A cooperative traffic method for networked autonomous driving vehicles under a dedicated left-turn signal

Abstract

The present invention proposes a method for the coordinated passage of networked autonomous driving vehicles under a dedicated left-turn signal. The method is mainly divided into three parts. First, the left-turn trajectory curves corresponding to the two exit lanes are planned by obtaining static channelization information of the intersection; then, the shortest left-turn trajectory of the two exit lanes is selected; finally, with the goal of maximizing the vehicle traffic efficiency at the intersection, while ensuring safety, the left-turn traffic plan is implemented. Within the allowed left-turn range, the exit lane selection index is calculated based on the distance and speed of the two adjacent vehicles, and the exit lane is selected. The corresponding left-turn trajectory is followed to safely and quickly pass through the intersection, thereby improving the traffic efficiency of left-turn vehicles.

Description

Technical Field

[0001] The present invention relates to the field of traffic strategies for autonomous driving at intersections, and in particular to a method for cooperative passage of networked autonomous driving vehicles under a dedicated left-turn signal. Background Art

[0002] Traffic accidents are frequent at urban intersections, particularly when left-turning vehicles have complex trajectories. With the development of next-generation information technologies such as 5G, the Industrial Internet, and big data, autonomous vehicles can rapidly interact with each other and share information. Therefore, leveraging the advantages of autonomous vehicles' information exchange to enable left-turning vehicles to pass through intersections efficiently and safely has become a crucial research topic.

[0003] Left-turn trajectories are highly unstable and dynamic, and left turns at intersections involve large curvature. Compared to straight-line trajectory planning, the complexity of the parameters and constraints involved in trajectory planning for this maneuver increases significantly, making the solution more difficult. By rationally planning the trajectories of left-turning vehicles at intersections, not only can the intersection's spatiotemporal resources be fully utilized, improving overall traffic efficiency and driving safety, but also the safety of vehicles. Current left-turn trajectory planning methods often use straight segments combined with circular curves, clothoid curves, polynomial curves, Bezier curves, and spline curves to characterize the trajectory, optimizing the target requirements based on these curves. However, most of these trajectory planning methods only select a single trajectory curve and fail to compare and select the best trajectory from multiple curves.

[0004] In terms of vehicle traffic strategies and motion optimization at intersections, PATH research has shown that when vehicles operate in convoys, the passenger vehicle capacity of each lane can be increased by 2-3 times compared to the capacity of traditional lanes. At the same time, Chaudhary used a convoy identification system to optimize traffic flow at intersections; Jiang used convoys as design parameters for traffic signal timing to minimize traffic delays at major-minor intersections; Jin et al. used the Big M method to linearize the optimization problem and then used linear programming to solve it to find the shortest vehicle travel time; Wu et al. proposed a dynamic programming algorithm to obtain the shortest queue length of vehicles queuing at unsignalized intersections under the premise that the convoy will not be interrupted, reducing the queuing time and delay time of vehicles; Chang Can established an optimization model for different traffic flows at unsignalized intersections with total travel time and average travel time as the targets and solved it using a genetic algorithm. The above research shows that the performance of the convoy-based algorithm can better adapt to the problem of optimizing intersection traffic efficiency. However, most current studies take the convoy's travel time as the optimization objective, and consider the convoy's headway, speed, acceleration and other motion parameters as safety constraints. There are few studies that set optimized travel strategies for multiple exit lanes.

[0005] Based on this, this paper proposes a cooperative passage method for networked autonomous vehicles under a dedicated left-turn signal. Different from a single left-turn exit lane, this method involves optimal trajectory planning of multiple left-turn exit lanes after entering the intersection from a dedicated left-turn entrance lane, and generates a left-turn passage strategy based on hazard state judgment, so as to maximize the safe and efficient passage of left-turn vehicles through the intersection during the passage period. Summary of the Invention

[0006] The invention herein aims to optimize the motion trajectory, increase the exit lane selection, and improve the traffic efficiency of the intersection on the basis of allowing the left-turning networked autonomous driving vehicle to pass through the intersection safely. To achieve the above purpose, this patent proposes a method for the coordinated passage of networked autonomous driving vehicles under a left-turn dedicated signal. The research scenario of the present invention is a common cross-shaped intersection, where both the entrance and exit lanes are three-lane. Left-turning vehicles can choose exit lanes 1 and 2 close to the inside, and the outermost exit lane 3 is not within the research scope. For specific scenario settings, see the intersection channelization diagram. The specific implementation steps of this method are as follows:

[0007] Step 1: Based on the static channelization information of the intersection, a coordinate system is established with the midpoint of the entrance lane stop line as the origin, the direction perpendicular to the entrance lane stop line as the X-axis, and the entrance lane stop line as the Y-axis. Three trajectory planning methods are used: Bezier curve, Archimedean spiral, and quintic polynomial to generate the trajectory curve L corresponding to the vehicle selecting exit lane i (i = 1, 2) from the left-turn entrance lane. ij (j=1,2,3):

[0008] (1) Generate the left-turn trajectory curve L of the vehicle selecting exit lane i (i = 1, 2) using the third-order Bezier curve i1 :

[0009] x i1 (h)=(1-h i ) 3 x i-0 +3h i (1-h i ) 2 x i-1 +3h i 2 (1-h i )x i-2 +h i 3 x i-3 ,h i ∈[0,1]

[0010] y i1 (h)=(1-h i ) 3 y i-0 +3h i (1-hi ) 2 y i-1 +3h i 2 (1-h i )y i-2 +h i 3 y i-3 ,h i ∈[0,1]

[0011]

[0012] Among them, x i1 、y i1 Generate the horizontal and vertical coordinates of the left-turn trajectory of the vehicle selecting exit lane i using a third-order Bezier curve;

[0013] P0=(x i-0 ,y i-0 )=(0,0);

[0014]

[0015] Among them, P0, P1, P2, and P3 are the four control points of the third-order Bezier curve. P0 is the coordinate origin, P1 is a point on the X-axis, the horizontal coordinate is half of the horizontal coordinate corresponding to the midpoint of the exit lane i stop line, the horizontal coordinate of P2 is the horizontal coordinate corresponding to the midpoint of the exit lane i stop line, the vertical coordinate is half of the vertical coordinate of the stop line in the north entrance direction of the intersection, P3 is the midpoint of the exit lane i stop line, L is the lane width, C w The width of the pedestrian crossing;

[0016] (2) Using the Archimedean spiral to generate the left-turn trajectory curve L for the vehicle selecting exit lane i (i = 1, 2) i2 :

[0017]

[0018] Among them, x i2 、y i2 The Archimedean spiral is used to generate the horizontal and vertical coordinates of the left-turn trajectory of the vehicle selecting exit lane i, θ i is the angle between the coordinate point in the left-turn trajectory and the positive direction of the X-axis;

[0019] (3) Use the fifth-order polynomial to generate the left-turn trajectory curve L of the vehicle selecting exit lane i (i = 1, 2) i3 :

[0020]

[0021]

[0022] Among them, x i3 、y i3 To generate the horizontal and vertical coordinates of the left-turn trajectory of the vehicle selecting exit lane i using the fifth-order polynomial curve, p iv ,q iv (v = 1, 2, 3, 4, 5) are the coefficients of the fifth-order polynomial curve, T is the average time required for vehicles to complete a left turn at a common cross-type intersection with a left-turn lane, and a max is the maximum acceleration allowed for vehicles at the intersection, v0 is the average initial speed of the vehicle when it starts to turn left;

[0023] Step 2: Based on the six trajectory curves corresponding to different exit lanes i (i = 1, 2) obtained in step 1, calculate the shortest left-turn trajectory length corresponding to exit lane i:

[0024] L1=min(L 1j )

[0025] L2=min(L 2j )

[0026] Where L1 is the length of the shortest left-turn trajectory curve l1 corresponding to exit lane 1, and L2 is the length of the shortest left-turn trajectory curve l2 corresponding to exit lane 2;

[0027] Step 3: Define the vehicle V during the period when left turn is allowed. k The decision time period is V k The front car V k-1 The distance from the stop line is L c Time starts to V k-1 The time for entering the intersection is cut off, where L c For vehicle V k-1 Vehicle length; Vehicle V during the decision time period k According to the front car V k-1 The distance and speed between the vehicles are calculated, the exit lane selection index is selected, and the corresponding left-turn traffic plan is executed; for safety reasons, if the speed of the left-turning vehicle reaches v max When you can no longer accelerate, press v max Constant speed, v max The maximum speed for normal driving on urban roads is stipulated; the specific implementation plan is as follows:

