CN114528692A - Reusable rocket landing stage feasible region calculation method based on numerical optimization - Google Patents

Reusable rocket landing stage feasible region calculation method based on numerical optimization Download PDF

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CN114528692A
CN114528692A CN202210039847.5A CN202210039847A CN114528692A CN 114528692 A CN114528692 A CN 114528692A CN 202210039847 A CN202210039847 A CN 202210039847A CN 114528692 A CN114528692 A CN 114528692A
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reusable rocket
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王聪
宋征宇
***
巩庆海
胡凤荣
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Beijing Aerospace Automatic Control Research Institute
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Abstract

The application provides a numerical optimization-based method for calculating a feasible domain of a landing stage of a reusable rocket, which comprises the following steps: determining a motion equation of a landing section of a reusable rocket; determining constraints of a reusable rocket landing segment; determining an optimized objective function of a reusable rocket landing segment; and calculating the feasible region of the landing section of the reusable rocket according to the motion equation, the constraint and the optimization objective function. The method and the device calculate the feasible region of the reusable rocket landing segment through the motion equation, the constraint and the optimization objective function of the reusable rocket landing segment, so that the calculation of the feasible region of the reusable rocket landing segment fully considers the motion and constraint characteristics of the landing segment process, and further the convergence of the calculation of the feasible region of the reusable rocket landing segment is improved.

Description

Reusable rocket landing stage feasible region calculation method based on numerical optimization
Technical Field
The application relates to the field of carrier rocket control, in particular to a reusable rocket landing segment feasible region calculation method based on numerical optimization.
Background
In order to realize safe landing of the reusable rocket, the speed, the position, the attitude and the mass of the rocket at the landing moment are required to simultaneously meet terminal constraint conditions, and the limited thrust adjusting capacity of a rocket engine and larger rotational inertia in the rocket landing process are considered.
In order to ensure the attitude stability of the rocket body, an attitude control system needs to be designed into an over-damping system with a slow response speed, so that the adaptability of the rocket to speed and position deviation in a landing section is compressed, and the whole speed and position of the carrier rocket in the landing section are required to be always in a physically feasible region.
Therefore, the reusable rocket landing stage feasible region calculation method is particularly important.
Disclosure of Invention
In order to solve one of the technical defects, the application provides a reusable rocket landing segment feasible region calculation method based on numerical optimization.
In a first aspect of the application, a reusable rocket landing segment feasible region calculation method based on numerical optimization is provided, and the method comprises the following steps:
determining a motion equation of a landing section of the reusable rocket;
determining constraints of a landing segment of a reusable rocket;
determining an optimized objective function of a landing segment of a reusable rocket;
and calculating the feasible region of the landing section of the reusable rocket according to the motion equation, the constraint and the optimization objective function.
Optionally, the reusable rocket is moved in a longitudinal plane in the feasible region.
Optionally, the determining an equation of motion for a landing segment of a reusable rocket comprises:
under a target coordinate system, determining a motion equation of a landing section of the reusable rocket as follows:
Figure BDA0003469742070000021
Figure BDA0003469742070000022
D＝0.5ρSrefCD||V||V；
the origin O of the target coordinate system is at a landing point, the OY axis is vertical to the target point and points to the sky on the local horizontal plane, and the OX axis points to a launching point on the target point and the local horizontal plane;
in order to solve for the first derivative operator,
Figure BDA0003469742070000023
is the included angle between the thrust vector and the OX axis, r is the position vector, V is the velocity vector, m is the total mass of the reusable rocket, g is the projection vector of the gravity acceleration under the target coordinate system, T is the thrust amplitude of the engine, IspIs specific impulse of engine, g0Is the acceleration of gravity on the sea level,
Figure BDA0003469742070000024
for pitch angular velocity, ρ is the atmospheric density, SrefAs reference area, CDIs the aerodynamic drag coefficient.
Optionally, in the target coordinate system, the reusable rocket in the landing stage of the reusable rocket is a particle, and the reusable rocket responds to the program angle instruction in real time, and the engine thrust is along the axial direction of the reusable rocket.
Optionally, the determining constraints for the landing segment of the reusable rocket comprises:
determining a process constraint for a reusable rocket landing leg;
determining an initial state constraint of a landing segment of a reusable rocket;
terminal state constraints for a reusable rocket landing leg are determined.
Optionally, the determining process constraints for the reusable rocket landing leg comprises:
and determining the thrust amplitude inequality constraint, the pitch angle speed inequality constraint, the altitude inequality constraint and the speed inequality constraint of the landing section of the reusable rocket.
Optionally, the thrust magnitude inequality is constrained by:
Tmin≤T(t)≤Tmax；
wherein T is any time of landing segment of the reusable rocket, T (T) is the thrust amplitude of the engine at the time T, TminFor minimum value of motive thrust, TmaxThe maximum value of the motive thrust.
Optionally, the pitch rate inequality is constrained by:
Figure BDA0003469742070000025
wherein t is any time of the landing segment of the reusable rocket,
Figure BDA0003469742070000031
is the pitch angle rate at time t,
Figure BDA0003469742070000032
is the maximum pitch rate.
Optionally, the pitch angle inequality is constrained by:
Figure BDA0003469742070000033
wherein the content of the first and second substances,
Figure BDA0003469742070000034
the maximum deviation between the pitch angle and 90 degrees.
Optionally, the height inequality constraint is:
y(t)≥0；
wherein t is any time of the landing section of the reusable rocket, and y (t) is the height of the time t.
Optionally, the speed inequality is constrained by:
Vy(t)≤0；
wherein t is any time of landing segment of the reusable rocket, Vy(t) is the longitudinal velocity at time t.
Optionally, the determining an initial state constraint for a landing segment of the reusable rocket comprises:
and determining a position vector, a longitudinal velocity equation constraint and a quality equation constraint of the landing segment of the reusable rocket.
Optionally, the position vector and longitudinal velocity equation is constrained by:
r0＝r(t0)，
Figure BDA0003469742070000035
wherein, t0For the initial moment of the landing stage of the reusable rocket, r0Position vector for the initial point of landing of reusable rocket, r (t)0) Is a position vector at the initial time instant,
Figure BDA0003469742070000036
longitudinal velocity, V, of the initial point of landing of a reusable rockety(t0) Longitudinal velocity at the initial moment.
Optionally, the mass equation is constrained to:
m0＝m(t0)；
wherein, t0For the initial moment of landing of the reusable rocket, m0Mass of the initial point of landing stage of reusable rocket, m (t)0) Is the quality at the initial moment.
Optionally, the determining a terminal state constraint of the reusable rocket landing leg comprises:
and determining longitudinal equality constraint and transverse inequality constraint of the landing segment of the reusable rocket.
Optionally, the longitudinal equation is constrained by:
y(tf)＝0；
wherein, tfTo make repeatedlyTerminal time with rocket landing segment, y (t)f) Is tfThe height of the moment.
Optionally, the lateral inequality constraint is:
Figure BDA0003469742070000041
Figure BDA0003469742070000042
Figure BDA0003469742070000043
Figure BDA0003469742070000044
m(tf)≥mmin；
wherein, tfFor terminal moments of reusable rocket landing segments, x (t)f) Is tfThe lateral position of the moment of time,
Figure BDA0003469742070000045
maximum deviation of lateral position, Vx(tf) Is tfThe lateral velocity at the moment in time,
Figure BDA0003469742070000046
for the maximum deviation of the lateral velocity,
Figure BDA0003469742070000047
is tfThe angle between the thrust vector at that moment and the axis OX,
Figure BDA0003469742070000048
maximum deviation between terminal pitch angle and 90 degrees, m (t)f) Is tfMass at time mminIn order to be able to reuse the rocket with the minimum mass,
Figure BDA0003469742070000049
at minimum landing velocity, Vy(tf) Is tfThe longitudinal velocity at the moment.
