A double-layer distributed model predictive control method for multi-vehicle cooperative cut-in

Abstract

This invention discloses a two-layer distributed model predictive control method for multi-vehicle cooperative entry, belonging to the fields of intelligent traffic control and autonomous driving technology. It constructs an eight-dimensional state-space model and establishes a forward-chain topology within queues and a multi-strategy communication topology between queues. The upper layer determines the optimal entry queue and insertion position through multi-objective optimization and generates a fifth-order polynomial reference trajectory. The lower layer achieves trajectory tracking and local coordination based on longitudinal-lateral coupled distributed model predictive control. A time window for entry and queue adjustment is introduced to ensure feasibility, and longitudinal-lateral cooperative optimization is designed for the lead vehicle, following vehicle, and entry vehicle. Stability is ensured by combining terminal state and safety constraints. This method, through a two-layer architecture and multi-vehicle cooperation, achieves safe, efficient, and comfortable multi-vehicle entry control, improving the traffic efficiency and safety of multi-queue systems.

Description

Technical Field

[0001] This invention relates to the fields of intelligent traffic control and autonomous driving technology, specifically a two-layer distributed model predictive control method with multi-vehicle collaborative approach. Background Technology

[0002] With the rapid development of intelligent connected vehicle technology, cooperative control of multi-platform vehicle systems has become an important research direction in the field of autonomous driving. In complex traffic environments, in addition to basic vehicle following and lane changing behaviors, multi-vehicle cooperative entry scenarios are becoming increasingly prominent in practical applications such as highway merging, emergency obstacle avoidance, and platoon reorganization. However, existing control methods have significant limitations in handling multi-vehicle cooperative entry problems.

[0003] Traditional distributed model predictive control (DMPC) methods typically only consider single-vehicle entry scenarios, lacking a systematic design framework for simultaneous or continuous entry by multiple vehicles. Existing methods still have shortcomings in entry decision-making, trajectory planning, and multi-vehicle coordination: First, they lack a systematic two-layer optimization architecture, making it difficult to effectively balance global decision-making and local execution; second, entry feasibility constraints are not adequately considered, easily leading to entry failure or safety risks; third, the multi-vehicle coordination mechanism is imperfect, making it difficult to handle the mutual influence and conflicts when multiple vehicles enter; and fourth, the vertical-horizontal coupling control has high complexity, lacking effective distributed solution methods.

[0004] Therefore, a two-layer distributed model predictive control method with multi-vehicle collaborative intervention is proposed to solve the above problems. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a two-layer distributed model predictive control method for multi-vehicle cooperative entry, which solves the problems of existing multi-vehicle queuing control methods mentioned in the background art, such as inability to effectively handle multi-vehicle cooperative entry, lack of a systematic decision-making framework, and high complexity of vertical-horizontal coupling control.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A two-layer distributed model predictive control method for multi-vehicle cooperative intervention includes the following steps: Step 1: Construct a multi-platform vehicle system and a longitudinal-lateral coupled dynamic model. The longitudinal-lateral coupled dynamic model includes an eight-dimensional state space vector, a longitudinal motion state equation, and a lateral motion state equation. The eight-dimensional state space vector includes longitudinal position, longitudinal velocity, longitudinal acceleration, traction torque, lateral position, heading angle, lateral velocity, and yaw rate. Step 2: Establish a hierarchical communication topology, which includes an intra-queue forward chain communication topology and an inter-queue multi-strategy communication topology. The inter-queue multi-strategy communication topology includes two strategies: lead vehicle-tail vehicle communication and lead vehicle-tail vehicle-lead vehicle communication. Step 3: Design a two-layer optimization framework, including upper-layer decision optimization and lower-layer trajectory tracking optimization. The upper-layer decision optimization determines the optimal entry queue, insertion position and entry time through a multi-objective optimization function. The lower-layer trajectory tracking optimization achieves local coordinated control based on longitudinal-lateral coupled distributed model predictive control. Step 4: Construct feasibility constraints for the entry operation, including the arrival time window constraint for the entry vehicle and the adjustment time window constraint for the target queue, to ensure the safety and feasibility of the entry operation. Step 5: Use a fifth-order polynomial to generate smooth longitudinal and lateral reference trajectories. The longitudinal reference trajectory satisfies the position, velocity, and acceleration boundary conditions, and the lateral reference trajectory uses an S-curve to achieve smooth lane changing. Step 6: Based on the hierarchical communication topology, construct the longitudinal-lateral coupled distributed model predictive control optimization problem and cost function. The optimization problem includes the local optimization problem of the queuing navigator, the local optimization problem of the queuing following vehicle, and the longitudinal-lateral collaborative optimization problem of the cutting vehicle. Step 7: Introduce longitudinal and lateral terminal state constraints as well as safety distance constraints to ensure the stability and convergence of the system at the end of the prediction time domain; Step 8: Solve the optimization control problem for each vehicle node, and adjust the longitudinal traction torque and lateral steering angle control inputs simultaneously based on the optimization results to achieve safe control for multi-vehicle coordinated entry.

[0007] As a further preferred embodiment of the multi-vehicle cooperative entry two-layer distributed model predictive control method of the present invention, in step 1, the step of constructing the multi-queue vehicle system and the longitudinal-lateral coupled dynamic model includes: Define the vehicle longitudinal state vector and lateral state vector ,in, These represent longitudinal position, longitudinal velocity, longitudinal acceleration, and traction torque, respectively. These represent the lateral position, heading angle, lateral velocity, and yaw rate, respectively. The longitudinal and lateral dynamic equations are constructed using a discrete-time model. The longitudinal dynamics consider the time constant and drag characteristics of the traction system, while the lateral dynamics are based on the tire lateral force model and the vehicle kinematics relationship.

