CN111930145B - Hypersonic aircraft reentry trajectory optimization method based on sequence convex programming - Google Patents

Hypersonic aircraft reentry trajectory optimization method based on sequence convex programming Download PDF

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CN111930145B
CN111930145B CN202010855016.6A CN202010855016A CN111930145B CN 111930145 B CN111930145 B CN 111930145B CN 202010855016 A CN202010855016 A CN 202010855016A CN 111930145 B CN111930145 B CN 111930145B
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CN111930145A (en
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蔡光斌
徐慧
黄月平
杨小冈
席建祥
胡来红
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Rocket Force University of Engineering of PLA
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Abstract

The invention relates to a hypersonic aircraft reentry trajectory optimization method based on sequential convex programming. Establishing a hypersonic reentry dynamic model considering conventional path constraints; performing variable replacement on the obtained model by using the height and the dynamic pressure to obtain an equivalent reentry model; selecting a new control quantity, and simplifying a reentry model; carrying out convex processing and discretization processing on the simplified reentry model, so that the original non-convex reentry trajectory optimization problem becomes a convex problem which can be solved; and solving the convex problem by using a sequential convex programming algorithm to obtain an optimal track. According to the invention, the model is subjected to variable replacement by using the height and the dynamic pressure, so that the model is simplified, and the complexity in solving is reduced; the original non-convex reentry trajectory optimization problem is converted into a convex problem which can be solved by using a sequence convex programming algorithm, and the optimal trajectory solving time is greatly prolonged. Simulation experiments verify that the optimal trajectory can be rapidly solved by the method.

Description

Hypersonic aircraft reentry trajectory optimization method based on sequence convex programming
Technical Field
The invention relates to the technical field of reentry trajectory optimization of hypersonic aircrafts, in particular to a reentry trajectory optimization method of a hypersonic aircraft based on sequential convex programming.
Background
The rapid optimization problem of the reentry trajectory of the hypersonic aircraft is one of key difficult problems in the research of the hypersonic aircraft, the rapid planning of the accurate reentry trajectory has great practical significance to the subsequent maneuvering and guidance process, and the rapid optimization problem also has profound influence on theoretical research.
At present, the research on the theory related to the hypersonic aircraft has become a new technical highland and research hotspot in aviation and military, but the problem of optimizing the reentry trajectory of the rapid hypersonic aircraft is still an unsolved serious difficult problem. Especially, it is still a very challenging problem to require real-time planning of new trajectory paths during the flight.
The goal of trajectory optimization of the reentry section of the hypersonic flight vehicle is to generate a flight trajectory which meets various path constraints, states, control quantities and terminal boundary value constraint conditions and realizes a certain optimal target, so that the hypersonic flight vehicle can safely reach an area near a target point from a reentry point. In the existing research stage, the hypersonic aircraft reentry trajectory optimization problem is solved, and commonly used optimization algorithms include an analytic method and a numerical method. However, the reentry dynamic model of the hypersonic aircraft is too complex, so that the problems of strong coupling and strong nonlinearity among the controlled variable state quantities exist, and the analytic result is difficult to obtain by using an analytic method. The numerical method comprises a direct method and an indirect method, wherein the direct method has the advantages of simple algorithm principle, low influence of the convergence rate on the initial value estimation precision, easy local optimization of a solution result and large solution calculation amount. The indirect method has the advantages that the solving result meets the optimal necessary condition and the solving precision is high, the principle derivation is complex and tedious, the dependence degree of the convergence speed on the estimation value of the initial value of the covariance variable is high, the physical significance of the covariance variable is not clear, the reasonable initial value is difficult to obtain through effective analysis, the specific process constraint is converted into the equivalent terminal constraint, and the like. In recent years, requirements for planning time are increasing on the problem of optimizing reentry trajectories of hypersonic aircrafts, and the requirements for planning time cannot be met in the prior art.
Disclosure of Invention
The invention aims to provide a hypersonic aircraft reentry trajectory optimization method based on sequential convex programming, which can reduce complexity, reduce calculated amount and shorten trajectory optimization solving time.