Optionally, the determining an optimized objective function for a landing segment of a reusable rocket comprises:
determining an optimized objective function of the landing segment of the reusable rocket as follows:
Jmax＝-Vx(t0)，Jmin＝Vx(t0)
wherein, t0For the initial moment of the landing stage of the reusable rocket, Vx(t0) Transverse velocity at the initial moment, Jmax、JminAre all optimization objective functions.
Optionally, the determining an optimized objective function for a landing segment of a reusable rocket comprises:
determining an optimized objective function of a landing segment of the reusable rocket:
Figure BDA00034697420700000410
wherein, t0For the initial moment of the landing phase of the reusable rocket, tfIn order to be able to reuse the terminal moment of the rocket landing segment,
Figure BDA00034697420700000411
is the angle between the thrust vector at time t and the axis OX, Jmax、JminAre all optimization objective functions.
Optionally, the calculating a reusable rocket landing leg feasible region according to the equation of motion, constraints and optimization objective function comprises:
constructing a landing segment trajectory planning problem based on the motion equation, the constraint and the optimization objective function;
in the initial state, the numerical optimization algorithm is used for solving the problem of JmaxLand track for optimizing objective functionThe trace planning problem is solved by obtaining the upper boundary of the horizontal initial speed, and in the initial state, the numerical optimization algorithm is used for solving the problem of JminObtaining a lower boundary of the transverse initial speed for the land segment trajectory planning problem of the optimization objective function;
a landing leg feasible region is calculated based on the upper and lower boundaries.
Optionally, the initial state includes an initial instruction value range, an initial height value range, an initial transverse position value range, and an initial longitudinal speed value range.
Optionally, in the initial state, solving with J using a numerical optimization algorithmmaxObtaining an upper boundary of the lateral initial velocity for optimizing the land-based trajectory planning problem of the objective function, and solving with J using a numerical optimization algorithm in an initial stateminObtaining a lower boundary of the lateral initial velocity for a land trajectory planning problem that optimizes an objective function, comprising:
selecting a first number of samples within the range of the initial mass value;
selecting a second number of samples within the range of the initial height value;
selecting a third number of samples from the range of the initial transverse position;
selecting a fourth number of samples within the range of the initial longitudinal speed;
traversing the initial state, and solving for J by using a numerical optimization algorithm based on the selected samplesmaxA land track planning problem for optimizing the objective function to obtain an upper boundary of the transverse initial velocity, and traversing the initial state, based on the selected samples, solving the problem of J by using a numerical optimization algorithmminAnd obtaining a lower boundary of the transverse initial speed for optimizing the land segment trajectory planning problem of the objective function.
Optionally, the calculating the landing leg feasible region based on the upper boundary and the lower boundary includes:
based on the first number, the second number, the third number, the fourth number, the upper boundary and the lower boundary, the following landing segment feasible regions are formed:
Figure BDA0003469742070000051
N＝I×J×K×L；
wherein I is a first number, J is a second number, K is a third number, L is a fourth number, x0maxIs the maximum value, x, in the range of values for the initial lateral position0minIs the minimum value in the range of values of the initial lateral position,
Figure BDA0003469742070000061
in order to be the upper boundary of the window,
Figure BDA0003469742070000062
is the lower boundary, x is the lateral position, y is the longitudinal position, VxIs the transverse velocity.
In a second aspect of the present application, there is provided an electronic device comprising:
a memory;
a processor; and
a computer program;
wherein the computer program is stored in the memory and configured to be executed by the processor to implement the method according to the first aspect.
In a third aspect of the present application, there is provided a computer readable storage medium having a computer program stored thereon; the computer program is executed by a processor to implement the method according to the first aspect as described above.
The application provides a numerical optimization-based method for calculating a feasible domain of a landing segment of a reusable rocket, which comprises the following steps: determining a motion equation of a landing section of the reusable rocket; determining constraints of a landing segment of a reusable rocket; determining an optimized objective function of a landing segment of a reusable rocket; and calculating the feasible domain of the landing segment of the reusable rocket according to the motion equation, the constraint and the optimization objective function. The method and the device calculate the feasible region of the reusable rocket landing segment through the motion equation, the constraint and the optimization objective function of the reusable rocket landing segment, so that the calculation of the feasible region of the reusable rocket landing segment fully considers the motion and constraint characteristics of the landing segment process, and further the convergence of the calculation of the feasible region of the reusable rocket landing segment is improved.
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The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the application and together with the description serve to explain the application and not to limit the application. In the drawings:
fig. 1 is a schematic flowchart of a method for calculating a feasible region of a landing segment of a reusable rocket based on numerical optimization according to an embodiment of the present disclosure;
fig. 2 is a flowchart of another method for calculating a feasible region of a landing segment of a reusable rocket based on numerical optimization according to an embodiment of the present disclosure.
Detailed Description
In order to make the technical solutions and advantages of the embodiments of the present application more apparent, the following further detailed description of the exemplary embodiments of the present application with reference to the accompanying drawings makes it clear that the described embodiments are only a part of the embodiments of the present application, and are not exhaustive of all embodiments. It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict.
In the process of realizing the application, the inventor finds that in order to realize safe landing of the reusable rocket, the speed, the position, the attitude and the quality of the rocket at the landing moment are required to meet the terminal constraint condition at the same time, and the limited thrust adjusting capacity of a rocket engine and larger rotational inertia in the rocket landing process are considered. In order to ensure the attitude stability of the rocket body, an attitude control system needs to be designed into an over-damping system with a slow response speed, so that the adaptability of the rocket to speed and position deviation in a landing section is compressed, and the whole speed and position of the carrier rocket in the landing section are required to be always in a physically feasible region. Therefore, the reusable rocket landing stage feasible region calculation method is particularly important.
In view of the above problems, an embodiment of the present application provides a method for calculating a feasible domain of a landing segment of a reusable rocket based on numerical optimization, where the method includes: determining a motion equation of a landing section of the reusable rocket; determining constraints of a landing segment of a reusable rocket; determining an optimized objective function of a landing segment of a reusable rocket; and calculating the feasible domain of the landing segment of the reusable rocket according to the motion equation, the constraint and the optimization objective function. The method and the device calculate the feasible region of the reusable rocket landing segment through the motion equation, the constraint and the optimization objective function of the reusable rocket landing segment, so that the calculation of the feasible region of the reusable rocket landing segment fully considers the motion and constraint characteristics of the landing segment process, and further the convergence of the calculation of the feasible region of the reusable rocket landing segment is improved.
Referring to fig. 1, the implementation process of the reusable rocket landing segment feasible region calculation method based on numerical optimization provided by the embodiment is as follows:
when the calculation of the feasible region is performed by the calculation method of the reusable rocket landing segment based on numerical optimization provided by the embodiment, the reusable rocket can be assumed to move in the longitudinal plane, and after the feasible region in the longitudinal plane is obtained, the longitudinal plane is rotated around the longitudinal axis, so that the three-dimensional feasible region of the landing segment can be obtained.
101, determining a motion equation of a landing segment of the reusable rocket.
The reusable rocket landing segment feasible region calculation method based on numerical optimization provided by the embodiment assumes that the reusable rocket in the feasible region moves in the longitudinal plane. After the feasible region in the longitudinal plane is obtained, the three-dimensional feasible region of the landing segment can be obtained by rotating the longitudinal plane around the longitudinal axis.
Thus, this step may describe the motion of the reusable rocket powered soft landing stage in a target coordinate system.
