Non-signalized intersection mixed vehicle group cooperative passing method based on information dynamic game

Abstract

The invention relates to a non-signalized intersection mixed vehicle group cooperative passing method based on an information dynamic game, and belongs to the technical field of intelligent traffic. The method comprises the following steps: constructing an urban non-signalized intersection mixed traffic scene, and dividing a non-signalized intersection area; according to the divided non-signalized intersection area and the obtained heterogeneous vehicle information difference, a mixed vehicle group subgroup division scheme is established, and a mixed vehicle group information dynamic game joint judgment rule is established; respectively establishing heterogeneous vehicle longitudinal kinematics models, establishing a hybrid vehicle group game priority collaborative decision-making mechanism, and constructing a hybrid vehicle group collaborative driving revenue function; and then a hybrid vehicle group driving strategy is optimized through the Stackelberg equilibrium theory, and the optimal control input with the hybrid vehicle group cooperative driving income maximization as the target is obtained through a reverse induction method. For a non-signalized intersection mixed traffic scene, the method can effectively ensure that vehicles safely, orderly and quickly pass through, and the passing efficiency is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of intelligent transportation, and relates to a method for coordinated passage of mixed-traffic vehicle groups at an unsignalized intersection based on information dynamic game. Background Art

[0002] In the context of the development of intelligent driving technology towards the deep integration of intelligence and networking, connected autonomous vehicles, as the pioneers of this trend, are gradually showing their unique advantages in complex traffic environments. With their excellent environmental perception capabilities, connected autonomous vehicles can obtain surrounding traffic information in real time and accurately through hardware devices such as laser radar, cameras, and ultrasonic sensors; at the same time, their efficient information processing mechanism, combined with advanced algorithms and cloud computing platforms, can quickly analyze and make decisions; and precise control execution strategies ensure the safety and smooth driving of vehicles under various road conditions.

[0003] However, with the continuous advancement of intelligent driving technology, the future traffic environment will gradually evolve towards heterogeneity. This trend means that connected autonomous vehicles and traditional human drivers will form a complex mixed traffic scenario. This mixed traffic scenario not only includes different types of vehicles, but also involves drivers with different driving habits and reaction speeds, as well as constantly changing traffic rules and road conditions.

[0004] At unsignalized intersections, the collaborative decision-making and control of vehicles has become a research hotspot that needs to be solved urgently. At unsignalized intersections, the collaborative decision-making and control between connected autonomous vehicles and traditional human drivers is a huge challenge. Connected autonomous vehicles rely on advanced sensors, communication technologies, and algorithms to make decisions, while traditional human drivers rely on the driver's observation, judgment, and reaction. There are significant differences between the two in terms of decision-making speed, accuracy, and information sharing, which makes it difficult to form an effective collaborative mechanism. For example, when a connected autonomous vehicle detects an impending collision risk and attempts to slow down or avoid it, a traditional human driver may not be able to respond in time due to the driver's delayed response or misjudgment, thereby increasing the risk of an accident.

[0005] Existing research on collaborative decision-making and control of vehicles at unsignalized intersections mostly focuses on the traffic environment of purely connected automated vehicles. These studies usually assume that all vehicles are highly intelligent and networked, can share traffic information in real time, and make collaborative decisions based on unified rules and algorithms. However, in real mixed traffic scenarios, this assumption is obviously not true. Traditional human drivers cannot obtain information about surrounding vehicles in real time due to the lack of networking capabilities, nor can they make decisions based on unified algorithms. Therefore, existing collaborative decision-making and control methods are difficult to directly apply to mixed traffic scenarios. Summary of the invention

[0006] In view of this, the purpose of the present invention is to provide a collaborative passing method for mixed vehicle groups at unsignalized intersections based on information dynamic game, aiming to solve the dilemma that existing collaborative decision-making and control methods are difficult to be directly applied to the mixed traffic scenario at unsignalized intersections.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] A collaborative passing method for mixed vehicle groups at unsignalized intersections based on information dynamic game, the method comprising the following steps:

[0009] Construct a mixed traffic scenario for urban unsignalized intersections, divide the vehicle group clustering area, vehicle speed planning area and vehicle merging area for the unsignalized intersection area, and represent the potential conflict area in the vehicle merging area;

[0010] According to the divided unsignalized intersection area and the obtained differences in heterogeneous vehicle information, establish a subgroup division scheme for the mixed vehicle group, and establish a joint determination rule for information dynamic game of the mixed vehicle group in the vehicle speed planning area;

[0011] Establish longitudinal kinematic models for heterogeneous vehicles respectively, establish a collaborative decision-making mechanism for game priorities of the mixed vehicle group in the unsignalized intersection area, and construct a collaborative driving revenue function for the mixed vehicle group that combines driving safety, comfort, efficiency and economy;

[0012] Based on the collaborative decision-making mechanism for game priorities of the mixed vehicle group and the collaborative driving revenue function, optimize the driving strategy of the mixed vehicle group through the Stackelberg equilibrium theory, and use the backward induction method to obtain the optimal control input aiming at maximizing the collaborative driving revenue of the mixed vehicle group.

[0013] Furthermore, the process of constructing a mixed traffic scenario for urban unsignalized intersections includes:

[0014] Set a number of lanes in each driving direction, which at least include a left-turn lane, a straight-through lane and a right-turn lane, and all lanes drive according to the corresponding lanes; the construction of the mixed traffic scenario can be adjusted accordingly according to the specific situation of the actual unsignalized intersection;

[0015] Roadside sensors are installed on both sides of the road to collect the state information of all vehicles on the road. Among them, connected autonomous vehicles obtain the state information of other connected autonomous vehicles through vehicle-to-vehicle communication, and obtain the state information of other traditional human-driven vehicles through vehicle-to-road communication;

[0016] Traditional human-driven vehicles rely on the driver's perception to obtain the state information of the vehicle immediately in front of them;

[0017] The area of the unsignalized intersection is divided into a vehicle group clustering area, a vehicle speed planning area, and a vehicle merging area; the mixed vehicle groups will enter at the initial speed. All three areas are squares centered on the unsignalized intersection. Among them, the side length of the vehicle group clustering area is f meters, which is used for dividing and sorting the mixed vehicle groups; the side length of the vehicle speed planning area is g meters, which is used for the dynamic game of the mixed vehicle groups; the side length of the vehicle speed merging area is h meters, which is used for the mixed vehicle groups to pass through the unsignalized intersection orderly with the optimal acceleration obtained through the game, and f > g > h > 0;

[0018] In the vehicle merging area, the intersection points of different vehicle driving trajectories are represented as potential conflict areas where collisions may occur.