In order to achieve the purpose, the invention provides the following scheme:
a hypersonic aircraft reentry trajectory optimization method based on sequential convex programming comprises the following steps:
s101, establishing a reentry dynamic model of the hypersonic aircraft based on a geocentric rectangular coordinate system;
s102, combining the reentry dynamic model of the hypersonic flight vehicle, considering end point constraint and conventional path constraint, and establishing a model of the reentry trajectory optimization problem of the hypersonic flight vehicle under the condition of multiple constraints;
s103, aiming at the model of the reentry trajectory optimization problem, taking height as an independent variable and dynamic pressure as state quantity replacement speed to obtain a superhigh reentry trajectory optimization problem model after variable replacement;
s104, introducing new control quantity to further convert the variable-replaced super reentry trajectory optimization problem model to obtain a reentry motion model with decoupled state quantity and control quantity;
s105, carrying out convex processing on the reentry motion model;
s106, performing discrete processing on the reentry motion model after the convex processing to obtain a track optimization problem which can be solved by using a sequence convex planning method;
and S107, solving the track optimization problem by using a sequential convex planning method.
Optionally, the reentry dynamics model of the hypersonic aircraft is:
Figure BDA0002646116700000021
Figure BDA0002646116700000022
Figure BDA0002646116700000023
Figure BDA0002646116700000024
Figure BDA0002646116700000025
Figure BDA0002646116700000026
wherein h is the ground center distance of the aircraft, and V is the aircraftThe earth relative speed psi and gamma are respectively the course angle and track angle of the aircraft, and the longitude theta latitude where the aircraft is located
Figure BDA0002646116700000027
The method is a main factor for judging the path constraint of the aircraft, m and g are the mass of the aircraft and the gravity acceleration of the current geocentric distance, and the lateral slip angle sigma and the attack angle alpha of the aircraft respectively control the transverse and longitudinal guidance profiles in the aircraft guidance strategy; d ═ ρ V 2 S ref C D P V ═ L and/2 2 S ref C L And/2 is the aerodynamic drag and lift of the aircraft during flight, where ρ is the air density at the current altitude of the aircraft, S is the reference cross-sectional area of the aircraft, C L And C D The sideslip angle σ and the angle of attack α are control quantities, respectively, and are aerodynamic parameters related to the angle of attack α of the aircraft.
Optionally, the hypersonic aircraft reentry trajectory optimization problem model under the multi-constraint condition is as follows:
Figure BDA0002646116700000031
Figure BDA0002646116700000032
Figure BDA0002646116700000033
Figure BDA0002646116700000034
Figure BDA0002646116700000035
Figure BDA0002646116700000036
constraints that need to be met:
|X(t f )-X f |≤ε X
Figure BDA0002646116700000037
Figure BDA0002646116700000038
q＝0.5ρV 2 ≤q max ；
|X(t f )-X f |≤ε X the end-point constraints are represented and,
Figure BDA0002646116700000039
is a matrix of aircraft states, epsilon X Is a small constant matrix, in which X (t) f ) Representing the state quantity, X, obtained by the terminal time algorithm f Representing the target state quantity, epsilon, of the terminal time X The smaller the aircraft trajectory optimization target end point state is, the closer the aircraft trajectory optimization target end point state is to the preset state of the task, and the better the trajectory optimization effect is;
Figure BDA00026461167000000310
Figure BDA00026461167000000311
and q is 0.5 ρ V 2 ≤q max Are all conventional path constraints including heat flow rate constraints, overload constraints and dynamic pressure constraints, wherein
Figure BDA00026461167000000312
In order to be a heat flow rate constraint,
Figure BDA00026461167000000313
for overload restraint, q is 0.5 rho V 2 ≤q max In order to achieve the dynamic pressure constraint,
Figure BDA00026461167000000314
maximum values of heat flow rate, overload and dynamic pressure, K, respectively, during flight of the aircraft Q ＝7.9686×10 -5 Js 2 /(m 3.5 kg 0.5 ) Is the heat flow rate constant.
