A vehicle lane-changing trajectory planning method based on a fifth-order Bezier curve

Abstract

The application provides a vehicle lane-changing trajectory planning method based on a five-order Bezier curve in an automatic driving environment, which mainly comprises three parts, first, a crossing traffic efficiency improvement method based on a risk degree in the automatic driving environment is used to obtain permission conditions of vehicle entry and exit of a crossing, including speed, a current lane, a target lane and the like, and the permission conditions are used as initial and terminal constraints of a trajectory planning model; then, a single vehicle model of vehicle kinematics is used as a basis, constraints of lateral acceleration in a vehicle lane-changing process are considered, and the constraints are used as one of boundary constraints of trajectory planning; a geometric circle is used as a safety domain of the vehicle, critical conditions of position relations of the vehicle with other vehicles in the vehicle lane-changing process are calculated, and collision avoidance is used as the second boundary constraint of trajectory planning; finally, an optimization objective function which comprehensively considers multiple targets such as safety, traffic efficiency, energy consumption and emission is established, different weights are given to the optimization objective function items, different priorities of the multiple targets are realized, and a complete lane-changing trajectory planning model is formed.

Description

Technical Field

[0001] This invention relates to the field of vehicle motion optimization at intersection connecting road sections in an autonomous driving environment, specifically to a vehicle lane-changing trajectory planning method based on a fifth-order Bézier curve. Background Technology

[0002] Intersections, as crucial nodes in road networks, significantly impact traffic efficiency through their traffic patterns. Vehicle control strategies on connecting road segments at intersections have a substantial influence on intersection efficiency. Vehicle traffic flow on connecting road segments is a major focus of urban transportation. Lane-changing and following strategies on these segments affect the operational status and efficiency of the intersection and the entire road network. Therefore, platooning control, coordinated lane-changing, and trajectory planning on connecting road segments are hot research topics in intelligent transportation systems.

[0003] Currently, research on vehicle lane-changing trajectory planning has yielded many results. On the one hand, scholars have established vehicle lane-changing trajectory planning methods based on models such as genetic algorithms, rolling time domain, and neural networks, and solved the models using optimal control theory. However, existing research mostly focuses on highway scenarios, with high speed limits, low density, and long straight sections as the basic modeling conditions, which is far removed from the intersection connecting road segment scenario focused on in this invention. On the other hand, regarding the type of trajectory curve, scholars often use polynomial curves and Bézier curves to fit vehicle lane-changing trajectories. For lane-changing behavior, the vehicle trajectory requires continuous and smooth curvature, and the yaw angle of the vehicle during driving should be within a safe range. To avoid accidents, the lane-changing trajectory should also be as short as possible. Higher-order Bézier curves have the advantages of zero curvature at the beginning and end and smoothness without abrupt changes, making them more suitable than polynomial curves for fitting lane-changing trajectories in the intersection connecting road segment scenario.

[0004] Although there are many existing technologies for vehicle lane change trajectory planning, their application scenarios are relatively limited, and further research is needed to address other scenarios. Summary of the Invention

[0005] The present invention is proposed based on the above-mentioned situation of the prior art. The technical problem to be solved by the present invention is to provide a vehicle lane-changing trajectory planning method for intersection connecting road sections.

[0006] To solve this technical problem, the technical solution provided by the present invention includes: 1. A method for planning vehicle lane-changing trajectories for intersection connecting road sections, characterized by comprising the following steps:

[0007] Step 1: Establish a Cartesian coordinate system with the vehicle's lane-changing position as the origin and the vehicle's forward direction as the positive x-axis. Decouple the six control points of the fifth-order Bézier curve horizontally and vertically, and based on the central symmetry of the curve, transform the x-coordinates of the six control points into functions of the x-coordinates of the first and second control points.

[0008] Step 2: Determine the initial and final constraints of the lane-changing trajectory planning based on the intersection entry and exit permit conditions given by the intersection cooperative traffic strategy; whereby...

[0009] The conditions for permitting entry and exit at an intersection include: the lanes from which a vehicle exits from the previous intersection and enters the next intersection, which determines the ordinate of the six control points of the fifth-order Bézier curve; and the final position of the vehicle after completing the lane change, i.e., the starting point of the solid lane line, which determines the maximum value of the abscissa of the third control point.

[0010] Step 3: Considering the motion characteristics of individual vehicles and the interaction between vehicles, establish boundary constraints for lane-changing trajectory planning, using maximum lateral acceleration and collision avoidance as critical conditions; whereby...

