Automatic driving non-signalized intersection traffic conflict control method based on space-time network

Abstract

The invention discloses an automatic driving non-signalized intersection traffic conflict control method based on a space-time network, and the method comprises the steps: carrying out the preprocessing: determining an intersection traffic conflict control range, and carrying out the grid division, after the vehicle arrives at the control area, the speed, the position, the acceleration, the lane entering time, the intentional steering time and the intersection control area time of the vehicle are reported to the central manager; a request is sent when the vehicle arrives, and the central manager judges whether the vehicle is allowed to enter; solving the space-time network control model and the trajectory reconstruction model, and feeding back the specific driving trajectory to the vehicle; the vehicle runs according to the running track fed back by the central manager and safely passes through the intersection; according to the invention, the path of the autonomous vehicle at the intersection is changed based on the path of the unconventional intersection, and the traffic conflict control of the non-signalized intersection in the pure automatic driving environment is explored, so that the traffic efficiency of the intersection is better improved.

Description

Technical Field

[0001] The present invention relates to the technical field of traffic conflict control at signal - free intersections in a fully autonomous driving environment, and particularly to a traffic conflict control method for autonomous driving at signal - free intersections based on a spatio - temporal network. Background Art

[0002] In recent years, with the development of social economy and the acceleration of urbanization, the vehicle ownership has been continuously increasing, and urban traffic congestion has become serious. Urban intersections are important connection points of the urban road network and are prone to becoming the "bottlenecks" in the entire road network. The development of autonomous driving technology has made it possible for the emergence of signal - free intersections in cities (in the context of intelligent networking, getting rid of traditional traffic signal control, and through information sharing between autonomous vehicles and a central manager, vehicles self - organize to pass through the intersection). Traffic conflict control at signal - free intersections in an autonomous driving environment refers to adjusting the trajectories of vehicles at intersections, including the time when vehicles enter the intersection, the driving paths within the intersection, driving speeds, etc., to ensure that no conflict point is occupied by two or more vehicles at the same time and to ensure the safe operation of vehicles.

[0003] The control of signal - free intersections mainly focuses on how to separate the conflicts of vehicles at intersections. Related research is divided into two categories: (1) traditional space separation + changed time separation; (2) changed space separation + changed time separation. Among them, the first category is based on the vehicle paths of conventional intersections and separates conflicts in time by controlling the passing times of conflicting vehicles at traffic conflict points. This type of research can be further divided into three sub - categories: rule - based, model - based, and data - based.

[0004] (1) Traditional space separation + changed time separation:

[0005] 1. Rule - based:

[0006] Rule - based traffic conflict control mainly considers factors such as vehicle arrival order and vehicle weights, specifies rules for the passing order of vehicles at intersections, and according to the rules, the control center determines the passing order of vehicles. In this type of research, the vehicle speed usually remains constant or several different fixed speed values are given. With the goal of maximizing the number of vehicles released per unit time at the intersection and with the constraint of intersection operation safety, the passing order and passing speed of vehicles at the intersection are determined by trying from high speed to low speed in sequence.

[0007] Dresner and Stone first proposed the signal - free control strategy AIM (Autonomous Intersection Management) for the autonomous driving environment, which is a reservation - based "First come first served" (FCFS) system. In this control strategy, the intersection is divided into grids, and each vehicle needs to request to reserve a grid trajectory to pass through the intersection. The central manager will decide whether to allow the request based on the "First come first served" (FCFS) rule and safety constraints. Based on the initial FCFS model, some scholars also considered human - driven vehicles and priority vehicles. Based on the M / G / 1 queuing theory, Yu et al. derived an estimation method for the intersection capacity based on the FCFS rule, and the results also verified that FCFS performs mediocrely under high - traffic demand and a large number of conflicts. Levin et al. revealed that using the reservation - based method on the primary and secondary roads will increase vehicle travel delays.

[0008] The control strategy based on FCFS reservation laid the foundation for the research on traffic conflict control at signal - free intersections in the autonomous driving environment and has been continuously improved in subsequent studies. Considering the value difference of drivers' priorities in different trips, some scholars proposed an auction - based autonomous intersection management scheme, which grants the right - of - way to the first vehicle with the highest bid instead of the first - arrived vehicle. The research results show that, compared with FCFS, the auction - based rule can reduce the vehicle queue length on the high - demand approach to a certain extent. However, in the auction - based right - of - way allocation rule, since vehicles in the same lane need to pass in sequence, the travel time of the queuing vehicles in front of the vehicle with a higher bid will also be reduced, and this characteristic may limit the willingness to pay a higher fee for the right - of - way. One disadvantage of FCFS is that it allocates the intersection road rights according to the request time and performs worse than signal control at unbalanced intersections. Lukose et al. combined signal control and the FCFS reservation rule and proposed two reservation strategies: Weighted based and Phased based. The first Weighted based strategy considers the number of vehicles in each flow direction and weights the delays of vehicles turning in different directions according to the green - light duration, which can improve the traffic efficiency in the heavy - traffic flow direction while avoiding the random allocation of FCFS. The second Phased based strategy is similar to signal control and allows conflict - free right - hand turn control. When the vehicle request does not conflict with the trajectory of the vehicle currently having the right - of - way and meets the safety requirements, the vehicle obtains the right - of - way. Bouderba et al. studied a more realistic right - hand vehicle priority rule based on V2X (Vehicle - to - Everything) technology.

[0009] 2. Based on the model:

[0010] The problems existing in the rule-based vehicle passing sequence control scheme mainly include only considering the arrival of the current vehicle, only focusing on the interests of the current vehicle, ignoring the arrival of vehicles within a certain period of time, and being unable to achieve global system optimization. At the same time, at intersections with unbalanced traffic flows such as main roads and secondary roads, it is easy to cause problems such as over-saturation of intersections and excessive delays. Li et al. first constructed a vehicle passing sequence generation tree based on safe driving for this concept, and selected the passing plan with the minimum time cost as the actual driving plan, realizing the transformation from a reservation-based method to a model-based method. This scheme is an enumeration method, which reduces the number of enumerations by pruning in advance with the help of the generation tree. Lee et al. were the first to establish a relevant mathematical model to solve the problem of optimizing the vehicle sequence at intersections, aiming to minimize the overlap of vehicle trajectories, and proposed a non-linear intersection vehicle cooperative control model to optimize the trajectories of individual vehicles. However, due to the non-linearity of the model, the computational burden is relatively large, which limits the application and promotion of the model. Deng et al. established a conflict point occupancy time graph model, and by adjusting the vehicle speed, ensured that each conflict point is occupied by only one vehicle at a moment. Yao et al. proposed a two-stage optimization method to allocate the vehicle passing sequence and calculate the arrival trajectories of each CAV. In the first stage, a 0-1 mixed integer linear program was proposed to minimize vehicle delay, and in the second stage, a multi-vehicle optimal trajectory control model was established to minimize fuel consumption. However, there are two problems with the above models. One is that for the convenience of calculation, only the straight traffic flow on the oncoming approach is considered; the other is that it is assumed that the lane functions of the approach are fixed and vehicle lane changes are not considered.

[0011] In terms of considering multi-directional vehicle flow turning, Kamal et al. established a conflict pair risk function to characterize the conflict magnitude between two conflicting vehicles at the moving trajectory points within the intersection, and established a vehicle trajectory optimization model with the goal of minimizing risk to coordinate vehicles. Due to the non-linearity of the conflict pair risk function, the model is not conducive to handling large-scale problems. Levin et al. established a mixed integer linear model considering the passing weight of emergency vehicles to calculate the vehicle entry time and speed at the intersection, and proposed an autonomous intersection management model. Compared with FCFS, this method replaces the vehicle trajectory reservation in FCFS with conflict point constraints, and establishes a model to obtain the vehicle's allowed entry time. Also based on conflict point control, Yu et al. established a linear model with the aim of minimizing delay to determine the vehicle entry time at the intersection. However, in the above models of conflict point control, the vehicle speed is a fixed value, and no more options are provided for vehicle speed selection. Lu et al. discretized time and proposed two mixed integer linear unsignalized control models based on whether to consider the safety distance to solve the passing trajectory of vehicles at the intersection. The difference between the two strategies lies in whether to provide a fail-safe buffer zone for vehicles to improve vehicle safety performance. The results show that after introducing the fail-safe buffer zone, the vehicle platoon will exhibit behavior similar to signal control, that is, the vehicles will automatically form several groups and pass through the intersection in their respective groups. However, in this model, the vehicle arrival time is the vehicle entry time at the intersection, and when two vehicles arrive densely, the model is not applicable. Qian used the alternating iterative descent method to allocate the optimal entry time for each vehicle. Dynamic programming and production scheduling models have also been applied to the modeling. To speed up the solution, Wu designed a solution method based on the ant colony heuristic algorithm. Xu compared the performance of Monte Carlo tree search, FCFS, and dynamic sorting models in terms of travel time, energy consumption, computation time, and fairness. The research shows that Monte Carlo tree search and dynamic sorting are superior to FCFS.