[0028] (1) Definition of the dangerous state index δ t,k :Characterize vehicle V k The dangerous state of the vehicle V k VV with the car in front k-1 The distance and speed are judged; if the vehicle VV k V with the car in front k-1 The distance between vehicles is less than or equal to L cAnd vehicle V k The speed is greater than the front vehicle V k-1 When the speed is in serious danger, record δ t,k is 1, if the vehicle V k V with the car in front k-1 The distance between vehicles is greater than L c And vehicle V k The speed is greater than the front vehicle V k-1 When the speed is in a general dangerous state, record δ t,k for If the vehicle V k The speed of the vehicle in front is less than or equal to V k-1 When the speed is , it is in a non-dangerous state, record δ t,k is 0, the formula is as follows:

[0029]

[0030] Among them, t is a certain moment in the decision time period, Δd t,k is the vehicle V at time t k V with the car in front k-1 Real-time vehicle distance, v t,k 、v t,k-1 is the vehicle V at time t k 、V k-1 Speed ​​of the vehicle;

[0031] (2) Calculation of exit channel selection index Dt k : According to the vehicle V at the time interval Δt within the decision time period k The dangerous state value δ t,k Calculation yields:

[0032]

[0033] Among them, t i is a moment in the ith time interval within the decision time period, i.e., t = t i , N is the N time intervals within the decision time period, and N dangerous state indices can be calculated

[0034] The specific process of the left-turn autonomous driving queue cooperative passage strategy is as follows:

[0035] When k=1, vehicle V k Select Exit 1 and follow the left turn trajectory and maximum acceleration a corresponding to Exit 1 in step 2. max Accelerate to complete the left turn, where a max The maximum acceleration allowed at the intersection; when k>1, the vehicle V k According to the exit road selection index Dt k To choose the exit lane, the car in front of you Vk-1 After entering the intersection, drive at a constant speed to the stop line and complete the left turn according to the corresponding left turn trajectory. When the vehicle V k Select exit 1, when When the vehicle V k Select exit 2;

[0036] Vehicle V k When entering an intersection, determine the V k-1 Whether to enter the same exit lane, if not, then the vehicle V k With a max Accelerate to complete the left turn; if so, under the following collision avoidance constraints of the two vehicles, that is, the minimum safe headway ε is guaranteed between the two vehicles to avoid collision, where d min For the minimum headway, the vehicle V k With a max Accelerate to complete the left turn. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a block diagram of the overall concept of the present invention;

[0038] Figure 2 Create diagrams for intersection channelization and coordinates. DETAILED DESCRIPTION

[0039] The present invention is described in detail below with reference to the accompanying drawings and embodiments. It should be understood that this example is only used to illustrate the present invention and is not intended to limit the scope of the present invention. The overall concept of the cooperative traffic method of networked autonomous driving vehicles under a left-turn dedicated signal provided by the present invention is as follows: Figure 1 As shown, the specific implementation method includes the following steps:

[0040] Step 1: Based on the static channelization information of the intersection, a coordinate system is established with the midpoint of the entrance lane stop line as the origin, the direction perpendicular to the entrance lane stop line as the X-axis, and the entrance lane stop line as the Y-axis. Three trajectory planning methods are used: Bezier curve, Archimedean spiral, and quintic polynomial to generate the trajectory curve L corresponding to the vehicle selecting exit lane i (i = 1, 2) from the left-turn entrance lane. ij (j=1,2,3):

[0041] (1) Generate the left-turn trajectory curve L of the vehicle selecting exit lane i (i = 1, 2) using the third-order Bezier curve i1 :

[0042] x i1 (h)=(1-h i ) 3 x i-0 +3h i (1-hi ) 2 x i-1 +3h i 2 (1-h i )x i-2 +h i 3 x i-3 ,h i ∈[0,1]

[0043] y i1 (h)=(1-h i ) 3 y i-0 +3h i (1-h i ) 2 y i-1 +3h i 2 (1-h i )y i-2 +h i 3 y i-3 ,h i ∈[0,1]

[0044]

[0045] Among them, x i1 、y i1 Generate the horizontal and vertical coordinates of the left-turn trajectory of the vehicle selecting exit lane i using a third-order Bezier curve;

