CN113327441A - Network-connection automatic vehicle speed control and track optimization method based on highway confluence area - Google Patents

Network-connection automatic vehicle speed control and track optimization method based on highway confluence area Download PDF

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CN113327441A
CN113327441A CN202110166416.0A CN202110166416A CN113327441A CN 113327441 A CN113327441 A CN 113327441A CN 202110166416 A CN202110166416 A CN 202110166416A CN 113327441 A CN113327441 A CN 113327441A
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speed
acceleration
time
distance
vehicle
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CN113327441B (en
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郝威
戎栋磊
吴其育
张兆磊
龚野
王正武
王杰
吴伟
吕能超
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Changsha University of Science and Technology
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    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/09—Arrangements for giving variable traffic instructions
    • G08G1/0962—Arrangements for giving variable traffic instructions having an indicator mounted inside the vehicle, e.g. giving voice messages
    • G08G1/0967—Systems involving transmission of highway information, e.g. weather, speed limits
    • G08G1/096708—Systems involving transmission of highway information, e.g. weather, speed limits where the received information might be used to generate an automatic action on the vehicle control
    • G08G1/096725—Systems involving transmission of highway information, e.g. weather, speed limits where the received information might be used to generate an automatic action on the vehicle control where the received information generates an automatic action on the vehicle control
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • G06Q10/047—Optimisation of routes or paths, e.g. travelling salesman problem
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/065—Traffic control systems for road vehicles by counting the vehicles in a section of the road or in a parking area, i.e. comparing incoming count with outgoing count
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/09—Arrangements for giving variable traffic instructions
    • G08G1/0962—Arrangements for giving variable traffic instructions having an indicator mounted inside the vehicle, e.g. giving voice messages
    • G08G1/0967—Systems involving transmission of highway information, e.g. weather, speed limits
    • G08G1/096766—Systems involving transmission of highway information, e.g. weather, speed limits where the system is characterised by the origin of the information transmission
    • G08G1/096783—Systems involving transmission of highway information, e.g. weather, speed limits where the system is characterised by the origin of the information transmission where the origin of the information is a roadside individual element

Abstract

The invention discloses a network connection automatic vehicle speed control and track optimization method based on a highway confluence area, which is used for judging whether a CAV enters an accelerating lane or not, and starting to execute T if the CAV enters the accelerating lane1The control step of (2): t is1Judging T according to the obtained data1The speed, the distance between the vehicle and the front and rear vehicles, and the acceleration distribution are controlled based on the speed1The lowest speed requirement of driving into the main road is achieved, and T is drawn1Accelerating the lane acceleration trajectory diagram, and starting to execute trajectory optimization: t is1Safely converging into the main road by the acceleration lane and drawing T1～T5The whole-course track diagram of (1) is T of a highway confluence area1And merging the data into the main road to provide visual track display. The invention relates to a network-connected automatic vehicle speed control based on a highway confluence areaThe speed control and trajectory optimization method is oriented to mixed traffic flow under the future trend, and the speed control and trajectory optimization method is beneficial to improving the stability and safety of the mixed traffic flow in the highway confluence area.

Description

Network-connection automatic vehicle speed control and track optimization method based on highway confluence area
Technical Field
The invention belongs to the technical field of CAV (vehicle velocity and trajectory control), and relates to a network connection automatic vehicle velocity control and trajectory optimization method based on a highway confluence area.
Background
In recent years, with the rapid development and wide application of traffic infrastructure, the rapid development of intelligent traffic and intelligence is promoted. The intelligent network environment and the vehicle-road cooperation technology provide reliable system guarantee and technical support for a traffic system under the human-vehicle-road-cloud integration. The proposal of the compendium of traffic compendium pushes the development of the intelligent traffic system to a new height and a new strategy. Among traffic flow elements, a trend of a mixed traffic flow from "full-man vehicles" to "partially man-made vehicles + partially intelligent networked vehicles + partially automated vehicles" has been developed gradually, and the traffic flow will gradually tend to be automated with the technology continuously updated.
Aiming at the research of the mixed traffic flow, the CAV is expected to improve the operation quality of the mixed traffic flow from the aspect of microscopic traffic flow dynamics, and an effective method is provided for solving the problems of traffic jam and the like. Based on the existing novel infrastructure construction and updating and the rapid development of the vehicle information interaction technology, the traditional traffic flow gradually tends to be heterogeneous, and the technical researches on the operation efficiency, traffic safety emission and the like of the mixed traffic flow have more prospect and value; aiming at the research of vehicle speed control, the research is influenced by the complex environment of an urban main road, and the research starts from a highway, and the downstream speed is adjusted based on the characteristic change of the upstream traffic flow, so that the overall regulation and control of the traffic flow are realized. Meanwhile, the speed control is influenced by multiple factors (weather, driver characteristics and road characteristics), so that the real-time speed control and track optimization method still lags behind.
The CAV-oriented speed control and trajectory planning still have the following defects: (1) the existing research is mostly developed from full HVs or full CAVs, so that the existing method has certain hysteresis, CAV has high following rate and high accuracy, and the mixed traffic flow research oriented to fusing CAV under an acceleration lane has higher application value and landing practicability; (2) the existing speed control methods mostly use traffic flow as a research object, namely, speed control and evaluation are carried out on macroscopic traffic flow, and effective research is not carried out on speed control and track optimization when a specific CAV is converged into a main road in an acceleration lane.
Therefore, in order to solve the problems in the prior art, a method for network connection automatic vehicle speed control and trajectory optimization based on a highway merging area needs to be provided.
Disclosure of Invention
The embodiment of the invention aims to provide a network connection automatic vehicle speed control and track optimization method based on a highway confluence area, which realizes a full-process control framework that CAV meets the requirement of the lowest speed of a main road converging under the safety premise, realizes the speed control of the CAV on an acceleration lane and the main road and the track control of the CAV converging from the acceleration lane of the highway to the main road under the mixed traffic flow, and solves the problems in the prior art.
