Motion curve parking path planning method based on Ackerman model

Abstract

The invention discloses a parking path planning method based on an Ackerman model motion curve in the technical field of parking path planning, and the method comprises the following steps: obtaining a vehicle door allowable opening angle of a vehicle based on an adjacent obstacle of a target parking space, and building a vehicle passenger loading and getting-on and getting-off comfort characterization model, the vehicle door allowable opening angle is the vehicle door allowable opening angle adjacent to the obstacle and the opening angle required by passengers to get on and off the vehicle. According to the method, the vehicle getting-on and getting-off comfort of the vehicle passengers and the objects and the parking time are brought into the optimal design of the parking path, the vehicle getting-on and getting-off comfort of the passengers and the objects and the parking efficiency are improved, the dimensionality of the path parameters is reduced by presetting the vehicle motion parameters and the parking path mode, the parking path planning efficiency is improved, and the user experience is improved. And the real-time requirement is met.

Description

Technical Field

[0001] The present invention relates to the technical field of parking path planning, in particular to a parking path planning method based on an Ackerman model motion curve. Background Art

[0002] In recent years, with the rapid development of intelligent transportation and autonomous driving, automated parking path planning and vehicle motion planning have garnered widespread attention from both academia and industry. Automated parking technology offers a broad range of application prospects. It can significantly reduce driver stress during parking, effectively simplify parking procedures, and significantly reduce parking-related accidents, thereby improving parking safety and efficiency. Currently, existing parking planning methods are primarily based on curve fitting, which typically employs polynomial curves, segmented curves, and B-spline curves for parking path design. These methods offer simple design, short computational times, and strong numerical optimization capabilities. Other approaches include graph search-based methods, sampling-based methods, and intelligent algorithm-based methods. For example, hybrid A* algorithms, RRT algorithms, genetic algorithms, and neural network algorithms are employed to design parking paths and thus achieve automated parking operations.

[0003] Existing parking path planning methods all assume the final parking state is ideal: the vehicle is precisely parked in the center of the target parking space, with the sideline parallel to the edge of the space. However, actual application scenarios are far more complex. First, manual and automated parking modes coexist. Due to varying degrees of manual parking proficiency among drivers, it is often difficult for adjacent vehicles in the target parking space to achieve the ideal parking position. For example, in parking lots in older residential communities, where parking spaces are scarce and lack clear signage, some drivers park haphazardly to increase parking capacity, resulting in irregular parking and seriously interfering with the normal parking of adjacent vehicles. Second, due to the current state of autonomous driving technology, automated parking requires at least one safety officer to monitor the vehicle. Furthermore, the complex environmental conditions within parking lots present numerous challenges. In parking lots at large shopping malls, logistics parks, and ports, load-bearing columns, walls, and other structures limit the opening angle of vehicle doors. When vehicles navigate between containers in a park, they face the challenge of operating equipment densely packed together and confined space. They must not only avoid collisions with containers and equipment, but also consider the loading and unloading of cargo. For example, in port container parking lots, where containers are densely packed, vehicles must precisely plan their paths to ensure doors open properly and cargo enters and exits smoothly during loading and unloading. These factors are particularly significant in perpendicular parking scenarios, compromising passenger comfort and potentially preventing them from entering and exiting the vehicle. For example, in perpendicular parking spaces in underground parking lots, improperly parked adjacent vehicles or the presence of supporting columns can restrict the door opening angle, significantly impacting passengers, especially those carrying large luggage or with limited mobility. Furthermore, existing parking path planning methods often require additional smoothing and curvature continuity optimization to generate paths, which increases the risk of collisions and reduces parking safety. In complex scenarios with frequent vehicle and passenger traffic, such as airport parking lots, even the slightest deviation in path planning can lead to collisions with surrounding objects or pedestrians.

[0004] In summary, the existing automatic parking method is not suitable for complex scenarios where there are obstacles on both sides of the target parking space. In addition, during the parking process, it is unable to comprehensively consider the parking path planning issues such as the comfort of passengers getting on and off the vehicle, the convenience of vehicle loading and exiting, parking safety and parking efficiency, and the use effect is poor. Summary of the Invention

[0005] The purpose of the present invention is to provide a parking path planning method based on the Ackerman model motion curve to solve the parking path planning problem mentioned above, which is not suitable for complex scenarios where there are obstacles on both sides of the target parking space, and cannot comprehensively consider factors such as passenger boarding and alighting comfort, vehicle loading and exit convenience, parking safety and parking efficiency during the parking process.

[0006] To achieve the above object, the present invention provides the following technical solutions: A parking path planning method based on an Ackerman model motion curve comprises the following steps: S1: Obtaining the vehicle's door opening angle based on the obstacles adjacent to the target parking space, and establishing a vehicle passenger boarding and alighting comfort model, wherein the door opening angle is the door opening angle allowed by the obstacles and the door opening angle required for boarding and alighting by the passenger; S2: constructing a vehicle basic motion curve library based on the Ackerman model, wherein the vehicle basic motion curve library includes a plurality of vehicle basic motion curves, and obtaining the time required for the vehicle to pass the corresponding vehicle according to the vehicle basic motion curves; S3: Establishing a four-segment parking path pattern based on the basic motion curve, including a transition path, a maneuvering path, an approach path, and an adjustment path, and generating a parking path connecting any starting state and target point state near the target parking space, so as to reduce the parameter dimension of the basic motion curve of the vehicle; S4: Establishing a multi-objective optimization model for a parking path, wherein the multi-objective optimization model for the parking path is based on constraints such as the vehicle being completely within the target parking space in the final parking state, parking path parameters, smooth boarding and disembarking of passengers and cargo, smooth entry and exit of passengers and cargo into and out of the parking space, and collision avoidance; S5: Transforming and solving the parking path multi-objective optimization model based on the penalty function to obtain an automatic parking path.

