A method for optimizing the dynamic model of path tracking error for autonomous vehicles

Abstract

The present invention discloses a path tracking error dynamic model optimization method for an autonomous driving vehicle. The method comprises the following steps: designing an LQR controller for the path tracking error dynamic model, obtaining an LQR controller output according to an LQR controller state quantity, and using the LQR controller output as an input quantity of the path tracking error dynamic model; adding a feedforward control control quantity to the input quantity of the path tracking error dynamic model to eliminate the steady-state error of the path tracking error dynamic model; performing multi-objective optimization on the weighting coefficients in the LQR controller using an NSGA3 algorithm; recording the weighting coefficients in the LQR controller corresponding to each vehicle speed value to obtain the optimal values ​​of the weighting coefficients of the LQR controller; and substituting the optimal values ​​of the weighting coefficients of the LQR controller into the LQR controller to obtain an optimized path tracking error dynamic model, thereby improving the path tracking accuracy of the vehicle's lateral motion and the adaptability of the controller.

Description

Technical Field

[0001] The present invention relates to the field of automobile control technology, and in particular to a lateral control method for an autonomous driving vehicle. Background Art

[0002] Lateral motion control is a core technology in autonomous driving. Based on the target path information from the upper-level decision-making planning LQR controller, it outputs corresponding steering control commands to control the vehicle along the target path. The effectiveness of lateral motion control not only affects the accuracy of the vehicle's ability to follow the target path, but also affects the vehicle's overall stability and comfort.

[0003] Currently, mainstream control strategies for lateral motion controllers in autonomous driving include pure tracking algorithms, PID control, sliding mode control, optimal control, and model predictive control. Among them, the LQR controller is widely used in the field of lateral motion control in autonomous driving due to its clear physical meaning of model parameters and relatively good versatility. However, in most related studies, there is no definitive analytical method for determining the weighting coefficients (i.e., weighting matrix) in the LQR controller. Currently, most literature on optimizing the weighting coefficients in LQR controllers primarily transforms multi-objective optimization into single-objective optimization by setting weights. While this simplifies the multi-objective optimization problem, it is nearly impossible to set weights that match actual conditions. Furthermore, the existing LQR controller design process often relies on the designer's subjective experience to determine the weighting coefficients through trial and error, which to some extent limits the path tracking accuracy and controller adaptability. Summary of the Invention

[0004] The present invention provides a path tracking error dynamics model optimization method for an autonomous driving vehicle, which is used to improve the path tracking accuracy of the vehicle's lateral motion and improve the adaptability of the controller.

[0005] To achieve the above effects, the technical solutions of the present invention are as follows:

[0006] A method for optimizing a path tracking error dynamics model of an autonomous vehicle, applied to the autonomous vehicle, comprises the following steps:

[0007] S1: Establish a vehicle dynamics model and design a path tracking error dynamics model based on the vehicle dynamics model;

[0008] S2: Design an LQR controller for the path tracking error dynamics model, obtain the LQR controller output according to the LQR controller state, and use the LQR controller output as the input of the path tracking error dynamics model;

[0009] S3: adding a control amount of feedforward control to the input amount of the path tracking error dynamics model to eliminate the steady-state error of the path tracking error dynamics model;

[0010] S4: Use the NSGA3 algorithm to perform multi-objective optimization on the weighting coefficients in the LQR controller;

[0011] S5: Repeat S4 until every speed value in the speed range is traversed, record the weighting coefficient in the LQR controller corresponding to each speed value, and obtain the optimal value of the LQR controller weighting coefficient; substitute the optimal value of the LQR controller weighting coefficient into the LQR controller to obtain the optimized path tracking error dynamic model.

[0012] Furthermore, step S1 establishes a vehicle dynamics model specifically by establishing a vehicle dynamics model based on the vehicle's force conditions, only considering the vehicle's lateral and longitudinal force conditions, assuming that the steering angles and cornering stiffnesses of the two wheels on the front and rear axles of the vehicle are equal, the rear wheels of the vehicle do not steer, and ignoring the effect of air resistance on the vehicle, simplifying the vehicle into a two-degree-of-freedom single-vehicle model; according to Newton's second law combined with the force conditions of the front and rear wheels of the vehicle, we have:

[0013] ma y =F yf cos(δ)+F yr (1)

[0014] Where m is the vehicle's mass; a y is the Y-axis acceleration; F yf is the vehicle front wheel cornering force, F yr is the vehicle rear wheel cornering force;

[0015] According to the moment balance and the forces on the front and rear wheels of the vehicle, the distance between the force point and the center of gravity of the vehicle is:

[0016]

[0017] Where I is the vehicle's Z-axis moment of inertia; φ is the angle between the vehicle's axle and the X-axis. is the second-order derivative of the angle between the vehicle's axle and the X-axis; δ is the vehicle's front wheel turning angle; b is the vehicle's rear suspension length;

[0018] Assuming that the vehicle's front wheel steering angle δ is extremely small, cos(δ)≈1, then equations (1) and (2) can be rewritten as:

[0019] ma y =C αf α f +C αr α r (3)

[0020]

[0021] Where C af 、C αrare the lateral stiffness of the front and rear wheels of the vehicle respectively; a f 、a r are the sideslip angles of the front and rear wheels respectively; a is the length of the vehicle's front suspension;

[0022] Vehicle Y-axis acceleration a y Expressed as:

[0023]

[0024] Where, Represents the second-order derivative of the vehicle's y-axis velocity, v x Indicates the vehicle's X-axis speed; is the first derivative of the angle between the vehicle axle and the X-axis;

[0025] Side slip angle a of the front wheel f , rear wheel side slip angle a r Respectively expressed as:

[0026]

[0027]

[0028] In the formula represents the vehicle's Y-axis speed. Substituting equations (5) to (7) into equations (3) and (4), we obtain:

[0029]

[0030]

[0031] Where, is the second-order derivative of the angle between the vehicle's axle and the X-axis; the final vehicle dynamics model is:

[0032]

[0033] Right now

[0034] Where u = (δ), which represents the front wheel turning angle of the vehicle.

[0035] Furthermore, step S1 designs a path tracking error dynamic model, specifically by projecting the vehicle into a natural coordinate system and establishing a path tracking error dynamic model with lateral error and heading error relative to the desired path as state variables; projecting the vehicle coordinate system into a natural coordinate system, decoupling vehicle control into lateral control and longitudinal control, and reducing control complexity;

[0036] Assume the lateral error of the vehicle is d and the heading error is θ-θ r, θ is the heading angle, θr is the desired heading angle, the velocity of the projection point is S, and according to the relationship between the vectors, the lateral error d can be obtained as:

[0037]

[0038] Where, is the projection normal direction of the vehicle speed v in the natural coordinate system; taking the derivative of formula (11), we can get:

[0039]

[0040] Where, is the actual position of the vehicle, is the vehicle projection position vector, It is expressed as follows;

[0041]

[0042]

[0043] Where v represents the vehicle speed; τ is the direction of the vehicle speed v, τ r is the projection tangent direction of the vehicle speed v in the natural coordinate system; Substitute equations (13) and (14) into equation (12), and according to β is the angle between the vehicle speed v and the X axis; we get:

[0044]

[0045]

[0046] At the same time, β, As a small amount close to 0, equation (15) can be rewritten as:

[0047]

[0048] Let the lateral error e d =d, then the heading error So,

[0049]

[0050]

[0051]

[0052]

[0053] Combining Equations (17) to (20) with the dynamic model of Equation (10) yields the path tracking error dynamic model: for:

[0054]

[0055] Where,

[0056]

[0057] Furthermore, step S3 is specifically as follows: adding a feedforward control quantity δ on the basis of the LQR controller f To eliminate the LQR controller; after adding feedforward control, the input of the path tracking error dynamic model is obtained as follows:

[0058] u(k)=-Ke rr (k)+δ f (twenty four)

[0059] Substituting equation (24) into equation (21), we can obtain the stabilized e rr :

[0060]

[0061] Where, ) is the desired road curvature information, and the curvature information is and The ratio of

[0062] Expand the above formula to get:

[0063]

[0064] Where k1 and k3 are the parameters in the LQR controller feedback gain matrix K; the lateral error e d The steady-state error of is eliminated by the feedforward control, while the heading error The steady-state error of cannot be eliminated; let The control quantity δ of feedforward control f Expressed as:

[0065]

[0066] Furthermore, in step S4, the NSGA3 algorithm is used to perform multi-objective optimization on the weight coefficients in the LQR controller. Specifically, the elements in the weight matrix R are set to fixed values, and the NSGA3 algorithm is used to optimize the weight coefficients q1, q2, q3, and q4 in the weight matrix Q of the LQR controller in step S2. This realizes multi-objective optimization of the weight coefficients in the LQR controller, which can be expressed as:

[0067]

[0068] Where L is the fitness function of the NSGA3 algorithm.