[0019] Furthermore, for the vehicle group subgroup division scheme, it includes: the mixed vehicle groups in the vehicle group clustering area consist of connected automated vehicles as leading vehicles and traditional human-driven vehicles as following vehicles. When a vehicle v on the left-turn or straight-through lane enters the vehicle group clustering area, if the vehicle is a connected automated vehicle, the vehicle is divided into the next mixed vehicle group as the head vehicle; if the vehicle is a traditional human-driven vehicle, the vehicle is divided into the previous mixed vehicle group as the following vehicle. Among them, the head vehicle in the mixed vehicle group can obtain the state information of other vehicles in the same vehicle group.

[0020] Furthermore, the joint decision-making rules for the mixed vehicle groups participating in the game in the vehicle speed planning area include a distance decision-making rule and a time window prediction decision-making rule. Among them,

[0021] According to the distance relationship between the game problem of the mixed vehicle groups and the vehicle speed planning area of the unsignalized intersection, the distance decision-making rule is defined:

[0022]

[0023] In the formula, is the abscissa or ordinate of the set entry position of the vehicle speed planning area of the unsignalized intersection, is the abscissa or ordinate of the last conflict area in the road trajectory where the mixed vehicle group is located, is the abscissa or ordinate of the position of the head vehicle of the l-th mixed vehicle group at time t, where The abscissa values are compared on the roads in the east-west direction, and the ordinate values are compared on the roads in the north-south direction; * is north, south, west, or east; representing different orientations of the intersection, # is lt or s, representing the left-turn or straight-through lane; the subscript "0" represents the head vehicle of the mixed vehicle group;

[0024] By predicting the time window relationship of the corresponding mixed vehicle group passing through the same conflict area at time t, the time window prediction decision-making rule is defined:

[0025]

[0026] In the formula, is the time prediction window for the mixed vehicle group l to pass through the conflict area, where is the predicted time for the leading vehicle of the mixed vehicle group l to reach the conflict area, is the predicted time for the trailing vehicle of the mixed vehicle group l to pass through the conflict area, is the time prediction window for the mixed vehicle group k to pass through the conflict area, represents the situation where the mixed vehicle group l and the mixed vehicle group k will collide in the conflict area. The symbol || represents the logical relationship "or", T gap,l,k is the time interval between the former passing through the conflict area and the latter reaching the conflict area when the time prediction windows of the two mixed vehicle groups do not overlap, T safe is the safety time interval, T gap,l,k ≤T safe represents the situation where the two mixed vehicle groups do not collide, but the time interval for passing through the conflict area is less than the safety time interval;

[0027] According to the distance determination rule and the time window prediction determination rule, define the joint determination rule for the mixed vehicle group to participate in the game:

[0028] Mar game = Mar d &&Mar t

[0029] In the formula, "&&" represents the logical relationship "and". When Mar d and Mar t are both 1, it means that the mixed vehicle group will participate in the game.

[0030] Furthermore, in the defined time window determination rule, T gap,l,k The expressions of are as follows:

[0031]

[0032] In the formula, s confilct,# is the distance from the conflict area to the lane where the mixed vehicle group l is located, is the position of the stop line of the vehicles in this lane, is the speed of the leading vehicle of the mixed vehicle group l at time t, is the length of the vehicle group of the mixed vehicle group l at time t, is the speed of the trailing vehicle of the mixed vehicle group l at time t, N is the number of vehicles in the mixed vehicle group l, is the length of the leading vehicle, is the distance between the i-th following vehicle and the (i - 1)-th vehicle in the mixed vehicle group l. The (i - 1)-th vehicle is also the immediate preceding vehicle of the i-th following vehicle.

[0033] Furthermore, in the established heterogeneous vehicle longitudinal kinematic model, the expression of the connected and automated vehicle (CAV) longitudinal kinematic model is as follows:

[0034]

[0035] In the formula, represents the speed of the connected and automated vehicle (CAV) c in the mixed traffic flow group l at time t, represents the abscissa or ordinate of the position of the connected and automated vehicle (CAV) c in the mixed traffic flow group l at time t; represents the acceleration of the connected and automated vehicle (CAV) c in the mixed traffic flow group l at time t; represents the control input of the connected and automated vehicle (CAV) at time t; represents the derivative of the speed of the connected and automated vehicle (CAV) c in the mixed traffic flow group l at time t;

[0036] The expression of the traditional human-driven vehicle longitudinal kinematic model is as follows:

[0037]

[0038] In the formula, represents the speed of the traditional human-driven vehicle (HV) h in the mixed traffic flow group l at time t, represents the abscissa or ordinate of the position of the traditional human-driven vehicle (HV) h in the mixed traffic flow group l at time t; represents the acceleration of the traditional human-driven vehicle (HV) h in the mixed traffic flow group l at time t; represents the derivative of the speed of the traditional human-driven vehicle (HV) h in the mixed traffic flow group l at time t;

[0039] In the established game priority collaborative decision-making mechanism for the mixed traffic flow group, if then the mixed traffic flow group l has a higher driving priority than the mixed traffic flow group k;

[0040] During the driving process, the following vehicles in the mixed traffic flow group rely on human drivers for control, and the corresponding car-following model expression is as follows:

[0041]

[0042] In the formula, α, β, and γ are all gain coefficients, d des is the desired headway, is the acceleration of vehicle i - 1 at the previous time step T; is the acceleration of vehicle i at the previous time step T; the subscripts "i" and "i - 1" respectively represent the i-th and (i - 1)-th vehicles in the mixed traffic flow group l.