[0011] The boundary constraints considering the motion characteristics of a single vehicle include: deriving the critical values ​​of the vehicle lane-changing trajectory curve parameters based on the vehicle's maximum lateral acceleration using a single vehicle model of vehicle kinematics; the boundary constraints considering vehicle-to-vehicle motion interaction include: deriving the critical values ​​of the vehicle lane-changing trajectory curve parameters based on the tangency of the two vehicle safety domains using a geometric circle as the vehicle's safety domain.

[0012] Step 4: Consider objectives such as traffic efficiency, safety, and comfort, and assign weights to each to establish a multi-objective optimization objective function; whereby...

[0013] Traffic efficiency is characterized by the length of the track. The longer the track, the longer the time it takes for vehicles to change lanes, and the longer the impact on surrounding vehicles. Safety is characterized by the maximum yaw angle of the vehicle during lane changing. The smaller the yaw angle, the smoother the track and the less impact on the speed of surrounding vehicles. Comfort is characterized by the variance of the entire track. The smaller the variance, the smaller the curvature fluctuation of the track, the smaller the lateral acceleration, and the better the passenger experience.

[0014] Step 5: The constraints and objective function in the above steps constitute a complete trajectory planning model. Solve this model to obtain the target trajectory.

[0015] Preferably, determining the trajectory planning model includes:

[0016] The S001 fifth-order Bézier curve is determined by 6 control points, defined as P. i For i = 0, 1, 2, 3, 4, 5, its parametric equation is expressed by the following formula:

[0017]

[0018] A Cartesian coordinate system is established with the vehicle's lane-changing position as the origin and the vehicle's forward direction as the positive x-axis. The six control points of the fifth-order Bézier curve are decoupled horizontally and vertically. Based on the curve's central symmetry, the x-coordinates of the six control points are transformed into functions of the x-coordinates of the second and third control points, expressed by the following formula:

[0019]

[0020] On the connecting road segment of S002 at the associated intersection, the vehicle's trajectory is affected by the intersection's entry and exit permitting conditions. Therefore, the trajectory optimization problem for intelligent connected vehicles on this segment needs to consider the initial and final constraints of the associated intersection on trajectory planning. Through the cooperative passage strategy of intelligent connected vehicles at the intersection, the lanes for vehicles leaving the previous intersection and entering the next intersection, as well as the maximum distance allowed by actual road conditions for vehicles to complete lane-changing behavior, can be determined. The former determines the direction of lane changing and the number of lanes crossed, while the latter determines the upper bound of the feasible region of trajectory planning. The initial and final constraints considering intersection entry and exit conditions are expressed by the following formula:

[0021]

[0022] Where w is the width of a single lane, d f The furthest distance a vehicle can travel to complete a lane-changing maneuver under actual road conditions.

[0023] Ignoring dynamic characteristics such as sideslip angle, and assuming that the two front wheels of the vehicle have equal sideslip angles, a single-vehicle kinematic model can be established as follows:

[0024]

[0025] Where v is the speed of the center of mass, δ f Let X and Y be the vehicle coordinates, ψ be the heading angle, and l be the front wheel deflection angle. f Let l represent the front wheelbase and the overall wheelbase, respectively. Using vector u = [δ...] f ,a] T As input, the vector ξ = [X,Y,ψ,v] T As a state variable.

[0026] Due to the inherent performance characteristics of the vehicle, its lateral acceleration has an upper bound, which leads to one of the lower bounds of the feasible region for the lane-changing trajectory. The turning radius is minimized when the vehicle reaches its maximum lateral acceleration, i.e.:

[0027]

[0028] From geometric relations, we have Right now:

[0029] Among them, a y,min This is the maximum lateral acceleration of the vehicle, typically ranging from 0.2g to 0.4g.

[0030] During the lane change process in S003, interaction with vehicles in the target lane also needs to be considered, mainly manifested in collision avoidance constraints. A geometric circle is used as the vehicle's safe domain, and the critical condition of the two vehicles' safe domains being externally tangent to each other's geometric circles is considered, thus obtaining another lower bound of the feasible domain of the lane change trajectory.

[0031] According to geometric relations, we have:

[0032]

[0033] L 2 +B 2 =r 2

[0034] Where L and B represent the length and width of the vehicle, respectively. Therefore, to avoid a collision with a vehicle in the target lane, we have:

[0035]

[0036] Where d2 is the distance traveled by vehicles in the target lane.