[0012] In terms of allowing vehicle lane changes, Zohdy et al. divided the intersection into three regions: the maximum speed driving region, the vehicle lane change allowed region, and the internal control region of the intersection, optimized the vehicle trajectory with the goal of minimizing delay, and developed a simulation model. However, this model has a non-linear function, which will affect the solution efficiency and accuracy of large models. Considering the operation of arterial vehicles, on the basis that all lanes within the intersection range allow vehicles to go straight, turn left, or turn right, Yu et al. proposed a mixed integer linear programming (MILP) model with the goal of minimizing the total delay to jointly optimize the operation of arterial CAVs. The model jointly optimizes the longitudinal position and lane change behavior of each vehicle. Liu Yang et al. first optimized the lane for vehicles to enter the intersection and the lane for vehicles to leave the intersection, and then optimized the vehicle's internal running trajectory.

[0013] 3. Based on data:

[0014] Data-based methods mainly achieve traffic conflict control at unsignalized intersections in the autonomous driving environment based on data-driven technologies such as deep learning. Wang et al. considered the crossing of vehicles at intersections, the trajectory optimization of road segments, and the road network path optimization, and proposed a cooperative autonomous traffic organization method for CAVs in a multi-intersection road network. Guo et al. constructed a multi-agent reinforcement system for unsignalized intersections based on a semi-cooperative Nash Q-learning method combining single-agent Q-learning and Nash equilibrium. Zhao et al. transformed the state, action, reward, and cost functions into a constrained Markov game problem based on multi-agent deep reinforcement learning to improve the calculation speed and traffic efficiency. Wu et al. modeled the vehicle passing sequence through intersections as a multi-agent Markov decision process, aiming to minimize the vehicle passing time, and solved the vehicle passing sequence based on multi-agent learning. Compared with optimization-based and rule-based methods, although the data-based method model can improve the solving speed and efficiency, due to the limitations of the data-based method itself, the interpretability and transferability of the model are poor.

[0015] (2) Change spatial separation + change temporal separation:

[0016] The research on changing spatial separation + changing temporal separation is mainly divided into two categories. One is the flexible lane function (FLF) that does not fix the lane function at intersections, and the other is special rhythm control.

[0017] FLF means that the lane function of the approach lanes at intersections is not fixed. Under this lane plan, CAVs on any lane of the approach lane can turn into any downstream lane without forced lane changes. Li et al. built a VISSIM simulation platform based on the FCFS rule to test the operation and safety performance of FLF. The research shows that when the traffic demand is lower than 1650 pcu / h, FLF significantly improves the traffic efficiency at intersections. The comparison with optimized signal control shows that it can increase the traffic capacity of intersections by nearly 33%. Based on the FLF design, Wu et al. proposed two mixed-integer linear models based on the FCFS rule and the global optimal model based on a sliding time window to optimize the vehicle entry time, entry lane, and departure lane selection. In terms of considering global optimization in FLF, He et al. proposed a conflict-avoidance-based method to coordinate all approaching vehicles to cross the intersection at a constant speed, aiming to minimize the total time allowed for vehicles to enter the intersection. Jiang et al. compared FLF and the lane-fixed plan in detail. The results show that although FLF can increase vehicle traffic efficiency, after adjusting the shortest collision interval of conflicting vehicles, the fault tolerance performance of the system is worse.

[0018] Mitrovic et al. proposed a combined alternate-direction lane assignment and reservation-based intersection control (CADLARIC) scheme by studying the distribution of through, left-turn, and right-turn vehicles in the approach lanes and the departure flow intervals of vehicles from the departure lanes at intersections. In CADLARIC, left-turn vehicles are arranged to travel in the leftmost lane, and a reservation method similar to FCFS is used to handle conflicts among through vehicles within the intersection. After removing the fixed lane function constraints, Mitrovic's research team proposed combined flexible lane assignment and reservation-based intersection control (CFLARIC). In CFLARIC, lanes are allowed to have functions of through + right-turn or through + left-turn. Azadi F compared the number of stops and delays of different lane setting strategies under the same traffic flow level and turning ratios through simulation and gave a recommended vehicle function division method for different traffic flows. Amouzadi et al. transformed the intersection vehicle control problem into a problem based on vehicle dynamic trajectories, ensuring that there are no overlapping vehicle trajectories at each moment and no other vehicles within the safe vehicle spacing. With the goal of minimizing vehicle delay and fuel consumption, the vehicle trajectories are solved by applying the theory of the dual problem of convex optimization. Since the objective of the model is to minimize the travel time of vehicles, vehicle paths tend to be straight lines from the starting point to the ending point.

[0019] Rhythmic Control (RC) is a traffic conflict control scheme proposed by the research team at Tsinghua University in recent years. In this control scheme, by resetting the positions of each lane at intersections and maintaining a spacing between adjacent lanes to provide adjacent headway times, vehicles can pass through intersections without stopping according to the preset speed and entry time. The greatest advantage of this scheme is that vehicles enter intersections at a predefined interval, which is computationally simple and can improve the traffic capacity of intersections. Since a distance needs to be maintained between adjacent lanes, the cost of rhythmic control is that the intersection area will expand, which is not conducive to the renovation of existing intersections and is also not conducive to the application of this scheme in cities where land is at a premium. The research team also studied the application of rhythmic control in road networks, its application in the control of knot intersections, and the performance of rhythmic control under mixed traffic flows.

[0020] However, there are mainly two problems in current research:

[0021] First, it ignores the advantages of spatial separation in traditional traffic conflict control. Most of the traffic conflict control at unsignalized intersections currently is based on the fixed traffic conflicts of vehicle passing paths at traditional intersections. Then, conflict time separation rules or optimization models are established to solve the vehicle passing trajectories. Its control means still follows the process of first converting random conflicts into fixed conflicts and then completing conflict time separation based on the fixed conflicts. Based on the fixed vehicle paths, the time for vehicles to enter the intersection and the passing speed are optimized, ignoring the potential of changing the vehicle operation paths at the intersection to optimize conflict spatial separation in this process.

[0022] Second, the advantages of autonomous driving technology in controlling vehicle forward movements and enabling information interaction between vehicles are not fully utilized. The traditional traffic conflict control is divided into two steps: spatial separation and time separation of conflict points. On the one hand, it is due to the limited hardware conditions such as vehicles and communication facilities. On the other hand, it is to ensure the safe operation of vehicles under manual driving and avoid threatening traffic operation safety by changing the lane functions and vehicle driving paths at intersections. Under the condition of manual driving, it is not feasible to not fix the vehicle driving paths at intersections. However, in a mature autonomous driving environment, the conditions for coordinated control of traffic conflict space and time are available. The current research ignores this advantage of autonomous driving technology at unsignalized intersections. Currently, the research on traffic conflict control at unsignalized intersections in an autonomous driving environment mainly includes two categories: "traditional spatial separation + changing time separation" and "changing spatial separation + changing time separation". The current research mainly focuses on the former. The research results of the latter show that changing conflict spatial separation can reduce the average vehicle delay at intersections to a certain extent. The former usually based on the fixed traffic conflicts of vehicle passing paths at traditional conventional intersections, by establishing conflict time separation rules or optimization models to solve the vehicle passing trajectories, ignoring the potential of changing the vehicle driving paths at intersections and optimizing conflict spatial separation. Summary of the Invention

[0023] To solve the problems existing in the prior art, the object of the present invention is to provide a traffic conflict control method for autonomous driving at unsignalized intersections based on a spatio-temporal network. The present invention changes the paths of autonomous vehicles at intersections based on unconventional intersection paths, explores traffic conflict control at unsignalized intersections in a pure autonomous driving environment, so as to better improve the traffic efficiency at intersections.

[0024] To achieve the above object, the technical solution adopted by the present invention is: A traffic conflict control method for autonomous driving at unsignalized intersections based on a spatio-temporal network, including the following steps:

[0025] Step 1. Pretreatment: Define the traffic conflict control range of the intersection and divide it into grids. After the vehicle arrives at the control area, it reports its speed, position, acceleration, entering lane, intended turning, and the time of arriving at the intersection control area to the central manager;

[0026] Step 2: The arriving vehicle sends a request, and the central manager determines whether to allow the vehicle to enter;

[0027] Step 3: Solve the spatio-temporal network control model and the trajectory reconstruction model, and feedback the specific driving trajectory to the vehicle;

[0028] Step 4: The vehicle drives according to the driving trajectory fed back by the central manager and safely passes through the intersection.

