Non-signalized intersection vehicle collision avoidance strategy method based on differential game

Abstract

The invention discloses a non-signalized intersection vehicle collision avoidance strategy method based on a differential game, and each vehicle can select to make a decision independently and can act in a cooperative mode. The problem is described as a dynamic differential game, that is, two vehicles make decisions according to the expected behavior of the opposite vehicle. The method considers a non-cooperative game (the vehicle only optimizes the own cost) and a cooperative game (the vehicle coordinates a decision to optimize the joint cost). Different from a traditional discrete game theory in which the acceleration of a vehicle is divided into a plurality of segments, the method provided by the invention proposes a differential game to generate an acceleration signal of continuous time, and the signal can be freely changed during the crossing period of the whole intersection. The effectiveness of the differential game method is verified through analogue simulation, and compared with a traditional discrete game theory method, the method can enable the vehicle to pass through the non-signal intersection more quickly, and meanwhile, the requirements for safety and comfort are met.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-agent coordinated control, and in particular to a vehicle collision avoidance strategy method at an unsignalized intersection based on differential game. Background Art

[0002] Due to the complexity of intersection traffic and environment, intelligent vehicles are prone to accidents when passing through intersections. Therefore, it is of great significance to resolve conflicts between traffic owners at intersections. In particular, traffic flow control at unsignalized intersections is challenging. First, it plays an important role in determining road capacity, especially in urban and rural areas; second, traffic accidents at unsignalized intersections are usually more frequent than those at intersections with traffic lights. Intersection rules at unsignalized intersections have a great impact on road traffic safety. In order to improve the traffic efficiency of unsignalized intersections, it is necessary to understand the traffic dynamics of intersections and find the best control strategy that can resolve intersection conflicts.

[0003] With the development of wireless communication technology, vehicles can communicate with each other through vehicle-to-infrastructure (V2I) or vehicle-to-vehicle (V2V) technology. Through V2I and V2V, vehicles can collect and share information about other vehicles, such as maneuvering instructions and trajectories, to obtain traffic conditions near intersections and optimize their movements and route selection. Today, there are mainly two cooperative driving strategies at unsignalized intersections, namely "temporary negotiation-based" strategies and "planning-based" strategies. The fundamental difference between these two strategies lies in how they determine the order of vehicles passing through intersections. The "temporary negotiation" method uses a greedy search method to seek solutions, resulting in a "first come, first served" solution model, which is not optimal from the perspective of collective interests.

[0004] In contrast, game theory, with its rigorous mathematical analysis, is widely used to resolve conflicts between vehicles. Game theory can quantify the decision-making process of vehicles, ensuring that vehicles can choose the best action at every moment while achieving the best individual or collective goals. Abdelghaffar et al. introduced Nash negotiation into cooperative game theory, enabling multiple vehicles with specific goals to reach a consensus, so that vehicles can cooperate and benefit. Zhang et al. studied the problem of unsignalized intersection traffic considering traffic flow and energy dissipation from the perspective of game theory, applied the prisoner's dilemma game at unsignalized intersections, and studied the impact of the adopted method on traffic capacity, but the study did not consider the interaction between the two vehicles.

[0005] Chen et al. proposed a game theory-based intelligent vehicle conflict decision model that considers safety, efficiency, and comfort to select the best driving strategy. Wang et al. proposed a game theory-based hierarchical control strategy to improve travel efficiency in non-signalized areas for the priorities and interactions of intelligent connected vehicles (CAVs). Li et al. discussed a game theory approach to simulate the decision-making process of vehicles at non-signalized intersections.

[0006] That is, vehicles are divided into different types and their priorities are determined to avoid conflicts. Wang et al. studied cooperative and non-cooperative games at unsignalized intersections, established Nash games with discrete decision-making strategies to describe non-cooperative behaviors, and verified that cooperative games can obtain optimal solutions. Wang et al. developed a lane change and following vehicle prediction method in highway scenarios based on optimal control and dynamic game theory, and explained that one of the main challenges of applying differential game theory to traffic navigation control is to design appropriate parameters of the cost function to ensure the stability of the controller.

[0007] However, in the above studies, the game theory solutions for unsignalized intersections are discrete in nature, which means that the intersection traffic process is divided into multiple fixed time periods, and different strategies are adopted in each period.

