Chain caw platoon shaping improvement swarm control method based on virtual guided berth

Abstract

The application discloses a kind of chain CAV queue shaping improvement swarm control methods based on virtual guiding berth, first, intelligent network connection unmanned vehicle team is the research object, the force between each unmanned vehicle in the system of unmanned vehicle intelligent agent is described using nonlinear function relationship;Second, the chain unmanned vehicle queue shaping improvement swarm control algorithm based on multiple virtual guiding berth is designed.The results show that the algorithm realizes the safe, rapid and stable constraint of different initial states, different number of intelligent network connection unmanned vehicles into regular chain queue (single / double chain) and drives out the intersection without signal light, and all unmanned vehicles maintain reasonable spacing, avoid collision while speed gradually reaches agreement during the completion of swarm process, realize the stable planning and tracking of intelligent network connection unmanned vehicle team, which is of great significance to improve the driving safety and road traffic efficiency of unmanned vehicle queue.

Description

Technical Field

[0001] This invention belongs to the field of autonomous driving technology, specifically an improved congestion control method for chain-type unmanned vehicle (CAV) queuing formation at traffic light-free intersections based on virtual guided parking spaces, or more simply, an improved congestion control method for chain-type CAV queuing formation based on virtual guided parking spaces. Background Technology

[0002] In recent years, intelligent platooning, as an efficient and energy-saving advanced driving mode, has received increasing attention from academia and industry, and has been applied on a small scale in some business scenarios, such as SF Express logistics transportation, airport shuttle buses, and JD.com's AGV unmanned transport vehicles. Current research on intelligent platooning focuses on standardized road scenarios with clear traffic signals and well-defined driving rules, while research on non-standardized road scenarios lacking traffic signal control and with ambiguous driving planning is scarce. For example... Figure 1 As shown, after several intelligent vehicle convoys enter an unsignalized intersection, some vehicles may leave the original convoy and merge into a new convoy, regrouping into several new intelligent vehicle convoys before exiting the intersection. Considering the limited time and space for driving through intersections and the lack of clear traffic signal control, how to achieve efficient diversion and orderly merging of intelligent vehicle convoys at unsignalized intersections, providing driving safety and intersection traffic efficiency, has become a pressing challenge and pain point that needs to be addressed.

[0003] Current research on the safe and efficient passage of intelligent vehicle fleets (or intelligent vehicles) through unsignalized intersections is relatively limited. It can be broadly categorized into the following three types:

[0004] (1) Intersection scheduling optimization based on path planning involves discretizing the intersection into a grid and then using global or local path optimization algorithms such as Dijkstra and A* to optimize the driving path of intelligent vehicles. This type of algorithm has a simple model, short search time, and can obtain the shortest path in complex environments. However, its application scenarios are mostly in static environments, and some parameters are manually selected, which is highly subjective and has certain errors. It is not suitable for scheduling scenarios with a large number of moving vehicles and it is difficult to achieve the formation of unmanned vehicle queues at intersections without traffic lights.

[0005] (2) Optimization based on the dynamic model of vehicle lane change: This involves taking a single intelligent vehicle in a vehicle platoon as the research object, constructing its dynamic model during lane change, analyzing and designing corresponding vehicle stability control methods, and extending this to the diversion and aggregation behavior of intelligent vehicle platoons at intersections. Most of these platoon stability control methods are limited to longitudinal control of vehicle platoons, with relatively few studies on the control of multi-vehicle platoons in curves and complex environments. Furthermore, they are mostly concentrated on simple structured straight roads and are not suitable for the formation of unmanned vehicle platoons at complex intersections with a large number of moving vehicles.

[0006] (3) Biomimetic optimization control based on swarm intelligence, which involves optimizing the behavior of intelligent vehicle fleets at intersections by mimicking the social behavior of biological populations such as ant colonies and bee colonies in group activities. This type of method has strong applicability and flexibility to changes in environment, parameters and tasks, and is well-suited for scheduling complex intersection scenarios with a large number of moving vehicles. It can obtain the shortest path in complex environments, but its global search capability is weak, and the optimization time is significantly affected by the distribution of individuals. Moreover, most studies have not formed a regular chain queue after implementing biomimetic optimization control on intelligent vehicle fleets (or intelligent vehicles), and there is still room for further improvement in the traffic efficiency of intersections without traffic lights.

[0007] It is evident that existing solutions for "diversion-aggregation" of intelligent vehicle fleets at intersections have certain shortcomings in terms of traffic efficiency and operational stability. There is still a significant gap between these solutions and their practical application in unsignalized intersections on open roads, indicating room for further optimization and improvement.

[0008] Considering factors such as individual capabilities and control objectives, multi-vehicle queuing systems can be viewed as a type of multi-agent system (MAS). Their queuing formation control falls under multi-agent formation control, a typical distributed cooperative control method originating from bionics. Swarm control of multi-agent systems has attracted attention and research across various fields, with research results widely applied in areas such as autonomous submarines, unmanned aerial vehicle (UAV) formations, and underwater robot formations.

[0009] In distributed cooperative control of multi-vehicle intelligent agents, the "consistency" problem is the most fundamental control problem. When multiple agents interact and influence each other according to specific control laws to achieve consistency or sharing of individual states, we usually call it "consistency." Scholars have conducted extensive research on the "consistency" problem from various perspectives, achieving numerous significant advances and results. As early as 1987, scholars characterized it, proposing three basic control criteria: separation, aggregation, and velocity verification. In 2006, Olfati-Saber proposed a class of multi-agent consistency control algorithms based on velocity consistency combined with artificial potential field functions. Based on the biological swarming phenomenon, they established the famous BOIDS computer model and proposed three rules: separation, aggregation, and velocity consistency. Based on this, Jond et al. considered multi-agent systems with three information topologies and studied vehicle queuing formation control. Fernando et al., following a distributed control scheme, performed swarm control on aerial robot swarms according to the collective behavior rules of "diversion-aggregation and velocity alignment," enabling the multi-agent system to achieve velocity consensus while avoiding collisions in real time.

[0010] Based on existing literature, domestic scholars such as Sun Ning et al. proposed an intelligent vehicle optimization scheduling scheme for unsignalized intersections based on an enhanced Dijkstra algorithm. They comprehensively considered the direction weight, safety weight, and priority weight of vehicles in each grid, formulated a dynamic grid weight assignment principle, and then searched for the path with the shortest travel time. Lian Yindong et al. proposed an improved A* path planning algorithm based on a vision-guided multi-AGV system. This algorithm uses the dynamic time consumption generated by the AGVs during movement as a reference indicator to realize path planning and conflict avoidance strategies for multiple AGVs in the path network, improving the utilization efficiency of fixed road network resources. Zhang Weibao et al. proposed a concentric circle fast search random tree (RRT) algorithm, which uses a concentric circle sampling strategy to reduce the time required for path planning. It considers factors such as vehicle posture in the nearest neighbor selection method, exhibiting strong spatial path search capabilities and improving the quality of intelligent vehicle path planning in complex environments. However, in high-dimensional complex environments, it is computationally time-consuming, complex, and prone to getting trapped in local optima.