[0069] Furthermore, in step S4, the weighting coefficients in the LQR controller are optimized by multiple objectives, specifically,

[0070] Step S4.1: Initialize the population: Initialize the parameters of the NSGA3 algorithm: maximum number of iterations, population size, crossover probability, mutation probability; generate an initial population P of size N according to the LQR controller weight coefficients q1, q2, q3, q4 t , each individual Xi=(i=1,2,…N) in the population is a decision variable, and the individual initial value is set to the random value of the LQR controller weight coefficient;

[0071] Step S4.2: Population non-dominated sorting: The individuals in the population are divided into several levels according to their mutual dominance relationship, all individuals in the population are normalized and associated with the reference point;

[0072] Step S4.3: Use traditional genetic operators to perform inheritance: select, cross, and mutate the population to generate a descendant population Q with a population size of N. t ;

[0073] Step S4.4: Merge populations: Merge the parent and offspring populations to form a population R of size 2N t =P t ∪Q t , perform non-dominated sorting, normalize the individuals in the population and associate the individuals with the reference point to obtain the non-dominated sorting result;

[0074] Step S4.5: Elite retention strategy: select the population R from the merged population according to the non-dominated sorting result. t Select the first N individuals as the parent population P t+1 ;

[0075] Step S4.6: If Gen is not equal to the maximum number of iterations set value, then Gen = Gen + 1, and return to step S4.3; if Gen is equal to the maximum number of iterations set value, the iteration is terminated and the optimal Pareto solution is output; that is, when the number of iterations is equal to the set value, the population with N individuals after the iteration is used as the Pareto optimal solution, forming an actual frontier surface that is closest to the theoretical frontier surface.

[0076] Furthermore, the step S4.2 of population non-dominated sorting specifically includes: sorting the population non-dominated into several different non-dominated layers (F1, F2, ...), and successively adding the solutions of each non-dominated layer to the new population S t Until the new population S t The size is equal to N, and the last frontier is assumed to be F1. If the new population S t The size of is equal to N, then the initial population P of the next iteration t+1 =St , if the new population S t If the size is greater than N, a selection operation based on the reference point is performed, the objective function is standardized and a reference set is created, a mapping relationship between the population individuals and the reference point is constructed, and the mapping relationship is the distance relationship between the population individuals and the reference point. The population closest to the reference point is selected to join the new population S t Until the new population S t The size of is equal to N.

[0077] Furthermore, step S4.5 is as follows: select and generate a new population: select the first N individuals as the parent population P t+1 , by the tth generation, a t For population P t The best individual in the parent population P t+1 For the new generation population, if the parent population P t+1 There is no superior individual a t The best individual, then the best individual a t Join the parent population P t+1 As the parent population P t+1 individuals.

[0078] Furthermore, step S5 obtains the optimal value of the weighted coefficient of the LQR controller as follows: repeat step S4, traverse the vehicle speed values ​​of the preset step size at low, medium and high speeds, obtain a set of Pareto optimal solutions each time step S4 is executed, and use the Pareto optimal solution as the optimal value of the weighted coefficient of the LQR controller; and record one of the sets of Pareto optimal solutions after the iteration, until each vehicle speed value in the speed range is traversed, record the weighted coefficient in the LQR controller corresponding to each vehicle speed value, and obtain the optimal value of the weighted coefficient of the LQR controller.

[0079] It should be noted that, in the formula of the present invention, one dot on a letter represents the first-order derivative of the letter quantity, and two dots represent the second-order derivative.

[0080] The Pareto optimal solution is a set of K values. The Pareto optimal solution at each vehicle speed, i.e., the gain matrix of the LQR controller, is no longer required to be calculated using NSGA3. The Pareto optimal solution is provided to the LQR controller.

[0081] In the above scheme, the present invention takes the path tracking error model as the research object, designs the LQR controller, considers the expected curvature information of the road, and adds the control quantity of feedforward control to eliminate the steady-state error of the LQR controller; uses the global search optimization capability of the NSGA3 algorithm to perform multi-objective optimization on the weighted coefficients of the LQR controller, improves the design efficiency of the LQR controller, ensures the optimal control performance, and provides new ideas for subsequent lateral control strategies of autonomous driving vehicles.

[0082] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0083] The present invention adds a feedforward control variable to the general lateral motion LQR controller to eliminate the steady-state error of the path tracking error dynamic model. By utilizing the global search capability of the NSGA3 algorithm, the lateral error and heading error of the vehicle path tracking are used as the objective function to calculate the optimal value of the weighting coefficient, thereby reducing the complexity of the LQR controller, improving the accuracy of the LQR controller, and ensuring that the LQR controller has a good tracking control effect on the target path. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] The accompanying drawings are for illustrative purposes only and are not to be construed as limiting the present invention. To better illustrate the present embodiment, certain components of the accompanying drawings may be omitted, enlarged, or reduced in size, and do not represent the dimensions of actual products. It is understandable to those skilled in the art that certain well-known structures and their descriptions may be omitted from the accompanying drawings.