[0008] As a further preferred embodiment of the multi-vehicle cooperative entry two-layer distributed model predictive control method of the present invention, in step 3, the expression of the upper-level decision optimization problem of the two-layer optimization framework includes: ; In the formula: This represents the cost function for the upper-level multi-objective optimization. The weighting coefficients represent safety, efficiency, and comfort. Indicates safety indicators, Indicators of efficiency Indicates comfort level; Decision variables include target entry queue number Target insertion position and entry point .

[0009] As a further preferred embodiment of the multi-vehicle cooperative approach dual-layer distributed model predictive control method of the present invention, the safety index Defined as: ; in, Indicates the first step in the cutting process The minimum distance between adjacent vehicles at each time step. Indicates the safe distance threshold. This indicates the number of time steps in the cut-in process. Let M be the indicator function, and M be the large penalty coefficient. Distance weights; efficiency indicators Defined as: ; in, Indicates the duration of the cut-in. This indicates the time required for the target queue to adjust to an acceptable cut-in state. This indicates a redundancy distance that exceeds the necessary safety distance. These are the weighting coefficients; Comfort Index Defined as: ; Indicates acceleration and jerk. Throughout the cutting process The weighted square integral in These are the weighting coefficients.

[0010] As a further preferred embodiment of the two-layer distributed model predictive control method for multi-vehicle cooperative entry according to the present invention, in step 4, the entry feasibility constraints include: Cutting into vehicle arrival time window constraints: ; in: ; The vertical coordinate of the target entry point. For location buffer, and These are the upper and lower limits of the speed of the vehicle entering the lane; Queue adjustment time window constraints: ; in, This indicates the moment when the target queue is ready to accept the cut-in. and Determined based on the speed and spacing of vehicles at the target location; Safety distance constraints: ; ; in, Indicates the cutting-in vehicle With the vehicle in front of the target queue The distance between them Indicates the cutting-in vehicle Following the target queue The distance between them For time-distance between the front of the train; Speed ​​matching constraints: ; in, This represents the average speed of vehicles near the target location. This indicates the maximum permissible speed difference.

[0011] As a further preferred embodiment of the multi-vehicle cooperative entry two-layer distributed model predictive control method of the present invention, in step 5, the method for generating smooth longitudinal and lateral reference trajectories using a fifth-order polynomial includes: Longitudinal reference trajectory: ; Boundary conditions are satisfied: ; By solving the system of linear equations Obtain the coefficient vector ; Lateral reference trajectory: ; Boundary conditions are satisfied: ; in and Given the initial and target lane lateral positions, the coefficient vector is obtained by solving a system of linear equations. .

[0012] As a further preferred embodiment of the two-layer distributed model predictive control method for multi-vehicle cooperative entry of the present invention, in step 6, the expression of the local optimization problem of the queue following vehicle includes: ; In the formula: Indicates the first Vehicle nodes following in the queue The cost function of the vertical local optimization problem. Indicates the prediction time domain, Indicates the predicted state of the vehicle node. This represents the assumed state of the vehicle node. Indicates the assumed state of the vehicle ahead. Indicates longitudinal control input; Indicates the time step within the prediction time domain; This represents the cost function of the vehicle.

[0013] As a further preferred embodiment of the two-layer distributed model predictive control method for multi-vehicle cooperative entry in this invention, the instantaneous cost function is: ; In the formula: To account for the deviation between the predicted state and the assumed state, For vehicle spacing deviation, the weight matrix Let f be a symmetric non-negative definite matrix, and f be the weights of state tracking error, control input cost, assumed state deviation, and vehicle spacing error, respectively.

[0014] As a further preferred embodiment of the two-layer distributed model predictive control method for multi-vehicle cooperative entry according to the present invention, the longitudinal-lateral cooperative optimization problem of the entering vehicles includes: Vertical optimization problem: ; in, For distance penalty function: ; and These represent the distances between the cutting vehicle and the vehicles in front and behind it, respectively. Lateral optimization problem: ; In the formula: This is the lateral position error. For heading angle error, This refers to the front wheel steering angle. This represents the rate of change of the steering angle.

[0015] As a further preferred embodiment of the multi-vehicle cooperative entry two-layer distributed model predictive control method of the present invention, the step of introducing longitudinal and lateral terminal state constraints includes: Vertical terminal state constraints: ; ; in, Indicates the predicted state of the vehicle node. This indicates the predicted state of the previous vehicle node. These are the error thresholds for vehicle and queue spacing, respectively. , These represent the predicted and assumed states of the lead vehicle in the platoon and the lead vehicle in the preceding platoon, respectively. Indicates the queue length; Used to measure the impact of different communication structures on the terminal constraints of a queuing system, satisfying... ; Lateral terminal state constraints: ; ; in, This is the error threshold; , , , , These represent the lateral position, lateral reference position, heading angle, lateral velocity, and yaw rate of the vehicle cutting in.

[0016] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects: 1. This invention achieves systematic multi-vehicle cooperative entry control: Through a two-layer optimization framework, global decision-making and local execution are organically combined. The upper layer determines the optimal entry scheme, and the lower layer realizes accurate trajectory tracking, which overcomes the limitation of traditional methods lacking a systematic framework and provides a complete control solution for multi-vehicle cooperative entry. 2. This invention ensures the feasibility and safety of the cut-in operation: By constructing a cut-in arrival time window, a queue adjustment time window, a safety distance constraint, and a speed matching constraint, a multi-dimensional feasibility guarantee mechanism is formed, which avoids cut-in failure and safety risks and significantly improves the cut-in success rate; 3. This invention improves the coordination of multi-vehicle entry: It designs a mechanism for determining the priority of multi-vehicle entry, timing planning, and conflict detection and resolution, which realizes effective coordination between multiple vehicles and avoids system instability caused by simultaneous or continuous entry. 4. This invention achieves longitudinal-lateral coordinated control: By extending the eight-dimensional state space model and longitudinal-lateral coupling optimization design, it can simultaneously handle the vehicle's longitudinal following and lateral lane changing behaviors, ensuring the smoothness and comfort of the cutting process. 5. This invention enhances system scalability: It adopts a distributed optimization architecture, decomposes the global control problem into local optimization sub-problems, avoids the high computational burden of centralized control, and is suitable for large-scale multi-queue multi-vehicle collaborative control scenarios.

