CN118424296A - Real-time track planning method, device, medium and product based on track analysis solution - Google Patents

Abstract

The invention discloses a real-time track planning method, device, medium and product based on a track analytic solution, and relates to the technical field of track planning. The method comprises the following steps: acquiring a track analysis solution and a path point constraint of an aircraft; determining a track parameterized expression based on the track resolution; according to the path point constraint, the track parameterization expression and the track constraint, converting the optimal control problem of track parameterization expression planning into a multi-stage profile parameter planning problem; carrying out iterative solution on the multi-stage profile parameter planning problem by utilizing a modified Newton method, and determining optimal no-fly zone avoidance real-time track planning parameters; and controlling the aircraft based on the no-fly zone avoidance real-time track planning parameters. According to the invention, the correction Newton method is utilized to carry out iterative solution on the multi-stage profile parameter planning problem, so that the efficiency and the accuracy of real-time track planning for avoiding in the no-fly zone can be improved.

Description

A real-time trajectory planning method, device, medium and product based on trajectory analytical solution

Technical Field

The present invention relates to the field of trajectory planning technology, and in particular to a real-time trajectory planning method, device, medium and product based on trajectory analytical solution.

Background technique

In the field of hypersonic glide vehicle (HGV) control, no-fly zone avoidance is the process of using trajectory analysis design methods to generate trajectories in real time under the premise of a known decision path, including trajectory analysis prediction, multi-stage trajectory parameterization solution, and tracking guidance. When avoiding a no-fly zone, the HGV has large lateral maneuvers, and its dynamics have aerodynamic characteristics of large angle of attack and large roll angle, which makes the lateral and longitudinal motions strongly coupled and highly nonlinear. At present, the multi-stage trajectory parameterization solution mostly uses the Gaussian algorithm, which has a large amount of calculation and is difficult to converge, reducing the efficiency and accuracy of real-time trajectory planning.

Summary of the invention

The purpose of the present invention is to provide a real-time trajectory planning method, device, medium and product based on trajectory analytical solution, which can improve the efficiency and accuracy of real-time trajectory planning for avoiding no-fly zones.

To achieve the above-mentioned purpose, the present invention provides the following scheme: a real-time trajectory planning method based on trajectory analytical solution, comprising: obtaining the trajectory analytical solution and path point constraints of the aircraft; the trajectory analytical solution is obtained by the upper-level path decision-making, according to the no-fly zone information and the state of the aircraft, establishing the analytical error relationship between the motion equation and the perturbation analytical solution, converting the analytical error relationship into a high-order deformation equation and solving it recursively.

A trajectory parameterization expression is determined based on the trajectory analytical solution.

According to the path point constraints, trajectory parameterized expressions and trajectory constraints, the optimal control problem of trajectory parameterized expression planning is transformed into a multi-stage profile parameter planning problem.

The modified Newton method is used to iteratively solve the multi-stage profile parameter planning problem to determine the optimal no-fly zone avoidance real-time trajectory planning parameters.

The aircraft is controlled based on the no-fly zone avoidance real-time trajectory planning parameters.

A computer device comprises: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement a real-time trajectory planning method based on trajectory analytical solution.

A computer-readable storage medium stores a computer program, which, when executed by a processor, implements a real-time trajectory planning method based on trajectory analytical solution.

A computer program product comprises a computer program, which, when executed by a processor, implements a real-time trajectory planning method based on trajectory analytical solution.

According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

The purpose of the present invention is to provide a real-time trajectory planning method, device, medium and product based on trajectory analytical solution, which obtains the most economical no-fly zone avoidance trajectory for lateral maneuvering by controlling the lateral and longitudinal flight profiles in sections. The method converts the conventional trajectory planning optimal control problem into a multi-stage parameter planning problem containing only 2n +1 trajectory parameterized expression profile parameters, the iterative process is fully analytical, the code is fully adjustable and controllable, and has real-time application capabilities.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

FIG1 is a flow chart of a real-time trajectory planning method based on trajectory analytical solution provided in Embodiment 1 of the present invention;

FIG. 2 is a schematic diagram of a parameterized form of a lateral acceleration profile provided in Example 1 of the present invention.