[0011] Xu Liwei et al. conducted in-depth research on the multi-agent swarm formation control mechanism based on the distributed hierarchical control method, explored the coupling relationship between the stability of the vehicle dynamics system and the multi-agent formation control, and ensured the stability and efficiency of the multi-vehicle queuing system. Qiao Fengliang et al. studied the multi-vehicle queuing control strategy at unsignalized intersections based on the forward-leader communication topology and model prediction hierarchical control method. By optimizing vehicle gaps and resolving right-of-way conflicts between vehicles, they achieved gap passage and simultaneous passage of more phases, further improving the passage efficiency of multi-vehicle queuing at unsignalized intersections.

[0012] Li et al. used an improved genetic algorithm to determine the traffic order at intersections and calculate the optimal vehicle trajectory, reducing the average traffic delay at intersections. Wang Guiqing et al. used an elite ant colony algorithm to select the optimal communication path at intersections, effectively improving intersection traffic efficiency. Many scholars have also incorporated new ideas into the congestion control of multi-agent systems, such as traction control and adaptive dynamic programming. Gao Jingying et al., based on the idea of ​​traction control, utilized information interaction between agents to achieve congestion among the vast majority of agents in the group; this control method has good applicability in complex motion situations. Zhao Yuyang et al. studied the online optimal consensus control algorithm for multi-agent systems based on adaptive dynamic programming, optimizing the consensus control algorithm with neural networks to further improve the stable planning and tracking of multi-agent formations. Other scholars have used other biomimetic algorithms for formation control of unmanned vehicles. Zhi Yichen et al. used an improved pigeon flock algorithm and a leader-follower method to achieve formation control of unmanned vehicles, adding corresponding weight indicators to the algorithm's geomagnetic operator to improve the algorithm's planning efficiency in the overall path, enabling unmanned vehicles to move in a set formation.

[0013] In the areas of drone and robot formation, Li Siyuan et al. designed an improved swarm control strategy for collision-free cooperative motion of satellite swarms, combining the artificial potential field method to achieve collision-free group motion of the swarm and reach asymptotic stability. Carlos et al., addressing the problem of time-varying formation and swarm behavior in robot networks, introduced the concept of "virtual velocity" and proposed a swarm control algorithm for time-varying robot formations, employing a hierarchical control approach to achieve robot swarming. Zheng Lanxiang et al. proposed a vision-based swarm control strategy, ensuring that drone swarms efficiently complete swarming while avoiding internal collisions and obstacles. Fu Xiaowei et al. designed a position and velocity consistency control law based on consistency theory between drones in the swarm and between drones and the virtual leader, combining the artificial potential field method to achieve the formation and maintenance of swarm formations while avoiding dynamic obstacles. However, most scholars' research has failed to form regular chain queues after applying swarm control to multi-unmanned vehicle intelligent agent systems. Furthermore, many scholars' research, due to ideal algorithm conditions, is not applicable to situations where the communication capabilities of multi-unmanned vehicle intelligent agent systems at intersections without traffic lights are limited, or where the communication radius of CAVs is limited. Summary of the Invention

[0014] The technical problem this invention aims to solve is to address the issues of poor formation stability and low traffic efficiency of intelligent connected unmanned vehicle (VAV) convoys when passing through intersections without traffic lights. This invention provides an improved congestion control method based on virtual guided parking spaces for chain-like CAV convoy formation. Taking intelligent connected unmanned vehicle convoys as the research object, this method improves upon the traditional artificial potential function, using nonlinear functional relationships to describe the interaction forces between the VAVs in a multi-VAV intelligent agent system. Furthermore, to solve the local optimal "blocking" problem caused by the artificial potential function method in achieving position and distance control and to form a regular chain-like convoy, an improved congestion control algorithm based on multiple virtual guided parking spaces is designed. This algorithm exhibits high stability, enabling intelligent connected unmanned vehicles with different initial states and numbers to safely, quickly, and stably exit intersections without traffic lights in a regular chain-like convoy (single / double chain). During the congestion process, all VAVs maintain reasonable spacing, avoid collisions, and gradually achieve consistent speed, realizing stable planning and tracking of intelligent connected unmanned vehicle convoy formation. This is of great significance for improving the safety of unmanned vehicle convoy driving and road traffic efficiency.

[0015] To achieve the above-mentioned technical objectives, the technical solution adopted by the present invention is as follows:

[0016] An improved congestion control method based on chained CAV queue formation using virtual guided berths includes:

[0017] Step 1: At an intersection without traffic lights, there are several intelligent connected unmanned vehicle convoys. There are n intelligent connected vehicles (CAVs) in the several intelligent connected unmanned vehicle convoys. The intelligent connected vehicles (CAVs) are simply referred to as vehicles. The n vehicles constitute a multi-unmanned vehicle intelligent agent system.

[0018] Step 2: Each vehicle has a different initial state, and its dynamic equations are as follows:

[0019]

[0020] In the formula, Indicates vehicle v i The position vector at time t; Indicates vehicle v i The velocity vector at time t; u i (t) represents vehicle v i Control input at time t;

[0021] Step 3, let vehicle v i The wireless broadcast coverage area is a circular area with radius R, centered on the vehicle's center of gravity. i All vehicles within the coverage area of ​​the wireless broadcast are connected to vehicle v i Wireless communication connection, all vehicles located in the aforementioned circular area constitute vehicle v at the current time t. i Neighbor set N i (t);

[0022] Step 4, based on vehicle v i With neighboring set N i The existence of edges between vehicles in (t) characterizes the system network graph M at time t. i (t) and the corresponding connection matrix C i (t);

[0023] Step 5: Create a virtual, movable guide berth for each vehicle. The number of virtual guide berths corresponding to n vehicles in different initial states is m. The dynamic equation of the virtual guide berth is as follows:

[0024]

[0025] In the formula, Indicates vehicle v i The corresponding virtual guide berth's position vector at time t; Indicates vehicle v i The corresponding velocity vector of the virtual guided berth at time t; Indicates vehicle v i The corresponding acceleration vector of the virtual guided berth at time t;

[0026] Step 6: Initialize the initial position and initial speed of m virtual guided parking spaces, and n vehicles in the intersection without traffic lights have different initial positions and speeds;

[0027] Step 7: Calculate vehicle v i and vehicle v j Virtual force function:

[0028]

[0029] In equation (3), the independent variable x represents vehicle v. i and vehicle v j σ-norm distance, ρ h (·) represents the distance collision potential function constructed using concavity and convexity functions, which is a scalar function that smoothly varies between 0 and 1; θ a θ b θ c Represents a constant coefficient, satisfying 0 < θ a <θ b , ||R|| represents the σ-norm of the vehicle's perception radius R; ||d|| represents the σ-norm of the ideal distance d that needs to be maintained between vehicles;

[0030]

[0031] In the formula, h represents the region in the spatial domain that is most affected by the potential energy field; within the region [0, h], when ρ h (x) = 1, the vehicle is subjected to a virtual force function. The impact is greatest outside the region [0,h], ρ h (x) decreases from 1 to 0, then It also decreases accordingly to 0;