[0008] Solving this mixed-integer problem is very difficult due to the multidimensionality of the combinatorial strategy space. Moreover, the optimal control law obtained is piecewise constant, which is an ideal situation that is usually not satisfied in practice. The control law, such as the acceleration of the vehicle, is continuous-time and time-varying. To address this problem, inspired by differential game theory, we employ it to obtain the competitive and cooperative behaviors of autonomous vehicles at unsignalized intersections.

[0009] Among them, dynamic differential games consider the time evolution effects of participants according to their dynamics, so they are more convenient in studying and solving problems involving multi-agent systems. It has been widely used in many fields such as economics, computer science, and military. Dynamic differential games can consider multiple participants pursuing their own goals, which can be competitive or cooperative. To the best of the author's knowledge, most of the current work adopts discrete decision models to solve the traffic control flow problem at unsignalized intersections, while dynamic differential games are rarely used. Summary of the invention

[0010] The technical problem to be solved by the present invention is to overcome the above technical defects and provide a vehicle collision avoidance strategy method for an unsignalized intersection based on differential game taking into account non-cooperative game and cooperative game.

[0011] To solve the above technical problems, the technical solution provided by the present invention is: a vehicle collision avoidance strategy method for unsignalized intersections based on differential games, comprising the following steps: Step S1: establishing a vehicle communication model and path planning to achieve information sharing between vehicles; Step S2: designing a non-cooperative game model, establishing the dynamic equation of the vehicle, and determining the acceleration control strategy; Step S3: designing a cooperative game model to describe the driving decisions of the vehicle and minimize the total time for the two vehicles to pass through the intersection; Step S4: solving the optimal control strategy based on Step S2 and Step S3 to obtain the optimal feedback control strategy; Step S5: performing numerical simulation and simulation verification to improve driving safety.

[0012] Preferably, the step S1 includes using V2V communication technology to achieve information sharing between vehicles, wherein the information includes obtaining the instant position, speed and acceleration of adjacent vehicles;

[0013] The future motion state model of the vehicle is:

[0014]

[0015] Where: i and j are two vehicle participants, and the continuous state vector is defined for the controlled vehicle i Where X i ,Y i represents the lateral and longitudinal positions of vehicle i, V i represents the speed of vehicle i, and defines the control vector u(u=a i ) is the acceleration of vehicle i, and the size of i is limited by the radius parameter T i >0 correlation.

[0016] Preferably, the time required for the vehicle i to travel to the collision point under the current driving information is:

[0017]

[0018] The collision penalty between vehicle i and vehicle j at the collision point is:

[0019]

[0020] Determine the Nash feedback equilibrium strategy of each participant, that is, the strategy set satisfy:

[0021]

[0022] Preferably, step S3 further includes designing a joint state vector and a control vector to describe the driving decision of each vehicle, determining the goal to maximize common interests, and constructing a joint cost function including the safety cost, efficiency cost, stability cost and control cost of each vehicle;

[0023] Specifically, define the joint state vector Φ = [X i ,Y i ,V i ,X j ,Y j ,V j ] Τ and control vector u = [a i ,a j ] Τ As an extended state space and control space;

[0024] The system dynamic equation is:

[0025]

[0026] By minimizing the joint prediction cost J, the optimal control U is obtained, and the function form is:

[0027]

[0028] The Nash feedback equilibrium strategy of each participant is:

[0029] J[Φ,u * ,Φ(t 0 )]≤J[Φ,u,Φ(t 0 )].

[0030] Preferably, step 4 includes determining the optimal acceleration control law of the non-cooperative game and the cooperative game based on the Pontryagin maximum principle, establishing and solving the state and adjoint state dynamic equations of the vehicle, and obtaining the optimal feedback control strategy to minimize the cost function of the vehicle;

[0031] Including: Considering the driving cost function and system dynamics equation in the non-cooperative game model to define the Hamiltonian H as:

[0032]

[0033] Among them, λ is the accompanying variable;

[0034] When minimizing the objective function:

[0035]

[0036] Based on the Pontryagin maximum principle and u * =argmin u H[Φ,u,λ,t,Φ(t 0 )] to solve, where u represents a feasible solution that satisfies constraint 2;