[0007] As a further solution of the present invention: in S1, the adjacent obstacle is divided into a plurality of obstacle line segments, and the door opening angle α is calculated according to the plurality of obstacle line segments;

[0008] Among them, α is the allowable opening angle of the door, α M is the maximum opening angle of the door without interference, α0, α m , α B , α U and α P⊥ They represent the endpoint Q0 when the door is not opened, the endpoint Q when the door is opened to the maximum angle, and m , the lower endpoint O of the obstacle segment LB , the upper endpoint O of the obstacle segment LU 、P ⊥ The angle between the line connecting the door pivot point P and the positive direction of the X axis, α s0 is the safety angle, α IN is the door opening angle allowed under the interference of obstacle line segment, l D is the door length, d m The distance between the door axis and the obstacle line segment O LU O LBThe shortest distance, d m The calculation formula is as follows;

[0009] Among them, Pm is the distance between the door and the obstacle line segment O LU O L The intersection point, α P⊥ P ⊥ The angle between the line connecting the door pivot point P and the positive direction of the X-axis; Allowable opening angle α of the door under the interference of obstacle line segment IN According to whether the interference of the obstacle line segment on the door is a line constraint or a point constraint, α IN The calculation formula is;

[0010] Among them, α P and α L These are the allowed opening angles of the door under point constraint and line constraint respectively.

[0011] As a further solution of the present invention: the door opening angle α required for passengers to get on and off the vehicle is calculated based on the preset space required for passengers to get off the vehicle with their luggage. r , α r The calculation formula is;

[0012] Among them, α r The door opening angle required for passengers and cargo to get on and off the vehicle, d r is the redundancy distance, W t is the size of the passenger and cargo, and k is a logical variable indicating whether there is a passenger or cargo at the door.

[0013] As a further solution of the present invention: an angle margin is obtained based on the allowable door opening angle and the door opening angle required for passengers and objects to get on and off the vehicle;

[0014] Among them, Δα j is the door angle margin, which corresponds to the comfort variable for passengers getting on and off the vehicle. j is the allowable opening angle of door j, α rj The door opening angle required for door j when passengers and luggage can get on and off the vehicle; A comfort characterization model for passengers getting on and off the vehicle with cargo is derived based on the angle margin;

[0015] Among them, Δα is the comfort of passengers getting on and off the vehicle, Δα ijis the angle margin of door j under the influence of obstacle segment i, n O is the number of obstacle segments, n D The number of doors.

[0016] As a further solution of the present invention: in S2, the vehicle speed, acceleration, equivalent front wheel steering angle, and equivalent front wheel steering acceleration are preset, a coordinate system is established with the center of the vehicle rear axle, and an Ackermann model of the vehicle with respect to time is established based on the Ackermann model;

[0017] Among them, x E is the horizontal coordinate of the center of the vehicle's rear axle, y E is the vertical coordinate of the rear axle center of the vehicle, θ is the vehicle heading angle, t is the time, φ is the equivalent front wheel turning angle, l A is the vehicle wheelbase, v is the vehicle speed; According to the vehicle Ackerman model, a number of basic vehicle motion curves are obtained to obtain a smooth path that satisfies the vehicle kinematics and has continuous curvature, wherein the basic vehicle motion curves include a clothoid curve-arc-deceleration curve, an acceleration curve-arc-clothoid curve, a clothoid curve-arc-clothoid curve, an acceleration curve-arc-deceleration curve, a uniform deceleration line, and a uniform speed line; The central angle δ of the clothoid curve-arc-deceleration curve, acceleration curve-arc-clothoid curve, clothoid curve-arc-clothoid curve and acceleration curve-arc-deceleration curve is the difference between the heading angles θ1 and θ2 of the vehicle at the two end points of the curve, which is positively correlated with the movement time. The time to pass the curve with the central angle δ is obtained by discrete calculation and fitting. The corresponding time function is

[0018] The time required for the vehicle to pass is obtained according to the time function.