[0046] P0=(x i-0 ,y i-0 )=(0,0);

[0047]

[0048] Among them, P0, P1, P2, and P3 are the four control points of the third-order Bezier curve. P0 is the coordinate origin, P1 is a point on the X-axis, the horizontal coordinate is half of the horizontal coordinate corresponding to the midpoint of the exit lane i stop line, the horizontal coordinate of P2 is the horizontal coordinate corresponding to the midpoint of the exit lane i stop line, and the vertical coordinate is half of the vertical coordinate of the stop line in the north entrance direction of the intersection, P3 is the midpoint of the exit lane i stop line, L is the lane width, C w The width of the pedestrian crossing;

[0049] (2) Using the Archimedean spiral to generate the left-turn trajectory curve L for the vehicle selecting exit lane i (i = 1, 2) i2 :

[0050]

[0051] Among them, x i2 、y i2 The Archimedean spiral is used to generate the horizontal and vertical coordinates of the left-turn trajectory of the vehicle selecting exit lane i, θ i is the angle between the coordinate point in the left-turn trajectory and the positive direction of the X-axis;

[0052] (3) Use the fifth-order polynomial to generate the left-turn trajectory curve L of the vehicle selecting exit lane i (i = 1, 2) i3 :

[0053]

[0054]

[0055] Among them, x i3 、y i3 To generate the horizontal and vertical coordinates of the left-turn trajectory of the vehicle selecting exit lane i using the fifth-order polynomial curve, p iv ,q iv (v = 1, 2, 3, 4, 5) are the coefficients of the fifth-order polynomial curve, T is the average time required for vehicles to complete a left turn at a common cross-type intersection with a left-turn lane, and a max is the maximum acceleration allowed for vehicles at the intersection, v0 is the average initial speed of the vehicle when it starts to turn left;

[0056] Step 2: Based on the six trajectory curves corresponding to different exit lanes i (i = 1, 2) obtained in step 1, calculate the shortest left-turn trajectory length corresponding to exit lane i:

[0057] L1=min(L 1j )

[0058] L2=min(L 2j )

[0059] Where L1 is the length of the shortest left-turn trajectory curve l1 corresponding to exit lane 1, and L2 is the length of the shortest left-turn trajectory curve l2 corresponding to exit lane 2;

[0060] Step 3: Define the vehicle V during the period when left turn is allowed. k The decision time period is V k The front car V k-1 The distance from the stop line is L c Time starts to V k-1 The time for entering the intersection is cut off, where L c For vehicle V k-1 Vehicle length; Vehicle V during the decision time period k According to the front car V k-1The distance and speed between the vehicles are calculated, the exit lane selection index is selected, and the corresponding left-turn traffic plan is executed; for safety reasons, if the speed of the left-turning vehicle reaches v max When you can no longer accelerate, press v max Constant speed, v max The maximum speed for normal driving on urban roads is stipulated; the specific implementation plan is as follows:

[0061] (1) Definition of the dangerous state index δ t,k :Characterize vehicle V k The dangerous state of the vehicle V k V with the car in front k-1 The distance and speed are judged; if the vehicle V k V with the car in front k-1 The distance between vehicles is less than or equal to L c And vehicle V k The speed is greater than the front vehicle V k-1 When the speed is in serious danger, record δ t,k is 1, if the vehicle V k V with the car in front k-1 The distance between vehicles is greater than L c And vehicle V k The speed is greater than the front vehicle V k-1 When the speed is in a general dangerous state, record δ t,k for If the vehicle V k The speed of the vehicle in front is less than or equal to V k-1 When the speed is , it is in a non-dangerous state, record δ t,k is 0, the formula is as follows:

[0062]

[0063] Among them, t is a certain moment in the decision time period, Δd t,k is the vehicle V at time t k V with the car in front k-1 Real-time vehicle distance, v t,k 、v t,k-1 is the vehicle V at time t k 、V k-1 Speed ​​of the vehicle;

[0064] (2) Calculation of exit channel selection index Dt k : According to the vehicle V at the time interval Δt within the decision time period k The dangerous state value δ t,k Calculation yields:

[0065]

[0066] Among them, t iis a moment in the ith time interval within the decision time period, i.e., t = t i , N is the N time intervals within the decision time period, and N dangerous state indices can be calculated

