Calculation Method for Feasible Region of Reusable Rocket Landing Stage Based on Numerical Optimization

Abstract

The present application provides a method for calculating the feasible region of the landing section of a reusable rocket based on numerical optimization. The method includes: determining the motion equation of the landing section of the reusable rocket; determining the constraints of the landing section of the reusable rocket; determining the optimization objective function of the landing section of the reusable rocket; and calculating the feasible region of the landing section of the reusable rocket according to the motion equation, constraints and optimization objective function. By calculating the feasible region of the landing section of the reusable rocket through the motion equation, constraints and optimization objective function of the landing section of the reusable rocket, the calculation of the feasible region of the landing section of the reusable rocket fully considers the motion and constraint characteristics of the landing section process, thereby improving the convergence of the calculation of the feasible region of the landing section of the reusable rocket.

Description

Technical Field

[0001] This application relates to the field of launch vehicle control, and particularly to a method for calculating the feasible region of the landing section of a reusable rocket based on numerical optimization. Background Art

[0002] To achieve the safe landing of a reusable rocket, it is required that the speed, position, attitude, and mass of the rocket at the landing moment simultaneously satisfy the terminal constraint conditions, considering the limited thrust adjustment ability of the rocket engine and the large moment of inertia during the rocket landing process.

[0003] To ensure the stability of the rocket body attitude, the attitude control system needs to be designed as an overdamped system with a slow response speed, thus compressing the adaptability of the rocket to speed and position deviations during the landing section. It is required that the speed and position of the launch vehicle must always be within the physically feasible region throughout the landing section.

[0004] Therefore, the method for calculating the feasible region of the landing section of a reusable rocket is particularly important. Summary of the Invention

[0005] To solve one of the above technical defects, this application provides a method for calculating the feasible region of the landing section of a reusable rocket based on numerical optimization.

[0006] In the first aspect of this application, a method for calculating the feasible region of the landing section of a reusable rocket based on numerical optimization is provided. The method includes:

[0007] Determine the motion equation of the landing section of the reusable rocket;

[0008] Determine the constraints of the landing section of the reusable rocket;

[0009] Determine the optimization objective function of the landing section of the reusable rocket;

[0010] Calculate the feasible region of the landing section of the reusable rocket according to the motion equation, constraints, and optimization objective function.

[0011] Optionally, the reusable rocket moves in the longitudinal plane within the feasible region.

[0012] Optionally, the step of determining the motion equation of the landing section of the reusable rocket includes:

[0013] In the target coordinate system, determine the motion equation of the landing section of the reusable rocket as:

[0014]

[0015] D = 0.5ρS ref C D ||V||V;

[0016] Among them, the origin O of the target coordinate system is at the landing point, the OY axis is perpendicular to the local horizontal plane of the target point and points to the sky, and the OX axis is in the local horizontal plane of the target point and points to the launch point;

[0017] is the first derivative operator, is the 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 gravitational acceleration in the target coordinate system, T is the engine thrust amplitude, I sp is the specific impulse of the engine, g0 is the gravitational acceleration at sea level, is the pitch angular velocity, ρ is the atmospheric density, S ref is the reference area, C D is the aerodynamic drag coefficient.

[0018] Optionally, in the target coordinate system, the reusable rocket in the landing section of the reusable rocket is a particle, and the reusable rocket responds to the program angle command in real time, and the engine thrust is along the axis of the reusable rocket.

[0019] Optionally, the determination of the constraints of the landing section of the reusable rocket includes:

[0020] Determine the process constraints of the landing section of the reusable rocket;

[0021] Determine the initial state constraints of the landing section of the reusable rocket;

[0022] Determine the terminal state constraints of the landing section of the reusable rocket.

[0023] Optionally, the determination of the process constraints of the landing section of the reusable rocket includes:

[0024] Determine the thrust amplitude inequality constraint, pitch angle inequality constraint, pitch angular velocity inequality constraint, altitude inequality constraint, and velocity inequality constraint of the landing section of the reusable rocket.

[0025] Optionally, the thrust amplitude inequality constraint is:

[0026] T min ≤T(t)≤T max ;

[0027] Among them, t is any moment in the landing section of the reusable rocket, T(t) is the engine thrust amplitude at time t, T min is the minimum value of the engine thrust, T max is the maximum value of the engine thrust.

[0028] Optionally, the pitch angular velocity inequality constraint is:

[0029]

[0030] Among them, \(t\) is any moment in the landing section of the reusable rocket, is the pitch angular velocity at moment \(t\), is the maximum value of the pitch angular velocity.

[0031] Optionally, the pitch angle inequality constraint is:

[0032]

[0033] Among them, is the maximum deviation between the pitch angle and 90 degrees.

[0034] Optionally, the height inequality constraint is:

[0035] y(t)≥0;

[0036] Among them, \(t\) is any moment in the landing section of the reusable rocket, and y(t) is the height at moment \(t\).

[0037] Optionally, the velocity inequality constraint is:

[0038] V y (t)≤0;

[0039] Among them, \(t\) is any moment in the landing section of the reusable rocket, and V y (t) is the longitudinal velocity at moment \(t\).

[0040] Optionally, the determination of the initial state constraint of the reusable rocket landing section includes:

[0041] Determine the position vector and longitudinal velocity equality constraints, and mass equality constraints of the reusable rocket landing section.