[0043] Furthermore, for the collaborative driving revenue function of the mixed vehicle group, ensure that the mixed vehicle group participating in the game can drive at the optimal speed in each game time period. Considering the actual driving needs, it is established from the aspects of driving safety, driving comfort, driving efficiency, and driving economy, including the following contents:

[0044] Regarding safety, establish an anti-collision constraint, that is, before the high-priority mixed vehicle group completely passes through the conflict area, the low-priority mixed vehicle group cannot enter the conflict area, and define the time when the low-priority mixed vehicle group arrives at the conflict area during the game process That is, the time when the leading vehicle arrives at the conflict area, and the expression is as follows:

[0045]

[0046] In the formula, is the acceleration of the leading vehicle of the mixed vehicle group k at time t;

[0047] Define the time when the high-priority mixed vehicle group l completely passes through the conflict area That is, the time when the leading vehicle arrives at the conflict area, and the expression is as follows:

[0048]

[0049] In the formula, Δt correction is a correction constant;

[0050] The driving safety revenue function of the mixed vehicle group The expression is as follows:

[0051]

[0052] In the formula, N is the number of vehicles in the mixed vehicle group, ω i is the weight coefficient of vehicle i in the mixed vehicle group, is the safety time coefficient, and μ 1 、μ 2 are the safety distance coefficients, is the distance traveled by the leading vehicle of the mixed vehicle group k when the mixed vehicle group l completely passes through, d safe is the safe driving spacing between mixed vehicle groups;

[0053] Regarding comfort, the driving comfort revenue function of the mixed vehicle group l The expression is as follows:

[0054]

[0055] In the formula, a max is the maximum vehicle acceleration, a min is the minimum vehicle acceleration;

[0056] Regarding efficiency, the expression of the efficiency benefit function for the mixed vehicle group l is as follows:

[0057]

[0058] In the formula, η 1 , η 2 are weight coefficients, and η 1 + η 2 = 1, ε is an infinitesimal quantity; v des represents the expected speed of vehicle travel, and v max represents the maximum speed of vehicle travel;

[0059] Regarding economy, first establish the expression of the vehicle fuel consumption model, which is expressed as:

[0060]

[0061] In the formula, f c is the fuel consumption function of the vehicle traveling at a stable speed , and f a is the acceleration fuel consumption function of the vehicle when the speed is ; q 0 , q 1 , q 2 , q 3 , r 0 , r 1 , r 2 are all fuel consumption related coefficients;

[0062] Then the expression of the travel economy benefit function is as follows:

[0063]

[0064] Based on the above four benefit functions of the mixed vehicle group, the expression of the total benefit function of the mixed vehicle group is as follows:

[0065]

[0066] In the formula, ρ 1 , ρ 2 , ρ 3 , ρ 4 are the weight coefficients corresponding to the four benefit functions, and ρ 1 + ρ 2 + ρ 3 + ρ 4 = 1.

[0067] Furthermore, it is characterized in that: based on the collaborative decision-making mechanism of the mixed traffic flow group game priority and the collaborative driving revenue function, optimizing the driving strategy of the mixed traffic flow group by the Stackelberg equilibrium theory in the information dynamic game includes:

[0068] Based on the sequentiality of the dynamic game, the mixed traffic flow group with the highest priority can directly take the action with the maximum revenue based on the prediction of the actions of the mixed traffic flow groups in the subsequent corresponding conflict areas. It is:

[0069]

[0070] In the formula, is the action taken by the mixed traffic flow group l, is the set of actions of the mixed traffic flow group v when the mixed traffic flow group l takes the action ; the third subscript "1, 2, 3" respectively represents the priority order of the mixed traffic flow group in the current game time period.

[0071] The mixed traffic flow group with a lower priority predicts the actions of the mixed traffic flow groups in the subsequent corresponding conflict areas and takes the action with the maximum revenue under the condition that the mixed traffic flow group with a higher priority takes the optimal action.

[0072]

[0073] Regarding the driving behavior of the mixed traffic flow group seeking the maximum revenue as a Stackelberg equilibrium problem in the dynamic game, under the condition that the mixed traffic flow group with the highest priority has the maximum revenue, when the following conditions are met, the Stackelberg equilibrium is achieved:

[0074]

[0075] In the formula, m e is the driving behavior of the mixed traffic flow group with a lower priority, M follower is the set of driving behaviors of the mixed traffic flow group with a lower priority, m 1 is the driving behavior of the mixed traffic flow group with the highest priority, M 1 is the set of driving behaviors of the mixed traffic flow group with the highest priority.

[0076] Furthermore, the process of obtaining the optimal control input with the goal of maximizing the collaborative driving revenue of the mixed traffic flow group by using the backward induction method is as follows:

[0077] According to the priority order of the mixed traffic flow group, calculate the optimal acceleration solution starting from the mixed traffic flow group with the lowest priority in any branch Gradually rise to the optimal acceleration solution of the mixed traffic flow group with the highest priority Furthermore, solve the optimal acceleration solutions of all branch mixed traffic flow groups The calculation method adopts the receding horizon strategy, and the expression is as follows:

[0078]

[0079] where Z is the total length of the prediction horizon, λ is the gain coefficient, is the prediction of the total revenue at time step t + σT at time t, and the optimal control input of the leading vehicle of the mixed traffic flow at time t is obtained by solving the maximum revenue prediction.

[0080] In the present invention, the meanings of some parameters are as follows:

[0081] represents the abscissa or ordinate of the position of the i-th vehicle inside the mixed traffic flow group l in the * direction and lane # at time t. Specifically, the abscissa value is taken on the road in the east-west direction, and the ordinate value is taken on the road in the north-south direction. respectively represent the speed and acceleration of the vehicle at time t; where the superscript * is north, south, west or east, representing different directions of the intersection, l is the serial number of the mixed traffic flow group in the lane where it is located, i is the serial number of the vehicle inside the mixed traffic flow group, and # is lt or s, representing the left-turn or straight-through lane; represents the driving behavior adopted by the mixed traffic flow group l with priority h in the * direction and lane #, where the subscript "h" represents the priority serial number.

[0082] The beneficial effects of the present invention are as follows:

[0083] In the present invention, the connected and automated vehicle is used as the leading vehicle, and the traditional human-driven vehicle is used as the following vehicle to form a mixed traffic flow group. The optimal driving speed is obtained through the information dynamic game method. This approach makes full use of the leading and collaborative roles of the connected and automated vehicle, enabling the traditional human-driven vehicle to pass through the unsignalized intersection without conflict at an appropriate speed under the guidance of the connected and automated vehicle. This collaborative decision-making and control method not only improves the safety of the unsignalized intersection but also significantly enhances the traffic efficiency.

[0084] The present invention uniquely designs a dynamic game joint determination rule and a game priority mechanism from the perspective of the mixed traffic flow group. The emergence of this mechanism fills the gap in the field of collaborative decision-making of the mixed vehicle group in the prior art. Through the application of the dynamic game theory, the present invention can adjust the decision-making behaviors of each vehicle in real time and dynamically, ensuring that in a complex traffic environment, each vehicle can make an optimal decision according to the current road conditions, the behaviors of other vehicles, and its own driving goals. This ability of dynamic adjustment greatly improves the orderliness and safety of the mixed vehicle group passing through the unsignalized intersection.

