CN115857325A - Polynomial trajectory based energy management guidance method and storage medium - Google Patents

Polynomial trajectory based energy management guidance method and storage medium Download PDF

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CN115857325A
CN115857325A CN202211228907.4A CN202211228907A CN115857325A CN 115857325 A CN115857325 A CN 115857325A CN 202211228907 A CN202211228907 A CN 202211228907A CN 115857325 A CN115857325 A CN 115857325A
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order
derivative
lateral displacement
angle
height
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CN115857325B (en
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陈曦
尚腾
程晓明
张惠平
禹春梅
靳蕊溪
胡凤荣
李明华
郑卓
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Beijing Aerospace Automatic Control Research Institute
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Abstract

An energy management guidance method and a storage medium based on polynomial trajectories solve the problem that the speed and the altitude exceed the constraint for realizing the requirement of a larger range, and belong to the field of aircraft guidance and control. The technical scheme comprises the following steps: obtaining a height third-order derivative and a lateral displacement third-order derivative under a kinematic equation; respectively describing the altitude and the lateral displacement of the aircraft by utilizing a fifth-order polynomial of time; determining all boundary constraints of the height and lateral displacement of the aircraft, determining polynomial coefficients in the two fifth-order polynomials, and solving a third-order derivative of the two fifth-order polynomials; and obtaining the attack angle change rate and the sideslip angle change rate of the control quantity, and further obtaining the attack angle and the sideslip angle of each guidance period for guidance control. The invention can enhance the robustness of the control system and meet the implementation requirement of rapid planning.

Description

Polynomial trajectory based energy management guidance method and storage medium
Technical Field
The invention relates to an energy management guidance method and a storage medium based on a polynomial trajectory, and belongs to the field of aircraft guidance and control.
Background
The solid carrying energy management technology is mainly used for meeting the requirements of various tasks and simultaneously meeting uncertain complex flight conditions such as large-range disturbance, aerodynamic influence, structural errors and the like in the flight process, autonomously realizes capacity management under the condition of multi-task requirements, ensures the performance stability of an aircraft under various uncertain conditions and improves the guidance precision in a larger range. Since aircraft using solid engines are generally designed to meet maximum range energy requirements, prior art solutions typically achieve the goal of dissipating excess energy by adjusting the pitch angle in the plane of the jet when less than range application is required or when uncertainty in the deviation is present. The prior art scheme has the following defects: 1) Under the condition of uncertain deviation, the existing solid engine energy management strategy has the defects that the pitch angle is too large and exceeds the height and speed constraints due to too large energy dissipation; 2) In order to achieve a large range of the aircraft, the existing method can only achieve the purpose of consuming excessive energy in the shooting plane by adjusting the pitch angle, but the existing method may cause the pitch angle to be adjusted too much, which has high requirements on the structure and performance characteristics of the aircraft.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the defects of the prior art are overcome, and the problem that the speed and the height exceed the constraint to meet the requirement of a large range is solved.
The purpose of the invention is realized by the following technical scheme:
a polynomial trajectory based energy management guidance method comprises the following steps:
obtaining a third-order derivative of height and a third-order derivative of lateral displacement under the kinematics equation according to the kinematics equation of the aircraft in a longitudinal plane and the kinematics equation in a lateral plane;
respectively describing the altitude and the lateral displacement of the aircraft by utilizing a fifth-order polynomial of time; determining all boundary constraints of the height and lateral displacement of the aircraft, determining polynomial coefficients in the two fifth-order polynomials by using all the boundary constraints, and solving a third-order derivative of the two fifth-order polynomials;
and obtaining the attack angle change rate and the sideslip angle change rate of the controlled variable by utilizing the height third derivative and the lateral displacement third derivative under the kinematic equation and the third derivatives of the two fifth-order polynomials, and further obtaining the attack angle and the sideslip angle of each guidance period for guidance control.