[0042] Optionally, the position vector and longitudinal velocity equality constraints are:

[0043] r0 = r(t0),

[0044] Among them, \(t0\) is the initial moment of the reusable rocket landing section, \(r0\) is the position vector of the initial point of the reusable rocket landing section, \(r(t0)\) is the position vector at the initial moment, is the longitudinal velocity of the initial point of the reusable rocket landing section, and V y (t0) is the longitudinal velocity at the initial moment.

[0045] Optionally, the mass equality constraint is:

[0046] m0 = m(t0);

[0047] Among them, \(t_0\) is the initial moment of the landing section of the reusable rocket, \(m_0\) is the mass at the initial point of the landing section of the reusable rocket, and \(m(t_0)\) is the mass at the initial moment.

[0048] Optionally, determining the terminal state constraints of the reusable rocket landing section includes:

[0049] Determining the longitudinal equality constraint and the lateral inequality constraint of the reusable rocket landing section.

[0050] Optionally, the longitudinal equality constraint is:

[0051] y(t f ) = 0;

[0052] where \(t\) f is the terminal moment of the reusable rocket landing section, and \(y(t\) f ) is the altitude at time \(t\) f .

[0053] Optionally, the lateral inequality constraint is:

[0054]

[0055]

[0056]

[0057]

[0058] m(t f ) ≥ m min ;

[0059] where \(t\) f is the terminal moment of the reusable rocket landing section, \(x(t\) f ) is the lateral position at time \(t\) f , is the maximum deviation of the lateral position, \(V\) x (t f ) is the lateral velocity at time \(t\) f , is the maximum deviation of the lateral velocity, is the angle between the thrust vector and the OX axis at time \(t\) f , is the maximum deviation between the terminal pitch angle and 90 degrees, \(m(t\) f ) is the mass at time \(t\) f , \(m\) min is the minimum mass of the reusable rocket, is the minimum landing speed, \(V\) y (tf ) is the longitudinal velocity at time t f .

[0060] Optionally, the determination of the optimization objective function for the reusable rocket landing section includes:

[0061] The determined optimization objective function for the reusable rocket landing section is:

[0062] J max = -V x (t0), J min = V x (t0)

[0063] where t0 is the initial time of the reusable rocket landing section, and V x (t0) is the lateral velocity at the initial time, and J max and J min are both optimization objective functions.

[0064] Optionally, the determination of the optimization objective function for the reusable rocket landing section includes:

[0065] The determined optimization objective function for the reusable rocket landing section:

[0066]

[0067] where t0 is the initial time of the reusable rocket landing section, t f is the terminal time of the reusable rocket landing section, is the angle between the thrust vector and the OX axis at time t, and J max and J min are both optimization objective functions.

[0068] Optionally, the calculation of the feasible region of the reusable rocket landing section according to the motion equation, constraints, and optimization objective function includes:

[0069] Constructing a landing section trajectory planning problem based on the motion equation, constraints, and optimization objective function;

[0070] In the initial state, using a numerical optimization algorithm to solve the landing section trajectory planning problem with J max as the optimization objective function to obtain the upper boundary of the lateral initial velocity, and, in the initial state, using a numerical optimization algorithm to solve the landing section trajectory planning problem with J min as the optimization objective function to obtain the lower boundary of the lateral initial velocity;

[0071] Calculating the feasible region of the landing section based on the upper boundary and the lower boundary.

[0072] Optionally, the initial state includes an initial instruction value range, an initial height value range, an initial lateral position value range, and an initial longitudinal velocity value range.

[0073] Optionally, in the initial state, a numerical optimization algorithm is used to solve the land segment trajectory planning problem with J max as the optimization objective function to obtain the upper boundary of the initial lateral velocity, and, in the initial state, a numerical optimization algorithm is used to solve the land segment trajectory planning problem with J min as the optimization objective function to obtain the lower boundary of the initial lateral velocity, including:

[0074] Select the first number of samples within the initial mass value range;

[0075] Select the second number of samples within the initial height value range;

[0076] Select the third number of samples within the initial lateral position value range;

[0077] Select the fourth number of samples within the initial longitudinal velocity value range;

[0078] Traverse the initial state, and based on the selected samples, use a numerical optimization algorithm to solve the land segment trajectory planning problem with J max as the optimization objective function to obtain the upper boundary of the initial lateral velocity, and, traverse the initial state, and based on the selected samples, use a numerical optimization algorithm to solve the land segment trajectory planning problem with J min as the optimization objective function to obtain the lower boundary of the initial lateral velocity.

[0079] Optionally, calculating the landing segment feasible region based on the upper and lower boundaries includes:

[0080] Based on the first number, the second number, the third number, the fourth number, the upper boundary, and the lower boundary, form the following landing segment feasible region:

[0081]

[0082] N = I × J × K × L;

[0083] where I is the first number, J is the second number, K is the third number, L is the fourth number, x 0max is the maximum value in the initial lateral position value range, x 0min is the minimum value in the initial lateral position value range, is the upper boundary, is the lower boundary, x is the lateral position, y is the longitudinal position, and V x is the lateral velocity.

[0084] In a second aspect of the present application, there is provided an electronic device, comprising:

[0085] a memory;

[0086] a processor; and

[0087] a computer program;

[0088] wherein, the computer program is stored in the memory and is configured to be executed by the processor to implement the method as described in the first aspect above.

[0089] In a third aspect of the present application, there is provided a computer-readable storage medium, on which a computer program is stored; the computer program is executed by a processor to implement the method as described in the first aspect above.