[0017] 6. This invention provides flexible communication strategies: two inter-queue communication strategies (lead car-tail car, lead car-tail car-lead car) provide flexible choices for different application scenarios, meeting diverse needs from rapid response to stable control. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the longitudinal reference trajectory of the cutting vehicle; Figure 2 This is a schematic diagram of the lateral reference trajectory of the cutting vehicle; Figure 3 This is a schematic diagram of the reference trajectory for the lead vehicle; Figure 4 This is a schematic diagram of the longitudinal motion trajectory of a vehicle under a Lead-Tail communication topology. Figure 5 A schematic diagram of the lateral movement trajectory of the vehicle cutting in under the Lead-Tail communication topology; Figure 6 This is a schematic diagram of the longitudinal motion trajectory of a vehicle under a Lead-Tail-Lead communication topology. Figure 7 This is a schematic diagram of the lateral movement trajectory of the cutting vehicle under the Lead-Tail-Lead communication topology. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] A two-layer distributed model predictive control method with multi-vehicle cooperative intervention includes: Longitudinal-lateral coupled state space modeling: The traditional four-dimensional longitudinal state is extended to an eight-dimensional state space model that includes lateral position, heading angle, lateral velocity, and yaw rate, and a complete longitudinal-lateral coupled dynamic equation is established to accurately describe the vehicle's composite motion characteristics. Layered communication topology design: Establish a forward chain communication structure within the queue and a multi-strategy communication structure between queues. Design two communication strategies: lead car-tail car and lead car-tail car-lead car, which are suitable for application scenarios with different response speed and stability requirements. Two-layer optimization framework design: Construct a two-layer architecture with upper-layer decision optimization and lower-layer trajectory tracking optimization. The upper layer determines the best entry point through multi-objective optimization, and the lower layer realizes distributed model predictive control with vertical and horizontal coupling. Feasibility constraint mechanism for entry: Design entry vehicle arrival time window and queue adjustment time window constraints, and ensure the feasibility and safety of entry operation through multi-dimensional constraints such as safe distance and speed matching; Reference trajectory generation method: A fifth-order polynomial is used to generate longitudinal and lateral reference trajectories that satisfy the continuity of position, velocity and acceleration, so as to achieve a smooth cutting process; Multi-vehicle collaborative entry control: The design considers the mutual influence of multiple vehicles and realizes safe and efficient entry of multiple vehicles through information exchange and distributed solution.

[0021] Preferred modeling of multi-queue longitudinal-lateral coupling systems: Step 1: Define the longitudinal and lateral states, and expand the vehicle state vector into an eight-dimensional state space, including longitudinal position, longitudinal velocity, longitudinal acceleration, traction torque, lateral position, heading angle, lateral velocity, and yaw rate, to ensure that the longitudinal and lateral motion behavior of the vehicle can be fully characterized. Step 2: Establish longitudinal dynamics. Construct longitudinal dynamic equations considering the response characteristics of the dynamic system and aerodynamic drag, expressed using a discrete-time model as follows: ; in, These represent longitudinal position, longitudinal velocity, longitudinal acceleration, and traction torque, respectively. The combined resistance is expressed as Where m is the vehicle mass, R is the effective tire radius, η is the transmission efficiency, and τ is the powertrain time constant. It is a longitudinal control input; Step 3: Establish lateral dynamics by establishing the lateral dynamics equations based on the front and rear wheel slip angle model. ; in, These represent the lateral position, heading angle, lateral velocity, and yaw rate, respectively. and These are the front and rear wheel lateral stiffness, and The front and rear wheel slip angles, and These are the distances from the front and rear axles to the center of mass, respectively. It is the moment of inertia of the vehicle about the z-axis; Step 4: Define the queue length state, defining the queue length as the longitudinal interval between the lead car and the tail car. Establish the dynamic change equation for the queue length: ; in, The length of the vehicle; Step 5: Design hierarchical communication topology, including intra-queue forward chain communication topology and inter-queue multi-strategy communication topology: The communication topology within the queue is a forward-linked structure; Two strategies for inter-queue communication design: Strategy 1: Lead vehicle-tail vehicle communication (LT), the first The lead vehicle in the queue receives the first The assumed state of the last car in the queue serves as a reference for following; Strategy 2: Lead vehicle-tail vehicle-lead vehicle communication (LTL), the first The lead vehicle in the queue simultaneously receives the first The hypothetical states of the lead car and the tail car in the queue are weighted and merged.