Preferably, according to a kinematics equation of the aircraft in a longitudinal plane and a kinematics equation of the aircraft in a lateral plane, a second derivative of height and a second derivative of lateral displacement under the kinematics equation are obtained firstly, an attack angle change rate and a side slip angle change rate are selected as control variables, and the second derivative of height and the second derivative of lateral displacement under the kinematics equation are derived to obtain a third derivative of height and a third derivative of lateral displacement under the kinematics equation.
Preferably, when the derivation is performed on the second derivative of the height and the second derivative of the lateral displacement in the kinematic equation, the full derivative of the aerodynamic coefficient with respect to time is ignored.
Preferably, the second derivatives of height and lateral displacement under the kinematic equation are:
Figure 423612DEST_PATH_IMAGE001
in the formula
Figure 855731DEST_PATH_IMAGE002
Figure 746326DEST_PATH_IMAGE003
Figure 543381DEST_PATH_IMAGE004
Figure 152217DEST_PATH_IMAGE005
Wherein, the first and the second end of the pipe are connected with each other,
Figure 325709DEST_PATH_IMAGE006
in order to be the flying height,
Figure 647975DEST_PATH_IMAGE007
in order to be the speed of the vehicle,
Figure 615931DEST_PATH_IMAGE008
in order to form the inclination angle of the trajectory,
Figure 712063DEST_PATH_IMAGE009
is aircraft thrust, D is aerodynamic resistance, L is aerodynamic lift, Z is aerodynamic resistance,
Figure 423667DEST_PATH_IMAGE010
is the angle of attack, m is the aircraft mass,
Figure 288855DEST_PATH_IMAGE011
in order to realize the side slip angle,
Figure 490029DEST_PATH_IMAGE012
is the acceleration of gravity at the current altitude,
Figure 73457DEST_PATH_IMAGE013
is the angle between the target vector and the incident plane,
Figure 323173DEST_PATH_IMAGE014
for the current point of the latitude, there is,
Figure 308447DEST_PATH_IMAGE015
is the current point longitude, and is the current point longitude,
Figure 431255DEST_PATH_IMAGE016
the deviation angle of the trajectory is the deviation angle of the trajectory,
Figure 501979DEST_PATH_IMAGE017
in order to obtain the latitude of the emitting point,
Figure 555385DEST_PATH_IMAGE018
to be the longitude of the point of transmission,
Figure 395165DEST_PATH_IMAGE019
the number of black dots above the parameter represents the number of derivations for the angle of incidence.
Preferably, the boundary constraints include energy, starting point velocity, ending point velocity, ballistic inclination, ballistic declination, angle of attack, side slip angle, mass, and latitude and longitude.
Preferably, the vehicle ignores earth rotation in the longitudinal in-plane kinematic equations and in the lateral in-plane kinematic equations.
Preferably, the altitude and the lateral displacement of the aircraft are each described by a fifth order polynomial of time as:
Figure 875825DEST_PATH_IMAGE020
wherein the content of the first and second substances,
Figure 230583DEST_PATH_IMAGE021
in order to be the time of flight,
Figure 87681DEST_PATH_IMAGE022
is a coefficient of the zeroth order of the height,
Figure 781967DEST_PATH_IMAGE023
is a first-order coefficient of the height,
Figure 433529DEST_PATH_IMAGE024
is a second-order coefficient of height,
Figure 478845DEST_PATH_IMAGE025
is a third-order coefficient of height,
Figure 185639DEST_PATH_IMAGE026
is a fourth order coefficient of the height,
Figure 609798DEST_PATH_IMAGE027
is a fifth-order coefficient of the height,
Figure 190515DEST_PATH_IMAGE028
is the zeroth order coefficient of the lateral displacement,
Figure 519866DEST_PATH_IMAGE029
is a first order coefficient of the lateral displacement,
Figure 718766DEST_PATH_IMAGE030
is the second order coefficient of the lateral displacement,
Figure 122065DEST_PATH_IMAGE031
being the third order coefficient of the lateral displacement,
Figure 381008DEST_PATH_IMAGE032
is the fourth order coefficient of the lateral displacement,
Figure 135338DEST_PATH_IMAGE033
is a fifth order coefficient of the lateral displacement,
Figure 183934DEST_PATH_IMAGE034
is a fifth order polynomial of height over time,
Figure 707319DEST_PATH_IMAGE035
a fifth order polynomial of lateral displacement over time,
Figure 137164DEST_PATH_IMAGE036
is the starting time.
