CN111351488B - Intelligent trajectory reconstruction reentry guidance method for aircraft - Google Patents

Intelligent trajectory reconstruction reentry guidance method for aircraft Download PDF

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CN111351488B
CN111351488B CN202010141607.7A CN202010141607A CN111351488B CN 111351488 B CN111351488 B CN 111351488B CN 202010141607 A CN202010141607 A CN 202010141607A CN 111351488 B CN111351488 B CN 111351488B
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aircraft
track
roll angle
reentry
guidance
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CN111351488A (en
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胥彪
李翔
冯建鑫
李爽
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
    • B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
    • B64G1/242—Orbits and trajectories
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/24—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 specially adapted for cosmonautical navigation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/044—Recurrent networks, e.g. Hopfield networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/045—Combinations of networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods
    • G06N3/084—Backpropagation, e.g. using gradient descent

Abstract

The invention discloses an aircraft intelligent track reconstruction reentry guidance method, which comprises the steps of generating an offline reference track by adopting a numerical optimization method according to an aircraft reentry initial state and various constraint conditions; setting waypoints and calculating corresponding reachable domains; setting 5 normalization parameters to establish the relation between the optimal track and the roll angle according to the characteristics of the change of the roll angle of the optimal track, providing an optimization method for solving the corresponding roll angle parameter by using a search algorithm, then selecting sample data points in an reachable domain, calculating training data off line and training based on a BP (back propagation) neural network; tracking a reference track by adopting a guidance method; when the height of the waypoint is reached, generating a new track by using the trained neural network model; and completing the track reconstruction, tracking a new track by the aircraft, and continuing to complete the reentry guidance. The method greatly reduces the calculation time of track reconstruction, reduces the influence of optimization time on the guidance performance, and further improves the guidance precision of the reentry vehicle in the reentry section.

Description

Intelligent trajectory reconstruction reentry guidance method for aircraft
Technical Field
The invention relates to the technical field of aircraft guidance, in particular to an intelligent track reconstruction reentry guidance method for an aircraft.
Background
The reentry of the aircraft refers to the process of safely landing on the ground by braking the aircraft into the atmosphere after the aircraft such as a recoverable satellite, an airship, an aerospace vehicle and a hypersonic aircraft complete a predetermined space task. With the continuous progress and development of aerospace technology, in order to cope with the intense competition, all the scientific and technological strong countries in the world put higher requirements on the guidance precision of the reentry and return of the aircraft. Therefore, the method has important practical value and strategic significance for researching the guidance method of the reentry segment of the aircraft.
The guidance method of the reentry section of the reentry aircraft at present is generally divided into reference trajectory guidance and prediction correction guidance, and a reduced-order kinetic model is mostly adopted. The reference track guidance method is to design a reference profile (such as a resistance acceleration profile) in an off-line manner according to requirements in advance, store the reference profile in an on-board computer, and design a guidance law according to real-time tracking errors to track the track on line. However, the method excessively depends on the reference track generated off-line, and the processing of interference and faults in the reentry flight is not flexible enough and often cannot be accurately tracked on line; the prediction correction guidance algorithm does not depend on a standard track, continuously predicts the terminal state in the flight process, corrects the control quantity according to the deviation from the expected terminal state, has higher accuracy of the falling point and is insensitive to the reentry initial condition. However, such methods need strong on-board computer performance to improve the calculation speed and guarantee the real-time performance of the prediction result, and are currently difficult to be applied in engineering.
The flight path of the reentry aircraft is directly related to the complex mechanical environment in which the reentry aircraft is located, the traditional aircraft reference path guidance algorithm designs an optimal reference flight path in advance through an optimization algorithm, and the guidance control algorithm is utilized to enable the aircraft to overcome external interference and fly along the designed path as much as possible, so that the aircraft reaches a target area. However, in the actual reentry flight process of the aircraft, due to the large flight airspace, the large change of the flight speed and the violent change of the dynamic parameters, the flight guidance control system presents high nonlinearity and unknown uncertainty, and the aircraft is difficult to fly strictly according to the track optimized in advance or the designed track. The introduction of the track on-line generation technology enables the aircraft to rapidly plan a track meeting various reentry constraints on line again according to the current state and the operation and control capability when the aircraft deviates from the designed reference track due to the external interference, namely, the track reconstruction is carried out on line, and then the updating guidance instruction is fed back in real time, so that the aircraft tracks a new optimized track and reaches a specified target area.
In the aspect of a track reconstruction technology, because the speed of the reentry vehicle is high, how to improve the calculation efficiency of a numerical track optimization algorithm and how to strengthen the rapid track generation capability is a problem which needs to be solved urgently. The online generation of the aircraft trajectory by adopting the pseudo-spectral method is a hot research direction in recent years, as described in journal of national defense science and technology university journal 2015, volume 37, phase 4, pages 1-8 of the pseudo-spectral method and application review thereof in the field of aircraft trajectory optimization design. The pseudo-spectrum method converts the continuous reentry trajectory optimization problem into a nonlinear programming problem, obtains the optimal reentry trajectory by solving the nonlinear programming problem through numerical values, avoids the problems caused by a large amount of mathematical operations, and has the characteristics of high precision and high efficiency. However, the pseudo-spectrum method utilizes a global polynomial to perform interpolation, interpolation errors are difficult to control, and grid points in the whole interval are simultaneously densified, so that the optimization burden is increased. In addition, many aspects of the pseudo-spectrum method theory need to be improved, for example, how to further reduce the calculation time of the pseudo-spectrum method, so that the online generation speed of the track is increased, and the real-time performance of track reconstruction is guaranteed.
The artificial neural network is an algorithmic mathematical model simulating animal neural network behavior characteristics and performing distributed parallel information processing. The network achieves the purpose of processing information by adjusting the mutual connection relationship among a large number of internal nodes depending on the complexity of the system, and has self-learning and self-adapting capabilities. And the artificial neural network designed aiming at the complex optimization problem can exert the high-speed computing capability of the computer and has the capability of searching the optimal solution at high speed.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects of the prior art, the invention provides an intelligent track reconstruction reentry guidance method for an aircraft.