And when describing the landing section mass center motion equation, the reusable rocket in the landing section of the reusable rocket is taken as a mass point, the influence of engine thrust, aerodynamic force and mass change on the motion process of the reusable rocket is considered, the dynamic process of motion around the mass center attitude is ignored, and the reusable rocket attitude can respond to the program angle command in real time (namely the reusable rocket responds to the program angle command in real time). In addition, the engine thrust is always along the reusable rocket axial direction (i.e., the engine thrust is along the reusable rocket axial direction).
Namely, under a target coordinate system, determining the motion equation of the landing section of the reusable rocket as follows:
Figure BDA0003469742070000081
Figure BDA0003469742070000082
D＝0.5ρSrefCD||V||V。
the origin O of the target coordinate system is at the landing point, the OY axis is vertical to the local horizontal plane of the target point and points to the sky, and the OX axis points to the launching point in the local horizontal plane of the target point.
In order to solve for the first derivative operator,
Figure BDA0003469742070000083
is the included angle between the thrust vector and the OX axis, r is the position vector, V is the velocity vector, m is the total mass of the reusable rocket, g is the projection vector of the gravity acceleration under the target coordinate system, T is the engine thrust amplitude value, IspIs specific impulse of engine, g0Is the acceleration of gravity on the sea level,
Figure BDA0003469742070000084
for pitch angular velocity, ρ is the atmospheric density, SrefAs reference area, CDIs the aerodynamic drag coefficient.
The origin O of the target coordinate system is defined to be at the landing point, the OY axis is vertical to the local horizontal plane of the target point and points to the sky, and the OX axis points to the launching point in the local horizontal plane of the target point.
102, constraints for a reusable rocket landing segment are determined.
This step determines the process constraints, initial state constraints and terminal state constraints for the landing segment of the reusable rocket.
1. Process constraints for a reusable rocket landing leg are determined.
And process constraints including thrust amplitude, pitch angle speed, height and speed inequality constraints.
Therefore, in the process of determining the process constraint of the landing segment of the reusable rocket, the thrust amplitude inequality constraint, the pitch angle velocity inequality constraint, the altitude inequality constraint and the velocity inequality constraint of the landing segment of the reusable rocket are determined.
In particular, the method comprises the following steps of,
1) the thrust amplitude inequality is constrained as:
Tmin≤T(t)≤Tmax。
wherein T is any time of landing segment of the reusable rocket, T (T) is the thrust amplitude of the engine at the time T, TminFor minimum value of motive thrust, TmaxThe maximum value of the motive thrust.
2) The pitch angle inequality is constrained as:
Figure BDA0003469742070000091
wherein the content of the first and second substances,
Figure BDA0003469742070000092
the maximum deviation between the pitch angle and 90 degrees (i.e. the maximum deviation allowed between the pitch angle and 90 degrees).
3) The pitch angular velocity inequality is constrained as:
Figure BDA0003469742070000093
wherein t is any time of the landing segment of the reusable rocket,
Figure BDA0003469742070000094
is the pitch angle rate at time t,
Figure BDA0003469742070000095
the maximum pitch rate (i.e., the maximum allowable pitch rate).
4) The height inequality is constrained as:
y(t)≥0。
wherein t is any time of the landing section of the reusable rocket, and y (t) is the height of the time t.
5) The speed inequality is constrained as:
Vy(t)≤0。
wherein t is any time of landing segment of the reusable rocket, Vy(t) is the longitudinal velocity at time t.
2. Initial state constraints for a landing segment of a reusable rocket are determined.
In the process of determining the initial state constraint of the landing segment of the reusable rocket, the position vector, the longitudinal speed equation constraint and the quality equation constraint of the landing segment of the reusable rocket are determined.
In particular, the method comprises the following steps of,
1) the position vector and longitudinal velocity equation is constrained as:
r0＝r(t0)，
Figure BDA0003469742070000101
wherein, t0For the initial moment of the landing stage of the reusable rocket, r0Position vector for the initial point of landing of reusable rocket, r (t)0) Is a position vector at the initial time instant,
Figure BDA0003469742070000102
longitudinal velocity, V, of the initial point of landing of a reusable rockety(t0) Longitudinal velocity at the initial moment.
2) The mass equation is constrained as:
m0＝m(t0)。
wherein, t0For the initial moment of landing of the reusable rocket, m0For the initiation of the landing stage of a reusable rocketMass of (c), m (t)0) Is the quality at the initial moment.
Note that, in this embodiment and subsequent embodiments, the subscript 0 represents the state quantity at the initial point.
3. Terminal state constraints for a reusable rocket landing leg are determined.
The terminal state constraints include the sum of the longitudinal (i.e., y-direction) position equality constraints, and the transverse (i.e., x-direction) position, velocity, attitude, mass inequality constraints.
Therefore, in determining the terminal state constraint of the landing segment of the reusable rocket, the longitudinal equality constraint and the transverse inequality constraint of the landing segment of the reusable rocket are determined.
Wherein the longitudinal equality constraint is the longitudinal (y-direction) position equality constraint. The lateral inequality constraints include lateral (x-direction) position, velocity, attitude, mass inequality constraints.
In particular, the method comprises the following steps of,
1) the longitudinal equation is constrained to:
y(tf)＝0。
wherein, tfFor terminal moments of reusable rocket landing segments, y (t)f) Is tfThe height of the moment.
2) The transverse inequality constraints are:
Figure BDA0003469742070000111
Figure BDA0003469742070000112
Figure BDA0003469742070000113
Figure BDA0003469742070000114
m(tf)≥mmin。
wherein, tfFor terminal moments of reusable rocket landing segments, x (t)f) Is tfThe lateral position of the moment of time,
Figure BDA0003469742070000115
for maximum deviation of lateral position (i.e. maximum deviation allowed for lateral position), Vx(tf) Is tfThe lateral velocity at the moment in time,
Figure BDA0003469742070000116
for the lateral velocity maximum deviation (i.e. lateral velocity allowed maximum deviation),
Figure BDA0003469742070000117
is tfThe angle between the thrust vector at that moment and the axis OX,
Figure BDA0003469742070000118
m (t) is the maximum deviation between the terminal pitch angle and 90 degrees (i.e. the maximum deviation allowed between the terminal pitch angle and 90 degrees)f) Is tfMass at time mminIn order to be able to reuse the rocket with the minimum mass,
Figure BDA0003469742070000119
at a minimum landing speed (i.e., minimum allowable landing speed), Vy(tf) Is tfThe longitudinal velocity at the moment.
Note that, in this embodiment and the subsequent embodiments, the subscript f represents a desired terminal state quantity.
103, an optimized objective function of the landing segment of the reusable rocket is determined.
To obtain the initial horizontal velocity boundary of the landing segment of a reusable rocket, the maximum (minimum) lateral (i.e., x-direction) velocity V at the initial time may be selectedx(t0) As an optimization objective function, the sum of the pitch angles during the maximum (minimum) landing process can also be taken as the optimization objective function.
If the maximum (small) initial time lateral (i.e. x-direction) speed is selectedDegree Vx(t0) As an optimization objective function, the optimization objective function is:
Jmax＝-Vx(t0)，Jmin＝Vx(t0)
wherein, t0For the initial moment of the landing stage of the reusable rocket, Vx(t0) Transverse velocity at the initial moment, Jmax、JminAre all optimization objective functions.
If the maximum (small) pitch angle accumulation sum in the landing process is selected as the optimization objective function, the optimization objective function is as follows:
Figure BDA00034697420700001110
wherein, t0For the initial moment of the landing phase of the reusable rocket, tfIn order to be able to reuse the terminal moment of the rocket landing segment,
Figure BDA0003469742070000121
is the angle between the thrust vector at time t and the axis OX, Jmax、JminAre all optimization objective functions.
And 104, calculating the feasible region of the landing section of the reusable rocket according to the motion equation, the constraint and the optimization objective function.
When the step is realized, the following steps are carried out:
1. and constructing a landing stage trajectory planning problem based on the motion equation, the constraint and the optimization objective function.
