Automatic driving path planning method based on full-pure embedding and trajectory following

Abstract

The invention provides an automatic driving path planning method based on full-pure embedding and trajectory following. The method comprises the following steps: acquiring a corresponding automatic driving vehicle and path planning data; establishing a vehicle path planning model; converting the vehicle path planning model into a nonlinear planning form and constructing a corresponding embedded system; solving an embedding system of the path planning model by using a full-pure embedding method to obtain a path planning function of the autonomous vehicle; and returning the path drawing function of the autonomous vehicle to the vehicle, and performing path and vehicle control. According to the fast and flexible full-pure embedding method and the brand-new path planning method based on track following, the defects that an existing common automatic driving path planning method is low in convergence speed, irregular in convergence domain and the like are overcome; meanwhile, the defects that an existing iteration method based on a prediction-correction interior point method and the like is large in calculation amount, long in consumed time, large in storage space consumption and the like are overcome; and the calculation efficiency, the scale and the precision are remarkably improved.

Description

Technical Field

[0001] The present invention relates to the field of autonomous driving technology, and in particular to an autonomous driving path planning method based on holomorphic embedding and trajectory following. Background Art

[0002] Path planning is a key component of autonomous vehicle motion planning and is closely related to the safety of vehicle driving and the comfort experience of passengers. In urban traffic scenarios, autonomous vehicles need to navigate in complex and changing 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 starting configuration and the target configuration so that every point in the function is in the collision-free space. For autonomous vehicles, especially those with passengers, path planning not only needs to calculate a safe path, but more importantly, a comfortable path, that is, a path with comfortable changes in geometric properties.

[0004] Among the many research results on nonlinear programming problems, the interior point method of existing technology has advantages such as polynomial time complexity and is one of the most promising excellent algorithms. However, the solution methods of classic nonlinear and planning problems based on iterative ideas have several common defects:

[0005] 1. Iterative methods such as the prediction-correction interior point method will inevitably involve multiple calculations of the Jacobian matrix, as well as multiple prediction and correction calculations. Therefore, this method is computationally intensive and time-consuming.

[0006] 2. When solving optimization problems, the prediction-correction interior point method may make it difficult for the algorithm to converge because the prediction point may jump out of the convergence domain. In addition, the convergence domain of traditional nonlinear optimization methods is irregular and may even have a fractal structure, making it difficult to determine its boundary.

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

[0008] 4. The iterative method only calculates a limited number of approximate points on the center trajectory, making it difficult to characterize the convergence behavior of the interior point method. Summary of the invention

[0009] In view of the shortcomings of the prior art, the present invention provides an autonomous driving path planning method based on holomorphic embedding and trajectory following. The present invention solves the defects of the existing commonly used autonomous driving path planning methods such as slow convergence speed and irregular convergence domain, while also solving the defects of the existing prediction-correction interior point method such as large amount of calculation, long time consumption, and high storage space consumption. The present invention can completely and effectively follow the solution curve and characterize the behavior of the solution curve.

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

[0011] S1), obtaining corresponding autonomous 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 embedded system;

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

[0015] S5) transmitting the parameters of the path planning function of the autonomous driving vehicle back to the vehicle to perform path and vehicle control.

[0016] Preferably, step S1) 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.

[0017] Preferably, step S1) comprises the following steps:

[0018] S11) Use GPS, inertial navigation system (IMU) and high-precision map technology to obtain the precise position and road information of the vehicle in the global coordinate system;

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

[0020] Preferably, step S11) specifically includes:

[0021] 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 path segment l along the reference line is obtained l ; Assign acceleration weights w1, w2, w3; Determine the objective function based on the loss function expression;

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

[0023] Preferably, step S12) specifically includes:

[0024] S121), based on the vehicle perception data, uniformly sample m points on the lth segment of the path to obtain the cumulative distance σ of the m points on each segment of the road l lj , j∈(0,m) and its upper and lower boundary data of the distance obstacle Determine the set of inequality constraints

[0025] Preferably, in step S2), a vehicle path planning model is established, which specifically includes the following steps:

[0026] S21), for each path l, a quintic spline function f is used 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 formula, 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;

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

[0030]

[0031] 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);

[0032] S23), the objective function is expressed as about the variable a l0 ~a l5 Quadratic function of (l=1,…,p):

[0033]

[0034] S24) Establishing an equality constraint set and inequality constraint set

[0035] Preferably, in step S24), the equality constraint set Includes equality constraints at the initial and end points and smoothness constraints between segments.