[0085] Figure 1 A flowchart of a method provided in an embodiment of the present invention;

[0086] Figure 2 A flowchart of multi-objective optimization of the weighting coefficients in the LQR controller in step 4 provided in an embodiment of the present invention;

[0087] Figure 3a is a vehicle dynamics model diagram provided by an embodiment of the present invention;

[0088] Figure 3b is a vehicle coordinate conversion diagram provided by an embodiment of the present invention;

[0089] Figure 4a is a schematic diagram of lateral error provided by an embodiment of the present invention;

[0090] Figure 4b is a schematic diagram of heading error provided by an embodiment of the present invention;

[0091] Figure 4c This is a schematic diagram of a path tracking result provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0092] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. 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.

[0093] Notes on terms in the text:

[0094] LQR: linearquadraticregulator, linear quadratic regulator;

[0095] NSGA3: non-dominated sorted genetic algorithm-Ⅲ; NSGA3 algorithm.

[0096] Example 1

[0097] For easier understanding, see Figure 1-Figure 2 An embodiment of a method for optimizing a path tracking error dynamics model of an autonomous driving vehicle provided by the present invention includes the following steps:

[0098] S1: Establish a vehicle dynamics model and design a path tracking error dynamics model based on the vehicle dynamics model;

[0099] S2: Design an LQR controller for the path tracking error dynamics model, obtain the LQR controller output according to the LQR controller state, and use the LQR controller output as the input of the path tracking error dynamics model;

[0100] S3: adding a control amount of feedforward control to the input amount of the path tracking error dynamics model to eliminate the steady-state error of the path tracking error dynamics model;

[0101] S4: Use the NSGA3 algorithm to perform multi-objective optimization on the weighting coefficients in the LQR controller;

[0102] S5: Repeat S4 until every speed value in the speed range is traversed, record the weighting coefficient in the LQR controller corresponding to each speed value, and obtain the optimal value of the LQR controller weighting coefficient; substitute the optimal value of the LQR controller weighting coefficient into the LQR controller to obtain the optimized path tracking error dynamic model.

[0103] Step S1 establishes a vehicle dynamics model. Specifically, the vehicle dynamics model is established based on the vehicle's force conditions, only considering the vehicle's lateral and longitudinal forces. It is assumed that the steering angles and cornering stiffnesses of the two wheels on the front and rear axles of the vehicle are equal, the rear wheels of the vehicle do not steer, and the effect of air resistance on the vehicle is ignored. The vehicle is simplified to a two-degree-of-freedom single vehicle model. According to Newton's second law and the force conditions of the front and rear wheels of the vehicle, the following is obtained:

[0104] ma y =F yf cos(δ)+F yr (1)

[0105] Where m is the vehicle's mass; a yis the Y-axis acceleration; F yf is the vehicle front wheel cornering force, F yr is the vehicle rear wheel cornering force;

[0106] According to the moment balance and the forces on the front and rear wheels of the vehicle, the distance between the force point and the center of gravity of the vehicle is:

[0107]

[0108] Where I is the vehicle's Z-axis moment of inertia; φ is the angle between the vehicle's axle and the X-axis. is the second-order derivative of the angle between the vehicle's axle and the X-axis; δ is the vehicle's front wheel turning angle; b is the vehicle's rear suspension length;

[0109] Assuming that the vehicle's front wheel steering angle δ is extremely small, cos(δ)≈1, then equations (1) and (2) can be rewritten as:

[0110] ma y =C αf α f +C αr α r (3)

[0111]

[0112] Where C af 、C αr are the lateral stiffness of the front and rear wheels of the vehicle respectively; a f 、a r are the sideslip angles of the front and rear wheels respectively; a is the length of the vehicle's front suspension;

[0113] Vehicle Y-axis acceleration a y Expressed as:

[0114]

[0115] Where, Represents the second-order derivative of the vehicle's y-axis velocity, v x Indicates the vehicle's X-axis speed; is the first derivative of the angle between the vehicle axle and the X-axis;

[0116] Side slip angle a of the front wheel f , rear wheel side slip angle a r Respectively expressed as:

[0117]

[0118]

[0119] In the formula represents the vehicle's Y-axis speed. Substituting equations (5) to (7) into equations (3) and (4), we obtain:

[0120]

[0121]

[0122] Where, is the second-order derivative of the angle between the vehicle's axle and the X-axis; the final vehicle dynamics model is:

[0123]

[0124] Right now

[0125] Where u = (δ), which represents the front wheel turning angle of the vehicle.