Preferably, the third derivative of height and the third derivative of lateral displacement under the kinematic equation are:
Figure 113210DEST_PATH_IMAGE037
。
preferably, the attack angle and the sideslip angle of each guidance period are as follows:
Figure 653913DEST_PATH_IMAGE038
wherein the content of the first and second substances,
Figure 359700DEST_PATH_IMAGE039
in order to be the time of flight,
Figure 694867DEST_PATH_IMAGE040
in order to simulate the step size,
Figure 423788DEST_PATH_IMAGE041
is an angle of attack, and is,
Figure 502603DEST_PATH_IMAGE042
the number of black dots above the parameter represents the number of derivative operations for the sideslip angle.
A computer readable storage medium having stored thereon computer program instructions which, when loaded and executed by a processor, cause the processor to perform the polynomial trajectory based energy management guidance method described above.
Compared with the prior art, the invention has the following beneficial effects:
(1) According to the invention, the height and lateral position curves are approximated in a polynomial manner, so that the problem that the height and the speed exceed the constraint due to overlarge energy dissipation in the traditional alternating current maneuvering energy management strategy is solved;
(2) The invention can meet the task requirement of a larger range by the polynomial trajectory-based energy management method, and the range is wider than that of the traditional method;
(3) The method can meet the speed and height constraints while consuming the residual energy, the flying heights of the method are basically consistent, and the speed distribution is in a more reasonable range;
(4) The method can enhance the robustness of the control system and meet the implementation requirement of rapid planning.
Drawings
FIG. 1 is a graph of speed versus time for an embodiment of the present invention.
Figure 2 is a graph of ballistic inclination angle versus time for an embodiment of the present invention.
FIG. 3 is a graph of sideslip angle versus time for an embodiment of the present invention.
FIG. 4 is a graph of angle of attack versus time for an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
Example 1:
a polynomial trajectory based energy management guidance method comprises the following steps:
(1) Kinematic model
Considering neglecting earth rotation, the kinematic equation of the aircraft in the longitudinal plane is as follows:
Figure 125214DEST_PATH_IMAGE043
（1）
wherein R is the flight altitude, t is the flight time, v is the velocity,
Figure 631282DEST_PATH_IMAGE044
is a trajectory inclination angle, T is aircraft thrust, D is aerodynamic resistance, L is aerodynamic lift,
Figure 164943DEST_PATH_IMAGE045
is the angle of attack, m is the aircraft mass,
Figure 47449DEST_PATH_IMAGE046
the acceleration of gravity at the current altitude.
The equations of motion of the aircraft in the lateral plane are as follows:
Figure 399933DEST_PATH_IMAGE047
（2）
wherein, the first and the second end of the pipe are connected with each other,
Figure 342481DEST_PATH_IMAGE048
is the angle between the target vector and the incident plane,
Figure 842732DEST_PATH_IMAGE049
for the angle of incidence, d is the distance from the current position to the emission plane, i.e. the lateral displacement,
Figure 263349DEST_PATH_IMAGE050
for the current point of the latitude, there is,
Figure 985187DEST_PATH_IMAGE051
current point longitude, where:
Figure 833057DEST_PATH_IMAGE052
（3）
in the formula (I), the compound is shown in the specification,
Figure 758287DEST_PATH_IMAGE053
in order to obtain the latitude of the emitting point,
Figure 982595DEST_PATH_IMAGE054
is the transmission point longitude.