[0019] As a further solution of the present invention: in said S3, the transition path includes two sections of clothoid curve-circular arc-clothoid curve and a section of uniform straight line, and the parameters of the clothoid curve-circular arc-clothoid curve are obtained by the intermediate node S T The heading angle θ T Determine that the calculation formula of the clothoid curve-circular arc-clothoid curve is:

[0020] Among them, H CAC (θ1, θ2) is the vertical height of the clothoid-arc-clothoid curve with an initial heading angle of θ1 and an ending heading angle of θ2, θ cr is the critical angle, and the initial heading angle is θ cr The vertical height y of the clothoid-arc-clothoid curve with the ending heading angle of 0 n+2 -ys ,θ n+2 is the heading angle of the starting point of the maneuvering path, θ s is the heading angle of the starting point, y n+2 is the ordinate of the starting point of the maneuvering path, y s is the ordinate of the starting point, n is the number of maneuvers; The length L of the uniform straight line including the curve in the transition path T , the length of the curve L T The calculation formula is;

[0021] Among them, L CAC (θ1, θ2) is the horizontal length of the clothoid curve-arc-clothoid curve with an initial heading angle of θ1 and an end heading angle of θ2, x n+2 is the horizontal coordinate of the starting point of the maneuvering path, x s is the horizontal coordinate of the starting point; The maneuvering path includes a section of clothoid curve-circular arc-deceleration curve / uniform deceleration straight line, several sections of acceleration motion-circular arc-deceleration motion curves and a section of acceleration motion-circular arc-clothoid curve; The entry path includes a straight line with uniform speed; The adjustment path includes a section of clothoid curve-circular arc-deceleration curve; The central angle δ of the clothoid curve-circular arc-deceleration curve of the adjustment path A for; , where θ et The final vehicle heading angle for passengers to load and get on board; Based on the vehicle's initial and final states, the parameters of the four parking path patterns are the central angle vector δ of the maneuvering path and the length L of the entry path. S ; and generate a parking path connecting any starting state and target point state near the target parking space to reduce the parameter dimension of the vehicle's basic motion curve.

[0022] As a further solution of the present invention: in S4, the parking path multi-objective optimization model includes optimization variables, comfort objective function and constraint conditions, and the optimization variable X is;

[0023] Among them, X is the optimization variable, [x eT , y eT , θ eT ] is the final parking state of the target vehicle, (x eT , y eT ) is the final coordinate of the rear axle center of the target vehicle; θ eTis the final heading angle of the target vehicle, δ is the center angle vector of the maneuvering path curve, L S is the length of the entry path segment; The comfort objective function includes the target vehicle's boarding and alighting comfort and the comfort of adjacent vehicles;

[0024] Among them, f1(X) is the comfort objective function, Δα T is the target vehicle’s boarding and alighting comfort, Δα L is the comfort of getting on and off the left adjacent vehicle, Δα R is the comfort of getting on and off the right adjacent vehicle, η A The comfort weight for getting on and off the adjacent vehicle; Constructing the objective function of parking time based on the time function of the basic path

[0025] Among them, f2(X) is the parking time objective function, T M is the time to pass the maneuvering path, δ i is the central angle of each curve in the maneuvering path; The constraints include the vehicle being completely within the target parking space in the final parking state, parking path parameters, passengers and cargo being able to get on and off the vehicle smoothly, passengers and cargo being able to enter and exit the parking space smoothly, and collision avoidance. The constraints for passengers and cargo being able to get on and off the vehicle smoothly are:

[0026] When Δα T When the rate is ≥30%, the target vehicle meets the requirement that passengers and cargo can get on and off the vehicle smoothly; Obtain a multi-objective optimization model for parking paths;

[0027] Among them, f ob (X) is the optimization objective function, g i (X) is the constraint condition, and N is the number of constraints.

[0028] As a further solution of the present invention: in S5, the parking path multi-objective optimization model is converted into an unconstrained optimization of optimization variables within a preset interval based on a penalty function to obtain a comfort optimization objective function and a parking time optimization objective function, wherein the comfort optimization objective function and the parking time optimization objective function are:

[0029]

[0030] Among them, f 1C(X) is the comfort optimization objective function with penalty function, f 2C (X) is the parking time optimization objective function with a penalty function, C1 is the comfort penalty constant, C2 is the parking time penalty constant, and J is the nonlinear constraint set including the smooth boarding and disembarking of passengers and cargo, the smooth entry and exit of passengers and cargo into and out of parking spaces, and collision avoidance constraints; Based on the comfort optimization objective function and the parking time optimization objective function, a multi-objective optimization model of a parking path with a penalty function is obtained. The multi-objective optimization model of a parking path with a penalty function is:

[0031] Among them, f obC (X) is the optimization objective function with penalty function, X D The feasible domain of optimization variables under other constraints; The automatic parking path is obtained by solving the problem, wherein the automatic parking path is an optimal parking path with high comfort and short parking time for passengers to load and get on and off the vehicle.

[0032] Compared with the prior art, the present invention has the following beneficial effects: 1. This solution improves the comfort of boarding and alighting for passengers and cargo, as well as parking time, in the optimized design of parking paths. By presetting vehicle motion parameters and parking path patterns, it reduces the dimensionality of path parameters, improves the efficiency of parking path planning, and meets real-time requirements.

[0033] 2. This solution uses the vehicle's basic motion curve based on the Ackerman model for path design, directly deriving a smooth path that meets vehicle kinematics and has continuous curvature, avoiding the increased collision risk caused by path smoothing. At the same time, it improves parking smoothness and reduces tire wear and steering assist pressure.