[0029] As a further improvement of the present invention, in Step 1, the control area includes a spatio-temporal network coordination area and an approach control area; the spatio-temporal network coordination area is a rectangle formed by extending the stop lines of each approach. The intersection space range in the coordination area is divided into grids of the same size, and the movement of the vehicle in the coordination area is characterized by the connection method between the grids; the approach control area is the range of the intersection approach after removing the coordination area from the control area, and the length of the approach control area is defined as l a , the spatio-temporal network diagram G(S,E) of the coordination area, where S is the set of grids and E is the set of directed edges; the grid set S = {s1, s2,..., s m} represents the set of single grids divided in the coordination area. The single set is divided into three subsets, the starting point set S o = {os1, os2,..., os n}, the end point set S d = {ds1, ds2,..., ds q}, and the other point set Among them, the starting point set S o indicates that this grid point is the starting point of the path, and the vehicle can only start from this point and drive into the coordination area. The end point set S d indicates that the grid point is the end point of the path, and the vehicle can only leave the coordination area after reaching this point. The other point set refers to the set of other grid points in the grid set excluding the starting point and the end point; the vehicle is initially allowed to move in four directions: up, down, left, and right at each grid. When there is a grid in the target moving direction of the vehicle, a directed edge is formed. Define the starting grid s i , the target grid s j , and the directed edge is e ij = (s i , s j ); all directed edges form the directed edge set E; regardless of the direction of the edge, define the undirected edge set

[0030] Define the time set T = {Δt, Δt,..., kΔt}, where Δt is the unit time step and k is the total number of steps that can be divided within the time range; define the time step pair set TP = {TP1, TP2,..., TP m}, where TP1 = {(Δt, 2Δt),..., [(k - 1)t, kΔt]}, TP2 = {(Δt, 3Δt), (2Δt, 4Δt),..., [(k - 2)t, kΔt]}, TP m = {(Δt, mΔt), (2Δt, 2 + mΔt),..., [(k - m)t, kΔt]}; the number m of step pairs represents the maximum number of time steps allowed to differ between the starting time and the ending time in each time step group; different numbers of time step pairs represent different times required for the vehicle to move between grids. The value needs to meet the vehicle kinematic requirements and is determined by the maximum speed and the side length distance of a single grid;

[0031] Define the spatio - temporal network grid n ij and the spatio - temporal network grid set N, n ij ∈N; the spatio - temporal network grid n ij = (t i , s j ), representing the s i grid at time t j ; Define the spatio - temporal network edge l ijpq and the spatio - temporal network edge set L, l ijpq ∈L; the spatio - temporal network edge l ijpq connects adjacent spatio - temporal network grids n ij and grid n pq , that is, it allows the vehicle to travel from the s i grid at time t j to the s q grid, and the arrival time is t p , that is, l ijpq = (n ij , n pq ) = [(t i , s j ), (t p , s q )].

[0032] As a further improvement of the present invention, the specific steps of step two are as follows:

[0033] The central manager determines whether to allow vehicles to enter the control area based on whether the number of coordinated vehicles in the existing intersection control area is saturated. If allowed, the central manager calculates the earliest arrival time of the vehicle at the coordinated area and the latest departure time of the vehicle from the coordinated area according to the arrival time and vehicle type reported by the vehicle, and then proceeds to step three. If not allowed, the vehicle needs to immediately decelerate and stop. The earliest arrival time of the vehicle at the coordinated area is equal to the moment when the vehicle enters the control area plus the time required for the vehicle to travel through the approach control area at the maximum speed. The latest departure time of the vehicle from the coordinated area is equal to the earliest arrival time of the vehicle at the coordinated area plus the longest time for the vehicle to pass through the coordinated area. Among them, the longest time for the vehicle to pass through the coordinated area is related to the vehicle type. If the vehicle is an emergency vehicle, the longest time for the vehicle to leave the coordinated area is the time when the vehicle enters the coordinated area plus the fastest time to pass through the coordinated area. Assuming that the fastest time for the vehicle to pass through the coordinated area is t1, if the vehicle is an ordinary vehicle, the longest time for the vehicle to pass through the coordinated area is set to t2 respectively, and it is required that t1 < t2.

[0034] As a further improvement of the present invention, in step three, the spatio-temporal network control model is specifically as follows:

[0035] Consider a vehicle set D = {1, 2,..., z} with z vehicles, and the type of vehicle d is b d , b d ∈{B1, B2}, where B1 represents emergency vehicles and B2 represents ordinary vehicles; the starting cell corresponding to vehicle d is os d , and the ending cell is ds d ; the moment when the vehicle enters the control area is t d , the earliest time for the vehicle to enter the coordinated area is T d,EA , and the latest time to leave the coordinated area is T d,LD ; according to the analysis of the central manager and vehicle priorities, calculate T d,EA and T d,LD ; where l a is the length of the approach control area, and t1 and t2 are the times for emergency vehicles and ordinary vehicles to pass through the coordinated area respectively:

[0036] T d,EA = t d + l a / v max , d ∈ D

[0037]

[0038] Define two 0-1 variables x d,l and x d,et to represent the position of vehicle d in the spatio-temporal network graph G(S, E); x d,l indicates whether vehicle d occupies the spatio-temporal edge l ijpq, if it occupies, then x d,l = 1, indicating that vehicle d at time t i to t p within the range from point s j moves to point s q , if it does not occupy, then x d,l = 0; x d,et refers to whether vehicle occupies edge e at time t ij , if it occupies then x d,et = 1, otherwise x d,et = 0; variables and variable need to meet the requirement of value consistency in the same time period [t i , t p ; when vehicle d occupies edge e i to t p within the range and e jq = (s j , s q ), the spatio-temporal edge variable and the variable of whether the edge is occupied at the corresponding time However, when the variable of whether the edge is occupied at the corresponding time , since there may be multiple time pairs, it is impossible to determine which specific spatio-temporal edge variable But there must be a sum of 1 for all spatio-temporal edge occupancy variables that contain this edge and the time pair contains time t;

[0039] A spatio-temporal network control model is established with the goal of minimizing vehicle delay; minimizing vehicle delay is transformed into the vehicle leaving the intersection as fast as possible; the model objective function is as follows.

[0040]

[0041] Among them, T d,LDA represents the time when vehicle d leaves the coordination area, which can be represented by the value of the end point time corresponding to the spatio-temporal edge where the vehicle occupies its corresponding end point.

[0042] As a further improvement of the present invention, the constraints of the empty network control model are specifically as follows:

[0043] (1) Vehicle path continuity constraint: It is required that the vehicle must start from the starting point and finally reach the end point; at each grid point, the vehicle will not appear out of thin air or disappear out of thin air; that is, if it is a grid in the starting point set, then there is only the departure of the vehicle in the corresponding spatio-temporal edge, and no arrival of the vehicle; similarly, for the grid in the end point set, there is only arrival and no departure; for other grid points, if there is a departure, there must be an arrival:

[0044]

[0045] (2) A vehicle can only occupy one edge at a moment:

[0046]

[0047] (3) An undirected edge can be occupied by at most one vehicle at a moment, that is, an undirected edge can accommodate at most one vehicle at a moment to ensure the safety of vehicle operation:

[0048]

[0049] (4) Vehicle order constraint: At each starting point, vehicles follow the rule of first come, first served; the vehicle that arrives at the coordination area first occupies the spatio-temporal edge corresponding to the starting point grid; since the path inside the coordination area is not fixed, the vehicle that enters the coordination area first does not necessarily leave the coordination area first; define T d,EAA to represent the actual time when vehicle d is allowed to enter the coordination area, and δ ij is a 0-1 variable indicating the earliest arrival order of vehicles i and j with the same starting point. If vehicle i arrives earlier than vehicle j, δ ij = 1, otherwise, δ ij = 0:

[0050] T j,EAA -T i,EAA >(δ ij -1)M

[0051] T j,EAA -T i,EAA <δ ij M

[0052] When vehicle i arrives earlier than vehicle j, δ ij = 1, and it is required that T j,EAA >T i,EAA When vehicle i arrives earliest than vehicle j, δ ij = 0, and it is required that T j,EAA <T i,EAA ;

[0053] (5) No circular path can occur: The requirement that no circular path can occur can be transformed into that the number of spatio-temporal paths starting from each grid by vehicles must be less than or equal to 1; when there is a circular path, at the starting point of the loop, the vehicle still needs to start from this point. At this time, the number of spatio-temporal paths starting from this point is 2.

