Vehicle following motion planning method for slope road section

Abstract

The invention discloses a vehicle following motion planning method for a curved slope road section. The method comprises the steps of 1, collecting geometric characteristic factor information of the curved slope road section, geometric and kinetic parameters of an automobile and following data of a front automobile; 2, calculating an artificial potential field resultant force of the vehicle in the transverse direction of the road based on an artificial potential field algorithm; 3, constructing an IDM-based improved vehicle state prediction model, and considering the influence of the maximum speed of a non-deviating path on a curved slope road section; 4, acquiring a real-time path planning coordinate point at the next moment; and 5, obtaining a smooth planned path by using a cubic Bezier curve. According to the invention, the vehicle following safety and driving comfort of the vehicle at the slope can be improved, and the possibility of dangerous traffic accidents such as collision, sideslip and rollover is avoided, so that the accident rate and delay rate of the road are reduced, and the traffic capacity of the slope road section is improved.

Description

Technical Field

[0001] The present invention belongs to the field of automatic driving and intelligent transportation, and specifically refers to a method based on an artificial potential field algorithm and an intelligent driving model (IDM) that comprehensively considers road surface information of a curved and sloping road section, as well as geometric and dynamic parameters of a vehicle during the process of following motion planning of a vehicle on a curved and sloping road section. Specifically, it refers to a method for following motion planning of a vehicle on a curved and sloping road section. Background Art

[0002] Curved and sloping sections are an important part of the road. Due to their complex traffic environment and poor driver vision, they are prone to traffic accidents such as rollovers, skidding, and rear-end collisions. Studies have shown that accidents with high mortality rates, such as collisions, scratches, rollovers, and falls, often occur on curved and sloping sections. In order to reduce safety accidents on curved and sloping sections and accelerate the implementation of autonomous driving technology on complex sections, it is of practical significance to design a motion planning method for autonomous driving vehicles to avoid collisions, skidding, and rollovers on curved and sloping sections.

[0003] Scholars have conducted numerous studies on car-following models, and have been continuously improving traffic flow theoretical models and conducting in-depth research. Many types of car-following models have emerged, including stimulus-response models, safety distance models, meta-automaton models, and intelligent driving models. The above models have simplified the influencing factors in the car-following process to varying degrees, and have insufficient consideration of road conditions and the geometric and dynamic parameters of the car, making it difficult to be effectively applied on complex roads.

[0004] Most of the existing research models are based on straight road research. A small number of following models improve the following model on straight sections by considering road linearity, curve curvature, curve friction coefficient, etc. to form an extended curve following model. Curved and sloping sections are rarely involved, but there are a large number of curved and sloping sections on actual roads, especially in the mountainous areas of western my country. Therefore, solving the path planning problem on curved and sloping sections will promote the application of autonomous driving technology on complex sections and accelerate the implementation of autonomous driving technology on complex sections. Curved and sloping sections are more complex than straight road environments, and require continuous detection of changes in the surrounding environment to obtain real-time information, and continuous updating of planned paths to cope with environmental changes. Therefore, real-time following motion planning must be carried out to ensure that autonomous driving vehicles can always stay on a safe path. Summary of the invention

[0005] The present invention aims to solve the deficiencies of the above-mentioned prior art and proposes a vehicle following motion planning method for a curved and sloping road section, so as to plan a continuous and stable vehicle following path on the curved and sloping road section, thereby improving the safety and driving comfort of the vehicle following on the curved and sloping road section, avoiding the possibility of dangerous traffic accidents such as collision, skidding, and rollover, reducing the accident rate and delay rate of the road, and improving the traffic capacity of the curved and sloping road section.

[0006] In order to achieve the above-mentioned purpose, the present invention adopts the following technical scheme:

[0007] The vehicle following motion planning method for a curved and sloping road section of the present invention is characterized in that the curved and sloping road section is a road section having a slope, a superelevation of a road surface, and a curvature at the same time, and assuming that the autonomous driving vehicle is the nth vehicle and the preceding vehicle following is the n-1th vehicle, the following path planning method comprises the following steps:

[0008] Step 1: Take the road slope of the curved road section as the reference and superelevation The center of curvature of the lane centerline at is the origin O, the direction from the origin O to the lane centerline and parallel to the earth is the X-axis, the direction perpendicular to the X-axis and parallel to the earth is the Y-axis, and the Z-axis is determined by the right-hand method, thus establishing a Cartesian coordinate system. , in the Cartesian coordinate system Collecting geometric characteristic factor information of the curved and sloping road section, geometric and dynamic parameters of the nth vehicle, 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 to plan the trajectory of the nth vehicle;

[0010] Step 3: Based on the information, parameters and data collected in step 1, a vehicle state prediction model at time t based on the intelligent driving model IDM is constructed to plan the trajectory of the nth vehicle;

[0011] Step 4: Artificial potential field based on time t and the vehicle state prediction model at time t, calculate the position coordinates of the real-time path planning coordinates of the nth vehicle on the curved slope section at time t+1 ;

[0012] Step 5: Use formula (47) to calculate the Bezier curve , so as to use the cubic Bezier curve to obtain a smooth planning path E(x, y, z) in the Cartesian coordinate system;

[0013] (47)

[0014] In formula (47), Is a parameter with a value range of ; The position coordinates of the real-time path planning coordinate points obtained in step 4 are recorded as , Indicates that the nth vehicle is in The position coordinates of the real-time path planning coordinate points at the moment, Indicates that the nth vehicle is in The position coordinates of the real-time path planning coordinate points at the moment, represents the position coordinates of the real-time path planning coordinate point of the nth vehicle at the tth time, Indicates that the nth vehicle is in The position coordinates of the real-time path planning coordinate points at the moment;

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

[0016] The vehicle following motion planning method for a curved and sloping road section described in the present invention is also characterized in that step 1 comprises:

[0017] Step 1.1: Collect geometric characteristic factor information of curved and sloping road sections;