[0034] 3. This solution reduces the path parameter dimensionality by presetting vehicle motion parameters and four parking path patterns: transition path, maneuvering path, entry path, and adjustment path. It also uses a penalty function approach to transform the multi-objective optimization model for parking paths with multiple nonlinear constraints into an unconstrained optimization problem with optimization variables within a preset range. This reduces the time required for parking path planning and meets real-time requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 A schematic diagram showing the permitted and required door opening angles of a vehicle under the influence of adjacent obstacles; Figure 2 Schematic diagram of motion parameters corresponding to the basic motion curve of the vehicle based on the Ackerman model; Figure 3 Schematic diagram of the central angle of the vehicle's basic motion curve; Figure 4 Schematic diagram of the four parking path modes: transition, maneuver, entry, and adjustment; Figure 5 Schematic diagram of the final parking path solution selected for multi-objective optimization. DETAILED DESCRIPTION

[0036] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0037] Example: See also Figure 1-Figure 5 A parking path planning method based on an Ackerman model motion curve includes the following steps: S1: Obtain the vehicle's door opening angle based on the obstacles adjacent to the target parking space, and establish a vehicle passenger loading and unloading comfort characterization model, where the door opening angle is the angle allowed by the obstacles and the angle required for passengers to load and unload. S2: constructing a vehicle basic motion curve library based on the Ackerman model, the vehicle basic motion curve library including a number of vehicle basic motion curves, and obtaining the time required for the vehicle to pass the corresponding basic motion curves; S3: The basic motion curve is used to establish a four-segment parking path pattern consisting of a transition path, a maneuvering path, an approach path, and an adjustment path. A parking path is generated near the target parking space, connecting any starting state and target point state, to reduce the parameter dimension of the vehicle's basic motion curve. S4: Establishing a multi-objective optimization model for the parking path. The multi-objective optimization model for the parking path is based on the constraints of ensuring that the vehicle is completely within the target parking space in the final parking state, parking path parameters, smooth boarding and disembarking of passengers and cargo, smooth entry and exit of passengers and cargo into and out of the parking space, and collision avoidance. S5: Based on the penalty function, the parking path multi-objective optimization model is transformed and solved to obtain the automatic parking path.

[0038] Specifically, the present invention incorporates the comfort of passengers and cargo getting on and off the vehicle and the parking time into the optimized design of the parking path, thereby improving the comfort of passengers and cargo getting on and off the vehicle and the parking efficiency. Based on the basic vehicle motion curve of the Ackerman model, a four-segment parking path pattern is established, including a transition path, a maneuvering path, an entry path, and an adjustment path. A smooth path with continuous curvature that meets the vehicle kinematic requirements is directly generated, effectively avoiding the increased collision risk due to path smoothing, while improving parking smoothness, reducing tire wear and the pressure on the power steering system. By presetting vehicle motion parameters and parking path patterns, the dimensionality of path parameters is reduced, the efficiency of parking path planning is improved, and real-time requirements are met.

[0039] Preferably, Figure 1 As shown, in S1, based on the allowable door opening angle of the target vehicle under the influence of the adjacent obstacles in the target parking space and the opening angle required to ensure smooth boarding and disembarking of passengers and cargo, the adjacent obstacles are divided into several obstacle line segments. The allowable door opening angle under the influence of all obstacle line segments is calculated. First, it is determined whether the obstacle line segment will interfere with the opening of the door. If it does not interfere, the door angle can be opened to the maximum. The adjacent obstacles are divided into several obstacle line segments, and the allowable door opening angle α is calculated based on the several obstacle line segments.

[0040] Among them, α is the allowable opening angle of the door, α M is the maximum opening angle of the door without interference, α0, α m , α B , α U and α P⊥ They represent the endpoint Q0 when the door is not opened, the endpoint Q when the door is opened to the maximum angle, and m , the lower endpoint O of the obstacle segment LB , the upper endpoint O of the obstacle segment LU 、P ⊥ The angle between the line connecting the door pivot point P and the positive direction of the X axis, α s0 is the safety angle, α IN is the door opening angle allowed under the interference of obstacle line segment, l D is the door length, d m The distance between the door axis and the obstacle line segment O LU O LB The shortest distance, d m The calculation formula is as follows;

[0041] Among them, Pm is the distance between the door and the obstacle line segment O LU O L The intersection point, α P⊥ P⊥ The angle between the line connecting the door pivot point P and the positive direction of the X-axis; Allowable opening angle α of the door under the interference of obstacle line segment IN According to whether the interference of the obstacle line segment on the door is a line constraint or a point constraint, α IN The calculation formula is;

[0042] Among them, α P and α L These are the allowed opening angles of the door under point constraint and line constraint respectively.

[0043] As a further solution of the present invention: the door opening angle α required for passengers to get on and off the vehicle is calculated based on the preset space required for passengers to get off the vehicle with their belongings. r , α r The calculation formula is;

[0044] Among them, α r The door opening angle required for passengers and cargo to get on and off the vehicle, d r is the redundancy distance, W t is the size of the passenger and cargo, and k is a logical variable indicating whether there is a passenger or cargo at the door.

[0045] Preferably, Figure 1 As shown, the angle margin is obtained based on the door opening angle allowed and the door opening angle required for passengers and cargo to get on and off the vehicle;

[0046] Among them, Δα j is the door angle margin, which corresponds to the comfort variable for passengers getting on and off the vehicle. j is the allowable opening angle of door j, α rj The door opening angle required for door j when passengers and luggage can get on and off the vehicle; Based on the angle margin, a characterization model of passenger comfort when loading and unloading is derived;

[0047] Among them, Δα is the comfort of passengers getting on and off the vehicle, Δα ij is the angle margin of door j under the influence of obstacle segment i, n O is the number of obstacle segments, n D The number of doors.