The technical scheme is as follows: in order to realize the purpose, the invention adopts the following technical scheme:
the method for reconstructing the intelligent track of the aircraft and re-entering the guidance comprises the following steps:
(1) optimizing a reference track by using a numerical optimization method under the condition of meeting path constraint and controlled variable constraint according to the reentry initial state of the aircraft and the reentry terminal target constraint condition;
(2) selecting flight path points at certain heights on the reference track generated in the step (1) as waypoints for executing track reconstruction, and calculating the reachable domain range of the aircraft at the height of each waypoint by using an optimization method according to the initial state of the aircraft, the path constraint and the control quantity constraint;
(3) selecting a sampling density with a proper size according to the guidance precision requirement, selecting a large number of data points in each obtained reachable domain range, obtaining a roll angle curve parameter by utilizing a search algorithm according to the state quantity of each data point based on the idea of parameterization roll angle, namely generating a corresponding reference track meeting terminal constraint, and generating a sample data set according to a group of roll angle curve parameters corresponding to one data point;
(4) respectively taking the state quantity of each data point in each sample data set as input, taking corresponding roll angle parameters as output, carrying out multiple BP neural network algorithm training, and completing the training of each neural network after multiple iterations when the value of the loss function reaches the required error or the maximum iteration times;
(5) tracking the reference track generated in the step (1) on line by adopting a guidance method for tracking the resistance acceleration;
(6) when the actual flight track height of the aircraft reaches the set waypoint height, inputting the real-time state information of the aircraft into the neural network corresponding to the waypoint generated in the step (4) to obtain a group of roll angle parameters, substituting the roll angle parameters into a kinematic model formula to obtain a new resistance acceleration reference curve, namely re-planning a reference track to realize rapid track reconstruction;
(7) continuing to adopt the guidance method in the step (5) to track the track and reconstruct the newly generated track, and updating the guidance instruction; and (4) when the actual flight track reaches the reachable domain of the next waypoint, repeating the track reconstruction process in the step (6), and finally completing the whole re-entry guidance process.
Further, the three-degree-of-freedom kinematic model of the aircraft atmosphere reentry segment adopted in the step (1) is as follows:
Figure BDA0002398252010000031
wherein r is the distance from the centroid of the aircraft to the geocentric, namely the sum of the height h of the aircraft and the average radius Re of the earth, V is the speed of the aircraft,
Figure BDA0002398252010000032
is latitude, theta is longitude, gamma is track angle, i.e., the angle between the velocity and the local horizontal plane, psi is heading angle, i.e., the angle between the projection of the velocity on the horizontal plane and the east-ward direction, and sigma is roll angle, i.e., the angle of rotation of the aircraft about the velocity vector; g is the acceleration of gravity;
Figure BDA0002398252010000033
wherein m isvThe mass of the aircraft is S, the aerodynamic reference area of the aircraft is S, rho is the atmospheric density, D is the resistance acceleration, L is the lift acceleration, CDIs the coefficient of aerodynamic drag, CLIs the aerodynamic lift coefficient.
Further, the initial state of the step (1) is:
Figure BDA0002398252010000034
wherein, r (t)0),θ(t0),
Figure BDA0002398252010000035
V(t0),ψ(t0),γ(t0) Respectively the distance from the centroid of the aircraft to the geocentric, the longitude, the latitude, the speed, the course angle and the track angle of the aircraft at the initial moment of the reentry section of the aircraft;
and (3) path constraint:
(a) the heat flow constraint is:
Figure BDA0002398252010000041
wherein the content of the first and second substances,
Figure BDA0002398252010000042
as heat flow rate, kqIs the coefficient of heat flow of the aircraft,
Figure BDA0002398252010000043
is the upper allowable heat flow rate limit;
(b) the dynamic pressure constraint is:
Figure BDA0002398252010000044
wherein q is the incoming flow pressure, q ismaxIs an allowable upper limit of dynamic pressure;
(c) the overload constraints for the reentry process are:
Figure BDA0002398252010000045
wherein the content of the first and second substances,
Figure BDA0002398252010000046
in order to overload the aircraft with a load,
Figure BDA0002398252010000047
is the allowable overload upper limit;
re-entering terminal target constraint:
(a) reentry terminal conditions, including altitude and speed limits:
h(tf)≥hf,V(tf)≤Vf (7)；
wherein, h (t)f),V(tf) Respectively the altitude and the speed, h, at the end of the reentry section of the aircraftf,VfRespectively the altitude and speed limit values at the end of the reentry section of the aircraft;
(b) and (3) latitude and longitude constraint:
Figure BDA0002398252010000048
wherein, θ (t)f),
Figure BDA0002398252010000049
Longitude and latitude, theta, respectively, at the end of the reentry section of the aircraftf,
Figure BDA00023982520100000410
Respectively the longitude and latitude of the terminal target point;
and (3) controlling quantity constraint:
σmin＜|σ|＜σmax (9)；
wherein σminFor minimum value of allowable roll angle, σmaxIs the maximum allowable roll angle; the purpose of limiting the roll angle is to reserve a certain adjustment margin for trajectory tracking and transverse guidance;
the objective function is:
J＝-khh(tf)+kγ[γ(tf)-γf]2 (10)；
wherein k ishIs a height coefficient, kγAs track angle coefficient, gamma (t)f) Track angle, gamma, at the end of the reentry sectionfIs the target track angle.
Further, in the step (1), because the aircraft is not subjected to the action of the external force exerted by people in the reentry process, the law of conservation of energy is satisfied, and the energy of the aircraft is represented by the following formula:
Figure BDA0002398252010000051
therefore, when the terminal energy position is reached, if the aircraft can reach the terminal target height, the terminal speed of the aircraft can also meet the requirement; energy is therefore used as an argument in trajectory planning;
further, five normalized parameters EDR and ECR are used in the step (3)1、ECR2EHF, PHF design roll angle curves, where EDR, ECR1、ECR2EHF is an energy parameter and represents the moment when the roll angle changes; the PHF is a tail-segment rolling angle parameter and represents the size of a tail-segment constant rolling angle; a corresponding roll angle curve may be generated for a given set of parameters;
five normalized energy parameters EDR, ECR1、ECR2The value ranges of the EHF and the PHF are 0-1;
EDR is standard energy value of moment for adjusting roll angle, and ECR is parameter1The standard energy value of the first sign change time of the roll angle, parameter ECR2The standard energy value at the second sign changing moment of the roll angle is obtained, and the parameter EHF is the standard energy value for adjusting the height of the aircraft at the beginning entering the tail section; the constant roll angle sigma at the tail section of the flight can be adjusted by changing the value of the parameter PHFHFTo control the final height, the expression:
σHF＝PHFσmax+(1-PHF)σmin (12)；
under the conditions of given reentry initial state, terminal target constraint, path constraint and control quantity constraint, a group of parameters P (EDR, ECR) meeting the requirements is obtained by searching through a genetic algorithm1，ECR2EHF, PHF), then substituting the corresponding roll angle curve into a kinematic equation, i.e. a kinematic model formula, to generate a reference trajectory; firstly, establishing a mapping relation between roll angle parameters and a longitudinal stroke, a transverse stroke, a height and a track angle according to a kinematic equation:
P(EDR,ECR1,ECR2,EHF,PHF)→eDR(P)，eCR(P)，Fh(P)，Fγ(P) (13)；
wherein e isDR(P)，eCR(P)，Fh(P)，Fγ(P) respectively representing the longitudinal error, the transverse error, the terminal height and the track angle of the aircraft;