[0037] S004 comprehensively considers the safety, comfort, and traffic efficiency during lane changing. The objective function mainly considers the following aspects: First, the maximum curvature value during lane changing should be minimized, and the curvature change should be as smooth and continuous as possible; second, the vehicle yaw angle should be minimized, and the maximum value should be less than 45°; finally, under sufficiently safe conditions, the lane changing distance should be as short as possible to improve traffic efficiency and avoid potential risks. Therefore, the objective function of the lane changing trajectory planning problem for intersection connecting road sections can be expressed as:

[0038]

[0039] Where D represents the variance, and ω represents the variance. i i = 1, 2, 3, 4 are weight parameters.

[0040] The vehicle lane-changing trajectory optimization model based on the fifth-order Bézier curve in S005 can be expressed as:

[0041]

[0042] Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the overall concept of the present invention;

[0044] Figure 2aThis is a schematic diagram of a fifth-order Bézier curve;

[0045] Figure 2b This is a schematic diagram of the horizontal and vertical decoupling of a fifth-order Bézier curve;

[0046] Figure 3a This is a schematic diagram of vehicle kinematics for single-vehicle motion;

[0047] Figure 3b This is a schematic diagram of the critical condition for maximum lateral acceleration;

[0048] Figure 3c This is a schematic diagram of the critical conditions for avoiding collisions. Detailed Implementation

[0049] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. It should be understood that this example is for illustrative purposes only and is not intended to limit the scope of the invention. The overall conceptual framework of a vehicle lane-changing trajectory planning method based on a fifth-order Bézier curve provided by the present invention is shown in the following diagram. Figure 1 As shown, the specific implementation method includes the following steps:

[0050] Step 1, as follows Figure 2a As shown, a fifth-order Bézier curve is determined by six control points, defined as P. i If i = 0, 1, 2, 3, 4, 5, then the parametric equation of the fifth-order Bézier curve is expressed by the following equation:

[0051] t is a parameter

[0052] like Figure 2b As shown, a Cartesian coordinate system is established with the vehicle's lane-changing position as the origin and the vehicle's forward direction as the positive x-axis. The six control points of the fifth-order Bézier curve are decoupled horizontally and vertically. Based on the curve's central symmetry, the x-coordinates of the six control points are transformed into functions of the x-coordinates of the second and third control points, expressed by the following formula:

[0053]

[0054] Step 2: On the connecting road segments of associated intersections, the vehicle's trajectory is affected by the entry and exit permitting conditions of the intersections. Therefore, the trajectory optimization problem for intelligent connected vehicles on this road segment needs to consider the initial and final constraints of the associated intersections on trajectory planning. Through the cooperative passage strategy of intelligent connected vehicles at intersections, the lanes for vehicles to leave the previous intersection and enter the next intersection, as well as the furthest distance allowed by actual road conditions for vehicles to complete lane-changing behavior, can be determined. The former determines the direction of lane changing and the number of lanes crossed, while the latter determines the upper bound of the feasible region of trajectory planning. The initial and final constraints considering intersection entry and exit conditions are expressed by the following formula:

[0055]

[0056] Where w is the width of a single lane, d f The furthest distance a vehicle can travel to complete a lane-changing maneuver under actual road conditions.

[0057] Step 3: Considering the motion characteristics of individual vehicles and the interaction between vehicles, and using maximum lateral acceleration and collision avoidance as critical conditions, establish boundary constraints for lane-changing trajectory planning. The specific implementation steps of Step 3 are as follows:

[0058] Step 31 as follows Figure 3a As shown, ignoring dynamic characteristics such as sideslip angle, and assuming that the sideslip angles of the two front wheels of the vehicle are equal, a single-vehicle kinematic model can be established as follows:

[0059]

[0060] Where v is the speed of the center of mass, δ f Let X and Y be the front wheel deflection angle, ψ be the vehicle coordinates, and l be the heading angle. f Let l represent the front wheelbase and the overall wheelbase, respectively. Using vector u = [δ...] f ,a] T As input, the vector ξ = [X,Y,ψ,v] T As a state variable.