[0018] A data collection vehicle equipped with a global positioning system (GPS), an inertial measurement unit (IMU), a laser radar and a camera is used to collect and process data on the curved and sloping road section to obtain geometric characteristic factor information of the curved and sloping road section, including: any coordinate point on the center line of the lane , any coordinate point on the lane centerline The road slope , Ultra High , Road width , the radius of curvature at the center line of the lane in the polar coordinate system and the polar angle at the lane centerline ; The polar coordinate system is based on the coordinate points on the lane centerline is the pole, and the direction parallel to the X-axis is established as the polar axis;

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

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

[0021] Extract the position information of vehicle No. n-1 at time t , the speed of vehicle n-1 at time t and acceleration , the position information of vehicle No. n at time t , the speed of vehicle No. n at time t ; and get the polar coordinates of vehicle No. n-1 at time t and the polar coordinates of vehicle No. n at time t ,in, and Respectively expressed in coordinates The polar angle and polar diameter of the n-1th vehicle in the polar coordinate system established with the direction parallel to the X-axis as the polar axis, and Respectively expressed in coordinates The polar angle and polar diameter of the nth vehicle in the polar coordinate system established with φ as the pole and the direction parallel to the X-axis as the polar axis.

[0022] Furthermore, the step 2 comprises:

[0023] Step 2.1: Use equation (1) to calculate the outer boundary of the lane that the nth vehicle must travel within at time t: and the inner boundary to ensure driving within the lane ;

[0024] (1)

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

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

[0027] The force analysis of vehicle No. n is performed, and the critical conditions for the front wheel to slip at time t are obtained using equations (13) and (14). Critical conditions for side slip with rear wheels , using formula (16) to obtain the critical condition for the rollover of the nth vehicle at time t , and thus use formula (17) to obtain the boundary conditions of the entire trajectory of vehicle n at time t ;

[0028] (13)

[0029] (14)

[0030] (16)

[0031] (17)

[0032] In formula (13) to formula (17), represents the acceleration due to gravity, represents the lateral force coefficient; for The road surface slope at the lane centerline at ;

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

[0034] Using formula (22), we can get the gravitational force of the target point C of the lane centerline on the center of mass M of the nth vehicle at time t: , using formula (23) to obtain the repulsive force of the outer side of the lane on the mass center M of the nth vehicle at time t , using formula (24) to obtain the repulsive force of the inner side of the lane on the mass center M of the nth vehicle at time t , and then use formula (25) to get the resultant force of vehicle n at the center of mass M at time t :

[0035] (twenty two)

[0036] (twenty three)

[0037] (twenty four)

[0038] (25)

[0039] In formula (22) to formula (25), is a vector differential operator used to represent the gradient, is the gravitational constant, is the distance between the center of mass M of the nth vehicle at time t and the target point C on the center line of the lane, The vector direction is from the center of mass point M of the nth vehicle at time t to the target point C; represents the threshold distance of repulsion, represents the repulsion constant, express The distance to the center of mass M of vehicle No. n at time t, The vector direction from Points to the center of mass point M of vehicle No. n at time t; express and The maximum value between the two is the distance to the center of mass M of the nth vehicle at time t, The vector direction from Points to the center of mass M of vehicle No. n at time t

[0040] Furthermore, the step 3 comprises:

[0041] Step 3.1: Calculate the arc distance on the lane centerline between the vehicle No. n-1 and the vehicle No. n at time t on the curved slope section ;

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

[0043] (33)

[0044] In formula (33), Indicates the friction coefficient between the wheel and the road;

[0045] Step 3.3: Use formula (34) to build the vehicle state prediction model at time t based on IDM:

[0046] (34)

[0047] In formula (34), represents the acceleration of vehicle No. n at time t, represents the maximum acceleration expected by vehicle No. n, represents the expected speed of vehicle No. n, represents the acceleration index, It represents the minimum safe distance between the nth vehicle and the n-1th vehicle to avoid collision. It represents the safe headway between vehicle No. n and vehicle No. n-1. represents the speed difference between vehicle No. n and vehicle No. n-1 at time t, represents the comfortable deceleration of vehicle No. n; represents the relative speed between vehicle No. n and vehicle No. n-1 at time t The desired distance to be maintained, with:

[0048] (35)

[0049] Step 3.4: calibrate the parameters of the improved IDM following model using the vehicle following trajectory data on the curved slope section, thereby determining the parameters of the improved IDM following model, including: expected maximum acceleration , Expected vehicle speed , minimum safe distance to avoid collision , comfortable deceleration .

[0050] Furthermore, the step 3.1 includes:

[0051] Step 3.1.1: Polar angle of vehicle No. n and Vehicle polar angle The coordinate points on the center line of the lane Coordinate parameterization is performed to construct the parameterized equation of the lane centerline using equation (26): ;

[0052] (26)

[0053] In formula (26), Representing parameterized equations Parameters, They represent the projection coordinates of the lane centerline along the X-axis and Y-axis in the Cartesian coordinate system, respectively. Indicates the projection coordinate of the lane centerline along the Z axis in the Cartesian coordinate system;

[0054] Step 3.1.2: Use equation (27) to get the small arc length on the lane centerline :

[0055] (27)

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

[0057] Step 3.1.3: Use equation (28) to calculate the arc distance between the vehicle No. n-1 and the vehicle No. n at time t on the curved slope section: :

[0058] (28)

[0059] In formula (28), express The parameters at express Parameters at .

