A double-layer optimization control method and system for expressway entrance ramp merging area

Abstract

This invention discloses a two-layer optimization control method and system for merging zones at expressway entrance ramps. Based on the initial state information of vehicles entering the merging control area of ​​the expressway entrance ramp, a graph-based shortest path algorithm is used to determine the optimal merging sequence and allocate arrival times for each vehicle. Based on the allocated optimal merging sequence and the arrival times of each vehicle, trajectory planning is performed and sent to each vehicle. A directed graph is used to describe the process of determining the merging sequence. An improved shortest path algorithm using predicted vehicle travel delays as edge weights determines the optimal merging sequence. Based on unconstrained Hamiltonian analysis, a time adjustment algorithm is designed to ensure vehicles meet speed and acceleration constraints, making it safer and more practical. An algorithm for finding the optimal prediction window is designed using the Pareto optimality principle, ensuring all vehicles meet the maximum speed constraint, maximizing traffic efficiency, and ensuring vehicles meet speed constraints while minimizing fuel consumption.

Description

Technical Field

[0001] This invention belongs to the field of traffic engineering control, specifically relating to a two-layer optimization control method and system for the merging zone of expressway entrance ramps. Background Technology

[0002] Intelligent connected vehicle technology integrates high-tech fields such as sensor technology, computer technology, communication technology, information processing technology, and control technology. Intelligent connected vehicles can obtain real-time information about surrounding vehicles and roadside control units through vehicle-to-vehicle and vehicle-to-infrastructure communication. It has enormous development potential in the transportation sector, and its prospects are widely regarded as promising. However, intelligent connected vehicles frequently cause traffic congestion at merging points on expressway entrance ramps, significantly reducing traffic efficiency. From a practical perspective, designing control methods specifically for merging points on expressway entrance ramps is of great significance.

[0003] Existing control methods for merging zones at expressway entrance ramps mostly take a single-level approach, separating vehicle sequence determination from vehicle trajectory planning. These methods primarily include rule-based and optimization-based approaches. However, for common traffic scenarios like expressway entrance ramp merging zones, a single-level approach is insufficient to alleviate traffic congestion. Furthermore, there is a coupling relationship between determining vehicle sequence and planning vehicle trajectory; how to connect these two is also a research challenge. Current methods cannot effectively improve the efficiency of vehicle merging at expressway entrance ramps. Summary of the Invention

[0004] The purpose of this invention is to provide a two-layer optimization control method and system for the merging zone of expressway entrance ramps, so as to overcome the problems of congestion and low merging traffic efficiency of existing vehicles merging at expressway entrance ramps.

[0005] A two-layer optimization control method for the merging zone of an expressway entrance ramp includes the following steps:

[0006] S1, real-time acquisition of initial status information of vehicles entering the merging control area of ​​the expressway entrance ramp;

[0007] S2, based on the initial state information of vehicles entering the merging control area of ​​the expressway entrance ramp, uses a graph-based shortest path algorithm to determine the optimal merging sequence and allocate the arrival time of each vehicle;

[0008] S3, based on the allocated optimal merging sequence and the arrival time of each vehicle, performs trajectory planning and sends it to each vehicle;

[0009] S4, each vehicle uses model predictive control to track trajectory planning until it passes through the merged area.

[0010] Preferably, the initial state information of the vehicle includes the vehicle's initial position, speed, and acceleration.

[0011] Preferably, the initial position, velocity, and acceleration of vehicle i are respectively The maximum acceleration and maximum velocity are a max and v max ;

[0012] Calculate the shortest arrival time for all vehicles: the shortest arrival time t for vehicle i. min Including acceleration process time t acc and cruise process time t cruise The calculation process is as follows:

[0013]

[0014]

[0015]

[0016] Preferably, based on the initial state information of vehicles entering the merging control area of ​​the expressway entrance ramp, a directed graph of the optimal merging sequence is constructed, and the optimal merging sequence can be obtained by finding the shortest path in the directed graph.

[0017] Preferably, the shortest path algorithm is used to obtain the optimal merging sequence with the goal of minimizing vehicle travel delay.

[0018] Preferably, auxiliary variables D and L are constructed, where D(i,j) represents the expression from V (0,0) to V (m,n) The length of the shortest path, L(i,j) represents the lane of the currently selected vehicle. If the vehicle selects the main lane, L(i,j) = 1, otherwise L(i,j) = 0.