the main task of the adopted search algorithm is to seek a group of suitable roll angle parameters P, so that the parameters P not only meet the constraint conditions of the reentry process, but also can minimize the errors of the longitudinal and transverse processes, and simultaneously increase the height of the terminal as much as possible, namely, the following three objective functions are met:
Figure BDA0002398252010000061
wherein k ishIs a height coefficient, kγAs track angle coefficient, gammafA target track angle;
further, each reachable domain obtained in the step (3) is divided into m small regions, and in consideration of the large reachable domain range, in order to improve the calculation efficiency, the closer to the reference track the smaller regions are, the more dense the divided small regions are; then, randomly selecting n data points in each cell, wherein the number of the data points selected in each reachable domain is mn, and the state information of each data point
Figure BDA0002398252010000062
Taking the state quantities as reentry initial states, satisfying the original constraint conditions, and solving by using the search algorithm in the step (3) to obtain each group of roll angle curve parameters Pmi(EDRmi，ECR1mi，ECR2mi，EHFmi，PHFmi) And a corresponding resistance acceleration profile DmiI.e. to plan a new reference trajectory TmiGenerating a data set Q { X) from the respective state quantities and roll angle parametersmi，Pmi}。
Further, the state quantity X in the data set Q is used in the step (4)miAs the input of BP neural network, the roll angle curve parameter P corresponding to the state quantitymiAs the output of BP neural network, training and testing the neural network to approximately obtain the sum of the aircraft state quantitiesThe relationship between the corresponding roll angle curve parameters; randomly dividing a data set Q into training sets Q according to a proper proportion1And test set Q2(ii) a Each fixed height hjWaypoint reachable field d of 1, 2, …, NjA corresponding neural network N needs to be trainedjTraining a BP neural network model by using MATLAB simulation software; the BP neural network model is composed of an input layer, an output layer and one or more hidden layers, wherein the neurons in the same layer are independent, an input signal passes through the neurons of the hidden layers from the neurons of the input layer in sequence, and is finally transmitted to the neurons of the output layer, if an error exists between a value obtained by the output layer and a target value, an error back propagation operation is executed, and a weight value and a threshold value of the network are continuously adjusted according to the error, so that the optimal effect is achieved.
Furthermore, in the step (6), due to the existence of large uncertain interference in the reentry process, the actual flight track reaches the first fixed height h1In the meantime, the actual position deviates from the reference track waypoint, and at this time, the current aircraft state quantity is used
Figure BDA0002398252010000063
As an input quantity, to a neural network N1A set of roll angle curve parameters P is obtained by real-time calculation1＝[EDR1,ECR11,ECR21,EHF1,PHF1]The obtained roll angle control amount σ1Substituting into equation of motion, i.e. regenerating a new trajectory T on line1And then the control system starts to track a new track to realize track reconstruction.
Has the advantages that: compared with the prior art, the invention firstly provides a method for generating the optimal reference trajectory off line based on the idea of parameterization roll angle, then the BP neural network is trained in advance by utilizing the sample data in the reachable domain to obtain the relation between the state quantity and the roll angle parameter, and a new trajectory can be generated on line in real time through the trained neural network algorithm. Because the flight environment of the reentry aircraft has great uncertainty, the motion model has strong nonlinearity, and the rapid track generation capability can better overcome the larger tracking error generated in the actual reentry guidance process, thereby realizing robust tracking guidance under the interference and uncertainty conditions, improving the accuracy of the reentry section reaching the target point of the terminal, and having important engineering application value.
Drawings
FIG. 1 is a flow chart of an aircraft intelligent trajectory reconstruction reentry guidance method of the present invention;
FIG. 2 is a graph of the change in aircraft altitude according to the present invention;
FIG. 3 is a graph illustrating the change in speed of an aircraft according to the present invention;
FIG. 4 is a graph illustrating the roll angle variation of an aircraft according to the present invention;
FIG. 5 is a graph of the heat flow profile of an aircraft according to the present invention;
FIG. 6 is a graph of the dynamic pressure change of an aircraft according to the present invention;
FIG. 7 is a graph illustrating the variation in aircraft overload according to the present invention;
FIG. 8 is a schematic representation of the reach of an aircraft according to the present invention;
FIG. 9 is a schematic illustration of a parameterized roll angle curve according to the present invention;
FIG. 10 is a diagram of a neural network architecture according to the present invention;
FIG. 11 is a flow chart of an intelligent trajectory reconstruction algorithm in accordance with the present invention;
FIG. 12 is a graph of aircraft altitude change for the trackless reconstruction guidance method of the present invention;
FIG. 13 is a graph of aircraft roll angle variation for the trackless reconstruction guidance method of the present invention;
FIG. 14 is a graph of the change in aircraft drag acceleration for the trackless reconstruction guidance method of the present invention;
FIG. 15 is a graph of the change of latitude and longitude of an aircraft in the trackless reconstruction guidance method of the present invention;
FIG. 16 is a graph of aircraft altitude change using the intelligent trajectory reconstruction guidance method of the present invention;
FIG. 17 is a graph of aircraft roll angle change using the intelligent trajectory reconstruction guidance method of the present invention;
FIG. 18 is a graph of the change in aircraft drag acceleration using the intelligent trajectory reconstruction guidance method of the present invention;
FIG. 19 is a graph of latitude and longitude changes of an aircraft using the intelligent trajectory reconstruction guidance method of the present invention;
FIG. 20 is a comparison graph of simulation results of two guidance methods according to the present invention.
Detailed Description
The technical solution of the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1, the method for reconstructing and re-entering guidance of the intelligent trajectory of the aircraft provided by the invention comprises the following steps:
the method comprises the following steps: generating an off-line reference track according to the initial reentry flight state of the aircraft and the constraint condition; according to the state quantities of the aircraft at the reentry initial time, such as speed, longitude and latitude, altitude, course angle, flight path angle and the like, and reentry terminal target constraint conditions, under the conditions of meeting the path constraints and control quantity constraints of overload, dynamic pressure, heat flow and the like, a reference track is optimized by using a numerical optimization method;
the embodiment adopts a simplified three-degree-of-freedom kinematic model of an atmosphere reentry section of the aircraft;
Figure BDA0002398252010000081
wherein r is the distance from the centroid of the aircraft to the geocentric, namely the sum of the height h of the aircraft and the average radius Re of the earth, V is the speed of the aircraft,
Figure BDA0002398252010000082
is latitude and theta is longitude. Gamma is the track angle, i.e. the angle between the speed and the local horizontal plane. Psi is the heading angle, i.e. the speed is in the horizontal planeThe angle between the upper projection and the orthodontics direction. σ is the roll angle, i.e., the angle of rotation of the aircraft with respect to the velocity vector. g is the acceleration of gravity.
Figure BDA0002398252010000083
Wherein m isvThe mass of the aircraft is S, the aerodynamic reference area of the aircraft is S, rho is the atmospheric density, D is the resistance acceleration, L is the lift acceleration, CDIs the coefficient of aerodynamic drag, CLIs the aerodynamic lift coefficient.