[0037] The adjoint state dynamic equation is:

[0038]

[0039] The optimal acceleration control law of the vehicle under the non-cooperative control strategy:

[0040]

[0041] The controller's adjoint variable dynamic equation satisfies the following differential equation:

[0042]

[0043] The optimal acceleration u and state trajectory are effectively solved through numerical iterative algorithms;

[0044] The optimal acceleration control law of the vehicle under the non-cooperative control strategy:

[0045]

[0046] Preferably, the step S5 includes verifying the traffic efficiency and safety of vehicles at intersections without signal lights in different scenarios through simulation;

[0047] In the non-cooperative game model, the specific form of the driving cost function is as follows:

[0048] f 1 (Φ(t),u(t),t)=a 1 G(Φ i ,Φ j ,u)+a 2 TP(Φ i )+a 3 (V d -V i ) 2 +a 4 (u) 2

[0049] f 2 (Φ(t),u(t),t)=a 1 G(Φ i ,Φ j ,u)+a 2 TP(Φ i )+a 3 (V d -V i ) 2 +a 4 (u) 2

[0050] In the cooperative game model, the specific form of the driving cost function is as follows:

[0051]

[0052] f 2 (Φ(t),u(t),t)=∑ c＝i,j α 1 G(Φ c ,Φ c-1 ,u)+α 2 TP(Φ i )+α 3 (V d -V c ) 2 +α 4 (u) 2 .

[0053] The advantages of the present invention compared with the prior art are:

[0054] The present invention describes the difficult problem of two vehicles passing through an unsignalized intersection as a dynamic differential game, where the controlled vehicle makes decisions based on the expected behavior of the other vehicle;

[0055] The present invention considers both non-cooperative games (vehicles optimize only their own costs) and cooperative games (vehicles coordinate decisions to optimize common costs);

[0056] Unlike the traditional discrete game theory method that divides the vehicle acceleration into multiple segments, the proposed differential game generates a continuous-time acceleration signal that can change freely during the entire intersection. Therefore, the vehicle can pass the intersection faster while meeting safety and comfort requirements. Numerical simulations are performed to verify the effectiveness of the proposed method. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 . is a block diagram of the method principle of an embodiment of the present invention;

[0058] Figure 2 Schematic diagram of cooperative driving at an unsignalized intersection;

[0059] Figure 3 This is the speed change diagram of the two vehicles under the non-cooperative controller;

[0060] Figure 4 It is the speed variation diagram of the two vehicles under the cooperative controller;

[0061] Figure 5 It is the speed change diagram of the two vehicles under the discrete decision method. DETAILED DESCRIPTION

[0062] The present invention is further described in detail below in conjunction with the accompanying drawings.

[0063] A vehicle collision avoidance strategy method for an unsignalized intersection based on differential game includes the following steps:

[0064] Step S1: Establish vehicle communication model and path planning

[0065] When vehicles are driving on a one-way street and cannot change lanes, V2V communication technology is used to share information between vehicles, ensuring perfect wireless communication without information loss or delay. Each vehicle can obtain driving information such as the immediate position, speed, and acceleration of adjacent vehicles in order to pass through intersections without signal lights. Use mathematical expressions to describe this problem and give the future motion state equations of the vehicle model.

[0066] Step S2: Design a non-cooperative (competitive) game model

[0067] The independent decision-making process of the vehicle is regarded as a non-cooperative game, and the dynamic equation of the vehicle is established to determine its acceleration control strategy. The operating cost function of the vehicle is designed to include safety cost, efficiency cost, speed stability cost and control cost to ensure safety and driving comfort.

[0068] Step S3: Design cooperative game model

[0069] Considering the cooperative game scenario, the model is established, and the joint state vector and control vector are designed to describe the driving decision of each vehicle. The goal is to maximize the common benefit and minimize the total time for the two vehicles to pass the intersection. The joint cost function includes the safety, efficiency, stability and control cost of each vehicle.

[0070] Step S4: Solving the optimal control strategy

[0071] Based on the Pontryagin Maximum Principle (PMP), the optimal acceleration control law for non-cooperative and cooperative games is determined. By establishing and solving the state and adjoint state dynamic equations of the vehicle, the optimal feedback control strategy is obtained to minimize the cost function of the vehicle. The control strategy of each vehicle can be solved by an iterative numerical algorithm.