[0061] like Figure 3b As shown, due to the vehicle's inherent performance characteristics, its lateral acceleration has an upper bound, which leads to one of the lower bounds of the feasible region for the lane-changing trajectory. The turning radius is minimized when the vehicle reaches its maximum lateral acceleration, i.e.:

[0062]

[0063] From geometric relations, we have Right now:

[0064] Among them, a y,min This is the maximum lateral acceleration of the vehicle, typically ranging from 0.2g to 0.4g.

[0065] Step 32: During lane changing, interaction with vehicles in the target lane also needs to be considered, primarily in terms of collision avoidance constraints. For example... Figure 3c The diagram shows a geometric circle as the safety domain of the vehicle, and considers the critical condition that the geometric circles of the safety domains of the two vehicles are externally tangent, thus obtaining another lower bound of the feasible domain of the lane-changing trajectory.

[0066] According to geometric relations, we have:

[0067]

[0068] L 2+B 2 =r 2

[0069] Where L and B represent the length and width of the vehicle, respectively. Therefore, to avoid a collision with a vehicle in the target lane, we have:

[0070]

[0071] Where d2 is the distance traveled by vehicles in the target lane.

[0072] Step 4: Considering the safety, comfort, and traffic efficiency during lane changing, the objective function mainly considers the following aspects: First, the maximum curvature value during lane changing should be as small as possible, and the curvature change should be as smooth and continuous as possible; second, the vehicle yaw angle should be as small as possible, and the maximum value should be less than 45°; finally, under sufficiently safe conditions, the lane changing distance should be as short as possible to improve traffic efficiency and avoid potential risks. Therefore, the objective function for the lane changing trajectory planning problem of intersection connecting road segments can be expressed as:

[0073]

[0074] Where D represents the variance, and ω represents the variance. i i = 1, 2, 3, 4 are weight parameters.

[0075] Step 5, the vehicle lane-changing trajectory optimization model based on the fifth-order Bézier curve can be expressed as:

[0076]

[0077]

[0078] 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 protection scope of the present invention.

Claims

1. A vehicle lane-changing trajectory planning method based on fifth-order Bézier curves, characterized in that, Includes the following steps: Step 1: Establish a Cartesian coordinate system with the vehicle's lane-changing position as the origin and the vehicle's forward direction as the positive x-axis. Decouple the six control points of the fifth-order Bézier curve in both the horizontal and vertical directions. Based on the central symmetry of the curve, transform the x-coordinates of the six control points into functions of the x-coordinates of the first and second control points. Step 2: Determine the initial and final constraints of the lane-changing trajectory planning based on the intersection entry and exit permit conditions given by the intersection cooperative traffic strategy; in The conditions for permitting entry and exit at the intersection include: the lanes from which a vehicle exits from the previous intersection and enters the next intersection, which determines the ordinate of the six control points of the fifth-order Bézier curve; and the final position of the vehicle after completing the lane change, i.e., the starting point of the solid lane line, which determines the maximum value of the abscissa of the third control point. Step 3: Considering the motion characteristics of individual vehicles and the interaction between vehicles, establish boundary constraints for lane-changing trajectory planning, using maximum lateral acceleration and collision avoidance as critical conditions; whereby... The boundary constraints considering the motion characteristics of a single vehicle include: based on the single vehicle model of vehicle kinematics, deriving the critical values ​​of the vehicle lane-changing trajectory curve parameters according to the maximum lateral acceleration of the vehicle; the boundary constraints considering vehicle-to-vehicle motion interaction include: using a geometric circle as the vehicle safety domain, deriving the critical values ​​of the vehicle lane-changing trajectory curve parameters according to the tangency of the safety domains of two vehicles. Step 4: Consider objectives such as traffic efficiency, safety, and comfort, and assign weights to each to establish a multi-objective optimization objective function; where... Traffic efficiency is characterized by the length of the track. The longer the track, the longer the time it takes for vehicles to change lanes, and the longer the impact on surrounding vehicles. Safety is characterized by the maximum yaw angle of the vehicle during lane changing. The smaller the yaw angle, the smoother the track and the less impact on the speed of surrounding vehicles. Comfort is characterized by the variance of the entire track. The smaller the variance, the smaller the curvature fluctuation of the track, the smaller the lateral acceleration, and the better the passenger experience. Step 5: The constraints and objective function in the above steps constitute a complete trajectory planning model; solve the model to obtain the target trajectory.