The technical scheme adopted by the embodiment of the invention is as follows: the network connection automatic vehicle speed control and track optimization method based on the highway confluence area comprises the following steps:
s1, a roadside detector located at the junction of the acceleration lane and the ramp judges whether an intelligent networked automatic vehicle (CAV) enters the acceleration lane, if not, the CAV runs according to a CACC or ACC following model, and the roadside detector judging process is repeatedly executed; if the CAV enters the acceleration lane, the operation goes to S2;
s2, a control step for starting to execute CAV: CAV into acceleration lane is T1，T1Front vehicle in acceleration lane is T2The rear vehicle is T3，T1The front vehicle in the main road is T4The rear vehicle is T5；T2～T5Adopting an HV car following model or a CV car following model; acquiring traffic density and flow in an acceleration lane section based on a roadside detector; method for acquiring all vehicles T on acceleration lane and main road based on vehicle-road cooperative system and remote traffic microwave radar detector RTMS1～T5Real-time velocity set v1～v5Position set p1～p5And acceleration set a1～a5For data input as S3 and data input as S4, and proceeds to S3;
s3, start speed control: the CAV judges the speed distribution condition, the vehicle distance condition and the acceleration distribution condition of the CAV and front and rear vehicles according to the real-time speed set, the position set and the acceleration set on the acceleration lane obtained in the step S2, the CAV vehicles reach the lowest speed requirement of driving into the main road before reaching the tail end of the acceleration lane based on speed control, the safe driving condition is always met, the acceleration track graph of the CAV acceleration lane is drawn, and the operation enters the step S4;
s4, starting to execute track optimization: the CAV is safely converged into the main road by the acceleration lane, and the S5 is entered;
s5, drawing an optimized track graph of the whole CAV convergence process based on the CAV acceleration track graph drawn by S3 and the main road convergence track graph drawn by S4 of the self-acceleration lane, and simultaneously drawing T2～T5The whole-course track graph provides visual track display for the CAV of the highway confluence area to converge into the main road.
Further, in S3, the speed control is started, specifically including the steps of:
s31, judgment T1Safety conditions for performing speed control: judging whether the speed control behavior at the moment reaches a safety condition meeting the minimum safety distance between vehicles, if so, entering S32, otherwise, driving the CAV with the vehicle model according to the ACC until the safety condition is met, and then entering S32；
S32、T1Starting to execute speed control for accelerating to enter the main road: dividing an acceleration lane road section into i units according to the distribution position of a road side detector to obtain T1Traffic q of the located uniti(t), traffic density ρi(T) and T1Real-time speed v of front and rear vehicles2，i、v3，iReal time position p2，i、p3，iReal time acceleration a2，i、a3，iSolving for T1Desired speed of the unit in question, for T1Performing speed control to make T1Real-time speed of the motor is adjusted to the expected speed in real time until T1The speed of the main road reaches the lowest speed requirement of driving into the main road;
s33, in each cell, T1A real-time speed determination is performed if T1If the lowest speed requirement of merging into the main road is met and the speed difference requirement, the acceleration difference requirement and the distance requirement of merging are met, drawing a CAV acceleration lane acceleration trajectory diagram, and entering S4; if T1If the minimum speed demand for merging into the main road is not met, S32 is repeated in the next unit until the speed regulation is reached to the demand for entering S4, and the flow proceeds to S4.
Further, in S31, the function of the safety condition is as follows:
Figure BDA0002933808640000031
in the formula (f)acc·safetyIs a safety condition function; a is a logarithmic coefficient; t' is T1And T2A minimum safe distance of; t is T1And T3Minimum safe distance, Δ p12Is T1And T2Of (d), Δ p13Are respectively T1And T3The pitch of (2).
Further, in S32, T1The desired velocity at the unit is shown by the following equation:
Figure BDA0002933808640000032
in the formula, v1，i(T +1) represents the ith unit T on the road section at the moment of T +11Desired speed of v1，i(T) is the ith unit T on the road section at the time T1T' is the control time step length, tau is the lag time caused by the density change of the traffic flow in front, v2，i(T) is the ith unit T on the road section at the time T2Real time velocity v of3，i(T) is the ith unit T on the road section at the time T3L is the length of each unit on the road section, η is the model parameter, ρi+1(t) is the traffic density of the (i +1) th unit on the road section at the time t, rhoi(t) is the traffic density of the ith unit on the outgoing road section at the time t, and kappa is a model parameter.
Further, T1Traffic q of the located unitiThe calculation of (t) is shown below:
Figure BDA0002933808640000033
in the formula (I), the compound is shown in the specification,
Figure BDA0002933808640000034
denotes the average speed of the i-th unit on the outgoing section at time t, λ denotes the number of lanes, ρi(t) represents the traffic density of the ith unit on the outgoing road section at the time t;
the traffic density of the ith unit on the road section at the time t +1 is calculated as follows:
Figure BDA0002933808640000035
in the formula, ρi(t +1) is the traffic density of the ith unit on the road section at the moment of t +1, rhoi(T) is the traffic density of the ith unit on the road section driven out at the time T, T' is the control time step length, and L is the length of each unit on the road section; λ represents the number of lanes; q. q.si-1(t) the traffic volume of the i-1 unit on the road section is driven out at the moment t; q. q.si(t) a time tTraffic volume of the i-th cell.
Further, when T is2Is HV, T3At CV, T2The following model adopts an optimized speed model, T3The following model adopts an intelligent driving model;
T2real-time velocity v of2，iThe equation (t) is shown below:
Figure BDA0002933808640000041
in the formula, v2，i(T) is the ith unit T on the road section at the time T2The real-time speed of (a) is a function of the distance between the vehicle heads, a2，i(T) i-th unit T on the road section at time T2Real-time acceleration of, rhoi(t) is the traffic density of the ith unit on the road section at the time t, rhocrRepresenting a critical density of the road segment;
T3real-time velocity v of3，iThe equation (t) is shown below:
Figure BDA0002933808640000042
in the formula, v3，i(T) is the ith unit T on the road section at the time T3Real time speed of a3，i(T) is the ith unit T on the road section at the time T3Real-time acceleration of the vehicle.
