A vehicle following motion planning method for curved and sloping roads

Abstract

This invention discloses a vehicle following motion planning method for curved and sloping road sections, comprising: 1. collecting information on the geometric features of the curved and sloping road section, the geometric and dynamic parameters of the vehicle, and the following data of the preceding vehicle; 2. calculating the artificial potential field force of the vehicle in the lateral direction of the road based on an artificial potential field algorithm; 3. constructing a vehicle state prediction model based on an improved IDM (Inductively Coupled Model) that considers the influence of the maximum speed without deviating from the path on the curved and sloping road section; 4. obtaining the real-time path planning coordinates at the next moment; 5. obtaining a smooth planned path using cubic Bézier curves. This invention can improve the safety and driving comfort of vehicles following other vehicles on curved and sloping roads, avoid the possibility of dangerous traffic accidents such as collisions, skidding, and rollovers, thereby reducing the accident rate and delay rate of such roads and improving the traffic capacity of curved and sloping road sections.

Description

Technical Field

[0001] This invention belongs to the field of autonomous driving and intelligent transportation. Specifically, it refers to a method for planning vehicle car-following motion on curved and sloping road sections, which comprehensively considers the road surface information, vehicle geometry and dynamic parameters, and is based on artificial potential field algorithm and intelligent driving model (IDM). In particular, it is a method for planning vehicle car-following motion on curved and sloping road sections. Background Technology

[0002] Curved and sloping road sections, as an important part of roads, are prone to traffic accidents such as rollovers, skidding, and rear-end collisions due to their complex traffic environment and poor driver visibility. Studies have shown that accidents with high fatalities, such as collisions, scrapes, rollovers, and falls, often occur on curved and sloping road sections. To reduce safety accidents on curved and sloping road sections and accelerate the deployment of autonomous driving technology on complex road surfaces, designing a motion planning method for autonomous vehicles to avoid collisions, skidding, and rollovers on curved and sloping road sections is of practical significance.

[0003] Numerous studies have been conducted on car-following models, continuously refining traffic flow theory models and conducting in-depth research. Many types of car-following models have emerged, including stimulus-response models, safe distance models, meta-automatic models, and intelligent driving models. However, these models simplify the influencing factors in the car-following process to varying degrees, and they do not adequately consider road conditions and the geometric and dynamic parameters of vehicles, making them difficult to apply effectively on complex road surfaces.

[0004] Most existing research models are based on straight-line studies. A small number of car-following models improve upon straight-line car-following models by considering road linearity, curve curvature, and curve friction coefficient, forming extended curve car-following models. Few models address curved and sloping road sections, yet numerous such sections exist on real roads, especially in the mountainous areas of western my country. Therefore, solving the path planning problem on curved and sloping road sections is crucial for promoting the application of autonomous driving technology on complex road surfaces and accelerating its implementation. Curved and sloping road environments are more complex than straight-line environments, requiring continuous monitoring of changes in the surrounding environment to obtain real-time information and continuously update the planned path to adapt to these changes. Therefore, real-time car-following motion planning is essential to ensure that autonomous vehicles always stay on a safe path. Summary of the Invention

[0005] This invention addresses the shortcomings of existing technologies by proposing a vehicle following motion planning method for curved and sloping road sections. The aim is to plan a continuous and stable vehicle following path on curved and sloping road sections, thereby improving the safety and driving comfort of vehicles following each other on curves and slopes, avoiding the possibility of dangerous traffic accidents such as collisions, skidding, and rollovers, reducing the accident rate and delay rate of the road, and improving the traffic capacity of curved and sloping road sections.

[0006] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0007] The present invention provides a vehicle following motion planning method for curved and sloping road sections, characterized in that the curved and sloping road section simultaneously has slope, road surface superelevation, and curvature, and assuming that the autonomous driving vehicle is vehicle number n and the vehicle following is vehicle number n-1, the following path planning method includes the following steps:

[0008] Step 1: Based on the road surface slope of the aforementioned curved section and super high The origin O is the center of curvature of the lane centerline. The X-axis is the direction from the origin O to the lane centerline and parallel to the ground. The Y-axis is the direction perpendicular to the X-axis and parallel to the ground. The Z-axis is determined by the right-hand rule, thus establishing a Cartesian coordinate system. In the Cartesian coordinate system The following data are collected: geometric feature information of the curved and sloping road section, geometric and dynamic parameters of vehicle n, and vehicle following data of the curved and sloping road section at time t.

[0009] Step 2: Based on the information, parameters, and data collected in Step 1, construct the artificial potential field force of vehicle n at time t. , used for trajectory planning of vehicle number n;

[0010] Step 3: Based on the information, parameters and data collected in Step 1, construct a vehicle state prediction model at time t based on the Intelligent Driving Model (IDM) for trajectory planning of vehicle number n.

[0011] Step 4: Force based on the artificial potential field at time t Using the vehicle state prediction model at time t, calculate the real-time path planning coordinates of vehicle n on the curved and sloping road section at time t+1. ;

[0012] Step 5: Calculate the Bézier curve using equation (47). Thus, a smooth planning path E(x,y,z) in the Cartesian coordinate system is obtained using cubic Bézier curves.

[0013] (47)

[0014] In equation (47), It is a parameter, and its value range is... The location coordinates of the real-time path planning points obtained in step 4 are denoted as follows: , This indicates that vehicle number n is in the nth position. The real-time path planning coordinates of the points at each moment. This indicates that vehicle number n is in the nth position. The location coordinates of the real-time path planning points at each moment. This represents the position coordinates of the real-time path planning point of vehicle number n at time t. This indicates that vehicle number n is in the nth position. The position coordinates of the real-time path planning points at any given moment;

[0015] Step 6: After assigning t+1 to t, return to step 2 and execute sequentially to plan the driving path of vehicle n in real time.