[0126] The vehicle dynamics model parameters used in this embodiment are as follows: αf 、C αr All are -11000 N / rad; m is 1412 kg; a and b are 1.015 m and 1.895 m respectively; I is 1536.7 kg·m 2 ;

[0127] Specifically, such as Figure 3a 、 Figure 3b As shown, step S1 designs the path tracking error dynamic model, specifically by projecting the vehicle into the natural coordinate system and establishing the path tracking error dynamic model with the lateral error and heading error relative to the desired path as state variables; projecting the vehicle body coordinate system into the natural coordinate system, decoupling the vehicle control into lateral control and longitudinal control, and reducing the complexity of the control;

[0128] Assume the lateral error of the vehicle is d and the heading error is θ-θ r , θ is the heading angle, θr is the desired heading angle, the velocity of the projection point is S, and according to the relationship between the vectors, the lateral error d can be obtained as:

[0129]

[0130] Where, is the projection normal direction of the vehicle speed v in the natural coordinate system; taking the derivative of formula (11), we can get:

[0131]

[0132] Where, is the actual position of the vehicle, is the vehicle projection position vector, It is expressed as follows;

[0133]

[0134]

[0135] Where v represents the vehicle speed; τ is the direction of the vehicle speed v, τ r is the projection tangent direction of the vehicle speed v in the natural coordinate system; Substitute equations (13) and (14) into equation (12), and according to β is the angle between the vehicle speed v and the X axis; we get:

[0136]

[0137]

[0138] At the same time, β, As a small amount close to 0, equation (15) can be rewritten as:

[0139]

[0140] Let the lateral error e d =d, then the heading error So,

[0141]

[0142]

[0143]

[0144]

[0145] Combining Equations (17) to (20) with the dynamic model of Equation (10) yields the path tracking error dynamic model: for:

[0146]

[0147] Where,

[0148]

[0149] Specifically, step S2 designs an LQR controller; specifically:

[0150] The LQR controller includes the LQR controller state quantity of the control object and the quadratic function of the control quantity; the following energy function J is taken as the LQR controller:

[0151]

[0152] Where Q and R are the weighting coefficients in the LQR controller. The weighting coefficients in the LQR controller are the weighting matrix, Q = diag[q1,q2,q3,q4], R = [r], x k is the state quantity of the LQR controller, u k is the input of the LQR controller; the output of the LQR controller u(k) is used as the input of the path tracking error dynamics model, and the output of the LQR controller u(k) is:

[0153] u(k)=-Ke rr (k) (23)

[0154] Where K is the LQR controller feedback gain matrix, x k =e rr (k), e rr (k) is the state quantity of the LQR controller at time k.

[0155] Among them, the elements in the weighting matrix Q represent the importance of the lateral deviation, lateral deviation change rate, heading deviation, and heading deviation change rate in the LQR controller state. The larger the value, the faster the corresponding target approaches the target state; the elements in the weighting matrix R represent the restrictions on the control quantity output. The larger the value, the greater the restriction on the control quantity. However, the coefficients of the weighting matrices Q and R are not the larger the better, and the balance between the elements must be considered.

[0156] Specifically, step S3 is as follows: adding a feedforward control quantity δ on the basis of the LQR controller f To eliminate the LQR controller; after adding feedforward control, the input of the path tracking error dynamic model is obtained as follows:

[0157] u(k)=-Ke rr (k)+δ f (twenty four)

[0158] Substituting equation (24) into equation (21), we can obtain the stabilized e rr :

[0159]

[0160] Where, ) is the desired road curvature information, and the curvature information is and The ratio of

[0161] Expand the above formula to get:

[0162]

[0163] Where k1 and k3 are the parameters in the LQR controller feedback gain matrix K; the lateral error ed The steady-state error of is eliminated by the feedforward control, while the heading error The steady-state error of cannot be eliminated; let The control quantity δ of feedforward control f Expressed as:

[0164]

[0165] The function of the LQR controller is to consume a small amount of energy to make the components of the LQR controller state vector approach the target state when the LQR controller state deviates from or fails to reach the target state.

