start at different initial speeds, but successfully track the expected speed of the leading vehicle, thus... Correspondingly, Figure 12 The yaw angles of all vehicles in the convoy are given. and yaw angle The trajectory, and the corresponding errors of all following vehicles. and It can be seen that all the following vehicles and They all gradually converge to 0.

[0111] The above experiments describe in detail the effectiveness of the algorithm of the present invention. Based on the experimental data and comparison with existing vehicle control methods, the advantages of the present invention are as follows:

[0112] 1. Capable of handling nonlinear systems and complex tasks: This invention uses a system model for prediction, optimizing the control input within each control cycle to adapt to the nonlinear characteristics of the system. It can handle highly complex tasks, such as high-speed vehicle driving and navigating complex intersections, flexibly optimizing the control strategy at each time step. In contrast, control algorithms such as PID, LQR, and Stanley are typically used for linear systems and have poor adaptability to nonlinear systems. They are easily limited by system nonlinearity and constraints, failing to meet the demands of complex environments and tasks.

[0113] 2. Constraint Handling and Multi-Objective Optimization Capabilities: This invention can easily integrate constraints, such as wheel steering angle constraints and speed constraints, introducing these constraints into the optimization problem so that the controller can find the optimal solution within the constraints. Simultaneously, this invention can handle multiple objectives and constraints, such as simultaneously considering minimizing error, minimizing energy consumption, and avoiding collisions. In contrast, control algorithms such as PID, LQR, and Stanley are relatively complex in handling constraints and typically can only handle a single objective, making it difficult to find a balance between multiple objectives.

[0114] 3. Excellent path tracking accuracy and robustness: This invention can predict future states and incorporate these predictions into the optimization process, achieving more accurate path tracking. Furthermore, because optimization is performed in each control cycle, it can better handle system disturbances and uncertainties. (Based on experimental data...) Figure 5 and Figure 9 As shown, the path tracking accuracy error is extremely small, while control algorithms such as PID, LQR, and Stanley have very low tracking accuracy under nonlinear and constraint conditions, and are easily affected by external disturbances, resulting in poor robustness.

[0115] In addition to the advantages mentioned above, this invention employs a distributed algorithm, allowing multiple models to describe different system behaviors, thus better adapting to complex nonlinear systems. The distributed nature means that multiple controllers can work in parallel, reducing the burden on the central controller, thereby improving computational efficiency and helping to reduce computational complexity. Through the collaborative work among distributed controllers, the actions of multiple vehicles can be better coordinated, avoiding collisions and congestion, and improving the overall efficiency of the traffic system.

Claims

1. A vehicle queuing cooperative predictive control method in a curve scenario, characterized in that: Includes the following steps: Step 1: Define the communication topology of the vehicle queue; A queue consisting of vehicles is created, whose indices are , and drives on a curved road; the vehicles represent the leading vehicle, which drives forward at a constant longitudinal speed, denoted by ; the indices of the following vehicles are from to , and each vehicle receives the state information of other vehicles according to the corresponding communication topology; The communication topology of the vehicle queue is represented by a directed graph. To model, its node set edge set Adjacency matrix Indicates from node To the node There exists a directional edge representing a vehicle. Received vehicle Information; Represented as: ； when At that time, the vehicle It is a vehicle The neighbor, then the vehicle The neighbor set is represented as ； If there exists a root node such that any other node in the directed graph G can be reached through at least one path originating from the root node, then the directed graph G is said to contain a directed spanning tree; the communication topology G of a vehicle queue contains a directed spanning tree and is unidirectional, that is, information is only transmitted from the vehicle in front to the vehicle behind; unidirectional communication topologies include the leading vehicle following (PF) topology, the leading vehicle-leader following (PLF) topology, and the two leading vehicles following (TPF) topology. Step 2: Establish the vehicle dynamics model; Step 2.1: Vehicle construction exist Differential equations in the coordinate system are used to derive a vehicle dynamics model with three degrees of freedom: ； ； ； Among them, subscript Representing the a car, and This refers to the front and rear tires, and in the formula above, they are related to... The relevant symbols all represent tire forces; They represent the first The resultant longitudinal force on the front and rear tires of a vehicle. They represent the first The resultant lateral force on the front and rear tires of a vehicle; the rear wheel steering angle is 0, meaning the longitudinal and lateral forces on the tires are equal to the forces acting on the center of the rear wheel; based on the tire slip angle... or Tire slip ratio or Road surface friction coefficient and vertical load The longitudinal and lateral forces of each front or rear wheel are obtained; the HB Pacejka tire model is used to describe the changes in tire forces; if the tire's sideslip angle is small, the sideslip force is approximated as a linear function of the sideslip angle; the longitudinal force is approximated as a linear function of the slip ratio, and then the tire force model is obtained. Based on the tire model, the magic formula, and the geodetic coordinate system transformation formula, the state-space equation of the complete vehicle dynamics model is expressed as: ； Define state variables Control input variables The detailed format is as follows: ； State variables in equation (1.7) For the team, the first The longitudinal speed of the vehicle, For lateral velocity, Yaw rate, The yaw angle is an intermediate variable. Expressed as yaw rate for distinction and , and These are the geodetic coordinates after the vehicle body coordinates have been transformed. For rotational inertia, This is the distance from the center of the front wheel. The distance from the rear wheel to the center. For the stiffness of the front wheels, For the stiffness of the rear wheels, For the mass of the vehicle; control input variables and The first The steering angle and acceleration of a vehicle's wheels; Step 2.2: The differential equation is transformed into a difference equation, which is achieved using the explicit Euler method; First, we define an initial value problem for a first-order differential equation: ； The initial time, This is the initial state. It is a known function of time and state; Replace the differential with the first-order positive difference quotient, that is, in the th order... time: ； Represents discrete time intervals; Using the difference quotients described above, the differential equation is transformed into an explicit difference equation: ； Explicit difference equations provide the means to... arrive The recursive form is obtained, and based on the initial values, the numerical solutions of each step of the differential equation are obtained sequentially; Step 2.3: Next, the state-space equations of the vehicle dynamics model are transformed into discrete time intervals according to step 2.

