A method for modeling vehicle trajectory at deformed intersections

Abstract

The present invention discloses a method for modeling the running trajectory of vehicles at a deformed intersection. A plane rectangular coordinate system is established on the roads in each direction of the intersection, and the geometric conditions and the number of lanes of the entrance and exit roads in each direction of the intersection are determined. According to the plane rectangular coordinate system on the roads in each direction of the intersection, the boundary line equations of the entrance and exit roads in each direction of the intersection in each coordinate system are determined. The plane rectangular coordinate system in each direction of the intersection is normalized, and the boundary line equations of the entrance and exit roads in each direction of the intersection are normalized in the same coordinate system. The running trajectory equations of vehicles in each direction in the intersection are determined by combining straight lines and circular curves. The vehicle running trajectory in the deformed intersection is standardized and modeled, which can be applied to plane intersections with any geometric conditions, and there is no restriction on the entrance and exit roads where the vehicles running at the intersection are located. It has wide applicability and is helpful for fine management and control of the running safety and traffic efficiency of vehicles at the intersection.

Description

Technical Field

[0001] The invention relates to the technical field of vehicle traffic control at road intersections, and in particular to a method for modeling vehicle running trajectories at deformed intersections. Background Art

[0002] A road intersection is formed by the intersection of two or more roads. It is an important node for turning and evacuating vehicles and pedestrians in the urban road network. In the urban road network, the most common intersection is the cross intersection, which is not only efficient but also conducive to traffic organization and management. However, with the continuous increase of urban roads, a large number of multi-road intersections or irregular crosses or T-shaped intersections, i.e., deformed intersections, have been generated due to various objective factors such as terrain and buildings.

[0003] Deformed intersections have problems such as large intersection area, unsmooth line shape, and many traffic conflict points, which make it difficult to organize traffic at the intersection and difficult to manage. The traffic efficiency is low, and it is easy to cause traffic congestion and even traffic accidents. It will also affect the smoothness of the entire traffic network. However, if the deformed intersection is forcibly transformed into a regular cross-shaped intersection by changing the road line shape, it may cause problems such as building demolition and vegetation destruction, which will not only generate a large amount of manpower, material resources, and financial resources, but also affect the normal life of nearby residents and the normal operation of road traffic.

[0004] With the continuous advancement of refined management of urban road intersections, some legacy deformed intersections have become a major problem in traffic management. These deformed intersections are often not formed by the intersection of east-west and north-south roads, but contain one or more inclined roads, and the number of entrance and exit roads is asymmetric. Therefore, it is difficult to standardize the running trajectory of vehicles in deformed intersections, making it even more difficult to manage and control them in a refined manner. Summary of the invention

[0005] Based on the problems raised by the above background technology, the purpose of the present invention is to provide a method for modeling vehicle operation trajectories at deformed intersections, to regularize the representation of deformed intersections, to solve the problem of chaotic traffic at deformed intersections, to reduce the impact of deformed intersections on traffic, and to improve the traffic efficiency of deformed intersections.

[0006] The present invention is achieved through the following technical solutions:

[0007] A first aspect of the present invention provides a method for modeling vehicle running trajectories at an abnormal intersection, comprising the following steps:

[0008] Step 1: Obtain the geometric information and lane information of the entrance and exit roads in each direction of the deformed intersection, and establish a plane rectangular coordinate system in the corresponding direction based on the geometric information and lane information of the entrance and exit roads;

[0009] Step 2: Determine the boundary line equation of the import lane and the boundary line equation of the export lane in the corresponding direction in the plane rectangular coordinate system in the corresponding direction;

[0010] Step 3: Normalize the plane rectangular coordinate system in all directions of the deformed intersection to generate a normalized plane rectangular coordinate system;

[0011] Step 4: Establish a vehicle running trajectory equation from the entrance lane i to the exit lane j based on the normalized plane rectangular coordinate system.

[0012] In the above technical scheme, since the deformed intersection is often not formed by the intersection of east-west and north-south roads, and contains one or more inclined roads, and the number of entrance lanes and exit lanes is asymmetric, it is difficult to standardize the modeling of the running trajectory of vehicles in the deformed intersection. The present invention uses step 1 to establish a plane rectangular coordinate system for the intersections in each direction respectively, and constrains the boundaries of the entrance lane and the corresponding exit lane during the vehicle driving process through step 2, and then normalizes the plane rectangular coordinate system containing lane boundary constraints established by steps 1 to 2 through step 3, and normalizes the plane rectangular coordinate system of the exit lane to the plane rectangular coordinate system of the entrance lane, thereby obtaining a normalized plane rectangular coordinate system, which can be used to characterize the exit lane and the entrance lane at the same time, and then provides a coordinate system that matches the deformed intersection for the standardized modeling of the running trajectory of vehicles in the deformed intersection, which is conducive to the correct modeling of the running trajectory of vehicles in the deformed intersection.