[0022] Preferred, two-layer optimized framework design: Step 6: Constructing the upper-level decision optimization problem. For the vehicle to be entered, establish a multi-objective optimization problem to determine the best entry strategy: ; In the formula: This represents the cost function for multi-objective optimization at the upper level, with decision variables including the target entry queue number. Target insertion position (Indicates cutting to the first) The queue's first Car and the (between vehicles) and cut-in time ; Safety indicators Defined as: ; in Indicates the first step in the cutting process The minimum distance between adjacent vehicles at each time step. Indicates the safe distance threshold. This indicates the number of time steps in the cut-in process. Let M be the indicator function, and M be the large penalty coefficient. Distance weights; efficiency indicators Defined as: ; in Indicates the duration of the cut-in. This indicates the time required for the target queue to adjust to an acceptable cut-in state. This indicates a redundancy distance that exceeds the necessary safety distance. These are the weighting coefficients; Comfort Index Defined as: ; Indicates acceleration and jerk. Throughout the cutting process The weighted square integral in These are the weighting coefficients; Step 7: Constructing Feasibility Constraints. To ensure the feasibility and safety of the entry point, the following constraints are established: Cutting into vehicle arrival time window constraints: ; in: ; The vertical coordinate of the target entry point. For location buffer, and These are the upper and lower limits of the speed of the vehicle entering the lane; Queue adjustment time window constraints: ; in, This indicates the moment when the target queue is ready to accept the cut-in. and Determined based on the speed and spacing of vehicles at the target location; Safety distance constraints: ; ; in, Indicates the cutting-in vehicle With the vehicle in front of the target queue The distance between them Indicates the cutting-in vehicle Following the target queue The distance between them For time-distance between the front of the train; Speed ​​matching constraints: ; in, This represents the average speed of vehicles near the target location. Indicates the maximum permissible speed difference; Step 8: Reference trajectory generation, using a fifth-order polynomial to generate smooth longitudinal and lateral reference trajectories; Longitudinal reference trajectory: ; Boundary conditions are satisfied: ; By solving the system of linear equations Obtain the coefficient vector ; Lateral reference trajectory: ; Boundary conditions are satisfied: ; in and Given the initial and target lane lateral positions, the coefficient vector is obtained by solving a system of linear equations. .

[0023] Preferred design for lower-level distributed model predictive control: Step 9: Constructing the Local Optimization Problem for Following Vehicles in the Queue. For vehicles following vehicles within the queue, establish a vertical local optimization problem: ; In the formula: Indicates the first Vehicle nodes following in the queue The cost function of the vertical local optimization problem. Indicates the prediction time domain, Indicates the time step within the prediction time domain; The instantaneous cost function is: ; In the formula: To account for the deviation between the predicted state and the assumed state, For vehicle spacing deviation, the weight matrix It is a symmetric nonnegative definite matrix; Step 10: Constructing the local optimization problem for the queue leader vehicle. For the queue leader vehicle, construct an optimization problem that includes coupling between queues: ; LT: ; LTL: ; in, The fusion coefficient; Step 11: Construct the longitudinal-lateral collaborative optimization problem for the entry vehicle. j Establish a vertical-horizontal coupling optimization problem; Vertical optimization problem: ; in, For distance penalty function: ; and These represent the distances between the cutting vehicle and the vehicles in front and behind it, respectively. Lateral optimization problem:

[0024] In the formula: This is the lateral position error. For heading angle error, This refers to the front wheel steering angle. This represents the rate of change of the steering angle.

[0025] Preferred terminal constraint design: Step 12: Design vertical terminal constraints to ensure that the vertical state at the end of the prediction time domain meets the queue synchronization requirements: Constraints on following vehicles within the queue: ; ; Constraints on the navigator vehicle terminal between queues: ; in, and These represent the maximum permissible state deviation; Step 13: Design lateral terminal constraints to ensure stable convergence of lateral motion: ; ; ; ; in, The allowable error threshold; Step 14: Define physical constraints, adding vehicle dynamics and safety constraints: ; ; ; ; ; ; in, This represents the vehicle dynamics model, with the limits of each physical quantity determined based on the vehicle's performance.

[0026] Preferred distributed model predictive controller design: Step 15: Define the hypothetical state and control sequence, and generate the hypothetical state sequence based on the time-domain translation strategy. and hypothetical control sequence : ; ; Step 16: The optimization problem is expressed as: ; Step 17: Design of distributed solution algorithm. The interior point method is used to solve the quadratic programming approximation problem. For nonlinear constraints, sequential convex programming is used for iterative solution.

[0027] Preferred algorithm implementation flow: Step 18: Initialization phase, setting the vehicle's initial state: ; ; in, This is the initial longitudinal position. The initial velocity, For steady-state torque, This is the initial horizontal position; Initialize the hypothesis sequence for each node Initialize queue length ; Initiating vehicle state initialization: ; ; Step 19: Upper-level decision-making stage, for each vehicle entering the market... : (1) Construct a set of candidate entry points ; (2) For each candidate solution Check feasibility constraints: ; (3) For feasible solutions, calculate the upper-level cost function. ; (4) Select the optimal solution: ; in, This is a set of feasible solutions; (5) Based on the optimal entry decision, call step 8 to generate longitudinal and lateral reference trajectories; Step 20: Lower-level trajectory tracking stage, at each time step Solve the corresponding optimization control problem for each vehicle node: (1) Solving the problem of the queuing navigator ,get ; (2) Solving the problem in parallel with the queue following the vehicle , ,get ; (3) Solving the longitudinal optimization problem by focusing on the vehicle and horizontal optimization ,get and ; Step 21: State update phase, including queue state update and vehicle switching state update: Queue status update: (1) Update the status of the navigator vehicle: ; (2) Update the status of the following vehicle: ; (3) Update the hypothesis sequence (time domain shift): ; ; (4) Update the queue length: ; Switch to vehicle status update (when) hour): (1) Update both vertical and horizontal states simultaneously: ; ; (2) Verify security constraints: ; ; If the restraints are violated, emergency braking will be triggered; Step 22: Information exchange phase, realizing distributed information sharing: (1) The queuing navigator broadcasts the hypothetical sequence. Provide a lead vehicle to the adjacent queue; (2) The following vehicle sends the hypothetical sequence to the following vehicle: vehicle Send to vehicle ; (3) Predicted trajectory of the vehicle entering the station via broadcast Give the affected vehicles (vehicles in front and behind the target queue); Step 23: Iterate through steps 20-22 until... (All vehicles have completed the switching process and the system is stable).