Detailed ways

The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in 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 creative work are within the scope of protection of the present invention.

The purpose of the present invention is to provide a real-time trajectory planning method, device, medium and product based on trajectory analytical solution, which can improve the efficiency and accuracy of real-time trajectory planning for avoiding no-fly zones.

In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

Embodiment 1: As shown in FIG1 , a real-time trajectory planning method based on trajectory analytical solution in this embodiment includes: Step 101: Obtaining trajectory analytical solution and path point constraints of an aircraft. The trajectory analytical solution is obtained by the upper-level path decision-making, according to the no-fly zone information and the state of the aircraft, establishing an analytical error relationship between the motion equation and the perturbation analytical solution, converting the analytical error relationship into a high-order deformation equation and recursively solving it.

Step 102: Determine a trajectory parameterization expression based on the trajectory analytical solution.

Step 103: According to the path point constraints, the trajectory parameterized expression and the trajectory constraints, the trajectory parameterized expression planning optimal control problem is converted into a multi-stage profile parameter planning problem.

Step 104: Use the modified Newton method to iteratively solve the multi-stage profile parameter planning problem to determine the optimal no-fly zone avoidance real-time trajectory planning parameters.

Step 105: Control the aircraft based on the real-time trajectory planning parameters for avoiding the no-fly zone.

Among them, the multi-stage profile parameter planning problem is:

.

Where, J is the objective function of the multi-stage profile parameter planning problem; The independent variable The value at the i -th path point; The independent variable The value at the i-1th waypoint; n is the total number of waypoints in the waypoint constraint; is the first-order coefficient of lift acceleration profile; is the zero-order coefficient of lift acceleration profile; is the independent variable longitudinal range; Analyze expressions for velocity; Analyze the expression for the horizontal process; is the lift acceleration at the end of the segment; is the initial lift acceleration; For terminal voyage; is the initial voyage; is the terminal velocity; The terminal horizontal stroke.

Step 104 includes: Step 104-1: using the Lagrange multiplier method, the multi-stage profile parameter planning problem is transformed into an unconstrained parameter optimization problem, and the Lagrange equation is determined.

Step 104 - 2: Calculate the initial profile parameters of each iterative profile, solve the Lagrangian equation according to the initial profile parameters, and obtain the initial Lagrangian multiplier.

Step 104-3: Use the initial Lagrange multiplier as the iteration parameter of the first iteration of the Lagrange equation.

Step 104-4: Get the current step length.

Step 104-5: Set the number of iterations j=1.

Step 104-6: Determine the Jacobian matrix at the jth iteration and the Hessian matrix at the jth iteration according to the iteration parameters at the jth iteration.

Step 104-7: Determine the iteration parameters at the j+1th iteration according to the Jacobian matrix at the jth iteration and the Hessian matrix at the jth iteration.

Step 104 - 8 : Determine the Jacobian matrix at the j+1th iteration according to the iteration parameter at the j+1th iteration.

Step 104 - 9 : judging whether the convergence tolerance condition is satisfied according to the Jacobian matrix at the j+1th iteration and the current step length, and obtaining a first judgment result.

Step 104-10: If the first judgment result is no, then update the current step length, increase the value of the iteration number j+1 by 1, and return to step 104-7. Updating the current step length includes: determining the ratio of the current step length to the step length change as the updated current step length.

Step 104 - 11: If the first judgment result is yes, determine whether the current step length is within a preset step length range to obtain a second judgment result.

Step 104 - 12: If the second judgment result is no, update the current step length, increase the value of the iteration number j+1 by 1, and return to step 104 - 7.

Step 104 - 13 : If the second judgment result is yes, then determine the iteration parameters at the j+1th iteration as the optimal no-fly zone avoidance real-time trajectory planning parameters.

The convergence tolerance condition is:

.

in, is the Jacobian matrix at the j+1th iteration; is the Jacobian matrix at the jth iteration; is the current step length; is the convergence tolerance.

Step 104-12 includes: determining the ratio of the current step length to the step length change as the updated current step length.

Step 104-2 includes: Step 104-2-1: Order Initial value of the first-order term of the profile The value of is 0, and an analytical solution is obtained; the analytical solution includes a velocity analytical solution, a heading angle analytical solution and a lateral range analytical solution.