[0072] The non-cooperative game and cooperative game models are solved by numerical iteration method to obtain the acceleration trajectory and state trajectory of the vehicle. The traffic efficiency and safety of vehicles at intersections without signal lights under different scenarios are verified by simulation to ensure that the proposed game theory control strategy can improve driving efficiency and avoid collisions.

[0073] Step S1:

[0074] First, we use mathematical representation to describe this problem. Unless otherwise specified, "vehicle" and "player" in this study refer to vehicles crossing an unsignalized intersection. The two vehicles i and j are regarded as two players. Specifically, for the controlled vehicle i, the continuous state vector is defined as Where X i ,Y irepresents the lateral and longitudinal positions of vehicle i, V i represents the speed of vehicle i. Define the control vector u(u=a i ) is the acceleration of vehicle i. The following vehicle model is used to predict its future motion state:

[0075]

[0076] Under the initial condition Φ(t 0 ), the goal is to control each vehicle to cross the intersection as quickly as possible from its initial position while avoiding collisions and ensuring a certain degree of comfort. The size of vehicle i and the radius parameter T i >0 correlation, adjust the radius parameter T i To maximize the coverage of the size of vehicle i. Due to the different vehicles passing through the intersection, they may have different sizes or shapes. Generally speaking, the present invention takes the center of mass of the vehicle as the origin and determines the radius as the distance between the origin of the vehicle and the point farthest from it.

[0077] Step S2:

[0078] Determine vehicle i as the research object and another vehicle as a competitor. V2V communication technology allows both parties to perfectly perceive the decisions of their competitors when optimizing their respective strategies. In this case, each vehicle passing through an unsignalized intersection chooses the corresponding operation by considering the driving information of other vehicles, while passing through as quickly as possible to maximize the safety and comfort of the vehicle. Therefore, considering the driving strategies of competitor vehicles, the goal of vehicle i is to minimize the time to pass through the intersection (from detecting the opponent to passing the potential collision point). In other words, each vehicle needs to determine the control vector u of the feedback control strategy to guide itself from the initial position to the predefined goal (passing the intersection) and avoid collision. This problem can be described as a non-cooperative Nash game with two players within the framework of dynamic differential games. This non-cooperative game can be transformed into the problem of minimizing a single cost function. Considering the vehicle's motion state (1) and the given initial driving information, the predicted cost J is minimized to obtain the time from time t 0 To time t f The optimal control vector u is

[0079]

[0080] in

[0081]

[0082] st

[0083] V i ∈[0,V max] (4)

[0084] a i ∈[a min ,a max ]. (5)

[0085] Where f represents the operating cost, constraint (4) stipulates that the vehicle's speed is non-negative throughout the time period and must not exceed the maximum speed, and constraint (5) stipulates that the vehicle's acceleration is limited to a certain range. In the non-cooperative game model, the driving cost function is defined as follows:

[0086] f(Φ(t),u(t),t)=a 1 G(Φ i ,Φ j ,u)+a 2 YP(Φ i )+a 3 (V d -V i ) 2 +a 4 (u) 2 (6)

[0087] Among them, V d is the expected speed of the vehicle on the current road, P i is the position of vehicle i (X i ,Y i ), a 1 ,a 2 ,a 3 ,a 4 is the weighting coefficient, TP i is the time required for vehicle i to travel to the collision point under the current driving information.

[0088]

[0089] Function G(Φ i ,Φ j ,u) is used to add the collision penalty between vehicle i and vehicle j at the collision point, that is,

[0090]

[0091] The problem of unsignalized intersection control design is to determine the Nash feedback equilibrium strategy for each participant, that is, the strategy set satisfy

[0092]

[0093] Here, the driving cost function (6) contains four terms. The first term is the safety cost, which defines the safety of the vehicle. It is related to the time difference between two vehicles reaching the intersection collision point. Each vehicle must pass the intersection at a different time, where formula (8) represents the time difference between two vehicles passing consecutively. When two vehicles arrive at the intersection collision point at the same time, they will be subject to a greater penalty. The second term is the efficiency cost, which means that the vehicle is expected to pass the intersection in a faster time. Note that the safety cost and efficiency cost are the main factors to be considered and have a larger weight. The third term is the vehicle's stable speed, which means that each vehicle should travel at a stable and average speed. The fourth term is the control cost, which aims to punish large acceleration or deceleration operations, because excessive changes in acceleration or deceleration can also lead to a poor driving experience, which is an important indicator of driving comfort.