[0032] Step 8: Calculate vehicle v i Control input at time t:

[0033]

[0034] In the formula, q i (t-1) points to q j The direction vector of (t-1) is given by parameter ε, which represents the constant for calculating the σ-norm distance and satisfies ε > 0. All represent positive numbers; Indicates vehicle v i and vehicle v j The virtual force function, ||q j (t-1)-qi (t-1)|| represents the vehicle v at time t-1. i and vehicle v j σ-norm distance; M represents a network diagram of a multi-autonomous vehicle intelligent agent system. i The corresponding connection matrix C (t-1) i (t-1) The element in the i-th row and j-th column;

[0035] Step 9:

[0036] (9.1) Continuously update the position vector and velocity vector of all virtual guide berths, thereby optimizing the movement trajectory of each virtual guide berth at intersections without traffic lights;

[0037] (9.2) Vehicle v i Based on the received virtual parking space and vehicle v i The position and speed information of vehicles in the neighboring set at a certain moment are used to adjust the control input of the vehicle at the next moment in real time according to formula (5) in step 8, and then update the position and speed of the vehicle according to formula (1) in step 2.

[0038] (9.3) Update the position and speed of all vehicles according to the method in step (9.2), and finally guide all vehicles to the corresponding virtual guide parking spaces.

[0039] As a further improved technical solution of the present invention, a roadside unit (RSU) is installed at intersections without traffic lights, and the RSU is wirelessly connected to the intelligent connected vehicle (CAV).

[0040] In step 5, a virtual movable virtual guide parking space is created for each vehicle using the Roadside Unit (RSU); in step 6, the initial positions and initial speeds of the m virtual guide parking spaces are initialized using the RSU; in step 9, the position vectors and speed vectors of all virtual guide parking spaces are continuously updated using the RSU, thereby optimizing the movement trajectory of each virtual guide parking space at intersections without traffic lights.

[0041] As a further improvement to the present invention, in step 9, vehicle v i Receive the road test unit (RSU) sending the data related to vehicle v i The corresponding virtual guided parking space has its position and speed information at a certain moment, and receives vehicle v i The vehicles in the neighboring set send their own position and speed information at a certain moment, and adjust their own control input in real time according to formula (5) in step 8.

[0042] As a further improvement of the present invention, in step 9, when the following formula is satisfied, all vehicles are guided to the corresponding virtual guidance parking spaces respectively;

[0043]

[0044]

[0045]

[0046] Equation (6) represents minimizing the mean positional deviation of n vehicles and their corresponding virtual guide parking spaces at the current time t. Equations (6a) and (6b) are constraints; p i (t) represents vehicle v i The velocity vector at time t; Indicates vehicle v i The corresponding velocity vector of the virtual guided berth at time t; ||q i (t)-q j (t)|| represents the vehicle v at time t. i and vehicle v j The σ-norm distance between them, Q t Q represents the location information of n vehicles in a fleet of intelligent connected unmanned vehicles at time t. t ={q1(t),q2(t),q3(t),…,q n (t)}; This represents the location information of the virtual guided parking spaces corresponding to n vehicles at time t.

[0047]

[0048]

[0049] δ i (t) represents vehicle v i The position deviation of the vehicle v from the corresponding virtual guided parking space at the current time t. i The σ-norm distance between the virtual guide berth and the corresponding virtual guide berth at the current time t.

[0050] The beneficial effects of this invention are as follows:

[0051] (1) This paper takes CAVP as the research object. First, the mathematical optimization model is used to accurately characterize the CAV queue constraint forming process at intersections without traffic lights. Second, the traditional artificial potential function is improved to realize the CAV distance control in the chain-type unmanned vehicle queue forming process at intersections without traffic lights. Combined with the improved artificial potential function, an improved congestion control algorithm for chain-type unmanned vehicle queue forming based on multiple virtual guided parking spaces is designed. This solves the local optimal "blocking" problem caused by the use of artificial potential function to achieve position distance control. It innovatively realizes the single and double queue constraint forming control of CAV chain at intersections without traffic lights, improves the efficiency and stability of multi-vehicle queue constraint forming congestion control, and increases the limit of distributed control theory research results in the field of intelligent transportation.

[0052] (2) This invention introduces the concept of Virtual Guided Parking (VP) and uses a multi-agent congestion control algorithm with VP to safely, quickly and stably constrain CAVs with different initial states at the intersection into a regular chain queue before they leave the intersection. This effectively improves the safety of unmanned vehicle queue driving, enhances the space utilization of the intersection and the efficiency of transportation. It is of great significance for the future application and promotion of CAVP in the field of transportation.

[0053] (3) When there are multiple VPs in the system, CAVs in different initial states can safely, quickly and stably exit the intersection in a regular chain queue, and all vehicles maintain a reasonable distance and gradually reach the same speed while avoiding collisions during the swarming process; it realizes stable planning and tracking of CAV queue formation, effectively solving the problems of poor formation stability and low traffic efficiency of connected unmanned vehicle fleets when passing through intersections without traffic lights; at the same time, it is also applicable to situations where the communication capabilities of multiple unmanned vehicle intelligent agent systems at intersections without traffic lights are limited and the communication radius of CAVs is limited. Attached Figure Description

[0054] Figure 1 This is a diagram of a conflict model at an intersection.

[0055] Figure 2 This is a diagram showing the constraint formation of CAV queues at a traffic light-free intersection.

[0056] Figure 3 This is a graph showing the change of potential force with relative distance.

[0057] Figure 4 This is a diagram showing the formation of a chain-like autonomous vehicle queue based on multiple VPs.

[0058] Figure 5 This is a diagram showing the position and status of each unmanned vehicle at different times.

[0059] Figure 5 (a) shows the position status of each unmanned vehicle at T=0s.

[0060] Figure 5 (b) shows the position status of each unmanned vehicle at T=50s.

[0061] Figure 5 (c) shows the position status of each unmanned vehicle at T=100s.

[0062] Figure 5 The diagram in Figure d shows the position and status of each unmanned vehicle at time T = 200s.

[0063] Figure 6 Images of unmanned vehicles in a single-queue (top) and double-queue (bottom) configuration at different times.

[0064] Figure 6 (a) is a diagram of a single-queue unmanned vehicle in a chain when T = 0s.

[0065] Figure 6 (b) shows a chain-like single-queue unmanned vehicle diagram at T=120s.

[0066] Figure 6 (c) is a diagram of a single-row unmanned vehicle in a chain at T = 240s.

[0067] Figure 6 The diagram in (d) shows the unmanned vehicles in a chain-like double queue at T=0s.

[0068] Figure 6 (e) is a diagram of a chain-like double-queue unmanned vehicle at T=120s.

[0069] Figure 6 (f) is a diagram of a chain-like double-queue unmanned vehicle at T = 240s.

[0070] Figure 7 The quantized motion trajectory diagram of the chain queue under the control of the input formula (15).

[0071] Figure 7 (a) is a quantized motion trajectory diagram of a single-chain queue.

[0072] Figure 7 (b) is a quantized motion trajectory diagram of a double-chain queue.