Step 104-2-2: Based on the velocity analytical solution, construct the terminal velocity constraint analytical expression of each sub-segment trajectory.

Step 104-2-3: Inversely solve the multiple terminal velocity constraint analytical expressions to obtain the corresponding Profile parameters; The profile is the drag acceleration profile; The profile is the lift acceleration profile.

Step 104-2-4: Based on the analytical solution of the horizontal distance, obtain the analytical expression of the terminal horizontal distance of each sub-segment trajectory.

Step 104-2-5: Inversely solve the multiple terminal horizontal path analytical expressions to obtain the corresponding Section parameters.

Step 104-2-6: Based on multiple Section parameters and multiple The profile parameters construct the initial Lagrange multipliers.

The terminal velocity constraint analytical expression is:

.

in, is the terminal velocity constraint; is the terminal longitudinal distance; is the radius of the Earth; for Section parameters The initial value of is the analytical solution for velocity; is the average radial distance;

The profile parameters are:

.

Where g is the acceleration due to gravity;

The terminal cross-distance analytical formula is:

.

The profile parameters are:

.

in, is the terminal traverse constraint of the sub-segment trajectory; The independent variable The value at the i-th path point; The independent variable The value at the i-1th path point; Indicates average speed;

The Jacobian matrix is:

.

in, is the Jacobian matrix at the jth iteration; is the partial derivative of the Lagrangian function with respect to the parameter p; is the partial derivative of the Lagrangian function with respect to the parameter λ; is the first derivative of the performance index; For the co-state; is the partial derivative of the constraint function with respect to the parameter p; is the constraint function;

The Hessian matrix is:

.

in, is the Hessian matrix; , , and All are Hessian matrix elements; is the second-order derivative of the performance index; is the transpose of the first-order derivative of the constraint function; is the second-order derivative of the constraint function.

According to the trajectory parameterization expression, a parameterized model of the trajectory planning problem is established, and a flight profile parameter solution method is designed to generate a no-fly zone avoidance trajectory in real time. First, since the trajectory parameterization expression is controlled by the lateral and longitudinal flight profiles, that is, the component of the lift-to-drag ratio on the plumb plane ( profile) and the component of lift acceleration in the horizontal plane ( profile), so a parameterized profile is designed to transform the trajectory planning optimal control problem into a multi-stage profile parameter planning problem; then, a customized real-time solution method for the multi-stage profile parameter planning problem is proposed, and the initial value and descent gradient of parameter iteration are selected analytically; finally, a parameter iteration solution algorithm based on the modified Newton method is designed to realize the real-time application of the trajectory planning problem.

1 Parametric modeling of multi-stage trajectory planning.

According to the no-fly zone avoidance path obtained by the upper-level path decision, the trajectory is divided into segments by path point segmentation points, and a multi-stage profile parameter equation is established. Based on the homotopy analytical solution of the trajectory, the flight profile parameter equation, the re-entry terminal constraint, the path point constraint and the minimum control force performance index, the no-fly zone avoidance trajectory planning problem is transformed into a multi-stage trajectory parameterized expression profile parameter planning problem.

Based on the trajectory homology analytical solution, in the generalized equatorial coordinate system, the flight longitudinal distance As independent variables, we can get the flight speed V and the horizontal range. , the trajectory parameterized expression of the track deviation angle ξ , so as to make an analytical prediction of the terminal flight state. Among them, the trajectory is planned by Section and The profile is controlled. The profile controls speed and range and determines the longitudinal flight trajectory; The profile controls the heading and range, determining the lateral flight trajectory.

The present invention will Section and The section form is designed as follows:

(1)

in, is the component of the lift acceleration of the i -th trajectory in the horizontal plane, The independent variable The value at each path point, the third minor formula is Connection constraints for sections, A schematic diagram of the cross-section is shown in FIG2 . _i is the section control parameter to be solved, 2 n +1 in total.