Namely, the landing segment trajectory planning problem for solving the initial horizontal velocity boundary is constructed according to the motion equation, the constraint and the optimization objective function described in the above step 101-103.
For example, the following:
minJmaxorJmin
Figure BDA0003469742070000122
Tmin≤T(t)≤Tmax，
Figure BDA0003469742070000123
y(t)≥0，Vy(t)≤0，
r0＝r(t0)，
Figure BDA0003469742070000124
m0＝m(t0)，
y(tf)＝0，
Figure BDA0003469742070000125
Figure BDA0003469742070000126
m(tf)≥mmin。
2. in the initial state, the numerical optimization algorithm is used for solving the problem of JmaxObtaining an upper boundary of the lateral initial velocity for optimizing the land-based trajectory planning problem of the objective function, and solving with J using a numerical optimization algorithm in an initial stateminAnd obtaining a lower boundary of the transverse initial speed for optimizing the land segment trajectory planning problem of the objective function.
Wherein the initial state comprises an initial instruction value range [ m ]0min，m0max]Initial height value range [ y0min，y0max]Initial transverse position value range [ x ]0min，x0max]Initial longitudinal velocity value range
Figure BDA0003469742070000127
In the step (a), the step (b),
1) selecting a first number of samples (i.e. in [ m ]) within the range of the initial mass value0min，m0max]Take I samples in).
2) Selecting a second number of samples within the range of the initial height value (i.e. in [ y ]0min，y0max]Take J samples in).
3) Selecting a third number of samples (i.e., at [ x ]) within the range of initial lateral position values0min，x0max]Take K samples in).
4) A fourth number of samples is taken over the range of initial longitudinal velocity values (i.e., over the range of initial longitudinal velocity values)
Figure BDA0003469742070000131
Take L samples in).
5) Traverse the initial state (i.e. the initial instruction value range m0min，m0max]Initial height value range [ y0min，y0max]Initial transverse position value range [ x ]0min，x0max]Initial longitudinal velocity value range
Figure BDA0003469742070000132
) Based on the selected samples, using a numerical optimization algorithm to solve the problem by JmaxTo optimize the land-segment trajectory planning problem of the objective function, obtain the upper bound of the lateral initial velocity, and traverse the initial state (i.e., the initial instruction value range [ m ]0min，m0max]Initial height value range [ y0min，y0max]Initial transverse position value range [ x ]0min，x0max]Initial longitudinal velocity value range
Figure BDA0003469742070000133
) Based on the selected samples, using a numerical optimization algorithm to solve the problem by JminAnd obtaining a lower boundary of the transverse initial speed for optimizing the land segment trajectory planning problem of the objective function.
3. A landing leg feasible region is calculated based on the upper and lower boundaries.
This step will form the following landing leg feasible regions based on the first number, the second number, the third number, the fourth number, the upper boundary and the lower boundary:
Figure BDA0003469742070000134
N＝/×J×K×L。
wherein I is a first number, J is a second number, K is a third number, L is a fourth number, x0maxFor the maximum value, x, in the range of values for the initial lateral position0minIs the minimum value in the range of values of the initial lateral position,
Figure BDA0003469742070000135
in order to be the upper boundary of the window,
Figure BDA0003469742070000136
is the lower boundary, x is the lateral position, y is the longitudinal position, VxIs the transverse velocity.
When calculating the feasible region of the landing segment of the reusable rocket, defining the initial mass value range as m0min，m0max]Selecting I samples in the range, and setting the range of initial height as [ y0min，y0max]Selecting J samples in the range, wherein the range of the initial transverse (namely x direction) position value is [ x0min，x0max]Selecting K samples in the range, wherein the range of the initial longitudinal speed is
Figure BDA0003469742070000141
L samples were taken within this range. Sequentially traversing the four initial states, and respectively solving the upper boundary of the corresponding transverse (namely x-direction) initial speed
Figure BDA0003469742070000142
And a lower boundary
Figure BDA0003469742070000143
A total of N ═ I × J × K × L samples can be obtained, which collectively constitute the landing leg feasible region
Figure BDA0003469742070000144
The reusable rocket landing segment feasible region calculation method based on numerical optimization converts the landing segment feasible region solution problem into a numerical optimization problem. The method comprises the steps of firstly considering process constraint conditions such as a reusable rocket equation of motion, engine thrust adjusting capacity, an attitude angle, an attitude angular velocity, altitude, speed and the like, taking safe landing speed, position, attitude and quality as terminal constraint conditions, constructing a landing stage track planning problem for solving an initial horizontal speed boundary under the condition that the quality, the altitude, the longitudinal speed and the position in a horizontal plane are given as initial states, circularly solving the planning problem by traversing the initial states (the quality, the altitude, the longitudinal speed and the position in the horizontal plane) of the landing stage, if the problem has a feasible solution, the landing initial state belongs to a feasible domain range, and the upper and lower boundaries of the solved horizontal speed are the feasible domain boundary of the landing stage corresponding to the initial state, otherwise, the corresponding initial state is not in the feasible domain range. And counting all landing initial states and corresponding upper and lower horizontal speed boundaries in the range of the feasible region to obtain the feasible region of the landing segment of the reusable rocket.
The method for calculating the feasible region of the reusable rocket landing segment based on the numerical optimization fully considers the characteristics of the process constraint and the terminal constraint of the landing segment, converts the problem of analyzing the feasible region of the reusable rocket landing segment into a trajectory planning problem convenient for numerical solution, and obtains quantized feasible regions by traversing different initial states.
In addition, according to the numerical optimization-based reusable rocket landing segment feasible region calculation method provided by the embodiment, by analyzing the characteristic of the state quantity of the reusable rocket landing process, a complex and difficult-to-converge multi-objective optimization problem is converted into a single-objective trajectory planning problem for traversing and solving an initial horizontal velocity boundary, and the convergence of the feasible region solution is improved.
In addition, the method for calculating the feasible region of the reusable rocket landing segment based on numerical optimization constructs a trajectory planning problem taking the sum of the attitude angles of the maximum (minimum) landing process as an objective function by analyzing the relationship between the initial horizontal velocity boundary and other state quantities, and improves the rapidity of the trajectory planning.
Referring to fig. 2, a process for implementing the numerical optimization based reusable rocket landing segment feasible region calculation method provided by the present embodiment is described again. Firstly, describing a motion equation of a rocket (namely, a reusable rocket) landing segment, describing process constraints of the rocket (namely, the reusable rocket) landing segment, describing initial state constraints of the rocket (namely, the reusable rocket) landing segment, describing terminal state constraints of the rocket (namely, the reusable rocket) landing segment, and describing an initial horizontal velocity boundary optimization objective function of the rocket (namely, the reusable rocket) landing segment. And then, based on the description, constructing a landing segment trajectory planning problem for solving the initial horizontal velocity boundary, then solving the initial horizontal velocity boundary by using a numerical algorithm, and finally traversing the initial state of the landing segment to obtain a reusable rocket landing segment feasible region.
The reusable rocket landing segment feasible region calculator based on numerical optimization converts the landing segment feasible region solving problem into a numerical optimization problem, and obtains quantized feasible regions by traversing different initial states.
The method comprises the steps of firstly considering process constraint conditions such as a reusable rocket equation of motion, engine thrust adjusting capacity, an attitude angle, an attitude angular velocity, altitude, speed and the like, taking safe landing speed, position, attitude and quality as terminal constraint conditions, constructing a landing stage track planning problem for solving an initial horizontal speed boundary under the condition that the quality, the altitude, the longitudinal speed and the position in a horizontal plane are given as initial states, circularly solving the planning problem by traversing the initial states (the quality, the altitude, the longitudinal speed and the position in the horizontal plane) of the landing stage, if the problem has a feasible solution, the landing initial state belongs to a feasible domain range, and the upper and lower boundaries of the solved horizontal speed are the feasible domain boundary of the landing stage corresponding to the initial state, otherwise, the corresponding initial state is not in the feasible domain range. And counting all landing initial states and corresponding upper and lower horizontal speed boundaries in the range of the feasible region to obtain the feasible region of the landing segment of the reusable rocket.