[0073] Figure 8 This is a graph showing the change in position error.

[0074] Figure 9 This is a graph showing the variation of speed (longitudinal / lateral) error.

[0075] Figure 10 A graph showing the change in the mean queue position error when the number of CAVs is changed.

[0076] Figure 11The graph shows the change in the mean longitudinal velocity error of the queue when the number of CAVs is changed.

[0077] Figure 12 The graph shows the change in the mean lateral velocity error of the queue when the number of CAVs is changed. Detailed Implementation

[0078] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings:

[0079] This embodiment addresses the challenges of poor platooning stability and low traffic efficiency in connected and automated vehicle (CAVP) platoons when navigating intersections without traffic lights. It proposes an improved congestion control method for multi-agent systems with multiple virtual parking (VP), specifically a chain-based CAVP queue formation improvement congestion control method. First, taking connected and automated vehicle platoons (CAVPs) as the research object, the traditional artificial potential function is improved, using nonlinear functional relationships to describe the interaction forces between autonomous vehicles in the multi-agent system. Second, to solve the local optimal "blocking" problem caused by the artificial potential function method in achieving position distance control and to form a regular chain queue, an improved congestion control algorithm for chain-based CAVP queue formation based on multiple virtual parking is designed. The stability of the algorithm is proven using the Lyapunov stability method and the LaSalle invariance principle. Finally, simulations of chain-based (single / double-chain) CAVP queue formation control are performed using Matlab and compared with the traditional congestion control algorithm based on the artificial potential function. The results show that the algorithm enables intelligent connected unmanned vehicles with different initial states and different numbers to safely, quickly, and stably exit traffic light-free intersections in a regular chain queue (single / double chain) with constraints. Moreover, all unmanned vehicles maintain a reasonable distance and avoid collisions while gradually achieving consistent speed during the swarming process. This achieves stable planning and tracking of intelligent connected unmanned vehicle queue formation, which is of great significance for improving the safety of unmanned vehicle queue driving and road traffic efficiency.

[0080] 1. System Model:

[0081] 1.1 Modeling of intersections without traffic lights:

[0082] Consider as Figure 2The illustrated signalless intersections each contain six lanes in both directions (three entrances and three exits). Assume each vehicle in the intelligent fleet is equipped with an onboard sensing unit capable of acquiring real-time vehicle status parameters and perceiving the road traffic environment, including but not limited to speed, heading, real-time location, and overtaking warning information. Simultaneously, each vehicle is also equipped with a wireless transceiver, accessing wireless channels via LTE 3GPP to periodically broadcast CAM messages and exchange information with other vehicles in the vicinity.

[0083] This paper utilizes the basic concept of "virtual navigation" to create a virtual mobile virtual parking space (MVP) for each vehicle in an intelligent vehicle fleet. By optimizing the movement trajectory of each virtual virtual parking space at unsignalized intersections, the "divergence-merging" process of the intelligent vehicle fleet is coordinated and controlled. This gradually guides each vehicle in the intelligent vehicle fleet to its corresponding target location, enabling the safe and efficient reorganization of the intelligent vehicle fleet at unsignalized intersections and its orderly departure from the intersection.

[0084] 1.2 Prerequisites:

[0085] (1) Neighborhood and Euclidean distance:

[0086] Taking a certain intelligent fleet of vehicles v i For example, suppose its wireless broadcast coverage area is a circular area with radius R, centered at the vehicle's center of gravity. All vehicles within the wireless broadcast coverage area constitute the vehicle v at time t. i Neighbor set N i (t), as shown in equation (1):

[0087] N i (t)={j:||q ij (t)||≤R i,j=1,2,…,n,j≠i} (1);

[0088] In the formula, ||q ij (t)|| represents the vehicle v at time t. i and v j The σ-norm distance between vehicles is calculated using the σ-norm instead of the Euclidean norm. The σ-norm is differentiable everywhere, and its specific definition is shown in equation (2):

[0089]

[0090] In the formula, the parameter ε represents the constant for calculating the σ-norm distance, and satisfies ε>0.

[0091] (2) Intelligent fleet and multi-agent system:

[0092] Consider the "divergence-convergence" process of several intelligent vehicle fleets at a traffic light-free intersection, which can be described as a multi-agent system consisting of n vehicles. Assume each agent (i.e., vehicle) has a different initial state, and its dynamic equation is shown in equation (3):

[0093]

[0094] In the formula, For vehicle v i The position vector at the current time t; For vehicle v i The velocity vector at time t; u i (t) represents vehicle v i The control input at time t consists of three parts, as shown in equation (4):

[0095]

[0096] In the formula, As a virtual guidance term based on potential energy gradient, the potential energy gradient function is used to guide vehicles to move quickly to the designated target parking space, while maintaining a reasonable safe distance between vehicles to avoid collisions. This is a guide speed control term used to control the vehicles to gradually reach the same speed during the merging process. It is the control feedback item of the virtual guide berth, used to adjust the state parameters of each vehicle, such as speed, heading, acceleration, etc., so that when the merging is completed, it can follow the virtual guide berth to move to the target berth and form a new intelligent fleet.

[0097] (3) Virtual guided berths:

[0098] The number of virtual VPs corresponding to n CAVs with different initial states is m. The VP can be equivalent to the rigid virtual structure of the CAV, and its dynamic equation can be simply stated as:

[0099]

[0100] In the formula, and These are the position vector, real-time velocity vector, and real-time acceleration vector of the virtual guided berth at time t, respectively.

[0101] 1.3 System Model:

[0102] Definition 1 (Discrete Vehicle Position Information). Assume a vehicle v in a scenario without traffic lights at an intersection. i And the corresponding virtual guided berth's position information at time t is q i (t), Under the CAV queue constraint forming control strategy at a signalless intersection, the position information of n vehicles and their corresponding virtual guide parking spaces in a fleet of intelligent vehicles at time t can be defined as a set Q. t and Specifically, as shown in equations (6) and (7). Where m = n.

[0103] Q t ={q1(t),q2(t),q3(t),…,q n (t)} (6);

[0104]

[0105] Definition 2 (Vehicle position deviation and mean position deviation). Given the position information Q of all vehicles at an intersection without traffic lights at time t. t and Assume there are v vehicles in an intelligent fleet. i The position deviation of the corresponding virtual guide berth at the current time t is δ. i (t), then the mean positional deviation of all vehicles can be defined as Specifically, see equations (8) and (9).

[0106]

[0107]

[0108] Based on the above definition, the “divergence-aggregation” process of n vehicles in several intelligent fleets at an unsignalized intersection can be described as a mathematical optimization problem as shown in Equation (10).

[0109]

[0110]

[0111]

[0112] Equation (10) is the objective function for the safe and efficient "diversion-merging" of n vehicles in a fleet of intelligent vehicles at an unsignalized intersection, i.e., minimizing the positional deviation between each vehicle and the corresponding virtual guide parking space. i (t) represents vehicle v i The velocity vector at time t; Indicates vehicle v iThe velocity vector of the corresponding virtual guided berth at time t. Equations (10a) and (10b) are constraints. Specifically, equation (10a) requires that all vehicles maintain a consistent speed after being reorganized into a new intelligent fleet through "divergence-mergence"; equation (10b) requires that all vehicles maintain a minimum safe distance during the "divergence-mergence" process to avoid collisions.