[0054]

[0055] (6) A vehicle cannot occupy an undirected edge multiple times, that is, a vehicle will not move forward and backward or pass repeatedly on this edge:

[0056]

[0057] (7) Comfort constraint: The path meets the requirements that the vehicle does not repeatedly pass through a certain path and there is no circular path, but there are a large number of turns of the vehicle in this path, and the vehicle turns repeatedly many times within a short distance, which is not conducive to the driving safety and comfort of the vehicle; in order to make the trajectory as smooth as possible, a constraint on the vehicle turning is added to the constraint conditions, and each vehicle is only allowed to execute at most three turns within the intersection; define a 0-1 variable to represent whether to turn from edge (s i , s j ) to edge (s p , s q ). If a turn is required, the value is 1, otherwise the value is 0:

[0058]

[0059] As a further improvement of the present invention, the trajectory reconstruction model is specifically as follows:

[0060] On the basis of meeting the requirements of the output result of the spatio-temporal network model control, considering the comfort of the vehicle driver, a continuous and smooth vehicle trajectory is fitted; based on the discrete vehicle trajectory optimization model, considering the spatio-temporal network constraints, a vehicle trajectory reconstruction model at the intersection is established:

[0061] In the two-dimensional coordinate system established at the intersection, the state X(t) of the vehicle at time t and the vehicle control variables are expressed as:

[0062] X(t) = [x(t), y(t), θ(t), v(t)] Τ

[0063] U(t) = [k(t), a(t)] Τ

[0064] where x(t), y(t), θ(t), v(t) are the abscissa, ordinate, steering angle and speed at the corresponding moment respectively; k(t), a(t) are the steering angle change rate and acceleration at this moment respectively; the steering angle change rate is related to the turning radius and is the reciprocal of the turning radius;

[0065] Then the state of the vehicle at the next moment is:

[0066]

[0067] Regard the center point coordinates of each grid point as the position that the vehicle expects to reach at that moment; set the objective function as the root mean square error of the trajectory:

[0068]

[0069] Where n is the number of points used to fit the vehicle trajectory, and c(X(t)) represents the cost of the vehicle at time t, which is used to measure the squared Euclidean distance between the actual position (x(t), y(t)) of the vehicle at this time and the expected position of the grid point, that is, the center point (x0(t), y0(t)):

[0070] c(X(t)) = (x(t) - x0(t)) 2 +(y(t) - y0(t)) 2 。

[0071] As a further improvement of the present invention, the constraint conditions of the trajectory reconstruction model are specifically as follows:

[0072] (1) The position of the vehicle at this time cannot exceed the boundary points of the grid point:

[0073]

[0074] Where respectively represent the minimum and maximum abscissa of the grid point where the vehicle is located at time t, respectively represent the minimum and maximum ordinate of the grid point where the vehicle is located at time t; the boundary points are obtained through the solution results of the spatio-temporal network;

[0075] (2) Constraints on the maximum speed and minimum acceleration of the vehicle:

[0076] 0 < v(t) < v max

[0077] a min <a(t)<a max

[0078] (3) Constraint on passenger comfort, achieved by constraining the change in vehicle acceleration:

[0079]

[0080] Where j min ,j max respectively represent the minimum braking jerk and the maximum braking jerk, and take j min =-j max ;

[0081] (4) Vehicle turning radius constraint:

[0082]

[0083] Where r min is the minimum turning radius considering safety and passenger comfort; k(t) represents the reciprocal of the vehicle turning radius at time t.

[0084] (5) Lateral acceleration constraint:

[0085] -g(e + f s ) ≤ v(t) 2 k(t) ≤ g(e + f s )

[0086] where g is the gravitational acceleration, e is related to the height difference of the road where the vehicle travels, and f s represents the friction coefficient;

[0087] (6) Curvature change constraint: The change in the turning radius needs to satisfy the curvature constraint:

[0088]

[0089] The beneficial effects of the present invention are:

[0090] (1) The import lane does not require a fixed lane division function: In the spatio-temporal network control model of the present invention, vehicles can reach the destination export lane from any import lane, compared with other signal-free intersection control schemes with fixed import lane functions. The number of vehicle lane changes is reduced.

[0091] (2) Left-turning vehicles have more abundant left-turn paths to choose from: Since the present invention discretizes the range of the intersection coordination area into grids, and represents the vehicle's passing path at the intersection through the connection of the grids. When the coordination area is large enough, left-turning vehicles do not need to pass through the intersection in the conventional left-turn way of intersections. For example, vehicles at the south import can first turn right in the coordination area to reach the east import and then go straight from the east import to the east export lane.

[0092] (3) Priority can be given to emergency vehicles: In signal-free intersection control, the priority of emergency vehicles is generally given by increasing their weights in the objective function, such as the weight of vehicle delay, to give priority to the passage of emergency vehicles. Although this modeling method can give priority to emergency vehicles to a certain extent, usually due to the need to consider the delays of other vehicles in the model solution, it cannot ensure that emergency vehicles pass first. In the present invention, priority is given to emergency vehicles by reducing the longest passing time of emergency vehicles in the coordination area, and adjusting the time for all vehicles to enter the coordination area, which can ensure that emergency vehicles pass through the intersection without delay.

[0093] (4) It can represent the passing paths of vehicles at any conventional or unconventional intersections: Currently, there is little research on traffic conflict control at signal-free intersections under unconventional intersections. By adjusting the range of the coordination control area and the connection matrix between grids in the spatio-temporal network model of the present invention, the passing trajectories of vehicles under different intersection designs can be represented, and a control model for signal-free intersections under unconventional intersections can be modeled. Description of the Drawings

[0094] Figure 1 Schematic diagram of intersection area division in the embodiment of the present invention;

[0095] Figure 2 Schematic diagram of an example of a spatio-temporal network diagram in the embodiment of the present invention;

[0096] Figure 3 Schematic diagram of an example of an unreasonable vehicle path in the embodiment of the present invention;

[0097] Figure 4 Schematic diagram of the intersection coordinate system in the embodiment of the present invention

[0098] Figure 5 Schematic diagram of the comparison of control model delays in the embodiment of the present invention;

[0099] Figure 6 Example diagram of the left-turn vehicle flow path in the embodiment of the present invention. Detailed implementation manners

[0100] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0101] Embodiment

[0102] Model assumptions. To meet the model requirements, the following model assumptions are made:

[0103] (1) The central manager has powerful data storage and computing capabilities, and the data transmission delay is negligible. After the vehicle sends the corresponding information, it can obtain the next driving trajectory;

[0104] (2) The vehicle has a high level of automation and also obeys the management of the central manager, and can drive according to the feedback driving trajectory;

[0105] (3) In this embodiment, the vehicle is regarded as a particle to study the vehicle's motion trajectory. In the spatio-temporal network model, microscopic vehicle motion models such as the vehicle's steering angle and sideslip angle are not considered. After obtaining the grid points corresponding to vehicle passage, the vehicle driving trajectory is obtained based on the trajectory reconstruction model considering vehicle kinematic constraints.

[0106] This embodiment focuses on the traffic conflict control method at unsignalized intersections in the context of autonomous driving. Based on a pure autonomous driving environment, with the spatial separation of conflict points at intersections (vehicle paths at intersections) as the main research object, considering the temporal separation of conflict points (vehicle running speeds at intersections), in-depth research on traffic conflict control at unsignalized intersections is carried out. With the goal of ensuring the safety of vehicle passage at intersections and improving the traffic efficiency at intersections, taking autonomous driving vehicles as the control object, based on traffic conflict control theory, innovatively changing the paths of autonomous driving vehicles at intersections based on unconventional intersection paths, exploring traffic conflict control at unsignalized intersections in a pure autonomous driving environment, so as to better improve the traffic efficiency at intersections.

[0107] The spatio-temporal network control model established in this embodiment mainly describes the movement process of vehicles in the spatio-temporal control coordination area of intersections, that is, with the goal of the vehicle passing through the spatio-temporal network coordination area as quickly as possible, determining the time for each vehicle to enter the coordination area and the grid movement within the coordination area. The spatio-temporal network control model has the following advantages:

[0108] (1) The function of fixed lane division on the approach is not required. In the spatio-temporal network control model of this embodiment, vehicles can reach the destination exit lane from any approach lane. For example, Figure 1 Vehicles in the leftmost lane of the south approach can go straight to the north exit, turn left to the west exit, or turn right to the east exit. Compared with other signal-free intersection control schemes with fixed approach lane functions, the number of vehicle lane changes is reduced.

[0109] (2) Left-turning vehicles have more abundant left-turn paths to choose from. Since the scope within the intersection coordination area in this embodiment is discretized into grids, and the connection of grids represents the passing path of vehicles at intersections. When the coordination area is large enough, left-turning vehicles do not need to pass through the intersection in the conventional left-turn way. For example, south approach vehicles can first turn right within the coordination area to reach the east approach and then go straight from the east approach to the east exit.

[0110] (3) Priority can be given to emergency vehicles. In the control of signal-free intersections, regarding the priority of emergency vehicles, it is generally to increase its weight in the objective function, such as the vehicle delay, to give priority to the passage of emergency vehicles. Although this modeling method can give priority to emergency vehicles to a certain extent, usually because the solution of the model also needs to consider the delays of other vehicles, it cannot ensure that emergency vehicles pass first. In this embodiment, priority is given by reducing the maximum passing time of emergency vehicles in the coordination area, and adjusting the time for all vehicles to enter the coordination area, which can ensure that emergency vehicles pass through the intersection without delay.

[0111] (4) It can represent the passing paths of vehicles at any conventional or unconventional intersections. Currently, there is little research on traffic conflict control at signal-free intersections under unconventional intersections. By adjusting the scope of the coordination control area and the connection matrix between grids in the spatio-temporal network model of this embodiment, the passing trajectories of vehicles under different intersection designs can be represented, and a control model for signal-free intersections under unconventional intersections can be modeled.

[0112] The spatio-temporal network control model for signal-free intersections based on non-fixed paths mainly includes four control steps:

[0113] Step 1: Pretreatment:

[0114] Pretreatment mainly clarifies the traffic conflict control scope of the intersection and divides grids. The control scope is as Figure 1As shown in the figure. After the vehicle arrives at the control area, it needs to report to the central manager the vehicle's speed, position, acceleration, entry lane, intended turn (straight, left, right), and the time of arrival at the intersection control area.