[0036] As a preferred embodiment, 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:

[0037] β eq χ=b eq ;

[0038] In the formula, β eq Represents about σ l , l = 1, ..., p and its power coefficient matrix; b eq =[τ0 τ′0 a 15 … τ″ e …0] T ; χ = [a 10 … a 15 … a p0 … a p5 ] T .

[0039] Preferably, in step S24), the inequality constraint set Including boundary constraints on sampling points, expressed as:

[0040] β ieq χ≥b ieq ;

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

[0042] β ieq χ-z=b ieq ;

[0043] Among them, β ieq Represents about σ l , l = 1, ..., p and its power coefficient matrix;

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

[0045]

[0046] They respectively represent the upper and lower boundaries of the obstacle from the j-th point on the l-th path.

[0047] Preferably, in step S3), the objective function g(x) is converted into a nonlinear programming form, that is:

[0048]

[0049] 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 S23); The coefficient matrix of the first-order terms 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.

[0050] Preferably, 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] in,

[0055] In the formula, The parameters y(h), x(h), s(h), and h of the dual function are all variables to be optimized; diag(x) represents a diagonal matrix with x as the diagonal element; x 0 ,y 0 ,s 0 ,h 0 are the initial values ​​of variables x, y, s, and h respectively.

[0056] Preferably, in step S4), the embedding system of the path planning model is solved by using the holomorphic embedding method, which specifically includes the following steps:

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

[0058] h(α)=∑ q≥0 h q α q ;

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

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

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

[0062] In the formula, q represents the order of the power series term; x jq and jq denote the qth power series coefficient of the jth component of the vector function 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;

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

[0064]

[0065] S43), Substitute formula (5) into formula (2)-(4) and formula (6), and we get:

[0066]

[0067] In the formula, Respectively represent the coefficient vectors of the qth order power series of vector functions x, y, s; h q represents the coefficient of the qth order power series of the vector function h; denote the initial values ​​of the j-th component of x and s respectively;

[0068] 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 coefficients are:

[0069] When q=1:

[0070]

[0071] When q≥2;

[0072]

[0073] 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 approximate function based on the existing power series information to expand the effective interval, and finally obtain the path planning function of the autonomous driving vehicle.

[0074] Preferably, in step S5), the vehicle receives And calculate the trajectory of the p-segment path Realize the generation and execution of vehicle control instructions.

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

[0076] 1. The fast and flexible full-morphic embedding method and the new path planning method of trajectory following of the present invention solve the defects of the existing common automatic driving path planning methods such as slow convergence speed and irregular convergence domain. It also solves the defects of the existing prediction-correction interior point method such as large amount of calculation, long time consumption and large storage space consumption.

[0077] 2. The present invention adopts the holomorphic embedding method, based on the idea of ​​piecewise rational approximation, and proposes a non-iterative trajectory following method to solve the path planning problem of autonomous driving, and then gives an approximate solution function expression, which effectively solves the problems of many iterations, large amount of calculation, and easy correction failure when the traditional numerical method tracks the center trajectory. The method is applied to solving the path planning problem of autonomous driving facing multi-obstacle scenarios;

[0078] 3. Compared with traditional methods, the present invention has significant improvements in computing efficiency, scale and accuracy. Moreover, when solving path planning nonlinear programming, 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 It is a schematic diagram of the process of solving the path planning model based on holomorphic embedding of the present invention. DETAILED DESCRIPTION

[0081] The specific implementation of the present invention will be further described below in conjunction with 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), obtaining corresponding autonomous driving vehicle and path planning data;

[0084] In this embodiment, the vehicle and path planning data include 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. The steps include:

[0085] S11) Use GPS, inertial navigation system (IMU) and high-precision map technology to obtain the precise location and road information of the vehicle 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 path segment 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 of various orders; 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), based on the vehicle perception data, uniformly sample m points on the lth segment of the path to obtain the cumulative distance σ of the m points on each segment of the road l lj , j∈(0,m) and its upper and lower boundary data of the distance obstacle Determine the set of inequality constraints

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

[0091] S21), for each path l, a quintic spline function f is used 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 formula, 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;

[0094] S22), establish the objective function of vehicle path planning, that is, to minimize the driving distance and smooth the path during the path driving process, so as to achieve the purpose of less fuel consumption, and the expression of the objective function g(x) is:

[0095]

[0096] 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);

[0097] S23), the objective function is expressed as about the variable a l0 ~a l5 Quadratic function of (l=1,…,p):

[0098]

[0099] in,

[0100]

[0101]

[0102] S24) Establishing an equality constraint set and inequality constraint set Among them, the equality constraint set Including the equality constraints of the initial point and the end point and the smoothness constraints between the segments; the inequality constraint set Include boundary constraints on the sampling points.