[0016] The vehicle following motion planning method for curved and sloping road sections described in this invention is also characterized in that step 1 includes:

[0017] Step 1.1: Collect information on the geometric characteristics of the curved and sloping road section;

[0018] A data acquisition vehicle equipped with a GPS, IMU, LiDAR, and camera was used to collect and process data on the curved road section, obtaining geometric feature information of the curved road section, including: coordinates of any point on the lane centerline. Any coordinate point on the center line of the lane Road surface slope Ultra-high Road width The radius of curvature at the centerline of the lane in polar coordinates The extreme angle at the center line of the lane The polar coordinate system is based on the coordinate points on the lane centerline. The pole is defined, and the polar axis is established with the direction parallel to the X-axis as the polar axis;

[0019] Step 1.2: Collect the geometric and dynamic parameters of vehicle number n, including: vehicle curb weight m, vehicle width d, track width b, front wheelbase L1, rear wheelbase L2, and center of gravity height h. g ;

[0020] Step 1.3: Collect vehicle following trajectory data under the curved and sloping road section;

[0021] Extract the position information of vehicle number n-1 at time t. The speed of vehicle number n-1 at time t and acceleration The location information of vehicle number n at time t. The speed of vehicle number n at time t And obtain the polar coordinates of vehicle number n-1 at time t. The polar coordinates of vehicle number n at time t ,in, and Represented by coordinates Let X be the pole, and let X be the polar angle and polar radius of the (n-1)th vehicle in a polar coordinate system with the direction parallel to the X-axis as the polar axis. and Represented by coordinates The polar angle and polar radius of the nth vehicle in a polar coordinate system established with the pole as the pole and the direction parallel to the X-axis as the polar axis.

[0022] Furthermore, step 2 includes:

[0023] Step 2.1: Calculate the outer boundary of the lane at time t for vehicle n using equation (1). and the inner boundary to ensure driving within the lane ;

[0024] (1)

[0025] In equation (1), for The radius of curvature at the centerline of the lane; for The width of the road surface at the center line of the lane; for Superelevation at the center line of the lane;

[0026] Step 2.2: Determine the boundary conditions for the safe trajectory of vehicle n at time t. ;

[0027] Force analysis was performed on vehicle n, and the critical conditions for front wheel sideslip at time t were obtained using equations (13) and (14). Critical conditions for rear wheel sideslip Using equation (16), we obtain the critical condition for the nth vehicle to tilt at time t. Thus, the boundary conditions of the entire trajectory of vehicle n at time t can be obtained using equation (17). ;

[0028] (13)

[0029] (14)

[0030] (16)

[0031] (17)

[0032] In equations (13)-(17), Represents gravitational acceleration, Indicates the lateral force coefficient; for The road surface slope at the center line of the lane;

[0033] Step 2.3: Calculate the net potential force of vehicle n at time t. ;

[0034] Using equation (22), we can obtain the gravitational force exerted by the target point C on the lane centerline on the center of mass M of the nth vehicle at time t. Using equation (23), the repulsive force exerted by the outer side of the lane on the center of mass M of vehicle n at time t can be obtained. Using equation (24), the repulsive force of the inner side of the lane on the center of mass M of vehicle n at time t can be obtained. Thus, the resultant force of the nth vehicle at the center of mass M at time t can be obtained using equation (25). :

[0035] (twenty two)

[0036] (twenty three)

[0037] (twenty four)

[0038] (25)

[0039] In equations (22)-(25), It is a vector differential operator used to represent the gradient. The gravitational constant, It is the distance between the centroid M of vehicle n at time t and the target point C on the lane centerline. The vector direction points from the centroid M of vehicle n at time t to the target point C; This represents the threshold distance at which the repulsive force is applied. Represents the repulsive force constant. express The distance from the center of mass M of vehicle n at time t. The vector direction from Pointing to the centroid M of vehicle n at time t; express and The distance from the maximum value between the two values ​​to the centroid M of vehicle n at time t. The vector direction from The center of mass M of vehicle n at time t

[0040] Furthermore, step 3 includes:

[0041] Step 3.1: Calculate the arc distance between the (n-1)th vehicle and the nth vehicle on the lane centerline at time t on the curved road section. ;

[0042] Step 3.2: Calculate the maximum speed of vehicle n at time t without deviating from the path using equation (33). ;

[0043] (33)

[0044] In equation (33), This represents the coefficient of friction between the wheel and the road surface;

[0045] Step 3.3: Construct a vehicle state prediction model at time t based on IDM using equation (34):

[0046] (34)

[0047] In equation (34), This represents the acceleration of vehicle number n at time t. This represents the expected maximum acceleration of vehicle number n. This represents the expected speed of vehicle number n. Indicates the acceleration index, This represents the minimum safe distance between vehicle n and vehicle n-1 to avoid a collision. This represents the safe headway between vehicle n and vehicle n-1. This represents the difference in speed between vehicle n and vehicle (n-1) at time t. This represents the comfortable deceleration of vehicle number n. This represents the relative speed between vehicle n and vehicle (n-1) at time t. The desired distance to maintain, and:

[0048] (35)

[0049] Step 3.4: Use the vehicle following trajectory data under the curved and sloping road section to calibrate the parameters of the improved IDM following model, thereby determining the parameters in the improved IDM following model, including: the expected maximum acceleration. Vehicle desired speed Minimum safe distance to avoid collision Comfort deceleration .

[0050] Furthermore, step 3.1 includes:

[0051] Step 3.1.1: Set the polar angle of vehicle n. and the vehicle polar angle Coordinates of the center line between lanes Coordinate parameterization is performed, and then the parameterized equation of the lane centerline is constructed using equation (26). ;

[0052] (26)

[0053] In equation (26), Representing parameterized equations The parameters, These represent the projected coordinates of the lane centerline along the X and Y axes in a Cartesian coordinate system, respectively. This represents the projected coordinates of the lane centerline along the Z-axis in a Cartesian coordinate system.

[0054] Step 3.1.2: Use equation (27) to obtain the small arc length on the center line of the lane. :

[0055] (27)

[0056] In equation (27), , , These represent the rates of change of the coordinate point (x, y, z) along the X-axis, Y-axis, and Z-axis in the Cartesian coordinate system, respectively. Representing parameterized equations exist The tangent vector at the point;

[0057] Step 3.1.3: Calculate the arc distance between vehicle number n-1 and vehicle number n at time t on the curved road section using equation (28). :

[0058] (28)

[0059] In equation (28), express The parameters at that location, express The parameters at that location.

[0060] Furthermore, step 4 includes:

[0061] Step 4.1: Calculate the acceleration of vehicle n at time t using equation (34). ;

[0062] Step 4.2: Use equation (36) to obtain the speed of vehicle n at time t+1. ;

[0063] (36)

[0064] In equation (36), This is a time step from time t to time t+1;

[0065] Step 4.3: Take The coordinates of the center line of the lane are Coordinates of the center line of the lane Let S be the origin of the Frenet coordinate system. Let S be the longitudinal direction of the road along the center line of the lane and P be the transverse direction of the road perpendicular to the center line of the lane. Thus, the Frenet coordinate system (S, P) is established.