[0094] Step S3:

[0095] When two vehicles detect each other, they can cooperate when passing through the intersection. Through V2V communication, the controlled vehicles can exchange information and cooperate to improve the efficiency of the entire intersection. In this case, the decision-making process can be described as a cooperative game. Define the joint state vector Φ = [X i ,Y i ,V i ,X j ,Y j ,V j ] Τ and control vector u = [a i ,a j ] Τ As an extended state space and control space.

[0096] The system dynamic equation is:

[0097]

[0098] Here, each vehicle considers maximizing the common benefit with the other vehicle, that is, minimizing the total time for the two vehicles to pass the intersection collision point while ensuring safety and comfort. This problem can be expressed in the framework of differential games and transformed into a problem of minimizing the joint cost function. Considering the dynamic state of the vehicle (Formula 10), under the condition of given initial driving information, the optimal control U can be obtained by minimizing the joint prediction cost J, and its cost function form is:

[0099]

[0100] The cooperation cost in formula (11) indicates that the goal of the cooperative vehicles is to minimize the joint cost function, which consists of the safety, efficiency, balance and control costs of all vehicles. In this cooperative scenario, the Nash feedback equilibrium strategy of each participant is determined by the following formula:

[0101] J[Φ,u * ,Φ(t 0 )]≤J[Φ,u,Φ(t 0 )]. (12)

[0102] Step S4:

[0103] The optimization algorithm is based on the Pontryagin Maximum Principle (PMP). First, consider the objective function (Formula 6) and the system dynamics equation (Formula 1) to define the Hamiltonian H as

[0104]

[0105] Where λ is the accompanying variable. In order to minimize the objective function (Formula 6), the following two necessary conditions must be met:

[0106]

[0107]

[0108] Based on PMP and u * =argmin u H[Φ,u,λ,t,Φ(t 0 )], where u represents a feasible solution that satisfies the constraints (Formula 5)

[0109] These conditions make the optimal control input a function of the system state and the adjoint state. In addition, it can be seen from the necessary conditions that the adjoint variable must satisfy the following dynamic equation:

[0110]

[0111] For non-cooperative games, using the above solution method based on the Pontryagin Maximum Principle (PMP), combined with the performance objective function (Formula 6) and system dynamics (Formula 1), the optimal acceleration control law of the vehicle under the non-cooperative control strategy can be obtained by the following equation:

[0112]

[0113] Among them, λ vi Indicates speed V iThe scenario considered in the present invention is a straight road, and the coordinate system is constructed with the collision point as the origin. When the vehicle does not deviate from the current driving direction, one component of the state vector is always zero, so the speed vector of the vehicle in one direction is also always zero. When vehicle i is traveling in the horizontal direction, the marginal cost λ of the longitudinal position in the simplified system vi is 0. Similarly, if vehicle i is traveling in the vertical direction, the marginal cost of the lateral position in the simplified system is is 0. Therefore, the controller's adjoint variable dynamic equation satisfies the following differential equation:

[0114]

[0115]

[0116] The above equations (17-19) can be effectively solved by numerical iteration algorithm. By solving the state and adjoint state dynamic equations, the optimal acceleration u and state trajectory can be obtained.

[0117] For cooperative games, as for non-cooperative games, the initial conditions and constraints of state variables and control variables in cooperative games are the same. Considering the objective function (11) and the system dynamics equation (10), the optimal acceleration control law of each vehicle under the cooperative game control strategy can be obtained by solving the following equation:

[0118]

[0119]

[0120] It can be seen that the optimal acceleration of the cooperative vehicle is similar to that of the non-cooperative vehicle. For cooperative control of connected autonomous vehicles (CAVs), the control derivation of acceleration is the same as that of non-cooperative games. The adjoint state dynamic equations can be solved by referring to equations (18) and (19), and the case of non-cooperative games is determined in the same way. It should be noted that cooperative games are a dynamic game model that coordinates the behaviors of connected vehicles (also called participants) to seek the optimal strategy to minimize the joint cost (11). The cooperative equations also show the interdependence of vehicle control decisions, because the prediction cost is determined by the acceleration and state trajectory of each vehicle. The only difference lies in the calculation method of the prediction cost. In non-cooperative games, the prediction costs of autonomous vehicles are calculated independently, while the control outputs of competing vehicles are regarded as known variables and obtained by the V2V system from the driving information at the previous sampling time.