[0090] The present application provides a method for calculating the feasible region of the landing section of a reusable rocket based on numerical optimization. The method includes: determining the motion equation of the landing section of the reusable rocket; determining the constraints of the landing section of the reusable rocket; determining the optimization objective function of the landing section of the reusable rocket; and calculating the feasible region of the landing section of the reusable rocket according to the motion equation, constraints and optimization objective function. The present application calculates the feasible region of the landing section of the reusable rocket through the motion equation, constraints and optimization objective function of the landing section of the reusable rocket, so that the calculation of the feasible region of the landing section of the reusable rocket fully considers the motion and constraint characteristics of the landing section process, thereby improving the convergence of the calculation of the feasible region of the landing section of the reusable rocket. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] The drawings described herein are used to provide a further understanding of the present application and form a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation of the present application. In the drawings:

[0092] Figure 1 is a schematic flow chart of a method for calculating the feasible region of the landing section of a reusable rocket based on numerical optimization provided by an embodiment of the present application;

[0093] Figure 2 is a schematic flow chart of another method for calculating the feasible region of the landing section of a reusable rocket based on numerical optimization provided by an embodiment of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0094] In order to make the technical solutions and advantages in the embodiments of the present application clearer and more understandable, the following further describes the exemplary embodiments of the present application in detail with reference to the drawings. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than an exhaustive list of all embodiments. It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments can be combined with each other.

[0095] In the process of implementing this application, the inventors found that to achieve the safe landing of a reusable rocket, it is required that the speed, position, attitude, and mass of the rocket simultaneously meet the terminal constraint conditions at the moment of landing. Considering the limited thrust adjustment ability of the rocket engine and the large moment of inertia during the landing process of the rocket. To ensure the stable attitude of the rocket body, the attitude control system needs to be designed as an overdamped system with a relatively slow response speed, thus reducing the adaptability of the rocket to speed and position deviations during the landing section. It is required that the speed and position of the launch vehicle must always be within the physically feasible region throughout the landing section. Therefore, the calculation method for the feasible region of the reusable rocket landing section is particularly important.

[0096] To address the above problems, an embodiment of this application provides a calculation method for the feasible region of the reusable rocket landing section based on numerical optimization. The method includes: determining the motion equation of the reusable rocket landing section; determining the constraints of the reusable rocket landing section; determining the optimization objective function of the reusable rocket landing section; and calculating the feasible region of the reusable rocket landing section based on the motion equation, constraints, and optimization objective function. This application calculates the feasible region of the reusable rocket landing section through the motion equation, constraints, and optimization objective function of the reusable rocket landing section, enabling the calculation of the feasible region of the reusable rocket landing section to fully consider the motion and constraint characteristics of the landing section process, thereby improving the convergence of the calculation of the feasible region of the reusable rocket landing section.

[0097] See Figure 1 , the implementation process of the calculation method for the feasible region of the reusable rocket landing section based on numerical optimization provided in this embodiment is as follows:

[0098] When calculating the feasible region using the calculation method for the feasible region of the reusable rocket landing section based on numerical optimization provided in this embodiment, it can be assumed that the reusable rocket moves in the longitudinal plane. After obtaining the feasible region in the longitudinal plane, the three-dimensional feasible region of the landing section can be obtained by rotating the longitudinal plane around the longitudinal axis.

[0099] 101. Determine the motion equation of the reusable rocket landing section.

[0100] Since the calculation method for the feasible region of the reusable rocket landing section based on numerical optimization provided in this embodiment assumes that the reusable rocket in the feasible region moves in the longitudinal plane. After obtaining the feasible region in the longitudinal plane, the three-dimensional feasible region of the landing section can be obtained by rotating the longitudinal plane around the longitudinal axis.

[0101] Therefore, this step can describe the motion of the reusable rocket during the powered soft landing section in the target coordinate system.

[0102] When describing the centroid motion equation of the landing stage, the reusable rocket in the landing stage of the reusable rocket is regarded as a particle, considering the influence of engine thrust, aerodynamic force, and mass change on the motion process of the reusable rocket, ignoring the dynamic process of the attitude motion around the centroid, and believing that the attitude of the reusable rocket can respond to the program angle instruction in real time (i.e., the reusable rocket responds to the program angle instruction in real time). In addition, the engine thrust is always along the axis of the reusable rocket (i.e., the engine thrust is along the axis of the reusable rocket).

[0103] That is, in the target coordinate system, the motion equation of the landing stage of the reusable rocket is determined as follows:

[0104]

[0105] D = 0.5ρS ref C D ||V||V。

[0106] Among them, the origin O of the target coordinate system is at the landing point, the OY axis is perpendicular to the local horizontal plane of the target point and points to the sky, and the OX axis is in the local horizontal plane of the target point and points to the launch point.

[0107] is the first derivative operator, is the 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 gravitational acceleration in the target coordinate system, T is the engine thrust amplitude, I sp is the specific impulse of the engine, g0 is the gravitational acceleration at sea level, is the pitch angular velocity, ρ is the atmospheric density, S ref is the reference area, C D is the aerodynamic drag coefficient.

[0108] Among them, it is defined that the origin O of the target coordinate system is at the landing point, the OY axis is perpendicular to the local horizontal plane of the target point and points to the sky, and the OX axis is in the local horizontal plane of the target point and points to the launch point.

[0109] 102, determine the constraints of the landing stage of the reusable rocket.