Optionally, the hypersonic reentry trajectory optimization problem model after variable replacement is as follows:
Figure BDA0002646116700000041
Figure BDA0002646116700000042
Figure BDA0002646116700000043
Figure BDA0002646116700000044
Figure BDA0002646116700000045
after the independent variables are converted, the reentry equation becomes 5 constraints, dynamic pressure is used as a state quantity to replace speed, the dynamic pressure constraint is naturally met, and the heat flow rate and the overload constraint in the conventional path constraint are recorded as:
Figure BDA0002646116700000046
in the formula (I), the compound is shown in the specification,
Figure BDA0002646116700000047
for the heat flow rate and dynamic pressure during flight,
Figure BDA0002646116700000048
n max maximum values of heat flow rate and dynamic pressure during flight, respectively;
noting the new state quantity as x ═ theta phi q gamma psi] T Then the constraints that the reentry trajectory optimization problem needs to satisfy become:
|x(h f )-x f |≤ε X
Figure BDA0002646116700000049
optionally, the introducing a new controlled variable further transforms the hypersonic reentry trajectory optimization problem model after the variable replacement to obtain a reentry motion model with decoupled state quantities and controlled variables, and specifically includes:
the method comprises the following steps: selecting a new control quantity mu 1 、μ 2 And mu 3 ，
Figure BDA00026461167000000410
Figure BDA00026461167000000411
Figure BDA00026461167000000412
Where L is lift, m is aircraft speed, and σ is roll angle, a new controlled variable constraint is derived from the new controlled variable relationship:
Figure BDA00026461167000000413
step two: and substituting the new control quantity into the hypersonic reentry trajectory optimization problem model after the variable replacement to obtain a reentry motion model with decoupled state quantity and control quantity:
Figure BDA00026461167000000414
wherein x is [ theta φ q [ ]γ ψ] T Is a new state quantity; u ═ mu 1 μ 2 μ 3 ] T Is the newly selected control quantity;
Figure BDA0002646116700000051
is a function related to the state quantity;
Figure BDA0002646116700000052
is a coefficient matrix of the new control quantity;
then the reentry optimization problem constraint becomes:
|x(h f )-x f |≤ε X
Figure BDA0002646116700000053
Figure BDA0002646116700000054
optionally, the performing a convex process on the reentry motion model specifically includes: the method comprises the following steps: performing first-order Taylor expansion on the reentry motion model;
Figure BDA0002646116700000055
step two: controlling quantity constraint to carry out relaxation quantization;
μ 3 cosσ max ≤μ 1 ≤μ 3 cosσ min
μ 3min ≤μ 3 ≤μ 3max
μ 1 2 +μ 2 2 ≤μ 3 2
step three: performing first-order Taylor expansion on the process constraint;
Figure BDA0002646116700000056
step four: introducing a trust domain constraint:
|x-x * |≤τ
after the convex processing, the hypersonic reentry trajectory optimization problem is described as follows:
Figure BDA0002646116700000061
Figure BDA0002646116700000062
|x-x * |≤τ
μ 3 cosσ max ≤μ 1 ≤μ 3 cosσ min
μ 3min ≤μ 3 ≤μ 3max
μ 1 2 +μ 2 2 ≤μ 3 2
Figure BDA0002646116700000063
x(h 0 )＝x 0 ,x(h f )＝x f
in the formula, theta f 、φ f The latitude and longitude of the aircraft obtained for the final algorithm,
Figure BDA0002646116700000064
is the target longitude and latitude.
Optionally, the step of performing discrete processing on the reentry motion model after the convex processing to obtain a trajectory optimization problem that can be solved by using a sequential convex planning method specifically includes:
the method comprises the following steps: the value range [ h ] of the independent variable 0 ,h f ]Equally spaced discretization into N intervals yields:
the independent variables are discretized as: h is a total of 0 ,h 1 ,h 2 ,…,h n-1 ,h n ；
The state quantity is discretized into: x is the number of 0 ,x 1 ,x 2 ,…,x n-1 ,x n ；
The controlled variable is discrete as: u shape 0 ,U 1 ,U 2 ,…,U n-1 ,U n ；
Step two: and (3) performing approximate dispersion on the kinetic equation obtained in the fifth step by adopting a trapezoidal method, wherein the obtained equation is as follows:
Figure BDA0002646116700000065
step three: discretizing the conventional path constraints to become:
Figure BDA0002646116700000066
the description of the finally obtained reentry trajectory optimization problem is as follows:
Figure BDA0002646116700000071
optionally, the solving the trajectory optimization problem by using the sequential convex programming method specifically includes:
the method comprises the following steps: set k to 0, set initial state x (h) 0 ) Initial trajectory x 0 Obtaining the integral of a given control quantity constant value, wherein k is the number of times of sequence convex programming;
step two: for k ≧ 1, in the kth iteration, the discrete problem for S106 utilizes the previously obtained trajectory x k-1 Obtaining [ x ] k U k ]；
Step three: check if sequence convergence condition sup | x is satisfied k -x k-1 If the condition is met, turning to the step four, otherwise, turning to the step two if k is k + 1;
step four: obtaining the optimal track x k The iteration stops.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
according to the invention, by using an independent variable replacement method, the height is used as the independent variable, and the dynamic pressure replacement speed is used as the state quantity, so that the state quantity of the reentry kinetic equation is reduced, and the complexity is reduced. According to the invention, by selecting a new control quantity, the problem of coupling of the control quantity and the state quantity in the reentry kinetic equation is solved, the calculation quantity of the problem is reduced, and the calculation time is shortened. According to the method, the original non-convex reentry trajectory optimization problem is converted into the convex problem through the convexity and the discretization, and the problem is solved by adopting a sequential convex planning method, so that the optimal trajectory is obtained, and the trajectory optimization time is greatly reduced.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart of a hypersonic aircraft reentry trajectory optimization method based on sequential convex programming according to the invention;