[0013] In the normalized plane rectangular coordinate system constructed in steps 1 to 3, the geometric and structural features of the deformed intersection are used to analyze the driving trajectory of the vehicle from the entrance lane i to its corresponding exit lane j, and the vehicle running trajectory in the deformed intersection is standardized and modeled by combining straight and circular motion, which can be applied to plane intersections with any geometric conditions. In this way, the problem of traffic interweaving chaos in the deformed intersection is solved, the impact of the deformed intersection on traffic is reduced, and the traffic efficiency of the deformed intersection is improved.

[0014] In an optional embodiment, the step 1 includes the following steps:

[0015] Get the geometric information and lane information of the entrance and exit lanes in the D direction; where d v Indicates the width of the motorway, expressed in d g Indicates the width of the central isolation zone of the intersection, represents the number of lanes between the D-direction import lane i and the central isolation zone of the intersection, Indicates the number of lanes between the exit lane j corresponding to the import lane i in the D direction and the central isolation zone of the intersection;

[0016] The plane rectangular coordinate system in the D direction is established with the vertex of the middle line between the entrance and exit lanes of the deformed intersection in the D direction as the origin and the straight line passing through the origin and parallel to the lane as the Y axis. The plane rectangular coordinate system in the D direction includes the coordinate system X DA -O DA -Y DA and coordinate system X DE -O DE -Y DE .

[0017] In an optional embodiment, determining the equation of the boundary line of the import lane and the equation of the boundary line of the export lane in the D direction in the plane rectangular coordinate system in the D direction in step 2 comprises the following steps:

[0018] In the coordinate system X DA -O DA -Y DA In , the left boundary line equation of the D direction import lane i and the right boundary line equation of the D direction import lane i are established respectively; among them,

[0019] The equation of the left boundary line of the D-direction import lane i is as follows:

[0020]

[0021] in, The x value represents the equation of the left boundary line of the D-direction import lane i;

[0022] The equation of the right boundary line of the D-direction import lane i is as follows:

[0023]

[0024] in, The x value represents the equation of the right boundary line of the D-direction import lane i;

[0025] In the coordinate system X DE -O DE -Y DE In , the equations of the left boundary line of the exit lane j corresponding to the D-direction import lane i and the right boundary line of the exit lane j corresponding to the D-direction import lane i are established respectively; wherein,

[0026] The left boundary line equation of the exit lane j corresponding to the import lane i in the D direction is expressed as follows:

[0027]

[0028] in, The x value represents the left boundary line equation of the exit lane j corresponding to the import lane i in the D direction;

[0029] The right boundary line equation of the exit lane j corresponding to the import lane i in the D direction is expressed as follows:

[0030]

[0031] in, Represents the x value of the right boundary equation of the exit lane j corresponding to the import lane i in the D direction.

[0032] In an optional embodiment, step 3 includes the following steps:

[0033] Step 31: From the coordinate system X DE -O DE -Y DE Take any point P(x DE ,y DE ), calculate the point P(x DE ,y DE ) in the coordinate system X DA -O DA -Y DA The coordinates (x DA ,y DA ), and obtain a conversion formula; wherein the conversion formula is expressed as follows:

[0034]

[0035] Among them, (x E0 ,y E0 ) represents point O DE In the coordinate system X DA -O DA -Y DA The coordinates in θ AE Represents the coordinate axis X DA With coordinate axis X DE The angle between them rotating in the counterclockwise direction;

[0036] Step 32: Use the conversion formula to transform the coordinate system X DE -O DE -Y DE The left boundary line equation of the exit lane j corresponding to the import lane i in the D direction and the right boundary line equation of the exit lane j corresponding to the import lane i in the D direction are transformed into the coordinate system X DA -O DA -Y DA middle.

[0037] In an optional embodiment, in step 32, the coordinate system X is converted intoDE -O DE -Y DE The left boundary line equation of the exit lane j corresponding to the import lane i in the D direction is transformed into the coordinate system X DA -O DA -Y DA middle:

[0038]

[0039] in, Represents the coordinate system X DA -O DA -Y DA The left boundary line equation of the exit lane j corresponding to the import lane i in the D direction;

[0040] Use the conversion formula to transform the coordinate system X DE -O DE -Y DE The right boundary line equation of the exit lane j corresponding to the import lane i in the D direction is transformed into the coordinate system X DA -O DA -Y DA middle:

[0041]

[0042] in, Represents the coordinate system X DA -O DA -Y DA The right boundary line equation of the exit lane j corresponding to the import lane i in the D direction.