[0110] This step will determine the process constraints, initial state constraints, and terminal state constraints of the landing stage of the reusable rocket.

[0111] 1. Determine the process constraints of the landing stage of the reusable rocket.

[0112] The process constraints include thrust amplitude, pitch angle, pitch angular velocity, altitude, and velocity inequality constraints.

[0113] Therefore, in the process of determining the process constraints of the reusable rocket's landing section, the thrust amplitude inequality constraint, pitch angle inequality constraint, pitch angular velocity inequality constraint, altitude inequality constraint, and velocity inequality constraint of the reusable rocket's landing section will be determined.

[0114] Specifically,

[0115] 1) The thrust amplitude inequality constraint is:

[0116] T min ≤T(t)≤T max .

[0117] Where t is any moment in the reusable rocket's landing section, T(t) is the engine thrust amplitude at time t, T min is the minimum value of the engine thrust, and T max is the maximum value of the engine thrust.

[0118] 2) The pitch angle inequality constraint is:

[0119]

[0120] Where, is the maximum deviation between the pitch angle and 90 degrees (i.e., the maximum allowed deviation between the pitch angle and 90 degrees).

[0121] 3) The pitch angular velocity inequality constraint is:

[0122]

[0123] Where t is any moment in the reusable rocket's landing section, is the pitch angular velocity at time t, is the maximum value of the pitch angular velocity (i.e., the maximum allowed pitch angular velocity).

[0124] 4) The altitude inequality constraint is:

[0125] y(t)≥0.

[0126] Where t is any moment in the reusable rocket's landing section, and y(t) is the altitude at time t.

[0127] 5) The velocity inequality constraint is:

[0128] V y (t)≤0.

[0129] Where t is any moment in the reusable rocket's landing section, and V y (t) is the longitudinal velocity at time t.

[0130] 2. Determine the initial state constraints of the reusable rocket's landing section.

[0131] In the process of determining the initial state constraints of the reusable rocket landing section, the position vector and longitudinal velocity equality constraints, and the mass equality constraints of the reusable rocket landing section will be determined.

[0132] Specifically,

[0133] 1) The position vector and longitudinal velocity equality constraints are:

[0134] r0 = r(t0),

[0135] where t0 is the initial moment of the reusable rocket landing section, r0 is the position vector of the initial point of the reusable rocket landing section, r(t0) is the position vector at the initial moment, is the longitudinal velocity at the initial point of the reusable rocket landing section, and V y (t0) is the longitudinal velocity at the initial moment.

[0136] 2) The mass equality constraint is:

[0137] m0 = m(t0).

[0138] where t0 is the initial moment of the reusable rocket landing section, m0 is the mass of the initial point of the reusable rocket landing section, and m(t0) is the mass at the initial moment.

[0139] It should be noted that in this embodiment and subsequent embodiments, the subscript 0 represents the state quantity of the initial point.

[0140] 3. Determine the terminal state constraints of the reusable rocket landing section.

[0141] The terminal state constraints include the longitudinal (i.e., y - direction) position equality constraint, and the lateral (i.e., x - direction) position, velocity, attitude, and mass inequality constraints.

[0142] Therefore, in determining the terminal state constraints of the reusable rocket landing section, the longitudinal equality constraint and the lateral inequality constraint of the reusable rocket landing section will be determined.

[0143] Among them, the longitudinal equality constraint is the longitudinal (y - direction) position equality constraint. The lateral inequality constraints include the lateral (x - direction) position, velocity, attitude, and mass inequality constraints.

[0144] Specifically,

[0145] 1) The longitudinal equality constraint is:

[0146] y(t f ) = 0.

[0147] where t fFor the terminal moment of the reusable rocket's landing phase, y(t f ) is the altitude at time t f .

[0148] 2) The lateral inequality constraint is:

[0149]

[0150]

[0151]

[0152]

[0153] m(t f ) ≥ m min .

[0154] Among them, t f is the terminal moment of the reusable rocket's landing phase, x(t f ) is the lateral position at time t f , is the maximum lateral position deviation (i.e., the maximum allowable lateral position deviation), V x (t f ) is the lateral velocity at time t f , is the maximum lateral velocity deviation (i.e., the maximum allowable lateral velocity deviation), is the angle between the thrust vector and the OX axis at time t f , is the maximum deviation between the terminal pitch angle and 90 degrees (i.e., the maximum allowable deviation between the terminal pitch angle and 90 degrees), m(t f ) is the mass at time t f , m min is the minimum mass of the reusable rocket, is the minimum landing velocity (i.e., the minimum allowable landing velocity), V y (t f ) is the longitudinal velocity at time t f .

[0155] It should be noted that in this embodiment and subsequent embodiments, the subscript f represents the desired terminal state quantity.

[0156] 103. Determine the optimization objective function for the reusable rocket's landing phase.

[0157] To obtain the initial horizontal velocity boundary of the reusable rocket's landing phase, the maximum (minimum) initial lateral (i.e., x-direction) velocity V x(t0) As the optimization objective function, it is also possible to maximize (minimize) the cumulative sum of the pitch angles during the landing process as the optimization objective function.

[0158] If the maximum (minimum) of the initial lateral (i.e., x - direction) velocity V x (t0) is selected as the optimization objective function, then this optimization objective function is:

[0159] J max = - V x (t0), J min =V x (t0)

[0160] where t0 is the initial moment of the landing section of the reusable rocket, and V x (t0) is the lateral velocity at the initial moment, and J max 、J min are both optimization objective functions.