[0066] Using equation (38), establish the transformation matrix from Frenet coordinate system (S,P) to Cartesian coordinate system. ;

[0067] (38)

[0068] In equation (38), This indicates the lateral deviation of vehicle n from the center line in the lane;

[0069] Step 4.4: Denote the coordinates of the centroid M of vehicle n in the Frenet coordinate system (S,P) as (s,p), and use equation (44) to obtain the coordinates of vehicle n in the Frenet coordinate system at time step. coordinates below ;

[0070] (44)

[0071] In equation (44), This represents the coordinates of vehicle n in the Frenet coordinate system (S,P) at time t. Represents the Frenet coordinate system The velocity of vehicle number n along the S-axis at time t. Represents the Frenet coordinate system The velocity of vehicle number n along axis P at time t. Represents the Frenet coordinate system The acceleration of vehicle number n along axis P at time t;

[0072] Step 4.5: Use equation (45) to obtain the increments of vehicle n along the S-axis and P-axis in the Frenet coordinate system (S,P) at time t+1. and :

[0073] (45)

[0074] Step 4.6: Use equation (46) to obtain the position coordinates of vehicle n in the Cartesian coordinate system at time t+1. , and record as ;

[0075] (46)

[0076] Step 4.7: From (0,0,z) n Let (t+1) be the pole, and establish the polar angle φ in the polar coordinate system with the direction parallel to the X-axis of the Cartesian coordinate system as the polar axis. n (t+1) and the radius r n (t+1) constitutes the polar coordinates (φ) of vehicle n at time t+1. n (t+1),r n (t+1)).

[0077] The present invention provides an electronic device, including a memory and a processor, characterized in that the memory is used to store a program that supports the processor in executing a car-following path planning method for a curved road section, and the processor is configured to execute the program stored in the memory.

[0078] The present invention discloses a computer-readable storage medium on which a computer program is stored, characterized in that the computer program, when executed by a processor, performs the steps of the following path planning method for the curved and sloping road section.

[0079] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0080] 1. This invention employs an artificial potential field algorithm, combining road surface information from curved and sloping sections with the vehicle's geometric and dynamic parameters, to constrain the lateral movement of autonomous vehicles on roads. By adjusting the lateral movement strategy of the autonomous vehicle in the lane in real time, the vehicle can adapt to irregular road surfaces in complex environments such as curves and slopes, thus improving driving safety on curved and sloping sections. The invention establishes safe trajectory boundary conditions and boundary conditions to ensure driving within the lane, based on road surface information from curved and sloping sections and the vehicle's geometric and dynamic parameters, providing a theoretical basis for avoiding skidding and rollover accidents. The artificial potential field algorithm, established laterally, guides the vehicle to travel as close to the lane centerline as possible. The computational mechanism of the artificial potential field algorithm is relatively simple, generating constraints based on distance and repulsion calculations, effectively reducing computational burden while ensuring a sufficiently fast response speed. It is also more in line with human driving habits, avoiding dangerous driving behaviors such as following the vehicle ahead too far from the lane centerline. This method improves the following safety of the planned path.

[0081] 2. The vehicle state prediction model based on IDM of this invention fully considers road surface information and the geometric and dynamic parameters of the vehicle on curved and sloping road sections, enabling it to quickly and accurately predict the vehicle's motion state during travel on such sections. In addition to planning the behavior of following vehicles, the IDM-based vehicle state prediction model also has collision avoidance capabilities, reflecting the impact of changes in relative speed and distance between the following and following vehicles, thus avoiding the risk of collisions. Calibrating the parameters of the IDM-based vehicle state prediction model using real data makes the model more suitable for curved and sloping road conditions.

[0082] 3. The known constraints required by this invention are moderate and can effectively reflect the driving status of autonomous vehicles on curved and sloping road sections. The conditions are easy to collect, and the accuracy of real data can be guaranteed. The model updates the driving status of the vehicle in real time, which is timely and the planned path is more accurate with smaller errors. Taking advantage of the advantages of cubic Bézier curves, such as fast calculation speed and smooth path generation, the trajectory points obtained by real-time trajectory planning are processed to obtain a smooth path. Attached Figure Description

[0083] Figure 1 This is a flowchart illustrating the overall process of the method of the present invention.

[0084] Figure 2 This is a schematic diagram of a road section with a combination of curves and slopes;

[0085] Figure 3 This is a schematic diagram of path planning for curved and sloping road sections based on artificial potential field algorithm and vehicle state prediction model based on IDM.

[0086] Figure 4 A schematic diagram illustrating the mechanical analysis of a car on a curve;

[0087] Figure 5 A schematic diagram illustrating the mechanical analysis of a car on a slope;

[0088] Figure 6 A schematic diagram of real-time path planning in the Frenet coordinate system;

[0089] Figure 7 This is a simulation flowchart of the entire process. Detailed Implementation

[0090] The method of the present invention will now be described in detail with reference to the accompanying drawings.

[0091] In this embodiment, as Figure 1 As shown, a car-following motion planning method for curved and sloping road sections combines data collection from three aspects: geometric feature information of the curved and sloping road section, vehicle geometric and dynamic parameters, and vehicle car-following data of the curved and sloping road section. It uses an artificial potential field algorithm and a vehicle state prediction model based on IDM to constrain the vehicle's lateral motion on the road and its motion along the path direction, respectively, to calculate real-time trajectory planning points. Then, it uses cubic Bézier curves to process the real-time trajectory planning points to obtain a smooth and continuous path for car-following motion planning. The curved and sloping road section is a road section with slope, road surface superelevation, and curvature. It is assumed that the autonomous vehicle is vehicle number n, and the vehicle following is vehicle number n-1, both being ordinary passenger vehicles. The influence of extreme weather such as rain, snow, fog, and haze is not considered. Specifically, it includes the following steps:

[0092] Step 1: Based on the road surface slope of the curved section and super high The origin O is the center of curvature of the lane centerline. The X-axis is the direction from the origin O to the lane centerline and parallel to the ground. The Y-axis is the direction perpendicular to the X-axis and parallel to the ground. The Z-axis is determined by the right-hand rule. Thus, a Cartesian coordinate system O-XYZ is established. Geometric feature information of the curved road section, geometric and dynamic parameters of vehicle n, and vehicle following data of the curved road section at time t are collected under the Cartesian coordinate system O-XYZ.

[0093] Step 1.1: Collect information on the geometric characteristics of the curved and sloping road section;

[0094] A data acquisition vehicle equipped with a GPS, IMU, LiDAR, and camera was used to collect data on the curved and sloping road section. Each sensor simultaneously collected information about the surrounding environment. The data processing functions of multi-sensor fusion and Kalman filtering provided by the open-source autonomous driving platform Autoware.ai were used to extract the lane line position and road width D, the position coordinates of the lane centerline, the radius of curvature of the lane centerline, the road slope β, and the superelevation θ.