[0113] 2. Improved congestion control algorithm for multiple virtual guided berths:

[0114] 2.1 Improved Artificial Potential Function:

[0115] In the research of multi-autonomous vehicle intelligent agent systems, CAVs can be approximated as super-large molecules. Interactions exist between vehicles, and the magnitude of these forces determines the energy related to the relative positions of the molecules. To effectively control the motion states of the CAVs in this multi-autonomous vehicle intelligent agent system, the interaction between CAVs is linked to their position and distance information to achieve the swarm control effect described in this paper. The designed artificial potential function must satisfy the following conditions:

[0116] (1) When ||q ij ||→0, ψ α (||q ij ||)→C, where C is a constant.

[0117] (2) When 0 < ||q ij When ||<R, there is a balance distance d between each unmanned vehicle, at which distance ψ α Find the unique minimum value.

[0118] (3) When 0 < ||q ij When ||<d, the unmanned vehicle i and unmanned vehicle j exhibit a repulsive force, which is inversely proportional to the distance between the unmanned vehicles.

[0119] (4) When d < ||q ij When || < R, the interaction between driverless car i and driverless car j is one of attraction, and this attraction is directly proportional to the distance between the two vehicles.

[0120] (5)ψ α It concerns the relative distance ||q between driverless car i and driverless car j. ij || is a nonnegative, differentiable function.

[0121] Some scholars have designed an unbounded artificial potential function based on the relative distance between intelligent agents, as shown in equation (11):

[0122]

[0123] However, this paper finds that the traditional artificial potential function can only satisfy conditions (4) and (5), and when R is infinitely large, the two agents will also be subject to the potential force generated by the potential function. In addition, during standardized road driving, when the distance between CAVs is too large, the front and rear vehicles cannot complete information exchange and adjust the vehicle state in real time through sensors and other detection devices, which is inconsistent with the actual situation. Therefore, the traditional artificial potential function is not suitable for the study of multi-vehicle queue constraint forming control. In order to improve the applicability of the artificial potential function and the objectivity of the control algorithm in this paper, the function is optimized and improved: by using the virtual force function between unmanned vehicle i and unmanned vehicle j By performing integration, the forces acting on each CAV in the multi-autonomous vehicle intelligent agent system are linked by a nonlinear functional relationship, and an improved artificial potential function that simultaneously satisfies conditions (1) to (5) is designed:

[0124]

[0125] In the formula, The virtual force function between the autonomous vehicles is shown in equation (13).

[0126]

[0127] In the formula, ρ h (·) is the distance collision potential function constructed using concave and convex functions. It is a scalar function that smoothly varies between 0 and 1, and its expression is shown in equation (14); θ a θ b θ c The coefficient is constant and satisfies 0 < θ a <θ b , ||R|| represents the σ norm of the vehicle's perception radius R; ||d|| represents the σ norm of the ideal distance d that each autonomous vehicle needs to maintain.

[0128]

[0129] In the formula, h is used to determine the region in the spatial domain that is most affected by the potential energy field, and the closer h is to 1, the greater the influence of autonomous vehicles on autonomous vehicles in its domain. In the region [0, h], when ρ h (x) = 1, the driverless car is subjected to a virtual force function. The impact is greatest outside this region. h (x) decreases from 1 to 0, then It also decreases accordingly to 0.

[0130] Based on the above improvements, this paper sets the ideal distance d = 5m between each intelligent unmanned vehicle in a traffic light-free intersection; the detection radius R = 6m; ​​and uses Matlab simulation to obtain the curve of the potential energy force between two intelligent unmanned vehicles in the system as a function of relative distance, as shown below. Figure 3 As shown.

[0131] Depend on Figure 3 It can be seen that the improved artificial potential function satisfies: when ||q ij When ||=||d||, both the potential energy and the virtual force between CAV are zero; ||q ij When ||<||d||, the repulsive force between CAVs gradually increases as the distance decreases; when ||q ij When ||>||d||, the attraction between CAVs gradually increases with increasing distance, but when ||q ij When ||>||R||, since the two are no longer within each other's sensing range, the virtual force is zero and the potential energy remains unchanged; it proves that the artificial potential energy function designed in this paper satisfies conditions (1) to (5) and realizes the CAV distance control of the chain-type unmanned vehicle queue formation process at intersections without traffic lights.

[0132] While the improved artificial potential function offers the advantage of real-time and rapid control, it is still only a distance-dependent function, effectively limiting its effectiveness to distance control between CAVs. Therefore, when CAVs with different initial states need to form a platoon, only a mesh structure can be created. Furthermore, as the number of CAVs increases, it easily falls into local optima and exhibits "blocking" phenomena. Therefore, to address the local optima and "blocking" problem caused by using the artificial potential function for distance control, and to achieve the goal of unmanned vehicle chain platooning formation control, this paper proposes an improved congestion control algorithm for chain-type unmanned vehicle platooning formation, combining the improved artificial potential function with a multi-agent swarm control algorithm and featuring multiple virtual guided berths.

[0133] 2.2 Improved congestion control algorithm based on VP-based chain queue shaping:

[0134] In a multi-vehicle intelligent agent system at an intersection without traffic lights, each vehicle (CAV) under controller control can interact with other vehicles by periodically broadcasting CAM messages. This paper utilizes a VP (Virtual Vehicle) to design a target formation for the autonomous vehicle convoy. In each chain-like convoy, all CPs (Consumer Vehicles) have the same speed, acceleration, and direction of motion. The VP dynamically guides the CAVs, adjusting their state parameters (speed, heading, and real-time position) in real time to ensure they reach their respective VPs within the intersection. This maintains consistency in the dynamic state parameters between the CAVs and their VPs, allowing them to exit the intersection in a regular chain-like formation while ensuring reasonable spacing and collision avoidance. Figure 4The diagram shows the formation process of a multi-VP chain of unmanned vehicles. Figure 4 middle, This represents the state parameters of vehicle v1 after the queue is formed at time t. Its corresponding virtual guided berth (VP) status parameters Maintain consistency. (The symbols within...) Represents agent v at time t i (Status parameters of any intelligent vehicle or virtual guided parking space VP) Represents a position vector. A set consisting of velocity vectors, for example The position vector of intelligent vehicle v1 at time t velocity vector The set that constitutes; This represents the position vector of the intelligent vehicle v1 at time t corresponding to the virtual guided parking space A. velocity vector A set of components. The meaning of the expression is the same as described above.

[0135] Chain formation control is implemented for vehicles located at different positions and traveling at different speeds. During the free-swarming process, the control input u of each CAV at time t is... i (t) consists of three parts:

[0136]

[0137] In the formula, For q i (t-1) points to q j The direction vector of (t-1), where the parameter ε represents the constant for calculating the σ-norm distance, and ε > 0; Represents positive numbers; The mathematical expression is shown in equation (13), which is the virtual force function between vehicles, ||q j (t-1)-q i (t-1)|| represents the vehicle v at time t-1. i and vehicle v j σ-norm distance; Network diagram of multi-unmanned vehicle intelligent agent system M i The corresponding connection matrix C (t-1) i (t-1) The element in the i-th row and j-th column.