[0085] The present invention comprehensively considers various requirements such as the driving safety, driving comfort, driving efficiency, and driving economy of a mixed vehicle group, and constructs a revenue function for the mixed vehicle group. By optimizing the revenue function of the mixed vehicle group, the present invention can find the optimal control input for the mixed vehicle group, that is, the optimal driving speed of each vehicle. This optimization method that comprehensively considers various factors makes the passage of the mixed vehicle group at an unsignalized intersection more efficient, economical, and comfortable.

[0086] Other advantages, objectives, and features of the present invention will be described to some extent in the subsequent specification, and to some extent, will be obvious to those skilled in the art based on the study of the following text, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the following specification. Brief Description of the Drawings

[0087] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be described in preferred detail below in conjunction with the drawings, where:

[0088] Figure 1 is a schematic diagram of the overall process of the coordinated passage method of a mixed vehicle group at an unsignalized intersection based on information dynamic game under the embodiment of the present invention;

[0089] Figure 2 is a schematic diagram of the traffic scenario at an unsignalized intersection under the embodiment of the present invention;

[0090] Figure 3 is a schematic diagram of the passage of a mixed vehicle group at an unsignalized intersection under the embodiment of the present invention;

[0091] Figure 4 is a schematic diagram of an example of the priority order of a vehicle group under the embodiment of the present invention. Detailed Embodiments

[0092] The following uses specific specific examples to illustrate the implementation manners of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific implementation manners. The details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the diagrams provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner. Without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0093] Among them, the attached drawings are only for illustrative purposes, showing only schematic diagrams rather than actual physical diagrams, and should not be construed as a limitation to the present invention; for better illustration of the embodiments of the present invention, some components in the attached drawings will be omitted, enlarged or reduced, which do not represent the dimensions of the actual product; for those skilled in the art, it is understandable that some well-known structures and their descriptions in the attached drawings may be omitted.

[0094] In the attached drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "rear", etc. indicating the orientation or positional relationship, they are based on the orientation or positional relationship shown in the attached drawings. This is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the terms describing the positional relationship in the attached drawings are only for illustrative purposes and should not be construed as a limitation to the present invention. For those of ordinary skill in the art, the specific meanings of the above terms can be understood according to specific circumstances.

[0095] Please refer to Figures 1 to 4 , which is a method for coordinated passing of a mixed vehicle group at an unsignalized intersection based on information dynamic game.

[0096] Taking into account the leading and coordinating roles of connected and automated vehicles, the present invention can use connected and automated vehicles as the leading vehicle and traditional human-driven vehicles as the following vehicles to form a mixed vehicle group. Through the information dynamic game method in the form of a vehicle group, and comprehensively considering the safety, driving efficiency, comfort and fuel economy requirements of the vehicle group to obtain the optimal driving speed, so as to guide traditional human-driven vehicles to pass through the unsignalized intersection without conflict at a suitable speed, improving the safety and passing efficiency of the unsignalized intersection.

[0097] Embodiment

[0098] This embodiment provides a detailed process of a method for coordinated passing of a mixed vehicle group at an unsignalized intersection based on information dynamic game, as shown in Figure 1 the overall process schematic diagram of the method for coordinated passing of a mixed vehicle group at an unsignalized intersection based on information dynamic game, which includes the following steps:

[0099] S1. Establish a mixed traffic scenario at an urban intersection without signal control, that is, a mixed traffic scenario at an unsignalized intersection, and divide the area near the unsignalized intersection into a vehicle group sub-division area, a vehicle speed planning area and a vehicle merging area;

[0100] Specifically, in step S1 of this embodiment, the following sub-steps are further included:

[0101] S11. Establish a mixed traffic scenario at an urban unsignalized intersection. In this scenario, several lanes are set in each driving direction, including at least a left-turn lane, a straight-through lane, and a right-turn lane, and all vehicles drive in accordance with the corresponding lanes. As shown in Figure 2 the schematic diagram of the traffic scenario at the unsignalized intersection in this embodiment. There are six lanes in each direction, including two left-turn lanes, straight-through lanes, and right-turn lanes in opposite directions, that is, three lanes are set in each driving direction, including one left-turn lane, one straight-through lane, and one right-turn lane. The construction of the mixed traffic scenario can be adjusted accordingly according to the specific conditions of the actual unsignalized intersection.

[0102] Roadside sensors are installed on both sides of the road to collect the status information of all vehicles on the road. Among them, connected automated vehicles can obtain the status information of other connected automated vehicles through vehicle-to-vehicle communication, and obtain the status information of other traditional human-driven vehicles through vehicle-to-road communication. Traditional human-driven vehicles rely on the driver's perception to obtain the status information of the vehicle immediately in front of them. Based on this, the unsignalized intersection and its nearby areas are divided into a vehicle group clustering area, a vehicle speed planning area, and a vehicle merging area. The mixed vehicle group will enter at an initial speed. All three areas are squares centered on the unsignalized intersection. The side length of the vehicle group clustering area is f meters, which is used for dividing and sorting the mixed vehicle group; the side length of the vehicle speed planning area is g meters, which is used for the dynamic game of the mixed vehicle group; the side length of the vehicle speed merging area is h meters, which is used for the mixed vehicle group to pass through the unsignalized intersection orderly with the optimal acceleration obtained from the game, and f > g > h > 0.

[0103] S12. Represent the intersection points of different vehicle driving trajectories in the vehicle merging area as potential conflict areas where collisions may occur. This is because vehicles on the left-turn lane and the straight-through lane may pose a potential collision threat to other vehicles in the left-turn and straight-through directions when passing through the unsignalized intersection.

[0104] S2. According to the area division rules and the differences in heterogeneous vehicle information acquisition in step S1, design a subgroup division scheme for the mixed vehicle group applicable to the clustering area, and a joint decision rule for the dynamic game of the mixed vehicle group information applicable to the vehicle speed planning area. The steps are as follows:

[0105] The mixed vehicle group in the vehicle group clustering area consists of a connected automated vehicle as the leading vehicle and a traditional human-driven vehicle as the following vehicle. When a vehicle v on the left-turn or straight-through lane enters the vehicle group clustering area, if the vehicle is a connected automated vehicle, the vehicle is divided into the next mixed vehicle group as the head vehicle. If the vehicle is a traditional human-driven vehicle, the vehicle is divided into the previous mixed vehicle group as the following vehicle. The head vehicle in the mixed vehicle group can obtain the status information of other vehicles in the same vehicle group.