[0095] like Figure 2 As shown in the schematic diagram of the curved road section, any coordinate point (x, y, z) on the centerline of the lane is defined by the road centerline, which is the basic reference line for road surface geometry. Ultra-high Road width The radius of curvature at the centerline of the lane in polar coordinates The extreme angle at the center line of the lane The polar coordinate system is established with the coordinate point (0,0,z) on the center line of the lane as the pole and the direction parallel to the X-axis as the polar axis; where the road surface slope... Describes the longitudinal slope of the lane along its longitudinal direction, superelevation. Describes the lane's angle of inclination in a cross-section; defines the radius of curvature at the lane's centerline. The extreme angle at the center line of the lane This is for calculations in subsequent steps.

[0096] Step 1.2: Collect the geometric and dynamic parameters of vehicle number n, including: vehicle curb weight m, vehicle width d, track width b, front wheelbase L1, rear wheelbase L2, and center of gravity height h. g The data collection method is as follows:

[0097] Vehicle n is filled with all fluids but without passengers. Its curb weight m is obtained using a dedicated vehicle weighing device. The vehicle width d, track width b, and the sum of the front wheelbase L1 and rear wheelbase L2 are measured using a laser rangefinder. The front wheelbase L1 and rear wheelbase L2 are then obtained using a three-point weighing method. The center of gravity height h is measured using an tilting method. g The entire measurement process was completed at the vehicle inspection station.

[0098] Step 1.3: Collect vehicle following trajectory data on curved and sloping road sections;

[0099] Four identical data collection vehicles, as described in step 1.1, simultaneously collect data on a winding, sloping road section. GPS is used to record the data collection location information, and the vehicle's trajectory is obtained by analyzing the changes in location over time. IMU sensors help capture the vehicle's motion state on the winding, sloping road section, used to measure the vehicle's acceleration. The collected data often contains noise or errors, which are processed using the autonomous driving platform Autoware.ai. The processed data will yield the following information:

[0100] Extract the position information of vehicle number n-1 at time t. The speed of vehicle number n-1 at time t and acceleration The location information of vehicle number n at time t. The speed of vehicle number n at time t And obtain the polar coordinates of vehicle number n-1 at time t. The polar coordinates of vehicle number n at time t ,in, and Represented by coordinates Let X be the pole, and let X be the polar angle and polar radius of the (n-1)th vehicle in a polar coordinate system with the direction parallel to the X-axis as the polar axis. and Represented by coordinates The polar angle and polar radius of the nth vehicle in a polar coordinate system established with the pole as the pole and the direction parallel to the X-axis as the polar axis are input as the initial state in step 3.

[0101] Step 2: Based on the information, parameters, and data collected in Step 1, construct the artificial potential field force of vehicle n at time t. , used for trajectory planning of vehicle number n;

[0102] like Figure 3 As shown, by analyzing the forces acting on vehicle n at time t, the safe trajectory boundary conditions for a skidding and rollover accident on a curved and sloping road section are determined. ;Pick The coordinates of the position at the center line of the lane are (x0, y0, z0), and this will be used as the target point C. Combined with the artificial potential field algorithm, a safe trajectory boundary condition will be established. and ensure the outer boundary of the lane for driving. and ensure the inner boundary of driving within the lane As an obstacle point, the resultant force of the center of mass M of vehicle n is calculated using an artificial potential field algorithm. and use combined force (t) Perform motion planning to ensure the car travels along the lane centerline; the polar coordinates (φ) of vehicle n at time t are known. n (t),r n (t)), let (t)). The coordinates of the lane centerline are (x0, y0, z0), and the radius of curvature is... Polar angle is The road surface slope is 、Extremely high The road width is ;

[0103] Step 2.1: Calculate the outer boundary of the lane at time t for vehicle n using equation (1). and ensure the inner boundary of driving within the lane ;

[0104] Because of the high fatality rate in traffic accidents on curved and sloping road sections, to prevent vehicles from entering the oncoming lane and colliding head-on, or from colliding with the guardrails on both sides of the lane and causing traffic congestion and secondary accidents, it is necessary to calculate the boundary for ensuring that vehicle n stays within the lane; such as Figure 3 As shown, by obtaining information about the lane centerline and vehicle width, the outer boundary of the lane for ensuring that the nth autonomous vehicle travels within the lane at time t is calculated using equation (1). and ensure the inner boundary of driving within the lane :

[0105] (1)

[0106] In equation (1), for The radius of curvature at the centerline of the lane; for The width of the road surface at the center line of the lane; for The superelevation at the center line of the lane.

[0107] Step 2.2: Determine the boundary conditions for the safe trajectory of vehicle n at time t. ;

[0108] To prevent the nth vehicle from skidding or overturning, it is necessary to define the safety trajectory boundary conditions for autonomous vehicles in the event of skidding or overturning. Calculations are performed. The stress on a vehicle on a curved or sloping road section is complex; its load is affected not only by the road surface superelevation. This results in uneven distribution on the inner and outer sides, and is also affected by the road slope. The uneven distribution of loads between the front and rear axles is caused by the influence of the road surface. Therefore, the stress analysis of vehicle n on curves and slopes is performed separately first, followed by a comprehensive analysis of the curve-slope section. The steps are as follows:

[0109] Step 2.2.1: Analyze the superelevation of vehicle n at time t. Lateral force when driving on a curve ;

[0110] like Figure 4 As shown, at time t, when driving on a curve, the sum of all forces acting on vehicle n must provide a radius-dependent turning radius for vehicle n. The centrifugal force in the direction of the lateral force is calculated using equation (2). :

[0111] (2)

[0112] In formula (2) =m* , The acceleration due to gravity is taken as 9.8 m / s². 2 ;

[0113] Step 2.2.2: Analyze the road surface of vehicle n at time t. Front and rear loads ;

[0114] For longitudinal slope roads, stress analysis is performed, such as Figure 5 As shown, the front and rear loads are calculated using equations (3) and (4). :

[0115] (3)

[0116] (4)

[0117] Step 2.2.3: Analyze the superelevation of vehicle n at time t. Vertical load on curve , , , ;

[0118] Assuming the vehicle enters the curve at a constant speed, its longitudinal velocity along the road at this moment can be approximated as its speed, and the tire acceleration can be considered as the vehicle's lateral acceleration. Figure 5 As shown, after analyzing and simplifying the vertical load, we have:

[0119] (5)

[0120] (6)

[0121] In equations (5) and (6), a1 is the lateral acceleration of the vehicle tire, which can be obtained from the lateral force coefficient of the tire. Calculations show that , , , The left front wheel, right front wheel, left rear wheel, and right rear wheel of the vehicle are respectively above the road surface. Vertical load on a curve.