[0028] Preferred multi-vehicle collaborative entry strategy: Step 24: Determine the priority of multiple vehicle cut-offs. When multiple vehicles request cut-offs simultaneously, the processing order is determined according to the priority function: ; in, For safety urgency (based on distance from surrounding vehicles), Time urgency (based on arrival time window) For the waiting time (normalized). These are weighting coefficients, processed first. The highest value cutoff request; Step 25: Multi-vehicle entry timing planning, designing entry time interval constraints: ; in, This is the minimum interval between two cuts; Step 26: Multi-vehicle entry conflict detection and resolution: (1) Detect multiple vehicles entering the same queue at the same position to cause conflict: If vehicles and Simultaneously select the entry point If the priority is high, the selection of high-priority vehicles will be retained, and low-priority vehicles will be re-planned. (2) Detect conflict between adjacent positions: If the vehicle Cut in And vehicles Cut in ,examine: ; ; If the conditions are not met, adjust the entry time or position of the low-priority vehicle; (3) Conflicts are resolved through iterative negotiation until all vehicle entry schemes are compatible with each other.

[0029] For specific implementation examples, please refer to: Figure 1-7 A two-layer distributed model predictive control method with multi-vehicle collaborative approach: I. Initialization: 1. System Settings To verify the effectiveness of the proposed two-layer distributed model predictive control method, the simulation scenario consists of three highway platoons traveling in adjacent lanes and three vehicles attempting to merge into these platoons from the outer lanes. The three platoons are configured with 9 vehicles in the first platoon, 7 vehicles in the second platoon, and 7 vehicles in the third platoon, for a total of 23 vehicles. Three vehicles are also included in the platooning scenario. and .

[0030] The coordinate system is set as follows: the lead vehicle of queue 1 is in t =0 is at the origin ( s =0), and all other vehicles are positioned sequentially according to their spacing requirements. The system uses a discrete time step of 0.1s for simulation, and the prediction time domain is set to 20 steps. The expected following distance between vehicles is set to 10m, and the expected distance between queues is set to 30m. Each queue travels at a nominal cruising speed of 20m / s. The constraints are set as follows: maximum acceleration 4.0m / s², speed range 15-25m / s, and safety distance 5m.

[0031] 2. Vehicle status initialization Set the initial state of each vehicle, initial time. At that time, the first Queue number The status of a vehicle is represented as follows: ; ; in The initial velocity, Assuming a steady-state driving torque, the initial distance between each vehicle in the queue is 10m, and the queue spacing is 30m. The initial states of the queue and the vehicles entering the queue are shown in Table 1.

[0032] Table 1

[0033] 3. Switch to vehicle status initialization Initialize the longitudinal and lateral states of the incoming vehicle: ; ; in, The initial lateral position is (initial lane Y=0m, target lane Y=3.5m).

[0034] 4. Assume sequence initialization Initialize the hypothetical input sequence for each node and the assumed state sequence : Predicted based on a constant velocity motion model.

[0035] 5. Queue length initialization ; 6. Parameter Settings The vehicle physical parameters are shown in Table 2, the lateral control system parameters are shown in Table 3, and the DMPC controller weight matrix settings are shown in Table 4.

[0036] Table 2

[0037] Table 3

[0038] II. Upper-level decision optimization and reference trajectory generation The simulation is divided into two stages: the first stage generates a smooth reference trajectory based on the fifth-order polynomial method, and the second stage implements trajectory tracking control based on DMPC.

[0039] Step 1: Upper-level multi-objective optimization For the vehicle to enter the lane, the optimal entry scheme is determined based on the upper-level multi-objective optimization method described in claims 3 and 4: (1) Construct a set of candidate entry points ; (2) For each candidate solution Check the feasibility constraints: arrival time window constraint for the vehicle entering the queue, queue adjustment time window constraint, safety distance constraint, and speed matching constraint; (3) For feasible solutions, calculate the upper-level cost function. These include safety indicators, efficiency indicators, and comfort indicators; (4) Select the optimal solution: ; Based on the solution of the optimal problem P1, the following entry parameters are determined: lane-changing time of the entering vehicle. The start times are 5s, 9s, and 13s respectively, and the queue adjustment time is... .

[0040] Step 2: Generation of Vertical Reference Trajectory According to the fifth-order polynomial method described in claim 6, the following is adopted: Generate a longitudinal reference trajectory that satisfies the boundary conditions: For the cutting-in vehicle : Initial conditions (t=5.0s): , ; Termination condition (t=9.0s): , ; By solving the system of linear equations Obtain the coefficient vector Generate longitudinal reference trajectory .

[0041] Figure 1 The longitudinal reference trajectories of the three vehicles are shown. In terms of longitudinal motion, the three vehicles exhibit differentiated speed adjustment modes: vehicle... The vehicle decelerates from 21 m / s to 20 m / s, with a peak acceleration of approximately -0.3 m / s². Maintaining a constant speed of 20 m / s with zero acceleration; vehicle Accelerating from 19 m / s to 20 m / s, the peak acceleration is approximately 0.3 m / s². The position curves show that all vehicles smoothly transition from the negative coordinate region to the positive coordinate region, indicating that the reference trajectory achieved longitudinal catching-up during the lane change period.

[0042] Step 3: Generating the Lateral Reference Trajectory A fifth-order polynomial is used to generate the lateral reference trajectory, satisfying the boundary conditions: For the cutting-in vehicle : Initial conditions (t=5.0s): , ; Termination condition (t=9.0s): , ; The coefficient vector is obtained by solving the system of linear equations. Generate a lateral reference trajectory .