[0060] Further, the step 4 comprises:

[0061] Step 4.1: Use equation (34) to calculate the acceleration of vehicle n at time t: ;

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

[0063] (36)

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

[0065] Step 4.3: Get The coordinate point at the center line of the lane is , with the coordinate point on the lane centerline The origin of the Frenet coordinate system is taken as the S axis, the direction along the lane centerline, i.e. the longitudinal direction of the road, is taken as the S axis, and the direction perpendicular to the lane centerline, i.e. the transverse direction of the road, is taken as the P axis, thereby establishing the Frenet coordinate system (S, P);

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

[0067] (38)

[0068] In formula (38), Indicates the lateral deviation of vehicle No. n from the center line in the lane;

[0069] Step 4.4: Let the coordinates of the center of mass M of the nth vehicle in the Frenet coordinate system (S, P) be (s, p), and use equation (44) to obtain the coordinates of the nth vehicle in the Frenet coordinate system at the time step The coordinates below ;

[0070] (44)

[0071] In formula (44), represents the coordinates of the nth vehicle at time t in the Frenet coordinate system (S, P), Represents the Frenet coordinate system The speed of vehicle No. n along the S axis at time t is, Represents the Frenet coordinate system The speed of vehicle No. n along the P axis at time t is, Represents the Frenet coordinate system The acceleration of vehicle No. n along the P axis at time t;

[0072] Step 4.5: Use equation (45) to obtain the increments of the nth vehicle 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 No. n at time t+1 in the Cartesian coordinate system: , and recorded as ;

[0075] (46)

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

[0077] The present invention provides an electronic device, comprising a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the method for following the car on a curved and sloping road section, and the processor is configured to execute the program stored in the memory.

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

[0079] Compared with the prior art, the present invention has the following beneficial effects:

[0080] 1. The present invention uses an artificial potential field algorithm established by combining the road surface information of the curved and sloping road section, the geometric and dynamic parameters of the car to constrain the lateral movement of the autonomous driving vehicle on the road. By adjusting the lateral movement strategy of the autonomous driving vehicle in the lane in real time, the vehicle can adapt to the irregular road surface in complex environments such as curves and ramps, and the driving safety on the curved and sloping road section is improved. The boundary conditions of the safe trajectory and the boundary conditions for ensuring driving in the lane are established in combination with the road surface information of the curved and sloping road section, the geometric and dynamic parameters of the car, to provide a theoretical basis for avoiding the occurrence of side slip and rollover accidents. An artificial potential field algorithm is established in the transverse direction of the road to make the car drive along the center line of the lane as much as possible. The calculation mechanism of the artificial potential field algorithm is relatively simple, and the constraints are generated based on the calculation of distance and repulsion, which can effectively reduce the calculation burden and ensure a sufficiently fast response speed. It is more in line with the driving habits of humans, and at the same time avoids the dangerous driving behavior of following the path of the leading vehicle deviating far from the center line of the lane. This method can improve the safety of following the planned path.

[0081] 2. The improved vehicle state prediction model based on IDM of the present invention fully considers the road surface information of the curved and sloping road section, the geometric and dynamic parameters of the car, and can quickly and accurately predict the movement state of the vehicle during driving on the curved and sloping road section. The improved vehicle state prediction model based on IDM not only performs behavior planning for the following vehicle, but also has a collision avoidance function, which can reflect the impact of the relative speed and relative distance changes between the front and rear vehicles on the following vehicle, and can avoid the risk of collision between the front and rear vehicles during the following process. Using real data to calibrate the parameters of the vehicle state prediction model based on IDM can make the model more suitable for the conditions of curved and sloping roads.

[0082] 3. The known constraints required by the present invention are moderate and can effectively reflect the driving state of the autonomous driving vehicle on curved and sloping sections. The conditions are easy to collect and the accuracy of the real data can be guaranteed. The model dynamically updates the driving state of the vehicle in real time, and the timeliness is strong. The planned path is more accurate and the error is smaller. With the advantages of fast calculation speed and smooth path generation of cubic Bezier curves, the trajectory points obtained by real-time trajectory planning are processed to obtain a smooth path. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 It is the overall flow chart of the method of the present invention;

[0084] Figure 2 This is a schematic diagram of a curved and sloped road section;

[0085] Figure 3 The schematic diagram of path planning for curved and sloping sections based on the artificial potential field algorithm and the vehicle state prediction model improved by IDM;

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

[0087] Figure 5 This is a schematic diagram of the mechanical analysis of a car on a ramp;

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

[0089] Figure 7 The simulation flow chart of the whole process is shown in Figure 2. DETAILED DESCRIPTION

[0090] The method of the present invention is described in detail below with reference to the accompanying drawings.

[0091] In this embodiment, Figure 1 As shown, a following motion planning method for a curved and sloping road section is to combine the data collection of three aspects: the geometric characteristic factor information of the curved and sloping road section, the geometric and dynamic parameters of the vehicle, and the vehicle following data of the curved and sloping road section, use the artificial potential field algorithm and the vehicle state prediction model improved based on IDM to constrain the vehicle's lateral movement of the road and the vehicle's movement state along the path direction respectively, and then calculate the real-time trajectory planning points, and then use the cubic Bezier curve to process the real-time trajectory planning points to obtain a smooth and continuous path following motion planning method; the curved and sloping road section is a road section with slope, road superelevation and curvature at the same time, and it is assumed that the autonomous driving vehicle is the nth vehicle, the following front vehicle is the n-1th vehicle, and both are ordinary passenger cars, and the influence of extreme weather such as rain, snow, fog and haze is not considered; specifically, the following steps are included:

[0092] Step 1: Take the slope of the curved road section as the reference and superelevation The center of curvature of the lane centerline at is taken as the origin O, the direction pointing from the origin O to the lane centerline and parallel to the earth is taken as the X-axis, the direction perpendicular to the X-axis and parallel to the earth is taken as the Y-axis, and the Z-axis is determined by the right-hand method, so as to establish a Cartesian coordinate system O-XYZ, and collect the geometric characteristic factor information of the curved and sloping section, the geometric and dynamic parameters of the nth vehicle, and the vehicle following data of the curved and sloping section at time t in the Cartesian coordinate system O-XYZ.