[0122] Step 2.2.4: Analyze the vertical load of vehicle n on the curved and sloping road section at time t. , , , ;

[0123] Based on step 2.2.3, neglecting the lateral acceleration of the vehicle tires and considering the road surface... The influence of the vertical load on vehicle n is calculated using equations (7)-(10), which yield the load on the left front wheel of vehicle n at time t on the curved and sloping road section. Right front wheel load Left rear wheel load Right rear wheel load :

[0124] (7)

[0125] (8)

[0126] (9)

[0127] (10)

[0128] Step 2.2.5: Analyze the critical condition for the front wheel of vehicle n to sideslip at time t. Critical conditions for rear wheel sideslip ;

[0129] The lateral forces on the front and rear axles of vehicle n on the curved and sloping road section were calculated using equations (11)-(12). , :

[0130] (11)

[0131] (12)

[0132] The boundary conditions for sideslip are similar to those on curves, i.e., the lateral force equals the adhesion force. Combining equations (7) to (12), we obtain equations (13) to (14). Using equations (13) and (14), we obtain the critical conditions for front wheel sideslip. The critical point at which the rear wheel sideslips :

[0133] (13)

[0134] (14)

[0135] Step 2.2.6: Analyze the critical conditions for vehicle n to overturn on the curved and sloping road section at time t. ;

[0136] When the lateral moment of the vehicle exceeds its stabilizing moment, the ground support force on the vehicle's wheels is zero, at which point the critical condition for rollover is reached. Taking the moment of this condition, we have:

[0137] (15)

[0138] Substituting equation (15) into equation (2), we can use equation (16) to calculate the critical condition for the nth vehicle to tilt. :

[0139] (16)

[0140] Combining equations (13)-(14) and (16), the boundary conditions for the safe trajectory are calculated using equation (17). :

[0141] (17)

[0142] Step 2.3: Calculate the net potential force of vehicle n at time t. .

[0143] Step 2.3.1: Calculate the artificial potential field of vehicle n at time t. ;

[0144] According to the artificial potential field algorithm, the magnitude of the gravitational force around the target point is mainly related to the distance between the center of mass M of vehicle n and the target point C on the lane centerline, thus yielding the gravitational potential energy. The function formula:

[0145] (18)

[0146] in, The gravitational constant, It is a vector whose magnitude represents the distance between the center of mass M of vehicle n and the target point C on the lane centerline, and the gravitational potential energy. The vector direction points from the center of mass M of vehicle n to the target point C; according to simulation experiments, the gravitational constant k a A value of 0.2 is most suitable, as it can simultaneously meet the requirements of efficiency and comfort.

[0147] Similarly, the factors determining the repulsive potential energy are also related to the center of mass M of vehicle n and the outer boundary of the drivable region R of vehicle n. The inner boundary of the drivable area R of vehicle n is and the boundary conditions for the safe trajectory of vehicle number n The distance between them is relevant; when the vehicle does not enter the influence range of the obstacle's repulsive potential field, that is, the threshold distance of the repulsive force. The vehicle is unaffected by the repulsive force of the potential field. The repulsive potential energy functions are obtained from equations (24) and (25). and :

[0148] (19)

[0149] (20)

[0150] (twenty one)

[0151] In equations (18)-(21), This represents the threshold distance at which the repulsive force is applied. Represents the repulsive force constant. It is a vector whose magnitude represents the outer boundary that ensures vehicle n travels within the lane at time t. The distance to the center of mass M of vehicle n, and the potential energy. The vector direction from Pointing to the centroid M of vehicle n; It is a vector whose magnitude represents the inner boundary of the lane at time t, ensuring that vehicle n is traveling within the lane. Boundary conditions for safe trajectory The distance from the maximum value between the two values ​​to the center of mass M of vehicle n, and the potential energy. The vector direction from (t) points to the centroid M of vehicle n; according to simulation experiments, the threshold distance for repulsive force is... The value is 1.75, the repulsion constant. A value of 0.05 is most suitable, as it can simultaneously meet the requirements of efficiency and comfort.

[0152] Step 2.3.2: Calculate the artificial potential field for vehicle n. The combined potential field force (t);

[0153] Using equation (22), we obtain the gravitational force between the target point C on the lane centerline and the center of mass M of the nth vehicle. Using equation (23), the repulsive force of the outer side of the lane on the center of mass M of vehicle n can be obtained. Using equation (24), the repulsive force of the inner side of the lane on the center of mass M of vehicle n can be obtained. Thus, the resultant force of the nth vehicle at the center of mass M can be obtained using equation (25). :

[0154] (twenty two)

[0155] (twenty three)

[0156] (twenty four)

[0157] (25)

[0158] In equations (22)-(25), It is a vector differential operator used to represent the gradient; such as Figure 3 As shown, under the influence of the net potential field force, the vehicle moves from high potential energy to low potential energy in the direction of the negative gradient of the net potential field.

[0159] Step 3: Based on the information, parameters and data collected in Step 1, construct a vehicle state prediction model at time t based on the Intelligent Driving Model (IDM) for trajectory planning of vehicle number n.

[0160] Step 3.1: Calculate the arc distance between vehicle n-1 and vehicle n on the lane centerline at time t on the curved road section. ;

[0161] Step 3.1.1: Take the polar angle of vehicle n. and the polar angle of vehicle number n-1 The position coordinates (x, y, z) of the center lines of the lanes are parameterized, and then the parameterized equation is constructed using equation (26).

[0162] (26)

[0163] like Figure 6 As shown in part (a), let the position coordinates (x, y, y) of vehicle number n-1 at time t be... n-1 (t),y n-1 (t),z n-1 Let F be point F, and let the position coordinates (x, t) of vehicle n at time t be... n (t),y n (t),z n (t) is point M, and the polar angle of vehicle n is taken. and the polar angle of vehicle number n-1 The coordinates (x, y, z) of the centerline points on the lanes are parameterized, i.e. Figure 6 The coordinates between point C and point F in part (a) are used to obtain the parametric equation (26), where, Representation of parameterized equations The parameters, These represent the projected coordinates of the lane centerline onto the horizontal plane along the X and Y axes in a Cartesian coordinate system, respectively. This represents the projected coordinates of the lane centerline along the Z-axis in a Cartesian coordinate system.