[0019] Preferably, the auxiliary variables D and L are initialized;

[0020] Construct the relevant vertex and edge weights for main road priority and ramp priority respectively, and calculate D(i,j), where i=0 or j=0;

[0021] Determine the remaining vertices V (i,j) The edge weights are determined until the entire directed graph is constructed:

[0022] Consider whether the current vertex and the vehicle at this vertex are coming from the same lane, and then calculate vertex V. (i,j) The edge weights ω(i,j,1) and ω(i,j,2);

[0023] D(i,j)=min{D(i-1,j)+ω(i-1,j,1),D(i,j-1)+ω(i,j-1,2)};

[0024] Obtain V from D(i,j) (0,0) to V (m,n) The length of the shortest path; obtain the optimal merging sequence from back to front based on L, and allocate vehicle merging time.

[0025] Preferably, optimal control is achieved using the Pontryagin principle, which involves initially planning the vehicle's trajectory and obtaining the arrival time of each vehicle.

[0026] Preferred, optimal control acceleration:

[0027] Optimal control speed:

[0028] Optimal vehicle position:

[0029] Among them, b i ,c i ,d i ,e i These are the coefficients used in Hamiltonian analysis to calculate the integral. Vehicle i in... Enter the controlled area at any time, The merging point is reached at a certain time. Combining the initial and final conditions, these coefficients are obtained by solving the following matrix equation. Given the initial and final conditions, the control coefficient b for each vehicle is calculated using the following formula. i ,c i ,d i ,e i .

[0030] A dual-layer optimization control system for the merging zone of an expressway entrance ramp includes a main control unit and an on-board unit;

[0031] The main control unit acquires the initial state information of vehicles entering the merging control area of ​​the expressway entrance ramp in real time through the on-board unit; based on the initial state information of vehicles entering the merging control area of ​​the expressway entrance ramp, the main control unit uses a graph-based shortest path algorithm to determine the optimal merging sequence and allocate the arrival time of each vehicle; based on the allocated optimal merging sequence and the arrival time of each vehicle, the main control unit performs trajectory planning and sends it to each vehicle through the on-board unit; each vehicle uses model predictive control to track the trajectory planning until it passes through the merging area.

[0032] Compared with the prior art, the present invention has the following beneficial technical effects:

[0033] This invention discloses a two-layer optimization control method for the merging zone of an expressway entrance ramp. Based on the initial state information of vehicles entering the merging control area of ​​the expressway entrance ramp, a graph-based shortest path algorithm is used to determine the optimal merging sequence and allocate the arrival time of each vehicle. Based on the allocated optimal merging sequence and the arrival time of each vehicle, trajectory planning is performed and sent to each vehicle, ensuring that all vehicles meet the maximum speed constraint, maximizing traffic efficiency, and ensuring that vehicles meet speed constraints while minimizing fuel consumption.

[0034] The process of determining the merging sequence is described using a directed graph. An improved shortest path algorithm with predicted vehicle travel delays as edge weights is designed to determine the optimal merging sequence. Based on unconstrained Hamiltonian analysis, a time adjustment algorithm is designed to ensure that vehicles meet speed and acceleration constraints, making it safer and more practical. Considering the characteristics of the MPC prediction window, an algorithm for finding the optimal prediction window is designed using the Pareto optimality principle, balancing computation time and fuel gain. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of a highway entrance ramp merging scenario in a fast embodiment of the present invention.

[0036] Figure 2 This is a framework diagram of the two-layer optimization control method in a quick embodiment of the present invention.

[0037] Figure 3 This is a flowchart of the two-layer optimized control in a fast embodiment of the present invention.

[0038] Figure 4 This is the directed graph of the optimal merging sequence in a fast embodiment of the present invention.

[0039] Figure 5a This is a comparison chart of the original velocity-time curve after applying the time adjustment algorithm; Figure 5b This is a comparison chart of the original vehicle speed-time curve after applying the time adjustment algorithm; Figure 5c This is a comparison chart of the original vehicle acceleration-time curve after applying the time adjustment algorithm. Detailed Implementation

[0040] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. 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 should fall within the scope of protection of the present invention.