(2) Polynomial trajectory based on energy management constraints
The height and lateral displacement may be expressed in a fifth order polynomial of time, namely:
Figure 309672DEST_PATH_IMAGE055
（4）
then, the energy, the velocities of the starting point and the ending point, the trajectory inclination angle, the trajectory deflection angle, the attack angle, the sideslip angle, the mass and the latitude and longitude constraints are converted into the constraints on the height and the lateral displacement through the three-degree-of-freedom kinematics and the lateral motion equation, and the boundary constraints are obtained as follows:
Figure 407072DEST_PATH_IMAGE056
（5）
according to 12 constraints in the formula (5), the method can be solved into the formula (4)
Figure 819598DEST_PATH_IMAGE057
To
Figure 582018DEST_PATH_IMAGE058
And
Figure 763601DEST_PATH_IMAGE059
to
Figure 218853DEST_PATH_IMAGE060
The value of (c).
And (3) solving a third derivative of the formula (4) to obtain a polynomial curve of the height and lateral displacement curve of the flight path:
Figure 180993DEST_PATH_IMAGE061
（6）
(3) Generation of guidance instructions
First, the second derivative information of the height and lateral displacement is obtained by the longitudinal kinematic equation (1) and the lateral kinematic equation (2):
Figure 747103DEST_PATH_IMAGE062
（7）
wherein
Figure 783192DEST_PATH_IMAGE063
，
Figure 409346DEST_PATH_IMAGE064
Is the trajectory inclination angle, coefficient
Figure 796465DEST_PATH_IMAGE065
And coefficient of
Figure 212271DEST_PATH_IMAGE066
The expression is as follows:
Figure 368446DEST_PATH_IMAGE067
（8）
Figure 165501DEST_PATH_IMAGE068
、
Figure 774337DEST_PATH_IMAGE069
and
Figure 10146DEST_PATH_IMAGE070
for the velocity system, the overload components in three directions are expressed as follows:
Figure 20827DEST_PATH_IMAGE071
（9）
wherein the content of the first and second substances,
Figure 988783DEST_PATH_IMAGE072
is the sideslip angle, and Z is the aerodynamic drag.
In the process of generating the guidance instruction, the attack angle change rate and the sideslip angle change rate are selected as control quantities, and in order to obtain the attack angle change rate and the sideslip angle change rate, the formula (7) can be obtained by derivation again:
Figure 84915DEST_PATH_IMAGE073
（10）
wherein the overload in three directions under the speed system is subjected to derivation to obtain
Figure 530940DEST_PATH_IMAGE074
（11）
Wherein, the first and the second end of the pipe are connected with each other,
Figure 661707DEST_PATH_IMAGE075
is the aerodynamic coefficient.
Obtained after ignoring the full derivative of the aerodynamic coefficient with respect to time
Figure 613614DEST_PATH_IMAGE076
（12）
Wherein, the first and the second end of the pipe are connected with each other,
Figure 197042DEST_PATH_IMAGE077
in order to be a characteristic area of the film,
Figure 446758DEST_PATH_IMAGE078
，
Figure 432031DEST_PATH_IMAGE079
，
Figure 741790DEST_PATH_IMAGE080
is a three-direction power coefficient of force,
Figure 812514DEST_PATH_IMAGE081
is at atmospheric density.
By substituting the formula (11) and the formula (12) into the formula (10), the third-order derivatives of the height and the lateral position can be obtained
Figure 928238DEST_PATH_IMAGE082
Rate of change of angle of attack
Figure 768018DEST_PATH_IMAGE083
And rate of change of sideslip angle
Figure 248678DEST_PATH_IMAGE084
The relationship (2) of (c).
The formula (6) describes a polynomial mode of the height and the lateral position, the formula (10) describes a kinematic model of the height and the lateral position, the model comprises two physical quantities of the change rate of the attack angle and the sideslip angle, and the joint formula (6) and the formula (10) can obtain a related expression of the change rate of the attack angle and the sideslip angle, and can be expressed by the following form:
Figure 541119DEST_PATH_IMAGE085
（13）
wherein
Figure 398216DEST_PATH_IMAGE086
、
Figure 92503DEST_PATH_IMAGE087
、
Figure 55648DEST_PATH_IMAGE088
And
Figure 100965DEST_PATH_IMAGE089
is the right side of the equal sign of formula (10)
Figure 496174DEST_PATH_IMAGE090
And
Figure 44967DEST_PATH_IMAGE084
is the formula coefficient corresponding to the independent variable,
Figure 133009DEST_PATH_IMAGE091
and
Figure 400042DEST_PATH_IMAGE092
the expression on the right side of the equal sign of formula (6) and formula (10) do not contain
Figure 395680DEST_PATH_IMAGE093
And
Figure 64559DEST_PATH_IMAGE084
the sum of the fractions of (a). That is, the formula (6) and the formula (10) are two different expression forms of two identical parameters, and thus two equations can be made to stand together and then the standing equations can be collated into the form of the formula (13).