The reference track guidance method firstly plans a reference track by using an optimization method under a given reentry initial state, and satisfies path constraint, terminal target constraint and control quantity constraint.
And entering an initial state again:
Figure BDA0002398252010000091
wherein, r (t)0),θ(t0),
Figure BDA0002398252010000092
V(t0),ψ(t0),γ(t0) The state quantity of the aircraft at the initial moment of the reentry segment.
And (3) path constraint:
(1) the heat flow constraint is:
Figure BDA0002398252010000093
wherein the content of the first and second substances,
Figure BDA0002398252010000094
as heat flow rate, the aircraft heat flow coefficient kq＝1.9027e-4，
Figure BDA0002398252010000095
The upper limit of the allowable heat flow rate.
(2) The dynamic pressure constraint is:
Figure BDA0002398252010000096
wherein q is the incoming flow pressure, q ismaxIs the upper limit of allowable dynamic pressure.
(3) The overload constraints for the reentry process are:
Figure BDA0002398252010000097
wherein the content of the first and second substances,
Figure BDA0002398252010000098
in order to overload the aircraft with a load,
Figure BDA0002398252010000099
is the upper limit of allowable overload.
Re-entering terminal target constraint:
(1) re-entry segment termination conditions, including altitude and speed limitations.
h(tf)≥hf,V(tf)≤Vf (7)；
Wherein, h (t)f),V(tf) Respectively the altitude and the speed, h, at the end of the reentry section of the aircraftf,VfRespectively altitude and speed limit values at the end of the reentry section of the aircraft.
(2) Location (latitude and longitude) constraints.
Figure BDA00023982520100000910
Wherein, θ (t)f),
Figure BDA00023982520100000911
Longitude and latitude, theta, respectively, at the end of the reentry section of the aircraftf,
Figure BDA00023982520100000912
Respectively, the longitude and latitude of the terminal target point.
And (3) controlling quantity constraint:
σmin＜|σ|＜σmax (9)；
wherein σminFor minimum value of allowable roll angle, σmaxIs the maximum allowable roll angle. The purpose of limiting the roll angle is to reserve some adjustment margin for trajectory tracking and lateral guidance.
Generally speaking, the goal of designing the optimal trajectory of the reentry segment is to make the terminal height as large as possible while satisfying various constraints, thereby improving the landing segment control capability and accuracy. However, the maximum height is generally achieved by re-entering the terminal climbing trajectory, which is a phenomenon that is less capable of controlling the final height. Research shows that if the final flight path angle is close to zero as much as possible, the flight height control capability can be ensured, and the climbing phenomenon can be avoided. Therefore, the following objective function is adopted when the optimal trajectory is designed in the embodiment:
J＝-khh(tf)+kγ[γ(tf)-γf]2 (10)；
wherein the height coefficient kh＝1m-1Coefficient of track angle kγ＝90deg-2Target track angle gammaf＝0°，γ(tf) Is the track angle at the end of the reentry segment.
Under the given reentry initial state and various constraint conditions, the objective function is taken as an optimization target, and under the allowed range of the voyage, a self-adaptive pseudo-spectrum method is adopted as an optimization method to work out the corresponding optimal tracks under different voyages.
The specific values of the reentry initial state and various constraints are as follows:
and entering an initial state again:
Figure BDA0002398252010000101
and (3) path constraint:
Figure BDA0002398252010000102
qmax＝50kpa/m2,
Figure BDA0002398252010000103
re-entering terminal target constraint: h isf＝15km,Vf＝300m/s，θf＝12°,
Figure BDA0002398252010000106
And (3) controlling quantity constraint: sigmamin＝10°,σmax＝80°。
Model parameters included in the aircraft reentry phase: coefficient of gravity mu of 3.986 × 1014m3/s2The average radius Re of the earth is 6378136m, and the reference area S of the aircraft is 12.88m2Coefficient of aerodynamic lift CL0.3892, coefficient of aerodynamic drag CD1.3479 and aircraft mass mv6800 kg. The atmospheric density model using an approximate exponential model, i.e.
Figure BDA0002398252010000104
Wherein the atmospheric density at sea level ρ0＝1.225kg/m3Earth atmospheric equivalent density altitude hs＝7200m。
Because the aircraft is not subjected to an artificially applied external force during reentry, the law of conservation of energy is satisfied, and the energy of the aircraft can be represented by the following formula:
Figure BDA0002398252010000105
so when the terminal energy position is reached, if the aircraft can be made to reach the terminal target altitude, the terminal speed will also reach the requirement. Energy is therefore used as an argument in trajectory planning.
The trajectory optimization results are shown in fig. 2-7. Fig. 2-4 are graphs of the change in altitude, velocity and roll angle, respectively. Fig. 5-7 illustrate the path constraints (heat flow, dynamic pressure, and overload) of the reentry trajectory. It can be seen that each path constraint is satisfied.
Step two: setting waypoints and calculating corresponding reachable domains; selecting flight path points at certain heights on the reference track generated in the step one as waypoints for executing track reconstruction, and calculating the reachable domain range of the aircraft at the height of each waypoint by using an optimization method according to the initial state of the aircraft, the path constraint and the control quantity constraint;
and selecting a position with a fixed height on the flight path as a waypoint for track reconstruction. In the embodiment of the invention, the selected heights are h1，h2，h3As waypoints, each height interval is of size Δ h. The number and the interval of the waypoints can be reasonably selected according to different reentry situations of the aircraft. Respectively calculating reachable domain ranges d at the heights of the three waypoints according to the track optimization method in the step one1，d2，d3. FIG. 8 is a schematic view of the reachable region of the aircraft, h0Is the initial re-entry point height.
The specific data selected in this embodiment is h0＝80km，h1＝60km，h2＝50km，h3＝40km。
Step three: generating a sample data set; based on the idea of parameterization of the roll angle, obtaining roll angle curve parameters by utilizing a search algorithm according to the state quantity of each data point;
through research on the characteristics of the optimal track, the rolling angle curve of the optimal track is found to have a certain formal rule, namely the rolling angle curve keeps the minimum value in the initial stage, increases to the maximum value after reaching a certain moment, and changes to the minimum value in the final stage. Therefore, 5 rolling angle parameters are set, and the 5 rolling angle parameters are utilized to establish the relation between the optimal track and the rolling angle parameters, so that the 5 parameters can be trained by using an artificial intelligent algorithm. Because the optimization process does not consider the transverse motion process, the invention provides a method for obtaining corresponding roll angle curves by respectively setting five parameters by taking the normalized standard energy E as an independent variable, so that the decoupling of the longitudinal stroke, the transverse stroke and the final height of the track is realized as much as possible, a track meeting the constraint is finally obtained, and the problem of solving the complicated track optimization is avoided.