[0106] S22. To determine the mixed vehicle platoons participating in the game, comprehensively considering the position of the mixed vehicle platoons, the time when the mixed vehicle platoons and the corresponding conflicting vehicle platoons reach the conflict area, and the principle of the game problem, a joint determination rule for the mixed vehicle platoons participating in the game within the vehicle speed planning area is defined. Among them, the joint determination rule includes a distance determination rule and a time window prediction determination rule. The specific content is as follows:

[0107] (1) According to the distance relationship between the game problem of the mixed vehicle platoons and the vehicle speed planning area of the unsignalized intersection, a distance determination rule is defined:

[0108]

[0109] In the formula, is the abscissa or ordinate of the set entry position of the vehicle speed planning area of the unsignalized intersection, is the abscissa or ordinate of the last conflict area in the road trajectory where the mixed vehicle platoon is located, is the abscissa or ordinate of the position of the leading vehicle of the l-th mixed vehicle platoon at time t, where The abscissa value is taken for comparison on the east-west oriented roads, and the ordinate value is taken for comparison on the north-south oriented roads. * is north, south, west or east, representing different orientations of the intersection, and # is lt or s, representing the left-turn or straight-through lane.

[0110] (2) By predicting the time window relationship of the corresponding mixed vehicle platoon passing through the same conflict area at time t, a time window prediction determination rule is defined:

[0111]

[0112] In the formula, is the time prediction window for the mixed vehicle platoon l to pass through the conflict area, where is the predicted time for the leading vehicle of the mixed vehicle platoon l to reach the conflict area, is the predicted time for the trailing vehicle of the mixed vehicle platoon l to pass through the conflict area, is the time prediction window for the mixed vehicle platoon k to pass through the conflict area, represents the situation where the mixed vehicle platoon l and the mixed vehicle platoon k will collide in the conflict area. The symbol || represents the logical relationship "or", T gap,l,k is the time interval between the former passing through the conflict area and the latter reaching the conflict area when the time prediction windows of the two mixed vehicle platoons do not overlap, T safe is the safety time interval, T gap,l,k ≤T safe represents the situation where the two mixed vehicle platoons do not collide, but the time interval for passing through the conflict area is less than the safety time interval, T gap,l,k The expression of T is as follows:

[0113]

[0114] In the formula, s confilct,# is the distance from the conflict area to the lane where the mixed traffic flow group l is located, is the position of the stop line of the vehicles in this lane, is the speed of the leading vehicle of the mixed traffic flow group l at time t, is the length of the vehicle group of the mixed traffic flow group l at time t, is the speed of the trailing vehicle of the mixed traffic flow group l at time t, N is the number of vehicles in the mixed traffic flow group l, is the length of the leading vehicle, is the distance between the following vehicle and the vehicle in front of it;

[0115] (3) According to the distance determination rule and the time window prediction determination rule, define the joint determination rule for the mixed traffic flow group to participate in the game:

[0116] Mar game = Mar d &&Mar t

[0117] In the formula, "&&" represents the logical relationship "and". When both Mar d and Mar t are 1, the mixed traffic flow group will participate in the game and dynamically adjust the vehicle speed to meet the road traffic demand.

[0118] S3. According to step S2, establish a heterogeneous vehicle longitudinal kinematic model, design a cooperative decision-making mechanism for the priority of the mixed traffic flow group in the area of unsignalized intersections, and construct a cooperative driving revenue function for the mixed traffic flow group in combination with the requirements of driving safety, driving comfort, driving efficiency and driving economy. The steps are as follows:

[0119] S31. Since the connected automated vehicle and the traditional human-driven vehicle have different driving characteristics, the expression of the longitudinal kinematic model of the connected automated vehicle is as follows:

[0120]

[0121] In the formula, represents the speed of the connected automated vehicle cav in the mixed traffic flow group l at time t, represents the abscissa or ordinate of the position of the connected automated vehicle cav in the mixed traffic flow group l at time t; represents the acceleration of the connected automated vehicle cav in the mixed traffic flow group l at time t; represents the control input of the connected automated vehicle cav at time t; represents the derivative of the speed of the connected automated vehicle cav in the mixed traffic flow group l at time t.

[0122] The expression of the longitudinal kinematic model of traditional human-driven vehicles is as follows:

[0123]

[0124] In the formula, represents the speed of the traditional human-driven vehicle hv in the mixed vehicle group l at time t, represents the speed of the traditional human-driven vehicle hv in the mixed vehicle group l at time t; represents the acceleration of the traditional human-driven vehicle hv in the mixed vehicle group l at time t; represents the derivative of the speed of the traditional human-driven vehicle hv in the mixed vehicle group l at time t.

[0125] S32. According to the time when the mixed vehicle group arrives at the conflict area defined in step S2, determine the game priority order of the mixed vehicle group in each game time period. If it means that the mixed vehicle group l arrives at the conflict area earlier, so it has a higher right of way to drive compared to the mixed vehicle group k. Therefore, it is beneficial to adopt a driving behavior with a greater benefit;

[0126] S33. During the driving process, the following vehicles in the mixed vehicle group rely on human drivers for control. The corresponding car-following model expression is as follows:

[0127]

[0128] In the formula, α, β, and γ are all gain coefficients, and d des is the desired headway, is the acceleration of vehicle i-1 at the previous time step T; is the acceleration of vehicle i at the previous time step T; the subscripts "i" and "i-1" respectively represent the i-th and (i-1)-th vehicles in the mixed vehicle group l. The leading vehicle in the mixed vehicle group obtains the control input through the driving benefit function during the dynamic game with other mixed vehicle groups. Therefore, to improve the traffic efficiency at unsignalized intersections and ensure that the mixed vehicle groups participating in the game can drive at the optimal speed in each game time period, considering the actual driving requirements, a driving benefit function for the mixed vehicle group is designed from four aspects: driving safety, driving comfort, driving efficiency, and driving economy.