[0115] The control area can be further divided into a spatio-temporal network coordination area and an approach control area. The spatio-temporal network coordination area is a rectangle formed by extending the stop lines of each approach. The intersection space within the coordination area is divided into grids of the same size, and the movement of vehicles within the coordination area is characterized by the connection method between the grids. The size of the spatio-temporal network coordination area is not completely fixed and can also be expanded to the approach area according to actual needs. The larger the coordination area, the more discrete spatio-temporal network grids there are, and the more vehicle paths characterized by grid connections there are. The size of the spatio-temporal network grid is required to accommodate a single vehicle.

[0116] The approach control area is mainly the range of the intersection approach within the control area excluding the coordination area. The length of the approach control area is defined as l a .

[0117] The spatio-temporal network diagram of the coordination area is G(S, E), where S is the set of grids and E is the set of directed edges. The set of grids S = {s1, s2,..., s m} represents the set of individual grids into which the coordination area is divided. This set can be further divided into three subsets: the starting point set S o = {os1, os2,..., os n}, the ending point set S d = {ds1, ds2,..., ds q} and the set of other points Among them, the starting point set S o indicates that this grid point is the starting point of the path. In this grid, the vehicle can only start from this point and drive into the coordination area. The ending point set S d indicates that the grid point is the ending point of the path. In this grid, the vehicle can only leave the coordination area after reaching this point. The set of other points refers to the set of other grid points in the grid set excluding the starting and ending points. The vehicle is initially allowed to move in four directions: up, down, left, and right in each grid. When there is a grid in the target moving direction of the vehicle, a directed edge is formed. Define the starting grid s i , the target grid s j , and the directed edge is e ij = (s i , s j ). All directed edges form the set of directed edges E. Without considering the direction of the edges, define the set of undirected edges

[0118] Define the time set \(T = \{\Delta t, \Delta t, \ldots, k\Delta t\}\), where \(\Delta t\) is the unit time step and \(k\) is the total number of steps that can be divided within the time range. Define the time step pair set \(TP=\{TP_1, TP_2, \ldots, TP m \}\), where \(TP_1=\{(\Delta t, 2\Delta t), \ldots, [(k - 1)t, k\Delta t]\}\), \(TP_2=\{(\Delta t, 3\Delta t), (2\Delta t, 4\Delta t), \ldots, [(k - 2)t, k\Delta t]\}\), \(\ldots\), \(TP m =\{(\Delta t, m\Delta t), (2\Delta t, 2 + m\Delta t), \ldots, [(k - m)t, k\Delta t]\}\). The number \(m\) of step pairs represents the maximum number of time steps allowed to differ between the starting time and the ending time in each time step group. Different numbers of time step pairs represent different times required for the vehicle to move between grids. The values need to meet the vehicle kinematics requirements, which are mainly determined by the maximum speed and the side length distance of a single grid.

[0119] Define the spatio - temporal network grid \(n ij and the spatio - temporal network grid set \(N\), \(n ij \in N\). The spatio - temporal network grid \(n ij =(t i , s j ), indicating the \(s i \) grid at time \(t j \). Define the connected spatio - temporal network edge \(l ijpq and the spatio - temporal network edge set \(L\), \(l ijpq \in L\). The spatio - temporal network edge \(l ijpq connects adjacent spatio - temporal network grids \(n ij and grid \(n pq \), that is, it allows the vehicle to travel from the \(s i \) grid at time \(t j \) to the \(s q \) grid, and the arrival time is \(t p \), that is, \(l ijpq =(n ij , n pq )=[(t i , s j ), (t p , s q )]. Taking Figure 2 the intersection with two import grids and two export grids set at each import as a simple example, the coordination area is discretized into 32 grids, of which 8 belong to the starting set and 8 belong to the ending set. Other point grids are represented by ordinary numbers. Taking the directed - edge path of os2 - 4 - 8 - 12 - 16 - ds5 in the figure as an example, when \(m = 2\), the corresponding spatio - temporal network diagram is as shown on the Figure 2 right side. In Figure 2 the spatio - temporal network grid \(n ij is represented by a blue circle, and the spatio - temporal network edge \(lijpq It is represented by a red straight line, and the arrow represents the direction of the edge.

[0120] Step 2: The arriving vehicle sends a request, and the central manager determines whether to allow the vehicle to enter.

[0121] Once the vehicle enters the control area, it needs to send a passing request to the central manager, mainly including the vehicle's current speed, position, acceleration, entering lane, vehicle type, intended turn (going straight, turning left, turning right), and the time to enter the intersection control area.

[0122] The central manager determines whether to allow the vehicle to enter the control area based on whether the number of coordinated vehicles in the existing intersection control area is saturated. If allowed, the central manager calculates the earliest arrival time of the vehicle at the coordination area and the latest departure time of the vehicle from the coordination area according to the arrival time and vehicle type reported by the vehicle, and then proceeds to Step 3. If not allowed, the vehicle needs to immediately decelerate and stop. The earliest arrival time of the vehicle at the coordination area is equal to the moment when the vehicle enters the control area plus the time required for the vehicle to travel through the approach control area at the maximum speed. The latest departure time of the vehicle from the coordination area is equal to the earliest arrival time of the vehicle at the coordination area plus the longest time for the vehicle to pass through the coordination area. Among them, the longest time for the vehicle to pass through the coordination area is related to the vehicle type. If the vehicle is an emergency vehicle, such as an ambulance, a fire truck, etc., the longest time for the vehicle to leave the coordination area is the time when the vehicle enters the coordination area plus the fastest time to pass through the coordination area. Assume that the fastest time for the vehicle to pass through the coordination area is t1. If the vehicle is an ordinary vehicle, the longest time for the vehicle to pass through the coordination area is set to t2 respectively, and it is required that t1 < t2.

[0123] Step 3: Solve the spatio-temporal network control model and the trajectory reconstruction model, and feedback the specific driving trajectory to the vehicle.

[0124] In this step, the central manager first solves the arrival time of the vehicle at the coordination area according to the spatio-temporal network control model of the earliest arrival time of the vehicle at the coordination area and the latest departure time of the vehicle from the coordination area, and obtains the driving trajectory of the vehicle in the coordination area based on the trajectory fitting model and feedbacks it to the vehicle.

[0125] 1. Spatio-temporal network model:

[0126] Consider a vehicle set D = {1, 2,..., z} with z vehicles, where the type of vehicle d is b d , b d ∈{B1, B2}, where B1 represents emergency vehicles and B2 represents ordinary vehicles. The starting cell corresponding to vehicle d is os d , and the ending cell is ds d . The moment when the vehicle enters the control area is t d , and the earliest time for the vehicle to enter the coordination area is T d,EA, the latest time to leave the coordination area is T d,LD . According to the analysis of the central manager and vehicle priorities, T can be calculated d,EA and T d,LD . Among them, l a is the length of the import lane control area, and t1 and t2 are the times for emergency vehicles and ordinary vehicles to pass through the coordination area respectively.

[0127] T d,EA = t d + l a / v max , d ∈ D (1)

[0128]

[0129] Define two 0-1 variables x d,l and x d,et to represent the position of vehicle d in the spatio-temporal network graph G(S,E). x d,l refers to whether vehicle d occupies the spatio-temporal edge l ijpq . If it occupies, then x d,l = 1, indicating that vehicle d moves from point s i to point s p within the time range from t j to t q . If it does not occupy, then x d,l = 0. x d,et refers to whether the vehicle occupies edge e ij at time t. If it occupies, then x d,et = 1, otherwise x d,et = 0. The variables and the variable need to meet the requirement of value consistency within the same time period [t i , t p . When vehicle d occupies edge e i to t p = (s jq , s j , s q ) within the time range, the spatio-temporal edge variable and the variable indicating whether the edge is occupied at the corresponding time But when the variable indicating whether the edge is occupied at the corresponding time , due to the possible existence of multiple time pairs, it is impossible to determine which specific spatio-temporal edge variable But there must be a sum of 1 for all spatio-temporal edge occupancy variables that include this edge and the time pair includes time t. Taking vehicle 5 in Figure 2 as an example, with edge e = (os2,4) and time 1, T t＝1 includes time pairs (0,1), (0,2), (1,2) and (1,3). When When The linearized relationship between the two variables is shown in Equations (3) and (4).

[0130]

[0131]

[0132] In Equation (3), T t is a set of time pairs containing the moment t. When the vehicle occupies the spatio-temporal edge l(t i , s j , t p , s q ), x d,l = 1, Equation (3) requires x d,et = 1, where When x d,l = 0, Equation (3) is relaxed. When the vehicle occupies the edge e at time t jq = (s j , s q ), x d,et = 1, the value of x d,l cannot be determined in Equation (3). Equation (4) requires that for the spatio-temporal network edge l composed of the corresponding edge e jq and the time pair T t containing the moment t, the sum of the edge occupancy variables is required to be greater than or equal to 1.

[0133] A spatio-temporal network control model is established with the goal of minimizing vehicle delay. Minimizing vehicle delay can be transformed into the vehicle leaving the intersection as quickly as possible. The model objective function is as follows.