[0164] Step 3.1.2: Use equation (27) to obtain the small arc length on the center line of the lane. :

[0165] (27)

[0166] In equation (27), , , These represent the rates of change of the coordinate point (x, y, z) along the X-axis, Y-axis, and Z-axis in the Cartesian coordinate system, respectively. Representing parameterized equations exist The tangent vector at the point;

[0167] Step 3.1.3: Use equation (28) to calculate the arc distance at time t between the positions of vehicle number n-1 and vehicle number n at time t on the curved road section. :

[0168] (28)

[0169] In equation (28), express The parameters at that location, express The parameters at that location.

[0170] Step 3.2: Calculate the maximum speed of vehicle n at time t without deviating from the path using equation (33). ;

[0171] Let the coefficient of friction between the wheel and the road surface be... In this method, the value is taken as 0.7, and the critical speed at which the nth vehicle will sideslip is established by equation (29). The critical speed for the rollover of vehicle n is established by equation (30). :

[0172] (29)

[0173] (30)

[0174] The critical speed at which the nth vehicle will skid is calculated using equations (31) and (32). The critical speed at which vehicle n overturns. And obtain the maximum speed of vehicle n without deviating from the path at time t. :

[0175] (31)

[0176] (32)

[0177] (33)

[0178] Step 3.3: Construct an IDM-based vehicle state prediction model using equation (34):

[0179] (34)

[0180] In equation (34), This represents the acceleration of vehicle number n at time t. This represents the expected maximum acceleration of vehicle number n. This represents the expected speed of vehicle number n. Indicates the acceleration index, The correction factor represents the curvature of the curve. Represents a symbolic function. Let represent the minimum radius at which vehicle n maintains safe driving at time t. This represents the correction factor for the ramp. This represents the minimum safe distance between vehicle n and vehicle n-1 to avoid a collision. This represents the safe headway between vehicle n and vehicle n-1 at time t. (t) represents the speed difference between vehicle n and vehicle (n-1) at time t. This represents the comfortable deceleration of vehicle number n. This represents the relative speed between vehicle n and vehicle (n-1) at time t. (t) is the desired distance to maintain, and we have:

[0181] (35)

[0182] As shown in equation (34), the model takes into account the effects of curves and longitudinal slope of the road. The maximum speed at which vehicle n does not deviate from the path at time t. The purpose of this consideration is to ensure that vehicle number n can travel on the planned route.

[0183] Step 3.4: Use vehicle following trajectory data on curved and sloping road sections to calibrate the parameters of the improved IDM following model; thereby determining the parameters in the improved IDM following model, including: the desired maximum acceleration. Vehicle desired speed Minimum safe distance to avoid collision Comfort deceleration .

[0184] Step 4: Force based on the artificial potential field at time t The vehicle state prediction model at time t (t) calculates the real-time path planning coordinates (x, y) of vehicle n on the curved and sloping road section at time t+1. n (t+1),y n (t+1),z n (t+1));

[0185] Step 4.1: Calculate the acceleration of vehicle n at time t using equation (34). ;

[0186] Step 4.2: Use equation (36) to obtain the speed of vehicle n at time t+1. ;

[0187] (36)

[0188] In equation (36), Let t be a time step from time t to time t+1. Considering that the sensor acquisition frequency of most autonomous vehicles at this stage is above 10Hz, The value is set to 0.1 seconds, which meets market demand, and the update frequency is fast and the control is timely.

[0189] Step 4.3: Take The coordinates of the center line of the lane are (x0, y0, z0). The coordinates of (x0, y0, z0) on the center line of the lane are taken as the origin of the Frenet coordinate system. The direction along the center line of the lane, i.e., the longitudinal direction of the road, is taken as the S-axis, and the direction perpendicular to the center line of the lane, i.e., the lateral direction of the road, is taken as the P-axis, thus establishing the Frenet coordinate system (S, P).

[0190] Given the polar coordinates (φ) of vehicle number n at time t. n (t),r n (t)), let (t)). The position coordinates of the lane centerline are (x0, y0, z0), and the radius of curvature is... for Polar angle for Road surface slope for Ultra-high for Road width for The Frenet-Serret framework is a local coordinate system in curve geometry that describes the motion of curves in three-dimensional space. Referring to the Frenet-Serret framework, and using the lane centerline as a reference, a local Frenet coordinate system (S, P) suitable for lane geometry is constructed: [Example...] Figure 6As shown in part (b), the origin of the coordinate system is the point (x0, y0, z0) on the lane centerline. The direction along the lane centerline is defined as the S-axis, representing the longitudinal direction of the lane, and the direction perpendicular to the lane centerline is defined as the P-axis, representing the lateral direction of the lane. This represents the lateral offset of a vehicle from the lane centerline. The centroid M of the nth vehicle is represented by the coordinates (s, p). The Frenet coordinates (S, P) are now converted to Cartesian coordinates (X, Y, Z). The core of this conversion lies in utilizing the position and local direction of the lane centerline. In the Frenet coordinate system, lateral offset can be represented by the normal vector. To define:

[0191] The normal vector is obtained using equation (37). :

[0192] (37)

[0193] Use equation (38) to convert Frenet coordinates (S, P) to Cartesian coordinates (X, Y, Z):

[0194] (38)

[0195] Step 4.4: Denote the coordinates of the centroid M of vehicle n in the Frenet coordinate system (S,P) as (s,p), and use equation (44) to obtain the coordinates of vehicle n in the Frenet coordinate system at time step. coordinates below .

[0196] Given that the coordinates of vehicle number n at time t are (x... n (t),y n (t),z n (t),φ n (t),r n (t)), using step 2.4.1 to establish Frenet coordinates (s,p) and convert them to Cartesian coordinates (t). The transformation relationship can be used to obtain the Frenet coordinates (s(t), p(t)) at time t; combined with the illustration Figure 3 It can be seen that the resultant force obtained in step 2 (t) represents the magnitude of the lateral force exerted by vehicle n on the lane. Using Newton's second law and equation (39), the acceleration a of vehicle n along the P-axis, i.e., the lateral motion, is calculated. p (t):

[0197] (39)

[0198] The lateral velocity at time t+1 is calculated using equation (40). Assuming At t=0, the value is 0:

[0199] (40)

[0200] Because the speed v of vehicle n at time t+1 is... n ( () represents the velocity along the path direction, v n ( This can be calculated in step 3, assuming The velocity along the S-axis at any given time, i.e., the velocity of longitudinal motion, is Assuming At t=0, the value is v n (0), calculated from equation (41) :

[0201] (41)

[0202] The lateral movement at time t+1 can be calculated from equations (42) and (43). and longitudinal movement :

[0203] (42)

[0204] (43)