In particular, the strategy uses five normalized parameters EDR, ECR1、ECR2EHF, PHF design roll angle curves, where EDR, ECR are defined1、ECR2EHF is an energy parameter and represents the moment when the roll angle changes; and defining the PHF as a tail-section rolling angle parameter which represents the size of a tail-section constant rolling angle. For a given set of parameters, a corresponding roll angle curve may be generated, as shown in FIG. 9, which is a schematic view of a roll angle curve that is parametrically designed, with the abscissa being the normalized standard energy and the ordinate being the aircraft roll angle, which is measured by σ at the moment the energy value reaches the EDRminAdjusted to sigmamax(ii) a Energy value to ECR1Changing the roll angle sign at the moment; energy value to ECR2Changing the sign of the roll angle again at the moment; when the energy value reaches the EHF moment, the tail-section constant roll angle stage is entered, and the roll angle is adjusted to another constant sigma according to the PHFHFTo ensure the terminal height.
Five normalized parameters EDR, ECR1、ECR2The value ranges of the EHF and the PHF are all 0-1.
And selecting a proper EDR (energy dispersive ratio), namely adjusting the standard energy value of the roll angle at the moment, so that the generated track can meet the longitudinal stroke requirement, and the larger the value is, the larger the track course is. Parameter ECR1I.e. the standard energy value of the first sign change time of the roll angle, parameter ECR2Namely the standard energy value at the second sign changing moment of the roll angle, the final traverse error of the aircraft can be better reduced through two roll angle inversions. The parameter EHF is a standard energy value for adjusting the height of the aircraft at the end of the initial entering period, and the constant roll angle sigma at the end of the flight can be adjusted by changing the value of the parameter PHFHFTo control the final height, the expression:
σHF＝PHFσmax+(1-PHF)σmin (12)；
after determining the trajectory generation strategy, the method comprisesObtaining a set of parameters P (EDR, ECR) meeting the requirements through searching by Genetic Algorithm (GA) under the constraint of the fixed reentry initial state, the terminal target, the path and the control quantity1，ECR2EHF, PHF) and then substituting the corresponding roll angle curve into the kinematic equation (i.e., kinematic model equation (1)) to generate a reference trajectory. Firstly, establishing a mapping relation between roll angle parameters and a longitudinal stroke, a transverse stroke, a height and a track angle according to a kinematic equation:
P(EDR,ECR1,ECR2,EHF,PHF)→eDR(P)，eCR(P)，Fh(P)，Fγ(P) (13)；
wherein e isDR(P)，eCR(P)，Fh(P)，Fγ(P) are the longitudinal error, lateral error, terminal altitude and track angle of the aircraft, respectively.
The main task of the search algorithm adopted by the embodiment of the invention is to seek a group of suitable roll angle parameters P, so that the parameters can meet the constraint conditions of the reentry process, the errors of the longitudinal and transverse courses can be minimized, and the height of the terminal can be increased as much as possible, namely, the following three objective functions are met:
Figure BDA0002398252010000121
wherein the height coefficient kh＝1m-1Coefficient of track angle kγ＝90deg-2Target track angle gammaf＝0°。
Then selecting a large number of data points in each reachable domain range according to the guidance precision requirement, and calculating to obtain corresponding roll angle curve parameters by using the search algorithm according to the state quantity of each data point, so as to generate a corresponding reference track meeting the terminal constraint, and generating a sample data set according to a group of roll angle curve parameters corresponding to one data point;
dividing each reachable domain into m small regions, considering that the reachable domain has a larger range, and increasing the calculation efficiencyThe closer the area of the reference track, the denser the divided small area. Then, randomly selecting n data points in each cell, wherein the number of the data points selected in each reachable domain is mn, and the state information of each data point
Figure BDA0002398252010000131
Figure BDA0002398252010000132
Using the state quantities as initial conditions, satisfying the original constraint conditions, and obtaining each set of roll angle curve parameters P by using the genetic algorithmmi(EDRmi，ECR1mi，ECR2mi，EHFmi，PHFmi) And a corresponding resistance acceleration profile DmiI.e. to plan a new reference trajectory Tmi. Generation of a data set Q { X) from state quantities and roll angle parametersmi，Pmi}。
The specific data selected in this embodiment is m-50 and n-100.
Step four: training a neural network algorithm by using the data set; respectively taking the state quantity of each data point in each sample data set as input and corresponding roll angle parameters as output, carrying out multiple BP (back propagation) neural network algorithm training, and completing the training of each neural network when the value of a loss function reaches the required error or the maximum iteration times after multiple iterations;
the characteristic analysis of the kinematic model and the optimal track shows that the roll angle curve parameter PmiAnd the state quantity X of the data point in the reachable domainmiThere are close relationships, but it is difficult to describe with a specific model. The BP (Back Propagation) neural network is a multilayer forward feedback neural network trained according to an error inverse Propagation algorithm, has strong self-learning capability, can fully mine the relation between data, approaches a nonlinear complex system to the maximum extent, and is one of the most widely applied neural network models at present. Therefore, the embodiment of the present invention uses the state quantity X in the data set QmiAs the input of BP neural network, the roll corresponding to the state quantityCorner curve parameter PmiAnd as the output of the BP neural network, training and testing the neural network to approximately obtain the relationship between the state quantity of the aircraft and the corresponding roll angle curve parameters. Randomly partitioning a data set Q into training sets Q1And test set Q2The ratios are set at 95% and 5%. Each fixed height hjWaypoint reachable field d where j is 1, 2, 3jA corresponding neural network N needs to be trainedjMATLAB simulation software can be used for training the neural network model.
The BP neural network model is composed of an input layer, an output layer and one or more hidden layers. The neurons in the same layer are independent of each other. The input signal passes through each hidden layer neuron from the input layer neuron in turn, and is finally transmitted to the output layer neuron. If the value obtained by the output layer has an error with the target value, the error back propagation operation is executed, and the weight and the threshold of the network are continuously adjusted according to the error, so that the best effect is achieved.
In this embodiment, a four-layer neural network structure as shown in fig. 10 is selected, that is, two hidden layers are included, so that the accuracy of the BP neural network model can be improved.
An input layer:
Figure BDA0002398252010000141
due to the height h of each reachable domainjThe flight height is constant, so the flight height is not used as a training input, and the input vector comprises five state elements.
Hidden layer: and determining the appropriate number of hidden layer nodes through experience and repeated experiments, wherein the number of the first hidden layer node is 5, and the number of the second hidden layer node is 4. The transfer function of the hidden layer is a hyperbolic tangent S-type (Sigmoid) function tansig which has a faster convergence rate and a wider output range than a logsig function. The function limits the output range of the neuron to the (-1, 1) interval, and the expression is as follows:
Figure BDA0002398252010000142
wherein the content of the first and second substances,
Figure BDA0002398252010000143
is an input value for the node and is,
Figure BDA0002398252010000144
is the output value of the node.