[0067] The specific process of the left-turn autonomous driving queue cooperative passage strategy is as follows:

[0068] When k=1, vehicle V k Select Exit 1 and follow the left turn trajectory and maximum acceleration a corresponding to Exit 1 in step 2. max Accelerate to complete the left turn, where a max The maximum acceleration allowed at the intersection; when k>1, the vehicle V k According to the exit road selection index Dt k To choose the exit lane, the car in front of you V k-1 After entering the intersection, drive at a constant speed to the stop line and complete the left turn according to the corresponding left turn trajectory. When the vehicle V k Select exit 1, when When the vehicle V k Select exit 2;

[0069] Vehicle V k When entering an intersection, determine the V k-1 Whether to enter the same exit lane, if not, then the vehicle V k With a max Accelerate to complete the left turn; if so, under the following collision avoidance constraints of the two vehicles, that is, the minimum safe headway ε is guaranteed between the two vehicles to avoid collision, where d min For the minimum headway, the vehicle V k With a max Accelerate to complete the left turn.

[0070] The above steps describe the implementation process of the present invention in detail, but the present invention is not limited to the specific details of the above embodiments. Anything within the scope of the present invention should not be excluded from the scope of protection of the present invention.

Claims

1. A method for cooperative passage of networked autonomous driving vehicles under a dedicated left-turn signal, characterized in that: The following steps are involved: Step 1: Based on the static channelization conditions of the intersection, a coordinate system is established with the midpoint of the stop line of the left-turn entrance lane as the origin, the direction perpendicular to the stop line of the left-turn entrance lane as the X-axis, and the stop line of the left-turn entrance lane as the Y-axis. Three trajectory planning methods are used: quintic polynomial, Bezier curve, and Archimedean spiral to generate the trajectory curve L corresponding to the left-turn vehicle selecting exit lane i (i = 1, 2). ij (j=1,2,3); Step 2: Based on the six trajectory curves corresponding to different exit lanes i (i=1, 2) obtained in step 1, calculate the shortest left-turn trajectory length corresponding to exit lane i; Step 3: Define the vehicle V during the period when left turn is allowed. k The decision time period is V k The front car V k-1 The distance from the stop line is L c Time starts to V k-1 The time for entering the intersection is cut off, where L c For vehicle V k-1 Vehicle length; Vehicle V during the decision time period k According to the front car V k-1 The distance and speed between the vehicles are calculated, the exit lane selection index is selected, and the corresponding left-turn traffic plan is executed; for safety reasons, if the speed of the left-turning vehicle reaches v max When you can no longer accelerate, press v max Constant speed, v max The maximum speed for normal driving on urban roads is stipulated; the specific implementation plan is as follows: (1) Definition of the dangerous state index δ t,k :Characterize vehicle V k The dangerous state of the vehicle V k V with the car in front k-1 The distance and speed are judged; if the vehicle V k V with the car in front k-1 The distance between vehicles is less than or equal to L c And vehicle V k The speed is greater than the front vehicle V k-1 When the speed is in serious danger, record δ t,k is 1, if the vehicle V k V with the car in front k-1 The distance between vehicles is greater than L c And vehicle V k The speed is greater than the front vehicle V k-1 When the speed is in a general dangerous state, record δ t,k for If the vehicle V k The speed of the vehicle in front is less than or equal to V k-1 When the speed is , it is in a non-dangerous state, record δ t,k is 0, the formula is as follows: Among them, t is a certain moment in the decision time period, Δd t,k is the vehicle V at time t k V with the car in front k-1 Real-time vehicle distance, v t,k 、v t,k-1 is the vehicle V at time t k 、V k-1 Speed ​​of the vehicle; (2) Calculation of exit channel selection index Dt k : According to the vehicle V at the time interval Δt within the decision time period k The dangerous state value δ t,k Calculation yields: Among them, t i is a moment in the ith time interval within the decision time period, i.e., t = t i , N is the N time intervals within the decision time period, and N dangerous state indices can be calculated The specific process of the left-turn autonomous driving queue cooperative passage strategy is as follows: When k=1, vehicle V k Select Exit 1 and follow the left turn trajectory and maximum acceleration a corresponding to Exit 1 in step 2. max Accelerate to complete the left turn, where a max The maximum acceleration allowed at the intersection; when k>1, the vehicle V k According to the exit road selection index Dt k To choose the exit lane, the car in front of you V k-1 After entering the intersection, drive at a constant speed to the stop line and complete the left turn according to the corresponding left turn trajectory. When the vehicle V k Select exit 1, when When the vehicle V k Select exit 2; Vehicle V k When entering an intersection, determine the V k-1 Whether to enter the same exit lane, if not, then the vehicle V k With a max Accelerate to complete the left turn; if so, under the following collision avoidance constraints of the two vehicles, that is, the minimum safe headway ε is guaranteed between the two vehicles to avoid collision, where d min For the minimum headway, the vehicle V k With a max Accelerate to complete the left turn.