Further, in S33, T is1The minimum speed requirement of the merging main road is met, and the merging speed difference requirement, the acceleration difference requirement and the interval requirement are met, and the method specifically comprises the following steps:
the minimum speed requirement function for merging into the main road is shown as follows:
vmain，min≤v1，i(t)＜vacc，max；
in the formula, vmain，minFor main road minimum speed requirement, vacc，maxThe requirement of the highest running speed of the acceleration lane is met;
the functions of the speed difference requirement, the acceleration difference requirement and the distance requirement are shown as follows:
fcondition(Δv，Δa，Δp)
＝fsafety(Δv12，Δv14，Δv15)∩fsafety(Δa12，Δa14，Δa15)
∩fsafety(Δp12，Δp14，Δp15)
in the formula (f)condition(Δ v, Δ a, Δ p) is a function of speed difference, acceleration difference and distance requirement; f. ofsafety(Δv12，Δv14，Δv15) Is a speed difference safety function; Δ v12Is T1And T2Velocity difference of (1), Δ v14Is T1And T4Velocity difference of (1), Δ v15Is T1And T5The speed difference of (2); f. ofsafety(Δa12，Δa14，Δa15) Is an acceleration difference safety function; Δ a12Is T1And T2Acceleration difference of Δ a14Is T1And T4Acceleration difference of Δ a15Is T1And T5The acceleration difference of (a); f. ofsafety(Δp12，Δp14，Δp15) Is a distance safety function; Δ p12Is T1And T2Of (d), Δ p14Is T1And T4Of (d), Δ p15Is T1And T5The pitch of (d);
wherein the speed difference safety function fsafety(Δv12，Δv14，Δv15) As shown in the following formula:
Figure BDA0002933808640000051
wherein the safety function f of the acceleration differencesafety(Δa12，Δa14，Δa15) As shown in the following formula:
Figure BDA0002933808640000052
wherein the distance safety function fsafety(Δp12，Δp14，Δp15) As shown in the following formula:
Figure BDA0002933808640000053
in the formula, T' is T1And T2、T5The relative safe headstock spacing; t is T1And T4The relative safe headwear distance.
Further, in S4, the method starts to perform trajectory optimization, and specifically includes the following steps:
s41, establishing a CAV track optimization model: t is1The initial time of convergence from the acceleration lane into the main road is t0After Δ T, T1And TiHead interval of delta p1iBecomes Δ p'1i，i＝2、4、5，T1An angle theta formed with the vehicle running direction is taken as T1In the course of the run-in, T1Merging the constant longitudinal acceleration, the transverse acceleration and the steering angle theta;
s42, in CAV track optimization model, using T1And T2Minimum safe distance, T1And T4Minimum safe distance, T1And T5The minimum safe interval is a safe entry index when T1And T2Oblique distance, T1And T4Oblique distance, T1And T5Are all more than or equal to T1And T2Minimum safe distance, T1And T4Minimum safe distance, T1And T5At minimum safe distance of, T1The merge main road operation is started and the CAV merge main road locus diagram from the acceleration lane is drawn, and the process proceeds to S5.
Further, in S42, T1And T2Is inclined by an inclined distance d12The function expression of (a) is as follows:
d12≥T′
Figure BDA0002933808640000054
in the formula (d)12Is T1And T2The slant distance of (d); t' is T1And T2A minimum safe distance of; theta is a steering angle; delta p'12After a time of Δ T T1And T2The distance between the car heads; l is the vehicle length; w is the vehicle width; s1yIs T1Longitudinal travel distance of;
wherein SIyThe expression of (c) is shown as follows:
Figure BDA0002933808640000055
in the formula, v1yIs T1Longitudinal speed of a1yIs T1Longitudinal acceleration of (a);
obtaining T based on the two formulas1And T2The minimum safety spacing T';
T1and T4Is inclined by an inclined distance d14The function expression of (a) is as follows:
d14≥T
d14＝(Δp′14-L)cosθ+(3-S1y)sinθ；
in the formula (d)14Is T1And T4The slant distance of (d); t is T1And T4A minimum safe distance of; theta is a steering angle; delta p'14After a time of Δ T T1And T4The distance between the car heads; l is the vehicle length; s1yIs T1Longitudinal travel distance of;
T1and T5Is inclined by an inclined distance d15The function expression of (a) is as follows:
d15≥T′
Figure BDA0002933808640000061
in the formula (d)15Is T1And T5The slant distance of (d); t' is T1And T5A minimum safe distance of; theta is a steering angle; delta p'15After a time of Δ T T1And T5The distance between the car heads; l is the vehicle length; and w is the vehicle width.
The embodiment of the invention has the beneficial effects that:
(1) the embodiment of the invention is constructed in a scene of a highway confluence area, and fully considers the minimum speed requirement and the safe confluence condition of the CAV converged into the main road from the acceleration lane under the mixed traffic flow by the speed control and track optimization strategy of the CAV converged into the main road from the acceleration lane.
(2) The embodiment of the invention is oriented to mixed traffic flow under the future trend, and the speed control and track optimization method is beneficial to improving the stability and safety of the mixed traffic flow in the expressway confluence area.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a research scenario diagram of an embodiment of the present invention.
Fig. 2 is a partial enlarged view of a study scene of an embodiment of the present invention.
FIG. 3 shows an embodiment T of the present invention1During the time of executing the import operation delta T1Schematic diagram of the change of the track of (1).
FIG. 4 shows an embodiment T of the present invention1Performing a merge operation for a time Δ T and T2The positional relationship of (2).
FIG. 5 shows an embodiment T of the present invention1Performing a merge operation for a time Δ T and T4The positional relationship of (2).
FIG. 6 is an implementation of the present inventionExample T1Performing a merge operation for a time Δ T and T5The positional relationship of (2).
Fig. 7 is a flowchart of a method for network connection automatic vehicle speed control and trajectory optimization based on a highway confluence area according to an embodiment of the invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 7, an embodiment of the present invention provides a network connection automatic vehicle speed control and trajectory optimization method based on a highway confluence area, including the following steps:
s1, judging whether an intelligent network connection automatic vehicle CAV enters an acceleration lane by a roadside detector positioned at the junction of the acceleration lane and a ramp, and if not, repeatedly executing S1; if the CAV enters the acceleration lane, the process proceeds to S2.