FIG. 2 is a longitude vs altitude plot obtained by the proposed method of the present invention;
fig. 3 is a comparative trace diagram obtained by the proposed method of the present invention and GPOPS2 method.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a hypersonic aircraft reentry trajectory optimization method based on sequence convex programming, which can reduce the complexity, reduce the calculated amount and shorten the trajectory optimization solution time.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
In recent years, due to the fact that requirements on planning time are higher and higher in the hypersonic aircraft reentry trajectory optimization problem, the convex optimization method is used to focus on the problem. The method for solving the reentry trajectory optimization problem of the hypersonic flight vehicle by using the convex optimization method has great advantages in solving speed, and can obtain a global optimal solution, so that the reentry trajectory optimization of hypersonic flight vehicles in real time becomes possible. Sequential convex programming is a commonly used method in convex optimization theory. The main idea of the sequential convex programming is to solve the sequential approximate convex subproblem to realize the convergence of the solution of the subproblem to the solution of the original problem. The invention adopts a shape independent variable replacing method, the height is taken as an independent variable, and the dynamic pressure replacing speed is taken as a state quantity, so that the state quantity of a reentry kinetic equation is reduced; selecting a new controlled variable, and solving the problem of coupling of the controlled variable and the state quantity in the reentry kinetic equation; the original reentry trajectory optimization problem is converted into a convex problem, and the sequential convex planning method is adopted to solve the convex problem, so that the optimal trajectory is obtained, the trajectory optimization time is greatly shortened, and the method has important engineering significance for online optimization of the reentry trajectory of the hypersonic aircraft.
FIG. 1 is a flowchart of a hypersonic aircraft reentry trajectory optimization method based on sequential convex programming. As shown in fig. 1, a hypersonic aircraft reentry trajectory optimization method based on sequential convex programming includes:
and S101, establishing a reentry dynamic model of the hypersonic aircraft based on the geocentric rectangular coordinate system.
The reentry dynamic model of the hypersonic aerocraft is as follows:
Figure BDA0002646116700000091
Figure BDA0002646116700000092
Figure BDA0002646116700000093
Figure BDA0002646116700000094
Figure BDA0002646116700000095
Figure BDA0002646116700000096
where h is the geocentric distance of the aircraft, V is the earth relative speed of the aircraft, psi and gamma are the heading angle and track angle of the aircraft, respectively, and the longitude theta latitude where the aircraft is located
Figure BDA0002646116700000097
The method is a main factor for judging the path constraint of the aircraft, m and g are the mass of the aircraft and the gravity acceleration of the current geocentric distance, and the lateral slip angle sigma and the attack angle alpha of the aircraft respectively control the transverse and longitudinal guidance profiles in the aircraft guidance strategy. D ═ ρ V 2 S ref C D P V is equal to L and/2 2 S ref C L And/2 is the aerodynamic drag and lift of the aircraft during flight, where ρ is the air density at the current altitude of the aircraft, S is the reference cross-sectional area of the aircraft, C L And C D In the model, the sideslip angle σ and the angle of attack α are control variables, respectively, an aerodynamic parameter related to the angle of attack α of the aircraft.
And S102, combining the reentry dynamic model of the hypersonic aircraft, considering end point constraint and conventional path constraint, and establishing a reentry trajectory optimization problem model of the hypersonic aircraft under a multi-constraint condition.
The hypersonic aircraft reentry trajectory optimization problem model under the multi-constraint condition is as follows:
Figure BDA0002646116700000101
Figure BDA0002646116700000102
Figure BDA0002646116700000103
Figure BDA0002646116700000104
Figure BDA0002646116700000105
Figure BDA0002646116700000106
constraints that need to be met:
|X(t f )-X f |≤ε X
Figure BDA0002646116700000107
Figure BDA0002646116700000108
q＝0.5ρV 2 ≤q max ；
|X(t f )-X f |≤ε X the end-point constraints are represented as,
Figure BDA0002646116700000109
is a matrix of aircraft states, epsilon X Is a small constant matrix, in which X (t) f ) Representing the state quantity, X, obtained by the terminal time algorithm f Representing the target state quantity, epsilon, of the terminal time X The smaller the aircraft trajectory optimization target end point state is, the closer the aircraft trajectory optimization target end point state is to the preset state of the task, and the better the trajectory optimization effect is;
Figure BDA00026461167000001010
Figure BDA00026461167000001011
and q is 0.5 ρ V 2 ≤q max Are all conventional path constraints including heat flow rate constraints, overload constraints and dynamic pressure constraints, wherein
Figure BDA00026461167000001012
In order to be a constraint on the heat flow rate,
Figure BDA00026461167000001013
for overload restraint, q is 0.5 rho V 2 ≤q max In order to achieve the dynamic pressure constraint,
Figure BDA00026461167000001014
maximum values of heat flow rate, overload and dynamic pressure, K, respectively, during flight of the aircraft Q ＝7.9686×10 -5 Js 2 /(m 3.5 kg 0.5 ) Is the heat flow rate constant.