[0121] When the present invention is specifically implemented:

[0122] An intelligent control strategy for two vehicles approaching an intersection without traffic lights from different directions, hoping that the vehicles can pass the intersection as quickly as possible while avoiding collision with the other vehicle. Figure 2 As shown in the figure, when the vehicles are driving on a one-way street and cannot change lanes. Each vehicle crosses the intersection in a straight line from a predetermined direction. The blue arrows represent the predetermined paths, and the red dots represent the collision points where the vehicles may collide. After entering the intersection, the vehicles can detect and share instantaneous driving information (such as the position, speed, and acceleration of adjacent vehicles) with each other using vehicle-to-vehicle (V2V) communication technology. To illustrate the control model, the following usage conditions are proposed:

[0123] (1) All vehicles are equipped with a V2V system to obtain the driving characteristics of other vehicles, which lays the foundation for the establishment of a game theory model.

[0124] (2) Provide perfect wireless communication between vehicles without information loss and communication delay.

[0125] Based on these situations, the control system of each vehicle evaluates its driving safety and then decides its control strategy by considering the feedback and response of the other vehicle. With the help of V2V communication technology, the two vehicles may implement different strategies. On the one hand, they regard their driving behavior as a non-cooperative game and act independently. On the other hand, the two vehicles coordinate and cooperate to pass the intersection, forming a cooperative game.

[0126] In order to verify the performance of the proposed method, the present invention conducted several simulation experiments in the above scenarios to demonstrate the basic working principle of the method and the effectiveness of the controller behavior.

[0127] consider Figure 2 When entering an unsignalized intersection and detecting a potential conflicting vehicle, the two vehicles detect each other's driving information.

[0128] Table I Initial driving information

[0129]

[0130]

[0131] The initial conditions of each vehicle are shown in Table I. First, the present invention tests the control effect of the non-cooperative game.

[0132] The vehicle is expected to accelerate when entering an unsignalized intersection and return to the vehicle's expected speed Vd after passing the intersection.

[0133] In the non-cooperative game model, the specific form of the driving cost function of each agent is as follows:

[0134] f 1(Φ(t),u(t),t)=a 1 G(Φ i ,Φ j ,u)+a 2 TP(Φ i )+a 3 (V d -V i ) 2 +a 4 (u) 2

[0135] f 2 (Φ(t),u(t),t)=a 1 G(Φ i ,Φ j ,u)+a 2 TP(Φ i )+a 3 (V d -V i ) 2 +a 4 (u) 2

[0136] In the cooperative game model, the driving cost function of each agent is as follows:

[0137]

[0138]

[0139] However, some cost items do not need to be included when leaving an intersection. Therefore, the cost functions for entering and leaving an intersection are different, which can be achieved by adjusting the weight coefficients. The coefficient values ​​are shown in Table II.

[0140] Table II Related parameter values

[0141]

[0142] In this experiment, both vehicles travel at the same speed and are at the same distance from the conflict point. If vehicle A and vehicle B are non-cooperative controllers, the best case scenario for vehicle A and vehicle B is to accelerate immediately and pass through the intersection at the fastest speed. Considering this situation, since the initial speed of vehicle B is larger, the response of vehicle B is to obtain a smaller acceleration and avoid accelerating through the intersection when colliding with vehicle A.

[0143] In this case, the speeds of the two vehicles are Figure 3As shown in the figure. If vehicle B makes the same decision as vehicle A, there is a risk of collision. This situation is worse and will result in higher costs. Therefore, vehicle B accelerates moderately, making its speed lower than vehicle A and letting vehicle A pass first. When vehicle B exits the intersection, it accelerates quickly and passes behind vehicle A, and both vehicles eventually return to their expected speed.