Since the reentry corridor of HGV is narrow and irregular, considering the flexibility and physical feasibility of the profile, the transverse profile is in the form of a piecewise polynomial, and the trajectory is divided into n sub-segments according to the number of path points n (including the end point), each of which is in linear form and connected at the path point. In addition, since a small angle of attack change rate is often used during the reentry glide process to minimize the change of the aircraft flow field, thereby reducing the change of the aerodynamic heating distribution on the aircraft, and the angle of attack directly affects the size of the lift-to-drag ratio, the present invention will The profile is set as a constant to conform to the actual physical meaning. In actual flight, it will be adjusted in the range near the profile parameters according to the deviation from the nominal profile, that is, the flight profile is corrected through closed-loop tracking and guidance, and terminal control is achieved on the basis of satisfying various process constraints.

In order to be consistent with the performance index of the no-fly zone avoidance path decision-trajectory planning problem, the performance index of the multi-stage trajectory parameterization expression profile parameter planning problem is also set to the minimum cumulative lateral control force. ,Available:

(2)

In addition, based on the terminal constraints of the reentry glide, the path point constraints obtained by the upper path decision, and the connection constraints between the sub-segments, combined with the homotopy analytical equation of the glide trajectory, the terminal constraint equation predicted by the trajectory parameterization expression is established. The terminal constraints include the terminal velocity Constraints, terminal positions, or horizontal travel Constraints, the path point constraints are the terminal traverse distances of each sub-segment trajectory Constraint, and the terminal horizontal distance of the nth track = .

Combining the above constraints and indicators, the optimal control problem of HGV no-fly zone avoidance trajectory planning can be simplified to a multi-stage parameter planning problem as shown below:

Problem 4.1 HGV no-fly zone avoidance multi-stage trajectory parameterization expression profile parameter planning problem:

(3)

in, The independent variable The value at each path point, and the vertical distance of the terminal of the nth track = , the initial longitudinal distance of the nth track =0, that is, the terminal longitudinal distance of each sub-segment trajectory. When the second sub-formula is calculated by analytical solution, the initial horizontal distance of the i -th segment trajectory is the terminal horizontal distance of the i -1-th segment trajectory, that is, =0, initial horizontal distance of the nth track = , i =1,…, n -1.

The optimization index is J ( p ), and the nonlinear equation system consisting of 2n constraints in formula (3) can be abbreviated as F ( p ) = 0, where is the optimization parameter vector. Then problem 4.1 can be simplified as follows:

(4)

Problem 4.1 is a parameter optimization problem with only equality constraints. According to optimization theory, the Lagrange multiplier method is used to transform it into an unconstrained parameter optimization problem. Define the Lagrange equation:

(5)

in, is the Lagrange multiplier vector to be solved, then the first-order necessary condition for the above problem is:

(6)

According to the first-order necessary conditions, a nonlinear equation group consisting of 4n +1 equations can be obtained, and the 4n +1 solution parameters of the nonlinear equation group are y =( p ; λ ). Therefore, the multi-stage trajectory profile parameter planning problem can be transformed into a nonlinear equation group (Equation (6)). The present invention adopts Newton's method to solve it.

2 Customization of multi-stage trajectory parameter planning.

Newton iteration method is one of the effective ways to solve parameter planning problems. However, when there are many iterative variables, the original Newton method is not easy to converge and is greatly affected by the initial value, making it difficult to apply in real time. To this end, the present invention proposes two customized strategies to solve the multi-stage trajectory profile parameter planning problem: ① customization of the initial value of the profile parameter iteration; ② customization of the profile parameter descent gradient.

2.1 Customization of initial values of profile parameter iteration.

Since the homotopy analytical solution of the trajectory is too complex and it is difficult to select the initial value, the analytical solution obtained by the present invention based on the perturbation theory is , an approximate feasible solution of the profile parameters is obtained analytically, which is used as the initial value of the Newton iteration method , in order to be sufficiently close to the convergence region.

make The initial value of the first-order term of the profile is , solve the analytical solution as the initial value of the iteration of the profile parameters. Among them, according to the terminal velocity constraint , solve for the parameters The initial value of , and according to the terminal trajectories of each sub-segment , solve for the parameters The initial value of , i =1,…, n . In addition, set , together as the initial value of Newton iteration , and further iterations are performed to obtain the precise values of the profile parameters.