[0093] Step 1.1: Collect geometric characteristic factor information of curved and sloping road sections;

[0094] A data collection vehicle equipped with a global positioning system (GPS), an inertial measurement unit (IMU), a lidar, and a camera is used to collect data on the curved and sloping road sections. Each sensor simultaneously collects information about the surrounding environment. The multi-sensor fusion and Kalman filtering data processing functions provided by the open source autonomous driving platform Autoware.ai are used to extract the lane line position and road width D, the position coordinates of the lane centerline, the curvature radius 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 slope section, any coordinate point (x, y, z) on the lane centerline. The road centerline is the basic reference line of the road surface geometry. This line defines the road surface slope at any coordinate point (x, y, z) on the lane centerline. , Ultra High , Road width , the radius of curvature at the center line of the lane in the polar coordinate system and the polar angle at the lane centerline ; 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; Among them, the road slope Describes the longitudinal slope of the lane along the longitudinal direction of the lane, superelevation Describes the inclination angle of the lane in the cross section; defines the radius of curvature at the center line of the lane and the polar angle at the lane centerline This is for the calculation of subsequent steps.

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

[0097] Fill the No. n vehicle with all the oil but without any passengers, and use a dedicated vehicle weighing device to get the vehicle curb weight m. Use a laser rangefinder to measure the vehicle width d, wheelbase b, sum of the front wheelbase L1 and rear wheelbase L2. Then use the three-point weighing method to get the front wheelbase L1 and rear wheelbase L2. Use the tilt method to measure the center of mass height h. g , the measurement process is completed at the vehicle inspection station;

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

[0099] Use the same four data collection vehicles in step 1.1 to collect data on the curved and sloping road sections at the same time, use GPS to record the data collection location information, and obtain the vehicle's driving trajectory by analyzing the change of location over time; IMU sensors can help capture the vehicle's motion state on the curved and sloping road sections and are used to measure the vehicle's acceleration; the collected data often contains noise or errors, and the autonomous driving platform Autoware.ai is used to process the data; after processing, the following information will be obtained:

[0100] Extract the position information of vehicle No. n-1 at time t , the speed of vehicle n-1 at time t and acceleration , the position information of vehicle No. n at time t , the speed of vehicle No. n at time t ; and get the polar coordinates of vehicle No. n-1 at time t and the polar coordinates of vehicle No. n at time t ,in, and Respectively expressed in coordinates The polar angle and polar diameter of the n-1th vehicle in the polar coordinate system established with the direction parallel to the X-axis as the polar axis, and Respectively expressed in coordinates The polar angle and polar diameter of the nth vehicle in the polar coordinate system are established with φ as the pole and the direction parallel to the X-axis as the polar axis; and they are input into step 3 as the initial state.

[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 to plan the trajectory of the nth vehicle;

[0102] like Figure 3 As shown in the figure, by analyzing the force of the nth vehicle at time t, the boundary conditions of the safe trajectory for a side slip or rollover accident on a curved slope are determined. ;Pick The position coordinates of the lane centerline at the position are (x0, y0, z0), and it is used as the target point C. Combined with the artificial potential field algorithm, the safe trajectory boundary condition and ensure the outer boundary of the lane and the inner boundary to ensure driving within the lane As an obstacle point, the artificial potential field algorithm is used to calculate the resultant force on the mass center M of the nth vehicle. , and use the combined force (t) to perform motion planning in order to make the car move along the center line of the lane; the polar coordinates of the nth vehicle at time t (φ n (t),r n (t)), let The coordinates of the lane centerline at is (x0, y0, z0), and the radius of curvature is , the polar angle is , the road slope is , super high , road width is ;

[0103] Step 2.1: Use equation (1) to calculate the outer boundary of the lane that the nth vehicle must travel within at time t: and the inner boundary to ensure driving within the lane ;

[0104] Due to the high fatality rate of traffic accidents on curved and sloping roads, in order to avoid a head-on collision caused by a car driving into the opposite lane, or colliding with the guardrails on both sides of the lane, causing traffic congestion and secondary traffic accidents, it is necessary to calculate the boundary of the nth vehicle to ensure that it drives within the lane; Figure 3 As shown in the figure, by obtaining the lane centerline and car width information, formula (1) is used to calculate the outer boundary of the lane that the autonomous driving vehicle No. n must travel within at time t. and the inner boundary to ensure driving within the lane :

[0105] (1)

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

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

[0108] In order to prevent the nth vehicle from skidding or rolling over, the boundary conditions of the safe trajectory of the autonomous vehicle for skidding or rolling over are required. The forces on the vehicle on the curved and sloping road are more complicated. The load will not only be affected by the super-high road surface, but also by the This results in uneven distribution inside and outside, and is affected by the slope of the road. The influence of the load distribution on the front and rear axles is uneven. Therefore, the force analysis of the vehicle No. n on the curve and slope is first performed separately, and then the curve and slope superposition sections are comprehensively analyzed. The steps are as follows:

[0109] Step 2.2.1: Analyze the situation of vehicle No. n at time t when the road surface is superelevated. The lateral force of the curve ;

[0110] like Figure 4 As shown in the figure, at time t, when the vehicle is driving on a curve, the sum of the forces it receives is enough to provide a radius for the nth vehicle to turn. The centrifugal force in the direction of :

[0111] (2)

[0112] In formula (2) =m* , is the acceleration due to gravity, which is 9.8 m / s 2 ;

[0113] Step 2.2.2: Analyze the situation of vehicle No. n on the road at time t. Front and rear loads ;

[0114] For longitudinal slope roads, force 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 situation of vehicle No. n at time t when the road surface is superelevated. Vertical load on the curve , , , ;

[0118] Assuming that the vehicle enters the curve at a constant speed, the longitudinal speed along the road direction at this moment can be equivalent to the vehicle's driving speed, and the tire acceleration can also be approximately regarded as the vehicle's lateral acceleration, such as Figure 5 As shown in the figure, 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 expressed by the lateral force coefficient of the tire: Calculated, , , , The left front wheel, right front wheel, left rear wheel and right rear wheel of the vehicle are respectively Vertical load on the curve.