[0041] In this embodiment, a schematic diagram of the merging area scenario at the expressway entrance ramp is shown below. Figure 1As shown, this invention discloses a two-layer optimization control method for the merging zone of expressway entrance ramps. All vehicles are intelligent connected vehicles, and the vehicles and the central control unit exchange information through vehicle-to-everything (V2X) devices. The framework of the two-layer optimization control method is as follows: Figure 2 As shown, it is divided into upper-level control and lower-level control. The entire method flow is as follows: Figure 3 As shown, the central control unit obtains the vehicle's initial state—its initial position, speed, and acceleration—through V2X devices. Based on this initial state, the central control unit determines the passage sequence and sends optimal acceleration control information to the vehicles. The vehicles then use model predictive control to track and control the vehicles according to this optimal acceleration control information, ensuring they travel as expected. The specific steps are as follows:

[0042] S1, real-time acquisition of initial status information of vehicles entering the merging control area of ​​the expressway entrance ramp;

[0043] The central control unit determines the optimal passage sequence based on the initial status information of vehicles in the controlled area.

[0044] All vehicles send their initial status information—initial position, speed, and acceleration—to the central control unit via V2X devices. The central control unit assigns unique IDs to vehicles on the main road and on the ramps, and calculates the shortest arrival time for each vehicle. The specific process is as follows:

[0045] (1) The initial position, velocity, and acceleration of vehicle i are respectively The maximum acceleration and maximum velocity are a max and v max .

[0046] (2) Calculate the shortest arrival time of all vehicles entering the merging control area of ​​the expressway entrance ramp: shortest arrival time t of vehicle i min Including acceleration process time t acc and cruise process time t cruise The calculation process is as follows:

[0047]

[0048]

[0049]

[0050] S2, based on the initial state information of vehicles entering the merging control area of ​​the expressway entrance ramp, uses a graph-based shortest path algorithm to determine the optimal merging sequence and allocate the arrival time of each vehicle;

[0051] The optimal merging sequence is determined with the goal of minimizing vehicle travel delay.

[0052] Based on the initial state information of vehicles entering the merging control area of ​​the expressway entrance ramp, construct as follows: Figure 4 The optimal merging sequence is shown in the directed graph G(V,E), where V and E represent the vertex set and edge set, respectively. (i,j) V is a vertex in a directed graph, representing the point where car i on the main road and car j on the ramp pass through. Based on the policy that vehicles cannot overtake, vehicles in the same lane pass through the merging point sequentially. Each vertex V... (i,j) Contains directed edge V (i,j) →V (i,j+1) and directed edge V (i,j) →V (i+1,j) Directed edge V (i,j) →V (i,j+1) This indicates that in this step, vehicles on the main road are granted the right to pass through the merging point. Directed edge V (i,j) →V (i+1,j) This indicates that vehicles on the ramp are granted the right to pass through the merging point in this step. The edge weights represent the predicted vehicle travel delays, V. (i,j) →V (i,j+1) and V (i,j) →V (i+1,j) The weights are denoted by ω(i,j,1) and ω(i,j,2), respectively. When i=0 or j=0, it indicates that all selected vehicles have been on the main road or on the ramps since the beginning, and the initial weight is ∞. Suppose there are m vehicles on the main road and n vehicles on the ramps in the control area. In the directed graph, starting from the origin V... (0,0) To the destination V (m,n) All paths contain all merge sequences, such as path V, where m=2, n=2. (0,0) →V (0,1) →V (0,2) →V (1,2) →V (2,2) This indicates that two vehicles on the ramp pass through the merging point first, and then two vehicles on the main road pass through. This is achieved by finding the point in the directed graph G(V,E) from V... (0,0) to V (m,n) The shortest path can be used to obtain the optimal merging sequence. Specifically, the shortest path algorithm is used to obtain the optimal merging sequence, constructing auxiliary variables D and L, where D(i,j) represents the path from V... (0,0) to V (m,n) The length of the shortest path, L(i,j) represents the lane of the currently selected vehicle. If the vehicle selects the main lane, L(i,j) = 1, otherwise L(i,j) = 0.

[0053] The specific steps of the shortest path algorithm are as follows:

[0054] 1) Initialize auxiliary variables D and L;

[0055] 2) Construct the relevant vertex and edge weights for main road priority and ramp priority respectively, and calculate D(i,j) and L(i,j), where i=0 or j=0;

[0056] 3) Determine the remaining vertices V (i,j) The edge weights are determined until the entire directed graph is constructed:

[0057] Consider whether the current vertex and the vehicle at this vertex are coming from the same lane, and then calculate vertex V. (i,j) The edge weights ω(i,j,1) and ω(i,j,2);

[0058] D(i,j)=min{D(i-1,j)+ω(i-1,j,1),D(i,j-1)+ω(i,j-1,2)};

[0059] L(i,j)=min{L(i-1,j)+ω(i-1,j,1),L(i,j-1)+ω(i,j-1,2)}.