[0166] Specifically, step S4 uses the NSGA3 algorithm to perform multi-objective optimization on the weighting coefficients in the LQR controller. Specifically, the lateral deviation, lateral deviation change rate, heading deviation, and heading deviation change rate in the LQR controller state are the main factors affecting vehicle path tracking, and the control quantity in the LQR controller has only one front wheel angle. Therefore, the elements in the weighting matrix R are set to fixed values, and the NSGA3 algorithm is used to optimize q1, q2, q3, and q4 in the weighting matrix Q of the LQR controller in step S2 to achieve multi-objective optimization of the weighting coefficients in the LQR controller, which can be expressed as:

[0167]

[0168] Where L is the fitness function of the NSGA3 algorithm.

[0169] Specifically, step S5 obtains the optimal value of the weighted coefficient of the LQR controller as follows: repeat step S4, traverse the vehicle speed values ​​of the preset step length at low, medium and high speeds, obtain a set of Pareto optimal solutions each time step S4 is executed, and use the Pareto optimal solution as the optimal value of the weighted coefficient of the LQR controller; and record one of the sets of Pareto optimal solutions after the iteration, until each vehicle speed value in the speed range is traversed, record the weighted coefficient in the LQR controller corresponding to each vehicle speed value, and obtain the optimal value of the weighted coefficient of the LQR controller.

[0170] Example 2

[0171] Specifically, based on Example 1, the solution is described in conjunction with specific implementation examples to further demonstrate the technical effects of this solution. Specifically:

[0172] like Figure 2 As shown, in step S4, the weighting coefficients in the LQR controller are optimized by multiple objectives, specifically,

[0173] Step S4.1: Initialize the population: Initialize the NSGA3 algorithm parameters, set the maximum number of iterations to 80, the population size to 100, the crossover probability to 0.7, and the mutation probability to 0.4; generate an initial population P of size N according to the LQR controller weight coefficients q1, q2, q3, and q4. t , each individual Xi=(i=1,2,…N) in the population is a decision variable, and the individual initial value is set to the random value of the LQR controller weight coefficient;

[0174] Step S4.2: Population non-dominated sorting: The individuals in the population are divided into several levels according to their mutual dominance relationship, and all individuals are normalized and associated with the reference point; specifically, the non-dominated sorting of the population is divided into several different non-dominated layers (F1, F2, ...), and the solutions of each non-dominated layer are successively added to the new population S t Until the new population S t The size is equal to N, and the last frontier is assumed to be F1. If the new population S t The size of is equal to N, then the initial population P of the next iteration t+1 =S t , if the new population S t If the size is greater than N, a selection operation based on the reference point is performed, the objective function is standardized and a reference set is created, a mapping relationship between the population individuals and the reference point is constructed, and the mapping relationship is the distance relationship between the population individuals and the reference point. The population closest to the reference point is selected to join the new population S t Until the new population S t The size of is equal to N;

[0175] Step S4.3: Use traditional genetic operators to perform inheritance: select, cross, and mutate the population to generate a descendant population Q with a population size of N. t ;

[0176] Step S4.4: Merge population: Merge the parent and offspring to form a population R of size 2N t =P t ∪Q t , perform non-dominated sorting, normalize the individuals in the population and associate them with reference points to obtain the non-dominated sorting result;

[0177] Step S4.5: Elite retention strategy: select the population R from the merged population according to the non-dominated sorting result. t Select the first N individuals as the parent population P t+1 ; Specifically: select the first N individuals as the parent population P t+1 ; By the tth generation, a t For population P t The best individual in the parent population P t+1 For the new generation population, if the parent population Pt+1 There is no superior individual a t The best individual, then the best individual a t Join the parent population P t+1 As the parent population P t+1 individuals;

[0178] Step S4.6: If Gen is not equal to the maximum number of iterations set value, then Gen = Gen + 1, and return to step S4.3; if Gen is equal to the maximum number of iterations set value, the iteration is terminated and the optimal Pareto solution is output; that is, when the number of iterations is equal to the set value, the population with N individuals after the iteration is used as the Pareto optimal solution, forming an actual frontier surface that is closest to the theoretical frontier surface.

[0179] FIG4 shows a comparison curve of the results of the LQR controller and the method of the present invention. Figure 4a The lateral error is controlled. It can be seen that the NSGA3 algorithm + LQR controller method of the present invention reduces the lateral error peak by nearly half compared with the traditional LQR controller. Figure 4b Schematic diagram of heading error. It can be seen that the NSGA3+LQR controller method of the present invention has a similar heading error as the traditional LQR controller. Figure 4c Path tracking result diagram; it can be seen that the NSGA3 algorithm + LQR controller method of the present invention is closer to the reference path (i.e. Figure 4c in the refpath).

[0180] Obviously, the above embodiments of the present invention are merely examples for the purpose of clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the claims of the present invention.