[0144] When two vehicles adopt a cooperative controller, they seek a coordinated strategy to minimize the joint cost, which is the collective optimal solution. Therefore, when vehicle B passes first, which makes the cost lower, vehicle B will immediately use a larger acceleration to accelerate, laying the foundation for passing before vehicle A. Since the vehicle speed limit has not reached the maximum value, both vehicles are in acceleration mode, and the time to pass the intersection is shortened. Compared with vehicle A in the non-cooperative controller, the passing time of vehicle A increased from 7.80 seconds to 8.90 seconds. This is because both vehicles in the non-cooperative controller choose to accelerate, while vehicle A is very close and will pass through the intersection at full speed after reaching the maximum speed. Vehicle B can only evade to avoid collision. The cooperative controller found the best result for the two vehicles. The speeds of the two vehicles and the distance between the two vehicles are as follows Figure 4 As shown, the joint cost is the lowest. It can be seen that the speed change is not drastic, which proves that the driving process of the vehicle is more comfortable.

[0145] Table III Crossover time under different conditions

[0146]

[0147] Wang et al. studied cooperative and non-cooperative games at unsignalized intersections and established a Nash game with a discrete decision strategy to describe the discrete decision method in non-cooperative behavior. The generated vehicle speed information is also simulated. Figure 5 As shown. In this case, vehicle A adopted a dominant strategy, accelerating to the maximum speed and maintaining that speed. Vehicle B made concessions and eventually passed the intersection. The total time to pass the intersection is compared with the method proposed in the present invention, as shown in Table III. The time required for the method proposed in the present invention to pass the unsignaled intersection is much less than the discrete decision-making method. After experimental measurement, the distance between the two vehicles is always greater than the sum of the safety radii of the two vehicles, which confirms the safety of the vehicle driving process. While ensuring safety, the running time of the non-cooperative controller is reduced by 21.83%, and the running time of the cooperative controller is further reduced by 23.18%.

[0148] The present invention proposes to use a dynamic differential game method to study the driving strategies of two vehicles passing through an unsignalized intersection, where the vehicles can act as independent individuals or in a collaborative manner. A differential game model is established to describe the competition and cooperation between vehicles. A control method based on optimal control is proposed. Compared with the discrete decision-making method, this method improves traffic efficiency while ensuring safety and comfort. The present invention uses simulation experiments to demonstrate the effectiveness of the method. In view of the development of CAV, this method has great potential, but there are also some limitations. First, the present invention can consider more complex traffic scenarios, including multi-lane intersections, which are most cases in the real world. Second, the present invention has stable and interference-free V2V communication without any information loss or delay. In the future, the model of the present invention can be extended to consider random interference in V2V communication at non-signalized intersections.

[0149] The present invention and its embodiments are described above, and such description is not restrictive. The drawings show only one embodiment of the present invention, and the actual structure is not limited thereto. In short, if ordinary technicians in the field are inspired by it, without departing from the purpose of the invention, they can design a structure and embodiment similar to the technical solution without creativity, which should belong to the protection scope of the present invention.

Claims

1. A vehicle collision avoidance strategy method for unsignalized intersections based on differential game, characterized by: The following steps are involved: Step S1: Establish vehicle communication model and path planning to achieve information sharing between vehicles; Step S2: design a non-cooperative game model, establish the dynamic equation of the vehicle, and determine the acceleration control strategy; Step S3: Design a cooperative game model to describe the driving decisions of the vehicles and minimize the total time for the two vehicles to pass through the intersection; Step S4: solving the optimal control strategy based on step S2 and step S3 to obtain the optimal feedback control strategy; Step S5: Perform numerical simulation and simulation verification to improve driving safety.

2. The method for avoiding collisions at unsignalized intersections based on differential game according to claim 1, characterized in that: The step S1 includes using V2V communication technology to achieve information sharing between vehicles, wherein the information includes obtaining the instant position, speed and acceleration of adjacent vehicles; The future motion state model of the vehicle is: Where: i and j are two vehicle participants, and the continuous state vector is defined for the controlled vehicle i Where X i ,Y i represents the lateral and longitudinal positions of vehicle i, V i represents the speed of vehicle i, and defines the control vector u(u=a i ) is the acceleration of vehicle i, and the magnitude of i is related to the radius parameter T i >0 correlation.