And S103, aiming at the model of the reentry trajectory optimization problem, taking the height as an independent variable and taking the dynamic pressure as a state quantity replacement speed to obtain the model of the reentry trajectory optimization problem after variable replacement.
The hypersonic reentry trajectory optimization problem model after variable replacement is as follows:
Figure BDA0002646116700000111
Figure BDA0002646116700000112
Figure BDA0002646116700000113
Figure BDA0002646116700000114
Figure BDA0002646116700000115
after the independent variables are converted, the reentry equation becomes 5 constraints, dynamic pressure is used as a state quantity to replace speed, the dynamic pressure constraint is naturally met, and the heat flow rate and the overload constraint in the conventional path constraint are recorded as:
Figure BDA0002646116700000116
in the formula (I), the compound is shown in the specification,
Figure BDA0002646116700000117
for the heat flow rate and dynamic pressure during flight,
Figure BDA0002646116700000118
n max respectively, the maximum values of the heat flow rate and the dynamic pressure during flight.
Noting the new state quantity as x ═ theta phi q gamma psi] T Then the constraints that the reentry trajectory optimization problem needs to satisfy become:
|x(h f )-x f |≤ε X
Figure BDA0002646116700000119
and S104, introducing a new control quantity to further convert the variable-replaced super reentry trajectory optimization problem model to obtain a reentry motion model with decoupled state quantity and control quantity. The method comprises the following steps:
the method comprises the following steps: selecting a new control quantity mu 1 、μ 2 And mu 3 ，
Figure BDA00026461167000001110
Figure BDA00026461167000001111
Figure BDA00026461167000001112
Where L is lift, m is aircraft speed, σ is roll angle, and a new controlled variable constraint is derived from the relationship of the new controlled variables:
Figure BDA00026461167000001113
step two: and substituting the new control quantity into the hypersonic reentry trajectory optimization problem model after the variable replacement to obtain a reentry motion model with decoupled state quantity and control quantity:
Figure BDA00026461167000001114
wherein x is [ theta phi q gamma psi ═ x] T Is a new state quantity; u ═ mu 1 μ 2 μ 3 ] T Is the newly selected control quantity;
Figure BDA0002646116700000121
is a function related to the state quantity;
Figure BDA0002646116700000122
is a coefficient matrix of the new control quantity;
then the reentry optimization problem constraint becomes:
|x(h f )-x f |≤ε X
Figure BDA0002646116700000123
Figure BDA0002646116700000124
and S105, carrying out convex processing on the reentry motion model. The method specifically comprises the following steps:
the method comprises the following steps: performing first-order Taylor expansion on the reentry motion model;
Figure BDA0002646116700000125
step two: controlling quantity constraint to carry out relaxation quantization;
μ 3 cosσ max ≤μ 1 ≤μ 3 cosσ min
μ 3min ≤μ 3 ≤μ 3max
μ 1 2 +μ 2 2 ≤μ 3 2
step three: performing first-order Taylor expansion on the process constraint;
Figure BDA0002646116700000126
step four: introducing a trust domain constraint:
|x-x * |≤τ
after the convex processing, the optimization problem of the hypersonic reentry trajectory is described as follows:
Figure BDA0002646116700000131
Figure BDA0002646116700000132
|x-x * |≤τ
μ 3 cosσ max ≤μ 1 ≤μ 3 cosσ min
μ 3min ≤μ 3 ≤μ 3max
μ 1 2 +μ 2 2 ≤μ 3 2
Figure BDA0002646116700000133
x(h 0 )＝x 0 ,x(h f )＝x f
in the formula, theta f 、φ f The latitude and longitude of the aircraft obtained for the final algorithm,
Figure BDA0002646116700000134
is the target longitude and latitude.