2. The vehicle lane-changing trajectory planning method based on a fifth-order Bézier curve according to claim 1, characterized in that, The trajectory planning model uses a fifth-order Bézier curve to fit the lane-changing trajectory, which has the advantages of initial and zero curvature and smooth, non-abrupt curves, making it suitable for fitting lane-changing trajectories.

3. The vehicle lane-changing trajectory planning method based on a fifth-order Bézier curve according to claim 1, characterized in that, The steps to determine the trajectory planning model include: The S001 fifth-order Bézier curve is determined by 6 control points and is defined as follows: Its parametric equation is expressed by the following equation: A Cartesian coordinate system is established with the vehicle's initial lane-changing position as the origin and the vehicle's forward direction as the positive x-axis. The six control points of the fifth-order Bézier curve are decoupled horizontally and vertically. Based on the curve's central symmetry, the x-coordinates of the six control points are transformed into functions of the x-coordinates of the second and third control points, expressed by the following formula: On the connecting road segment of S002 at the associated intersection, the vehicle's trajectory is affected by the permission conditions for entering and exiting the intersection. Therefore, the trajectory optimization problem for intelligent connected vehicles on this road segment needs to consider the initial and final constraints of the associated intersection on the trajectory planning. Through the cooperative passage strategy of intelligent connected vehicles at the intersection, the lanes for vehicles to leave the previous intersection and enter the next intersection, as well as the farthest distance allowed by actual road conditions for vehicles to complete lane-changing behavior, can be determined. The former determines the direction of lane changing and the number of lanes crossed, while the latter determines the upper bound of the feasible region of trajectory planning. The initial and final constraints considering the intersection entry and exit conditions are expressed by the following formula: in, For single-lane width, The furthest distance that a vehicle can travel to complete a lane-changing maneuver, provided that actual road conditions permit. Ignoring dynamic characteristics such as sideslip angle, and assuming that the two front wheels of the vehicle have equal sideslip angles, a single-vehicle kinematic model can be established as follows: in, For the center of gravity speed, For the front wheel deflection angle, For vehicle coordinates, For heading angle, These are the front wheelbase and the overall wheelbase, respectively; in vector... As input, vector As a state quantity; Due to the inherent performance characteristics of the vehicle, its lateral acceleration has an upper bound, which leads to one of the lower bounds of the feasible region for the lane-changing trajectory; the turning radius is minimized when the vehicle reaches its maximum lateral acceleration, i.e.: From geometric relations, we have ,Right now: in, The maximum lateral acceleration of the vehicle is typically taken as a value. ; During the lane change process of S003, the interaction with vehicles in the target lane also needs to be considered, which is mainly reflected in collision avoidance constraints. The geometric circle is used as the safety domain of the vehicle, and the critical condition of the geometric circles of the safety domains of the two vehicles being externally tangent is considered, thus obtaining another lower bound of the feasible domain of the lane change trajectory. According to geometric relations, we have: in, These are the length and width of the vehicle, respectively; therefore, to avoid a collision with vehicles in the target lane, we have: in, The distance traveled by vehicles in the target lane; S004 comprehensively considers the safety, comfort, and traffic efficiency during lane changing. The objective function mainly considers the following aspects: First, the maximum curvature value during lane changing should be minimized, and the curvature change should be as smooth and continuous as possible; second, the vehicle yaw angle should be minimized, and the maximum value should be less than [missing value]. Finally, under sufficiently safe conditions, the lane-changing distance should be as short as possible to improve traffic efficiency and avoid potential risks; therefore, the objective function of the lane-changing trajectory planning problem for intersection connecting road sections can be expressed as: in Represents variance. These are weight parameters; The vehicle lane-changing trajectory optimization model based on the fifth-order Bézier curve in S005 can be expressed as: 。 4. The vehicle lane-changing trajectory planning method based on a fifth-order Bézier curve according to claim 1, characterized in that, The proposed trajectory planning model is a dual continuous variable model with a closed feasible region, and therefore a solution is guaranteed.

5. The vehicle lane-changing trajectory planning method based on a fifth-order Bézier curve according to claim 1, characterized in that, Taking into full account the traffic characteristics of low speed limits, high density, and short straight sections in the intersection connecting road segments, the proposed trajectory planning model is suitable for this scenario.

6. The vehicle lane-changing trajectory planning method based on a fifth-order Bézier curve according to claim 1, characterized in that, A multi-objective optimization objective function was established, and the weight parameters can be dynamically adjusted according to the priority of the optimization objectives in practical application scenarios.

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