S2, using the judgment result obtained in the step S1, the CAV execution control step is started: as shown in FIG. 1, the CAV entering the acceleration lane is T1，T1Front vehicle in acceleration lane is T2The rear vehicle is T3，T1The front vehicle in the main road is T4The rear vehicle is T5(ii) a Since it is probabilistically rare that there is a CAV even in a preceding vehicle or a following vehicle when the CAV enters an acceleration lane or a main road, the present invention considers T2～T5As HV (Artificial vehicle) or CV (Internet vehicle), regardless of T2～T5In the case of CAV, T2～T5Adopting an HV car following model or a CV car following model, wherein the HV car following model comprises but is not limited to an OVM car following model, and the CV car following model comprises but is not limited to an IDM car following model; acquiring traffic density and flow in an acceleration lane section based on a roadside detector; obtaining acceleration vehicle based on vehicle road cooperative system and RTMSAll vehicles (T) on the road and main road1～T5) Real-time velocity set (v)1～v5) Position set (p)1～p5) And acceleration set (a)1～a5) For data input as S3 and data input as S4, and proceeds to S3;
the specific embodiment of the invention provides an optimized T in S22～T5Following model between the acceleration lane and the main road, in this particular embodiment, the CAV or T entering the acceleration lane1Front vehicle T2For HV, following model, in particular OVM, T1Rear vehicle T in accelerating lane3For CV, the following model specifically adopts IDM following model, T1At the front of the main road T4For CV, the following model specifically adopts IDM following model, T1Rear cars T on the main road5For HV, an OVM car following model is specifically adopted for the car following model, and the OVM car following model and the IDM car following model can better reflect the car following models of the CAV on the acceleration lane and the main road through multiple times of experimental verification, provide the car following model for acquiring the real-time speed set, the position set and the acceleration set of the CAV, the CV and the HV on the acceleration lane and the main road based on a vehicle road cooperation system and RTMS, further provide traffic data and the car following model for S3 and S4, and prepare for speed control and track optimization.
As shown in equation (1), an Optimized Velocity Model (OVM) is used as the HV following Model:
x″n(t+τ)＝α[V(xn-1(t)-xn(t))-x′n(t)] (1)
in formula (1), x ″)n(t + τ) represents the acceleration of the nth vehicle (HV acceleration) at time t + τ, t represents time, τ represents the delay time, is the sum of the reaction time of the driver and the mechanical response time of the vehicle, of the order of 0.1 seconds, the coefficient α represents the sensitivity of the driver, V is a function of the headway (HV headway from the preceding vehicle), xn-1(t) represents the position of the (n-1) th vehicle (preceding vehicle HV) at time t, xn(t) represents the position, x 'of the nth vehicle (HV) at time t'n(t) represents the speed of the nth vehicle (HV) at time t.
V is a function of headway (which considers a car as a particle) and represents the desired speed that the driver wishes to achieve at the current headway. The function is expressed as follows:
Figure BDA0002933808640000081
in formula (2): Δ x is the distance between the front and rear vehicle heads, vmaxIs the maximum speed; t' is the HV minimum safe distance.
The simple principle of the model is as follows: the driver firstly judges the distance x between the self-vehicle and the front vehiclen-1(t)-xn(t) and determining an ideal traveling speed V (x) of the vehiclen-1(t)-xn(t)). In general, ideal speed and actual speed x'n(t) there is a certain difference between them, and the driver judges this difference V (x)n-1(t)-xn(t))-x′n(t) and reducing this difference by controlling the acceleration of the vehicle to achieve the desired speed. Due to the time delay, the automobile can reach the expected acceleration at the moment of t + tau, and at the moment, the distance between the automobile heads changes, and a driver needs to make new adjustment.
As shown in equations (3) to (4), an Intelligent Driver Model (IDM) is used as the CV following Model:
Figure BDA0002933808640000082
Figure BDA0002933808640000083
in the formulae (3) and (4), an(t) acceleration at time t of the nth vehicle (CV); omega is starting acceleration; v. ofn(t) is the speed of the nth vehicle at time t; v. of0Is the initial speed; s*The expected distance of the driver in the current state; delta is an acceleration index; Δ v (t) is the speed difference between the front and rear vehicles; x is the number ofn-1(t) is the position of the (n-1) th vehicle at the time t; x is the number ofn(t) isThe position of the nth vehicle at the time t; s0Is a static safety distance parameter; s1Is a safety distance parameter related to the speed; t is CV minimum safe distance; d is comfort deceleration; ω is the maximum acceleration.
According to the traffic detection requirements of an acceleration lane and a main road, the specific embodiment of the invention arranges the road side detectors in an acceleration lane interval according to the unit distribution of 50m, arranges the road side detectors in a main road interval according to the unit distribution of 200m, acquires the traffic density and the traffic volume of each unit through each road side detector, and acquires all vehicles (T) in the acceleration lane and the main road based on a vehicle-road cooperative system and RTMS1～T5) Real-time velocity set (v)1～v5) Position set (p)1～p5) And acceleration set (a)1～a5) For S3 and S4, and proceeds to S3.
The vehicle-road cooperative system comprises vehicle-mounted ends carried on all vehicles in an acceleration lane and a main road, road side detectors distributed in an acceleration lane interval according to 50m as a unit, road side detectors distributed in a main road interval according to 200m as a unit as transmitting ends, and information interaction is carried out between the vehicle-mounted sections and the transmitting ends and among the transmitting ends through a wireless network to form the vehicle-road cooperative system. The vehicle-road cooperative system is the prior art, and only needs to realize information interaction between the vehicle and the road side detector, between the road side detectors and between the vehicles; the RTMS (remote traffic microwave radar detector) is arranged on a roadside detector, the detection of multi-lane stationary vehicles and running vehicles is realized by measuring the distance of a target in a microwave projection area, microwaves are transmitted to a road surface by utilizing the radar linear frequency modulation technical principle, and various traffic data of a traffic flow are obtained by carrying out high-speed real-time digital processing analysis on echo signals.
And S3, starting speed control, judging the speed distribution condition, the vehicle distance condition and the acceleration distribution condition of the CAV and the front and rear vehicles by the CAV according to the real-time speed set, the position set and the acceleration set on the acceleration lane obtained in the step S2, enabling the CAV vehicle to reach the lowest speed requirement of driving into the main road before reaching the tail end of the acceleration lane on the basis of the speed control model, always meeting the safe driving condition, drawing an acceleration track diagram of the CAV acceleration lane, and entering the step S4.