[0048] Preferably, Figure 2As shown, in S2, the vehicle speed, acceleration, equivalent front wheel angle and equivalent front wheel angular acceleration are preset, a coordinate system is established with the center of the vehicle rear axle, and an Ackerman model of the vehicle with respect to time is established based on the Ackerman model;

[0049] Among them, x E is the horizontal coordinate of the center of the vehicle's rear axle, y E is the vertical coordinate of the rear axle center of the vehicle, θ is the vehicle heading angle, t is the time, φ is the equivalent front wheel turning angle, l A is the vehicle wheelbase, v is the vehicle speed; According to the vehicle Ackerman model, several basic vehicle motion curves are obtained. Several basic vehicle motion curves form a basic vehicle motion curve library for parking path design. A smooth path that meets vehicle kinematics and has continuous curvature is obtained to avoid the increased collision risk caused by path smoothing. The vehicle speed, acceleration, equivalent front wheel angle, and equivalent front wheel angle acceleration are preset to reduce the parameter dimension of the parking path. The time required to pass each basic path is directly obtained to evaluate parking efficiency. Preset the vehicle's motion parameters to reduce the parameter dimension of the path. Preset the maximum speed of the vehicle to v m , the maximum equivalent front wheel turning angle is φ m The vehicle accelerates uniformly from rest to v m The time required is t v The equivalent front wheel turning angle increases uniformly from 0 to φ m The required time is also set as t v .like Figure 2 As shown, set different exercise time t m The basic motion curve is obtained by the change pattern of vehicle speed v and equivalent front wheel angle φ. Figure 2 As shown in (a), the vehicle speed is set in [0, t m -t v ] time is v m Remain unchanged, [t m -t v , t m ] time uniformly decreases to 0; the equivalent front wheel angle decreases to 0 in [0, t v ] increases uniformly from 0 to φ m ,[t v , t m -t v ] time is φ m Remain unchanged; [t m -t v , t m ] uniformly decreases to 0 during the movement time; when the movement time t m ≥2t vWhen t m <2t v When Figure 2 The motion parameters of acceleration-arc-clothoid curve (MAC), acceleration-arc-deceleration motion curve (MAM), cyclotron-arc-clothoid curve (CAC), uniform deceleration line (DL) and uniform speed line (UL) are set as follows: Figure 2 Middle (b), Figure 2 Middle (c), Figure 2 Middle (d), Figure 2 (e) and Figure 2 As shown in (f); The basic motion curves of the vehicle include the clothoid curve-arc-deceleration curve (CAM), the acceleration curve-arc-clothoid curve (MAC), the clothoid curve-arc-clothoid curve (CAC), the acceleration curve-arc-deceleration curve (MAM), the uniform deceleration line (DL) and the uniform speed line (UL); The central angle δ of the clothoid curve-arc-deceleration curve (CAM), acceleration curve-arc-clothoid curve (MAC), clothoid curve-arc-clothoid curve (CAC) and acceleration curve-arc-deceleration curve (MAM) is the difference between the heading angles θ1 and θ2 of the vehicle at the two end points of the curve. It is positively correlated with the movement time. The time to pass the curve with the central angle δ is obtained by discrete calculation and fitting. The corresponding time function is:

[0050] The time required for the vehicle to pass is obtained according to the time function.

[0051] Preferably, in S3, a parking path mode is set to generate a parking path connecting any starting state and target point state near the target parking space, further reducing the path parameter dimension, such as Figure 4 As shown in (a), a four-segment parking path pattern including transition path, maneuvering path, entry path and adjustment path is established based on the basic motion curve, as shown in Figure 4 As shown in (b), the transition path consists of two segments of clothoid curve-circular arc-clothoid curve and a uniform straight line. Its parameters are determined by the starting point state and the starting point state of the maneuvering path. The parameters of the clothoid curve-circular arc-clothoid curve are determined by the intermediate node S T The heading angle θ T OK, with Figure 4 In the embodiment in (b), the formula for calculating the clothoid curve-arc-clothoid curve is:

[0052] Among them, H CAC(θ1, θ2) is the vertical height of the CAC curve with an initial heading angle of θ1 and an ending heading angle of θ2, cr is the critical angle, and the initial heading angle is θ cr The vertical height y of the CAC curve with the ending heading angle of 0 n+2 -y s ,θ n+2 is the heading angle of the starting point of the maneuvering path, θ s is the heading angle of the starting point, y n+2 is the ordinate of the starting point of the maneuvering path, y s is the ordinate of the starting point, n is the number of maneuvers; The length L of the uniform straight line including the curve in the transition path T , the length of the curve L T The calculation formula is;