And S106, performing discrete processing on the reentry motion model after the convex processing to obtain a track optimization problem which can be solved by using a sequence convex planning method. The method specifically comprises the following steps:
the method comprises the following steps: the value range [ h ] of the independent variable 0 ,h f ]Equally spaced discretization into N intervals yields:
the independent variable is discrete as: h is a total of 0 ,h 1 ,h 2 ,…,h n-1 ,h n ；
The state quantity is discretized into: x is the number of 0 ,x 1 ,x 2 ,…,x n-1 ,x n ；
The controlled variable is discrete as: u shape 0 ,U 1 ,U 2 ,…,U n-1 ,U n ；
Step two: and (4) performing approximate dispersion on the kinetic equation obtained in the fifth step by adopting a trapezoidal method, wherein the obtained equation is as follows:
Figure BDA0002646116700000135
step three: discretizing the conventional path constraints to become:
Figure BDA0002646116700000136
the description of the finally obtained reentry trajectory optimization problem is as follows:
Figure BDA0002646116700000141
Figure BDA0002646116700000142
|x-x * |≤τ
μ 3 cosσ max ≤μ 1 ≤μ 3 cosσ min
μ 3min ≤μ 3 ≤μ 3max
μ 1 2 +μ 2 2 ≤μ 3 2
Figure BDA0002646116700000143
x(h 0 )＝x 0 ,x(h f )＝x f
and S107, solving the track optimization problem by using a sequential convex planning method. The method specifically comprises the following steps:
the method comprises the following steps: set k to 0, set initial state x (h) 0 ) Initial trajectory x 0 Obtaining the integral of a given control quantity constant value, wherein k is the number of times of sequence convex programming;
step two: when k is greater than or equal to 1,in the kth iteration, the discretization problem for S106 utilizes the previously obtained trajectory x k-1 Obtaining [ x ] k U k ]；
Step three: check if sequence convergence condition sup | x is satisfied k -x k-1 If the condition is met, turning to the step four, otherwise, turning to the step two if k is k + 1;
step four: obtaining the optimal track x k The iteration stops.
In S103, it is proposed to use the dynamic pressure instead of the velocity as the system state quantity, with the height as an independent variable. The system state quantity is changed into 5, and the calculation quantity in the solving process is reduced; in addition, dynamic pressure is used as a state quantity, and the state quantity is already constrained in the solving process, so that in path constraint, the dynamic pressure constraint is not needed to be referred again; the method of using the height in the middle as the time for independent variable replacement provides a good idea of simplifying calculation for the optimization problem of the reentry trajectory of the hypersonic aerocraft.
In S104, a new control amount related to the roll angle is selected, so that the reentry equation of motion originally in the form of a trigonometric function of the control amount becomes approximately linear with the new control amount. In the transformation of the model, the system state quantity and the control quantity are distinguished, the solving speed of the model is increased, and the complexity is simplified.
S105-S107 are processes of converting the non-convex problem of the original reentry trajectory optimization into a convex problem and solving by using sequential convex programming. The solution time for convex problems is generally shorter than that for non-convex problems. The simplified operation of the model in the previous step and the use of the sequence convex planning method greatly shorten the solving time of the optimization of the reentry trajectory of the hypersonic flight vehicle, and provide an important feasible thought for the subsequent research of the optimization problem of the online reentry trajectory of the hypersonic flight vehicle. Simulation experiments can prove that the method can greatly shorten the track optimization solving time.
After S107, a CAV model is adopted for simulation experiments, 72.062S of time spent on planning the CPU time of the track by using a GPOPS2 method for comparison is proved in the experiments, and 7.523S of time spent on planning the CPU time of the method are proved, so that the method can rapidly plan a reliable track, and the effectiveness of the method is proved.
The simulation experiment is described below.
And (3) carrying out a simulation experiment by adopting a CAV-H model and taking accurately and quickly planning the track of the hypersonic aircraft from the starting point to the end point as a target task.
Step one, adopting a general CAV-H hypersonic aircraft model to carry out experiments. The CAV-H parameters and hypersonic vehicle reentry mission data are shown in table 1.
And step two, constructing the convex problem description after the model conversion of the text by using a CVX tool kit, and obtaining the optimized track obtained by the text method.
And step three, solving the track of the same task by using a GPOPS2 toolkit.
And step four, comparing the data obtained by the two methods.