[0043] In an optional embodiment, step 4 includes the following steps:

[0044] Step 41: In coordinate system X DA -O DA -Y DA Set the vehicle entry point P in Ai (x Ai ,0) and the vehicle exit point P Ej (x Ej ,y Ej ), calculate the vehicle entry point P Ai To vehicle exit point P Ej The centerline equation of the running trajectory F DM ;

[0045] Step 42: Calculate the left boundary line equation F of the vehicle's running trajectory DL and the right boundary line equation F DR , respectively establish the running trajectory centerline equation F DM and the left boundary line equation F DL, right boundary line equation F DR The vehicle running trajectory equation is generated based on the correlation relationship between them.

[0046] In an optional embodiment, step 41 includes the following steps:

[0047] Calculate the vehicle entry point P Ai The corresponding lane center line L Ai and the lane centerline L Ai The equation of the perpendicular line L Ai ┴;

[0048] Calculate the vehicle exit point P Ej The corresponding lane center line L Ej and the lane centerline L Ej The equation of the perpendicular line L Ej ┴;

[0049] Determine the lane centerline L Ai With lane center line L Ej The intersection point O AE (x0, y0), lane centerline L Ai With the perpendicular line equation L Ai ┴Intersection Lane center line L Ej With the perpendicular line equation L Ej ┴The intersection Equation of perpendicular line L Ai ┴With the perpendicular line equation L Ej ┴ The intersection of

[0050] Using vehicle entry point P Ai , vehicle exit point P Ej , intersection point O AE , intersection Intersection Intersection Establish the centerline equation of the running trajectory in sections F DM .

[0051] In an optional embodiment, the running trajectory centerline equation F is established in sections DM include:

[0052] Calculate intersection points Intersection The distance between Calculate intersection points Intersection The distance between

[0053] With r v represents the optimal turning radius of the vehicle, and the distance and distance are equal to the vehicle's optimal turning radius r v ;

[0054] Construct a constraint formula to set the distance and distance Substitute the constraint formula to obtain the running track construction condition, determine the running track construction condition, and establish the running track centerline equation F in sections according to the determination result DM .

[0055] In an optional embodiment, the running trajectory centerline equation F DM include Three-segment driving trajectory;

[0056] Among them, the lane center line L is used Ai and intersection Build Driving trajectory equation of the section;

[0057] According to the judgment results, Segment and Driving trajectory equation of the section.

[0058] In an optional embodiment, according to the determination result, Segment and The driving trajectory equation of the section:

[0059] Determine the k in the running trajectory construction conditions Ej ≠0 intersection Intersection Intersection The intersection coordinates and lane centerline L Ej The center line equation of

[0060] Using k Ej Intersection point when ≠0 Intersection Intersection The intersection coordinates are constructed Driving trajectory equation of the section;

[0061] Using k Ej Lane centerline L ≠ 0 Ej Centerline equation and intersection point The intersection coordinates are constructed Driving trajectory equation of the section;

[0062] Determine the k in the running trajectory construction conditions Ej =0 intersection Intersection Intersection The intersection coordinates and lane centerline L Ej The center line equation of

[0063] Using k Ej =0 intersection point Intersection Intersection The intersection coordinates are constructed Driving trajectory equation of the section;

[0064] Using k Ej = 0 when the lane center line L Ej Centerline equation and intersection point The intersection coordinates are constructed Driving trajectory equation of the section.

[0065] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0066] The present invention uses a combination of straight and circular motion to standardize the vehicle running trajectory in a deformed intersection and model it. It can be applied to planar intersections with any geometric conditions and has no restrictions on the entrance and exit lanes where vehicles are running at the intersection. It has wide applicability and helps to finely manage and control the safety of vehicle operation and traffic efficiency at intersections. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and should not be regarded as limiting the scope. For those of ordinary skill in the art, other relevant drawings can be obtained based on these drawings without creative work. In the drawings:

[0068] Figure 1 This is a schematic diagram of the layout of a deformed intersection in Example 1 of the present invention;

[0069] Figure 2 This is a schematic diagram of the running trajectory of a left-turning vehicle at an abnormal intersection in Example 2 of the present invention;

[0070] Figure 3 This is a schematic diagram of the running trajectory of a straight-going vehicle at an abnormal intersection in Example 3 of the present invention;

[0071] Figure 4 The figure is a schematic diagram of the running trajectory of a vehicle turning right at an abnormal intersection in Example 4 of the present invention. DETAILED DESCRIPTION

[0072] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with embodiments and drawings. The exemplary embodiments of the present invention and their description are only used to explain the present invention and are not intended to limit the present invention.