Velocity analytical solution ⁾ only with The parameters of the profile are related to The analytical solution of is:

(7)

Right now:

(8)

Then the parameter k ₁₀ ⁰ can be inversely solved to obtain:

(9)

Furthermore, according to the heading angle He Hengcheng The analytical solution of each sub-segment trajectory is obtained Analytical expression, let , solve for the parameters . Because The analytical solution is introduced into After analyzing the formula, the integrand is not integrable. He Hengcheng The velocity is approximated as a constant .therefore, Available:

(10)

in, Indicates the terminal heading angle of the i-th trajectory.

Depend on The analytical solution of is:

(11)

Then the parameter The inverse solution is:

(12)

In summary, the initial value of Newton's iteration method is It can be expressed as follows:

(13)

The initial value obtained by this method is an approximate feasible solution to Problem 4.1, which is more conducive to the convergence of Newton's method than randomly selecting initial values.

2.2 Customization of profile parameter descent gradient.

In order to use the Newton iteration method, it is necessary to obtain the first and second order derivatives of the Lagrange equation, that is, the Jacobian matrix and the Hessian matrix Since the homotopy analytical solution uses many Gauss-Legendre integral formulas, the reverse derivation is difficult and the calculation is time-consuming. Therefore, the trajectory-based analytical solution is used to solve , , in order to speed up the computational efficiency of Newton's method iteration. Here, F ( p ) is obtained based on the homotopy analytical solution of the trajectory, and the analytical solution is only used for derivation.

The Lagrangian function can be expressed as follows:

(14)

in, is the lateral lift acceleration of the first trajectory, is the lateral lift acceleration of the second trajectory, is the lateral lift acceleration of the n-1th trajectory, is the lateral lift acceleration of the nth trajectory.

The Jacobian matrix of the Lagrangian function with respect to the iteration parameter y = [ p ; λ ] It can be expressed as follows:

(15)

The Hessian matrix of the Lagrangian function with respect to the iteration parameter y = [ p ; λ ] It can be expressed as follows:

(16)

Among them, , Write in the following format:

(17)

(18)

in, , , , , , , , , , , , , , , , , , , , , , , , and All are Heisen array elements; , , , , , , , , , , , , , , , , , , , , , , , and These are all constraint function gradient elements

Based on the analytical solution of the trajectory, the specific forms of the derivative components in equations (15) and (16) are analytically solved to obtain , The approximate analytical solution of . The analytical calculations of each component are given below.

First, based on the analytical solution, we introduce the calculation method of F ( p ) in equation (15). and each trajectory segment , used for derivation, as follows:

(19)

(20)

(twenty one)

in: is the analytical solution of the heading angle, The second polynomial is the third polynomial, dimensional polynomial coefficients, The longitudinal course of the kth trajectory.

(twenty two)

Write the Gauss-Legendre integral formula as the cumulative sum of functions at the quadrature nodes, , The present invention adopts the 10th order Legendre polynomial, Legendre Zero Determined by replacing the variables on the integral interval, Similarly, the integral coefficient on the integral interval [-1,1] By replacing the variables to the integral interval of each trajectory sub-segment ,Right now:

(twenty three)

Then, according to formula (19)-formula (21), formula (15) and formula (16) Each component can be solved analytically as follows:

(twenty four)

(25)

(26)

(27)

(28)

(29)

(30)

(31)

in, is the gradient element of the constraint function, is the gradient element of the constraint function, are the polynomial coefficients, is the gradient element of the constraint function, is the gradient element of the constraint function, is the analytical solution for the horizontal process, Lateral acceleration, is the gradient element of the constraint function, is the gradient element of the constraint function, is the gradient element of the constraint function, in equations (25) to (28) , in formula (29)-formula (31) .

Furthermore, the first-order derivative of the Lagrangian function in equation (15) with respect to the profile parameter p can be solved analytically as follows:

(32)

(33)

(34)

in, and are all Jacobian matrix elements, is the i-th longitudinal section, is the constraint function, and are the section coefficients, is the gradient element of the constraint function, and All are cooperative. , and They are all second-order derivative elements of constraint functions. and are all Hessian matrix elements, i = 1,…, n . Finally, let , the second-order derivative of the Lagrangian function with respect to the profile parameter p in equation (16) can be solved analytically as follows:

(35)

(36)

(37)

(38)

(39)

(40)

Through the above derivation, we can get the analytical form of each component in equation (15) and equation (16), thus obtaining , The analytical solution of ensures that the solution is updated in real time during the iteration process until the Newton method converges.