[0053] Among them, L CAC (θ1, θ2) is the horizontal length of the clothoid curve-arc-clothoid curve with an initial heading angle of θ1 and an end heading angle of θ2, x n+2 is the horizontal coordinate of the starting point of the maneuvering path, x s is the horizontal coordinate of the starting point; like Figure 4 As shown in (e), the maneuvering path includes a clothoid curve-circular arc-deceleration curve / uniform deceleration line, several acceleration motion-circular arc-deceleration motion curves, and an acceleration motion-circular arc-clothoid curve. The maneuvering path is determined by the number of maneuvers and the central angle of each curve, that is, by the central angle vector δ = [δ1, δ2, ..., δn]. In particular, the maneuvering path of a single maneuver (n = 1) consists of a DL curve and a MAC curve, and the maneuvering path of a secondary maneuver (n = 2) consists of a CAM curve and a MAC curve. like Figure 4 As shown in (c), the approaching path includes a straight line with a uniform velocity, whose length is L S Sure; The adjustment path includes a clothoid curve, an arc, and a deceleration curve. The adjustment path is a CAM curve, and its parameters are determined by the final state of the vehicle. like Figure 4 As shown in (d), the central angle δ of the clothoid curve-arc-deceleration curve of the adjustment path A for; , where θ et The final vehicle heading angle for passengers to load and get on board; Based on the vehicle's initial and final states, the parameters of the four parking path modes are the central angle vector δ of the maneuvering path and the length of the entry path L. S; and generate a parking path connecting any starting state and target point state near the target parking space to reduce the parameter dimension of the vehicle's basic motion curve.

[0054] Preferably, in S4, a multi-objective parking path optimization model is established, with the comfort of passengers getting on and off the target vehicle and adjacent vehicles and the parking time as optimization objectives, the final parking state of the vehicle and the parameters of the four parking paths as optimization variables, and the constraints of the vehicle being completely within the target parking space in the final parking state, the parking path parameter range, the smooth loading and unloading of passengers, the smooth entry and exit of passengers, and collision avoidance. By factoring the comfort of passengers getting on and off the vehicle into the parking path planning and taking the parking time into consideration, an optimal parking path with high comfort and short loading and unloading time is obtained. The multi-objective parking path optimization model includes optimization variables, a comfort objective function, and constraints, and the optimization variable X is:

[0055] Among them, X is the optimization variable, [x eT , y eT , θ eT ] is the final parking state of the target vehicle, (x eT , y eT ) is the final coordinate of the rear axle center of the target vehicle; θ eT is the final heading angle of the target vehicle, δ is the center angle vector of the maneuvering path curve, L S is the length of the entry path segment; The comfort objective function includes the target vehicle’s boarding and alighting comfort and the comfort of neighboring vehicles;

[0056] Among them, f1(X) is the comfort objective function, Δα T is the target vehicle’s boarding and alighting comfort, Δα L is the comfort of getting on and off the left adjacent vehicle, Δα R is the comfort of getting on and off the right adjacent vehicle, η A Weight for the comfort of getting on and off the adjacent vehicle; Constructing the objective function of parking time based on the time function of the basic path

[0057] Among them, f2(X) is the parking time objective function, T M is the time to pass the maneuvering path, δ i is the central angle of each curve in the maneuvering path; The constraints include the vehicle being completely within the target parking space in the final parking state, parking path parameters, passengers and cargo being able to get on and off the vehicle smoothly, passengers and cargo being able to enter and exit the parking space smoothly, and collision avoidance. The constraints for passengers and cargo being able to get on and off the vehicle smoothly are:

[0058] When Δα T When the rate is ≥30%, the target vehicle meets the requirement that passengers and cargo can get on and off the vehicle smoothly; Obtain a multi-objective optimization model for parking paths;

[0059] Among them, f ob (X) is the optimization objective function, g i (X) is the constraint condition, and N is the number of constraints.

[0060] Preferably, in S5, vehicle and parking space parameters, adjacent obstacle parameters, the initial state of the target vehicle, and the target parking space are input, a parking path multi-objective optimization model is solved, and an automatic parking path is obtained. Based on a penalty function, the parking path multi-objective optimization model is converted into an unconstrained optimization of optimization variables within a preset interval to obtain a comfort optimization objective function and a parking time optimization objective function. The comfort optimization objective function and the parking time optimization objective function are:

[0061] Among them, f 1C (X) is the comfort optimization objective function with penalty function, f 2C (X) is the parking time optimization objective function with a penalty function, C1 is the comfort penalty constant, C2 is the parking time penalty constant, and J is the nonlinear constraint set including the smooth boarding and disembarking of passengers and cargo, the smooth entry and exit of passengers and cargo into and out of parking spaces, and collision avoidance constraints; Based on the comfort optimization objective function and the parking time optimization objective function, the multi-objective optimization model of parking path with penalty function is obtained. The multi-objective optimization model of parking path with penalty function is:

[0062] Among them, f obC (X) is the optimization objective function with penalty function, X D The feasible domain of optimization variables under other constraints; The automatic parking path is obtained, which is the optimal parking path with high comfort and short parking time for passengers to load and unload. The penalty function method is used to transform the multi-objective optimization model of multiple nonlinear constrained parking paths into an unconstrained optimization problem with optimization variables within a certain range, and the multi-objective optimization algorithm is used to solve it, thereby reducing the parking path planning time. The multi-objective optimization model solves a set of optimal solutions, and the final solution is determined using the following principles: Figure 5 As shown in the figure, if the optimal solution set contains a solution that meets the comfortable boarding and alighting conditions (Δα ≥ 30%), the solution that meets the boarding and alighting comfort requirements and has the shortest parking time is selected. If the optimal solution set does not contain a solution that meets the boarding and alighting comfort requirements, the solution with the highest boarding and alighting comfort index is selected as the final solution. Based on the final solution, the optimal parking path with high boarding and alighting comfort and short parking time is obtained.