[0073] Example 1

[0074] Embodiment 1 of the present invention Figure 1 Taking the schematic diagram of the layout of an abnormal intersection as an example, a method for modeling the vehicle running trajectory of an abnormal intersection is provided, which includes the following steps:

[0075] Step 1: D v Indicates the width of the motorway; d g Indicates the width of the central isolation zone of the intersection; Indicates the number of lanes between the D-direction import lane i and the central isolation zone of the intersection; Indicates the number of lanes between the exit lane j corresponding to the import lane i in the D direction and the central isolation strip of the intersection.

[0076] Take the middle line vertex between the entrance and exit lanes in each direction of the deformed intersection as the origin, and the straight line passing through the origin and parallel to the lane as the Y axis to establish a plane rectangular coordinate system, and then the coordinate system X in the D direction can be obtained. DA -O DA -Y DA and coordinate system X DE -O DE -Y DE .

[0077] Step 2: In coordinate system X DA -O DA -Y DA In and They represent the x values ​​of the left boundary line equation and the right boundary equation of the D-direction import lane i respectively;

[0078] The equation of the left boundary line of the D-direction import lane i is as follows:

[0079]

[0080] The equation of the right boundary line of the D-direction import lane i is as follows:

[0081]

[0082] In the coordinate system X DE -O DE -Y DE In and They represent the x values ​​of the left boundary line equation and the right boundary equation of the exit lane j corresponding to the entry lane i in the D direction respectively;

[0083] The left boundary line equation of the exit lane j corresponding to the import lane i in the D direction is expressed as follows:

[0084]

[0085] The right boundary line equation of the exit lane j corresponding to the import lane i in the D direction is expressed as follows:

[0086]

[0087] Step 31: Set O DE In the coordinate system X DA -O DA -Y DA The coordinates in (x E0 ,y E0 ), let any point P be in the coordinate system X DE -O DE -Y DE The coordinates in (x DE ,y DE ), with θ AE Represents the coordinate axis X DA With coordinate axis X DE The angle between them rotating in the counterclockwise direction;

[0088] According to the axis shift formula and axis rotation formula, point P is in the coordinate system X DA -O DA -Y DA The coordinates in (x DA ,y DA ):

[0089]

[0090] Step 32: Use equation (5) to convert the coordinate system X DE -O DE -Y DE middle and The boundary line equation (3-4) is transformed into the coordinate system X DA -O DA -Y DA The left boundary line equation of the exit lane j corresponding to the import lane i in the D direction is obtained It is expressed as follows,

[0091]

[0092] The right boundary line equation of exit lane j corresponding to import lane i in direction D It is expressed as follows,

[0093]

[0094] It should be noted that, since the deformed intersection is often not formed by the intersection of east-west and north-south roads, and contains one or more inclined roads, and the number of entrance lanes and exit lanes is asymmetric, it is difficult to standardize the running trajectory of vehicles in the deformed intersection. The present invention uses step 1 to establish a plane rectangular coordinate system for the intersections in each direction, and constrains the boundaries of the entrance lane and the corresponding exit lane during the vehicle driving process through step 2, and then normalizes the plane rectangular coordinate system containing lane boundary constraints established by steps 1 to 2 through step 3, and normalizes the plane rectangular coordinate system of the exit lane to the plane rectangular coordinate system of the entrance lane, thereby obtaining a normalized plane rectangular coordinate system, which can be used to characterize the exit lane and the entrance lane at the same time, and then provides a coordinate system that matches the deformed intersection for the standardized modeling of the running trajectory of vehicles in the deformed intersection, which is conducive to the correct modeling of the running trajectory of vehicles in the deformed intersection.

[0095] Step 41: In coordinate system X DA -O DA -Y DA In the example, let P be the centerline entry point of the vehicle running track in the entrance lane i of the intersection D. Ai The coordinates are (x Ai ,0), exit point P Ej The coordinates are (x Ej ,y Ej ), where the coordinates are calculated as follows:

[0096]

[0097] Vehicle entry point P Ai The corresponding lane center line L Ai The expression is:

[0098] X=b Ai (8)

[0099] Vehicle exit point P Ej The corresponding lane center line L Ej The expression is:

[0100] Y=k Ej ·X+b Ej (9)

[0101] Among them, b Ai =x Ai ,

[0102] In equations (8) and (9), b Ai Indicates the vehicle entry point P Ai In the coordinate system X DA -O DA -Y DA The horizontal coordinate value in, that is, the lane center line L Ai The lateral distance from the center line of the central dividing strip of the intersection; k Ej Indicates the lane centerline L Ej In the coordinate system X DA -O DA -Y DA The slope of b Ej Indicates the lane centerline L Ej In the coordinate system X DA -O DA -Y DA Middle Y DA The intercept on the axis;

[0103] L Ai The equation of the perpendicular line L Ai ┴The expression is:

[0104] Y=b Ai⊥ (10)

[0105] L Ej The equation of the perpendicular line L Ej ┴The expression is:

[0106]