[0161] If the maximum (minimum) of the cumulative sum of the pitch angles during the landing process is selected as the optimization objective function, then this optimization objective function is:

[0162]

[0163] where t0 is the initial moment of the landing section of the reusable rocket, t f is the terminal moment of the landing section of the reusable rocket, is the angle between the thrust vector and the OX axis at time t, and J max 、J min are both optimization objective functions.

[0164] 104. Calculate the feasible region of the landing section of the reusable rocket according to the motion equation, constraints, and optimization objective function.

[0165] When implementing this step, it will:

[0166] 1. Construct a trajectory planning problem for the landing section based on the motion equation, constraints, and optimization objective function.

[0167] That is, construct a trajectory planning problem for the landing section to solve the boundary of the initial horizontal velocity according to the motion equation, constraints, and optimization objective function described in the above steps 101 - 103.

[0168] For example,

[0169] minJ max orJ min

[0170]

[0171] T min ≤T(t)≤Tmax , y(t) ≥ 0, V y (t) ≤ 0,

[0172] r0 = r(t0), m0 = m(t0),

[0173] y(t f ) = 0,

[0174] m(t f ) ≥ m min .

[0175] 2. At the initial state, use the numerical optimization algorithm to solve the land segment trajectory planning problem with J max as the optimization objective function to obtain the upper boundary of the initial lateral velocity, and, at the initial state, use the numerical optimization algorithm to solve the land segment trajectory planning problem with J min as the optimization objective function to obtain the lower boundary of the initial lateral velocity.

[0176] Among them, the initial state includes the initial command value range [m 0min , m 0max , the initial height value range [y 0min , y 0max , the initial lateral position value range [x 0min , x 0max , and the initial longitudinal velocity value range

[0177] This step will,

[0178] 1) Select the first number of samples within the initial mass value range (i.e., take I samples within [m 0min , m 0max ).

[0179] 2) Select the second number of samples within the initial height value range (i.e., take J samples within [y 0min , y 0max ).

[0180] 3) Select the third number of samples within the initial lateral position value range (i.e., take K samples within [x 0min , x 0max ).

[0181] 4) Select the fourth number of samples within the initial longitudinal velocity value range (i.e., take L samples within ).

[0182] 5) Traverse the initial state (i.e., the initial command value range [m0min , m 0max , the initial height value range is [y 0min , y 0max , the initial lateral position value range is [x 0min , x 0max , and the initial longitudinal velocity value range ). Based on the selected samples, use the numerical optimization algorithm to solve the landing section trajectory planning problem with J max as the optimization objective function to obtain the upper boundary of the initial lateral velocity, and traverse the initial state (i.e., the initial instruction value range [m 0min , m 0max , the initial height value range is [y 0min , y 0max , the initial lateral position value range is [x 0min , x 0max , and the initial longitudinal velocity value range ). Based on the selected samples, use the numerical optimization algorithm to solve the landing section trajectory planning problem with J min as the optimization objective function to obtain the lower boundary of the initial lateral velocity.

[0183] 3. Calculate the landing section feasible region based on the upper boundary and the lower boundary.

[0184] In this step, based on the first quantity, the second quantity, the third quantity, the fourth quantity, the upper boundary, and the lower boundary, the following landing section feasible region will be formed:

[0185]

[0186] N = / × J × K × L.

[0187] Where I is the first quantity, J is the second quantity, K is the third quantity, L is the fourth quantity, x 0max is the maximum value in the initial lateral position value range, x 0min is the minimum value in the initial lateral position value range, is the upper boundary, is the lower boundary, x is the lateral position, y is the longitudinal position, and V x is the lateral velocity.

[0188] When calculating the landing section feasible region of the reusable rocket, define the initial mass value range as [m 0min , m 0max , select I samples within this range, the initial height value range is [y 0min , y 0max , select J samples within this range, the initial lateral (i.e., x-direction) position value range is [x 0min , x 0max, select K samples within this range, and the initial longitudinal velocity value range is Select L samples within this range. Traverse the four initial states in turn, and solve the upper boundary of the corresponding initial lateral (i.e., x-direction) velocity and the lower boundary Then a total of N = I × J × K × L samples can be obtained, which together form the feasible region of the landing section

[0189] The method for calculating the feasible region of the landing section of a reusable rocket based on numerical optimization provided in this embodiment transforms the problem of solving the feasible region of the landing section into a numerical optimization problem. First, consider the process constraint conditions such as the motion equation of the reusable rocket, the engine thrust adjustment ability, the attitude angle, the attitude angular velocity, the altitude, and the velocity, and use the safe landing velocity, position, attitude, and mass as the terminal constraint conditions. Under the condition of given mass, altitude, longitudinal velocity, and position in the horizontal plane as the initial state, construct a landing section trajectory planning problem for solving the initial horizontal velocity boundary, and by traversing the initial state of the landing section (mass, altitude, longitudinal velocity, and position in the horizontal plane), use the numerical optimization algorithm to solve this planning problem iteratively. If there is a feasible solution to the problem, the landing initial state belongs to the feasible region range, and the obtained upper and lower bounds of the horizontal velocity are the boundaries of the feasible region of the landing section corresponding to this initial state; otherwise, the corresponding initial state is not within the feasible region range. Count all the landing initial states and the corresponding upper and lower bounds of the horizontal velocity within the feasible region range, and the feasible region of the reusable rocket landing section can be obtained.