S31, judgment T1Safety conditions for performing speed control: judging whether the speed control behavior at the moment reaches a safety condition meeting the minimum safety distance between vehicles, if so, entering S32, and if not, driving the CAV with the vehicle model according to the ACC until the safety condition is met, and then entering S32;
the safety condition means to avoid T when performing speed control1And T2、T3In the event of a collision, when T1And T2、T3Relative distance Δ p of12、Δp13The larger the size, the safer; when the relative distance Δ p12、Δp13When the vehicle becomes smaller, whether the speed control behavior at the moment can at least meet the minimum safe distance between the vehicles needs to be judged; the function of the safety condition is shown as formula (5), wherein 1 represents relative safety, and the smaller the numerical value is, the higher the risk is;
Figure BDA0002933808640000091
in the formula (5), facc·safetyIs a safety condition function; a is a logarithmic coefficient; t' is T1And T2A minimum safe distance of; t is T1And T3The minimum safe distance of.
When T is1Meeting the above safety condition, i.e. facc·safetyWhen the value is 1, the process proceeds to S32; otherwise, the CAV follows the ACC vehicle model to run until the safety condition is met, and then the operation goes to S32.
S32, T at this time1Starting to execute speed control for accelerating to enter the main road: dividing an acceleration lane road section into i units according to the distribution position of a road side detector to obtain T1Traffic q of the located uniti(t), traffic density ρi(T) and T1Real-time speed v of front and rear vehicles2，i、v3，iReal time position p2，i、p3，iReal time acceleration a2，i、a3，iSolving for T1Desired speed of the unit in question, for T1Performing speed control to make T1Real-time speed of the motor is adjusted to the expected speed in real time until T1The speed of the main road reaches the lowest speed requirement of driving into the main road.
T1Traffic q of the located uniti(t) is calculated as shown in equation (6):
Figure BDA0002933808640000101
in the formula (6), the reaction mixture is,
Figure BDA0002933808640000102
denotes the average speed of the i-th unit on the outgoing section at time t, λ denotes the number of lanes, ρi(t) represents the traffic density of the ith cell on the outgoing section at time t.
the traffic density of the ith unit on the road section at the moment of t +1 is calculated as shown in formula (7):
Figure BDA0002933808640000103
in the formula (7), ρi(t +1) is the traffic density of the ith unit on the road section at the moment of t +1, rhoi(T) is the traffic density of the ith unit on the outgoing road section at the time T, T' is the control time step (usually 10-20 s), and L is the length of each unit on the road section; λ represents the number of lanes; q. q.si-1(t) the traffic volume of the i-1 unit on the road section is driven out at the moment t; q. q.siAnd (t) is the traffic volume of the ith unit on the outgoing road section at the time t.
Obtaining T based on formulae (1) and (2)2The real-time velocity equation of (a) is as follows:
Figure BDA0002933808640000104
in the formula (8), v2，i(T) is the ith unit T on the road section at the time T2The real-time speed of (a) is a function of the distance between the vehicle heads, a2，i(T) i-th unit T on the road section at time T2Real-time acceleration of, rhoi(t) is the traffic density of the ith unit on the road section at the time t, rhocrRepresenting the critical density of the road segment.
Obtaining T based on formulae (3) and (4)3The real-time velocity equation of (a) is as follows:
Figure BDA0002933808640000105
in the formula (9), v3，i(T) is the ith unit T on the road section at the time T3Real time speed of a3，i(T) is the ith unit T on the road section at the time T3Real-time acceleration of the vehicle.
From equations (6) to (9), the desired velocity equation for the CAV is obtained as follows:
Figure BDA0002933808640000106
in the formula (10), v1，i(T +1) represents the ith unit T on the road section at the moment of T +11Desired speed of v1，i(T) is the ith unit T on the road section at the time T1Real time velocity of, Δ p12Is T1And T2Of (d), Δ p13Are respectively T1And T3τ is a lag time due to a change in density of the traffic flow ahead, v2，i(T) is the ith unit T on the road section at the time T2Real time velocity v of3，i(T) is the ith unit T on the road section at the time T3The eta is a model parameter, the preferred value range of the embodiment of the invention is 0.3-0.6, and rhoi+1(t) is the traffic flow density of the (i +1) th unit on the road section at the time t, kappa is a model parameter, and the preferred value range of the embodiment of the invention is 6-12.
By S32 for T1Performing speed control so that T1Within each unit sectionReal-time adjustments are made to follow the desired speed requirements.
S33, in each cell, T1(CAV) performs a real-time speed determination if T1If the lowest speed requirement of merging into the main road is met and the speed difference requirement, the acceleration difference requirement and the distance requirement of merging are met, drawing a CAV acceleration lane acceleration trajectory diagram, and entering S4; if T1If the minimum speed demand for merging into the main road is not met, S32 is repeated in the next unit until the speed regulation is reached to the demand for entering S4, and the flow proceeds to S4.
T does not appear under normal conditions1The reason why the lowest speed request to merge into the main road is not reached even after the entire acceleration lane is driven is that although the acceleration lane path is short, the time required for the CAV to accelerate to the lowest speed is short, and the vehicle speeds of the vehicles before and after the CAV also reach the lowest speed request to merge into the main road, and S33 mainly determines the timing at which the CAV that reaches the lowest speed request merges into the main road.
The CAV acceleration lane acceleration track graph comprises T1In the straight track of the acceleration lane, the main drawing parameters comprise T1The unit and the specific position when the lowest speed requirement of merging into the main road is reached, and T2/T3/T4/T5The resulting trajectory changes.
The minimum speed requirement function of merging into main path is T1The requirement of reaching the lowest running speed of the main road and being lower than the requirement of the highest running speed of the acceleration lane is met, and the formula (11) shows that:
vmain，min≤v1，i(t)＜vacc，max (11)
in the formula (11), vmain，minFor main road minimum speed requirement, vacc，maxThe method is the requirement of the highest driving speed of the acceleration lane.