[0138] The improved congestion control algorithm based on multi-VP chain-type unmanned vehicle queuing formation successfully avoids the local optimum "blocking" problem caused by distance control using the artificial potential function method. It enables CAVs with different initial states to safely, quickly, and stably exit the intersection without traffic lights in a regular chain queue (single / double chain). All CAVs maintain a reasonable distance and avoid collisions while gradually achieving consistent speed during the congestion process.

[0139] 2.3 Stability Theory Analysis:

[0140] Based on intelligent vehicle v i With neighboring set N i In time (t), the states where vehicles are connected are defined as follows: For a multi-agent system, assuming internal information connectivity and information exchange between agents (vehicles), then there is an edge between any two agents. Thus, a multi-autonomous vehicle agent system can be viewed as a network (system network graph), also called a graph, consisting of a set of N intelligent vehicle nodes and M edges connecting these N nodes. The corresponding system network graph M at time t is described. i (t), and the corresponding connection matrix C i (t), Degree Matrix I i (t) and the Laplace matrix L i (t)=C i (t)-I i (t). The Laplacian matrix L of the network graph M satisfies the following properties: the high-dimensional Laplacian matrix L is a general positive definite matrix, and for all non-zero real coefficient matrices Z, it satisfies:

[0141]

[0142] Obviously, if the network graph M is an undirected graph, then its Laplace matrix is ​​a symmetric positive semi-definite matrix.

[0143] For the dynamic equations of the multi-unmanned vehicle intelligent agent system described by equations (3) and (5), the improved artificial potential energy function (12) and the multi-virtual guided berth chain multi-agent swarm control algorithm (15) are applied for control. The initial energy U0 of the system is bounded, and the following theoretical analysis exists:

[0144] Theorem 1: Within the system, CAVs with different initial states can effectively control the position and distance between CAVs, without "blocking" and stably follow their respective VPs to form a regular chain queue.

[0145] Proof 1: Define the position difference and velocity difference between the unmanned vehicle i and VP at time t as x i (t)=q i (t)-q γ (t), vi (t)=p i (t)-p γ (t), then we have:

[0146]

[0147] The energy functions defined in equations (3), (4), and (12) are:

[0148]

[0149] In the formula, Clearly, the energy function U = U(q(t), p(t), p γ (t),q γ (t), X) is a positive semi-definite function. Combining equation (12), the time derivative of the system's energy function U is:

[0150]

[0151] In the formula, Since Q = CL(t) is a positive semi-definite matrix and U(t) ≤ 0, U(t) is a non-increasing function that varies with time. For any time t, U(t) ≤ U0, thus proving Theorem 1.

[0152] Theorem 2: All CAV velocities in the system will eventually converge to the velocity of VP.

[0153] Proof 2: Considering that U(t)≤U0, an invariant set can be defined:

[0154]

[0155] According to the La Salle invariance principle, the range of motion of all CAVs within the system will extend from Ω to the system's maximal invariant set. By Theorem 1, when the system reaches its maximal invariant set, v... i (t)=0, that is, p1≡p2≡…p n Therefore, Theorem 2 is proved.

[0156] Theorem 3: When the system is stable, the total potential energy reaches a local minimum.

[0157] Proof 3: When the system is in a steady state,

[0158] Then u = 0, and from equation (12) we can obtain:

[0159]

[0160] but:

[0161]

[0162] If the solution to equation (17) is the initial position vector of each CAV in the system and is a local maximum, then the relative distance between CAVs will not change when u = 0. However, for the system to maintain a stable equilibrium point, it can only be a solution that satisfies the local minimum of matrix u. Therefore, the total potential energy of the system is at its minimum when MAS is stable, and Theorem 3 is proved.

[0163] Theorem 4: Assume the initial energy of the system is U0 < (K+1)e * (e * =min ij (||q ij (t)||)>0,k∈z + If k = 0, then there will be at least k different CAVs in the system that will collide. Only when k = 0 will the CAVs in the system not collide.

[0164] Proof 4: From equation (16), we know that U is non-increasing and for The system satisfies U(t) ≤ U0. Assume the initial energy of the system is U0 < (K+1)e^(-t / t). * And given any time t1 > 0, at least k+1 CAVs will collide.

[0165] At time t1, there must be k+1 CAVs colliding with the system, and the system energy at this time is (k+1)min. ij (ψ α ||q ij (t)||). However, in Theorem 4, it is assumed that U0 < (k+1)min ij (ψ α ||q ij (t)||), at which point the energy U0≥U(t1)≥(k+1)min ij (ψ α ||q ij The two assumptions (t) contradict each other, so when t≥0, there will be no collisions between more than k CAVs in the system. Therefore, when k=0, there will be no collisions in the system, and Theorem 4 is proved.

[0166] 3. Simulation Analysis:

[0167] Numerical simulations of multi-vehicle queue formation control were conducted in the Matlab environment to verify the reliability of the control algorithm proposed in this paper. First, simulations were performed on the control of multiple CAV positions and distances based on an improved artificial potential function. Second, CAVP target formations were designed using VPs. Simulations of multi-vehicle queue formation control at a signalless intersection were carried out based on a multi-agent swarm control algorithm with multiple virtual guide berths (VPs). Based on the single queue formation control simulation, a chain-type double queue formation control simulation of a multi-unmanned vehicle intelligent agent system at the intersection was also performed. The main simulation parameter settings are shown in Table 1.

[0168] Table 1. Simulation parameter settings:

[0169]

[0170] 3.1 Multi-CAV Swarm Control Based on Improved Artificial Potential Function:

[0171] Consider 20 CAVs moving in a two-dimensional plane. Assume the wireless communication lines within the intersection area are stable, and each intelligent vehicle can reliably interact with all vehicles within its broadcast coverage area. The simulation process parameters are as follows to obtain the position state of each CAV at different times during the swarming process, such as... Figure 5 (a)- Figure 5 As shown in (d):

[0172] In the diagram, the blue hollow dots represent all vehicles in the multi-vehicle intelligent agent system; the blue lines represent the connections between the CAVs in the system, indicating that vehicles can communicate and exchange information; the direction and length of the red arrows represent the speed direction and speed magnitude of each CAV's movement, respectively.

[0173] By observing the positional states of each CAV in the system at different times during the swarming process based on the improved artificial potential function, it can be seen that at T=0s, 50s, and 100s, some CAVs in the multi-autonomous vehicle intelligent agent system begin to communicate and gradually establish connections. After a certain degree of swarming, the CAVs within the system have formed an organic whole. However, it is obvious that during the time period from T=100s to T=200s, a local optimum "blocking" phenomenon occurs within the system. Some CAVs lose contact with other autonomous vehicles and can only form a mesh structure, not a chain queue, thus failing to meet the control objective of CAVP constraint shaping.