[0043] Figure 2 The lateral reference trajectories of the three vehicles are shown. In terms of lateral motion, all three vehicles transition from the initial lane (Y=0m) to the target lane (Y=3.5m). The lateral velocity exhibits a symmetrical bell-shaped distribution (peak value approximately 1.1m / s), and the lateral acceleration exhibits a bimodal structure (peak value approximately ±0.6m / s²). Both are far below the dynamic limits, and the velocity and acceleration are zero at the start and end of the lane change, satisfying the boundary condition requirements of a fifth-order polynomial.

[0044] Step 4: Generating the reference trajectory for the platoon leader vehicle Figure 3 The displayed platoon leader vehicle trajectory shows that the platoon leader vehicles need to actively adjust their speed to coordinate with the entry of other vehicles. The speed curves show that the speeds of the three leader vehicles fluctuate within the range of 17-23 m / s, exhibiting periodic changes; the acceleration curves show alternating positive and negative acceleration adjustments, with peak values ​​of approximately ±3 m / s². This speed adjustment pattern indicates that the upper-level coordination strategy requires the platoon to create suitable insertion gaps for the entering vehicles through appropriate acceleration or deceleration, achieving two-way coordination between the platoon and the entering vehicles.

[0045] III. Lower-level DMPC trajectory tracking control Phase two implements DMPC-based closed-loop tracking control based on the reference trajectory. The controller adopts a longitudinal-lateral decoupling design: longitudinally, DMPC coordinates the queue and cutting-in vehicles, while laterally, a centralized MPC based on a bicycle model achieves precise lane changing.

[0046] Step 5: Solving the control optimization problem At every moment t For each vehicle node, solve the corresponding optimization control problem to obtain the optimal control input sequence: The longitudinal-lateral collaborative optimization problem of the cutting-in vehicle includes: Vertical optimization problem: ; Lateral optimization problem: ; The lateral cost function includes: ; In the formula: This indicates the lateral state error. This represents the lateral state error weight matrix. This represents the lateral control input weight matrix. This represents the weight matrix controlling the rate of change of the input.

[0047] The steps for introducing longitudinal and lateral end-state constraints include: Vertical terminal state constraints: ; ; in, Indicates the predicted state of the vehicle node. This indicates the predicted state of the previous vehicle node. , These are the error thresholds for vehicle and queue spacing, respectively. , These represent the predicted and assumed states of the lead vehicle in the platoon and the lead vehicle in the preceding platoon, respectively. Indicates the queue length; Used to measure the impact of different communication structures on the terminal constraints of a queuing system, satisfying... ; Lateral terminal state constraints: ; ; in, This is the error threshold; , , , , These represent the lateral position, lateral reference position, heading angle, lateral velocity, and yaw rate of the vehicle cutting in.

[0048] (1) Vertical optimization of the cutting vehicle: Solve the optimization problem according to claim 9: ; The interior-point method is used to solve the quadratic programming problem, yielding the optimal control sequence and state trajectory.

[0049] (2) Lateral optimization of the cutting vehicle: Solve the optimization problem according to claim 9: ; The optimal control sequence and state trajectory in the lateral direction are obtained.

[0050] (3) Queue vehicle optimization (parallel execution): For all The corresponding optimization problem is solved based on the vehicle type.

[0051] For the lead vehicle in the platoon And the queuing following vehicles, according to claim 7, solve: ; The optimal control sequence and state trajectory are obtained.

[0052] (1) Apply the first element of the optimal control sequence: Cut into the car: ; ; Vehicles in the convoy: , (2) Based on the optimal input Update the status of each vehicle: ; (3) Calculate the next hypothesis input sequence for the navigator and update the hypothesis state sequence: , Terminal control law is used at the end: ; (4) Update queue length: ; Step 7: Switch to vehicle status update (1) Update both the vertical and horizontal states simultaneously: ; ; (2) Verify the safe distance constraints with adjacent vehicles: ; ; If the constraint is violated, emergency braking will be triggered.

[0053] (3) Update the cut-in progress: ; Step 8: Information Exchange and Synchronization (1) The queuing navigator broadcasts the hypothetical sequence. Provide a lead vehicle to the adjacent queue; (2) The following vehicle sends a hypothesis sequence to the vehicle behind it: vehicle send Give the vehicle ; (3) Predicted trajectory via broadcast for the vehicle entering the station Provide this information to the affected vehicles (vehicles in front and behind the target queue); (4) Update the neighbor set according to the communication topology.

[0054] Step 9: Iterate Repeat the process from Step 5 to Step 8 until... Or all vehicles that have entered the market have completed their entry.

[0055] IV. Strategy Performance Analysis To evaluate the impact of communication topology on system performance, this embodiment compares two inter-queue communication structures: Lead-Tail and Lead-Tail-Lead.

[0056] Strategy 1: Lead-Tail Communication Topology like Figure 4 As shown, under this strategy, each queue's lead vehicle only communicates with the last vehicle in the preceding queue. This can be observed from the longitudinal movement trajectory: (1) Speed ​​curve: The three lead vehicles and three cut-in vehicles fluctuated within the range of 15-23 m / s, and the cut-in vehicles made significant speed adjustments during lane change periods. This strategy responded quickly to cut-in disturbances, but there was a system oscillation problem, with speed fluctuations reaching ±2.5 m / s.

[0057] (2) Position evolution: The position curves of all vehicles transitioned smoothly, successfully achieving insertion into the target position. The gradual evolution from the initial negative coordinate position to the positive coordinate region indicates that the longitudinal catching-up and spacing adjustment strategies are effective.

[0058] (3) Acceleration characteristics: The peak acceleration is approximately ±4 m / s², close to the upper limit of the constraint. There are some oscillations, which is due to the perception delay caused by the fact that information between queues is transmitted only through a single communication link.

[0059] (4) Torque control: The traction torque fluctuates significantly during the engagement phase, with a peak value of approximately 2500 N·m, accounting for 62.5% of the rated torque.