[0107] Combining equations (8-9), we get L Ai With L Ej The intersection coordinates O AE (x0,y0):

[0108] x0=b Ai , y0=k Ej b Ai +b Ej (12)

[0109] Combining equations (8) and (10), we get L Ai With L Ai ┴The intersection coordinates

[0110]

[0111] Combining equation (9) and equation (11), we get L Ej With L Ej ┴ The intersection coordinates

[0112]

[0113] Combining equations (10-11), we get L Ai ┴ With L Ej ┴ The intersection coordinates

[0114]

[0115] According to the point and Point Coordinates, substitute equation (13) and equation (15) into the distance formula between two points to obtain:

[0116]

[0117] According to the point and Point Coordinates, substitute equation (14-15) into the distance formula between two points to get:

[0118]

[0119] With r v represents the optimal turning radius of the vehicle, r v is a constant set according to the size of the intersection and the size of the vehicle. Let:

[0120]

[0121] Among them, b Ai⊥ <k Ej b Ai +b Ej , Substitute equation (16-17) into equation (18) and determine through inequality:

[0122] When k Ej >0 o'clock,

[0123]

[0124] When k Ej <0:

[0125]

[0126] In summary, in the coordinate system X DA -O DA -Y DA In the case of a vehicle in the entrance lane i of the intersection D, the vehicle enters from the entry point P Ai To exit point P Ej The centerline equation of the running trajectory F DM Can be divided into Three sections, including The segment is a linear motion, according to equations (8) and (13), we get The equation of the center line of the segment straight line running trajectory is shown in (23); The segment is circular motion, with r v represents the optimal turning radius of the vehicle, which can be obtained according to formula (13-15): The equation of the center line of the segment circular motion trajectory is shown in (24); The segment is a linear motion, according to equations (9) and (14), we get The equation of the center line of the segment straight line running trajectory is shown in (25);

[0127] X=b Ai ,Y∈[0,b A⊥i ](twenty three)

[0128]

[0129]

[0130] When k Ej = 0 when the center line equation of the vehicle running track F DM The expression calculation method is as follows:

[0131] When k Ej =0, L Ej The equation of the perpendicular line L Ej ┴ The expression is:

[0132] X=b Ej⊥ (26)

[0133] Combining equation (9) and equation (26), we get L Ej With L Ej ┴ The intersection coordinates

[0134]

[0135] Combining equation (10) and equation (26), we get L Ai ┴ With L Ej ┴ The intersection coordinates

[0136]

[0137] According to the point and Point Coordinates, substitute equation (13) and equation (28) into the distance formula between two points to obtain:

[0138]

[0139] According to the point and point O A * E Coordinates, substitute equation (27-28) into the distance formula between two points to obtain:

[0140]

[0141] make:

[0142]

[0143] Among them, b Ai⊥ <b Ej , Substitute equation (29-30) into equation (31) and determine through inequality:

[0144] b Ai⊥ =b Ej -r v (32)

[0145] When x Ej >x Ai hour,

[0146] b Ej⊥ =b Ai +r v (33)

[0147] When x Ej <x Ai hour,

[0148] b Ej⊥ =b Ai -r v (34)

[0149] At this time, according to formula (13) and formula (27-28), we can get The equation of the center line of the segment circular motion trajectory is shown in (35). According to equations (9) and (27), we can get The equation of the center line of the segment straight line running trajectory is shown in (36):

[0150]

[0151] Y=k Ej ·X+b Ej , X∈[min{x En , b Ej⊥} , max{x En , b Ej⊥}] (36)

[0152] Step 42: Obtain the vehicle entering the intersection D direction lane i from the entry point P through the above step 41. Ai To exit point P Ej The centerline equation of the running trajectory F DM , with w v represents the width of the vehicle running track, then the left boundary line equation of the vehicle running track is DL and the right boundary line equation F DR Both can be obtained correspondingly, and F DM The relationship is as follows:

[0153]

[0154] Among them, formula (37) represents the reduction of the turning radius of the left boundary line equation of the running trajectory for the left turning path: For a straight path, the equation of the left boundary line of the running track is translated to the left along the vertical direction of the center line. For a right-turn path, the turning radius of the left boundary line equation of the running track is increased. Formula (38) represents the turning radius of the right boundary line equation of the running trajectory for the left turning path. For a straight path, the equation of the right boundary line of the running trajectory is translated to the right along the perpendicular direction of the center line. For right-turn paths, the turning radius of the right boundary line equation of the running track is reduced.

[0155] Example 2

[0156] Based on Example 1, Example 2 of the present invention takes the running trajectory of left-turning vehicles at an abnormal intersection as an example, and provides a specific implementation process of the method for modeling the running trajectory of vehicles at an abnormal intersection:

[0157] For a deformed cross intersection, the middle line vertex O between the entrance and exit roads in the east, west, south and north directions is S , O E , O N , O W As the origin, take the straight line through the origin and parallel to the lane as the Y axis, and establish the X S -O S -Y S , X E -O E -Y E , X N -O N -Y N , X W -O W -Y W Plane rectangular coordinate system.