[0134]

[0135] Among them, T d,LDA represents the time when vehicle d leaves the coordination area, which can be represented by the value of the end point moment corresponding to the spatio-temporal edge where the vehicle occupies its corresponding end point.

[0136] The model constraints mainly include:

[0137] (1) Vehicle path continuity constraint. It is required that the vehicle must start from the starting point and finally reach the end point. At each grid point, the vehicle does not appear out of thin air and does not disappear out of thin air. That is, if it is a grid in the starting point set, then in the corresponding spatio-temporal edge, there is only the departure of the vehicle and no arrival of the vehicle. Similarly, for the grid in the end point set, there is only arrival and no departure. For other grid points, if there is a departure, there must be an arrival.

[0138]

[0139] (2) A vehicle can only occupy one edge at a moment.

[0140]

[0141] (3) An undirected edge can be occupied by at most one vehicle at a time, that is, an undirected edge can accommodate at most one vehicle at a time to ensure the safety of vehicle operation.

[0142]

[0143] (4) Vehicle order constraint. At each starting point, vehicles follow the rule of first come, first served. The vehicle that arrives at the coordination area first occupies the spatio-temporal edge corresponding to the starting grid. Since the path inside the coordination area is not fixed, the vehicle that enters the coordination area first does not necessarily leave the coordination area first. Define T d,EAA to represent the actual time when vehicle d is allowed to enter the coordination area, and δ ij is a 0-1 variable indicating the order in which vehicles i and j with the same starting point arrive at the starting point earliest. If vehicle i arrives earlier than vehicle j, δ ij = 1, otherwise, δ ij = 0.

[0144] T j,EAA - T i,EAA > (δ ij - 1)M

[0145] T j,EAA - T i,EAA < δ ij M (9)

[0146] In Equation (8), when vehicle i arrives earlier than vehicle j, δ ij = 1, and Equation (8) requires T j,EAA > T i,EAA , when vehicle i arrives earliest than vehicle j, δ ij = 0, and Equation (8) requires T j,EAA < T i,EAA .

[0147] (5) No circular paths can occur. This constraint is to ensure the rationality of the path. To represent this constraint, the requirement that no circular paths can occur can be transformed into the number of spatio-temporal paths starting from each grid by the vehicle must be less than or equal to 1. When there is a circular path, at the starting point of the loop, the vehicle still needs to start from this point. At this time, the number of spatio-temporal paths starting from this point is 2.

[0148]

[0149] (6) A vehicle cannot occupy an undirected edge multiple times, that is, the vehicle will not move forward and backward on this edge or pass through it repeatedly.

[0150]

[0151] (7) Comfort constraint. Although both constraint conditions (5) and (6) limit the traffic paths of vehicles at intersections to a certain extent, there may still be unreasonable vehicle paths where vehicles turn multiple times. Unreasonable vehicle paths are as shown in Figure 3 . This path meets the requirements that vehicles do not pass through a certain path repeatedly and there is no circular path, but there are a large number of turns in this path, and vehicles turn repeatedly multiple times within a short distance. The turning points are shown as gray circles in the figure, which is not conducive to vehicle driving safety and comfort. In order to make the trajectory as smooth as possible, a constraint on vehicle turning is added in this constraint condition. Each vehicle is only allowed to execute at most three turns within the intersection. Define a 0-1 variable to represent whether to turn from edge (s i , s j ) to edge (s p , s q ). If a turn is required, the value is 1, otherwise the value is 0.

[0152]

[0153] To linearize the comfort constraint (12), introduce a variable to represent whether edge (s i , s j ) and edge (s p , s q ) are occupied simultaneously. Only when both edges are occupied, the value of this variable is 1, otherwise the value is 0. The mathematical expression is as in (13).

[0154]

[0155] Introduce a 0-1 variable to linearize formula (13). If , it means the former is the smaller value, otherwise it means the latter is the smaller value. Constraint (12) is finally transformed into formula (14).

[0156]

[0157] In formula (14), when , When , there is meeting the corresponding numerical requirements of the variable.

[0158] 2. Trajectory reconstruction model:

[0159] The result finally obtained by the spatio-temporal network control model is discrete, that is, the position of the vehicle at a certain moment on the grid point. After the vehicle obtains this information, it still cannot completely determine the trajectory of the vehicle at the intersection. Therefore, in this subsection, a trajectory reconstruction model is proposed. On the basis of meeting the requirements of the output results of the spatio-temporal network model, considering the comfort of the vehicle driver, a continuous and smooth vehicle trajectory is fitted. Zhao et al. proposed a trajectory optimization model based on the discrete vehicle trajectory, considering driver comfort and dynamic constraints. A major advantage of this model is that it can make the model results as close as possible to the discrete points, meeting the requirement in the spatio-temporal network model that the vehicle should drive close to the center of the grid point. Based on this trajectory optimization model, considering spatio-temporal network constraints, this paper establishes a vehicle trajectory reconstruction model at the intersection.

[0160] Establish a two-dimensional coordinate system at the intersection as Figure 4 shown, and the state X(t) of the vehicle at time t and the vehicle control variables can be expressed as:

[0161] X(t) = [x(t), y(t), θ(t), v(t)] Τ

[0162] U(t) = [k(t), a(t)] Τ (15)

[0163] where x(t), y(t), θ(t), v(t) are the abscissa, ordinate, steering angle and speed at this moment respectively. k(t), a(t) are the steering angle change rate and acceleration at this moment respectively. The steering angle change rate is related to the turning radius and is the reciprocal of the turning radius.

[0164] Then the state of the vehicle at the next moment is:

[0165]

[0166] Since the trajectory of the vehicle in the intersection is restricted by the grid size and the grid it occupies, although it is assumed to be a particle in the research, it is still hoped that the movement trajectory of the vehicle is as close as possible to the center of the grid point to meet the actual traffic demand of the vehicle as much as possible. The center point coordinates of each grid point are regarded as the position that the vehicle expects to reach at this moment. Set the objective function as the root mean square error of the trajectory, as shown in Equation (17):

[0167]

[0168] where n is the number of points used to fit the vehicle trajectory, and c(X(t)) represents the cost of the vehicle at time t, which is mainly used to measure the squared Euclidean distance between the actual position (x(t), y(t)) of the vehicle at this moment and the expected position of the grid point - the center point (x0(t), y0(t)), as shown in Equation (18).

[0169] c(X(t)) = (x(t) - x0(t)) 2 + (y(t) - y0(t)) 2 (18)

[0170] The constraint conditions for trajectory reconstruction include:

[0171] (1) The position of the vehicle at this moment cannot exceed the boundary points of the grid point.

[0172]

[0173] Where respectively represent the minimum and maximum abscissa values of the grid point where the vehicle is located at time t, respectively represent the minimum and maximum ordinate values of the grid point where the vehicle is located at time t. The boundary points are obtained from the solution results of the spatio-temporal network.

[0174] (2) Constraints on the maximum speed and minimum acceleration of the vehicle.

[0175] 0 < v(t) < v max

[0176] a min < a(t) < a max (20)

[0177] (3) Constraints on passenger comfort, mainly achieved by constraining the change in vehicle acceleration.

[0178]

[0179] Where j min ,j max respectively represent the minimum braking jerk and the maximum braking jerk, and j min = -j max .

[0180] (4) Vehicle turning radius constraint.

[0181]

[0182] Where r min is the minimum turning radius considering safety and passenger comfort. k(t) represents the reciprocal of the vehicle turning radius at time t.

[0183] (5) Lateral acceleration constraint. For the vehicle during driving, for the same acceleration value, it is much more difficult to complete lateral acceleration than longitudinal acceleration. Therefore, the lateral acceleration needs to meet the vehicle's own motion requirements.

[0184] -g(e + f s) ≤ v(t) 2 k(t) ≤ g(e + f s ) (23)

[0185] where g is the gravitational acceleration, e is related to the height difference of the road on which the vehicle travels, and f s represents the friction coefficient.

[0186] (6) Curvature change constraint. According to vehicle dynamics, it takes time for a vehicle to make a turn, and the comfort of passengers also needs to be considered during the turning process. The change in the turning radius needs to satisfy the curvature constraint.

[0187]

[0188] Step 4: The vehicle travels along the driving trajectory feedback by the central manager and safely passes through the intersection.

[0189] The vehicle adjusts its speed according to the time it arrives at the coordination area and arrives at the coordination area on time. After entering the coordination area, it travels along the corresponding trajectory to pass through the intersection.

[0190] In the case study, the results of the model are compared with those of the classical FCFS control model, the conflict point control model (CCM) proposed by Levin, and the free lane following model (FLFM).