[0205] Using equation (44), we can obtain the time of vehicle n. During the process along the coordinates in the Frenet coordinate system :

[0206] (44)

[0207] Step 4.5: Use equation (45) to obtain the increments of vehicle n along the Frenet coordinate S-axis and P-axis at time t+1. and :

[0208] (45)

[0209] Step 4.6: Use equation (46) to obtain the position coordinates of vehicle n in the Cartesian coordinate system at time t+1. ;

[0210] Since the Frenet coordinates (s(t), p(t)) from time t to time t+ Frenet coordinates at time ( (This refers to a very small time step) The process is completed within a small timeframe, and the changes in curvature and polar angle are very small. Therefore, a local approximation method can be used to process it. The position coordinates (x, y, y) at time t+1 can be calculated using equation (46). n (t+1),y n (t+1),z n (t+1)):

[0211] (46)

[0212] Step 4.7: From (0,0,z) n Let (t+1) be the pole, and establish the polar angle in the polar coordinate system with the direction parallel to the X-axis of the Cartesian coordinate system as the polar axis. and polar radius The polar coordinates of vehicle n at time t+1 .

[0213] Step 5: Calculate the Bézier curve using equation (47). Thus, a smooth planning path E(x,y,z) in the Cartesian coordinate system is obtained using cubic Bézier curves.

[0214] The location coordinates of the real-time path planning points obtained in step 4 are denoted as follows: The position coordinates of the real-time path planning point at time t-2 are obtained. The location coordinates of the real-time path planning point at time t-1. The position coordinates of the real-time path planning point at time t. The location coordinates of the real-time path planning point at time t+1. Initially, after 2 After obtaining the four real-time path planning coordinates, proceed to step 5; use equation (47) to obtain the calculation formula for the Bézier curve:

[0215] (47)

[0216] In equation (47), It is a parameter with a value range of [0,1], used to ensure that the planned path is smooth enough. Each increment is 0.01, gradually increasing from 0 to 1, thus obtaining a smooth planning path E(x,y,z).

[0217] Step 6: After assigning t+1 to t, return to Step 2 and execute sequentially to plan the driving path of the nth vehicle in real time; when the vehicle's center of mass M moves to the target point C, the gravitational force is 0, meaning the vehicle is not affected by the potential field force in the lateral direction of the road, and the planned path is as follows. Figure 3As shown by the solid red line in the middle; the simulation process for the entire procedure is as follows: Figure 7 As shown.

[0218] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0219] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

Claims

1. A method for planning vehicle following motion on a curved and sloping road section, characterized in that, The curved and sloping road section is a road section that simultaneously has gradient, road surface superelevation, and curvature. Assuming that the autonomous driving vehicle is vehicle number n and the vehicle following is vehicle number n-1, the following car-following path planning method includes the following steps: Step 1: Based on the road surface slope of the aforementioned curved section and super high The origin O is the center of curvature of the lane centerline. The X-axis is the direction from the origin O to the lane centerline and parallel to the ground. The Y-axis is the direction perpendicular to the X-axis and parallel to the ground. The Z-axis is determined by the right-hand rule, thus establishing a Cartesian coordinate system. In the Cartesian coordinate system The following data are collected: geometric feature information of the curved and sloping road section, geometric and dynamic parameters of vehicle n, and vehicle following data of the curved and sloping road section at time t. Step 2: Based on the information, parameters, and data collected in Step 1, construct the artificial potential field force of vehicle n at time t. , used for trajectory planning of vehicle number n; Step 3: Based on the information, parameters and data collected in Step 1, construct a vehicle state prediction model at time t based on the Intelligent Driving Model (IDM) for trajectory planning of vehicle number n. Step 4: Force based on the artificial potential field at time t Using the vehicle state prediction model at time t, calculate the real-time path planning coordinates of vehicle n on the curved and sloping road section at time t+1. point; Step 5: Calculate the Bézier curve using equation (47). Thus, a smooth planning path in Cartesian coordinates can be obtained using cubic Bézier curves. ; (47) In equation (47), It is a parameter, and its value range is... The location coordinates of the real-time path planning points obtained in step 4 are denoted as follows: , This indicates that vehicle number n is in the nth position. The real-time path planning coordinates of the points at each moment. This indicates that vehicle number n is in the nth position. The location coordinates of the real-time path planning points at each moment. This represents the position coordinates of the real-time path planning point of vehicle number n at time t. This indicates that vehicle number n is in the nth position. The position coordinates of the real-time path planning points at any given moment; Step 6: [The sentence is incomplete and requires more context to be translated accurately.] After assigning the value to t, return to step 2 and execute sequentially to plan the driving path of vehicle n in real time.

2. The vehicle following motion planning method for curved and sloping road sections according to claim 1, characterized in that, Step 1 includes: Step 1.1: Collect information on the geometric characteristics of the curved and sloping road section; A data acquisition vehicle equipped with a GPS, IMU, LiDAR, and camera was used to collect and process data on the curved road section, obtaining geometric feature information of the curved road section, including: coordinates of any point on the lane centerline. Any coordinate point on the center line of the lane Road surface slope Ultra-high Road width The radius of curvature at the centerline of the lane in polar coordinates The extreme angle at the center line of the lane The polar coordinate system is based on the coordinate points on the lane centerline. The pole is defined, and the polar axis is established with the direction parallel to the X-axis as the polar axis; Step 1.2: Collect the geometric and dynamic parameters of vehicle number n, including: vehicle curb weight m, vehicle width d, track width b, front wheelbase L1, rear wheelbase L2, and center of gravity height h. g ; Step 1.3: Collect vehicle following trajectory data under the curved and sloping road section; Extract the position information of vehicle number n-1 at time t. The speed of vehicle number n-1 at time t and acceleration The location information of vehicle number n at time t. The speed of vehicle number n at time t And obtain the polar coordinates of vehicle number n-1 at time t. The polar coordinates of vehicle number n at time t ,in, and Represented by coordinates Let X be the pole, and let X be the polar angle and polar radius of the (n-1)th vehicle in a polar coordinate system with the direction parallel to the X-axis as the polar axis. and Represented by coordinates The polar angle and polar radius of the nth vehicle in a polar coordinate system established with the pole as the pole and the direction parallel to the X-axis as the polar axis.