Further, the control amount attack angle change rate and the sideslip angle change rate are obtained by solving equation (13). In each guidance period, the attack angle change rate and the sideslip angle change rate are integrated to obtain an attack angle and a sideslip angle
Figure 323502DEST_PATH_IMAGE094
（14）
Wherein
Figure 812252DEST_PATH_IMAGE095
Is the simulation step size.
And carrying out guidance control by utilizing the attack angle and the sideslip angle of each guidance period.
Example 2:
a polynomial trajectory based energy management guidance method comprises the following steps:
obtaining a third-order derivative of height and a third-order derivative of lateral displacement under the kinematics equation according to the kinematics equation of the aircraft in a longitudinal plane and the kinematics equation in a lateral plane;
respectively describing the altitude and the lateral displacement of the aircraft by utilizing a fifth-order polynomial of time; determining all boundary constraints of the height and lateral displacement of the aircraft, determining polynomial coefficients in the two fifth-order polynomials by using all the boundary constraints, and solving a third-order derivative of the two fifth-order polynomials;
and obtaining the attack angle change rate and the sideslip angle change rate of the controlled variable by utilizing the third derivative of height and the third derivative of lateral displacement under a kinematic equation and the third derivatives of two fifth-order polynomials, and further obtaining the attack angle and the sideslip angle of each guidance period for guidance control.
Optionally, according to a kinematics equation of the aircraft in a longitudinal plane and a kinematics equation of the aircraft in a lateral plane, a second derivative of the altitude and a second derivative of the lateral displacement under the kinematics equation are obtained first, an attack angle change rate and a side slip angle change rate are selected as control variables, the second derivative of the altitude and the second derivative of the lateral displacement under the kinematics equation are derived, and a third derivative of the altitude and a third derivative of the lateral displacement under the kinematics equation are obtained.
Optionally, when the derivation is performed on the second derivative of the height and the second derivative of the lateral displacement in the kinematic equation, the full derivative of the aerodynamic coefficient with respect to time is ignored.
Optionally, the second derivative of height and the second derivative of lateral displacement under the kinematic equation are:
Figure 814843DEST_PATH_IMAGE001
in the formula
Figure 338228DEST_PATH_IMAGE002
Figure 315543DEST_PATH_IMAGE003
Figure 557168DEST_PATH_IMAGE096
Figure 97871DEST_PATH_IMAGE005
Wherein the content of the first and second substances,
Figure 475763DEST_PATH_IMAGE006
in order to be the flying height,
Figure 76508DEST_PATH_IMAGE007
in order to be the speed of the vehicle,
Figure 539851DEST_PATH_IMAGE008
in order to form the inclination angle of the trajectory,
Figure 946561DEST_PATH_IMAGE009
is aircraft thrust, D is aerodynamic resistance, L is aerodynamic lift, Z is aerodynamic resistance,
Figure 444539DEST_PATH_IMAGE010
is the angle of attack, m is the aircraft mass,
Figure 950606DEST_PATH_IMAGE011
in order to realize the side slip angle,
Figure 166824DEST_PATH_IMAGE097
is the acceleration of gravity at the current altitude,
Figure 49329DEST_PATH_IMAGE013
is the angle between the target vector and the incident plane,
Figure 401813DEST_PATH_IMAGE014
for the current point of the latitude, there is,
Figure 78782DEST_PATH_IMAGE015
is the current point longitude, and is the current point longitude,
Figure 658379DEST_PATH_IMAGE016
the deviation angle of the trajectory is the deviation angle of the trajectory,
Figure 344576DEST_PATH_IMAGE017
in order to obtain the latitude of the emitting point,
Figure 551566DEST_PATH_IMAGE018
to be the longitude of the point of transmission,
Figure 665016DEST_PATH_IMAGE019
the number of black dots above the parameter represents the number of derivatives for the angle of incidence.