[0158] Take the S-turn left entrance lane as an example. Enter the entrance road after passing the intersection Exit Road, D v Indicates the width of the motorway; d g Indicates the width of the central isolation zone of the intersection; express The number of lanes between the approach lane and the central median of the intersection; express The number of lanes between the exit lane and the central median of the intersection; W In the coordinate system X S -O S -Y S The coordinates in (x W0 ,y W0 );θ SW Represents the coordinate axis X W With coordinate axis X S The angle between them rotating counterclockwise.

[0159] In the coordinate system X S -O S -Y S In and Respectively The x-values ​​of the left boundary equation and the right boundary equation of the inlet are expressed as follows:

[0160]

[0161] In the coordinate system X W -O W -Y W In and Respectively The x values ​​of the left boundary equation and the right boundary equation of the exit road are expressed as follows:

[0162]

[0163] Using formula (5), the coordinate system X W -O W -Y W middle and Boundary line equation converted to coordinate system X S -O S -Y S In, get Left boundary line equation of the exit road and the right boundary equation It is expressed as follows:

[0164]

[0165] Therefore, the entrance lane and exit lane of the deformed intersection can be normalized to the coordinate system X S -O S -Y S middle.

[0166] like Figure 2 As shown, in the coordinate system X S -O S -Y S The centerline of the S-turn left vehicle's running track is at the entry point P of the deformed intersection. Ai The coordinates are (x Ai ,0), exit point P Ej The coordinates are (x Ej ,y Ej ), θ SW Indicates the W-axis X W With S-axis X S The angle between them rotating counterclockwise, O W In the coordinate system X S -O S -Y S The coordinates in (x W0 ,y W0 ).in,

[0167] but Substituting into equation (21-22), we get:

[0168]

[0169]

[0170] The above b Ai ┴ and b Ej ┴ Substituting into equation (23-25), we get S -O S -Y S middle,

[0171] S turns left The center line equation of the segment line running track F SL1 The expression is:

[0172]

[0173] According to formula (37-38), S turns left. The equation of the left boundary line of the segment straight line running track is FSL1 Pan Left The equation of the right boundary line is F SL1 Pan Right

[0174] S turns left The centerline equation of the segment circular motion trajectory F SL2 The expression is:

[0175]

[0176] According to formula (37-38), S turns left. The equation of the left boundary line of the segment circular running track is F SL2 Reduced turning radius The equation of the right boundary line is F SL2 Increased turning radius

[0177] Example 3

[0178] Based on Example 1, Example 3 of the present invention takes the running trajectory of straight vehicles at an abnormal intersection as an example to provide a specific implementation process of the method for modeling the running trajectory of vehicles at an abnormal intersection:

[0179] like Figure 3 As shown, in the coordinate system X S -O S -Y S The centerline of the S-direction straight-moving vehicle's running track is at the entry point P of the deformed intersection. Ai The coordinates are (x Ai ,0), exit point P Ej The coordinates are (x Ej ,y Ej ), θ SN Represents the N-axis X N With S-axis X S The angle between them rotating counterclockwise, O N In the coordinate system X S -O S -Y S The coordinates in (x N0 ,y N0 ).in,

[0180] but Substituting into equation (19-20), we get:

[0181]

[0182] The above b Ai ┴ and bEj ┴ Substituting into equation (23-25), we get S -O S -Y S middle,

[0183] S-direction straight-moving vehicles The center line equation of the segment straight line running track F SS1 The expression is:

[0184]

[0185] According to formula (37-38), S is the straight-moving vehicle. The equation of the left boundary line of the segment straight line running track is F SS1 Pan Left The equation of the right boundary line is F SS1 Pan Right

[0186] S-direction straight-moving vehicles The centerline equation of the segment circular motion trajectory F SS2 The expression is:

[0187]

[0188] According to formula (37-38), S is the straight-moving vehicle. The equation of the left boundary line of the segment circular running track is F SS2 Increased turning radius The equation of the right boundary line is F SS2 Reduced turning radius

[0189] S-direction straight-moving vehicles The center line equation of the segment straight line running track F SS3 The expression is:

[0190]

[0191] According to formula (37-38), S is the straight-moving vehicle. The equation of the left boundary line of the segment straight line running track is F SS3 Pan Left The equation of the right boundary line is F SS3 Pan Right

[0192] Example 4

[0193] Based on Example 1, Example 4 of the present invention takes the running trajectory of a right-turning vehicle at an abnormal intersection as an example, and provides a specific implementation process of the method for modeling the running trajectory of a vehicle at an abnormal intersection:

[0194] like Figure 4 As shown, in the coordinate system X S -O S -Y S The centerline of the right-turning vehicle's running track is at the entry point P of the deformed intersection. Ai The coordinates are (x Ai ,0), exit point P Ej The coordinates are (x Ej ,y Ej ), θ SE Indicates E-axis X E With S-axis X S The angle between them rotating counterclockwise, O E In the coordinate system X S -O S -Y S The coordinates in (x E0 ,y E0 ).in,

[0195] but Substituting into equation (19-20), we get:

[0196]

[0197] The above b Ai ┴ and b Ej ┴ Substituting into equation (23-25), we get S -O S -Y S middle,

[0198] S turns right The center line equation of the segment straight line running track F SR1 The expression is:

[0199]

[0200] According to formula (37-38), S turns right. The equation of the left boundary line of the segment straight line running track is F SR1 Pan Left The equation of the right boundary line is F SR1 Pan Right

[0201] S turns right The centerline equation of the segment circular motion trajectory F SR2 The expression is:

[0202]

[0203] According to formula (37-38), S turns right. The equation of the left boundary line of the segment circular running track is F SR2 Increased turning radius The equation of the right boundary line is F SR2 Reduced turning radius

[0204] S turns right The center line equation of the segment straight line running track F SR3 The expression is:

[0205]

[0206] According to formula (37-38), S turns right. The equation of the left boundary line of the segment straight line running track is F SR3 Pan Left The equation of the right boundary line is F SR3 Pan Right

[0207] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for modeling vehicle running trajectories at deformed intersections, characterized in that: The steps include: Step 1: Obtain the geometric information and lane information of the entrance and exit roads in each direction of the deformed intersection, and establish a plane rectangular coordinate system in the corresponding direction based on the geometric information and lane information of the entrance and exit roads; Step 2: Determine the boundary line equation of the import lane and the boundary line equation of the export lane in the corresponding direction in the plane rectangular coordinate system in the corresponding direction; Step 3: Normalize the plane rectangular coordinate system in all directions of the deformed intersection to generate a normalized plane rectangular coordinate system; Step 4: establishing a vehicle running trajectory equation from the entrance lane i to the exit lane j based on the normalized plane rectangular coordinate system; The step 1 comprises the following steps: Get the geometric information and lane information of the entrance and exit lanes in the D direction; where d v Indicates the width of the motorway, expressed in d g Indicates the width of the central isolation zone of the intersection, represents the number of lanes between the D-direction import lane i and the central isolation zone of the intersection, Indicates the number of lanes between the exit lane j corresponding to the import lane i in the D direction and the central isolation zone of the intersection; The plane rectangular coordinate system in the D direction is established with the vertex of the middle line between the entrance and exit lanes of the deformed intersection in the D direction as the origin and the straight line passing through the origin and parallel to the lane as the Y axis. The plane rectangular coordinate system in the D direction includes the coordinate system X DA -O DA -Y DA and coordinate system X DE -O DE -Y DE ; Determining the boundary line equation of the inlet lane and the boundary line equation of the outlet lane in the D direction in the plane rectangular coordinate system in the D direction in step 2 includes the following steps: In the coordinate system X DA -O DA -Y DA In , the left boundary line equation of the D direction import lane i and the right boundary line equation of the D direction import lane i are established respectively; among them, The equation of the left boundary line of the D-direction import lane i is as follows: in, The x value represents the equation of the left boundary line of the D-direction import lane i; The equation of the right boundary line of the D-direction import lane i is as follows: in, The x value represents the equation of the right boundary line of the D-direction import lane i; In the coordinate system X DE -O DE -Y DE In , the equations of the left boundary line of the exit lane j corresponding to the D-direction import lane i and the right boundary line of the exit lane j corresponding to the D-direction import lane i are established respectively; wherein, The left boundary line equation of the exit lane j corresponding to the import lane i in the D direction is expressed as follows: in, The x value represents the left boundary line equation of the exit lane j corresponding to the entry lane i in the D direction; The right boundary line equation of the exit lane j corresponding to the import lane i in the D direction is expressed as follows: in, Represents the x value of the right boundary equation of the exit lane j corresponding to the import lane i in the D direction.

2. A method for modeling vehicle running trajectories at an abnormal intersection according to claim 1, characterized in that: The step 3 comprises the following steps: Step 31: From the coordinate system X DE -O DE -Y DE Take any point P(x DE ,y DE ), calculate the point P(x DE ,y DE ) in the coordinate system X DA -O DA -Y DA The coordinates (x DA ,y DA ), and obtain a conversion formula; wherein the conversion formula is expressed as follows: Among them, (x E0 ,y E0 ) represents point O DE In the coordinate system X DA -O DA -Y DA The coordinates in θ AE Represents the coordinate axis X DA With coordinate axis X DE The angle between them rotating in the counterclockwise direction; Step 32: Use the conversion formula to transform the coordinate system X DE -O DE -Y DE The left boundary line equation of the exit lane j corresponding to the import lane i in the D direction and the right boundary line equation of the exit lane j corresponding to the import lane i in the D direction are transformed into the coordinate system X DA -O DA -Y DA middle.