[0174] 3.2 Improved Swarm Control Based on VP-based Chain-like Unmanned Vehicle Queue Formation:

[0175] To address the local optimum "blocking" problem caused by distance control using the artificial potential function method, and to achieve the goal of unmanned vehicle (VAV) chain queuing formation control, this paper, based on the improved artificial potential function for multi-VAV (Vehicle Aerial Vehicle) swarm control, designs a CAVP (Vehicle Aerial Vehicle VP) target formation (single-chain VP-1 / double-chain VP-2) using VPs. VPs dynamically guide the VAVs, adjusting their state parameters (speed, heading, and real-time position) in real time, ensuring they reach their respective virtual guide parking positions within the intersection. This maintains consistency between the dynamic state parameters of the VAVs and their respective VPs, allowing them to form a regular chain queuing and exit the intersection while ensuring reasonable spacing and collision avoidance. The simulation parameter settings remain the same as in the previous section.

[0176] This section divides the simulation of a multi-agent congestion control algorithm with multiple virtual guided berths into two parts: First, a simulation experiment is conducted on the single-chain queue formation control of multiple CAVs at an unsignalized intersection; second, based on the single queue formation control, a simulation of a double-chain queue formation control of multiple CAVs at an intersection is added. Using equations (3) and (4), a chain queue constraint formation control simulation is performed on 20 CAVs at an unsignalized intersection, obtaining the CAV position states at different times for single / double-chain queues as follows: Figure 6 As shown in (a)-(f) in the figure. Analyzing the position and state of the CAVs at different times, it can be seen that during the chain queue formation control process of the multi-unmanned vehicle intelligent agent system, the CAVs always maintain contact with each other, the vehicles maintain a reasonable distance between each other and there is no "segmentation" phenomenon. While avoiding collisions, a reasonable distance is maintained, and finally a stable chain queue structure is formed before the vehicles leave the intersection.

[0177] In the diagram, the red hollow dots represent all CAVs in the multi-vehicle intelligent agent system; the blue lines connecting the red hollow dots represent the connection relationship between vehicles within the system, and the existence of the connection indicates that the vehicle-to-vehicle communication and information transmission are possible; the black * represents VP.

[0178] To more intuitively reflect the control effect of the algorithm in this paper, the quantized motion trajectory of the unmanned vehicle queue is drawn by chain-like queue quantization under the control input formula (15). The quantized motion trajectory of the unmanned vehicle queue in the intersection without traffic lights under the control input formula (15) is as follows: Figure 7 As shown in (a)-(b), each dashed line corresponds to the quantized motion trajectory of a CAV during the queue formation process. Analysis of the quantized motion trajectory of the chain queue clearly shows that the system achieves safe, rapid, and stable constraint-based chain queue formation for CAVs with different initial states. This realizes the constraint-based formation control of unmanned vehicle queues at traffic light-free intersections, further proving that the algorithm satisfies all control objectives of the proposed CAV chain-based single and double queue constraint-based formation control and possesses good stability.

[0179] Finally, this paper introduces three indicators—positional error, longitudinal velocity error, and lateral velocity error—in the CAV queuing formation process to evaluate the multi-autonomous vehicle queuing formation control effect when the number of CAVs changes, and quantifies the algorithm's control effect. For example... Figure 8 , Figure 9 As shown, with CAV numbers of 5, 10, 15, 20, and 25 vehicles respectively, the convergence time of positional distance error, longitudinal speed error, and lateral speed error between all CAVs and their respective VPs during the queuing formation process in a signalless intersection is displayed, as well as the final values ​​of positional distance error, longitudinal speed error, and lateral speed error between all CAVs and their respective VPs after queuing formation.

[0180] Depend on Figure 8 , Figure 9 It can be seen that as the number of CAVs increases, the convergence time of the positional distance error, longitudinal speed error, and lateral speed error between all CAVs and their respective VPs during the queuing process in the intersection without traffic lights shows an increasing trend. However, they all converge to the minimum value between 220s and 250s. After queuing, the final value of the positional distance error between all CAVs and their respective VPs is close to 0.9dm, the final value of the longitudinal speed error is close to 1m / s, and the final value of the lateral speed error is close to 0.001m / s. Moreover, there is no significant difference between the final values ​​of each error as the number of CAVs increases.

[0181] Figure 10 , Figure 11 , Figure 12 This represents the changes in the mean positional distance error, mean longitudinal velocity error, and mean lateral velocity error between all CAVs in the queue and their respective VPs at different time points as the number of CAVs changes. It can be seen that within an uncontrolled intersection, after a series of actions such as formation changes and obstacle avoidance, CAVs of different numbers and initial states can accurately reach their respective VPs and maintain consistent velocity vectors with their corresponding VPs, exhibiting good velocity consistency. Simultaneously, all CAVs can safely, quickly, and stably exit the uncontrolled intersection in a regular chain queue while maintaining the desired formation. Furthermore, during the swarming process, they maintain reasonable spacing, avoid collisions, and gradually achieve consistent speeds, further demonstrating that the algorithm presented in this paper has good stability and convergence in the formation of multi-CAV queues at uncontrolled intersections.

[0182] In summary, the advantages of the control strategy presented in this paper are mainly reflected in two aspects:

[0183] (1) The algorithm in this paper effectively solves the local optimal "blocking" problem caused by distance control by using artificial potential function method, improves the efficiency and stability of multi-vehicle queue constraint forming swarm control, and increases the limit of distributed control theory research results in the field of intelligent transportation of automobiles;

[0184] (2) The concept of virtual guided berth (VP) is introduced. The multi-agent swarm control algorithm with virtual guided berth is used to safely, quickly and stably constrain the CAVs with different initial states at the intersection into a regular chain queue before they leave the intersection. This effectively improves the safety of unmanned vehicle queue driving, enhances the space utilization of the intersection and the efficiency of transportation. It is of great significance for the future application and promotion of CAVP in the field of transportation.

[0185] 4. Conclusion:

[0186] (1) This paper proposes the concept of "Virtual Parking" (VP). Based on the relationship between distance and force between vehicles in the intelligent vehicle fleet, the traditional artificial potential function is improved. A "divergence-convergence" model of intelligent vehicle fleet at unsignalized intersections is constructed. A congestion control algorithm based on virtual parking cooperative guidance is proposed. At the same time, it is mathematically proven that multiple intelligent vehicle fleets diverge and converge at unsignalized intersections, achieving safe, rapid and stable CAVs with different initial states. The constraint is a regular chain queue that drives out of the intersection. All vehicles maintain a reasonable distance and avoid collisions while gradually achieving consistent speed during the congestion process.

[0187] (2) This paper takes CAVP as the research object. First, the mathematical optimization model is used to accurately characterize the CAV queue constraint forming process at intersections without traffic lights. Second, the traditional artificial potential function is improved to realize CAV distance control in the chain-type unmanned vehicle queue forming process at intersections without traffic lights. Combined with the improved artificial potential function, an improved congestion control algorithm for chain-type unmanned vehicle queue forming based on multiple virtual guided berths is designed. This solves the local optimal "blocking" problem caused by using the artificial potential function method to achieve position distance control. It innovatively realizes the single and double queue constraint forming control of CAV chain-type queues at intersections without traffic lights.