[0122] Step 2.2.4: Analyze the vertical load of vehicle No. n on the curved slope at time t , , , ;

[0123] Based on step 2.2.3, ignore the lateral acceleration of the vehicle tires and consider the road surface The influence of the vertical load on the nth vehicle is calculated by using equations (7)-(10) to obtain the left front wheel load of the nth vehicle on the curved slope at time t: , 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 conditions for the front wheel of vehicle n to skid at time t Critical conditions for side slip with rear wheels ;

[0129] The lateral force on the front and rear axles of the nth vehicle on the curved slope section is calculated using equations (11) and (12): , :

[0130] (11)

[0131] (12)

[0132] The boundary conditions for the occurrence of sideslip are similar to those on a curve, that is, the lateral force is equal to the adhesion force. Combining equations (7) to (12), we can obtain equations (13) to (14), and using equations (13) and (14), we can obtain the critical conditions for the occurrence of sideslip of the front wheel: The critical strip for side slip of the rear wheel :

[0133] (13)

[0134] (14)

[0135] Step 2.2.6: Analyze the critical conditions for the rollover of vehicle No. n on the curved slope at time t ;

[0136] When the lateral moment is greater than the vehicle's stabilizing moment, the ground support force on the vehicle's wheels is 0, and the critical condition for rollover is reached. The moment is:

[0137] (15)

[0138] Substituting equation (15) into equation (2), the critical condition for the rollover of the nth vehicle is calculated using equation (16): :

[0139] (16)

[0140] Combining equations (13)-(14) and (16), the safe trajectory boundary condition is calculated using equation (17): :

[0141] (17)

[0142] Step 2.3: Calculate the resultant 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 the nth vehicle and the target point C on the center line of the lane, thus obtaining the gravitational potential energy Function formula:

[0145] (18)

[0146] in, is the gravitational constant, is a vector whose magnitude represents the distance between the center of mass M of the nth vehicle and the target point C on the center line of the lane, gravitational potential energy The vector direction is from the mass center point M of the nth vehicle to the target point C; according to the simulation experiment test, the gravitational constant k a The most appropriate value is 0.2, which can meet the requirements of both efficiency and comfort.

[0147] Similarly, the factors that determine the repulsive potential energy are also related to the center of mass M of the nth vehicle and the outer boundary of the drivable area R of the nth vehicle. , the inner boundary of the driving area R of the nth vehicle is and the safe trajectory boundary conditions of vehicle n When the vehicle does not enter the influence range of the obstacle repulsive potential field, that is, the threshold distance of the repulsive force, , the vehicle is not affected by the repulsive force of the potential field. The repulsive potential energy function is obtained from equations (24) and (25) respectively: and :

[0148] (19)

[0149] (20)

[0150] (twenty one)

[0151] In formula (18) to formula (21), represents the threshold distance of repulsion, represents the repulsion constant, is a vector whose magnitude represents the outer boundary of the lane that the nth vehicle must travel within at time t. The distance to the center of mass M of the nth vehicle, potential energy The vector direction from Point to the center of mass point M of the nth vehicle; is a vector whose magnitude indicates the inner boundary of the lane that the nth vehicle ensures to travel within at time t. Boundary conditions for safe trajectories The maximum value between the distance to the center of mass M of the nth vehicle, the potential energy The vector direction from (t) points to the center of mass of the nth vehicle M; according to the simulation experiment test, the threshold distance of the repulsive force The value is 1.75, the repulsion constant 0.05 is the most appropriate value, which can meet the requirements of both efficiency and comfort.

[0152] Step 2.3.2: Calculate the nth vehicle based on the artificial potential field The combined force of the field (t);

[0153] Using formula (22), we can get the gravitational force of the target point C on the center of mass M of the lane centerline on the nth vehicle: , using formula (23) to obtain the repulsive force of the outer side of the lane on the mass center M of the nth vehicle , using formula (24) to obtain the repulsive force of the inner side of the lane on the mass center M of the nth vehicle , and then use formula (25) to get the resultant force of the nth vehicle at the center of mass M :

[0154] (twenty two)

[0155] (twenty three)

[0156] (twenty four)

[0157] (25)

[0158] In formula (22) to formula (25), is a vector differential operator used to represent the gradient; Figure 3 As shown, under the action of the combined potential field force, the vehicle moves from high potential energy to low potential energy, and the direction is the negative gradient direction of the combined potential field.

[0159] Step 3: Based on the information, parameters and data collected in step 1, a vehicle state prediction model at time t based on the intelligent driving model IDM is constructed to plan the trajectory of the nth vehicle;

[0160] Step 3.1: Calculate the arc distance on the lane centerline between vehicle No. n-1 and vehicle No. n at time t on the curved slope section ;

[0161] Step 3.1.1: Get the polar angle of the nth vehicle and the polar angle of vehicle n-1 The position coordinates (x, y, z) of the lane centerline are parameterized, and the parameterized equation is constructed using formula (26);

[0162] (26)

[0163] like Figure 6 As shown in part (a) of the figure, let the position coordinates (x n-1 (t),y n-1 (t),z n-1 (t)) is point F, and the position coordinates of vehicle No. n at time t (x n (t),y n (t),z n (t)) is point M, and the polar angle of vehicle No. n is taken and the polar angle of vehicle n-1 The coordinate points (x, y, z) on the lane centerline between are parameterized, that is, Figure 6 The coordinates between point C and point F in part (a) of the equation are given by parameterized equation (26), where Represents the parameterized equation Parameters, They represent the projection coordinates of the lane centerline on the horizontal plane along the X-axis and Y-axis in the Cartesian coordinate system, Indicates the projection coordinate of the lane centerline along the Z axis in the Cartesian coordinate system;

[0164] Step 3.1.2: Use equation (27) to get the small arc length on the lane centerline :

[0165] (27)

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

[0167] Step 3.1.3: Use equation (28) to calculate the arc distance between the positions of vehicle No. n-1 and vehicle No. n at time t on the curved slope section at time t: :

[0168] (28)

[0169] In formula (28), express The parameters at express Parameters at .