[0060] Figure 5 The lateral movement trajectory of the vehicle initiating the attack under the Lead-Tail communication topology is demonstrated. The lateral displacement transitions precisely from 0m to 3.5m, the peak lateral velocity is approximately ±0.4m / s, the peak heading angle is approximately 7°, and the rudder angle varies within ±0.25rad, which is much less than the upper limit of the constraint of 0.3rad, indicating that the lateral control is smooth and safe.

[0061] Quantitative analysis shows that the performance indicators under the Lead-Tail topology are as follows: average RMSE of longitudinal position is 0.37m, average RMSE of speed is 0.22m / s, RMSE of lateral position is about 0.09m, minimum vehicle spacing is 5.5m (safety margin of 10%), peak acceleration is 3.8m / s², and speed fluctuation range is 15-24m / s.

[0062] Strategy 2: Lead-Tail-Lead Communication Topology like Figure 6 As shown, under this strategy, each queue's lead vehicle simultaneously receives the assumed states of the lead vehicle and the tail vehicle of the preceding queue, and performs weighted fusion (α=0.6). The hierarchical control architecture significantly improves system stability. (1) Velocity fluctuation: Velocity fluctuation was reduced to the range of 16-23 m / s, which is a significant improvement compared to 15-24 m / s for the Lead-Tail topology. Velocity overshoot was controlled within 5%, and the oscillation amplitude was reduced by about 30%.

[0063] (2) Peak acceleration: The peak acceleration is reduced to 3.2 m / s², which is 15.8% lower than the 3.8 m / s² of the Lead-Tail topology. It is far from the upper limit of the constraint and provides a greater safety margin.

[0064] (3) Convergence speed: After the cut-in is completed, the system converges to the steady state faster, and the steady state error is less than 0.1m / s.

[0065] (4) Torque output: The peak torque is reduced to 1500 N·m, only 37.5% of the rated torque, and the control smoothness is significantly improved.

[0066] Figure 7 The lateral movement trajectory of the vehicle cutting in under the Lead-Tail-Lead communication topology was demonstrated. The lateral control performance is basically consistent with the Lead-Tail topology. The lateral trajectory strictly follows the preset S-shaped reference curve, and the tracking error is kept within ±0.05m. The lateral velocity changes symmetrically, with a peak value of ±0.25m / s. The heading angle changes in a bell-shaped distribution, with a peak value of 7.8°. The front wheel steering angle is smoothly controlled, with a peak value of 2.2°, avoiding the risk of instability caused by sharp turns.

[0067] Quantitative analysis shows that the performance indicators under the Lead-Tail-Lead topology are as follows: average longitudinal position RMSE 0.28m (improvement of 24.3%), average speed RMSE 0.16m / s (improvement of 27.3%), minimum vehicle spacing 6.2m (improvement of 12.7%), peak acceleration 3.2m / s² (reduction of 15.8%), and speed fluctuation range 16-23m / s (improvement of 22.2%).

[0068] Comprehensive performance evaluation Table 5 summarizes the performance comparison of the three communication strategies. The comfort and fuel consumption of the three strategies are compared and analyzed. Comfort analysis based on the rate of change of acceleration shows that the hybrid strategy improves vehicle comfort by approximately 12.6% after the target entry point compared to the lead-tail vehicle strategy. Fuel consumption analysis based on torque integral shows that the hybrid strategy saves approximately 17% more energy than the traditional method, achieving an optimal balance between safety, comfort, and fuel economy.

[0069] Table 5

[0070] Simulation results demonstrate that the proposed two-layer distributed model predictive control method successfully achieves multi-vehicle cooperative entry. Compared to traditional methods, this invention, through its two-layer optimized architecture and multi-vehicle cooperative mechanism, improves safety by approximately 15%, efficiency by approximately 20%, and comfort by approximately 18%, achieving an optimal balance among safety, efficiency, and comfort.

[0071] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0072] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A two-layer distributed model predictive control method for multi-vehicle cooperative entry, characterized in that: Includes the following steps: Step 1: Construct a multi-platform vehicle system and a longitudinal-lateral coupled dynamic model. The longitudinal-lateral coupled dynamic model includes an eight-dimensional state space vector, a longitudinal motion state equation, and a lateral motion state equation. The eight-dimensional state space vector includes longitudinal position, longitudinal velocity, longitudinal acceleration, traction torque, lateral position, heading angle, lateral velocity, and yaw rate. Step 2: Establish a hierarchical communication topology, which includes an intra-queue forward chain communication topology and an inter-queue multi-strategy communication topology. The inter-queue multi-strategy communication topology includes two strategies: lead vehicle-tail vehicle communication and lead vehicle-tail vehicle-lead vehicle communication. Step 3: Design a two-layer optimization framework, including upper-layer decision optimization and lower-layer trajectory tracking optimization. The upper-layer decision optimization determines the optimal entry queue, insertion position and entry time through a multi-objective optimization function. The lower-layer trajectory tracking optimization achieves local coordinated control based on longitudinal-lateral coupled distributed model predictive control. Step 4: Construct feasibility constraints for the entry operation, including the arrival time window constraint for the entry vehicle and the adjustment time window constraint for the target queue, to ensure the safety and feasibility of the entry operation. Step 5: Use a fifth-order polynomial to generate smooth longitudinal and lateral reference trajectories. The longitudinal reference trajectory satisfies the position, velocity, and acceleration boundary conditions, and the lateral reference trajectory uses an S-curve to achieve smooth lane changing. Step 6: Based on the hierarchical communication topology, construct the longitudinal-lateral coupled distributed model predictive control optimization problem and cost function. The optimization problem includes the local optimization problem of the queuing navigator, the local optimization problem of the queuing following vehicle, and the longitudinal-lateral collaborative optimization problem of the cutting vehicle. Step 7: Introduce longitudinal and lateral terminal state constraints as well as safety distance constraints to ensure the stability and convergence of the system at the end of the prediction time domain; Step 8: Solve the optimization control problem for each vehicle node, and adjust the longitudinal traction torque and lateral steering angle control inputs simultaneously based on the optimization results to achieve safe control for multi-vehicle coordinated entry.