Optionally, the boundary constraints include energy, starting point speed, ending point speed, trajectory inclination angle, trajectory deflection angle, attack angle, side slip angle, mass, and longitude and latitude.
Optionally, the earth rotation is neglected in the longitudinal in-plane kinematic equation and the lateral in-plane kinematic equation of the aircraft.
Optionally, the altitude and the lateral displacement of the aircraft are respectively described by a fifth order polynomial of time as:
Figure 590246DEST_PATH_IMAGE020
wherein the content of the first and second substances,
Figure 814554DEST_PATH_IMAGE021
in order to be the time of flight,
Figure 203947DEST_PATH_IMAGE022
is a coefficient of the zeroth order of the height,
Figure 488298DEST_PATH_IMAGE023
is a first-order coefficient of the height,
Figure 635246DEST_PATH_IMAGE024
is a second-order coefficient of height,
Figure 663244DEST_PATH_IMAGE025
is a high third-order coefficient of the height,
Figure 844827DEST_PATH_IMAGE026
is a fourth order coefficient of the height and,
Figure 300079DEST_PATH_IMAGE027
is a fifth order coefficient of the height of the image,
Figure 12951DEST_PATH_IMAGE028
is the zeroth order coefficient of the lateral displacement,
Figure 579062DEST_PATH_IMAGE029
is the first order coefficient of the lateral displacement,
Figure 615151DEST_PATH_IMAGE030
is the second order coefficient of the lateral displacement,
Figure 241305DEST_PATH_IMAGE031
being the third order coefficient of the lateral displacement,
Figure 362844DEST_PATH_IMAGE032
is the fourth order coefficient of the lateral displacement,
Figure 732646DEST_PATH_IMAGE033
is a fifth order coefficient of the lateral displacement,
Figure 951137DEST_PATH_IMAGE034
a fifth order polynomial of height over time,
Figure 748192DEST_PATH_IMAGE035
a fifth order polynomial of lateral displacement over time,
Figure 357028DEST_PATH_IMAGE036
is the starting time.
Optionally, the third derivative of height and the third derivative of lateral displacement under the kinematic equation are:
Figure 264941DEST_PATH_IMAGE037
。
optionally, the attack angle and the sideslip angle of each guidance period are:
Figure 275623DEST_PATH_IMAGE098
wherein the content of the first and second substances,
Figure 243579DEST_PATH_IMAGE039
in order to be the time of flight,
Figure 651295DEST_PATH_IMAGE040
in order to simulate the step size,
Figure 362899DEST_PATH_IMAGE041
in order to be the angle of attack,
Figure 493666DEST_PATH_IMAGE042
the number of black dots above the parameter represents the number of derivative operations for the sideslip angle.
A computer readable storage medium having stored thereon computer program instructions which, when loaded and executed by a processor, cause the processor to perform the above polynomial trajectory based energy management guidance method.
Example 3:
based on embodiment 1 or 2, different flight states are selected according to different terminal speed requirements, and selectable parameters include altitude, speed, ballistic inclination and lateral displacement. According to the terminal lateral displacement, a proper initial off-plane angle is selected, so that the number of the sideslip angle cannot be changed repeatedly, the amplitude of the sideslip angle can be effectively reduced, and the bending moment is reduced.