2. Difference equation: ； The discrete nonlinear model of the vehicle queue is obtained as follows: ； Output vector , where the matrix ; Step 3: Establish a local optimization problem based on tracking the trajectory of the preceding vehicle's delay; Step 3.1: Before designing a local optimization problem, first use Represents the prediction time domain and makes the control time domain equal The control input, state, and output sequences are defined within the prediction range for both the predicted and ideal states. The control input sequence under the prediction state is: The state sequence is The output sequence is ; Under ideal conditions, the control input sequence is: The state sequence is The output sequence is ; Step 3.2: set up Indicates vehicle Future time step The predictive control input will be at the current time step. The following determination is made; given the control input sequence. Current state Then the predicted state and output are in Place, Use respectively and This can be calculated iteratively using the following formula: ； Step 3.3: To achieve the desired longitudinal constant speed for each vehicle on curved roads and the expected driving path length The control objective, ideally, is that each vehicle in the queue follows the delayed trajectory of the leading vehicle, and the delay time of any vehicle is... yes Based on this idea, define each vehicle : ； Then for each car Propose an optimization problem : ； ； ； In optimizing the problem In equation (1.16), the feasible range of the wheel steering angle is constrained. Let represent the minimum and maximum angle ranges of the wheel, respectively. Equation (1.17) guarantees the terminal output of each vehicle. The terminal constraint is equal to the average historical terminal output of its neighboring vehicles. Step 4: Propose a distributed model predictive control algorithm for vehicle queuing on curved roads; Based on the local optimization problem, a distributed model predictive tracking control algorithm for vehicle platoons, namely the Delayed Trajectory Tracking (DMPC) algorithm, is proposed.

2. The vehicle queuing cooperative predictive control method in a curve scenario according to claim 1, characterized in that: The implementation method of the Delayed Trajectory Tracking (DMPC) algorithm is as follows: Step 4.1: Initialize the initial state of each vehicle using the Simulink system controller. ; set up Assume that each vehicle stores information about its neighboring vehicles. Historical and current output and input information: ； Step 4.2: from Start traversing to , from Start traversing to vehicles The loop begins; By solving local optimization problems ,vehicle Obtain the control input prediction sequence for the current time step: , ； vehicle The first item As the actual control input for the current time step, i.e. ; Step 4.3: vehicle Based on the actual control input at the current time step Update the state parameters of the nonlinear dynamic model for the next step. : ； Step 4.4: vehicle transmission and Receive and store the state sequences and control inputs of neighboring vehicles: , , ; Step 4.5: Update status at the next time step With output The process continues until the loop stops, storing the state sequence and output sequence in the working area; this enables distributed model predictive control for cooperative driving of vehicle platoons on curved roads.

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