An automatic driving path planning method based on holomorphic embedding and trajectory following

Abstract

The application provides an automatic driving path planning method based on holomorphic embedding and trajectory following, comprising the following steps: obtaining corresponding automatic driving vehicle and path planning data; establishing a vehicle path planning model; converting the vehicle path planning model into a nonlinear programming form and constructing a corresponding embedding system; solving the embedding system of the path planning model by using a holomorphic embedding method to obtain a path planning function of the automatic driving vehicle; and returning the path planning function of the automatic driving vehicle to the vehicle to control the path and the vehicle. The new path planning method of the fast and flexible holomorphic embedding method and the trajectory following solves the defects of the existing common automatic driving path planning method, such as slow convergence speed and irregular convergence domain, and also solves the defects of the existing iterative method based on the prediction-correction inner point method, such as large calculation amount, long time consumption and large storage space consumption; and the calculation efficiency, scale and precision are all significantly improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of automatic driving, and particularly relates to an automatic driving path planning method based on holomorphic embedding and trajectory following. BACKGROUND

[0002] Path planning is a key component of motion planning for autonomous vehicles, and is closely related to the safety of vehicle driving and the comfort experience of passengers. In urban traffic scenarios, autonomous vehicles need to shuttle in complex and changeable environments, such as roads blocked by many vehicles or obstacles on both sides. How to generate a feasible and smooth path in a complex environment makes path planning a very challenging problem.

[0003] The goal of path planning is to find a function in the configuration space (C-space) that connects the initial configuration and the target configuration, so that each point in the function is in the collision-free space. For autonomous vehicles, especially vehicles with passengers, path planning needs to not only calculate a safe path, but more importantly, calculate a comfortable path, that is, a path with comfortable changes in geometric properties.

[0004] Among the numerous research results on nonlinear programming problems, the interior point method of the prior art has the advantages of polynomial time complexity and is one of the excellent algorithms with great potential. However, the classical solution method of nonlinear programming problems based on iterative ideas has several common defects:

[0005] 1. The iterative method based on the interior point method of the prediction-correction method inevitably involves multiple calculations of the Jacobian matrix, and also involves multiple prediction and correction calculations, so the method has large calculation amount and long time consumption;

[0006] 2. The prediction-correction interior point method has difficulty in converging when solving optimization problems, because the prediction point may jump out of the convergence domain, and the convergence domain of the traditional nonlinear optimization method is irregular, and even a fractal structure may appear, making it difficult to determine its boundary;

[0007] 3. The quality of the solution depends on the selection of the initial point, and it is difficult to find a high-quality solution that makes the path safer and smoother;

[0008] 4. Using the iterative method only calculates a limited number of approximate points on the central trajectory, and it is difficult to describe the convergence behavior of the interior point method. SUMMARY

[0009] In view of the deficiencies of the prior art, the present application provides an automatic driving path planning method based on holomorphic embedding and trajectory following, which solves the defects of slow convergence speed and irregular convergence domain of the commonly used automatic driving path planning method, and also solves the defects of large calculation amount, long time consumption and large storage space consumption of the existing prediction-correction-based interior point method, and can completely and effectively follow the solution curve and depict the behavior of the solution curve.

[0010] The technical scheme of the present application is: an automatic driving path planning method based on holomorphic embedding and trajectory following, comprising the following steps:

[0011] S1), obtaining corresponding automatic driving vehicle and path planning data;

[0012] S2), establishing a vehicle path planning model;

[0013] S3), converting the vehicle path planning model into a nonlinear programming form and constructing a corresponding embedding system;

[0014] S4), using a holomorphic embedding method to solve the embedding system of the path planning model to obtain a path planning function of the automatic driving vehicle;

[0015] S5), returning the parameters of the path planning function of the automatic driving vehicle to the vehicle for path and vehicle control.

[0016] As a preferred, in step S1), the following steps are included: obtaining a smooth driving route from map data through a satellite navigation system; and optimizing path generation in a frenet frame through perception of the vehicle environment.

[0017] As a preferred, in step S1), the following steps are included:

[0018] S11), obtaining accurate position and road information of the vehicle in a global coordinate system by using GPS, inertial navigation system (IMU) and high-precision map technology;

[0019] S12), collecting environmental information around the vehicle through sensors installed on the vehicle.