[0063] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A parking path planning method based on Ackerman model motion curve, characterized in that: The following steps are involved: S1: Obtaining the vehicle's door opening angle based on the obstacles adjacent to the target parking space, and establishing a vehicle passenger boarding and alighting comfort model, wherein the door opening angle is the door opening angle allowed by the obstacles and the door opening angle required for boarding and alighting by the passenger; S2: constructing a vehicle basic motion curve library based on the Ackerman model, wherein the vehicle basic motion curve library includes a plurality of vehicle basic motion curves, and obtaining the time required for the vehicle to pass the corresponding vehicle according to the vehicle basic motion curves; S3: Establishing a four-segment parking path pattern based on the basic motion curve, including a transition path, a maneuvering path, an approach path, and an adjustment path, and generating a parking path connecting any starting state and target point state near the target parking space, so as to reduce the parameter dimension of the basic motion curve of the vehicle; S4: Establishing a multi-objective optimization model for a parking path, wherein the multi-objective optimization model for the parking path is based on constraints such as the vehicle being completely within the target parking space in the final parking state, parking path parameters, smooth boarding and disembarking of passengers and cargo, smooth entry and exit of passengers and cargo into and out of the parking space, and collision avoidance; S5: Transforming and solving the parking path multi-objective optimization model based on the penalty function to obtain an automatic parking path.

2. The parking path planning method based on the Ackerman model motion curve according to claim 1, characterized in that: In S1, the adjacent obstacle is divided into a plurality of obstacle line segments, and the door opening angle α is calculated based on the plurality of obstacle line segments; ； Among them, α is the allowable opening angle of the door, α M is the maximum opening angle of the door without interference, α0, α m , α B , α U and α P⊥ They represent the endpoint Q0 when the door is not opened, the endpoint Q when the door is opened to the maximum angle, and m , the lower endpoint O of the obstacle segment LB , the upper endpoint O of the obstacle segment LU 、P ⊥ The angle between the line connecting the door pivot point P and the positive direction of the X axis, α s0 is the safety angle, α IN is the door opening angle allowed under the interference of obstacle line segment, l D is the door length, d m The distance between the door axis and the obstacle line segment O LU O LB The shortest distance, d m The calculation formula is as follows; ； Among them, Pm is the distance between the straight line where the door is located and the obstacle line segment O LU O L The intersection point, α P⊥ P ⊥ The angle between the line connecting the door pivot point P and the positive direction of the X-axis; Allowable door opening angle α under obstacle segment interference IN According to whether the interference of the obstacle line segment on the door is a line constraint or a point constraint, α IN The calculation formula is; ； Among them, α P and α L These are the allowed opening angles of the door under point constraint and line constraint respectively.

3. The parking path planning method based on the Ackerman model motion curve according to claim 2, characterized in that: Calculate the door opening angle α required for passengers to get on and off the vehicle based on the preset space required for passengers to get off the vehicle with their luggage r , α r The calculation formula is; ； Among them, α r The door opening angle required for passengers and cargo to get on and off the vehicle, d r is the redundancy distance, W t is the size of the passenger and cargo, and k is a logical variable indicating whether there is a passenger or cargo at the door.

4. The parking path planning method based on the Ackerman model motion curve according to claim 3, characterized in that: Obtaining an angle margin based on the door's allowable opening angle and the door's opening angle required for passengers and cargo to get on and off the vehicle; ； Among them, Δα j is the door angle margin, which corresponds to the comfort variable for passengers getting on and off the vehicle. j is the allowable opening angle of door j, α rj The door opening angle required for door j when passengers and luggage can get on and off the vehicle; A comfort characterization model for passengers getting on and off the vehicle with cargo is derived based on the angle margin; ； Among them, Δα is the comfort of passengers getting on and off the vehicle, Δα ij is the angle margin of door j under the influence of obstacle segment i, n O is the number of obstacle segments, n D The number of doors.

5. The parking path planning method based on the Ackerman model motion curve according to claim 4 is characterized in that: In said S2, the vehicle speed, acceleration, equivalent front wheel steering angle and equivalent front wheel steering acceleration are preset, a coordinate system is established with the center of the rear axle of the vehicle, and an Ackermann model of the vehicle with respect to time is established based on the Ackermann model; ； Among them, x E is the horizontal coordinate of the center of the vehicle's rear axle, y E is the vertical coordinate of the rear axle center of the vehicle, θ is the vehicle heading angle, t is the time, φ is the equivalent front wheel turning angle, l A is the vehicle wheelbase, v is the vehicle speed; According to the vehicle Ackerman model, a number of basic vehicle motion curves are obtained to obtain a smooth path that satisfies the vehicle kinematics and has continuous curvature, wherein the basic vehicle motion curves include a clothoid curve-arc-deceleration curve, an acceleration curve-arc-clothoid curve, a clothoid curve-arc-clothoid curve, an acceleration curve-arc-deceleration curve, a uniform deceleration line, and a uniform speed line; The central angle δ of the clothoid curve-arc-deceleration curve, acceleration curve-arc-clothoid curve, clothoid curve-arc-clothoid curve and acceleration curve-arc-deceleration curve is the difference between the heading angles θ1 and θ2 of the vehicle at the two end points of the curve, which is positively correlated with the movement time. The time to pass the curve with the central angle δ is obtained by discrete calculation and fitting. The corresponding time function is ； The time required for the vehicle to pass is obtained according to the time function.