The method for calculating the feasible region of the landing segment of the reusable rocket based on numerical optimization determines the equation of motion of the landing segment of the reusable rocket; determining constraints of a reusable rocket landing segment; determining an optimized objective function of a landing segment of a reusable rocket; and calculating the feasible domain of the landing segment of the reusable rocket according to the motion equation, the constraint and the optimization objective function. In the embodiment, the feasible region of the reusable rocket landing segment is calculated through the motion equation, the constraint and the optimization objective function of the reusable rocket landing segment, so that the motion and constraint characteristics of the landing segment process are fully considered in the calculation of the feasible region of the reusable rocket landing segment, and the convergence of the calculation of the feasible region of the reusable rocket landing segment is further improved.
Based on the same inventive concept of a reusable rocket landing segment feasible region calculation method based on numerical optimization, the embodiment provides an electronic device, which comprises: memory, processor, and computer programs.
Wherein the computer program is stored in the memory and configured to be executed by the processor to implement the numerical optimization based reusable rocket landing leg feasible domain calculation method shown in figure 1 above.
In particular, the method comprises the following steps of,
an equation of motion for a landing segment of a reusable rocket is determined.
Constraints for a reusable rocket landing leg are determined.
An optimization objective function for a reusable rocket landing leg is determined.
And calculating the feasible domain of the landing segment of the reusable rocket according to the motion equation, the constraint and the optimization objective function.
Optionally, the reusable rocket in the feasible region moves in the longitudinal plane.
Optionally, determining an equation of motion for a landing segment of the reusable rocket comprises:
under a target coordinate system, determining a motion equation of a landing section of the reusable rocket as follows:
Figure BDA0003469742070000161
Figure BDA0003469742070000162
D＝0.5ρSrefCD||V||V。
wherein, the origin O of the target coordinate system is at the landing point, the OY axis is vertical to the target point local horizontal plane and points to the sky, and the OX axis points to the launching point in the target point local horizontal plane.
In order to solve for the first derivative operator,
Figure BDA0003469742070000163
is the included angle between the thrust vector and the OX axis, r is the position vector, V is the velocity vector, m is the total mass of the reusable rocket, g is the projection vector of the gravity acceleration under the target coordinate system, T is the thrust amplitude of the engine, IspIs specific impulse of engine, g0Is the acceleration of gravity on the sea level,
Figure BDA0003469742070000171
for pitch angular velocity, ρ is the atmospheric density, SrefAs reference area, CDIs the aerodynamic drag coefficient.
Optionally, in the target coordinate system, the reusable rocket in the landing stage of the reusable rocket is a particle, and the reusable rocket responds to the program angle instruction in real time, and the engine thrust is along the axial direction of the reusable rocket.
Optionally, determining constraints for the landing segment of the reusable rocket comprises:
process constraints for a reusable rocket landing leg are determined.
Initial state constraints for a landing segment of a reusable rocket are determined.
Terminal state constraints for a reusable rocket landing leg are determined.
Optionally, determining process constraints for the landing segment of the reusable rocket comprises:
and determining the thrust amplitude inequality constraint, the pitch angle speed inequality constraint, the altitude inequality constraint and the speed inequality constraint of the landing section of the reusable rocket.
Optionally, the thrust magnitude inequality is constrained by:
Tmin≤T(t)≤Tmax。
wherein T is any time of landing segment of the reusable rocket, T (T) is the thrust amplitude of the engine at the time T, TminFor minimum value of motive thrust, TmaxThe maximum value of the motive thrust.
Optionally, the pitch angular velocity inequality is constrained by:
Figure BDA0003469742070000172
wherein t is any time of the landing segment of the reusable rocket,
Figure BDA0003469742070000173
is the pitch angle rate at time t,
Figure BDA0003469742070000174
is the maximum pitch rate.
Optionally, the pitch angle inequality is constrained by:
Figure BDA0003469742070000175
wherein the content of the first and second substances,
Figure BDA0003469742070000176
the maximum deviation between the pitch angle and 90 degrees.
Optionally, the height inequality constraint is:
y(t)≥0。
wherein t is any time of the landing section of the reusable rocket, and y (t) is the height of the time t.
Optionally, the speed inequality is constrained by:
Vy(t)≤0。
wherein t is any moment of the landing section of the reusable rocket, Vy(t) is the longitudinal velocity at time t.
Optionally, determining an initial state constraint for a landing segment of the reusable rocket comprises:
and determining a position vector, a longitudinal velocity equation constraint and a quality equation constraint of the landing segment of the reusable rocket.
Optionally, the position vector and longitudinal velocity equation is constrained to:
r0＝r(t0)，
Figure BDA0003469742070000181
wherein, t0For the initial moment of the landing stage of the reusable rocket, r0Position vector for the initial point of the reusable rocket landing stage, r (t)0) Is a position vector at the initial time instant,
Figure BDA0003469742070000182
longitudinal velocity, V, of the initial point of landing of a reusable rockety(t0) Longitudinal velocity at the initial moment.
Optionally, the mass equation is constrained to:
m0＝m(t0)。
wherein, t0For the initial moment of landing of the reusable rocket, m0Mass of the initial point of landing stage of reusable rocket, m (t)0) Is the quality at the initial moment.
Optionally, determining a terminal state constraint for a landing segment of the reusable rocket comprises:
and determining longitudinal equality constraint and transverse inequality constraint of the landing segment of the reusable rocket.
Optionally, the longitudinal equation is constrained to:
y(tf)＝0。
wherein, tfFor terminal moments of reusable rocket landing segments, y (t)f) Is tfThe height of the moment.
Optionally, the lateral inequality constraint is:
Figure BDA0003469742070000183
Figure BDA0003469742070000184
Figure BDA0003469742070000185
Figure BDA0003469742070000186
m(tf)≥mmin。
wherein, tfFor terminal moments of reusable rocket landing segments, x (t)f) Is tfThe lateral position of the moment of time,
Figure BDA0003469742070000191
maximum deviation of lateral position, Vx(tf) Is tfThe lateral velocity at the moment in time,
Figure BDA0003469742070000192
for the maximum deviation of the lateral velocity,
Figure BDA0003469742070000193
is tfThe angle between the thrust vector at that moment and the axis OX,
Figure BDA0003469742070000194
maximum deviation between terminal pitch angle and 90 degrees, m (t)f) Is tfMass at time mminIn order to be able to reuse the rocket with the minimum mass,
Figure BDA0003469742070000195
at minimum landing velocity, Vy(tf) Is tfThe longitudinal velocity at the moment.
Optionally, determining an optimized objective function for the landing segment of the reusable rocket comprises:
determining an optimized objective function of the landing segment of the reusable rocket as follows:
Jmax＝-Vx(t0)，Jmin＝Vx(t0)
wherein, t0For the initial moment of the landing stage of the reusable rocket, Vx(t0) Transverse velocity at the initial moment, Jmax、JminAre all optimization objective functions.
Optionally, determining an optimized objective function for the landing segment of the reusable rocket comprises:
determining an optimized objective function of a landing segment of the reusable rocket:
Figure BDA0003469742070000196
wherein, t0For the initial moment of the landing phase of the reusable rocket, tfIn order to be able to reuse the terminal moment of the rocket landing segment,
Figure BDA0003469742070000197
is the angle between the thrust vector at time t and the axis OX, Jmax、JminAre all optimization objective functions.