[0190] The method for calculating the feasible region of the landing section of a reusable rocket based on numerical optimization provided in this embodiment fully considers the characteristics of the process constraints and terminal constraints in the landing section, transforms the problem of analyzing the feasible region of the landing section of a reusable rocket into a trajectory planning problem that is convenient for numerical solution, and obtains a quantified feasible region by traversing different initial states.

[0191] In addition, the method for calculating the feasible region of the landing section of a reusable rocket based on numerical optimization provided in this embodiment transforms the complex multi-objective optimization problem that is not easy to converge into a single-objective trajectory planning problem of traversing and solving the initial horizontal velocity boundary by analyzing the characteristics of the state variables in the landing process of the reusable rocket, improving the convergence of the feasible region solution.

[0192] Furthermore, the method for calculating the feasible region of the landing section of a reusable rocket based on numerical optimization provided in this embodiment constructs a trajectory planning problem with the maximum (minimum) cumulative sum of the attitude angles in the landing process as the objective function by analyzing the relationship between the initial horizontal velocity boundary and other state variables, improving the rapidity of the trajectory planning.

[0193] See Figure 2, the implementation process of the reusable rocket landing section feasible region calculation method based on numerical optimization provided in this embodiment is described again. First, describe the motion equation of the rocket (i.e., the reusable rocket) in the landing section, describe the process constraints of the rocket (i.e., the reusable rocket) in the landing section, describe the initial state constraints of the rocket (i.e., the reusable rocket) in the landing section, describe the terminal state constraints of the rocket (i.e., the reusable rocket) in the landing section, and describe the optimization objective function for the initial horizontal velocity boundary of the rocket (i.e., the reusable rocket) in the landing section. Then, based on the above descriptions, construct a landing section trajectory planning problem for solving the initial horizontal velocity boundary, and then use a numerical algorithm to solve the initial horizontal velocity boundary. Finally, traverse the initial state of the landing section to obtain the feasible region of the reusable rocket landing section.

[0194] The reusable rocket landing section feasible region calculation method based on numerical optimization in this embodiment transforms the problem of solving the feasible region of the landing section into a numerical optimization problem, and obtains a quantified feasible region by traversing different initial states.

[0195] First, consider the process constraint conditions such as the motion equation of the reusable rocket, the engine thrust adjustment ability, the attitude angle, the attitude angular velocity, the altitude, and the velocity. Take the safe landing velocity, position, attitude, and mass as the terminal constraint conditions. Under the condition of given mass, altitude, longitudinal velocity, and position in the horizontal plane as the initial state, construct a landing section trajectory planning problem for solving the initial horizontal velocity boundary, and use a numerical optimization algorithm to solve this planning problem iteratively by traversing the initial state of the landing section (mass, altitude, longitudinal velocity, and position in the horizontal plane). If the problem has a feasible solution, the landing initial state belongs to the feasible region range, and the upper and lower bounds of the obtained horizontal velocity are the feasible region boundaries corresponding to this initial state. Otherwise, the corresponding initial state is not within the feasible region range. Count all the landing initial states within the feasible region range and the corresponding upper and lower bounds of the horizontal velocity, and the feasible region of the reusable rocket landing section can be obtained.

[0196] The reusable rocket landing section feasible region calculation method based on numerical optimization provided in this embodiment determines the motion equation of the reusable rocket landing section; determines the constraints of the reusable rocket landing section; determines the optimization objective function of the reusable rocket landing section; calculates the feasible region of the reusable rocket landing section according to the motion equation, constraints, and optimization objective function. This embodiment calculates the feasible region of the reusable rocket landing section through the motion equation, constraints, and optimization objective function of the reusable rocket landing section, enabling the calculation of the feasible region of the reusable rocket landing section to fully consider the motion and constraint characteristics of the landing section process, thereby improving the convergence of the calculation of the feasible region of the reusable rocket landing section.

[0197] Based on the same inventive concept of the calculation method for the feasible region of the reusable rocket landing section based on numerical optimization, this embodiment provides an electronic device, which includes: a memory, a processor, and a computer program.

[0198] Among them, the computer program is stored in the memory and is configured to be executed by the processor to implement the above-mentioned Figure 1 calculation method for the feasible region of the reusable rocket landing section shown.

[0199] Specifically,

[0200] Determine the motion equation of the reusable rocket landing section.

[0201] Determine the constraints of the reusable rocket landing section.

[0202] Determine the optimization objective function of the reusable rocket landing section.

[0203] Calculate the feasible region of the reusable rocket landing section according to the motion equation, constraints, and optimization objective function.

[0204] Optionally, the reusable rocket moves in the vertical plane within the feasible region.

[0205] Optionally, determining the motion equation of the reusable rocket landing section includes:

[0206] In the target coordinate system, determine the motion equation of the reusable rocket landing section as:

[0207]

[0208] D = 0.5ρS ref C D ||V||V.

[0209] Among them, the origin O of the target coordinate system is at the landing point, the OY axis is perpendicular to the local horizontal plane of the target point and points to the sky, and the OX axis is in the local horizontal plane of the target point and points to the launch point.

[0210] is the first derivative operator, is the 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 gravitational acceleration in the target coordinate system, T is the engine thrust amplitude, I sp is the engine specific impulse, g0 is the sea-level gravitational acceleration, is the pitch angular velocity, ρ is the atmospheric density, S ref is the reference area, C D is the aerodynamic drag coefficient.