3 Parameterized solution algorithm for real-time trajectory planning.

On the basis of the customized method of multi-stage trajectory parameter planning, in order to improve the convergence range of parameter iteration, a multi-stage trajectory parameter solving algorithm based on the modified Newton method is designed to complete real-time trajectory planning.

The general expression of Newton's iteration method can be expressed as:

(41)

Among them, j is the number of iterations, and j = 0 is the initial value of the iteration.

The present invention adopts a customized modified Newton method to expand the convergence range and introduce a descending step length. The Newton iteration process is modified, and the one-dimensional line search criterion (Armjio criterion) is used to ensure that the result of each iteration is a descending process. This not only maintains the convergence speed of the Newton iteration, but also relaxes the requirements for the selection of initial values, thus improving the convergence characteristics of the iteration.

Modified Newton's method Modify the iterative formula of Newton's method as follows:

(42)

The initial value distance When the root is far away, if it cannot meet the following conditions:

(43)

The iteration will not converge. Once the initial value enters the convergence domain, Newton's method converges at a quadratic rate. Therefore, the purpose of the Armijo criterion is to select the iteration step size. So equation (43) holds true.

make is the descending direction at y ^j . According to the first-order Taylor expansion, if it satisfies:

(44)

Step length Satisfies the Armjio criterion, where are the complementary coefficients of the Taylor expansion.

Construct a one-dimensional line search and set the initial step size , if it does not satisfy equation (44), then The multiple decreases until it satisfies formula (44), and then selects the corresponding That's it.

Therefore, the parameterized solution algorithm for real-time trajectory planning to avoid no-fly zones is obtained as follows.

Initialization: the number of path points n of the avoidance path, the initial value of the HGV state x ₀ , the horizontal and vertical ranges of the path points , , terminal velocity , the homotopy analytical solution of the trajectory , analytical solution .

1: Set the number of iterations j = 0 and set the parameters of the modified Newton method .

2: Analytical calculation of iterative profile parameters and initial values of Lagrange multipliers (Formula (13)).

3: Analytical calculation of Lagrangian function with respect to iteration parameters The Jacobian matrix (Formula (15)).

4: while do.

5: Analytical calculation of Lagrangian function with respect to iteration parameters The Hessian matrix (Formula (16)).

6: Update the profile parameters and get (Formula (42)).

7: Analytical calculation of Lagrangian function with respect to iteration parameters The Jacobian matrix (Formula (15)).

8: while do.

9: .

10: Update the profile parameters and get (Formula (42)).

11: Analytical calculation of Lagrangian function with respect to iteration parameters The Jacobian matrix (Formula (15)).

12: endwhile.

13: Let j = j +1, y ^j = y ^{j +1} , .

14: .

15:endwhile.

16: return y ^j .

The algorithm steps can be summarized as follows:

1) Calculate the initial values of each iterative profile parameter and Lagrange multiplier .

2) Set the initial step size of Newton iteration .

3) Calculate the Lagrangian function with respect to the iteration parameter The Jacobian matrix and the Hessian matrix , get the updated parameters .

4) Calculation , determine whether the convergence tolerance ε _n is met. If so, the iteration stops and the optimal solution is output , otherwise, go to step 5).

5) Use 2-norm to measure vector and determine step size Does it satisfy the Armjio criterion? If so, let j = j +1. = , return to step 2), otherwise, keep making , update the parameters , until the Armjio criterion is met or is sufficiently small, let j = j +1, = , return to step 2).

The present invention proposes a parametric modeling, customization and iterative solution method for real-time trajectory planning problems based on trajectory homology analytical solutions. By controlling the lateral and longitudinal flight profiles in sections, a no-fly zone avoidance trajectory with the most economical lateral maneuvers is obtained. This method transforms the conventional trajectory planning optimal control problem into a multi-stage parameter planning problem containing only 2n+1 trajectory parameterized expression profile parameters. The iterative process is completely analytical, the code is fully adjustable and controllable, and has real-time application capabilities.