Optionally, calculating a reusable rocket landing leg feasible region according to the equation of motion, the constraint and the optimization objective function, comprising:
and constructing a landing segment trajectory planning problem based on the motion equation, the constraint and the optimization objective function.
In the initial state, the numerical optimization algorithm is used for solving the problem of JmaxObtaining an upper boundary of the lateral initial velocity for optimizing the land-based trajectory planning problem of the objective function, and solving with J using a numerical optimization algorithm in an initial stateminAnd obtaining a lower boundary of the transverse initial speed for optimizing the land segment trajectory planning problem of the objective function.
A landing leg feasible region is calculated based on the upper and lower boundaries.
Optionally, the initial state includes an initial instruction value range, an initial height value range, an initial transverse position value range, and an initial longitudinal speed value range.
Optionally, in an initial state, solving with J using a numerical optimization algorithmmaxObtaining an upper boundary of the lateral initial velocity for optimizing the land-based trajectory planning problem of the objective function, and solving with J using a numerical optimization algorithm in an initial stateminObtaining a lower boundary of the lateral initial velocity for a land trajectory planning problem that optimizes an objective function, comprising:
a first number of samples is selected within the range of initial mass values.
A second number of samples is taken over the range of initial height values.
A third number of samples is selected within the range of initial lateral position values.
A fourth number of samples is selected within the range of initial longitudinal velocity values.
Traversing the initial state, and solving by using a numerical optimization algorithm J based on the selected samplesmaxObtaining an upper boundary of the lateral initial velocity for optimizing the land-segment trajectory planning problem of the objective function, traversing the initial state, and solving the upper boundary by using a numerical optimization algorithm J based on the selected samplesminAnd obtaining a lower boundary of the transverse initial speed for optimizing the land segment trajectory planning problem of the objective function.
Optionally, calculating the landing leg feasible region based on the upper boundary and the lower boundary comprises:
based on the first number, the second number, the third number, the fourth number, the upper boundary and the lower boundary, the following landing segment feasible regions are formed:
Figure BDA0003469742070000201
N＝/×J×K×L。
wherein I is a first number, J is a second number, K is a third number, and L is a fourth numberNumber, x0maxFor the maximum value, x, in the range of values for the initial lateral position0minIs the minimum value in the range of values of the initial lateral position,
Figure BDA0003469742070000202
in order to be the upper boundary of the window,
Figure BDA0003469742070000203
is the lower boundary, x is the lateral position, y is the longitudinal position, VxIs the transverse velocity.
The present embodiment provides an electronic device, on which a computer program is executed by a processor to determine an equation of motion for a landing segment of a reusable rocket; determining constraints of a landing segment of a reusable rocket; determining an optimized objective function of a landing segment of a reusable rocket; and calculating the feasible domain of the landing segment of the reusable rocket according to the motion equation, the constraint and the optimization objective function. The electronic device provided by the embodiment calculates the feasible region of the reusable rocket landing segment through the motion equation, the constraint and the optimization objective function of the reusable rocket landing segment, so that the calculation of the feasible region of the reusable rocket landing segment fully considers the motion and constraint characteristics of the landing segment process, and further improves the convergence of the calculation of the feasible region of the reusable rocket landing segment.
Based on the same inventive concept of the reusable rocket landing segment feasible region calculation method based on numerical optimization, the present embodiment provides a computer on which a computer program may be stored. The computer program is executed by a processor to implement the numerical optimization based reusable rocket landing leg feasible domain calculation method shown in figure 1 above.
In particular, the method comprises the following steps of,
an equation of motion for a landing segment of a reusable rocket is determined.
Constraints for a reusable rocket landing leg are determined.
An optimized objective function for a reusable rocket landing leg is determined.
And calculating the feasible domain of the landing segment of the reusable rocket according to the motion equation, the constraint and the optimization objective function.
Optionally, the reusable rocket in the feasible region moves in the longitudinal plane.
Optionally, determining an equation of motion for a landing segment of the reusable rocket comprises:
under a target coordinate system, determining a motion equation of a landing section of the reusable rocket as follows:
Figure BDA0003469742070000211
Figure BDA0003469742070000212
D＝0.5ρSrefCD||V||V。
the origin O of the target coordinate system is at the landing point, the OY axis is vertical to the local horizontal plane of the target point and points to the sky, and the OX axis points to the launching point in the local horizontal plane of the target point.
In order to solve for the first derivative operator,
Figure BDA0003469742070000213
is the included angle between the thrust vector and the OX axis, r is the position vector, V is the velocity vector, m is the total mass of the reusable rocket, g is the projection vector of the gravity acceleration under the target coordinate system, T is the engine thrust amplitude value, IspIs specific impulse of engine, g0Is the acceleration of gravity on the sea level,
Figure BDA0003469742070000214
for pitch angular velocity, ρ is the atmospheric density, SrefAs reference area, CDIs the aerodynamic drag coefficient.
Optionally, in the target coordinate system, the reusable rocket in the landing stage of the reusable rocket is a particle, and the reusable rocket responds to the program angle instruction in real time, and the engine thrust is along the axial direction of the reusable rocket.
Optionally, determining constraints for the landing segment of the reusable rocket comprises:
process constraints for a reusable rocket landing leg are determined.
Initial state constraints for a landing segment of a reusable rocket are determined.
Terminal state constraints for a reusable rocket landing leg are determined.
Optionally, determining process constraints for the landing segment of the reusable rocket comprises:
and determining the thrust amplitude inequality constraint, the pitch angle speed inequality constraint, the altitude inequality constraint and the speed inequality constraint of the landing section of the reusable rocket.
Optionally, the thrust magnitude inequality is constrained by:
Tmin≤T(t)≤Tmax。
wherein T is any time of landing segment of the reusable rocket, T (T) is the thrust amplitude of the engine at the time T, TminFor minimum value of motive thrust, TmaxThe maximum value of the motive thrust.
Optionally, the pitch rate inequality is constrained by:
Figure BDA0003469742070000221
wherein t is any time of the landing segment of the reusable rocket,
Figure BDA0003469742070000222
is the pitch angle rate at time t,
Figure BDA0003469742070000223
is the maximum pitch rate.
Optionally, the pitch angle inequality is constrained by:
Figure BDA0003469742070000224
wherein the content of the first and second substances,
Figure BDA0003469742070000225
to be bent overMaximum deviation between elevation angle and 90 degrees.
Optionally, the height inequality constraint is:
y(t)≥0。
wherein t is any moment of the landing segment of the reusable rocket, and y (t) is the altitude at the moment t.
Optionally, the speed inequality is constrained by:
Vy(t)≤0。
wherein t is any time of landing segment of the reusable rocket, Vy(t) is the longitudinal velocity at time t.
Optionally, determining an initial state constraint for a landing segment of the reusable rocket comprises:
and determining a position vector, a longitudinal velocity equation constraint and a quality equation constraint of the landing segment of the reusable rocket.
Optionally, the position vector and longitudinal velocity equation is constrained to:
r0＝r(t0)，
Figure BDA0003469742070000231
wherein, t0For the initial moment of the landing stage of the reusable rocket, r0Position vector for the initial point of the reusable rocket landing stage, r (t)0) Is a position vector at the initial time instant,
Figure BDA0003469742070000232
longitudinal velocity, V, of the initial point of landing of a reusable rockety(t0) Longitudinal velocity at the initial moment.
Optionally, the mass equation is constrained to:
m0＝m(t0)。
wherein, t0For the initial moment of landing of the reusable rocket, m0Mass of the initial point of landing stage of reusable rocket, m (t)0) Is the quality at the initial moment.
Optionally, determining a terminal state constraint for a landing segment of the reusable rocket comprises:
and determining longitudinal equality constraint and transverse inequality constraint of the landing segment of the reusable rocket.