[0060] 4) Obtain V from D(i,j) (0,0) To V (m,n) The length of the shortest path.

[0061] 5) Obtain the optimal merging sequence from back to front based on L, and allocate vehicle merging time.

[0062] S3, Initial vehicle trajectory planning: The central control unit plans the vehicle's trajectory based on the assigned arrival time. Optimal control is achieved using Pontryagin's principle, initially planning the vehicle trajectories and obtaining the arrival times of each vehicle:

[0063] Optimal control acceleration:

[0064] Optimal control speed:

[0065] Optimal vehicle position:

[0066] Among them, b i ,c i ,d i ,e i These are the coefficients used in Hamiltonian analysis to calculate the integral. Vehicle i in... Enter the controlled area at any time, The merging point is reached at a certain time. Combining the initial and final conditions, these coefficients are obtained by solving the following matrix equation. Given the initial and final conditions, the control coefficient b for each vehicle is calculated using the following formula. i ,ci ,d i ,e i .

[0067]

[0068] A time adjustment algorithm is used to ensure that vehicles meet speed constraints and guarantee the arrival time of each vehicle. Based on the characteristics analyzed in the above optimal control method, the arrival time of vehicles can be adjusted to regulate vehicle speed; it is found that the vehicle speed meets the constraints after the time adjustment algorithm is applied.

[0069] The specific process of the time adjustment algorithm is as follows:

[0070] (1) Initialize the arrival time of the vehicles;

[0071] (2) Find the first vehicle in the merge sequence that violates the maximum speed constraint and proceed to (3).

[0072] (3) If the vehicle speed does not meet the maximum speed constraint, the final arrival time of the vehicle is backed up by one sampling time step, and the corresponding control law is recalculated. If the speed still does not meet the maximum speed constraint, the final arrival time of the vehicle is backed up by one sampling time step again until the vehicle speed meets the maximum speed constraint. The arrival time of the vehicle is then updated, and the delay caused by the input arrival time is recorded.

[0073] (4) Update the arrival time of subsequent vehicles and recalculate the vehicle speed. If the speed does not meet the constraints, proceed to (3).

[0074] S4, The vehicle uses model predictive control for tracking control: Model predictive control is a feedback control method that essentially seeks the optimal control for each control unit in the prediction time domain, selects only the control quantity in the control time domain as the control input, and continues in this way until the last time window is reached.

[0075] The vehicle uses model predictive control to compensate for interference with the merged trajectory sent by the central control unit, and uses model predictive control to track and control the optimal speed and position sent by the central control unit.

[0076] The pursuit optimization problem is transformed into the standard form of quadratic programming, with the objective function defined as follows:

[0077]

[0078] Where N is the prediction window size, R k Q is the reference trajectory, and Q and R are weight matrices. The first term represents the tracking error, and the second term represents the energy.

[0079] The selection of the prediction window in model predictive control has a significant impact on the control effect. A prediction window that is too small cannot fully utilize the advantages of predictive control and rolling optimization; a prediction window that is too large requires excessive computation time. Furthermore, simulation results show that the prediction window also affects fuel consumption gain. This paper utilizes the Pareto optimality principle to find an algorithm for the optimal prediction window, balancing computation time and fuel consumption gain. The specific steps are as follows:

[0080] (1) Gradually increase the size of the prediction window, calculate the fuel consumption F and record the calculation time T, and plot the FT curve. Calculate N times for each prediction window and take the average result.

[0081] (2) Identify the Pareto fronts on the Fourier Transform (FT) curve. At these Pareto fronts, optimizing one objective will lead to a significant deterioration of the other objective. Within the acceptable range of F and T, these points are considered as the best compromise points for different objectives based on actual needs, and one of them is selected as the "optimal" fit point for the problem.

[0082] (3) Find the corresponding optimal prediction window based on the Pareto optimal solution. Select the best compromise point between the two objectives, and then find the size of its corresponding prediction window. In practice, there may be several values ​​that satisfy the conditions, so any one of them can be used as a feasible solution.

[0083] The vehicle follows the trajectory plan and performs tracking control until it reaches the merging area. The central control unit designs the optimal prediction window size based on its computing power and fuel gain, and sets the remaining parameters for model predictive control. The vehicle then implements model predictive control according to these settings until it reaches the merging area.