Embodiment 2: A computer device comprises: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of a real-time trajectory planning method based on trajectory analytical solution in Embodiment 1.

Embodiment 3: A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a real-time trajectory planning method based on trajectory analytical solution in Embodiment 1.

Embodiment 4: A computer program product comprises a computer program, which, when executed by a processor, implements the steps of a real-time trajectory planning method based on trajectory analytical solution in Embodiment 1.

Embodiment 5: A computer device, which may be a database. The computer device includes a processor, a memory, an input/output interface (Input/Output, referred to as I/O) and a communication interface. Among them, the processor, the memory and the input/output interface are connected through a system bus, and the communication interface is connected to the system bus through the input/output interface. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store pending transactions. The input/output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a real-time trajectory planning method based on trajectory analytical solution in Embodiment 1 is implemented.

It should be noted that the object information (including but not limited to object device information, object personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in the present invention are all information and data authorized by the object or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant laws, regulations and standards of relevant countries and regions.

Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided by the present invention can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. As an illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The database involved in each embodiment provided by the present invention may include at least one of a relational database and a non-relational database. Non-relational databases may include distributed databases based on blockchains, etc., but are not limited to this. The processor involved in each embodiment provided by the present invention may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but are not limited to this.

The technical features of the above embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

The present invention uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only used to help understand the method and core ideas of the present invention. At the same time, for those skilled in the art, according to the ideas of the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims (10)

1. The real-time track planning method based on the track analysis solution is characterized by comprising the following steps of:

Acquiring a track analysis solution and a path point constraint of an aircraft; the track analysis solution is obtained by establishing an analysis error relation between a motion equation and a perturbation analysis solution according to the information of the no-fly zone and the state of the aircraft by an upper layer path decision, converting the analysis error relation into a high-order deformation equation and solving in a hierarchical manner;

Determining a track parameterized expression based on the track analytic solution;

According to the path point constraint, the track parameterization expression and the track constraint, converting the optimal control problem of track parameterization expression planning into a multi-stage profile parameter planning problem;

carrying out iterative solution on the multi-stage profile parameter planning problem by using a modified Newton method, and determining optimal no-fly zone avoidance real-time track planning parameters;

And controlling the aircraft based on the no-fly zone avoidance real-time track planning parameters.

2. The method of claim 1, wherein the multi-stage profile parameter planning problem is:

；

Wherein J is an objective function of the multi-stage profile parameter planning problem; Longitudinal distance as independent variable A value at the i-th path point; Longitudinal distance as independent variable A value at the i-1 st waypoint; n is the total number of path points in the path point constraint; The first-order term coefficient of the lift acceleration profile is obtained; The zero-order term coefficient of the lift acceleration profile; is an independent variable longitudinal distance; Is a velocity resolution expression; the expression is analyzed for the transverse journey; The acceleration is the end-of-segment lift acceleration; The initial lift acceleration is the section; The terminal voyage is the terminal voyage; is the initial voyage; is the terminal speed; Is the terminal journey.

3. The method for real-time trajectory planning based on trajectory analysis solution according to claim 1, wherein iteratively solving the multi-stage profile parameter planning problem by using a modified newton method to determine optimal no-fly zone avoidance real-time trajectory planning parameters comprises:

Utilizing a Lagrange multiplier method to solve the problem of unconstrained parameter optimization of the multi-stage profile parameter planning problem, and determining a Lagrange equation;

Calculating initial profile parameters of each iterative profile, and solving a Lagrangian equation according to the initial profile parameters to obtain an initial Lagrangian multiplier;

taking the initial Lagrangian multiplier as an iteration parameter in the 1 st iteration of the Lagrangian equation;

Acquiring a current step length;

Let iteration number j=1;

according to iteration parameters in the jth iteration, determining a jacobian matrix in the jth iteration and a hessian matrix in the jth iteration;

determining iteration parameters in the j+1th iteration according to the jacobian matrix in the j iteration and the hessian matrix in the j iteration;

Determining a jacobian matrix at the j+1th iteration according to the iteration parameters at the j+1th iteration;