[0020] As a preferred, in step S11), the following steps are included:

[0021] S111), dividing the path where the vehicle is located into p segments according to the spatial parameter σ of the guide rail, obtaining the cumulative distance d of each segment path l along the reference line l ; assigning acceleration weights w1, w2 and w3; determining the objective function according to the loss function expression;

[0022] S112), obtaining the initial position σ0, initial lateral offset τ0 and end position (σ e, τ e ) and the accumulated distance σ l and its derivatives; thus determining the set of equality constraints

[0023] As preferred, in step S12), specifically comprising:

[0024] S121), according to the vehicle perception data, evenly sampling m points on the lth segment of the path, obtaining the accumulated distance σ lj , j∈(0, m) and its upper and lower boundary data of distance to obstacles determining the set of inequality constraints

[0025] As preferred, in step S2), establishing the vehicle path planning model, specifically comprising the following steps:

[0026] S21), for each segment of the path l, adopting a quintic spline function f l (σ) represents:

[0027] f l (σ) = a l0 +a l1 σ+a l2 σ 2 +a l3 σ 3 +a l4 σ 4 +a l5 σ 5 , (0≤σ≤d l );

[0028] In the frenet coordinate system, the value range of parameter σ is the length d l from the current position of the vehicle to the default planned path; a l0 ~ a l5 ≥ 0 are the coefficient variables of the lth segment of the path;

[0029] S22), establishing the objective function of the vehicle path planning, the expression of the objective function g(x) is:

[0030]

[0031] wherein w1, w2, w3 represent the weight assignment of acceleration, f l ', f l '', f l ''' respectively represent the first derivative, the second derivative and the third derivative of f l (σ);

[0032] S23), expressing the objective function as a quadratic function of the variables a l0 ~ a l5 (l = 1,..., p):

[0033]

[0034] S24), establishing a set of equality constraints and a set of inequality constraints

[0035] As preferred, in step S24), the set of equality constraints includes equality constraints of the initial point and the end point and smooth constraints between segments.

[0036] As preferred, in step S24), since the equality constraints of the initial point and the end point and the smooth constraints between segments are all linear functions of the variables a l0 ,..., a l5 , l = 1,..., p, the equality constraints are uniformly expressed as:

[0037] β eq χ = b eq ;

[0038] In the formula, β eq represents a coefficient matrix of σ l , l = 1,..., p and its power; b eq = [τ0 τ'0 a 15 ... τ" e ... 0] T ; χ = [a 10 ... a 15 ... a p0 ... a p5 ] T .

[0039] As preferred, in step S24), the set of inequality constraints includes boundary constraints on sampling points, expressed as:

[0040] β ieq χ ≥ b ieq ;

[0041] By introducing a slack variable z > 0, the above inequality is converted into an equality constraint:

[0042] β ieq χ - z = b ieq ;

[0043] In the formula, β ieq represents a coefficient matrix of σ l , l = 1,..., p and its power.

[0044] χ = [a 10 … a 15 … a p0 … a p5 ] T ;

[0045]

[0046] respectively represent the upper and lower boundaries of the jth point on the ith path from the obstacle.

[0047] As preferred, in step S3), the objective function g(x) is transformed into a nonlinear programming form, i.e.:

[0048]

[0049] wherein, is the optimization variable; χ = [a 10 … a 15 … a p0 … a p5 ] T ; z is the slack variable; is the objective function; represents the coefficient matrix of the quadratic term of the objective function; H l (l = 1, …, p) is shown in S23); represents the coefficient matrix of the linear term of the constraint; represents the constant term of the constraint; represents the coefficient vector of the linear term of the objective function; T represents the bias operation.

[0050] As preferred, in step S3), the embedded system for constructing the path planning model is:

[0051] A T y(h) - Qx(h) + s(h) = (1 - h)(A T y 0 - Qx 0 + s 0 - c) + c; (2)

[0052] Ax(h) = (1 - h)(Ax 0 - b) + b; (3)

[0053] diag(x(h))s(h) = (1 - h)diag(x 0 (h)) · s 0 ; (4)

[0054] wherein,

[0055] wherein, are the dual function parameters y(h), x(h), s(h), h are the optimization variables to be solved; diag(x) represents a diagonal matrix with x elements as diagonal elements; x 0 , y 0 , s 0 , h 0 are the initial values of the variables x, y, s, h respectively.