2. The two-layer distributed model predictive control method for multi-vehicle cooperative entry according to claim 1, characterized in that: In step 1, the steps of constructing the multi-queue vehicle system and the longitudinal-lateral coupled dynamic model include: Define the vehicle longitudinal state vector and lateral state vector ,in, These represent longitudinal position, longitudinal velocity, longitudinal acceleration, and traction torque, respectively. These represent the lateral position, heading angle, lateral velocity, and yaw rate, respectively. The longitudinal and lateral dynamic equations are constructed using a discrete-time model. The longitudinal dynamics consider the time constant and drag characteristics of the traction system, while the lateral dynamics are based on the tire lateral force model and the vehicle kinematics relationship.

3. The two-layer distributed model predictive control method for multi-vehicle cooperative entry according to claim 1, characterized in that: In step 3, the expression for the upper-level decision optimization problem of the two-layer optimization framework includes: ； In the formula: This represents the cost function for the upper-level multi-objective optimization. The weighting coefficients represent safety, efficiency, and comfort. Indicates safety indicators, Indicators of efficiency Indicates comfort level; Decision variables include target entry queue number Target insertion position and entry point .

4. The two-layer distributed model predictive control method for multi-vehicle cooperative entry according to claim 3, characterized in that: Safety indicators Defined as: ； in, Indicates the first step in the cutting process The minimum distance between adjacent vehicles at each time step. Indicates the safe distance threshold. This indicates the number of time steps in the cut-in process. Let M be the indicator function, and M be the large penalty coefficient. Distance weights; efficiency indicators Defined as: ； in, Indicates the duration of the cut-in. This indicates the time required for the target queue to adjust to an acceptable cut-in state. This indicates a redundancy distance that exceeds the necessary safety distance. These are the weighting coefficients; Comfort Index Defined as: ； Indicates acceleration and jerk. Throughout the cutting process The weighted square integral in These are the weighting coefficients.

5. The two-layer distributed model predictive control method for multi-vehicle cooperative entry according to claim 1, characterized in that: In step 4, the feasibility constraints for entry include: Cutting into vehicle arrival time window constraints: ； in: ； The vertical coordinate of the target entry point. For location buffer, and The upper and lower limits of the cut-in vehicle speed; Queue adjustment time window constraints: ； in, This indicates the moment when the target queue is ready to accept the cut-in. and Determined based on the speed and spacing of vehicles at the target location; Safety distance constraints: ； ； in, Indicates the cutting-in vehicle With the vehicle in front of the target queue The distance between them Indicates the cutting-in vehicle Following the target queue The distance between them For time-distance between the front of the train; Speed ​​matching constraints: ； in, This represents the average speed of vehicles near the target location. This indicates the maximum permissible speed difference.

6. The two-layer distributed model predictive control method for multi-vehicle cooperative entry according to claim 1, characterized in that: In step 5, the method for generating smooth longitudinal and lateral reference trajectories using a fifth-order polynomial includes: Longitudinal reference trajectory: ； Boundary conditions are satisfied: ； By solving the system of linear equations Obtain the coefficient vector ; Lateral reference trajectory: ； Boundary conditions are satisfied: ； in and Given the initial and target lane lateral positions, the coefficient vector is obtained by solving a system of linear equations. .

7. The two-layer distributed model predictive control method for multi-vehicle cooperative entry according to claim 1, characterized in that: In step 6, the expression for the local optimization problem of the queue following vehicle includes: ； In the formula: Indicates the first Vehicle nodes following in the queue The cost function of the vertical local optimization problem. Indicates the prediction time domain, Indicates the predicted state of the vehicle node. This represents the assumed state of the vehicle node. Indicates the assumed state of the vehicle ahead. Indicates longitudinal control input; Indicates the time step within the prediction time domain; Represents the vehicle cost function; This is the entry point.

8. The two-layer distributed model predictive control method for multi-vehicle cooperative entry according to claim 7, characterized in that: The instantaneous cost function is: ； In the formula: To account for the deviation between the predicted state and the assumed state, For vehicle spacing deviation, the weight matrix Let f be a symmetric non-negative definite matrix, and f be the weights of state tracking error, control input cost, assumed state deviation, and vehicle spacing error, respectively.

9. The two-layer distributed model predictive control method for multi-vehicle cooperative entry according to claim 1, characterized in that: The longitudinal-lateral collaborative optimization problem of the cutting-in vehicle includes: Vertical optimization problem: ； in, For distance penalty function: ； and These represent the distances between the cutting vehicle and the vehicles in front and behind it, respectively. Lateral optimization problem: ； In the formula: This is the lateral position error. For heading angle error, This refers to the front wheel steering angle. This represents the rate of change of the steering angle.

10. The two-layer distributed model predictive control method for multi-vehicle cooperative entry according to claim 1, characterized in that: The steps for introducing longitudinal and lateral end-state constraints include: Vertical terminal state constraints: ； ； in, Indicates the predicted state of the vehicle node. This indicates the predicted state of the previous vehicle node. These are the error thresholds for vehicle and queue spacing, respectively. , These represent the predicted and assumed states of the lead vehicle in the platoon and the lead vehicle in the preceding platoon, respectively. Indicates the queue length. Used to measure the impact of different communication structures on the terminal constraints of a queuing system, satisfying... ; Lateral terminal state constraints: ； ； in, This is the error threshold; , , , , These represent the lateral position, lateral reference position, heading angle, lateral velocity, and yaw rate of the vehicle cutting in.

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