[0129] (1) The first condition to be ensured in the game of the mixed vehicle group is that before the high-priority mixed vehicle group completely passes through the conflict area, the low-priority mixed vehicle group cannot enter the conflict area, so as to avoid collisions. Therefore, define the time when the low-priority mixed vehicle group arrives at the conflict area during the game that is, the time when the leading vehicle arrives at the conflict area, and the expression is as follows:

[0130]

[0131] In the formula, is the acceleration of the leading vehicle at time t. Define the time when the high-priority mixed vehicle platoon completely passes through the conflict area That is, the time when the leading vehicle arrives at the conflict area, and the expression is as follows:

[0132]

[0133] In the formula, Δt correction is a correction constant to reduce the calculation error caused by the changes in time and the speed of the trailing vehicle. Based on this, the driving safety benefit function of the mixed vehicle platoon The expression is as follows:

[0134]

[0135] In the formula, N is the number of vehicles in the mixed vehicle platoon, ω i is the weight coefficient of vehicle i in the mixed vehicle platoon, is the safety time coefficient, and μ 1 、μ 2 are the safety distance coefficients, is the distance traveled by the leading vehicle of the mixed vehicle platoon k when the mixed vehicle platoon l completely passes through, d safe is the safe driving distance between mixed vehicle platoons.

[0136] (2) Frequent changes in the vehicle acceleration during driving will affect the passenger comfort. Therefore, the driving comfort benefit function of the mixed vehicle platoon The expression is as follows:

[0137]

[0138] In the formula, a max is the maximum value of the vehicle acceleration, a min is the minimum value of the vehicle acceleration.

[0139] (3) The driver will pay attention to the driving efficiency during driving, that is, is more inclined to drive at the expected speed. Therefore, the driving efficiency benefit function expression of the mixed vehicle platoon is as follows:

[0140]

[0141] In the formula, η 1 、η 2 are the weight coefficients, and η 1 +η 2 =1, ε is an infinitesimal quantity, v des represents the expected speed of vehicle driving, v max represents the maximum speed of vehicle driving.

[0142] (4) Drivers usually pay attention to adopting fuel-efficient driving strategies to save costs. Therefore, fuel economy needs to be considered when formulating driving strategies. The vehicle fuel consumption model expression is as follows:

[0143]

[0144] In the formula, f c is the fuel consumption function of the vehicle driving at a stable speed ; f a is the acceleration fuel consumption function of the vehicle when the speed is ; q 0 , q 1 , q 2 , q 3 , r 0 , r 1 , r 2 are all fuel consumption related coefficients. Therefore, the driving economy revenue function expression is as follows:

[0145]

[0146] (5) Based on the above four revenue functions of the mixed vehicle group, the total revenue function of the mixed vehicle group is expressed as follows:

[0147]

[0148] In the formula, ρ 1 , ρ 2 , ρ 3 , ρ 4 are the weight coefficients corresponding to the four revenue functions, and ρ 1 +ρ 2 +ρ 3 +ρ 4 = 1.

[0149] S4. According to the mixed vehicle group game priority collaborative decision-making mechanism designed in step S2 and the mixed vehicle group collaborative driving revenue function established in step S3, use the Stackelberg equilibrium theory in information dynamic game to optimize the driving strategy of the mixed vehicle group, and use the backward induction method to obtain the optimal control input with the goal of maximizing the collaborative driving revenue of the mixed vehicle group, in order to obtain the best driving state of the mixed vehicle group. The steps are as follows:

[0150] S41. As Figure 3Schematic diagram of the passing of mixed traffic groups at a signal - free intersection in the present embodiment shown. The mixed traffic group 1 in the west straight - through lane has potential collision risks with the mixed traffic group 1 in the north straight - through lane and the mixed traffic group 1 in the east left - turn lane in conflict areas 1 and 2 respectively. And the mixed traffic group 1 in the east straight - through lane has potential collision risks with the mixed traffic groups 1 and 2 in the north straight - through lane in conflict area 3. Based on the sequential nature of dynamic game, the mixed traffic group with the highest priority can directly adopt the behavior with the maximum benefit based on the prediction of the behaviors of the subsequent corresponding mixed traffic groups in the conflict areas.

[0151]

[0152] In the formula, is the behavior adopted by the mixed traffic group 1 in the west straight - through lane, is the set of behaviors of the mixed traffic group 1 in the north straight - through lane when the mixed traffic group 1 in the west straight - through lane adopts the behavior The third subscript "1, 2, 3" respectively represents the priority order of the mixed traffic group in the current game time period;

[0153] The mixed traffic group with a lower priority (such as the mixed traffic group 1 in the east straight - through lane) predicts the behaviors of the subsequent corresponding mixed traffic groups in the conflict areas and adopts the behavior with the maximum benefit when the mixed traffic group with a higher priority adopts the optimal behavior.

[0154] Therefore, the driving behavior of the above - mentioned mixed traffic groups seeking the maximum benefit can be regarded as a Stackelberg equilibrium problem in dynamic game. Under the condition that the mixed traffic group with the highest priority has the maximum benefit, when the following conditions are met, the Stackelberg equilibrium can be achieved:

[0155]

[0156] In the formula, m e is the driving behavior of the mixed traffic group with a lower priority, M follower is the set of driving behaviors of the mixed traffic group with a lower priority, m 1 is the driving behavior of the mixed traffic group with the highest priority, M 1 is the set of driving behaviors of the mixed traffic group with the highest priority.

[0157] S42. As Figure 4 shown in the schematic diagram of the priority order of the mixed traffic groups in the present embodiment, due to the existence of incredible threats in the dynamic game process, the backward induction method is used to solve the Stackelberg game equilibrium, and the optimal acceleration solution is calculated starting from the mixed traffic group with the lowest priority in any branch gradually rising to the optimal acceleration solution of the mixed traffic group with the highest priority and then solving the optimal acceleration solutions of all branch mixed traffic groups The calculation method adopts the receding horizon strategy, and the expression is as follows:

[0158]

[0159] In the formula, Z is the total length of the prediction horizon, λ is the gain coefficient, is the prediction of the total revenue at time step t + σT at time t. By solving the maximum revenue prediction, the optimal control input of the leading vehicle in the mixed traffic flow at time t is obtained, so as to improve the traffic efficiency of the unsignalized intersection on the premise of avoiding vehicle collisions.