[0056] As preferred, in step S4), the holomorphic embedding method is used to solve the embedding system of the path planning model, which specifically includes the following steps:

[0057] S41), assuming the arc length parameter as a, for each component in the solution function vector X=(x, y, s, h), write it as a power series expansion of the parameter a at 0:

[0058] h(a) = å q≥0 h q a q ;

[0059] x j (a) = å q≥0 x jq a q , 1≤j≤n;

[0060] y i (a) = å q≥0 y iq a q , 1≤i≤l; (5)

[0061] s j (a) = å q≥0 s jq a q , 1≤j≤n;

[0062] wherein q represents the order of the power series term; x jq and s jq represent the q-th order power series coefficients of the j-th component of the vector functions x and s respectively; h q represents the q-th order power series coefficients of the vector function h; y iq represents the q-th order power series coefficients of the i-th component of the vector function y; wherein x and s have n components, and y has l components;

[0063] S42), establish the arc length parameterization normalization equation:

[0064]

[0065] S43), bring formula (5) into formula (2)-(4), formula (6), obtain:

[0066]

[0067] In the formula, Respectively, the qth power series coefficient vector of vector function x, y, s is represented;h q The qth power series coefficient of vector function h is represented; Respectively, the initial value of the jth component of x and s is represented;

[0068] S44), by comparing the coefficients of the same power of α on both sides of formula (7)-(10), determine the equation group about unknown vector functions x jq , y iq , s jq , j=1, …, n;i=1, …, l and unknown h q By comparing the coefficients of α q On both sides of the equation, it is obtained that:

[0069] When q=1:

[0070]

[0071] When q≥2;

[0072]

[0073] S45), let X=(x, y, s, h), solve linear equations (11)-(18), obtain X kq (α), k=1, …, 2n+l+1, q≥1 power series expression, so as to construct rational approximation function according to the existing power series information, to expand the effective interval, finally obtain the path planning function of the autonomous vehicle.

[0074] As preferred, in step S5), the vehicle is controlled by receiving And calculating the trajectory of p section path Realize the generation and execution of vehicle control instruction.

[0075] The beneficial effects of the present application are:

[0076] 1、The present application is a new path planning method of rapid flexible holomorphic embedding method and trajectory following, which solves the defects of slow convergence speed and irregular convergence domain of the existing commonly used autonomous driving path planning method, and also solves the defects of large calculation amount, long time consumption and large storage space consumption of the existing interior point method based on prediction-correction;

[0077] 2. This paper uses a holomorphic embedding method, based on piecewise rational approximation, to propose a non-iterative trajectory following method for solving the autonomous driving path planning problem. This method then provides an approximate solution function expression, effectively addressing the problems of traditional numerical methods in tracking the center trajectory, such as the large number of iterations required, the high computational complexity, and the susceptibility to correction failures. This method is then applied to solving the path planning problem for autonomous driving in multi-obstacle scenarios.

[0078] 3. Compared with traditional methods, the present invention has significant improvements in computational efficiency, scale and accuracy. Moreover, when solving nonlinear path planning, the present invention can usually completely and efficiently track the solution curve and obtain high-quality optimal solutions, overcoming the defect that traditional methods can only calculate a limited number of approximate points on the central trajectory of the nonlinear system. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 It is a flow chart of the method of the present invention;

[0080] Figure 2 The figure is a flow chart of the present invention for solving the path planning model based on holomorphic embedding. DETAILED DESCRIPTION

[0081] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings:

[0082] like Figure 1 As shown, this embodiment provides an autonomous driving path planning method based on holomorphic embedding and trajectory following, comprising the following steps:

[0083] S1) Obtain corresponding autonomous driving vehicle and path planning data;

[0084] In this embodiment, the vehicle and path planning data includes obtaining a smooth driving route from map data through a satellite navigation system, and optimizing the path generation in a Frenet framework through perception of the vehicle environment. The steps include:

[0085] S11) Use GPS, Inertial Navigation Unit (IMU), and high-precision map technology to obtain the vehicle's precise position and road information in the global coordinate system; specifically, including:

[0086] S111), according to the spatial parameter σ of the guide rail, the path where the vehicle is located is divided into p segments, and the cumulative distance d of each segment of the path l along the reference line is obtained l ; Assign acceleration weights w1, w2, w3; Determine the objective function based on the loss function expression;

[0087] S112) Obtain the initial position σ0, initial lateral offset τ0, and end position (σ e , τe ) and the accumulated distance σ of the first segment l and its derivatives; thus determining the set of equality constraints