Claims

1. A path tracking error dynamics model optimization method for an autonomous vehicle, applied to an autonomous vehicle, characterized in that: The method comprises the following steps: S1: Establish a vehicle dynamics model and design a path tracking error dynamics model based on the vehicle dynamics model; The specific steps of establishing a vehicle dynamics model are as follows: based on the vehicle's force conditions, a vehicle dynamics model is established, and only the lateral and longitudinal forces of the vehicle are considered. It is assumed that the steering angles and cornering stiffness of the two wheels on the front and rear axles of the vehicle are equal, the rear wheels of the vehicle do not turn, and the effect of air resistance on the vehicle is ignored. The vehicle is simplified to a two-degree-of-freedom single vehicle model; according to Newton's second law and the force conditions of the front and rear wheels of the vehicle, the following are obtained: me y =F yf cos(δ)+F yr (1) Where m is the vehicle's mass; a y is the Y-axis acceleration; F yf is the vehicle front wheel cornering force, F yr is the vehicle rear wheel cornering force; According to the moment balance and the forces on the front and rear wheels of the vehicle, the distance between the force point and the center of gravity of the vehicle is: Where I is the vehicle's Z-axis moment of inertia; φ is the angle between the vehicle's axle and the X-axis. is the second-order derivative of the angle between the vehicle's axle and the X-axis; δ is the vehicle's front wheel turning angle; b is the vehicle's rear suspension length; Assuming that the vehicle's front wheel steering angle δ is extremely small, cos(δ)≈1, then equations (1) and (2) can be rewritten as: has y =C αf α f +C αr α r (3) Where C af 、C αr are the lateral stiffness of the front and rear wheels of the vehicle respectively; a f 、a r are the sideslip angles of the front and rear wheels respectively; a is the length of the vehicle's front suspension; Vehicle Y-axis acceleration a y Expressed as: Where, represents the second derivative of the vehicle's y-axis velocity, and vx represents the vehicle's x-axis velocity; is the first derivative of the angle between the vehicle axle and the X-axis; Side slip angle a of the front wheel f , rear wheel side slip angle a r Respectively expressed as: In the formula represents the vehicle's Y-axis speed. Substituting equations (5) to (7) into equations (3) and (4), we obtain: Where, is the second-order derivative of the angle between the vehicle's axle and the X-axis; the final vehicle dynamics model is: Right now Where, u = (δ), represents the vehicle's front wheel turning angle; The path tracking error dynamics model is designed by projecting the vehicle into the natural coordinate system and establishing a path tracking error dynamics model with the lateral error and heading error relative to the desired path as state variables. The vehicle coordinate system is projected into the natural coordinate system, and the vehicle control is decoupled into lateral control and longitudinal control to reduce the control complexity. Assume the lateral error of the vehicle is d and the heading error is θ-θ r , θ is the heading angle, θr is the desired heading angle, the velocity of the projection point is S, and according to the relationship between the vectors, the lateral error d can be obtained as: Where, is the projection normal direction of the vehicle speed v in the natural coordinate system; taking the derivative of formula (11), we can get: Where, is the actual position of the vehicle, is the vehicle projection position vector, It is expressed as follows; Where v represents the vehicle speed; τ is the direction of the vehicle speed v, τ r is the projection tangent direction of the vehicle speed v in the natural coordinate system; Substitute equations (13) and (14) into equation (12), and according to β is the angle between the vehicle speed v and the X axis; we get: At the same time, β, As a small amount close to 0, equation (15) can be rewritten as: Let the lateral error e d =d, then the heading error So, Combining Equations (17) to (20) with the dynamic model of Equation (10) yields the path tracking error dynamic model: for: Where, S2: Design an LQR controller for the path tracking error dynamics model, obtain the LQR controller output according to the LQR controller state, and use the LQR controller output as the input of the path tracking error dynamics model; Design an LQR controller; specifically: The LQR controller includes the LQR controller state quantity of the control object and the quadratic function of the control quantity; the following energy function J is taken as the LQR controller: Where Q and R are the weighting coefficients in the LQR controller. The weighting coefficients in the LQR controller are the weighting matrix, Q = diag[q1,q2,q3,q4], R = [r], x k is the state quantity of the LQR controller, u k is the input of the LQR controller; the output of the LQR controller u(k) is used as the input of the path tracking error dynamics model, and the output of the LQR controller u(k) is: u(k)=-I rr (k) (23) Where K is the LQR controller feedback gain matrix, x k =e rr (k), e rr (k) is the state quantity of the LQR controller at time k; S3: adding a control amount of feedforward control to the input amount of the path tracking error dynamics model to eliminate the steady-state error of the path tracking error dynamics model; Specifically: Add a feedforward control quantity δ on the basis of the LQR controller f To eliminate the LQR controller; after adding feedforward control, the input of the path tracking error dynamic model is obtained