[0160] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the present technical solution, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A method for coordinated passage of mixed-traffic vehicles at an unsignalized intersection based on information dynamic game, characterized in that: The method comprises the following steps: Construct mixed traffic scenarios at unsignalized intersections in cities, divide unsignalized intersections into vehicle clustering areas, speed planning areas, and vehicle merging areas, and indicate potential conflict areas in the vehicle merging areas; According to the divided unsignalized intersection area and the difference of heterogeneous vehicle information obtained, a mixed vehicle group subgroup division scheme is established, and a dynamic game joint judgment rule for mixed vehicle group information in the speed planning area is established; The longitudinal kinematic models of heterogeneous vehicles are established respectively, and the priority collaborative decision-making mechanism of mixed vehicle groups in the unsignalized intersection area is established, and the mixed vehicle group collaborative driving benefit function combining driving safety, comfort, efficiency and economy is constructed; Based on the priority collaborative decision-making mechanism and collaborative driving benefit function of mixed vehicle groups, the driving strategy of mixed vehicle groups is optimized through the Stackelberg equilibrium theory, and the reverse induction method is used to obtain the optimal control input with the goal of maximizing the collaborative driving benefit of mixed vehicle groups.

2. The method for cooperative passage of mixed-vehicle groups at unsignalized intersections based on information dynamic game according to claim 1, characterized in that: The process of establishing mixed traffic scenarios at unsignalized urban intersections includes: Several lanes are set in each driving direction, including at least a left-turn lane, a through lane and a right-turn lane, and all lanes are driven in corresponding lanes; the construction of mixed traffic scenes can be adjusted accordingly according to the specific conditions of the actual unsignalized intersection; Roadside sensors are installed on both sides of the road to collect status information of all vehicles on the road. Among them, connected autonomous vehicles obtain status information of other connected autonomous vehicles through vehicle-to-vehicle communication, and obtain status information of other traditional human-driven vehicles through vehicle-to-road communication; Traditional human driving relies on the driver's perception to obtain status information of the vehicle immediately in front of him; The unsignalized intersection area is divided into a vehicle grouping area, a speed planning area, and a vehicle merging area; the mixed vehicle group will enter at the initial speed. The three areas are all squares with the unsignalized intersection as the center. Among them, the side length of the vehicle grouping area is f meters, which is used for the division and sorting of mixed vehicle groups; the side length of the speed planning area is g meters, which is used for the dynamic game of mixed vehicle groups; the side length of the speed merging area is h meters, which is used for mixed vehicle groups to adopt the optimal acceleration obtained by the game to pass through the unsignalized intersection in an orderly manner, and f>g>h>0; In the vehicle merging area, the intersection point of different vehicle trajectories is represented as a potential conflict area where a collision may occur.

3. The method for cooperative passage of mixed-vehicle groups at unsignalized intersections based on information dynamic game according to claim 1, characterized in that: The vehicle group subgroup division scheme includes: the mixed vehicle group in the vehicle group subgrouping area is composed of a connected automatic vehicle as the leading vehicle and a traditional human-driven vehicle as the following vehicle. When a vehicle v on a left-turn or straight lane enters the vehicle group subgrouping area, if the vehicle is a connected automatic vehicle, the vehicle is divided into the next mixed vehicle group as the leading vehicle; if the vehicle is a traditional human-driven vehicle, the vehicle is divided into the previous mixed vehicle group as the following vehicle, wherein the leading vehicle in the mixed vehicle group can obtain the status information of other vehicles in the same vehicle group.

4. The method for coordinated passage of mixed-vehicle groups at unsignalized intersections based on information dynamic game according to claim 1, characterized in that: The joint decision rules for mixed traffic groups participating in the game in the speed planning area include distance decision rules and time window prediction decision rules, among which: According to the distance relationship between the mixed vehicle group game problem and the speed planning area of ​​the unsignalized intersection, the distance determination rule is defined: In the formula, is the horizontal or vertical coordinate of the entry position of the speed planning zone of the set unsignalized intersection, is the horizontal or vertical coordinate of the last conflict area in the road trajectory of the mixed vehicle group. is the horizontal or vertical coordinate of the position of the first vehicle in the mixed vehicle group at time t, where On roads in the east-west direction, the horizontal coordinate value is used for comparison, and on roads in the north-south direction, the vertical coordinate value is used for comparison; * stands for north, south, west or east; represents different directions of the intersection, # stands for lt or s, representing left turn or straight lane; the subscript "0" represents the leading vehicle in a mixed traffic group; By predicting the time window relationship of the corresponding mixed vehicle group passing through the same conflict area at time t, the time window prediction judgment rule is defined: In the formula, is the time prediction window for mixed vehicle group l to pass through the conflict area, where is the predicted time for the leading vehicle in the mixed vehicle group to arrive at the conflict area, is the predicted time for the last vehicle in the mixed traffic group to pass the conflict area, is the time prediction window for mixed vehicle group k to pass through the conflict area, Indicates that mixed vehicle group l and mixed vehicle group k will collide in the conflict area. The symbol || indicates the logical relationship "or". gap,l,k is the time interval between the former passing through the conflict area and the latter arriving at the conflict area when the time prediction windows of the two mixed traffic groups do not overlap, T safe is the safety time interval, T gap,l,k ≤T safe It indicates that there is no collision between two mixed vehicle groups, but the time interval between the vehicles passing through the conflict area is less than the safe time interval; According to the distance judgment rule and the time window prediction judgment rule, the joint judgment rule for mixed traffic vehicle groups to participate in the game is defined: Sea game =Sea d &&Sea t In the formula, "&&" represents the logical relationship "and", when Mar d With Mar t When both are 1, it means that the mixed vehicle group will participate in the game.

5. The method for cooperative passage of mixed-vehicle groups at unsignalized intersections based on information dynamic game according to claim 4, characterized in that: In the defined time window determination rules, T gap,l,k The expressions are: In the formula, s confilct,# is the distance from the conflict area to the lane where the mixed vehicle group l is located, is the position of the vehicle stop line in the lane, is the speed of the leading vehicle in the mixed vehicle group at time t, is the length of the mixed vehicle group l at time t, is the speed of the last vehicle in mixed vehicle group l at time t, N is the number of vehicles in mixed vehicle group l, As the leader of the lead vehicle, is the distance between the i-th following vehicle and the i-1-th vehicle in the mixed vehicle group l. The i-1-th vehicle is also the immediate preceding vehicle of the i-th following vehicle.