[0088] S12), collecting environmental information around the vehicle through sensors installed on the vehicle, specifically including:

[0089] S121), according to the vehicle perception data, uniformly sampling m points on the first segment path, obtaining the accumulated distance σ of the vehicle at m points on each segment path l lj , j ∈ (0, m) and its upper and lower boundary data of distance to obstacles determining the set of inequality constraints

[0090] S2), establishing a vehicle path planning model; specifically including the following steps:

[0091] S21), for each segment path l, using a quintic spline function f l (σ) represents:

[0092] f l (σ) = a l0 + a l1 σ + a l2 σ 2 + a l3 σ 3 + a l4 σ 4 + a l5 σ 5 , (0 ≤ σ ≤ d l );

[0093] In the frenet coordinate system, the value range of the parameter σ is the length d l from the current position of the vehicle to the default planned path; a l0 ~ a l5 ≥ 0 are coefficient variables of the first segment path;

[0094] S22), establishing the objective function of vehicle path planning, i.e. making the driving distance in the path driving process minimum and the path smooth to achieve the purpose of less fuel consumption, the expression of the objective function g(x) is:

[0095]

[0096] where w1, w2, w3 represent the weight assignment of acceleration, f l ', f l '', f l ''' respectively represent the first derivative, second derivative and third derivative of f l (σ).

[0097] S23), representing the objective function as a quadratic function with respect to the variable a l0 ~ a l5 (l = 1,..., p):

[0098]

[0099] wherein,

[0100]

[0101]

[0102] S24), establishing an equality constraint set and an inequality constraint set wherein, the equality constraint set includes equality constraints of initial and end points and smooth constraints between segments; the inequality constraint set includes boundary constraints on sampling points.

[0103] wherein, the equality constraints of initial and end points are:

[0104] assuming that the initial point is (σ0, τ0) is known; σ0 is the initial position of the parameter, τ0 is the initial lateral offset; the first order derivative and the second order derivative of the initial point (σ0, τ0) are (σ0, τ'0) and (σ0, τ"0) respectively;

[0105] assuming that the end point is (σ e , τ e ) is known; σ e represents the end position of the parameter, τ e represents the end lateral offset; assuming that the first order derivative and the second order derivative of the end point (σ e , τ e ) are (σ0, τ' e ) and (σ0, τ" e ) respectively; the following formula is obtained:

[0106]

[0107]

[0108] Correspondingly, the offset τ e , τ' e , τ" e of the end point position satisfy the equality constraints.

[0109] The smooth constraint between segments is a smooth operation at the connection, satisfying the function f l(σ) and its first-order continuous, second-order continuous, third-order continuous properties;

[0110] f l (σ l ); l+1 (σ0);

[0111] f l ′(σ l ); l+1 (σ0);

[0112] f l ″(σ l ); l+1 (σ0);

[0113] f l ″′(σ l ); l+1 (σ0);

[0114] That is, the relevant expression that the function f l (σ) satisfies the continuity requirement at the segmentation point l is:

[0115]

[0116] Wherein, σ0=0.

[0117] In this embodiment, since the equality constraints of the initial point and the end point and the smooth constraints between the segments are all linear functions about variables a l0 , …, a l5 , l=1, …, p, the equality constraints are uniformly expressed as:

[0118] β eq χ=b eq ;

[0119] In the formula, β eq represents a coefficient matrix about σ l , l=1, …, p and powers thereof; b eq =[τ0 τ′0 a 15 … τ″ e …0] T ; χ=[a 10 … a 15 … a p0 … a p5 ] T .

[0120] In this embodiment, the boundary constraint of the sampling point is that m points are uniformly sampled on the lth segment, whether these points hit the obstacle boundary is checked, and the point is found according to the road width and the surrounding obstacles The inequality constraint is calculated as follows:

[0121]

[0122] where σ lj represents the cumulative distance of the jth point in the lth path, respectively represent the upper and lower boundaries of the jth point on the lth path.

[0123] Therefore, the inequality constraint set includes the boundary constraint of the sampling point, denoted as β ieq χ≥b ieq ; where β ieq represents the coefficient matrix of σ l , l = 1, …, p and its power;

[0124] By introducing the slack variable z > 0, the above inequality is converted into an equality constraint β ieq χ-z = b ieq .