3. The method for modeling vehicle running trajectories at an abnormal intersection according to claim 2, characterized in that: In step 32, the coordinate system X is converted using the conversion formula DE -O DE -Y DE The left boundary line equation of the exit lane j corresponding to the import lane i in the D direction is transformed into the coordinate system X DA -O DA -Y DA middle: in, Represents the coordinate system X DA -O DA -Y DA The left boundary line equation of the exit lane j corresponding to the import lane i in the D direction; Use the conversion formula to transform the coordinate system X DE -O DE -Y DE The right boundary line equation of the exit lane j corresponding to the import lane i in the D direction is transformed into the coordinate system X DA -O DA -Y DA middle: in, Represents the coordinate system X DA -O DA -Y DA The right boundary line equation of the exit lane j corresponding to the import lane i in the D direction.

4. The method for modeling vehicle running trajectories at an abnormal intersection according to claim 1, characterized in that: The step 4 comprises the following steps: Step 41: In coordinate system X DA -O DA -Y DA Set the vehicle entry point P in Ai (x Ai ,0) and the vehicle exit point P Ej (x Ej ,y Ej ), calculate the vehicle entry point P Ai To vehicle exit point P Ej The centerline equation of the running trajectory F DM ; Step 42: Calculate the left boundary line equation F of the vehicle's running trajectory DL and the right boundary line equation F DR , respectively establish the running trajectory centerline equation F DM and the left boundary line equation F DL , right boundary line equation F DR The relationship between and is used to generate the vehicle running trajectory equation.

5. The method for modeling vehicle running trajectories at an abnormal intersection according to claim 4, characterized in that: The step 41 comprises the following steps: Calculate the vehicle entry point P Ai The corresponding lane center line L Ai and the lane centerline L Ai The equation of the perpendicular line L Ai ┴; Calculate the vehicle exit point P Ej The corresponding lane center line L Ej and the lane centerline L Ej The equation of the perpendicular line L Ej ┴; Determine the lane centerline L Ai With lane center line L Ej The intersection point O AE (x0, y0), lane centerline L Ai With the perpendicular line equation L Ai ┴Intersection Lane center line L Ej With the perpendicular line equation L Ej ┴The intersection Equation of perpendicular line L Ai ┴With the perpendicular line equation L Ej ┴The intersection Using vehicle entry point P Ai , vehicle exit point P Ej , intersection point O AE , intersection Intersection Intersection Establish the centerline equation of the running trajectory in sections F DM .

6. The method for modeling vehicle running trajectories at an abnormal intersection according to claim 5, characterized in that: Establish the centerline equation of the running trajectory in sections F DM include: Calculate intersection points Intersection The distance between Calculate intersection points Intersection The distance between With r v represents the optimal turning radius of the vehicle, and the distance and distance are equal to the vehicle's optimal turning radius r v ; Construct a constraint formula to set the distance and distance Substitute the constraint formula to obtain the running track construction condition, determine the running track construction condition, and establish the running track centerline equation F in sections according to the determination result DM .

7. A method for modeling vehicle running trajectories at an abnormal intersection according to claim 6, characterized in that: The running track centerline equation F DM include Three-segment driving trajectory; Among them, the lane center line L is used Ai and intersection Build Driving trajectory equation of the section; According to the judgment results, Segment and Driving trajectory equation of the section.

8. The method for modeling vehicle running trajectories at an abnormal intersection according to claim 7, characterized in that: According to the judgment results, Segment and The driving trajectory equation of the section: Determine the k in the running trajectory construction conditions Ej ≠0 intersection Intersection Intersection The intersection coordinates and lane centerline L Ej The center line equation of Using k Ej Intersection point when ≠0 Intersection Intersection The intersection coordinates are constructed Driving trajectory equation of the section; Using k Ej Lane centerline L ≠ 0 Ej Centerline equation and intersection point The intersection coordinates are constructed Driving trajectory equation of the section; Determine the k in the running trajectory construction conditions Ej =0 intersection Intersection Intersection The intersection coordinates and lane centerline L Ej The center line equation of Using k Ej =0 intersection point Intersection Intersection The intersection coordinates are constructed Driving trajectory equation of the section; Using k Ej = 0 when the lane center line L Ej Centerline equation and intersection point The intersection coordinates are constructed Driving trajectory equation of the section.

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