[0188] (3) When there are multiple VPs in the system, CAVs with different initial states can safely, quickly and stably exit the intersection in a regular chain queue, and all vehicles maintain a reasonable distance and gradually reach the same speed while avoiding collisions during the swarming process; stable planning and tracking of CAV queue formation is realized, which effectively solves the problems of poor formation stability and low traffic efficiency of connected unmanned vehicle fleets when passing through intersections without traffic lights.

[0189] (4) When the CAV in the system is equivalent to an intelligent node, factors such as incomplete information transmission between it and the virtual guided parking space are not fully considered, nor are situations such as multiple external interferences or communication delays taken into account. Future research can optimize the algorithm based on these factors to further promote the application of distributed control theory in intelligent transportation for automobiles.

[0190] The scope of protection of this invention includes, but is not limited to, the above embodiments. The scope of protection of this invention is defined by the claims. Any substitutions, modifications, or improvements to this technology that are easily conceived by those skilled in the art fall within the scope of protection of this invention.

Claims

1. An improved congestion control method for chain-type CAV queue formation based on virtual guided berths, characterized in that, include: Step 1: At an intersection without traffic lights, there are several intelligent connected unmanned vehicle convoys. There are n intelligent connected vehicles (CAVs) in the several intelligent connected unmanned vehicle convoys. The intelligent connected vehicles (CAVs) are simply referred to as vehicles. The n vehicles constitute a multi-unmanned vehicle intelligent agent system. Step 2: Each vehicle has a different initial state, and its dynamic equations are as follows: In the formula, Indicates vehicle v i The position vector at time t; Indicates vehicle v i The velocity vector at time t; u i (t) represents vehicle v i Control input at time t; Step 3, let vehicle v i The wireless broadcast coverage area is a circular area with radius R, centered on the vehicle's center of gravity. i All vehicles within the coverage area of ​​the wireless broadcast are connected to vehicle v i Wireless communication connection, all vehicles located in the aforementioned circular area constitute vehicle v at the current time t. i Neighbor set N i (t); Step 4, based on vehicle v i With neighboring set N i The existence of edges between vehicles in (t) characterizes the system network graph M at time t. i (t) and the corresponding connection matrix C i (t); Step 5: Create a virtual, movable guide berth for each vehicle. The number of virtual guide berths corresponding to n vehicles in different initial states is m. The dynamic equation of the virtual guide berth is as follows: In the formula, Indicates vehicle v i The corresponding virtual guide berth's position vector at time t; Indicates vehicle v i The corresponding velocity vector of the virtual guided berth at time t; Indicates vehicle v i The corresponding acceleration vector of the virtual guided berth at time t; Step 6: Initialize the initial position and initial speed of m virtual guide parking spaces, and n vehicles in the intersection without traffic lights have different initial positions and speeds; Step 7: Calculate vehicle v i and vehicle v j Virtual force function: In equation (3), the independent variable x represents vehicle v. i and vehicle v j σ-norm distance, ρ h (·) represents the distance collision potential function constructed using concavity and convexity functions, which is a scalar function that smoothly varies between 0 and 1; θ a θ b θ c Let θ represent constant coefficients, and satisfy 0 < θ a <θ b , ||R|| represents the σ-norm of the vehicle's perception radius R; ||d|| represents the σ-norm of the ideal distance d that needs to be maintained between vehicles; In the formula, h represents the region in the spatial domain that is most affected by the potential energy field; within the region [0, h], when ρ h (x) = 1, the vehicle is subjected to a virtual force function. The impact is greatest outside the region [0,h], ρ h (x) decreases from 1 to 0, then It also decreases accordingly to 0; Step 8: Calculate vehicle v i Control input at time t: In the formula, q i (t-1) points to q j The direction vector of (t-1) is given by parameter ε, which represents the constant for calculating the σ-norm distance and satisfies ε > 0. All represent positive numbers; Indicates vehicle v i and vehicle v j The virtual force function, ||q j (t-1)-q i (t-1)|| represents the vehicle v at time t-1. i and vehicle v j σ-norm distance; M represents the network diagram of a multi-autonomous vehicle intelligent agent system. i The corresponding connection matrix C (t-1) i (t-1) The element in the i-th row and j-th column; Step 9: (9.1) Continuously update the position vector and velocity vector of all virtual guide berths, thereby optimizing the movement trajectory of each virtual guide berth at intersections without traffic lights; (9.2) Vehicle v i Based on the received virtual parking space and vehicle v i The position and speed information of vehicles in the neighboring set at a certain moment are used to adjust the control input of the vehicle at the next moment in real time according to formula (5) in step 8, and then update the position and speed of the vehicle according to formula (1) in step 2. (9.3) Update the position and speed of all vehicles according to the method in step (9.2), and finally guide all vehicles to the corresponding virtual guide parking spaces.

2. The improved congestion control method for chain-type CAV queue formation based on virtual guided berths according to claim 1, characterized in that, At intersections without traffic lights, roadside units (RSUs) are installed, and the RSUs are wirelessly connected to connected vehicles (CAVs). In step 5, a virtual movable virtual guide parking space is created for each vehicle using the Roadside Unit (RSU); in step 6, the initial positions and initial speeds of the m virtual guide parking spaces are initialized using the RSU; in step 9, the position vectors and speed vectors of all virtual guide parking spaces are continuously updated using the RSU, thereby optimizing the movement trajectory of each virtual guide parking space at intersections without traffic lights.

3. The improved congestion control method for chain-type CAV queue formation based on virtual guided berths according to claim 1, characterized in that, In step 9, vehicle v i Receive the road test unit (RSU) sending the data related to vehicle v i The corresponding virtual guided parking space has its position and speed information at a certain moment, and receives vehicle v i The vehicles in the neighboring set send their own position and speed information at a certain moment, and adjust their own control input in real time according to formula (5) in step 8.

4. The improved congestion control method for chain-type CAV queue formation based on virtual guided berths according to claim 1, characterized in that, In step 9, when the following formula is satisfied, all vehicles are guided to their respective virtual guidance parking spaces. Equation (6) represents minimizing the mean positional deviation of n vehicles and their corresponding virtual guide parking spaces at the current time t. Equations (6a) and (6b) are constraints; p i (t) represents vehicle v i The velocity vector at time t; Indicates vehicle v i The corresponding velocity vector of the virtual guided berth at time t; ||q i (t)-q j (t)|| represents the vehicle v at time t. i and vehicle v j The σ-norm distance between them, Q t Q represents the location information of n vehicles in a fleet of intelligent connected unmanned vehicles at time t. t ={q1(t),q2(t),q3(t),…,q n (t)}; This represents the location information of the virtual guided parking spaces corresponding to n vehicles at time t. δ i (t) represents vehicle v i The position deviation of the vehicle v from the corresponding virtual guided parking space at the current time t. i The σ-norm distance between the virtual guide berth and the corresponding virtual guide berth at the current time t.

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