[0125] S3), the vehicle path planning model is converted into a nonlinear programming form and a corresponding embedded system is constructed;

[0126] In this embodiment, the objective function g(x) is converted into a nonlinear programming form, that is:

[0127]

[0128] where, is the optimization variable; χ = [a 10 … a 15 … a p0 … a p5 ] T ; z is the slack variable; is the objective function; represents the coefficient matrix of the quadratic term of the objective function; H l (l = 1, …, p) is shown in S23); represents the coefficient matrix of the constraint; represents the constant term of the constraint; represents the coefficient vector of the first-order term of the objective function; T represents the bias operation.

[0129] In this embodiment, the embedded system of the path planning model is:

[0130] A T y(h)-Qx(h)+s(h) = (1-h)(A T y0 -Qx 0 +s 0 -c)+c; (2)

[0131] Ax(h)=(1-h)(Ax 0 -b)+b; (3)

[0132] dtag(x(h))s(h)=(1-h)diag(x 0 (h))·s 0 ; (4)

[0133] in,

[0134] Where, The dual function parameters y(h), x(h), s(h), and h are all variables to be optimized; diag(x) represents a diagonal matrix with x elements as diagonal elements; x 0 ,y 0 , s 0 , h 0 are the initial values ​​of variables x, y, s, and h respectively.

[0135] S4) Solving the embedded system of the path planning model using the holomorphic embedding method to obtain the path planning function of the autonomous driving vehicle; specifically comprising the following steps:

[0136] S41) Assuming that the arc length parameter is α, for each component of the solution function vector X=(x, y, s, h), write it as a power series with parameter α expanded at 0:

[0137]

[0138] Where q represents the order of the power series term; x jq and s jq denotes the qth order power series coefficient of the jth component of the vector functions x and s respectively; h q represents the qth order power series coefficient of the vector function h; y iq represents the coefficient of the qth order power series of the i-th component of the vector function y, where x and s have n components and y has l components;

[0139] S42) Establish the arc length parameterization normalization equation:

[0140]

[0141] S43) Substitute formula (5) into formulas (2)-(4) and (6) to obtain:

[0142]

[0143] wherein, represent the q-th order power series coefficient vectors of the vector functions x, y, s, respectively; h q represents the q-th order power series coefficient of the vector function h; represent the initial values of the j-th components of x and s, respectively;

[0144] S44), determine the equations about unknown vector functions x jq , y iq , s jq , j = 1, …, n; i = 1, …, l and unknown h q by comparing the coefficients of the same power of α on both sides of equations (7)-(10): q

[0145] When q = 1:

[0146]

[0147] When q ≥ 2;

[0148]

[0149]

[0150] S45), set X = (x, y, s, h), solve the linear equations (11)-(18) to obtain X kq (α), k = 1, …, 2n+l+1, q ≥ 1, and the power series expression, so as to construct a rational approximation function according to the existing power series information, so as to expand the effective interval, and finally obtain the path planning function of the autonomous vehicle.

[0151] As preferred in this embodiment, in step S45), the following steps are specifically included:

[0152] S451), set the maximum order q of the power series part and the expansion max , the error threshold e * , the initial interval length Δα > 0, the minimum value range of the interval length 0 < δα < 1, and the reduction ratio ρ ∈ (0, 1);

[0153] S452), give the initial point X0 = [x 0 , y 0 , s 0 , h 0 ], and give the power series of the solution function vector X with respect to the arc length parameter α;

[0154]

[0155] wherein, X k ​denotes the kth component of X; X kθ denotes the qth power series coefficient of the kth component of X;

[0156] S453), substitute the power series into the embedding system (2)-(4), (6), to obtain the equation group (7)-(10) with the power series expansion coefficients as unknowns;

[0157] S454), when q=1, solve the equation group satisfied by (11)-(14) to obtain the first order power series coefficient of the kth component of X:

[0158] X k1 = (x j1 , y i1 , s j1 , h1), h=1, …, n, i=1, …, l;

[0159] When q≥2, substitute the q-1th power series coefficient of the kth component of X k(q-1) = (x j(q-1) , y i(q-1) , s j(q-1) , h (q-1) ) into (15)-(18), and solve the linear equation group to obtain the qth power series coefficient of the kth component:

[0160] X kq = (x jq , y iq , s jq , h q ), q=2, …, q max ;