[0103] The equality constraints of the initial point and the end point are:

[0104] Assume that the initial point (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] Assume that the end point is (σ e , τ e ) is known; σ e Indicates the end position of the parameter, τ e Indicates the end lateral offset; let the end point (σ e , τ e )The first-order and second-order derivatives are (σ0, τ′ e ) and (σ0, τ″ e ); obtained by the following formula:

[0106]

[0107]

[0108] Correspondingly, the offset τ of the end point position is obtained e , τ′ e , τ″ e Satisfied equality constraints.

[0109] The smoothing constraints between the segments are smoothed at the connection points to satisfy the function f l(σ) and its first-order continuous, second-order continuous, and third-order continuous properties;

[0110] f l (σ l )=f l+1 (σ0);

[0111] f l ′(σ l ) = f′ l+1 (σ0);

[0112] f l ″(σ l )=f″ l+1 (σ0);

[0113] f l ″′(σ l )=f″′ l+1 (σ0);

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

[0115]

[0116] Among them, σ0=0.

[0117] In this embodiment, 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:

[0118] β eq χ=b eq ;

[0119] In the formula, β eq Represents about σ l , l = 1, ..., p and its power coefficient matrix; 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 points is as follows: m points are uniformly sampled in the lth segment of the path, and the points are checked to see whether they hit the obstacle boundary. Then the inequality constraint is calculated as follows:

[0121]

[0122] Among them, σ lj represents the cumulative distance of the jth point in the lth path, They respectively represent the upper and lower boundaries of the obstacle from the j-th point on the l-th path.

[0123] Therefore, the inequality constraint set Including boundary constraints on sampling points, expressed as: β ieq χ≥b ieq ; Among them, β ieq Represents about σ l , l = 1, ..., p and its power coefficient matrix;

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

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

[0126] This embodiment converts the objective function g(x) into a nonlinear programming form, namely:

[0127]

[0128] 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 S23); The coefficient matrix of the first-order terms 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.

[0129] In this embodiment, the embedded system for constructing 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] In the formula, The parameters y(h), x(h), s(h), and h of the dual function are all variables to be optimized; diag(x) represents a diagonal matrix with x as the diagonal element; x 0 ,y 0 ,s 0 ,h 0 are the initial values ​​of variables x, y, s, and h respectively.

[0135] S4), using the holomorphic embedding method to solve the embedded system of the path planning model, and 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 in the solution function vector X=(x, y, s, h), write it as a power series expanded at 0 with parameter α:

[0137]

[0138] In the formula, q represents the order of the power series term; x jq and jq denote the qth power series coefficient of the jth component of the vector function 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 formula (2)-(4) and formula (6), and we get:

[0142]

[0143] In the formula, Respectively represent the coefficient vectors of the qth order power series of vector functions x, y, s; h q represents the coefficient of the qth order power series of the vector function h; denote the initial values ​​of the j-th component of x and s respectively;

[0144] 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 coefficients are:

[0145] When q=1:

[0146]

[0147] When q≥2;

[0148]

[0149]

[0150] 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 approximate function based on the existing power series information to expand the effective interval, and finally obtain the path planning function of the autonomous driving vehicle.

[0151] As a preferred embodiment of this invention, step S45) specifically includes the following steps:

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

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

[0154]

[0155] Among them, X krepresents the kth component of X; X kθ represents the qth order power series coefficient of the kth component of X;

[0156] S453), Substitute the power series into the embedded system (2)-(4), (6), and obtain the system of equations (7)-(10) with the coefficients of the power series expansion as unknowns;

[0157] S454), when q = 1, solve the equations satisfied by equations (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, the q-1th order power series coefficient X of the kth component of X k(q-1) =(x j(q-1) ,y i(q-1) ,s j(q-1) ,h (q-1) ) is substituted into equations (15)-(18) to solve the linear equations and obtain the q-order power series coefficient of the k-th component:

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

[0161] S455), using the power series information of vector X(α), construct a rational approximate function; that is, construct a rational approximate function of X=(x, y, s, h), which are respectively denoted as [m / n] x , [m / n] y , [m / n] s , [m / n] h ; Where m represents the order of the rational approximation numerator, and n represents the order of the rational approximation denominator;

[0162] S456) Assign the value X(Δα) at ​​the end point of the valid interval of the same embedded system as above to x # ,y # ,s # ,h # , as the value of the next valid interval of x, y, s, h at the starting point α = 0;

[0163] S457) Determine whether the error norm on both sides of the equations (7)-(10) is less than e in α∈[0, Δα]* ; If it is not satisfied, reduce Δα until it is satisfied; that is, find the error norm on both sides of equations (7)-(10) less than the threshold e * And Δα is as large as possible; specifically:

[0164] If Δα>δα, update Δα←ρΔα (where “←” indicates update); repeat step S307;

[0165] Otherwise, the calculation is terminated and the verification fails;

[0166] S458), Update x # ,y # ,s # ,h # , as the value of the next valid interval of x, y, s, h at the new starting point α = 0, repeat steps S452) to S457) until the condition is met

[0167] S459) Take the variable a in x l0 , …, a l5 The value of (l=1, ..., p) at h=1 Then the path planning function of the autonomous driving vehicle is That is the path trajectory of the p-segment planned path.