The function of the speed difference, the acceleration difference and the distance requirement is T1If the main road needs to meet the requirements of speed difference, acceleration difference and distance at the same time, as shown in formula (12), the analytic graph is shown in fig. 2:
fcondition(Δv，Δa，Δp)
＝fsafety(Δv12，Δv14，Δv15)∩fsafety(Δa12，Δa14，Δa15) (12)
∩fsafety(Δp12,Δp14,Δp15)
in the formula (12), fcondition(Δ v, Δ a, Δ p) is a function of speed difference, acceleration difference and distance requirement; f. ofsafety(Δv12，Δv14，Δv15) Is a speed difference safety function; Δ v12Is T1And T2Velocity difference of (1), Δ v14Is T1And T4Velocity difference of (1), Δ v15Is T1And T5The speed difference of (2); f. ofsafety(Δa12，Δa14，Δa15) Is an acceleration difference safety function; Δ a12Is T1And T2Acceleration difference of Δ a14Is T1And T4Acceleration difference of Δ a15Is T1And T5The acceleration difference of (a); f. ofsafety(Δp12，Δp14，Δp15) Is a distance safety function; Δ p12Is T1And T2Of (d), Δ p14Is T1And T4Of (d), Δ p15Is T1And T5The pitch of (2).
Wherein the speed difference safety function fsafety(Δv12，Δv14，Δv15) Comprises the following steps:
Figure BDA0002933808640000121
as shown in equation (13), the speed difference safety function is judged to be only safe (1) and unsafe (0), and T is obtained after the above conditions are set1(CAV) may determine whether the requirement of equation (13) is satisfied based on the speed information acquired in real time.
Wherein the safety function f of the acceleration differencesafety(Δa12，Δa14，Δa15) Comprises the following steps:
Figure BDA0002933808640000122
as shown in equation (14), the acceleration difference safety function is determined only to be safe (1) and unsafe (0), and T is set after the above conditions are set1(CAV) may determine whether the requirement of equation (14) is satisfied based on the acceleration information acquired in real time.
Wherein the distance safety function fsafety(Δp12，Δp14，Δp15) Comprises the following steps:
Figure BDA0002933808640000123
as shown in equation (15), the determination of the distance safety function is only safe (1) and unsafe (0), and T' is T1And T2、T5The relative safe headstock spacing; t is T1And T4The relative safe headwear distance.
S4, the track optimization model is started to be executed, the CAV is smoothly and safely converged into the main road from the acceleration lane, and the process goes to S5.
S41, as shown in FIG. 3, establishing a CAV track optimization model: t is1The initial time of convergence from the acceleration lane into the main road is t0After Δ T, T1And TiHead interval of delta p1iBecomes Δ p'1i，i＝2、4、5，T1An angle theta formed with the vehicle running direction is taken as T1In the course of the run-in, T1The constant longitudinal acceleration, the transverse acceleration and the steering angle theta are converged, and in the converging process, when the vehicle speed is higher, the longitudinal included angle formed by lane changing is smaller, so that the patent assumes that the transverse speed changes v1xWithout affecting the longitudinal velocity v1y(ii) a change; this patent does not consider T3(rear vehicle of acceleration lane) pair T1The influence of merging into the main road.
S42, in CAV track optimization model, T is to be realized1Safely converge into the main road with T1And T2Minimum safe distance, T1And T4Is the most important ofSmall safety distance, T1And T5The minimum safe interval is a safe entry index when T1And T2Oblique distance, T1And T4Oblique distance, T1And T5Are all more than or equal to T1And T2Minimum safe distance, T1And T4Minimum safe distance, T1And T5At minimum safe distance of, T1Starting to execute the main road convergence operation, drawing a CAV main road convergence trajectory diagram from the acceleration lane, and entering S5;
the step of converging the CAV self-accelerating lane into the main road track graph comprises the step of drawing T1The change in trajectory of the merging into the main road from the acceleration lane, and T2/T3/T4/T5The resulting trajectory changes.
First, for T1And T2Minimum safety interval of, T1The front vehicle T on the same lane with the front vehicle T2The motion track of (2) is shown in FIG. 4, and T is ensured1High efficiency of merging into the main road, requiring T1And T2Is inclined by an inclined distance d12Greater than or equal to the minimum safety distance, T1And T2Is inclined by an inclined distance d12Is expressed by the formula (16):
d12≥T′
Figure BDA0002933808640000131
in the formula (16), d12Is T1And T2The slant distance of (d); t' is T1And T2A minimum safe distance of; theta is a steering angle; delta p'12After a time of Δ T T1And T2The distance between the car heads; l is the vehicle length; w is the vehicle width; s1yIs T1Longitudinal travel distance.
Formula (17) is SIyExpression of (a):
Figure BDA0002933808640000132
in the formula (17), v1yIs T1Longitudinal speed of a1yIs T1Longitudinal acceleration of (2).
T is obtained based on the formulae (16) to (17)1And T2The minimum safe distance of.
Second, for T1And T4Minimum safety interval of, T1With front cars T on the main road4The motion trajectory of (2) is shown in fig. 5. T is1After the lane change is executed, the front vehicle is T4To ensure T1High efficiency of merging into the main road, requiring T1And T4Is inclined by an inclined distance d14Greater than or equal to the minimum safety distance, T1And T4The function expression of the diagonal distance of (a) is as follows:
Figure BDA0002933808640000133
in the formula (18), d14Is T1And T4The slant distance of (d); t is T1And T4A minimum safe distance of; theta is a steering angle; delta p'14After a time of Δ T T1And T4The distance between the car heads; l is the vehicle length; s1yIs T1Longitudinal travel distance.
Again, for T1And T5Minimum safety interval of, T1With front cars T on the main road5The motion trajectory of (2) is shown in FIG. 6, T1After the lane change is executed, the rear vehicle is T5To ensure T1High efficiency of merging into the main road, requiring T1And T5Is inclined by an inclined distance d15Greater than or equal to the minimum safety distance, T1And T5The function expression of the diagonal distance of (a) is as follows:
d15≥T′
Figure BDA0002933808640000134
in the formula (19), d15Is T1And T5The slant distance of (d); t' is T1And T5A minimum safe distance of; theta is a steering angle; delta p'15After a time of Δ T T1And T5The distance between the car heads; l is the vehicle length; and w is the vehicle width.