[0161] S455), use the power series information of the vector X(α) to construct the rational approximation function; that is, construct the rational approximation function of X=(x, y, s, h), denoted as [m / n] x , [m / n] y , [m / n] s , [m / n] h ; wherein, m represents the rational approximation numerator order, and n represents the rational approximation denominator order;

[0162] S456), assign the value X(Δα) at the end point of the effective interval of the same embedding system as above to x # , y # , s # , h # , as the value of x, y, s, h at the start point α=0 of the next effective interval;

[0163] S457), determine whether the error norm of both sides of the equation group (7)-(10) satisfies less than e* ; if not, then reduce Δα until it is satisfied; i.e. find the Δα that makes the error norm of both sides of equations (7)-(10) less than a threshold e * and as large as possible; specifically:

[0164] If Δα > δα, update Δα ← ρΔα (where "←" denotes update); repeat step S307;

[0165] Otherwise, terminate the calculation, and the verification fails;

[0166] S458), update x # , y # , s # , h # as the values of x, y, s, h at the new starting point α = 0 for the next segment of the valid interval; repeat steps S452) to S457) until the condition

[0167] S459), take the values of the variables a l0 ,..., a l5 (l = 1,..., p) at h = 1 The path planning function of the autonomous vehicle is i.e. the path trajectory of the p segments of the planned path.

[0168] S5), return the parameters of the path planning function of the autonomous vehicle to the vehicle, and perform path and vehicle control, wherein the vehicle receives and calculates the trajectory of the p segments of the path to generate and execute the vehicle control instructions.

[0169] The above embodiments and descriptions are only illustrative of the principles and best modes of the present application, and various changes and improvements can be made to the present application without departing from the spirit and scope of the present application, and such changes and improvements are all within the scope of the present application.

Claims

1. A path planning method for autonomous driving based on holomorphic embedding and trajectory following, characterized in that: The following steps are involved: S1) Obtain corresponding autonomous driving vehicle and path planning data; S2) Establishing a vehicle path planning model; specifically including the following steps: S21) For each path l, a quintic spline function f is used. l (σ) represents: f l (s)=a l0 +a l1 s+a l2 s 2 +a l3 s 3 +a l4 s 4 +a l5 s 5 ,(0≤σ≤d l ); Where, in the Frenet coordinate system, the value range of the parameter σ is the length d from the current position of the vehicle to the default planned path l ;a l0 ~a l5 ≥0 is the coefficient variable of the lth path; S22) Establishing the objective function of vehicle path planning, the expression of the objective function g(x) is: Among them, w1, w2, w3 represent the weight assignment of acceleration, f′ l ,f″ l ,f″′ l Respectively represent f l The first, second and third derivatives of (σ); S23), express the objective function as about variable a l0 ~a l5 Quadratic function of (l=1,…,p): in: S24) Establishing an equality constraint set and inequality constraint sets S3), transforming the vehicle path planning model into a nonlinear programming form and constructing a corresponding embedded system; Among them, the objective function g(x) is transformed into a nonlinear programming form, that is: in, is the optimization variable; χ=[a 10 …a 15 …a p0 …a p5 ] T ; z is the slack variable; is the objective function; Represents the coefficient matrix of the quadratic term of the objective function; H l (l=1, ..., p) as shown in step S23); The linear coefficient matrix representing the constraints; A constant term representing a constraint; Represents the coefficient vector of the first-order term of the objective function; T represents the bias operation; The embedded system for building the path planning model is: A T y(h)-Qx(h)+s(h)=(1-h)(A T y 0 -Qx 0 +s 0 -c)+c;(2) Ax(h)=(1-h)(Ax 0 -b)+b;(3) diag(x(h))s(h)=(1-h)diag(x 0 (h))·s 0 ;(4) in, Where, The dual function parameters y(h), x(h), s(h), and h are all variables to be optimized; diag(x) represents a diagonal matrix with x elements as diagonal elements; x 0 ,y 0 ,s 0 ,h 0 are the initial values ​​of variables x, y, s, and h respectively; S4), using the holomorphic embedding method to solve the embedding system of the path planning model to obtain the path planning function of the autonomous driving vehicle; S5) The parameters of the path planning function of the autonomous driving vehicle are transmitted back to the vehicle to perform path and vehicle control.

2. The autonomous driving path planning method based on holomorphic embedding and trajectory following according to claim 1, characterized in that: In step S1), the acquisition of the autonomous driving vehicle and path planning data includes obtaining a smooth driving route from map data through a satellite navigation system; and optimizing path generation in a Frenet framework through perception of the vehicle environment.