[0168] S5), the parameters of the path planning function of the autonomous driving vehicle are transmitted back to the vehicle to control the path and the vehicle, and the vehicle receives And calculate the trajectory of the p-segment path Realize the generation and execution of vehicle control instructions.

[0169] The above embodiments and descriptions are only for illustrating the principles and best embodiments of the present invention. Without departing from the spirit and scope of the present invention, the present invention may be subject to various changes and improvements, all of which fall within the scope of the present invention to be protected.

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), obtaining corresponding autonomous driving vehicle and path planning data; S2), establishing a vehicle path planning model; S3), transforming the vehicle path planning model into a nonlinear programming form and constructing a corresponding embedded system; S4), using the holomorphic embedding method to solve the embedding system of the path planning model, and obtain the path planning function of the autonomous driving vehicle; S5) transmitting the parameters of the path planning function of the autonomous driving vehicle back to the vehicle to perform path and vehicle control.

2. The method for autonomous driving path planning 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 method for autonomous driving path planning 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 path segment 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 end position (σ e ,τ e ) and the accumulated distance σ of the first segment l and its derivatives of various orders; thus determining the set of equality constraints 4. The method for autonomous driving path planning 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 path to obtain the cumulative distance σ of the m points on each path l of the vehicle lj ,j∈(0,n) and its upper and lower boundary data of the distance obstacle Determine the set of inequality constraints 5. The method for autonomous driving path planning based on holomorphic embedding and trajectory following according to claim 4, characterized in that: In step S2), a vehicle path planning model is established, which specifically includes 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 ); In the formula, 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), establish 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), the objective function is expressed as about the variable a l0 ~a l5 Quadratic function of (l=1,…,p): in: S24) Establishing an equality constraint set and inequality constraint set 6. The method for autonomous driving path planning based on holomorphic embedding and trajectory following according to claim 5, 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 the segments, the inequality constraint set Include boundary constraints on the sampling points.

7. The method for autonomous driving path planning based on holomorphic embedding and trajectory following according to claim 6, 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 ; In the formula, β eq Represents about σ l ,l=1,…,p and its power coefficient matrix; b eq =[τ0 τ′0 a 15 … τ′ e … 0] T ; χ = [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 respectively represent the upper and lower boundaries of the obstacle from the j-th point on the l-th path.

8. The method for autonomous driving path planning based on holomorphic embedding and trajectory following according to claim 7, characterized in that: In step S3), the objective function g(x) is converted into a nonlinear programming form, namely: 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 coefficient matrix of the first-order terms 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.

9. The method for autonomous driving path planning based on holomorphic embedding and trajectory following according to claim 8, characterized in that: In step S3), the embedded system of the path planning model is constructed as follows: 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, In the formula, The parameters y(h), x(h), s(h), and h of the dual function are all variables to be optimized; diag(x) represents a diagonal matrix with x as the diagonal element; x 0 ,y 0 ,s 0 ,h 0 are the initial values ​​of variables x, y, s, and h respectively.

10. The method for autonomous driving path planning based on holomorphic embedding and trajectory following according to claim 9, characterized in that: In step S4), the embedding system of the path planning model is solved by using the holomorphic embedding method, which specifically includes the following steps: S41), assuming that the arc length parameter is α, for each component in the solution function vector X = (x, y, s, h), write it as a power series expanded at 0 with parameter α: In the formula, q represents the order of the power series term; x jq and jq denote the qth power series coefficient of the jth component of the vector function 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 formula (2)-(4) and formula (6), and we get: In the formula, Respectively represent the qth order power series coefficient vectors of vector functions x, y, s; h q represents the coefficient of the qth order power series of the vector function h; denote 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 coefficients are: 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, so as to construct a rational approximate function based on the existing power series information to expand the effective interval and finally obtain the path planning function of the autonomous driving vehicle; Vehicles received by And calculate the path trajectory of the p-segment path Realize the generation and execution of vehicle control instructions.

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