6. The parking path planning method based on the Ackerman model motion curve according to claim 5, characterized in that: In S3, the transition path includes two sections of clothoid curve-circular arc-clothoid curve and a section of uniform straight line. The parameters of the clothoid curve-circular arc-clothoid curve are obtained by the intermediate node S T The heading angle θ T Determine that the calculation formula of the clothoid curve-circular arc-clothoid curve is: ； Among them, H CAC (θ1, θ2) is the vertical height of the clothoid-arc-clothoid curve with an initial heading angle of θ1 and an ending heading angle of θ2, θ cr is the critical angle, and the initial heading angle is θ cr The vertical height y of the clothoid-arc-clothoid curve with the ending heading angle of 0 n+2 -y s ,θ n+2 is the heading angle of the starting point of the maneuvering path, θ s is the heading angle of the starting point, y n+2 is the ordinate of the starting point of the maneuvering path, y s is the ordinate of the starting point, n is the number of maneuvers; The length L of the uniform straight line including the curve in the transition path T , the length of the curve L T The calculation formula is; ； Among them, L CAC (θ1, θ2) is the horizontal length of the clothoid curve-arc-clothoid curve with an initial heading angle of θ1 and an end heading angle of θ2, x n+2 is the horizontal coordinate of the starting point of the maneuvering path, x s is the horizontal coordinate of the starting point; The maneuvering path includes a section of clothoid curve-circular arc-deceleration curve / uniform deceleration straight line, several sections of acceleration motion-circular arc-deceleration motion curves and a section of acceleration motion-circular arc-clothoid curve; The driving path includes a straight line with uniform speed; The adjustment path includes a section of clothoid curve-circular arc-deceleration curve; The central angle δ of the clothoid curve-circular arc-deceleration curve of the adjustment path A for; , where θ et The final vehicle heading angle for passengers to load and get on board; Based on the vehicle's initial and final states, the parameters of the four parking path patterns are the central angle vector δ of the maneuvering path and the length L of the entry path. S ; and generate a parking path connecting any starting state and target point state near the target parking space to reduce the parameter dimension of the vehicle's basic motion curve.

7. The parking path planning method based on the Ackerman model motion curve according to claim 6, characterized in that: In S4, the parking path multi-objective optimization model includes optimization variables, comfort objective function and constraint conditions, and the optimization variable X is: ； Among them, X is the optimization variable, [x eT , y eT , θ eT ] is the final parking state of the target vehicle, (x eT , y eT ) is the final coordinate of the rear axle center of the target vehicle; θ eT is the final heading angle of the target vehicle, δ is the center angle vector of the maneuvering path curve, L S is the length of the entry path segment; The comfort objective function includes the target vehicle's boarding and alighting comfort and the comfort of adjacent vehicles; ； Among them, f1(X) is the comfort objective function, Δα T is the target vehicle’s boarding and alighting comfort, Δα L is the comfort of getting on and off the left adjacent vehicle, Δα R is the comfort of getting on and off the right adjacent vehicle, η A Weight for the comfort of getting on and off the adjacent vehicle; Constructing the objective function of parking time based on the time function of the basic path ； ； Among them, f2(X) is the parking time objective function, T M is the time to pass the maneuvering path, δ i is the central angle of each curve in the maneuvering path; The constraints include the vehicle being completely within the target parking space in the final parking state, parking path parameters, passengers and cargo being able to get on and off the vehicle smoothly, passengers and cargo being able to enter and exit the parking space smoothly, and collision avoidance. The constraints for passengers and cargo being able to get on and off the vehicle smoothly are: ； When Δα T When the rate is ≥30%, the target vehicle meets the requirement that passengers and cargo can get on and off the vehicle smoothly; Obtain a multi-objective optimization model for parking paths; ； Among them, f ob (X) is the optimization objective function, g i (X) is the constraint condition, and N is the number of constraints.

8. The parking path planning method based on the Ackerman model motion curve according to claim 7, characterized in that: In S5, the parking path multi-objective optimization model is converted into an unconstrained optimization of optimization variables within a preset interval based on a penalty function to obtain a comfort optimization objective function and a parking time optimization objective function. The comfort optimization objective function and the parking time optimization objective function are: ； ； Among them, f 1C (X) is the comfort optimization objective function with penalty function, f 2C (X) is the parking time optimization objective function with a penalty function, C1 is the comfort penalty constant, C2 is the parking time penalty constant, and J is the nonlinear constraint set including the ability of passengers and cargo to get on and off the vehicle smoothly, the ability of passengers and cargo to enter and exit the parking space smoothly, and collision avoidance constraints; Based on the comfort optimization objective function and the parking time optimization objective function, a multi-objective optimization model of a parking path with a penalty function is obtained. The multi-objective optimization model of a parking path with a penalty function is: ； Among them, f obC (X) is the optimization objective function with penalty function, X D The feasible domain of optimization variables under other constraints; The automatic parking path is obtained by solving the problem, wherein the automatic parking path is an optimal parking path with high comfort and short parking time for passengers to load and get on and off the vehicle.

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