An output layer: y ═ Pmi＝[EDRmi,ECR1mi,ECR2mi,EHFmi,PHFmi]，i∈[1,n]The output vector elements are five roll angle parameters. The output layer transfer function adopts a linear transfer function purelin, and the expression is as follows:
Figure BDA0002398252010000145
supervised learning of the neural network is a process of adjusting weights w and thresholds B between nodes of each layer to reduce network output errors.
Figure BDA0002398252010000146
Representing the weights of the input layer to the first hidden layer,
Figure BDA0002398252010000147
a threshold value representing a first hidden layer;
Figure BDA0002398252010000148
representing the weight between the two hidden layers,
Figure BDA0002398252010000149
a threshold value representing a second hidden layer;
Figure BDA00023982520100001410
representing the weight of the hidden layer to the output layer,
Figure BDA00023982520100001411
representing the threshold of the output layer. The output values of the hidden layer and the output layer are shown as follows:
Figure BDA00023982520100001412
the measure of the network output error is a loss function, the worse the accuracy of the neural network, the higher the value of the loss function. This embodiment belongs to the regression problem, so the loss function adopts the mean square error as shown in the following formula:
Figure BDA00023982520100001413
wherein C represents the error size, xsRepresents a sample, ysRepresenting the sample output value, ypRepresenting the actual output value and mn representing the total number of samples.
The Levenberg-Marquardt optimization method can achieve the advantages of combining a Gaussian-Newton algorithm and a gradient descent method by modifying parameters during execution, is very fast in training a neural network model using a square sum error-like loss function, and is the most widely used nonlinear least square algorithm. The weight value adjusting algorithm is as follows:
Δw＝-(JTJ+λI)-1JTe (19)；
j is a Jacobian matrix formed by first-order partial derivatives of the loss function to each weight, e is a network output error vector, and lambda is a damping factor. J in L-M algorithm when λ is largeTThe J term can be ignored and is degraded into a gradient descent algorithm; when λ is small, the above equation becomes a gauss-newton algorithm, in which λ is adaptively adjusted. The threshold is adjusted in the same manner as the weight. The embodiment of the invention adopts the training function corresponding to the algorithm to train the forward network.
The embodiment of the invention adopts a momentum gradient descent algorithm to adjust the weight and the threshold of each neuron, and the main idea is to update parameters instead of the original gradient after carrying out exponential weighted average on a series of gradients. The parameter updating formula of the momentum gradient descent method is as follows:
Figure BDA0002398252010000151
wherein
Figure BDA0002398252010000152
Is the current loss function pair weight wnAnd a threshold value BnPartial derivatives (gradients) of (a), using exponentially weighted averages of the preceding
Figure BDA0002398252010000153
And
Figure BDA0002398252010000154
are all linked to obtain a momentum gradient
Figure BDA0002398252010000155
Beta is a momentum factor, which influences the exponentially weighted average; α is the learning rate, i.e., the magnitude of each parameter update, affecting the convergence rate. The momentum term added here essentially corresponds to the damping term, since each exponentially weighted average gradient contains information about the previous gradient, the tendency of the learning process to oscillate is reduced, and convergence is improved.
During training, the training set Q is matched1The input data matrix and the output data matrix are normalized to the value of [ -1, 1 [ ]]And the learning and training efficiency of the network model is improved.
Establishing a BP neural network model of a back propagation algorithm, and setting network training parameters as follows: the training target error is set to 1 × 10-7The learning rate α is set to 0.05, the momentum factor β is set to 0.9, and the maximum number of iterations is set to 5000.
Based on training set Q1After a plurality of iterations, the training of the BP neural network is completed when the value of the loss function is converged within a set error range. Using test set Q2The data in the step (1) tests the network performance to finally obtain three neural networks N with better effect1，N2，N3Is divided intoRespectively corresponding to reachable domain d1，d2，d3。
Step five: tracking the reference track by using a guidance method; in other words, under the condition that uncertain factors such as aerodynamic coefficient, atmospheric density error and the like exist, a guidance method for tracking resistance acceleration is adopted to track the reference track generated in the step one on line.
Step six: completing track reconstruction; when the actual flight track height of the aircraft reaches the set waypoint height, inputting the real-time state information of the aircraft into the neural network corresponding to the waypoint generated in the fourth step to obtain a group of roll angle parameters, substituting the roll angle parameters into a kinematic model formula to obtain a new resistance acceleration reference curve, namely re-planning a reference track to realize rapid track reconstruction;
due to the fact that large uncertain interference exists in the reentry process, the actual flight track reaches the height h of the first fixed waypoint1In the meantime, the actual position deviates from the reference track waypoint, and at this time, the current aircraft state quantity is used
Figure BDA0002398252010000161
As an input quantity, to a neural network N1Instantaneously calculating and outputting a set of rolling angle curve parameters P1＝[EDR1,ECR11,ECR21,EHF1,PHF1]The obtained roll angle control amount σ1Substituting into the equation of motion, a new reference track T can be generated on line1And then the control system starts to track the new reference track to realize track reconstruction.
The flow chart of the intelligent track reconstruction algorithm is shown in fig. 11, the aircraft firstly tracks the optimal reference track generated offline through a guidance instruction in the initial stage, but due to the interference of uncertain factors such as atmospheric environment, the actual track of the aircraft can deviate from the reference track, when the route point at the corresponding height is reached, the state quantity is input into a pre-trained BP neural network model, a group of corresponding roll angle parameters is output, the change condition of the roll angle is substituted into a kinematic equation, a new reference track is generated online, and then the aircraft updates the guidance instruction and tracks the new track. And circulating until the reentry is finished, and finishing the intelligent track reconstruction process.
Step seven: the aircraft tracks a new track, and the reentry guidance is continuously completed, namely the guidance method in the step five is continuously adopted to track the track to reconstruct a newly generated track, and a guidance instruction is updated; when the actual flight track reaches the reachable domain of the next waypoint, repeating the track reconstruction process in the step six, and finally completing the whole re-entry guidance process;
and continuously tracking the newly generated reference track, and updating the guidance instruction. When the actual flight path reaches the second reachable area d2And repeating the track reconstruction process in the step six. Therefore, three times of track reconstruction are carried out in the whole re-entry guidance process. The reference track is continuously corrected, so that the tracking error is always kept in a small range, and the accuracy of reentry guidance is greatly improved.
Fig. 12-15 show the results of tracking the original reference trajectory without the intelligent trajectory reconstruction in the presence of + 20% aerodynamic coefficient error. Fig. 12 is a height variation curve, fig. 13 is a roll angle variation curve, fig. 14 is a resistance acceleration variation curve, and fig. 15 is a longitude and latitude variation curve.