S5, drawing an optimized track graph of the whole CAV convergence process based on the CAV acceleration track graph drawn by S3 and the main road convergence track graph drawn by S4 of the self-acceleration lane, and simultaneously drawing T2～T5The whole-course track graph provides visual track display for the CAV of the highway confluence area to converge into the main road.
According to the method, the CAV driving characteristics are fully considered, the requirement of the lowest speed of vehicles converging into a main road is considered under the specific scene of a confluence area, and a speed control and trajectory planning model constructed on the premise of meeting the safety and stability can provide technical support for improving the CAV driving characteristics and guarantee the traffic safety and efficiency under the mixed traffic flow trend.
The above description is only for the preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention shall fall within the protection scope of the present invention.

Claims (9)

1. The network connection automatic vehicle speed control and track optimization method based on the highway confluence area is characterized by comprising the following steps of:
s1, the roadside detector located at the junction of the acceleration lane and the ramp judges whether the intelligent networked automatic vehicle CAV enters the acceleration lane, and if the intelligent networked automatic vehicle CAV does not enter the acceleration lane, the roadside detector judging process is repeatedly executed; if the CAV enters the acceleration lane, the operation goes to S2;
s2, a control step for starting to execute CAV: CAV into acceleration lane is T1，T1Front vehicle in acceleration lane is T2The rear vehicle is T3，T1The front vehicle in the main road is T4The rear vehicle is T5；T2～T5Adopting an HV car following model or a CV car following model; traffic in acceleration lane section acquired based on roadside detectorThe flux density and the flux; method for acquiring all vehicles T on acceleration lane and main road based on vehicle-road cooperative system and remote traffic microwave radar detector RTMS1～T5Real-time velocity set v1～v5Position set p1～p5And acceleration set a1～a5For data input as S3 and data input as S4, and proceeds to S3;
s3, start speed control: the CAV judges the speed distribution condition, the vehicle distance condition and the acceleration distribution condition of the CAV and front and rear vehicles according to the real-time speed set, the position set and the acceleration set on the acceleration lane obtained in the step S2, the CAV vehicles reach the lowest speed requirement of driving into the main road before reaching the tail end of the acceleration lane based on speed control, the safe driving condition is always met, the acceleration track graph of the CAV acceleration lane is drawn, and the operation enters the step S4;
s4, starting to execute track optimization: the CAV is safely converged into the main road by the acceleration lane, and the S5 is entered;
s5, drawing an optimized track graph of the whole CAV convergence process based on the CAV acceleration track graph drawn by S3 and the main road convergence track graph drawn by S4 of the self-acceleration lane, and simultaneously drawing T2～T5The whole-course track graph provides visual track display for the CAV of the highway confluence area to converge into the main road.
2. The method for network connection automatic vehicle speed control and trajectory optimization based on the highway confluence area of claim 1, wherein in step S3, the starting of speed control comprises the following steps:
s31, judgment T1Safety conditions for performing speed control: judging whether the speed control behavior at the moment reaches a safety condition meeting the minimum safety distance between vehicles, if so, entering S32, and if not, driving the CAV to follow the vehicle model according to the delta CC until the safety condition is met, and then entering S32;
S32、T1starting to execute speed control for accelerating to enter the main road: dividing an acceleration lane road section into i units according to the distribution position of a road side detector to obtain T1Of the unitTraffic volume qi(t), traffic density ρi(T) and T1Real-time speed v of front and rear vehicles2，i、v3，iReal time position p2，i、p3，iReal time acceleration a2，i、a3，iSolving for T1Desired speed of the unit in question, for T1Performing speed control to make T1Real-time speed of the motor is adjusted to the expected speed in real time until T1The speed of the main road reaches the lowest speed requirement of driving into the main road;
s33, in each cell, T1A real-time speed determination is performed if T1If the lowest speed requirement of merging into the main road is met and the speed difference requirement, the acceleration difference requirement and the distance requirement of merging are met, drawing a CAV acceleration lane acceleration trajectory diagram, and entering S4; if T1If the minimum speed demand for merging into the main road is not met, S32 is repeated in the next unit until the speed regulation is reached to the demand for entering S4, and the flow proceeds to S4.
3. The method for network connection automatic vehicle speed control and trajectory optimization based on highway confluence area of claim 2, wherein in S31, the function of said safety condition is as follows:
Figure FDA0002933808630000021
in the formula (f)acc·safetyIs a safety condition function; a is a logarithmic coefficient; t' is T1And T2A minimum safe distance of; t is T1And T3Minimum safe distance, Δ p12Is T1And T2Of (d), Δ p13Are respectively T1And T3The pitch of (2).
4. The method for network connection automatic vehicle speed control and track optimization based on highway confluence area of claim 2, wherein in S32, T is1The desired velocity at the unit is shown by the following equation:
Figure FDA0002933808630000022
in the formula, v1，i(T +1) represents the ith unit T on the road section at the moment of T +11Desired speed of v1，i(T) is the ith unit T on the road section at the time T1T' is the control time step length, tau is the lag time caused by the density change of the traffic flow in front, v2，i(T) is the ith unit T on the road section at the time T2Real time velocity v of3，i(T) is the ith unit T on the road section at the time T3L is the length of each unit on the road section, η is the model parameter, ρi+1(t) is the traffic density of the (i +1) th unit on the road section at the time t, rhoi(t) is the traffic density of the ith unit on the outgoing road section at the time t, and kappa is a model parameter.
5. The method of claim 4, wherein T is T, T is T, T is a vehicle speed, T is a vehicle speed of the vehicle, T is a vehicle, T is a vehicle, T is1Traffic q of the located unitiThe calculation of (t) is shown below:
Figure FDA0002933808630000023
in the formula (I), the compound is shown in the specification,
Figure FDA0002933808630000024
denotes the average speed of the i-th unit on the outgoing section at time t, λ denotes the number of lanes, ρi(t) represents the traffic density of the ith unit on the outgoing road section at the time t;
the traffic density of the ith unit on the road section at the time t +1 is calculated as follows:
Figure FDA0002933808630000025
in the formula, ρi(t +1) is the traffic density of the ith unit on the road section at the moment of t +1, rhoi(T) is the traffic density of the ith unit on the road section driven out at the time T, T' is the control time step length, and L is the length of each unit on the road section; λ represents the number of lanes; q. q.si-1(t) the traffic volume of the i-1 unit on the road section is driven out at the moment t; q. q.siAnd (t) is the traffic volume of the ith unit on the outgoing road section at the time t.