Judging whether convergence tolerance conditions are met or not according to the Jacobian matrix and the current step length in the j+1th iteration, and obtaining a first judgment result;

If the first judgment result is negative, updating the current step length, increasing the value of the iteration times j+1 by 1, and returning to the step of determining a jacobian matrix at the jth iteration and a hessian matrix at the jth iteration according to the iteration parameters at the jth iteration;

if the first judgment result is yes, judging whether the current step length is in a preset step length range or not, and obtaining a second judgment result;

If the second judgment result is negative, updating the current step length, increasing the value of the iteration times j+1 by 1, and returning to the step of determining a jacobian matrix at the jth iteration and a hessian matrix at the jth iteration according to the iteration parameters at the jth iteration;

And if the second judgment result is yes, determining the iteration parameter in the j+1st iteration as the optimal no-fly zone avoidance real-time track planning parameter.

4. A real-time trajectory planning method based on trajectory analysis solution as claimed in claim 3, wherein said convergence tolerance condition is:

；

wherein, Is the jacobian matrix at the j+1th iteration; is the jacobian matrix at the jth iteration; Is the current step length; To converge tolerances.

5. The method for real-time trajectory planning based on trajectory analysis solution of claim 4, wherein said updating the current step size comprises:

And determining the ratio of the current step length to the step length variation as the updated current step length.

6. The method of real-time trajectory planning based on trajectory analysis solution according to claim 4, wherein calculating initial profile parameters of each iterative profile, solving lagrangian equations based on the initial profile parameters, and obtaining initial lagrangian multipliers, comprises:

Order the First order term initial value of profileThe numerical value of (2) is 0, and solving an analytic solution; the analytic solutions comprise a speed analytic solution, a course angle analytic solution and a transverse journey analytic solution;

based on the speed resolution, constructing a terminal speed constraint resolution of each sub-segment track;

inverse-solving a plurality of terminal speed constraint analysis types to obtain corresponding sub-segment tracks Profile parameters; The profile is a resistance acceleration profile; the profile is a lift acceleration profile;

obtaining a terminal traverse analysis formula of each sub-segment track according to the traverse analysis solution;

Inverse-solving a plurality of terminal traverse analyses to obtain corresponding sub-segment tracks Profile parameters;

According to a plurality of Profile parameters and a plurality ofThe profile parameters construct an initial lagrangian multiplier.

7. The method for real-time trajectory planning based on trajectory analysis solution of claim 6, wherein,

The terminal speed constraint analysis method comprises the following steps:

；

wherein, Is a terminal speed constraint; Is a terminal longitudinal path; Is the earth radius; Is that Profile parametersIs the initial value of (2); Is a velocity resolution; Is the average radial distance;

The said The profile parameters are:

；

Wherein g is gravitational acceleration;

the terminal transverse journey analytic formula is:

；

The said The profile parameters are:

；

wherein, Terminal traversal constraint for the sub-segment track; Longitudinal distance as independent variable A value at the i-th path point; Longitudinal distance as independent variable A value at the i-1 st waypoint; Representing the average speed;

The jacobian matrix is:

；

wherein, Is the jacobian matrix at the jth iteration; the bias of the parameter p is the Lagrangian function; A partial derivative of the Lagrangian function to the parameter lambda; Is the first order derivative of the performance index; is synergistic; partial derivatives of the parameter p for constraint functions; Is a constraint function;

the hessian matrix is as follows:

；

wherein, Is a hessian matrix;、、 And All are hessian matrix elements; Is the second derivative of the performance index; Transpose of the first order derivative of the constraint function; is the second derivative of the constraint function.

8. A computer apparatus, comprising: a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor executes the computer program to implement a real-time trajectory planning method based on a trajectory resolution solution as claimed in any one of claims 1 to 7.

9. A computer readable storage medium having stored thereon a computer program, which when executed by a processor implements a real-time trajectory planning method based on a trajectory analysis solution as claimed in any one of claims 1 to 7.

10. A computer program product comprising a computer program, characterized in that the computer program, when executed by a processor, implements a real-time trajectory planning method based on a trajectory analysis solution as claimed in any one of claims 1 to 7.