Fig. 16-19 show the result of tracking by combining the guidance method with the intelligent trajectory reconstruction algorithm provided by the present invention when + 20% aerodynamic coefficient error exists. Fig. 16 is a height variation curve, fig. 17 is a roll angle variation curve, fig. 18 is a resistance acceleration variation curve, and fig. 19 is a longitude and latitude variation curve.
FIG. 20 is a comparison of latitude and longitude curves for the two methods.
Table 1 below is data obtained by the intelligent trajectory reconstruction algorithm.
TABLE 1 trajectory reconstruction data
Figure BDA0002398252010000171
Wherein the roll angle parameter PjTo actually re-enter the processBP neural network NjAnd the track error is the distance between the reconstructed track terminal position and the target terminal position. The terminal height and velocity of each trajectory satisfy constraints.
The following table 2 shows a comparison of simulation results of different guidance methods.
TABLE 2 comparison of simulation results
Figure BDA0002398252010000172
According to the simulation results, the reentry terminal points of the two guidance methods meet the height and speed constraints, and compared with the guidance method adopting the intelligent track reconstruction algorithm, the guidance method greatly reduces the terminal position error and obviously improves the guidance precision.
According to the method, under the condition that various constraints are met, the online track generation speed is increased by using the neural network, the calculation time of track reconstruction is greatly reduced, the problem that the online track generation speed is low in the traditional track optimization method is solved, and the influence of the optimization time on the guidance performance is reduced, so that the guidance precision of the reentry vehicle in the reentry stage is further improved. Generating an off-line reference track by adopting a numerical optimization method according to the initial reentry flight state of the aircraft and various constraint conditions; setting waypoints and calculating corresponding reachable domains; setting 5 normalization parameters to establish the relation between the optimal track and the roll angle by summarizing the characteristics of the change of the roll angle of the optimal track, providing an optimization method for solving the corresponding roll angle parameter by utilizing a search algorithm, then selecting sample data points in a reachable domain, performing off-line calculation to obtain training data, and performing algorithm training based on a BP (back propagation) neural network; tracking a reference track by adopting a guidance method; when the height of the waypoint is reached, generating a new track by using the trained neural network model; and completing the track reconstruction, tracking a new track by the aircraft, and continuing to complete the reentry guidance. According to the method, under the condition that various constraints are met, the online track generation speed is increased by using the neural network, the calculation time of track reconstruction is greatly reduced, the problem that the online track generation speed is low in the traditional track optimization method is solved, and the influence of the optimization time on the guidance performance is reduced, so that the guidance precision of the reentry vehicle in the reentry stage is further improved.

Claims (7)

1. The method for reconstructing the intelligent track of the aircraft and re-entering the guidance is characterized by comprising the following steps of:
(1) optimizing a reference track by using a numerical optimization method under the condition of meeting path constraint and controlled variable constraint according to the reentry initial state of the aircraft and the reentry terminal target constraint condition;
(2) selecting flight path points at certain heights on the reference track generated in the step (1) as waypoints for executing track reconstruction, and calculating the reachable domain range of the aircraft at the height of each waypoint by using an optimization method according to the initial state of the aircraft, the path constraint and the control quantity constraint;
(3) selecting a sampling density with a proper size according to the guidance precision requirement, selecting a large number of data points in each obtained reachable domain range, obtaining a roll angle curve parameter by utilizing a search algorithm according to the state quantity of each data point based on the idea of parameterization roll angle, namely generating a corresponding reference track meeting terminal constraint, and generating a sample data set according to a group of roll angle curve parameters corresponding to one data point; specifically, the method comprises the following steps:
using five normalized parameters EDR, ECR1、ECR2EHF, PHF design roll angle curves, where EDR, ECR1、ECR2EHF is an energy parameter and represents the moment when the roll angle changes; the PHF is a tail-segment rolling angle parameter and represents the size of a tail-segment constant rolling angle; a corresponding roll angle curve may be generated for a given set of parameters;
five normalized energy parameters EDR, ECR1、ECR2The value ranges of the EHF and the PHF are 0-1;
EDR is standard energy value of moment for adjusting roll angle, and ECR is parameter1The standard energy value of the first sign change time of the roll angle, parameter ECR2The standard energy value at the second sign changing moment of the roll angle is used as the parameter EHF for the altitude adjustment of the tail section of the aircraft starting to enterA whole standard energy value; the constant roll angle sigma at the tail section of the flight can be adjusted by changing the value of the parameter PHFHFTo control the final height, the expression:
σHF＝PHFσmax+(1-PHF)σmin (1)；
wherein σminFor minimum value of allowable roll angle, σmaxIs the maximum allowable roll angle;
under the conditions of given reentry initial state, terminal target constraint, path constraint and control quantity constraint, a group of parameters P (EDR, ECR) meeting the requirements is obtained by searching through a genetic algorithm1，ECR2EHF, PHF), then substituting the corresponding roll angle curve into a kinematic equation, i.e. a kinematic model formula, to generate a reference trajectory; firstly, establishing a mapping relation between roll angle parameters and a longitudinal stroke, a transverse stroke, a height and a track angle according to a kinematic equation:
P(EDR,ECR1,ECR2,EHF,PHF)→eDR(P)，eCR(P)，Fh(P)，Fγ(P) (2)；
wherein e isDR(P)，eCR(P)，Fh(P)，Fγ(P) respectively representing the longitudinal error, the transverse error, the terminal height and the track angle of the aircraft;
the main task of the adopted search algorithm is to seek a group of suitable roll angle parameters P, so that the parameters P not only meet the constraint conditions of the reentry process, but also can minimize the errors of the longitudinal and transverse processes, and simultaneously increase the height of the terminal as much as possible, namely, the following three objective functions are met:
Figure FDA0003330948910000021
wherein k ishIs a height coefficient, kγAs track angle coefficient, gammafA target track angle;
(4) respectively taking the state quantity of each data point in each sample data set as input, taking corresponding roll angle parameters as output, carrying out multiple BP neural network algorithm training, and completing the training of each neural network after multiple iterations when the value of the loss function reaches the required error or the maximum iteration times;
(5) tracking the reference track generated in the step (1) on line by adopting a guidance method for tracking the resistance acceleration;
(6) when the actual flight track height of the aircraft reaches the set waypoint height, inputting the real-time state information of the aircraft into the neural network corresponding to the waypoint generated in the step (4) to obtain a group of roll angle parameters, substituting the roll angle parameters into a kinematic model formula to obtain a new resistance acceleration reference curve, namely re-planning a reference track to realize rapid track reconstruction;
(7) continuing to adopt the guidance method in the step (5) to track the track and reconstruct the newly generated track, and updating the guidance instruction; and (4) when the actual flight track reaches the reachable domain of the next waypoint, repeating the track reconstruction process in the step (6), and finally completing the whole re-entry guidance process.