TABLE 1 CAV-H parameters and flight mission data
Figure BDA0002646116700000151
According to simulation experiments, the hypersonic aircraft reentry trajectory optimization method based on the sequential convex programming can achieve the expected rapid trajectory optimization effect.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (4)

1. A hypersonic aircraft reentry trajectory optimization method based on sequential convex programming is characterized by comprising the following steps:
s101, establishing a reentry dynamic model of the hypersonic aircraft based on a geocentric rectangular coordinate system;
s102, combining the reentry dynamic model of the hypersonic aircraft, considering end point constraint and conventional path constraint, and establishing a reentry trajectory optimization problem model of the hypersonic aircraft under a multi-constraint condition, wherein the reentry dynamic model of the hypersonic aircraft is as follows:
Figure FDA0003800594310000011
Figure FDA0003800594310000012
Figure FDA0003800594310000013
Figure FDA0003800594310000014
Figure FDA0003800594310000015
Figure FDA0003800594310000016
wherein h is the geocentric distance of the aircraft, V is the earth relative speed of the aircraft, psi and gamma are the course angle and track angle of the aircraft respectively, the longitude theta and latitude phi of the aircraft are the main factors for judging the path constraint of the aircraft, and m and g are the mass of the aircraftAnd the gravity acceleration of the current earth center distance, the roll angle sigma and the attack angle alpha of the aircraft respectively control the transverse and longitudinal guidance profiles in the aircraft guidance strategy; d ═ ρ V 2 S ref C D P V ═ L and/2 2 S ref C L Per 2 is the aerodynamic drag and lift of the aircraft during flight, where ρ is the air density at the current altitude of the aircraft, S ref Is the reference cross-sectional area of the aircraft, C L And C D The aerodynamic parameters are related to the attack angle alpha of the aircraft respectively, and the roll angle sigma and the attack angle alpha are control quantities;
the hypersonic aircraft reentry trajectory optimization problem model under the multi-constraint condition is as follows:
Figure FDA0003800594310000021
Figure FDA0003800594310000022
Figure FDA0003800594310000023
Figure FDA0003800594310000024
Figure FDA0003800594310000025
Figure FDA0003800594310000026
constraints that need to be met:
|X(t f )-X f |≤ε X
Figure FDA0003800594310000027
Figure FDA0003800594310000028
q＝0.5ρV 2 ≤q max ；
|X(t f )-X f |≤ε X denotes the end point constraint, X ═ h, θ, φ, V, γ, ψ]Is a matrix of aircraft states, epsilon X Is a small constant matrix, where X (t) f ) Representing the state quantity, X, obtained by the terminal time algorithm f Representing the target state quantity, epsilon, of the terminal time X The smaller the aircraft track optimization target end point state is, the closer the aircraft track optimization target end point state is to the preset state of the task, the better the track optimization effect is, and q is dynamic pressure in the aircraft flight process;
Figure FDA0003800594310000029
and q is 0.5 ρ V 2 ≤q max Are all conventional path constraints including heat flow rate constraints, overload constraints and dynamic pressure constraints, wherein
Figure FDA00038005943100000210
In order to be a constraint on the heat flow rate,
Figure FDA00038005943100000211
for overload restraint, q is 0.5 rho V 2 ≤q max In order to achieve the dynamic pressure constraint,
Figure FDA00038005943100000212
maximum values of heat flow rate, overload and dynamic pressure, K, respectively, during flight of the aircraft Q ＝7.9686×10 -5 Js 2 /(m 3.5 kg 0.5 ) Is the heat flow rate constant;
s103, aiming at the model of the reentry trajectory optimization problem, taking height as an independent variable and dynamic pressure as state quantity replacement speed to obtain a hyper-reentry trajectory optimization problem model after variable replacement, wherein the hyper-reentry trajectory optimization problem model after variable replacement is as follows:
Figure FDA0003800594310000031
Figure FDA0003800594310000032
Figure FDA0003800594310000033
Figure FDA0003800594310000034
Figure FDA0003800594310000035
after the independent variables are converted, the reentry equation becomes 5 constraints, dynamic pressure is used as state quantity to replace speed, the dynamic pressure constraint is naturally met, and the heat flow rate and the overload constraint in the conventional path constraint are recorded as follows:
Figure FDA0003800594310000036
in the formula (I), the compound is shown in the specification,
Figure FDA0003800594310000037
for the heat flow rate and dynamic pressure during flight,
Figure FDA0003800594310000038
maximum values of heat flow rate and dynamic pressure during flight, respectively;
noting the new state quantity as x ═ theta phi q gamma psi] T Then the constraint that the reentry trajectory optimization problem needs to satisfy becomes:
|x(h f )-x f |≤ε X
Figure FDA0003800594310000039
and S104, introducing new control quantity to further convert the variable-replaced super reentry trajectory optimization problem model to obtain a reentry motion model with decoupled state quantity and control quantity, wherein the step comprises the following steps of:
the method comprises the following steps: selecting a new control quantity mu 1 、μ 2 And mu 3 ，
Figure FDA0003800594310000041
Where L is the lift, the new controlled variable constraint is derived from the relationship of the new controlled variables:
Figure FDA0003800594310000042
step two: and substituting the new control quantity into the hypersonic reentry trajectory optimization problem model after the variable replacement to obtain a reentry motion model with decoupled state quantity and control quantity:
Figure FDA0003800594310000043
wherein x is [ theta phi q gamma psi ═ x] T Is a new state quantity; u ═ mu 1 μ 2 μ 3 ] T Is the newly selected control quantity;
Figure FDA0003800594310000044
is related to state quantityA function;
Figure FDA0003800594310000045
is a coefficient matrix of the new control quantity;
then the reentry optimization problem constraint becomes:
|x(h f )-x f |≤ε X
Figure FDA0003800594310000051
Figure FDA0003800594310000052
s104, introducing new control quantity to further convert the variable-replaced super reentry trajectory optimization problem model to obtain a reentry motion model with decoupled state quantity and control quantity;
s105, carrying out convex processing on the reentry motion model;
s106, performing discrete processing on the reentry motion model after the convex processing to obtain a track optimization problem which can be solved by using a sequence convex planning method;
and S107, solving the track optimization problem by using a sequential convex planning method.