3. A vehicle collision avoidance strategy method at an unsignalized intersection based on differential game according to claim 2, characterized in that: The step S2 also includes considering the vehicle operation cost function: safety cost, efficiency cost, speed stability cost and control cost; The non-cooperative game model includes determining vehicle i as the object, considering another vehicle as a competitor, and obtaining the time from time t0 to time t by minimizing the prediction cost J. f The optimal control vector u is: in: Limited by: Condition one: V i ∈[0,V max ] Condition two: a i ∈[a min ,a max ]; Where f represents the operating cost, condition 1 stipulates that the vehicle's speed is non-negative throughout the time period, and condition 2 stipulates that the vehicle's acceleration is limited to the range; The driving cost function is defined as: f(Φ(t),u(t),t)=a1G(Φ i ,F j ,u)+a2TP(Φ i )+a3(V d -V i ) 2 +a4(u) 2 ; Where: V d is the expected speed of the vehicle on the current road, P i is the position of vehicle i (X i ,Y i ), a1, a2, a3, a4 are weighted coefficients, TP is the efficiency cost, G(Φ i ,Φ j ,u) is the security cost function.

4. The vehicle collision avoidance strategy method at an unsignalized intersection based on differential game according to claim 3 is characterized by: The time required for the vehicle i to travel to the collision point under the current driving information is: The collision penalty between vehicle i and vehicle j at the collision point is: Determine the Nash feedback equilibrium strategy of each participant, that is, the strategy set satisfy:

5. The vehicle collision avoidance strategy method at an unsignalized intersection based on differential game according to claim 4 is characterized by: The step S3 also includes designing a joint state vector and a control vector to describe the driving decision of each vehicle, determining the goal to maximize the common benefit, and constructing a joint cost function including the safety cost, efficiency cost, stability cost and control cost of each vehicle; Specifically, define the joint state vector Φ = [X i ,Y i ,V i ,X j ,Y j ,V j ] Τ and control vector u = [a i ,a j ] Τ As an extended state space and control space; The system dynamic equation is: By minimizing the joint prediction cost J, the optimal control U is obtained, and the function form is: The Nash feedback equilibrium strategy of each participant is: J[Φ,u * ,Φ(t0)]≤J[Φ,u,Φ(t0)]。 6. The vehicle collision avoidance strategy method at an unsignalized intersection based on differential game according to claim 5, characterized in that: The step 4 includes determining the optimal acceleration control law of the non-cooperative game and the cooperative game based on the Pontryagin maximum principle, establishing and solving the state and adjoint state dynamic equations of the vehicle, and obtaining the optimal feedback control strategy to minimize the cost function of the vehicle; Including: Considering the driving cost function and system dynamics equation in the non-cooperative game model to define the Hamiltonian H as: Among them, λ is the accompanying variable; When minimizing the objective function: Based on the Pontryagin maximum principle and u * =argmin u Solve H[Φ,u,λ,t,Φ(t0)], where u represents a feasible solution that satisfies constraint 2; The adjoint state dynamic equation is: The optimal acceleration control law of the vehicle under the non-cooperative control strategy: The controller's adjoint variable dynamic equation satisfies the following differential equation: The optimal acceleration u and state trajectory are effectively solved through numerical iterative algorithms; The optimal acceleration control law of the vehicle under the non-cooperative control strategy:

7. A vehicle collision avoidance strategy method for unsignalized intersections based on differential game according to any one of claims 1 to 6, characterized in that: The step S5 includes verifying the traffic efficiency and safety of vehicles at intersections without signal lights under different scenarios through simulation; In the non-cooperative game model, the specific form of the driving cost function is as follows: f1(Φ(t),u(t),t)=a1G(Φ i ,F j ,u)+a2TP(Φ i )+a3(V d -V i ) 2 +a4(u) 2 f2(Φ(t),u(t),t)=a1G(Φ i ,F j ,u)+a2TP(Φ i )+a3(V d -V i ) 2 +a4(u) 2 In the cooperative game model, the specific form of the driving cost function is as follows: f2(Φ(t),u(t),t)=∑ c＝i,j α1G(Φ c ,F c-1 ,u)+α2TP(Φ i )+α3(V d -V c ) 2 +α4(u) 2 。

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