2. The aircraft intelligent track reconstruction reentry guidance method according to claim 1, wherein the aircraft atmosphere reentry section three-degree-of-freedom kinematic model adopted in the step (1) is as follows:
Figure FDA0003330948910000022
wherein r is the distance from the centroid of the aircraft to the geocentric, namely the sum of the height h of the aircraft and the average radius Re of the earth, V is the speed of the aircraft,
Figure FDA0003330948910000031
is latitude, theta is longitude, gamma is track angle, i.e., the angle between the velocity and the local horizontal plane, psi is heading angle, i.e., the angle between the projection of the velocity on the horizontal plane and the east-ward direction, and sigma is roll angle, i.e., the angle of rotation of the aircraft about the velocity vector; g is the acceleration of gravity;
Figure FDA0003330948910000032
wherein m isvThe mass of the aircraft is S, the aerodynamic reference area of the aircraft is S, rho is the atmospheric density, D is the resistance acceleration, L is the lift acceleration, CDIs the coefficient of aerodynamic drag, CLIs the aerodynamic lift coefficient.
3. The aircraft intelligent track reconstruction reentry guidance method according to claim 1, wherein the reentry initial state in step (1) is:
Figure FDA0003330948910000033
wherein, r (t)0),θ(t0),
Figure FDA0003330948910000034
V(t0),ψ(t0),γ(t0) Respectively the distance from the centroid of the aircraft to the geocentric, the longitude, the latitude, the speed, the course angle and the track angle of the aircraft at the initial moment of the reentry section of the aircraft;
and (3) path constraint:
(a) the heat flow constraint is:
Figure FDA0003330948910000035
wherein the content of the first and second substances,
Figure FDA0003330948910000036
as heat flow rate, kqIs the heat flow coefficient of the aircraft, rho is the atmospheric density, V is the aircraft speed,
Figure FDA0003330948910000037
is the upper allowable heat flow rate limit;
(b) the dynamic pressure constraint is:
Figure FDA0003330948910000038
wherein q is the incoming flow pressure, q ismaxIs an allowable upper limit of dynamic pressure;
(c) the overload constraints for the reentry process are:
Figure FDA0003330948910000039
wherein the content of the first and second substances,
Figure FDA00033309489100000310
for aircraft overload, D is the resistance acceleration, L is the lift acceleration, mvIs the aircraft mass, g is the gravitational acceleration,
Figure FDA00033309489100000311
is the allowable overload upper limit;
re-entering terminal target constraint:
(a) reentry terminal conditions, including altitude and speed limits:
h(tf)≥hf,V(tf)≤Vf (10)；
wherein, h (t)f),V(tf) Respectively the altitude and the speed, h, at the end of the reentry section of the aircraftf,VfRespectively the altitude and speed limit values at the end of the reentry section of the aircraft;
(b) and (3) latitude and longitude constraint:
Figure FDA0003330948910000041
wherein, θ (t)f),
Figure FDA0003330948910000042
Respectively the longitude and latitude at the end of the aircraft re-entry segment,θf,
Figure FDA0003330948910000043
respectively the longitude and latitude of the terminal target point;
and (3) controlling quantity constraint:
σmin＜|σ|＜σmax (12)；
wherein σ is the roll angle, σminFor minimum value of allowable roll angle, σmaxIs the maximum allowable roll angle; the purpose of limiting the roll angle is to reserve a certain adjustment margin for trajectory tracking and transverse guidance;
the objective function is:
J＝-khh(tf)+kγ[γ(tf)-γf]2 (13)；
wherein k ishIs a height coefficient, kγAs track angle coefficient, gamma (t)f) Track angle, gamma, at the end of the reentry sectionfIs the target track angle.
4. The method for reconstructing the reentry guidance of the aircraft according to claim 1, wherein in the step (1), since the aircraft is not subjected to an external force applied by human during the reentry process, an energy conservation law is satisfied, and the energy of the aircraft is represented by the following formula:
Figure FDA0003330948910000044
wherein r is the distance from the centroid of the aircraft to the geocentric, namely the sum of the height h of the aircraft and the average radius Re of the earth, and V is the speed of the aircraft;
therefore, when the terminal energy position is reached, if the aircraft can reach the terminal target height, the terminal speed of the aircraft can also meet the requirement; energy is therefore used as an argument in trajectory planning.
5. The aircraft intelligent trajectory reconstruction re-entry guidance method according to claim 1, which isThe method is characterized in that each reachable domain obtained in the step (3) is divided into m small areas, and in order to improve the calculation efficiency, the divided small areas are more dense in the area closer to the reference track in consideration of larger reachable domain range; then, randomly selecting n data points in each cell, wherein the number of the data points selected in each reachable domain is mn, and the state information X of each data point ismi
Figure FDA0003330948910000051
Taking the state quantities as reentry initial states, satisfying the original constraint conditions, and solving by using the search algorithm in the step (3) to obtain each group of roll angle curve parameters Pmi(EDRmi，ECR1mi，ECR2mi，EHFmi，PHFmi) And a corresponding resistance acceleration profile DmiI.e. to plan a new reference trajectory TmiGenerating a data set Q { X) from the respective state quantities and roll angle parametersmi，Pmi}。
6. The method for reconstructing the reentry guidance of the intelligent trajectory of the aircraft according to claim 1, wherein the state quantity X in the data set Q is used in the step (4)miAs the input of BP neural network, the roll angle curve parameter P corresponding to the state quantitymiAs the output of the BP neural network, training and testing the neural network to approximately obtain the relationship between the state quantity of the aircraft and the corresponding roll angle curve parameter; randomly dividing a data set Q into training sets Q according to a proper proportion1And test set Q2(ii) a Each fixed height hjWaypoint reachable domain d of 1, 2, …, n, jjA corresponding neural network N needs to be trainedjN is the number of data points, and training of the BP neural network model is carried out by using MATLAB simulation software; the BP neural network model is composed of an input layer, an output layer and one or more hidden layers, each neuron in the same layer is independent, input signals pass through each hidden layer neuron from the input layer neuron in sequence, and are finally transmitted to the output layer neuron, if the value obtained by the output layer is equal to the target valueIf there is error, the error back propagation operation is executed, and the weight and the threshold of the network are continuously adjusted according to the error, thereby achieving the best effect.
7. The method for reconstructing the reentry guidance of the intelligent trajectory of the aircraft according to claim 1, wherein in the step (6), the actual flight trajectory reaches the first fixed altitude h due to the large uncertain disturbance existing in the reentry process1In the meantime, the actual position deviates from the reference track waypoint, and at this time, the current aircraft state quantity is used
Figure FDA0003330948910000052
As an input quantity, to a neural network N1A set of roll angle curve parameters P is obtained by real-time calculation1＝[EDR1,ECR11,ECR21,EHF1,PHF1]The obtained roll angle control amount σ1Substituting into equation of motion, i.e. regenerating a new trajectory T on line1And then the control system starts to track a new track to realize track reconstruction.
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