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

[0171] Assume the friction coefficient between the wheel and the road is , which is taken as 0.7 in this method, and the critical speed of the side slip of the nth vehicle is established by equation (29): , the critical speed of the rollover of the nth vehicle is established by formula (30): :

[0172] (29)

[0173] (30)

[0174] The critical speed of the side slip of the nth vehicle is calculated using equations (31) and (32) respectively: and the critical speed of the rollover of the nth vehicle , and obtain the maximum speed of the nth vehicle without deviating from the path at time t :

[0175] (31)

[0176] (32)

[0177] (33)

[0178] Step 3.3: Use formula (34) to build a vehicle state prediction model based on IDM:

[0179] (34)

[0180] In formula (34), represents the acceleration of vehicle No. n at time t, represents the maximum acceleration expected by vehicle No. n, represents the expected speed of vehicle No. n, represents the acceleration index, represents the correction factor of the curve curvature, represents the symbolic function, It represents the minimum radius for vehicle n to maintain safe driving at time t. represents the slope correction factor, It represents the minimum safe distance between the nth vehicle and the n-1th vehicle to avoid collision. represents the safe headway between vehicle No. n and vehicle No. n-1 at time t, (t) represents the speed difference between vehicle No. n and vehicle No. n-1 at time t, represents the comfortable deceleration of vehicle No. n; represents the relative speed between vehicle No. n and vehicle No. n-1 at time t (t) the distance desired to be maintained, with:

[0181] (35)

[0182] As shown in formula (34), the model takes into account the influence of curves and road longitudinal slope. The maximum speed of the nth vehicle without deviating from the path at time t The purpose of this consideration is to ensure that the nth vehicle can travel on the planned path.

[0183] Step 3.4: Use the vehicle following trajectory data on the curved slope section to calibrate the parameters of the improved IDM following model; thereby determining the parameters of the improved IDM following model, including: expected maximum acceleration , Expected vehicle speed , minimum safe distance to avoid collision , comfortable deceleration .

[0184] Step 4: Artificial potential field based on time t (t) and the vehicle state prediction model at time t, calculate the position coordinate point (x n (t+1),y n (t+1),z n (t+1));

[0185] Step 4.1: Use equation (34) to calculate the acceleration of vehicle n at time t: ;

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

[0187] (36)

[0188] In formula (36), is a time step from time t to time t+1. Considering that the acquisition frequency of sensors of autonomous driving vehicles is mostly above 10HZ at this stage, The value is 0.1 second, which can meet the market demand, with fast update frequency and timely control.

[0189] Step 4.3: Get The coordinate point at the center line of the lane is (x0, y0, z0), the coordinate point on the center line of the lane is (x0, y0, z0) as the origin of the Frenet coordinate system, the direction along the center line of the lane, that is, the longitudinal direction of the road, is the S axis, and the direction perpendicular to the center line of the lane, that is, the lateral direction of the road, is the P axis, thereby establishing the Frenet coordinate system (S, P);

[0190] The polar coordinates (φ) of vehicle No. n at time t are known. n (t),r n (t)), let The position coordinates of the lane centerline are (x0, y0, z0), and the radius of curvature is for , polar angle for , road slope for , Ultra High for , Road width for ; The Frenet-Serret frame is a local coordinate system in curve geometry that describes the motion of curves in three-dimensional space. Referring to the Frenet-Serret frame, taking the lane centerline as a reference, a local Frenet coordinate system (S, P) suitable for lane geometry is constructed: Figure 6As shown in part (b) of the figure, the point (x0, y0, z0) on the center line of the lane is taken as the origin of the coordinate system, the direction along the center line of the lane is set as the S axis, the longitudinal direction of the lane, and the direction perpendicular to the center line of the lane is set as the P axis, the lateral direction of the lane, indicating the lateral offset of the vehicle from the center line on the lane, and the coordinates (s, p) are used to represent the center of mass M of the nth vehicle; now the Frenet coordinates (S, P) are converted to Cartesian coordinates (X, Y, Z). The core of this is to use the position and local direction of the center line of the lane for conversion. In the Frenet coordinate system, the lateral offset can be obtained by the normal vector To define:

[0191] Using formula (37) we get the normal vector :

[0192] (37)

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

[0194] (38)

[0195] Step 4.4: Let the coordinates of the center of mass M of the nth vehicle in the Frenet coordinate system (S, P) be (s, p), and use equation (44) to obtain the coordinates of the nth vehicle in the Frenet coordinate system at the time step The coordinates below .

[0196] It is known that the coordinates of vehicle No. n at time t are (x n (t),y n (t),z n (t),φ n (t),r n (t)), use step 2.4.1 to establish the Frenet coordinates (s, p) and convert them into Cartesian coordinates ( ) can be converted into the Frenet coordinates (s(t), p(t)) at time t; combined with the schematic diagram Figure 3 It can be seen that the resultant force obtained in step 2 is (t) represents the lateral force of the nth vehicle moving in the lane. According to Newton's second law, the acceleration a of the nth vehicle moving along the P axis, i.e., the lateral acceleration a, is calculated using equation (39): p (t):

[0197] (39)

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

[0199] (40)

[0200] Since the speed v of vehicle No. n at time t+1 n ( ) represents the velocity along the path, v n ( ) can be calculated in step 3, assuming The speed along the S axis at any moment, that is, the speed of longitudinal motion is ,assuming At t=0, the value is v n (0), calculated by formula (41) :

[0201] (41)

[0202] The lateral movement at time t+1 can be calculated by equations (42) and (43) respectively: and vertical movement :

[0203] (42)

[0204] (43)

[0205] Using formula (44), we can get the time of vehicle n The process is along the coordinates in the Frenet coordinate system :

[0206] (44)

[0207] Step 4.5: Use equation (45) to obtain the increments of the nth vehicle 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 at time t+1 in the Cartesian coordinate system ;

[0210] Since the Frenet coordinates (s(t), p(t)) from the tth moment to the t+ The Frenet coordinates of the time ( ) is at a very small time step The curvature and polar angle of the process are very small, so the local approximation method can be used to process it. Combined with formula (46), the position coordinate (x) at the t+1 moment is calculated. n (t+1),y n (t+1),z n (t+1)):

[0211] (46)

[0212] Step 4.7: From (0,0,z n (t+1)) as the pole, and the direction parallel to the X-axis of the Cartesian coordinate system as the polar axis to establish the polar angle in the polar coordinate system and polar diameter Construct the polar coordinates of vehicle No. n at time t+1 .