[0084] This invention presents a two-layer optimization control method for merging zones at expressway entrance ramps. It employs a graph-based improved shortest path algorithm to determine the optimal merging sequence and allocate vehicle merging times, minimizing total vehicle delay. Vehicle trajectory planning is then performed. First, based on the allocated merging times, initial trajectory planning is directly conducted using Hamiltonian analysis. Second, a time adjustment algorithm ensures all vehicles meet maximum speed constraints, followed by secondary trajectory planning using Hamiltonian analysis. Finally, model predictive control is used for vehicle tracking control. This method jointly considers determining the merging sequence and planning the trajectory, coupling vehicle arrival time and vehicle position. Simulation experiments verify the effectiveness of the proposed method. This invention can efficiently complete merging while ensuring vehicles meet speed and acceleration constraints, and effectively reduces fuel consumption.

Claims

1. A two-layer optimization control method for the merging zone of an expressway entrance ramp, characterized in that, Includes the following steps: S1, real-time acquisition of initial status information of vehicles entering the merging control area of ​​the expressway entrance ramp; S2, based on the initial state information of vehicles entering the merging control area of ​​the expressway entrance ramp, uses a graph-based shortest path algorithm to determine the optimal merging sequence and allocate the arrival time of each vehicle; To minimize vehicle travel delay, the shortest path algorithm is used to obtain the optimal merging sequence. Constructing auxiliary variables and , Indicates from arrive The length of the shortest path, This indicates the lane currently selected for the vehicle. If the main lane is selected, ,otherwise ; S3, based on the allocated optimal merging sequence and the arrival time of each vehicle, performs trajectory planning and sends it to each vehicle; S4, each vehicle uses model predictive control to track trajectory planning until it passes through the merged area; The vehicle's initial state information includes its initial position, velocity, and acceleration; vehicle The initial position, velocity, and acceleration are respectively The maximum acceleration and maximum velocity are respectively and ; Calculate the shortest arrival time for all vehicles: vehicles Shortest arrival time Including acceleration process time and cruise process time The calculation process is as follows: （1） （2） （3）； Based on the initial state information of vehicles entering the merging control area of ​​the expressway entrance ramp, a directed graph of the optimal merging sequence is constructed. The optimal merging sequence can be obtained by finding the shortest path in the directed graph.

2. The dual-layer optimization control method for the merging zone of an expressway entrance ramp according to claim 1, characterized in that, Initialize auxiliary variables and ; Construct the relevant vertex and edge weights for main road priority and ramp priority respectively, and calculate... , or ; Determine the remaining vertices The edge weights are determined until the entire directed graph is constructed: Consider whether the current vertex and the vehicle at this vertex are coming from the same lane, and then calculate the vertex. edge weight and ; ； from Obtain arrive The length of the shortest path; from back to front according to Obtain the optimal merging sequence and allocate vehicle merging times.

3. The dual-layer optimization control method for the merging zone of an expressway entrance ramp according to claim 1, characterized in that, Optimal control is achieved using Pontryagin's principle, which involves initially planning the vehicle's trajectory and obtaining the arrival time of each vehicle.

4. The dual-layer optimization control method for the merging zone of an expressway entrance ramp according to claim 1, characterized in that, Optimal control acceleration: （4） Optimal control speed: （5） Optimal vehicle position: （6） in, These are the coefficients used in Hamiltonian analysis to calculate the integral; vehicles exist Enter the controlled area at any time, The merging point is reached at a given time. Combining the initial and final conditions, these coefficients are obtained by solving the following matrix equation. Given the initial and final conditions, the control coefficients for each vehicle are calculated using the following formula. : 。 5. A two-layer optimization control system for the merging zone of an expressway entrance ramp based on the method of claim 1, characterized in that, Includes the main control unit and the vehicle-mounted unit; The main control unit acquires the initial state information of vehicles entering the merging control area of ​​the expressway entrance ramp in real time through the on-board unit; based on the initial state information of vehicles entering the merging control area of ​​the expressway entrance ramp, the main control unit uses a graph-based shortest path algorithm to determine the optimal merging sequence and allocate the arrival time of each vehicle; based on the allocated optimal merging sequence and the arrival time of each vehicle, the main control unit performs trajectory planning and sends it to each vehicle through the on-board unit; each vehicle uses model predictive control to track the trajectory planning until it passes through the merging area.

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