[0211] Optionally, in the target coordinate system, the reusable rocket in the landing section of the reusable rocket is regarded as a particle, and the reusable rocket responds to the program angle command in real time, and the engine thrust is along the axis of the reusable rocket.

[0212] Optionally, determine the constraints of the landing section of the reusable rocket, including:

[0213] Determine the process constraints of the landing section of the reusable rocket.

[0214] Determine the initial state constraints of the landing section of the reusable rocket.

[0215] Determine the terminal state constraints of the landing section of the reusable rocket.

[0216] Optionally, determine the process constraints of the landing section of the reusable rocket, including:

[0217] Determine the thrust magnitude inequality constraint, pitch angle inequality constraint, pitch angular velocity inequality constraint, altitude inequality constraint, and velocity inequality constraint of the landing section of the reusable rocket.

[0218] Optionally, the thrust magnitude inequality constraint is:

[0219] T min ≤T(t)≤T max .

[0220] Where t is any moment in the landing section of the reusable rocket, T(t) is the engine thrust magnitude at time t, and T min is the minimum value of the engine thrust, and T max is the maximum value of the engine thrust.

[0221] Optionally, the pitch angular velocity inequality constraint is:

[0222]

[0223] Where t is any moment in the landing section of the reusable rocket, is the pitch angular velocity at time t, is the maximum value of the pitch angular velocity.

[0224] Optionally, the pitch angle inequality constraint is:

[0225]

[0226] Where, is the maximum deviation between the pitch angle and 90 degrees.

[0227] Optionally, the altitude inequality constraint is:

[0228] y(t)≥0.

[0229] Among them, \(t\) is any moment in the landing stage of the reusable rocket, and \(y(t)\) is the altitude at moment \(t\).

[0230] Optionally, the velocity inequality constraint is:

[0231] \(V\) y (t)\(\leq0\).

[0232] Among them, \(t\) is any moment in the landing stage of the reusable rocket, and \(V\) y (t) is the longitudinal velocity at moment \(t\).

[0233] Optionally, determine the initial state constraints of the reusable rocket landing stage, including:

[0234] Determine the position vector, longitudinal velocity equality constraint, and mass equality constraint of the reusable rocket landing stage.

[0235] Optionally, the position vector and longitudinal velocity equality constraints are:

[0236] \(r_0 = r(t_0)\),

[0237] Among them, \(t_0\) is the initial moment of the reusable rocket landing stage, \(r_0\) is the position vector of the initial point of the reusable rocket landing stage, \(r(t_0)\) is the position vector at the initial moment, is the longitudinal velocity at the initial point of the reusable rocket landing stage, and \(V\) y (t_0) is the longitudinal velocity at the initial moment.

[0238] Optionally, the mass equality constraint is:

[0239] \(m_0 = m(t_0)\).

[0240] Among them, \(t_0\) is the initial moment of the reusable rocket landing stage, \(m_0\) is the mass of the initial point of the reusable rocket landing stage, and \(m(t_0)\) is the mass at the initial moment.

[0241] Optionally, determine the terminal state constraints of the reusable rocket landing stage, including:

[0242] Determine the longitudinal equality constraint and lateral inequality constraint of the reusable rocket landing stage.

[0243] Optionally, the longitudinal equality constraint is:

[0244] \(y(t\) f ) = 0.

[0245] Among them, \(t\) f is the terminal moment of the reusable rocket landing stage, and \(y(t\) f ) is the altitude at moment \(t\) f .

[0246] Optionally, the lateral inequality constraint is:

[0247]

[0248]

[0249]

[0250]

[0251] m(t f ) ≥ m min .

[0252] Where, t f is the terminal time of the reusable rocket landing section, x(t f ) is the lateral position at time t f , is the maximum deviation of the lateral position, V x (t f ) is the lateral velocity at time t f , is the maximum deviation of the lateral velocity, is the angle between the thrust vector and the OX axis at time t f , is the maximum deviation between the terminal pitch angle and 90 degrees, m(t f ) is the mass at time t f , m min is the minimum mass of the reusable rocket, is the minimum landing velocity, V y (t f ) is the longitudinal velocity at time t f .

[0253] Optionally, determine the optimization objective function for the reusable rocket landing section, including:

[0254] Determine the optimization objective function for the reusable rocket landing section as:

[0255] J max = -V x (t0), J min = V x (t0)

[0256] Where, t0 is the initial time of the reusable rocket landing section, V x (t0) is the lateral velocity at the initial time, J max , J min are both optimization objective functions.

[0257] Optionally, determine the optimization objective function for the landing phase of the reusable rocket, including:

[0258] Determine the optimization objective function for the landing phase of the reusable rocket:

[0259]

[0260] where \(t_0\) is the initial time of the landing phase of the reusable rocket, and \(t\) f is the terminal time of the landing phase of the reusable rocket, is the angle between the thrust vector and the OX axis at time \(t\), and \(J\) max , \(J\) min are both optimization objective functions.

[0261] Optionally, calculate the feasible region for the landing phase of the reusable rocket according to the equations of motion, constraints, and optimization objective functions, including:

[0262] Construct a trajectory planning problem for the landing phase based on the equations of motion, constraints, and optimization objective functions.