Optionally, the longitudinal equation is constrained to:
y(tf)＝0。
wherein, tfFor terminal moments of reusable rocket landing segments, y (t)f) Is tfThe height of the moment.
Optionally, the lateral inequality constraint is:
Figure BDA0003469742070000233
Figure BDA0003469742070000234
Figure BDA0003469742070000235
Figure BDA0003469742070000236
m(tf)≥mnin。
wherein, tfFor terminal moments of reusable rocket landing segments, x (t)f) Is tfThe lateral position of the moment of time,
Figure BDA0003469742070000237
maximum deviation of lateral position, Vx(tf) Is tfThe lateral velocity at the moment in time,
Figure BDA0003469742070000238
for the maximum deviation of the lateral velocity,
Figure BDA0003469742070000239
is tfTime of dayThe angle between the thrust vector and the axis of OX,
Figure BDA00034697420700002310
maximum deviation between terminal pitch angle and 90 degrees, m (t)f) Is tfMass at time mminIn order to be able to reuse the rocket with the minimum mass,
Figure BDA00034697420700002311
at minimum landing velocity, Vy(tf) Is tfThe longitudinal velocity at the moment.
Optionally, determining an optimized objective function for the landing segment of the reusable rocket comprises:
determining an optimized objective function of the landing segment of the reusable rocket as follows:
Jmax＝-Vx(t0)，Jmin＝Vx(t0)
wherein, t0For the initial moment of the landing stage of the reusable rocket, Vx(t0) Transverse velocity at the initial moment, Jmax、JminAre all optimization objective functions.
Optionally, determining an optimized objective function for the reusable rocket landing leg comprises:
determining an optimized objective function of a landing segment of the reusable rocket:
Figure BDA0003469742070000241
wherein, t0For the initial moment of the landing phase of the reusable rocket, tfIn order to be able to reuse the terminal moment of the rocket landing segment,
Figure BDA0003469742070000242
is the angle between the thrust vector at time t and the axis OX, Jmax、JminAre all optimization objective functions.
Optionally, calculating a reusable rocket landing leg feasible region according to the equation of motion, the constraint and the optimization objective function, comprising:
and constructing a landing segment trajectory planning problem based on the motion equation, the constraint and the optimization objective function.
In the initial state, the numerical optimization algorithm is used for solving the problem of JmaxObtaining an upper boundary of the lateral initial velocity for optimizing the land-based trajectory planning problem of the objective function, and solving with J using a numerical optimization algorithm in an initial stateminAnd obtaining a lower boundary of the transverse initial speed for optimizing the land segment trajectory planning problem of the objective function.
A landing leg feasible region is calculated based on the upper boundary and the lower boundary.
Optionally, the initial state includes an initial instruction value range, an initial height value range, an initial transverse position value range, and an initial longitudinal speed value range.
Optionally, in an initial state, solving with J using a numerical optimization algorithmmaxObtaining an upper boundary of the lateral initial velocity for optimizing the land-based trajectory planning problem of the objective function, and solving with J using a numerical optimization algorithm in an initial stateminObtaining a lower boundary of the lateral initial velocity for a land trajectory planning problem that optimizes an objective function, comprising:
a first number of samples is selected within the range of initial mass values.
A second number of samples is taken over the range of initial height values.
A third number of samples is selected within the range of initial lateral position values.
A fourth number of samples is selected within the range of initial longitudinal velocity values.
Traversing the initial state, and solving by using a numerical optimization algorithm J based on the selected samplesmaxObtaining an upper boundary of the lateral initial velocity for optimizing the land-segment trajectory planning problem of the objective function, traversing the initial state, and solving the upper boundary by using a numerical optimization algorithm J based on the selected samplesminAnd obtaining a lower boundary of the transverse initial speed for optimizing the land segment trajectory planning problem of the objective function.
Optionally, calculating the landing leg feasible region based on the upper boundary and the lower boundary comprises:
based on the first number, the second number, the third number, the fourth number, the upper boundary and the lower boundary, the following landing leg feasible regions are composed:
Figure BDA0003469742070000251
N＝I×J×K×L。
wherein I is a first number, J is a second number, K is a third number, L is a fourth number, x0maxIs the maximum value, x, in the range of values for the initial lateral position0minIs the minimum value in the range of values of the initial lateral position,
Figure BDA0003469742070000252
in order to be the upper boundary of the field,
Figure BDA0003469742070000253
is the lower boundary, x is the lateral position, y is the longitudinal position, VxIs the transverse velocity.
The present embodiments provide a computer readable storage medium having a computer program thereon for execution by a processor to determine an equation of motion for a landing segment of a reusable rocket; determining constraints of a landing segment of a reusable rocket; determining an optimized objective function of a landing segment of a reusable rocket; and calculating the feasible domain of the landing segment of the reusable rocket according to the motion equation, the constraint and the optimization objective function. The computer-readable storage medium provided by the embodiment calculates the feasible region of the reusable rocket landing segment through the motion equation, the constraint and the optimization objective function of the reusable rocket landing segment, so that the calculation of the feasible region of the reusable rocket landing segment fully considers the motion and constraint characteristics of the landing segment process, and further improves the convergence of the calculation of the feasible region of the reusable rocket landing segment.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein. The scheme in the embodiment of the application can be implemented by adopting various computer languages, such as object-oriented programming language Java and transliterated scripting language JavaScript.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While the preferred embodiments of the present application have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all alterations and modifications as fall within the scope of the application.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present application without departing from the spirit and scope of the application. Thus, if such modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is intended to include such modifications and variations as well.

Claims (25)

1. A reusable rocket landing segment feasible region calculation method based on numerical optimization is characterized by comprising the following steps:
determining a motion equation of a landing section of the reusable rocket;
determining constraints of a landing segment of a reusable rocket;
determining an optimized objective function of a landing segment of a reusable rocket;
and calculating the feasible region of the landing section of the reusable rocket according to the motion equation, the constraint and the optimization objective function.
2. The method of claim 1, wherein the reusable rocket is moved within a longitudinal plane in the feasible region.
3. The method of claim 2, wherein determining an equation of motion for a landing segment of a reusable rocket comprises:
under a target coordinate system, determining a motion equation of a landing section of the reusable rocket as follows:
Figure FDA0003469742060000011
Figure FDA0003469742060000012
D＝0.5ρSrefCD||V||V；
the origin O of the target coordinate system is at a landing point, the OY axis is vertical to the target point and points to the sky on the local horizontal plane, and the OX axis points to a launching point on the target point and the local horizontal plane;
·in order to solve for the first derivative operator,
Figure FDA0003469742060000013
is the included angle between the thrust vector and the OX axis, r is the position vector, V is the velocity vector, m is the total mass of the reusable rocket, g is the projection vector of the gravity acceleration under the target coordinate system, T is the thrust amplitude of the engine, IspIs specific impulse of engine, g0Is the acceleration of gravity on the sea level,
Figure FDA0003469742060000014
for pitch angular velocity, ρ is the atmospheric density, SrefAs reference area, CDIs the aerodynamic drag coefficient.
4. The method of claim 3, wherein the reusable rocket in the landing stage of the reusable rocket is a particle in the target coordinate system, and wherein the reusable rocket responds to the program angle commands in real time with engine thrust along the axis of the reusable rocket.
5. The method of claim 3, wherein determining constraints for a landing segment of a reusable rocket comprises:
determining a process constraint for a reusable rocket landing leg;
determining an initial state constraint of a landing segment of a reusable rocket;
terminal state constraints for a reusable rocket landing leg are determined.
6. The method of claim 5, wherein determining process constraints for a landing segment of a reusable rocket comprises:
and determining the thrust amplitude inequality constraint, the pitch angle speed inequality constraint, the altitude inequality constraint and the speed inequality constraint of the landing section of the reusable rocket.