Simulating under different terminal speed constraints, namely terminal speed constraint distribution is 7400 to 8300m/s, wherein simulation results are shown in fig. 1 to 4, fig. 1 is a speed and time curve corresponding to the generated trajectory under different terminal speed constraints, fig. 2 is a trajectory inclination angle and time curve corresponding to the generated trajectory under different terminal speed constraints, fig. 3 is a sideslip angle and time curve corresponding to the generated trajectory under different terminal speed constraints, and fig. 4 is an attack angle and time curve corresponding to the generated trajectory under different terminal speed constraints; it can be seen from the above simulation diagram that the proposed energy management method based on polynomial trajectory can achieve different terminal speeds and can meet the requirement of energy management. The smaller the terminal velocity, the more energy needs to be dissipated, and the larger the magnitudes of the angle of attack and sideslip angle. As can be seen from the simulation result table, the speed distribution is 7400 to 8300m/s, and the height error is
Figure 632523DEST_PATH_IMAGE099
Within a speed error of
Figure 950372DEST_PATH_IMAGE100
Within the error of trajectory inclination angle
Figure 465667DEST_PATH_IMAGE101
Within an azimuthal error of
Figure 513258DEST_PATH_IMAGE101
Inward and lateral displacement of substantially
Figure 823016DEST_PATH_IMAGE102
Within. The planned trajectory can meet the requirement of management, and a terminal point with higher precision can be achieved. Each planned trajectory only needs to be within 1 s.
Those skilled in the art will appreciate that those matters not described in detail in the present specification are not particularly limited to the specific examples described herein.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to limit the present invention, and those skilled in the art can make possible variations and modifications of the present invention using the method and the technical contents disclosed above without departing from the spirit and scope of the present invention, and therefore, any simple modifications, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention are all within the scope of the present invention.

Claims (10)

1. A polynomial trajectory based energy management guidance method is characterized by comprising the following steps:
obtaining a third-order derivative of height and a third-order derivative of lateral displacement under the kinematics equation according to the kinematics equation of the aircraft in a longitudinal plane and the kinematics equation in a lateral plane;
respectively describing the altitude and the lateral displacement of the aircraft by utilizing a fifth-order polynomial of time; determining all boundary constraints of the height and lateral displacement of the aircraft, determining polynomial coefficients in the two fifth-order polynomials by using all boundary constraints, and solving a third derivative of the two fifth-order polynomials;
and obtaining the attack angle change rate and the sideslip angle change rate of the controlled variable by utilizing the third derivative of height and the third derivative of lateral displacement under a kinematic equation and the third derivatives of two fifth-order polynomials, and further obtaining the attack angle and the sideslip angle of each guidance period for guidance control.
2. The energy management guidance method according to claim 1, wherein according to a kinematic equation of the aircraft in a longitudinal plane and a kinematic equation of the aircraft in a lateral plane, a second derivative of the altitude and a second derivative of the lateral displacement under the kinematic equation are obtained first, an attack angle change rate and a lateral slip angle change rate are selected as control variables, and the second derivative of the altitude and the second derivative of the lateral displacement under the kinematic equation are derived to obtain a third derivative of the altitude and a third derivative of the lateral displacement under the kinematic equation.
3. The energy management guidance method of claim 2, wherein the derivation of the second derivative of height and the second derivative of lateral displacement under the kinematic equation ignores the full derivative of the aerodynamic coefficient over time.