[0191] Considering that the general vehicle length is 3.5 m and the general width of the approach lane is 3.5 m, the grid width is taken as 4 m. There are two choices for the time to move from one grid to another, 0.5 s and 1 s, that is, Δt and 2Δt, where Δt = 0.5 s, and the speeds are approximately 4 m / s (14.4 km / h) and 8 m / s (28.8 km / h). The grid division is as Figure 4 shown. Since the width of the approach lane is less than the grid width, only one starting grid is set for each approach lane in the spatio-temporal network model, and only one ending grid is set for each exit lane. The fastest passing times of left-turning and straight-going vehicles through the intersection are 9Δt and 12Δt respectively. The fastest passing times t1 and t2 of emergency vehicles and ordinary vehicles through the coordination area are set to 12Δt and 30Δt respectively. The speeds of the FCFS model, CCM model, and FLFM model are fixed at 8 m / s. The fastest passing times of straight-going and left-turning vehicles in all models are uniformly 4.5 s and 6 s. In the FCFS model, CCM model, and FLFM model, the vehicle delay is equal to the delay when the vehicle enters the intersection. In the spatio-temporal network model, the vehicle delay also needs to add the passing delay inside the intersection.

[0192] Temporarily disregarding right-turning vehicles, three traffic flow scenarios are set to test the arrival of vehicles: (1) the number of vehicles in each turning direction at each approach is the same (the scenario of consistent proportions), (2) the total traffic flow at each approach road is the same but the left-turn traffic flow is higher (the scenario of different left-turn proportions), and (3) certain vehicles are set as emergency vehicles (the scenario of emergency vehicle passing). The experiments use the tests of two different traffic flow arrival intervals and different traffic volumes in Table 1 and Table 2 as vehicle inputs. The main difference in traffic flow arrival between the two tests lies in the different time intervals of vehicle arrival. In Test 2, the traffic flow arrival intervals are closer, with an interval of 0.5 s. The experiments are completed on a personal computer equipped with an AMD processor and 16 GB of memory.

[0193] Table 1 Vehicle Input for Test 1 (All Vehicle Types Are Ordinary Vehicles)

[0194]

[0195] Scenario of consistent proportions:

[0196] In the scenario of consistent proportions, the traffic flow arrives according to the traffic flow design in the experiment. When only one grid is set at the approach, the delay comparisons of the three control schemes, namely the FCFS model, the CCM model, and the TSC model, are as Figure 5 shown. It can be obtained from the figure that the delay comparison results are as follows:

[0197] (1) The spatio-temporal network model can reduce the average vehicle delay. This is mainly because in the spatio-temporal network model, the passing paths of vehicles are no longer fixed, and there are more flexible passing schemes for vehicles to choose. This research result will be described in more detail in the part of different left-turn proportions.

[0198] (2) When the traffic volume is low, the FCFS control scheme can still arrange the passing of vehicles well. However, as the number of vehicles increases, the advantage of FCFS is not as obvious as that of the conflict point-based control model, which is in line with the existing research results.

[0199] Table 2 Vehicle Input for Test 2 (All Vehicle Types Are Ordinary Vehicles)

[0200]

[0201] Scenario of different left-turn proportions:

[0202] In the scenario of consistent proportions, the proportion of straight and left-turn traffic flows at each approach is 50%. To study the performance of the model under different left-turn proportions, the proportion of left-turn vehicles is increased in Test 2, and the proportion of straight and left-turn at each approach is adjusted to 1:3. The specific adjusted vehicle numbers are shown in Table 3.

[0203] Table 3 Adjusted Vehicle Numbers in Test 2 under Different Left-Turn Proportions

[0204]

[0205] After adjusting the vehicle path, the average vehicle delay of the spatio-temporal network model is 0, while the average vehicle delays of the FCFS model and the conflict point model are 3.86 s and 1.41 s respectively. The results show that after increasing the left-turn proportion, the average vehicle delay of the spatio-temporal network model is still the lowest, followed by the conflict point model, and finally the FCFS model. The spatio-temporal network model still performs the best, and after increasing the left-turn proportion, the average vehicle delay decreases. By analyzing the passing paths of left-turn vehicles at intersections under the spatio-temporal network model, it can be found that the passing paths of left-turn vehicles are indeed more flexible than those of vehicles passing through conventional intersections. Taking left-turn vehicles 4 and 5 at the south entrance as examples, the passing paths of the two vehicles are as Figure 6 shown Figure 6 In it, (a) is vehicle 4 and (b) is vehicle 5, and the paths turn at different positions at the intersection.

[0206] Emergency vehicle passing scenario:

[0207] The spatio-temporal network model has an advantage over the rhythm control model and the conflict point model. It can improve the arrangement degree of emergency vehicles at intersections by adjusting the latest departure time of emergency vehicles from intersections, ensuring the priority passing of emergency vehicles at intersections.

[0208] To illustrate the passing of emergency vehicles at intersections, in this case study, the shortest passing times of left-turn vehicles with delays in Test 2 under the scenario of consistent proportion, namely vehicle 5, vehicle 12, and vehicle 21, are adjusted from 30Δt to 12Δt, and the corresponding latest departure times are set to 16Δt, 14Δt, and 16Δt. Solving the spatio-temporal network model shows that the average vehicle delay at the intersection remains unchanged, still 0.43 s, but the delay of emergency vehicles is 0. The delays of vehicle 5, vehicle 12, and vehicle 21 are transferred to ordinary vehicles. The delays of ordinary vehicles 4, 11, 20, 24, 27, 28, and 29 increase, and the delays of vehicles 2, 3, 5, 10, 12, 19, 21, and 26 decrease. The comparison of the passing times of vehicles under ordinary vehicles and emergency vehicles is shown in Table 4.

[0209] Table 4 Comparison of vehicle passing times at intersections under ordinary vehicles and emergency vehicles (time unit: Δt)

[0210]

[0211]

[0212] The above-described embodiments merely represent specific embodiments of the present invention. Their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the patent for the present invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all fall within the protection scope of the present invention.

Claims

1. A method for controlling traffic conflicts at unsignalized intersections for autonomous driving based on spatiotemporal networks, characterized in that: The following steps are involved: Step 1: Preprocessing: Define the intersection traffic conflict control range and divide it into grids. After the vehicle arrives at the control area, it reports the vehicle's speed, position, acceleration, lane entry, intended turn, and time of arrival at the intersection control area to the central manager; Step 2: The arriving vehicle sends a request, and the central manager determines whether to allow the vehicle to enter; Step 3: Solve the spatiotemporal network control model and trajectory reconstruction model, and feed back the specific driving trajectory to the vehicle; Step 4: The vehicle drives according to the driving trajectory fed back by the central manager and passes the intersection safely.

2. The method for controlling traffic conflicts at unsignalized intersections based on spatiotemporal networks for automatic driving according to claim 1, characterized in that: In step 1, the control area includes a spatiotemporal network coordination area and an entrance road control area; the spatiotemporal network coordination area is a rectangle formed by extending the stop lines of each entrance road, and the spatial range of the intersection in the coordination area is divided into grids of uniform size, and the movement of vehicles in the coordination area is characterized by the connection between the grids; the entrance road control area is the range of the intersection entrance road after excluding the coordination area in the control area, and the length of the entrance road control area is defined as l a , the coordination zone spatiotemporal network graph G(S,E), where S is a grid set and E is a directed edge set; the grid set S = {s1,s2,...,s m } represents a single grid set into which the coordination area is divided. The single set is divided into three subsets. The starting point set S o ={os1,os2,...,os n }、End point set S d ={ds1,ds2,...,ds q } and other point sets The starting point set So indicates that the grid point is the starting point of the path, and the vehicle can only enter the coordination area from this point. d Indicates that the grid point is the end point of the path. The vehicle can only leave the coordination area after reaching this point. It refers to the set of grid points other than the starting point and the end point in the grid set; the vehicle is allowed to move in four directions, up, down, left, and right, at the beginning of each grid. When there is a grid in the target moving direction of the vehicle, a directed edge is formed, defining the starting grid s i , target point grid s j , the directed edge is e ij =(s i ,s j ); all directed edges form the directed edge set E; regardless of the direction of the edge, define the undirected edge set Define a time set T = {Δt, Δt, ..., kΔt}, where Δt is the unit time step and k is the total number of steps that can be divided within the time range; define a time step pair set TP = {TP1, TP2, ..., TP m }, where TP1={(Δt,2Δt),...,[(k-1)t,kΔt]}, TP2={(Δt,3Δt),(2Δt,4Δt)...,[(k-2)t,kΔt]}, TP m ={(Δt,mΔt),(2Δt,2+mΔt)...,[(km)t,kΔt]}; the number of step pairs m represents the maximum number of time steps allowed to differ between the starting time and the ending time in each time step group; Different numbers of time step pairs represent the different times required for the vehicle to move between grids. The values ​​need to meet the vehicle kinematic requirements, which are determined by the maximum speed and the side length of a single grid; Define the space-time network grid n ij and the space-time network grid set N,n ij ∈N; space-time network grid n ij =(t i ,s j ), indicating that at t i Moment of j Grid; define the connecting space-time network edge l ijpq and the spatiotemporal network edge set L,l ijpq ∈L; spatiotemporal network edge l ijpq Connect adjacent space-time network grids n ij and grid n pq , that is, the vehicle is allowed to i Time from s j Grid driving from s q Grid, arrival time is t p , i.e. l ijpq =(n ij ,n pq )=[(t i ,s j ),(t p ,s q )].