6. The method for coordinated passage of mixed-vehicle groups at unsignalized intersections based on information dynamic game according to claim 4, characterized in that: In the established heterogeneous vehicle longitudinal kinematics model, the longitudinal kinematics model expression of the connected automatic vehicle is as follows: In the formula, represents the speed of the connected automatic vehicle cav in the mixed vehicle group l at time t, The horizontal coordinate or vertical coordinate represents the position of the connected automatic vehicle cav in the mixed vehicle group l at time t; represents the acceleration of the connected automatic vehicle cav in the mixed vehicle group l at time t; represents the control input of the connected automatic vehicle cav at time t; represents the derivative of the speed of the connected automatic vehicle cav in the mixed vehicle group l at time t; The expression of the traditional human driving longitudinal kinematic model is as follows: In the formula, represents the speed of the traditional driver hv in the mixed vehicle group l at time t, The horizontal coordinate or vertical coordinate represents the position of the traditional human driver hv in the mixed vehicle group l at time t; represents the acceleration of the traditional driver hv in the mixed vehicle group l at time t; represents the derivative of the speed of the traditional human driver hv in the mixed vehicle group l at time t; In the established mixed vehicle group game priority collaborative decision-making mechanism, if Then the mixed vehicle group l has more driving priority than the mixed vehicle group k; During driving, the following vehicles in the mixed vehicle group rely on human drivers for control, and the corresponding following model expression is as follows: In the formula, α, β, and γ are gain coefficients, d des is the expected vehicle spacing, is the acceleration of vehicle i-1 at the previous time step T; is the acceleration of vehicle i at the previous time step T; The subscripts "i" and "i-1" represent the i-th and i-1-th vehicles in the mixed vehicle group l, respectively.

7. The method for coordinated passage of mixed-vehicle groups at unsignalized intersections based on information dynamic game according to claim 6, characterized in that: For the mixed vehicle group cooperative driving benefit function, it is ensured that the mixed vehicle group participating in the game can drive at the optimal speed in each game time period. The actual driving needs are comprehensively considered and established from the perspectives of driving safety, driving comfort, driving efficiency and driving economy, including the following contents: For safety, a collision avoidance constraint is established, that is, before the high-priority mixed vehicle group has completely passed the conflict area, the low-priority mixed vehicle group cannot enter the conflict area, and the time for the low-priority mixed vehicle group to reach the conflict area during the game is defined. That is, the time when the leading vehicle arrives at the conflict area, expressed as follows: In the formula, is the acceleration of the k-head vehicle in the mixed vehicle group at time t; Define the time it takes for a high-priority mixed vehicle group to completely pass through the conflict area That is, the time when the leading vehicle arrives at the conflict area, expressed as follows: In the formula, Δt correction is the correction constant; Driving safety benefit function of mixed vehicle group The expression is as follows: Where N is the number of vehicles in the mixed traffic group, ω i is the weight coefficient of vehicle i in the mixed vehicle group, is the safety time factor, and μ1 and μ2 are safety distance coefficients, is the distance traveled by the leading vehicle in mixed vehicle group k when mixed vehicle group l passes completely, d safe It is the safe driving distance between mixed traffic groups; For comfort, the driving comfort benefit function of mixed vehicle group l is The expression is as follows: In the formula, a max is the maximum acceleration of the vehicle, a min is the minimum value of vehicle acceleration; Regarding efficiency, the driving efficiency benefit function expression of mixed vehicle group l is as follows: In the formula, η1 and η2 are weight coefficients, and η1+η2=1, ε is an infinitesimal quantity; v des represents the expected speed of the vehicle, v max Indicates the maximum speed of the vehicle; In terms of economy, the vehicle fuel consumption model expression is first established, which is expressed as: In the formula, f c For vehicles at a steady speed Fuel consumption function under driving, f a The vehicle speed is The acceleration fuel consumption function at , q0, q1, q2, q3, r0, r1, r2 are all fuel consumption correlation coefficients; Then the driving economic benefit function is The expression is as follows: Based on the above four mixed vehicle group profit functions, the total profit function of the mixed vehicle group The expression is as follows: In the formula, ρ1, ρ2, ρ3, and ρ4 are the weight coefficients corresponding to the four profit functions, and ρ1+ρ2+ρ3+ρ4=1.

8. The method for coordinated passage of mixed-vehicle groups at unsignalized intersections based on information dynamic game according to claim 7, characterized in that: Based on the priority collaborative decision-making mechanism of mixed vehicle group game and the collaborative driving benefit function, the driving strategy of mixed vehicle group is optimized through the Stackelberg equilibrium theory in information dynamic game, including: Based on the sequential nature of dynamic games, the highest priority mixed vehicle group can directly take the most profitable action based on the behavior prediction of the subsequent mixed vehicle groups in the corresponding conflict area. for: In the formula, The behavior taken for mixed traffic group l, Take action for mixed vehicle group v in mixed vehicle group l The third subscript "1, 2, 3" represents the priority order of the mixed vehicle group in the current game time period; The lower priority mixed vehicle group predicts the behavior of the subsequent corresponding conflict area mixed vehicle group and takes the behavior with the greatest benefit when the higher priority mixed vehicle group takes the optimal behavior. The driving behavior of mixed vehicles seeking maximum benefits is regarded as a Stackelberg equilibrium problem in a dynamic game. Under the condition that the highest priority mixed vehicle group has the maximum benefit, the Stackelberg equilibrium is achieved when the following conditions are met: In the formula, m e is the driving behavior of the low-priority mixed vehicle group, M follower is the driving behavior set of the low priority mixed vehicle group, m1 is the driving behavior set of the highest priority mixed vehicle group, and M1 is the driving behavior set of the highest priority mixed vehicle group.

9. The method for coordinated passage of mixed-vehicle groups at unsignalized intersections based on information dynamic game according to claim 8, characterized in that: The process of using the reverse induction method to obtain the optimal control input with the goal of maximizing the cooperative driving benefits of mixed vehicle groups is as follows: According to the priority order of the mixed traffic group, the optimal acceleration solution is calculated starting from the lowest priority mixed traffic group in any branch. Gradually rise to the optimal acceleration solution for the highest priority mixed vehicle group Then, the optimal acceleration solution of all branch mixed traffic groups is solved. The calculation method adopts the backward time domain strategy, and the expression is as follows: Where Z is the total length of the prediction time domain, λ is the gain coefficient, In order to predict the total benefit of time step t+σT at time t, the optimal control input of the leading vehicle in the mixed vehicle group at time t is obtained by solving the maximum benefit prediction.

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