as follows: u(k)=-Ke rr (k)+δ f (24) Substituting equation (24) into equation (21), we can obtain the stabilized e rr : Where, ) is the desired road curvature information, and the curvature information is and The ratio of τ; Expand the above formula to get: Where k1 and k3 are the parameters in the LQR controller feedback gain matrix K; the lateral error e d The steady-state error of is eliminated by the feedforward control, while the heading error The steady-state error of cannot be eliminated; let The control quantity δ of feedforward control f Expressed as: S4: Use the NSGA3 algorithm to perform multi-objective optimization on the weighting coefficients in the LQR controller; Specifically, the elements in the weight matrix R are set to fixed values, and the weight coefficients q1, q2, q3, and q4 in the weight matrix Q of the LQR controller in step S2 are optimized using the NSGA3 algorithm to achieve multi-objective optimization of the weight coefficients in the LQR controller, which can be expressed as: Where L is the fitness function of the NSGA3 algorithm; The multi-objective optimization of the weighting coefficients in the LQR controller is performed as follows: Step S4.1: Initialize the population: Initialize the parameters of the NSGA3 algorithm: maximum number of iterations, population size, crossover probability, mutation probability; generate an initial population P of size N according to the LQR controller weight coefficients q1, q2, q3, q4 t , each individual Xi=(i=1,2,…N) in the population is a decision variable, and the individual initial value is set to the random value of the LQR controller weight coefficient; Step S4.2: Population non-dominated sorting: The individuals in the population are divided into several levels according to their mutual dominance relationship, all individuals in the population are normalized and associated with the reference point; Specifically, the non-dominated population is sorted into several different non-dominated layers (F1, F2, ...), and the solutions of each non-dominated layer are successively added to the new population S t Until the new population S t The size is equal to N, and the last frontier is assumed to be F1. If the new population S t The size of is equal to N, then the initial population P of the next iteration t+1 =S t , if the new population S t If the size is greater than N, a selection operation based on the reference point is performed, the objective function is standardized and a reference set is created, a mapping relationship between the population individuals and the reference point is constructed, and the mapping relationship is the distance relationship between the population individuals and the reference point. The population closest to the reference point is selected to join the new population S t Until the new population S t The size of is equal to N; Step S4.3: Use traditional genetic operators to perform inheritance: select, cross, and mutate the population to generate a descendant population Q with a population size of N. t ; Step S4.4: Merge populations: Merge the parent and offspring populations to form a population R of size 2N t =P t ∪Q t , perform non-dominated sorting, normalize the individuals in the population and associate the individuals with the reference point to obtain the non-dominated sorting result; Step S4.5: Elite retention strategy: select the population R from the merged population according to the non-dominated sorting result. t Select the first N individuals as the parent population P t+1 ; Specifically: Select to generate a new population: Select the first N individuals as the parent population P t+1 , by the tth generation, a t For population P t The best individual in the parent population P t+1 For the new generation population, if the parent population P t+1 There is no superior individual a t The best individual, then the best individual a t Join the parent population P t+1 As the parent population P t+1 individuals; Step S4.6: If Gen is not equal to the maximum number of iterations, then Gen = Gen + 1 and the process returns to step S4.

3. If Gen is equal to the maximum number of iterations, the iterations are terminated and the optimal Pareto solution is output. That is, when the number of iterations equals the set value, the population with N individuals after the iteration is considered the Pareto optimal solution, forming an actual frontier that is closest to the theoretical frontier. S5: Repeat S4 until every speed value in the speed range is traversed, record the weighting coefficient in the LQR controller corresponding to each speed value, and obtain the optimal value of the LQR controller weighting coefficient; substitute the optimal value of the LQR controller weighting coefficient into the LQR controller to obtain the optimized path tracking error dynamic model.

2. The method for optimizing a path tracking error dynamics model of an autonomous driving vehicle according to claim 1, wherein: Step S5 obtains the optimal value of the weighted coefficient of the LQR controller as follows: repeat step S4, traverse the vehicle speed values ​​of the preset step size at low, medium and high speeds, obtain a set of Pareto optimal solutions each time step S4 is executed, and use the Pareto optimal solution as the optimal value of the weighted coefficient of the LQR controller; and record one of the sets of Pareto optimal solutions after the iteration, until every speed value in the speed range is traversed, record the weighted coefficient in the LQR controller corresponding to each speed value, and obtain the optimal value of the weighted coefficient of the LQR controller.

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