7. The method of claim 6, wherein the thrust magnitude inequality is constrained by:
Tmin≤T(t)≤Tmax；
wherein T is any time of landing segment of the reusable rocket, T (T) is the thrust amplitude of the engine at the time T, TminFor minimum value of motive thrust, TmaxIs the maximum value of the motive thrust.
8. The method of claim 6, wherein the pitch rate inequality constraint is:
Figure FDA0003469742060000021
wherein t is any moment of the landing section of the reusable rocket,
Figure FDA0003469742060000022
is the pitch angle rate at time t,
Figure FDA0003469742060000023
is the pitch rate maximum.
9. The method of claim 6, wherein the pitch angle inequality is constrained by:
Figure FDA0003469742060000024
wherein the content of the first and second substances,
Figure FDA0003469742060000025
the maximum deviation between the pitch angle and 90 degrees.
10. The method of claim 6, wherein the height inequality constraint is:
y(t)≥0；
wherein t is any time of the landing section of the reusable rocket, and y (t) is the height of the time t.
11. The method of claim 6, wherein the velocity inequality constraint is:
Vy(t)≤0；
wherein t is any time of landing segment of the reusable rocket, Vy(t) is the longitudinal velocity at time t.
12. The method of claim 5, wherein determining an initial state constraint for a landing segment of a reusable rocket comprises:
and determining a position vector, a longitudinal velocity equation constraint and a quality equation constraint of the landing segment of the reusable rocket.
13. The method of claim 12, wherein the position vector and longitudinal velocity equation is constrained by:
Figure FDA0003469742060000031
wherein, t0For the initial moment of the landing stage of the reusable rocket, r0Position vector for the initial point of the reusable rocket landing stage, r (t)0) Is a position vector at the initial time instant,
Figure FDA0003469742060000032
longitudinal velocity, V, of the initial point of landing of a reusable rockety(t0) Longitudinal velocity at the initial moment.
14. The method of claim 12, wherein the quality equation is constrained by:
m0＝m(t0)；
wherein, t0For the initial moment of landing of the reusable rocket, m0Mass of the initial point of landing stage of reusable rocket, m (t)0) Is the quality at the initial moment.
15. The method of claim 5, wherein determining a terminal state constraint for a landing segment of a reusable rocket comprises:
and determining longitudinal equality constraint and transverse inequality constraint of the landing section of the reusable rocket.
16. The method of claim 15, wherein the longitudinal equation is constrained to:
y(tf)＝0；
wherein, tfFor terminal moments of reusable rocket landing segments, y (t)f) Is tfThe height of the moment.
17. The method of claim 15, wherein the lateral inequality constraint is:
Figure FDA0003469742060000033
Figure FDA0003469742060000034
Figure FDA0003469742060000035
Figure FDA0003469742060000036
m(tf)≥mmin；
wherein, tfFor terminal moments of reusable rocket landing segments, x (t)f) Is tfThe lateral position of the moment of time,
Figure FDA0003469742060000041
maximum deviation of lateral position, Vx(tf) Is tfThe lateral velocity at the moment in time,
Figure FDA0003469742060000042
for the maximum deviation of the lateral velocity,
Figure FDA0003469742060000043
is tfThe angle between the thrust vector at that moment and the axis OX,
Figure FDA0003469742060000044
maximum deviation between terminal pitch angle and 90 degrees, m (t)f) Is tfMass at time mminIn order to be able to reuse the rocket with the minimum mass,
Figure FDA0003469742060000047
at minimum landing velocity, Vy(tf) Is tfThe longitudinal velocity at the moment.
18. The method of claim 3, wherein determining an optimized objective function for a landing segment of a reusable rocket comprises:
determining an optimized objective function of the landing segment of the reusable rocket as follows:
Jmax＝-Vx(t0)，Jmin＝Vx(t0)
wherein, t0For the initial moment of the landing stage of the reusable rocket, Vx(t0) Transverse velocity at the initial moment, Jmax、JminAre all optimization objective functions.
19. The method of claim 3, wherein determining an optimized objective function for a landing segment of a reusable rocket comprises:
determining an optimized objective function of a landing segment of the reusable rocket:
Figure FDA0003469742060000045
wherein, t0For the initial moment of the landing phase of the reusable rocket, tfIn order to be able to reuse the terminal moment of the rocket landing segment,
Figure FDA0003469742060000046
is the angle between the thrust vector at time t and the axis OX, Jmax、JminAre all optimization objective functions.
20. The method of claim 18 or 19, wherein said calculating a reusable rocket landing leg feasible region from the equations of motion, constraints and optimization objective function comprises:
constructing a landing segment trajectory planning problem based on the motion equation, the constraint and the optimization objective function;
in the initial state, the numerical optimization algorithm is used for solving the problem of JmaxObtaining an upper boundary of the lateral initial velocity for optimizing the land-based trajectory planning problem of the objective function, and solving with J using a numerical optimization algorithm in an initial stateminObtaining a lower boundary of the transverse initial speed for the land segment trajectory planning problem of the optimization objective function;
a landing leg feasible region is calculated based on the upper and lower boundaries.
21. The method of claim 20, wherein the initial state comprises an initial command value range, an initial height value range, an initial lateral position value range, and an initial longitudinal velocity value range.
22. The method of claim 21, wherein in the initial state, the solution is solved for J using a numerical optimization algorithmmaxObtaining an upper boundary of the lateral initial velocity for optimizing the land-based trajectory planning problem of the objective function, and solving with J using a numerical optimization algorithm in an initial stateminObtaining a lower boundary of the lateral initial velocity for optimizing a land track planning problem of the objective function, comprising:
selecting a first number of samples within the range of the initial mass value;
selecting a second number of samples within the range of the initial height value;
selecting a third number of samples from the range of the initial transverse position;
selecting a fourth number of samples within the range of the initial longitudinal speed;
traversing the initial state, and solving for J by using a numerical optimization algorithm based on the selected samplesmaxObtaining an upper boundary of a transverse initial velocity for optimizing a land segment trajectory planning problem of an objective function, traversing the initial state, and solving for J by using a numerical optimization algorithm based on selected samplesminAnd obtaining a lower boundary of the transverse initial speed for optimizing the land segment trajectory planning problem of the objective function.
23. The method of claim 22, wherein calculating a landing leg feasible region based on the upper and lower boundaries comprises:
based on the first number, the second number, the third number, the fourth number, the upper boundary and the lower boundary, the following landing segment feasible regions are formed:
Figure FDA0003469742060000051
N＝I×J×K×L；
wherein I is a first number, J is a second number, K is a third number, L is a fourth number, x0maxFor the maximum value, x, in the range of values for the initial lateral position0minIs the minimum value in the range of values for the initial lateral position,
Figure FDA0003469742060000052
in order to be the upper boundary of the window,
Figure FDA0003469742060000053
is the lower boundary, x is the lateral position, y is the longitudinal position, VxIs the transverse velocity.
24. An electronic device, comprising:
a memory;
a processor; and
a computer program;
wherein the computer program is stored in the memory and configured to be executed by the processor to implement the method of any one of claims 1-23.
25. A computer-readable storage medium, having stored thereon a computer program; the computer program is executed by a processor to implement the method of any one of claims 1-23.
CN202210039847.5A 2022-01-14 2022-01-14 Reusable rocket landing stage feasible region calculation method based on numerical optimization Pending CN114528692A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115289917A (en) * 2022-08-12 2022-11-04 中山大学 Rocket substage landing real-time optimal guidance method and system based on deep learning

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115289917A (en) * 2022-08-12 2022-11-04 中山大学 Rocket substage landing real-time optimal guidance method and system based on deep learning
CN115289917B (en) * 2022-08-12 2023-02-28 中山大学 Rocket sublevel landing real-time optimal guidance method and system based on deep learning

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