2. The hypersonic aircraft reentry trajectory optimization method based on sequential convex programming according to claim 1, wherein the process of carrying out convex processing on the reentry motion model specifically comprises:
the method comprises the following steps: performing first-order Taylor expansion on the reentry motion model;
Figure FDA0003800594310000053
step two: controlling quantity constraint to carry out relaxation quantization;
μ 3 cosσ max ≤μ 1 ≤μ 3 cosσ min
μ 3min ≤μ 3 ≤μ 3max
μ 1 2 +μ 2 2 ≤μ 3 2
step three: performing first-order Taylor expansion on the process constraint;
Figure FDA0003800594310000054
step four: introducing a trust domain constraint:
|x-x * |≤τ
after the convex processing, the hypersonic reentry trajectory optimization problem is described as follows:
Figure FDA0003800594310000061
Figure FDA0003800594310000062
|x-x * |≤τ
μ 3 cosσ max ≤μ 1 ≤μ 3 cosσ min
μ 3min ≤μ 3 ≤μ 3max
μ 1 2 +μ 2 2 ≤μ 3 2
Figure FDA0003800594310000063
x(h 0 )＝x 0 ,x(h f )＝x f
in the formula, theta f 、φ f The latitude and longitude of the aircraft obtained for the final algorithm,
Figure FDA0003800594310000064
is the target longitude and latitude.
3. The hypersonic aircraft reentry trajectory optimization method based on sequential convex programming according to claim 2, wherein the reentry motion model after the convex processing is subjected to discrete processing to obtain a trajectory optimization problem which can be solved by the sequential convex programming method, and specifically comprises:
the method comprises the following steps: the value range [ h ] of the independent variable 0 ,h f ]Equally spaced discretization into N intervals yields:
the independent variable is discrete as: h is 0 ,h 1 ,h 2 ,…,h n-1 ,h n ；
The state quantity is discretized into: x is the number of 0 ,x 1 ,x 2 ,…,x n-1 ,x n ；
The controlled variable is discrete as: u shape 0 ,U 1 ,U 2 ,…,U n-1 ,U n ；
Step two: and (3) performing approximate dispersion on the kinetic equation obtained in the fifth step by adopting a trapezoidal method, wherein the obtained equation is as follows:
Figure FDA0003800594310000065
step three: discretizing the conventional path constraints to become:
Figure FDA0003800594310000066
the description of the finally obtained reentry trajectory optimization problem is as follows:
Figure FDA0003800594310000071
Figure FDA0003800594310000072
|x-x * |≤τ
μ 3 cosσ max ≤μ 1 ≤μ 3 cosσ min
μ 3min ≤μ 3 ≤μ 3max
μ 1 2 +μ 2 2 ≤μ 3 2
Figure FDA0003800594310000073
x(h 0 )＝x 0 ,x(h f )＝x f
4. the hypersonic aircraft reentry trajectory optimization method based on sequential convex programming according to claim 3, wherein the using of the sequential convex programming method to solve the trajectory optimization problem specifically comprises:
the method comprises the following steps: set k to 0, set initial state x (h) 0 ) Initial trajectory x 0 The number k is obtained by integrating a given control quantity constant value, and is the number of times of sequence convex programming;
step two: for k ≧ 1, in the kth iteration, the discrete problem for S106 utilizes the previously obtained trajectory x k-1 Obtaining [ x ] k U k ]；
Step three: check if sequence convergence condition sup | x is satisfied k -x k-1 If the condition is met, turning to the step four, otherwise, turning to the step two if k is k + 1;
step four: obtaining the optimal track x k The iteration stops.
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