4. The energy management guidance method of claim 2, wherein the second derivative of height and the second derivative of lateral displacement under the kinematic equation are:
Figure 425106DEST_PATH_IMAGE001
in the formula
Figure 342247DEST_PATH_IMAGE002
Figure 262929DEST_PATH_IMAGE003
Figure 658139DEST_PATH_IMAGE004
Figure 472511DEST_PATH_IMAGE005
Wherein, the first and the second end of the pipe are connected with each other,
Figure 294973DEST_PATH_IMAGE006
in order to be the flying height,
Figure 562007DEST_PATH_IMAGE007
in order to be able to speed up the vehicle,
Figure 823224DEST_PATH_IMAGE008
in order to form the inclination angle of the trajectory,
Figure 492102DEST_PATH_IMAGE009
is the thrust of the aircraft, D is the aerodynamic resistance, L is the aerodynamic lift, Z is the aerodynamic resistance,
Figure 485466DEST_PATH_IMAGE010
is the angle of attack, m is the aircraft mass,
Figure 239796DEST_PATH_IMAGE011
in order to realize the side slip angle,
Figure 976807DEST_PATH_IMAGE012
is the acceleration of gravity at the current height,
Figure 500193DEST_PATH_IMAGE013
is the angle between the target vector and the incident plane,
Figure 930037DEST_PATH_IMAGE014
for the current point of the latitude, there is,
Figure 906083DEST_PATH_IMAGE015
is the current point longitude, and is the current point longitude,
Figure 181207DEST_PATH_IMAGE016
the deviation angle of the trajectory is the deviation angle of the trajectory,
Figure 824678DEST_PATH_IMAGE017
in order to obtain the latitude of the emitting point,
Figure 159844DEST_PATH_IMAGE018
to be the longitude of the point of transmission,
Figure 888766DEST_PATH_IMAGE019
the number of black dots above the parameter represents the number of derivatives for the angle of incidence.
5. The energy management guidance method of claim 2, wherein the third derivative of height and the third derivative of lateral displacement under the kinematic equation are:
Figure 607061DEST_PATH_IMAGE020
。
6. the energy management guidance method of claim 1, wherein the all boundary constraints include energy, origin speed, destination speed, ballistic inclination, ballistic declination, angle of attack, sideslip angle, mass, latitude and longitude.
7. The energy management guidance method of claim 1, wherein the aircraft ignores earth rotation in longitudinal in-plane kinematic equations and in lateral in-plane kinematic equations.
8. The energy management guidance method of any one of claims 1 to 7, wherein the altitude and lateral displacement of the aircraft are each described by a fifth order polynomial of time as:
Figure 105038DEST_PATH_IMAGE021
wherein the content of the first and second substances,
Figure 876685DEST_PATH_IMAGE022
in order to be the time of flight,
Figure 827323DEST_PATH_IMAGE023
is a coefficient of the zeroth order of the height,
Figure 709829DEST_PATH_IMAGE024
is a first-order coefficient of the height,
Figure 62313DEST_PATH_IMAGE025
is a second-order coefficient of height,
Figure 739282DEST_PATH_IMAGE026
is a third-order coefficient of height,
Figure 177216DEST_PATH_IMAGE027
is a fourth order coefficient of the height,
Figure 597833DEST_PATH_IMAGE028
is a fifth-order coefficient of the height,
Figure 70403DEST_PATH_IMAGE029
is the zeroth order coefficient of the lateral displacement,
Figure 183853DEST_PATH_IMAGE030
is the first order coefficient of the lateral displacement,
Figure 250029DEST_PATH_IMAGE031
is the second order coefficient of the lateral displacement,
Figure 474337DEST_PATH_IMAGE032
is the third order coefficient of the lateral displacement,
Figure 535834DEST_PATH_IMAGE033
is a fourth order coefficient of the lateral displacement,
Figure 820184DEST_PATH_IMAGE034
is a fifth order coefficient of the lateral displacement,
Figure 232711DEST_PATH_IMAGE035
is a fifth order polynomial of height over time,
Figure 572294DEST_PATH_IMAGE036
a fifth order polynomial of lateral displacement over time,
Figure 753877DEST_PATH_IMAGE037
is the starting time.
9. The energy management guidance method of any one of claims 1 to 7, wherein the angle of attack and the angle of sideslip for each guidance cycle are:
Figure 943550DEST_PATH_IMAGE038
wherein the content of the first and second substances,
Figure 843373DEST_PATH_IMAGE039
in order to be the time of flight,
Figure 409483DEST_PATH_IMAGE040
in order to simulate the step size,
Figure 711152DEST_PATH_IMAGE041
is an angle of attack, and is,
Figure 806147DEST_PATH_IMAGE042
the number of black dots above the parameter represents the number of derivations for the sideslip angle.
10. A computer readable storage medium having stored thereon computer program instructions which, when loaded and executed by a processor, cause the processor to perform the method of any of claims 1 to 7.
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