[0213] Step 5: Use formula (47) to calculate the Bezier curve , so as to use the cubic Bezier curve to obtain a smooth planning path E(x, y, z) in the Cartesian coordinate system;

[0214] The position coordinates of the real-time path planning coordinate points obtained in step 4 are recorded as , get the position coordinates of the real-time path planning coordinate point at time t-2 , the position coordinates of the real-time path planning coordinate point at time t-1 , the position coordinates of the real-time path planning coordinate point at time t , the position coordinates of the real-time path planning coordinate point at time t+1 , initially, after 2 After obtaining the four real-time path planning coordinate points, execute step 5; use formula (47) to obtain the calculation formula of the Bezier curve:

[0215] (47)

[0216] In formula (47), is a parameter with a value range of [0,1]. In order to make the planned path smooth enough, Increase by 0.01 each time, gradually increasing from 0 to 1, thus obtaining a smooth planned path E(x, y, z).

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

[0218] In this embodiment, an electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the above 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 on the computer-readable storage medium, and the computer program executes the steps of the above method when executed by a processor.

Claims

1. A vehicle following motion planning method for a curved and sloping road section, characterized in that: The curved slope section is a section with slope, road superelevation and curvature at the same time, and assuming that the autonomous driving vehicle is the nth vehicle and the following vehicle is the n-1th vehicle, the following path planning method includes the following steps: Step 1: Take the road slope of the curved road section as an example. and superelevation The center of curvature of the lane centerline at is the origin O, the direction from the origin O to the lane centerline and parallel to the earth is the X-axis, the direction perpendicular to the X-axis and parallel to the earth is the Y-axis, and the Z-axis is determined by the right-hand method, thus establishing a Cartesian coordinate system. , in the Cartesian coordinate system Collecting geometric characteristic factor information of the curved and sloping road section, geometric and dynamic parameters of the nth vehicle, 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 to plan the trajectory of the nth vehicle; Step 3: Based on the information, parameters and data collected in step 1, a vehicle state prediction model at time t based on the intelligent driving model IDM is constructed to plan the trajectory of the nth vehicle; Step 4: Artificial potential field based on time t and the vehicle state prediction model at time t, calculate the position coordinates of the real-time path planning coordinate points of the nth vehicle on the curved slope section at time t+1 point; Step 5: Use formula (47) to calculate the Bezier curve , thus using cubic Bezier curves to obtain a smooth planning path in the Cartesian coordinate system ; (47) In formula (47), Is a parameter with a value range of ; The position coordinates of the real-time path planning coordinate points obtained in step 4 are recorded as , Indicates that the nth vehicle is in The position coordinates of the real-time path planning coordinate points at the moment, Indicates that the nth vehicle is in The position coordinates of the real-time path planning coordinate points at the moment, represents the position coordinates of the real-time path planning coordinate point of the nth vehicle at the tth time, Indicates that the nth vehicle is in The position coordinates of the real-time path planning coordinate points at the moment; Step 6: After assigning the value to t, return to step 2 and execute sequentially, so as to plan the driving path of the nth vehicle in real time.

2. The method for vehicle following motion planning on a curved and sloping road section according to claim 1, characterized in that: The step 1 comprises: Step 1.1: Collect geometric characteristic factor information of curved and sloping road sections; A data collection vehicle equipped with a global positioning system (GPS), an inertial measurement unit (IMU), a laser radar and a camera is used to collect and process data on the curved and sloping road section to obtain geometric characteristic factor information of the curved and sloping road section, including: any coordinate point on the center line of the lane , any coordinate point on the lane centerline The road slope , Ultra High , Road width , the radius of curvature at the center line of the lane in the polar coordinate system and the polar angle at the lane centerline ; The polar coordinate system is based on the coordinate points on the lane centerline is the pole, and the direction parallel to the X-axis is established as the polar axis; Step 1.2: Collect the geometric and dynamic parameters of the nth vehicle, including: vehicle curb weight m, vehicle width d, wheelbase b, front wheelbase L1, rear wheelbase L2, center of mass height h g ; Step 1.3: Collecting vehicle following trajectory data on the curved and sloping road section; Extract the position information of vehicle No. n-1 at time t , the speed of vehicle n-1 at time t and acceleration , the position information of vehicle No. n at time t , the speed of vehicle No. n at time t ; and get the polar coordinates of vehicle No. n-1 at time t and the polar coordinates of vehicle No. n at time t ,in, and Respectively expressed in coordinates The polar angle and polar diameter of the n-1th vehicle in the polar coordinate system established with the direction parallel to the X-axis as the polar axis, and Respectively expressed in coordinates The polar angle and polar diameter of the nth vehicle in the polar coordinate system established with φ as the pole and the direction parallel to the X-axis as the polar axis.