3. The method for controlling traffic conflicts at unsignalized intersections based on spatiotemporal network for automatic driving according to claim 2, characterized in that: The step 2 is specifically as follows: The central manager determines whether to allow the vehicle to enter the control area according to whether the number of coordinated vehicles in the existing intersection control area is saturated. If allowed, the central manager calculates the earliest time for the vehicle to arrive at the coordination area and the latest time for the vehicle to leave the coordination area according to the arrival time and vehicle type reported by the vehicle, and continues to step three. If not allowed, the vehicle needs to slow down and stop immediately; the earliest time for the vehicle to arrive at the coordination area is equal to the time when the vehicle enters the control area plus the time required for the vehicle to travel through the entrance road control area at the maximum speed; the latest time for the vehicle to leave the coordination area is equal to the earliest time for the vehicle to arrive at the coordination area plus the longest time for the vehicle to pass through the coordination area; the longest time for the vehicle to pass through the coordination area is related to the type of vehicle. If the vehicle is an emergency vehicle, the latest time for the vehicle to leave the coordination area is the time when the vehicle enters the coordination area plus the fastest time to pass through the coordination area; assuming that the fastest time for the vehicle to pass through the coordination area is t1, if the vehicle is an ordinary vehicle, the longest time for the vehicle to pass through the coordination area is set to t2, requiring t1<t2.

4. The method for controlling traffic conflicts at unsignalized intersections based on spatiotemporal network for automatic driving according to claim 3 is characterized in that: In step three, the spatiotemporal network control model is as follows: Consider a vehicle set D = {1,2,...,z} with z vehicles, and vehicle d belongs to type b. d , b d ∈{B1,B2}, where B1 represents an emergency vehicle and B2 represents an ordinary vehicle; the starting grid corresponding to vehicle d is os d , the end grid is ds d ; The time when the vehicle enters the control area is t d The earliest time a vehicle enters the coordination area is T d,EA , the latest time to leave the coordination area is T d,LD ; Calculate T based on the analysis of the central manager and vehicle priorities d,EA and T d,LD ; where l a is the length of the import control area, t1 and t2 are the time for emergency vehicles and ordinary vehicles to pass through the coordination area respectively: T d,EA =t d +l a / v max ,d∈D Define two 0-1 variables x d,l and x d,et To represent the position of vehicle d in the spatiotemporal network graph G(S,E); d,l Refers to whether vehicle d occupies the space-time edge l ijpq , if occupied, then x d,l =1, indicating that vehicle d is at time t i to p From point s j Move to point s q , if not occupied, then x d,l =0;x d,et It refers to whether the vehicle occupies edge e at time t ij , if occupied then x d,et =1, otherwise x d,et =0; variable and variables In the same period [t i ,t p ] needs to meet the value consistency requirement; when vehicle d is at time t i to p The range occupies the edge e jq =(s j ,s q ),the space-time boundary variable At the same time, the variable whether the edge is occupied at the corresponding time But when the edge is occupied at the corresponding time, the variable When , there may be multiple time pairs, it is impossible to determine which space-time edge variable But there must be a spacetime edge that contains this edge and whose time pair contains the time instant t, and the sum of the occupied variables is 1; A spatiotemporal network control model is established with the goal of minimizing vehicle delay; minimizing vehicle delay is converted into the fastest vehicle departure from the intersection; the model objective function is shown below. Among them, T d,LDA The time when vehicle d leaves the coordination area can be expressed by the end-point time value corresponding to the space-time edge where the vehicle occupies its corresponding end point.

5. The method for controlling traffic conflicts at unsignalized intersections based on spatiotemporal network for automatic driving according to claim 4 is characterized in that: The constraints of the empty network control model are as follows: (1) Vehicle path continuity constraint: The vehicle must start from the starting point and finally arrive at the destination. At each grid point, the vehicle will not appear or disappear out of thin air. That is, if the grid point is concentrated with the starting point, then the corresponding space-time edge only has the departure of the vehicle, but no arrival of the vehicle. Similarly, the grid point concentrated with the destination has only arrival, but no departure. For other grid points, if there is a departure, there must be an arrival: (2) A car can only occupy one edge at a time: (3) An undirected edge can be occupied by at most one vehicle at a time, that is, an undirected edge can accommodate at most one vehicle at a time to ensure the safety of vehicle operation: (4) Vehicle order constraint: At each starting point, vehicles follow the first-come, first-served rule; the vehicle that arrives at the coordination area first occupies the space-time edge corresponding to the starting grid first; since the path inside the coordination area is not fixed, the vehicle that enters the coordination area first may not necessarily leave the coordination area first; define T d,EAA represents the time when vehicle d is actually allowed to enter the coordination area, δ ij is a 0-1 variable indicating the order in which vehicles i and j with the same starting point arrive at the starting point first. If vehicle i arrives before vehicle j, δ ij =1, otherwise, δ ij =0: T j,EAA -T i,EAA >(δ ij -1)M T j,EAA -T i,EAA <δ ij M When vehicle i arrives before vehicle j, δ ij =1, requiring T j,EAA >T i,EAA , when vehicle i arrives earlier than vehicle j,δ ij =0, requiring T j,EAA <T i,EAA ; (5) No circular paths: The requirement that no circular paths should appear can be translated into the number of space-time paths that the vehicle can take from each grid must be less than or equal to 1. When a circular path exists, the vehicle must also start from the starting point of the loop. In this case, the number of space-time paths that start from this point is 2. (6) A vehicle cannot occupy an undirected edge multiple times, that is, the vehicle will not move forward or backward on the edge, or pass through it repeatedly: (7) Comfort constraint: The path meets the requirements that the vehicle does not pass through a certain path repeatedly and there is no circular path, but the vehicle has a large number of turns in the path and turns repeatedly in a short distance, which is not conducive to vehicle driving safety and comfort. In order to make the trajectory as smooth as possible, the constraint of vehicle turning is added to the constraint conditions. Each vehicle is only allowed to make a maximum of three turns in the intersection. Define 0-1 variables Indicates that from the edge (s i ,s j ) to edge(s p ,s q ) Whether to turn, if turning is required, the value is 1, otherwise the value is 0:

6. The method for controlling traffic conflicts at unsignalized intersections based on spatiotemporal networks for automatic driving according to claim 5 is characterized in that: The trajectory reconstruction model is specifically as follows: On the basis of meeting the requirements of the control output results of the spatiotemporal network model, a continuous and smooth vehicle trajectory is fitted considering the comfort of the vehicle driver; based on the discrete vehicle trajectory optimization model and considering the spatiotemporal network constraints, a vehicle trajectory reconstruction model at the intersection is established: In the two-dimensional coordinate system established at the intersection, the vehicle state X(t) at time t and the vehicle control variables are expressed as: X(t)=[x(t),y(t),θ(t),v(t)] Τ U(t)=[k(t),a(t)] Τ Where x(t), y(t), θ(t), v(t) are the horizontal coordinate, vertical coordinate, steering angle and speed at the corresponding time respectively; k(t), a(t) are the steering angle change rate and acceleration at that moment respectively; the steering angle change rate is related to the turning radius and is the inverse of the turning radius; The state of the vehicle at the next moment is: The coordinates of the center point of each grid point are regarded as the position that the vehicle is expected to reach at that moment; the objective function is set to the root mean square error of the trajectory: Where n is the number of points used to fit the vehicle trajectory, c(X(t)) represents the cost of the vehicle at time t, which is used to measure the squared Euclidean distance between the actual position of the vehicle at that time (x(t), y(t)) and the expected position of the grid point, that is, the center point (x0(t), y0(t)): c(X(t))=(x(t)-x0(t)) 2 +(y(t)-y0(t)) 2 。 7. The method for controlling traffic conflicts at unsignalized intersections based on spatiotemporal networks for automatic driving according to claim 6, characterized in that: The constraints of the trajectory reconstruction model are as follows: (1) The vehicle’s position at this moment cannot exceed the boundary point of the grid point: in They represent the minimum and maximum values ​​of the horizontal coordinates of the grid point where the vehicle is located at time t, They represent the minimum and maximum values ​​of the vertical coordinates of the grid point where the vehicle is located at time t respectively; the boundary points are obtained through the solution results of the space-time network; (2) Constraints on maximum vehicle speed and minimum acceleration: 0<v(t)<v max a min <a(t)<a max (3) Constraints on passenger comfort are achieved by constraining changes in vehicle acceleration: where j min ,j max Respectively represent the minimum braking jerk and the maximum braking jerk, take j min =-j max ; (4) Vehicle turning radius constraints: where r min It is the minimum turning radius considering safety and passenger comfort; k(t) represents the inverse of the vehicle turning radius at time t. (5) Lateral acceleration constraint: -g(e+f s )≤v(t) 2 k(t)≤g(e+f s ) Among them, g is the acceleration of gravity, e is related to the height difference of the road the vehicle is traveling on, and f is related to the height difference of the road the vehicle is traveling on. s represents the friction coefficient; (6) Curvature change constraint: The change of turning radius needs to satisfy the curvature constraint:

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