2. The method for cooperative passage of networked autonomous driving vehicles under a left-turn dedicated signal according to claim 1, characterized in that: According to the static channelization conditions of the intersection, the left-turn trajectory curve L of the vehicle selecting exit lane i (i=1, 2) is generated using the third-order Bezier curve. i1 : x i1 (h)=(1-h i ) 3 x i-0 +3h i (1-h i ) 2 x i-1 +3h i 2 (1-h i )x i-2 +h i 3 x i-3 ,h i ∈[0,1] the i1 (h)=(1-h i ) 3 the i-0 +3h i (1-h i ) 2 the i-1 +3h i 2 (1-h i ) the i-2 + h i 3 the i-3 , h i ∈[0,1] Among them, x i1 、y i1 Generate the horizontal and vertical coordinates of the left-turn trajectory of the vehicle selecting exit lane i using a third-order Bezier curve; P0=(x i-0 ,y i-0 )=(0,0); Among them, P0, P1, P2, and P3 are the four control points of the third-order Bezier curve. P0 is the coordinate origin, P1 is a point on the X-axis, the horizontal coordinate is half of the horizontal coordinate corresponding to the midpoint of the exit lane i stop line, the horizontal coordinate of P2 is the horizontal coordinate corresponding to the midpoint of the exit lane i stop line, and the vertical coordinate is half of the vertical coordinate of the stop line in the north entrance direction of the intersection, P3 is the midpoint of the exit lane i stop line, L is the lane width, C w The width of the crosswalk.

3. The method for cooperative passage of networked autonomous driving vehicles under a left-turn dedicated signal according to claim 2, characterized in that: According to the static channelization conditions of the intersection, the left-turn trajectory curve L of the vehicle selecting exit lane i (i=1, 2) is generated using the Archimedean spiral. i2 : Among them, x i2 、y i2 The Archimedean spiral is used to generate the horizontal and vertical coordinates of the left-turn trajectory of the vehicle selecting exit lane i, θ i It is the angle between the coordinate point in the left turn trajectory and the positive direction of the X axis.

4. The method for cooperative passage of networked autonomous driving vehicles under a left-turn dedicated signal according to claim 3, characterized in that: According to the static channelization conditions of the intersection, the left-turn trajectory curve L of the vehicle selecting exit lane i (i=1, 2) is generated using a fifth-order polynomial. i3 : Among them, x i3 、y i3 To generate the horizontal and vertical coordinates of the left-turn trajectory of the vehicle selecting exit lane i using the fifth-order polynomial curve, p iv ,q iv (v = 1, 2, 3, 4, 5) are the coefficients of the fifth-order polynomial curve, T is the average time required for vehicles to complete a left turn at a common cross-type intersection with a left-turn lane, and a max is the maximum acceleration allowed for vehicles at the intersection, and v0 is the average initial speed of the vehicle when it starts to turn left.

5. The method for cooperative passage of networked autonomous driving vehicles under a left-turn dedicated signal according to claim 4, characterized in that: According to the six trajectory curves corresponding to different exit lanes i (i = 1, 2) obtained in step 1, the shortest left-turn trajectory length corresponding to exit lane i is calculated: L1=min(L 1j ) <h2 style=";text-align:left;direction:ltr">L2=min(L<h2 style=";text-align:left;direction:ltr"> 2j <h2 style=";text-align:left;direction:ltr"> ) Among them, L1 is the length of the shortest left-turn trajectory curve l1 corresponding to exit lane 1, and L2 is the length of the shortest left-turn trajectory curve l2 corresponding to exit lane 2.

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