6. The method as claimed in claim 4, wherein the T is T, and T is T2Is HV, T3At CV, T2The following model adopts an optimized speed model, T3The following model adopts an intelligent driving model;
the T is2Real-time velocity v of2，iThe equation (t) is shown below:
Figure FDA0002933808630000031
in the formula, v2，i(T) is the ith unit T on the road section at the time T2The real-time speed of (a) is a function of the distance between the vehicle heads, a2，i(T) i-th unit T on the road section at time T2Real-time acceleration of, rhoi(t) is the traffic density of the ith unit on the road section at the time t, rhocrRepresenting a critical density of the road segment;
the T is3Real-time velocity v of3，iThe equation (t) is shown below:
Figure FDA0002933808630000032
in the formula, v3，i(T) is the ith unit T on the road section at the time T3Real time speed of a3，i(T) is the ith unit T on the road section at the time T3Real-time acceleration of the vehicle.
7. According to the rightThe method for network connection automatic vehicle speed control and track optimization based on highway confluence area according to claim 2, wherein in S33, T is1The minimum speed requirement of the merging main road is met, and the merging speed difference requirement, the acceleration difference requirement and the interval requirement are met, and the method specifically comprises the following steps:
the minimum speed requirement function for merging into the main road is shown as follows:
vmain，min≤v1，i(t)＜vacc，max；
in the formula, vmain，minFor main road minimum speed requirement, vacc，maxThe requirement of the highest running speed of the acceleration lane is met;
the functions of the speed difference requirement, the acceleration difference requirement and the distance requirement are shown as the following formulas:
fcondition(Δv，Δa，Δp)
＝fsafety(Δv12，Δv14，Δv15)∩fsafety(Δa12，Δa14，Δa15)∩fsafety(Δp12，Δp14，Δp15)
in the formula (f)condition(Δ v, Δ a, Δ p) is a function of speed difference, acceleration difference and distance requirement; f. ofsafety(Δv12，Δv14，Δv15) Is a speed difference safety function; Δ v12Is T1And T2Velocity difference of (1), Δ v14Is T1And T4Velocity difference of (1), Δ v15Is T1And T5The speed difference of (2); f. ofsafety(Δa12，Δa14，Δa15) Is an acceleration difference safety function; Δ a12Is T1And T2Acceleration difference of Δ a14Is T1And T4Acceleration difference of Δ a15Is T1And T5The acceleration difference of (a); f. ofsafety(Δp12，Δp14，Δp15) Is a distance safety function; Δ p12Is T1And T2Of (d), Δ p14Is T1And T4A distance ofp15Is T1And T5The pitch of (d);
wherein the speed difference safety function fsafety(Δv12，Δv14，Δv15) As shown in the following formula:
Figure FDA0002933808630000041
wherein the safety function f of the acceleration differencesafety(Δa12，Δa14，Δa15) As shown in the following formula:
Figure FDA0002933808630000042
wherein the distance safety function fsafety(Δp12，Δp14，Δp15) As shown in the following formula:
Figure FDA0002933808630000043
in the formula, T' is T1And T2、T5The relative safe headstock spacing; t is T1And T4The relative safe headwear distance.
8. The method for controlling the speed and optimizing the trajectory of the networked automatic vehicle based on the highway confluence area of claim 1, wherein in step S4, the step of starting to perform the trajectory optimization comprises the following steps:
s41, establishing a CAV track optimization model: t is1The initial time of convergence from the acceleration lane into the main road is t0After Δ T, T1And TiHead interval of delta p1iBecomes Δ p'1i，i＝2、4、5，T1An angle theta formed with the vehicle running direction is taken as T1In the course of the run-in, T1With constant longitudinal acceleration and transverse accelerationMerging the speed and the steering angle theta;
s42, in CAV track optimization model, using T1And T2Minimum safe distance, T1And T4Minimum safe distance, T1And T5The minimum safe interval is a safe entry index when T1And T2Oblique distance, T1And T4Oblique distance, T1And T5Are all more than or equal to T1And T2Minimum safe distance, T1And T4Minimum safe distance, T1And T5At minimum safe distance of, T1The merge main road operation is started and the CAV merge main road locus diagram from the acceleration lane is drawn, and the process proceeds to S5.
9. The method of claim 8, wherein the T42 is the speed control and trajectory optimization method for the network-connected automatic vehicles based on the highway confluence area1And T2Is inclined by an inclined distance d12The function expression of (a) is as follows:
d12≥T′
Figure FDA0002933808630000044
in the formula (d)12Is T1And T2The slant distance of (d); t' is T1And T2A minimum safe distance of; theta is a steering angle; delta p'12After a time of Δ T T1And T2The distance between the car heads; l is the vehicle length; w is the vehicle width; s1yIs T1Longitudinal travel distance of;
wherein SIyThe expression of (c) is shown as follows:
Figure FDA0002933808630000051
in the formula, v1yIs T1Longitudinal speed of a1yIs T1Longitudinal acceleration of (a);
obtaining T based on the two formulas1And T2The minimum safety spacing T';
T1and T4Is inclined by an inclined distance d14The function expression of (a) is as follows:
d14≥T
d14＝(Δp′14-L)cosθ+(3-S1y)sinθ；
in the formula (d)14Is T1And T4The slant distance of (d); t is T1And T4A minimum safe distance of; theta is a steering angle; delta p'14After a time of Δ T T1And T4The distance between the car heads; l is the vehicle length; s1yIs T1Longitudinal travel distance of;
T1and T5Is inclined by an inclined distance d15The function expression of (a) is as follows:
d15≥T′
Figure FDA0002933808630000052
in the formula (d)15Is T1And T5The slant distance of (d); t' is T1And T5A minimum safe distance of; theta is a steering angle; delta p'15After a time of Δ T T1And T5The distance between the car heads; l is the vehicle length; and w is the vehicle width.
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