3. The autonomous driving path planning method based on holomorphic embedding and trajectory following according to claim 2, characterized in that: In step S1), a dense and discrete sequence of points is used to represent the path in the Frenet framework; that is: S111), according to the spatial parameter σ of the guide rail, the path where the vehicle is located is divided into p segments, and the cumulative distance d of each segment of the path l along the reference line is obtained l ; Assign acceleration weights w1, w2, w3; Determine the objective function based on the loss function expression; S112) Obtain the initial position σ0, initial lateral offset τ0, and final position (σ e ,τ e ) and the cumulative distance σ of the first segment l and its derivatives of various orders; thereby determining the set of equality constraints 4. The autonomous driving path planning method based on holomorphic embedding and trajectory following according to claim 3, characterized in that: In step S1), based on the vehicle perception data, m points are uniformly sampled on the lth segment of the path to obtain the cumulative distance σ of the vehicle at m points on each segment of the path l lj ,j∈(0,m) and its upper and lower boundary data of the distance obstacle Determine the set of inequality constraints 5. The autonomous driving path planning method based on holomorphic embedding and trajectory following according to claim 1, characterized in that: In step S24), the equality constraint set Including the equality constraints of the initial and end points and the smoothness constraints between segments, the inequality constraint set Include boundary constraints on sampling points.

6. The autonomous driving path planning method based on holomorphic embedding and trajectory following according to claim 5, characterized in that: In step S24), since the equality constraints of the initial point and the end point and the smoothness constraints between the segments are all about the variable a l0 ,…,a l5 ,l=1,…,p is a linear function, so the equality constraint is uniformly expressed as: b eq x=b eq ; Where, β eq Represents about σ l ,l=1,…,p and its power coefficient matrix;b eq = [τ0 τ′0 a 15 … the e … 0] T ;x=[a 10 … a 15 … a p0 … a p5 ] T ; The boundary constraints on the sampling points are expressed as: b ieq x≥b ieq ; By introducing the slack variable z>0, the above inequality is transformed into an equality constraint: b ieq x-z=b ieq ; Among them, β ieq Represents about σ l ,l=1,…,p and its power coefficient matrix; x=[a 10 ,…,a 15 ,…,a p0 ,…,a p5 ] T ; They represent the upper and lower boundaries of the distance from the j-th point on the l-th path to the obstacle.

7. The autonomous driving path planning method based on holomorphic embedding and trajectory following according to claim 1, characterized in that: In step S4), the embedding system of the path planning model is solved using the holomorphic embedding method, which specifically includes the following steps: S41) Assuming the arc length parameter is α, for each component of the solution function vector X = (x, y, s, h), write it as a power series with parameter α expanded at 0: h(a)=∑ q≥0 h q a q ; x j (a)=∑ q≥0 x jq a q ,1≤j≤n; y i (a)=∑ q≥0 y iq a q ,1≤i≤l; (5) s j (a)=∑ q≥0 s jq a q ,1≤j≤n; Where q represents the order of the power series term; x jq and s jq denotes the qth order power series coefficient of the jth component of the vector functions x and s respectively; h q represents the qth order power series coefficient of the vector function h; y iq represents the coefficient of the qth order power series of the i-th component of the vector function y, where x and s have n components and y has l components; S42) Establish the arc length parameterization normalization equation: S43) Substitute formula (5) into formulas (2)-(4) and (6) to obtain: Where, Represents the qth order power series coefficient vector of vector function x, y, s respectively; h q represents the coefficient of the qth order power series of the vector function h; represent the initial values ​​of the j-th component of x and s respectively; S44) By comparing the coefficients of the same power of α on both sides of equations (7)-(10), determine the unknown vector function x jq ,y iq ,s jq ,j=1,…,n;i=1,…,l and unknown number h q By comparing the two sides of the equation α q The coefficient is: When q=1: When q≥2; S45) Let X = (x, y, s, h), solve the linear equations (11)-(18), and get X kq (α), k=1,…,2n+l+1,q≥1, and thus construct a rational approximation function based on the existing power series information to expand the effective interval and finally obtain the path planning function of the autonomous vehicle; Vehicles received And calculate the path trajectory of the p-segment path Realize the generation and execution of vehicle control instructions.

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