3. The vehicle following motion planning method for curved and sloping road sections according to claim 2, characterized in that, Step 2 includes: Step 2.1: Calculate the outer boundary of the lane at time t for vehicle n using equation (1). and the inner boundary that ensures driving within the lane ; (1) In equation (1), for The radius of curvature at the centerline of the lane; for The width of the road surface at the center line of the lane; for Superelevation at the center line of the lane; Step 2.2: Determine the boundary conditions for the safe trajectory of vehicle n at time t. ; Force analysis was performed on vehicle n, and the critical conditions for front wheel sideslip at time t were obtained using equations (13) and (14). Critical conditions for rear wheel sideslip Using equation (16), we obtain the critical condition for the nth vehicle to tilt at time t. Thus, the boundary conditions of the entire trajectory of vehicle n at time t can be obtained using equation (17). ; (13) (14) (16) (17) In equations (13)-(17), Represents gravitational acceleration, Indicates the lateral force coefficient; for The road surface slope at the center line of the lane; Step 2.3: Calculate the net potential force of vehicle n at time t. ; Using equation (22), we can obtain the gravitational force exerted by the target point C on the lane centerline on the center of mass M of the nth vehicle at time t. Using equation (23), the repulsive force exerted by the outer side of the lane on the center of mass M of vehicle n at time t can be obtained. Using equation (24), the repulsive force of the inner side of the lane on the center of mass M of vehicle n at time t can be obtained. Thus, the resultant force of the nth vehicle at the center of mass M at time t can be obtained using equation (25). : (22) (23) (24) (25) In equations (22)-(25), It is a vector differential operator used to represent the gradient. The gravitational constant, It is the distance between the centroid M of vehicle n at time t and the target point C on the lane centerline. The vector direction points from the centroid M of vehicle n at time t to the target point C; This represents the threshold distance at which the repulsive force is applied. Represents the repulsive force constant. express The distance from the center of mass M of vehicle n at time t. The vector direction from Pointing to the centroid M of vehicle n at time t; express and The distance from the maximum value between the two values ​​to the centroid M of vehicle n at time t. The vector direction from Point to the centroid M of vehicle n at time t.

4. The vehicle following motion planning method for a curved and sloping road section according to claim 3, characterized in that, Step 3 includes: Step 3.1: Calculate the arc distance between the (n-1)th vehicle and the nth vehicle on the lane centerline at time t on the curved road section. ; Step 3.2: Calculate the maximum speed of vehicle n at time t without deviating from the path using equation (33). ; (33) In equation (33), This represents the coefficient of friction between the wheel and the road surface; Step 3.3: Construct a vehicle state prediction model at time t based on IDM using equation (34): (34) In equation (34), This represents the acceleration of vehicle number n at time t. This represents the expected maximum acceleration of vehicle number n. This represents the expected speed of vehicle number n. Indicates the acceleration index, This represents the minimum safe distance between vehicle n and vehicle n-1 to avoid a collision. This represents the safe headway between vehicle n and vehicle n-1. This represents the difference in speed between vehicle n and vehicle (n-1) at time t. This represents the comfortable deceleration of vehicle number n. This represents the relative speed between vehicle n and vehicle (n-1) at time t. The desired distance to maintain, and: (35) Step 3.4: Use the vehicle following trajectory data under the curved and sloping road section to calibrate the parameters of the improved IDM following model, thereby determining the parameters in the improved IDM following model, including: the expected maximum acceleration. Vehicle desired speed Minimum safe distance to avoid collision Comfort deceleration .

5. The vehicle following motion planning method for a curved and sloping road section according to claim 4, characterized in that, Step 3.1 includes: Step 3.1.1: Set the polar angle of vehicle n. and the vehicle polar angle Coordinates of the center line between lanes Coordinate parameterization is performed, and then the parameterized equation of the lane centerline is constructed using equation (26). ; (26) In equation (26), Representing parameterized equations The parameters, These represent the projected coordinates of the lane centerline along the X and Y axes in a Cartesian coordinate system, respectively. This represents the projected coordinates of the lane centerline along the Z-axis in a Cartesian coordinate system. Step 3.1.2: Use equation (27) to obtain the small arc length on the center line of the lane. : (27) In equation (27), , , These represent the rates of change of the coordinate point (x, y, z) along the X-axis, Y-axis, and Z-axis in the Cartesian coordinate system, respectively. Representing parameterized equations exist The tangent vector at the point; Step 3.1.3: Calculate the first time step of the curved road section at time t using equation (28). The arc distance between vehicle number n and vehicle number n : (28) In equation (28), express The parameters at that location, express The parameters at that location.

6. The vehicle following motion planning method for a curved and sloping road section according to claim 5, characterized in that, Step 4 includes: Step 4.1: Calculate the acceleration of vehicle n at time t using equation (34). ; Step 4.2: Use equation (36) to obtain the speed of vehicle n at time t+1. ; (36) In equation (36), This is a time step from time t to time t+1; Step 4.3: Take The coordinates of the center line of the lane are Coordinates of the center line of the lane Let S be the origin of the Frenet coordinate system. Let S be the longitudinal direction of the road along the center line of the lane and P be the transverse direction of the road perpendicular to the center line of the lane. Thus, the Frenet coordinate system (S, P) is established. Using equation (38), establish the transformation matrix from Frenet coordinate system (S,P) to Cartesian coordinate system. ; (38) In equation (38), This indicates the lateral deviation of vehicle n from the center line in the lane; Step 4.4: Denote the coordinates of the centroid M of vehicle n in the Frenet coordinate system (S,P) as (s,p), and use equation (44) to obtain the coordinates of vehicle n in the Frenet coordinate system at time step. coordinates below ; (44) In equation (44), This represents the coordinates of vehicle n in the Frenet coordinate system (S,P) at time t. Represents the Frenet coordinate system The velocity of vehicle number n along the S-axis at time t. Represents the Frenet coordinate system The velocity of vehicle number n along axis P at time t. Represents the Frenet coordinate system The acceleration of vehicle number n along axis P at time t; Step 4.5: Use equation (45) to obtain the increments of vehicle n along the S-axis and P-axis in the Frenet coordinate system (S,P) at time t+1. and : (45) Step 4.6: Use equation (46) to obtain the position coordinates of vehicle n in the Cartesian coordinate system at time t+1. , and record as ; (46) Step 4.7: By Let the pole be the point in the polar coordinate system, and let the polar angle φ be the direction parallel to the X-axis of the Cartesian coordinate system. n (t+1) and the radius r n (t+1) constitutes the polar coordinates of vehicle n at time t+1. .

7. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing the following path planning method for any of the curved road sections described in claims 1-6, and the processor is configured to execute the program stored in the memory.

8. A computer-readable storage medium on which a computer program is stored, characterized in that, When the computer program is run by the processor, it performs the steps of the following path planning method for any of the curved and sloping road sections described in claims 1-6.

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