3. The method for vehicle following motion planning on a curved and sloping road section according to claim 2, characterized in that: The step 2 comprises: Step 2.1: Use equation (1) to calculate the outer boundary of the lane that the nth vehicle must travel within at time t: and the inner boundary to ensure driving within the lane ; (1) In formula (1), for The radius of curvature at the lane centerline; for The width of the road surface at the center line of the lane; for Superelevation at the lane centerline; Step 2.2: Determine the safe trajectory boundary conditions of vehicle n at time t ; The force analysis of vehicle No. n is performed, and the critical conditions for the front wheel to slip at time t are obtained using equations (13) and (14). Critical conditions for side slip with rear wheels , using formula (16) to obtain the critical condition for the rollover of the nth vehicle at time t , and thus use formula (17) to obtain the boundary conditions of the entire trajectory of vehicle n at time t ; (13) (14) (16) (17) In formula (13) to formula (17), represents the acceleration due to gravity, represents the lateral force coefficient; for The road surface slope at the lane centerline at ; Step 2.3: Calculate the resultant potential force of vehicle n at time t ; Using formula (22), we can get the gravitational force of the target point C of the lane centerline on the center of mass M of the nth vehicle at time t: , using formula (23) to obtain the repulsive force of the outer side of the lane on the mass center M of the nth vehicle at time t , using formula (24) to obtain the repulsive force of the inner side of the lane on the mass center M of the nth vehicle at time t , and then use formula (25) to get the resultant force of vehicle n at the center of mass M at time t : (22) (23) (24) (25) In formula (22) to formula (25), is a vector differential operator used to represent the gradient, is the gravitational constant, is the distance between the center of mass M of the nth vehicle at time t and the target point C on the center line of the lane, The vector direction is from the center of mass point M of the nth vehicle at time t to the target point C; represents the threshold distance of repulsion, represents the repulsion constant, express The distance to the center of mass M of vehicle No. n at time t, The vector direction from Points to the center of mass point M of vehicle No. n at time t; express and The maximum value between the two is the distance to the center of mass M of the nth vehicle at time t, The vector direction from Points to the center of mass M of vehicle No. n at time t.

4. The method for planning vehicle following motion on a curved and sloping road section according to claim 3, characterized in that: The step 3 comprises: Step 3.1: Calculate the arc distance on the lane centerline between the vehicle No. n-1 and the vehicle No. n at time t on the curved slope section ; Step 3.2: Use equation (33) to calculate the maximum speed of vehicle n without deviating from the path at time t: ; (33) In formula (33), Indicates the friction coefficient between the wheel and the road; Step 3.3: Use formula (34) to build the vehicle state prediction model at time t based on IDM: (34) In formula (34), represents the acceleration of vehicle No. n at time t, represents the maximum acceleration expected by vehicle No. n, represents the expected speed of vehicle No. n, represents the acceleration index, It represents the minimum safe distance between the nth vehicle and the n-1th vehicle to avoid collision. It represents the safe headway between vehicle No. n and vehicle No. n-1. represents the speed difference between vehicle No. n and vehicle No. n-1 at time t, represents the comfortable deceleration of vehicle No. n; represents the relative speed between vehicle No. n and vehicle No. n-1 at time t The desired distance to be maintained, with: (35) Step 3.4: calibrate the parameters of the improved IDM following model using the vehicle following trajectory data on the curved slope section, thereby determining the parameters of the improved IDM following model, including: expected maximum acceleration 、Desired vehicle speed , Minimum safe distance to avoid collision , comfortable deceleration .

5. The method for planning vehicle following motion on a curved and sloping road section according to claim 4, characterized in that: The step 3.1 comprises: Step 3.1.1: Polar angle of vehicle No. n and Vehicle polar angle The coordinate points on the center line of the lane Coordinate parameterization is performed to construct the parameterized equation of the lane centerline using equation (26): ; (26) In formula (26), Representing parameterized equations Parameters, They represent the projection coordinates of the lane centerline along the X-axis and Y-axis in the Cartesian coordinate system, respectively. Indicates the projection coordinate of the lane centerline along the Z axis in the Cartesian coordinate system; Step 3.1.2: Use equation (27) to get the small arc length on the lane centerline : (27) In formula (27), , , Respectively represent the rate of change of the coordinate point (x, y, z) along the X-axis, Y-axis and Z-axis in the Cartesian coordinate system; Representing parameterized equations exist The tangent vector at ; Step 3.1.3: Use equation (28) to calculate the first The arc distance between vehicle No. and vehicle No. n : (28) In formula (28), express The parameters at express Parameters at .

6. The method for planning vehicle following motion on a curved and sloping road section according to claim 5, characterized in that: The step 4 comprises: Step 4.1: Use equation (34) to calculate the acceleration of vehicle n at time t: ; Step 4.2: Use equation (36) to get the speed of vehicle n at time t+1 ; (36) In formula (36), is a time step from time t to time t+1; Step 4.3: Get The coordinate point at the center line of the lane is , with the coordinate point on the lane centerline The origin of the Frenet coordinate system is taken as the S axis, the direction along the lane centerline, i.e. the longitudinal direction of the road, is taken as the S axis, and the direction perpendicular to the lane centerline, i.e. the transverse direction of the road, is taken as the P axis, thereby establishing the Frenet coordinate system (S, P); Use equation (38) to establish the transformation relationship matrix from the Frenet coordinate system (S, P) to the Cartesian coordinate system: ; (38) In formula (38), Indicates the lateral deviation of vehicle No. n from the center line in the lane; Step 4.4: Let the coordinates of the center of mass M of the nth vehicle in the Frenet coordinate system (S, P) be (s, p), and use equation (44) to obtain the coordinates of the nth vehicle in the Frenet coordinate system at the time step The coordinates below ; (44) In formula (44), represents the coordinates of the nth vehicle at time t in the Frenet coordinate system (S, P), Represents the Frenet coordinate system The speed of vehicle No. n along the S axis at time t is, Represents the Frenet coordinate system The speed of vehicle No. n along the P axis at time t is, Represents the Frenet coordinate system The acceleration of vehicle No. n along the P axis at time t; Step 4.5: Use equation (45) to obtain the increments of the nth vehicle 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 No. n at time t+1 in the Cartesian coordinate system: , and recorded as ; (46) Step 4.7: As the pole, the polar angle φ in the polar coordinate system is established with the direction parallel to the X-axis of the Cartesian coordinate system as the polar axis n (t+1) and the polar radius r n (t+1) constitutes the polar coordinates of vehicle No. 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 to execute the car-following path planning method for a curved and sloping road section as described in any one of claims 1-6, and the processor is configured to execute the program stored in the memory.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for planning a car-following path on a curved and sloping road section described in any one of claims 1 to 6 are executed.

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