[0263] At the initial state, use a numerical optimization algorithm to solve the trajectory planning problem for the landing phase with \(J\) max as the optimization objective function to obtain the upper bound of the initial lateral velocity, and at the initial state, use a numerical optimization algorithm to solve the trajectory planning problem for the landing phase with \(J\) min as the optimization objective function to obtain the lower bound of the initial lateral velocity.

[0264] Calculate the feasible region for the landing phase based on the upper and lower bounds.

[0265] Optionally, the initial state includes the initial command value range, the initial altitude value range, the initial lateral position value range, and the initial longitudinal velocity value range.

[0266] Optionally, at the initial state, use a numerical optimization algorithm to solve the trajectory planning problem for the landing phase with \(J\) max as the optimization objective function to obtain the upper bound of the initial lateral velocity, and at the initial state, use a numerical optimization algorithm to solve the trajectory planning problem for the landing phase with \(J\) min as the optimization objective function to obtain the lower bound of the initial lateral velocity, including:

[0267] Select the first number of samples within the initial mass value range.

[0268] Select the second number of samples within the initial altitude value range.

[0269] Select the third number of samples within the initial lateral position value range.

[0270] Select the fourth number of samples within the initial longitudinal velocity value range.

[0271] Traverse the initial state, and based on the selected samples, use a numerical optimization algorithm to solve the landing segment trajectory planning problem with J max as the optimization objective function to obtain the upper boundary of the initial lateral velocity, and traverse the initial state. Based on the selected samples, use a numerical optimization algorithm to solve the landing segment trajectory planning problem with J min as the optimization objective function to obtain the lower boundary of the initial lateral velocity.

[0272] Optionally, calculate the landing segment feasible region based on the upper and lower boundaries, including:

[0273] Based on the first quantity, the second quantity, the third quantity, the fourth quantity, the upper boundary, and the lower boundary, form the following landing segment feasible region:

[0274]

[0275] N = / × J × K × L.

[0276] Where I is the first quantity, J is the second quantity, K is the third quantity, L is the fourth quantity, and x 0max is the maximum value in the initial lateral position value range, and x 0min is the minimum value in the initial lateral position value range, is the upper boundary, is the lower boundary, x is the lateral position, y is the longitudinal position, and V x is the lateral velocity.

[0277] The electronic device provided in this embodiment, on which the computer program is executed by the processor to determine the motion equation of the reusable rocket landing segment; determine the constraints of the reusable rocket landing segment; determine the optimization objective function of the reusable rocket landing segment; calculate the feasible region of the reusable rocket landing segment according to the motion equation, constraints, and optimization objective function. The electronic device provided in this embodiment calculates the feasible region of the reusable rocket landing segment through the motion equation, constraints, and 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, thereby improving the convergence of the calculation of the feasible region of the reusable rocket landing segment.

[0278] Based on the same inventive concept of the method for calculating the feasible region of the reusable rocket landing segment based on numerical optimization, this embodiment provides a computer on which a computer program is stored. The computer program is executed by the processor to implement the above Figure 1 shown method for calculating the feasible region of the reusable rocket landing segment based on numerical optimization.

[0279] Specifically,

[0280] Determine the motion equations for the landing phase of a reusable rocket.

[0281] Determine the constraints for the landing phase of a reusable rocket.

[0282] Determine the optimization objective function for the landing phase of a reusable rocket.

[0283] Calculate the feasible region for the landing phase of a reusable rocket based on the motion equations, constraints, and optimization objective function.

[0284] Optionally, the reusable rocket moves in the vertical plane within the feasible region.

[0285] Optionally, determine the motion equations for the landing phase of a reusable rocket, including:

[0286] In the target coordinate system, determine the motion equations for the landing phase of a reusable rocket as:

[0287]

[0288] D = 0.5ρS ref C D ||V||V.

[0289] Where, the origin O of the target coordinate system is at the landing point, the OY axis is perpendicular to the local horizontal plane of the target point and points to the sky, and the OX axis is in the local horizontal plane of the target point and points to the launch point.

[0290] is the first derivative operator, is the 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 gravitational acceleration in the target coordinate system, T is the engine thrust amplitude, I sp is the engine specific impulse, g0 is the sea-level gravitational acceleration, is the pitch angular velocity, ρ is the atmospheric density, S ref is the reference area, C D is the aerodynamic drag coefficient.

[0291] Optionally, in the target coordinate system, the reusable rocket in the landing phase of the reusable rocket is a particle, and the reusable rocket responds to the program angle command in real time, and the engine thrust is along the axis of the reusable rocket.

[0292] Optionally, determine the constraints for the landing phase of a reusable rocket, including:

[0293] Determine the process constraints for the landing phase of a reusable rocket.

[0294] Determine the initial state constraints for the landing phase of a reusable rocket.

[0295] Determine the terminal state constraints for the landing phase of the reusable rocket.

[0296] Optionally, determine the process constraints for the landing phase of the reusable rocket, including:

[0297] Determine the thrust magnitude inequality constraint, pitch angle inequality constraint, pitch rate inequality constraint, altitude inequality constraint, and velocity inequality constraint for the landing phase of the reusable rocket.

[0298] Optionally, the thrust magnitude inequality constraint is:

[0299] T min ≤ T(t) ≤ T max .

[0300] where t is any moment during the landing phase of the reusable rocket, T(t) is the engine thrust magnitude at time t, T min is the minimum engine thrust, and T max is the maximum engine thrust.

[0301] Optionally, the pitch rate inequality constraint is:

[0302]

[0303] where t is any moment during the landing phase of the reusable rocket, is the pitch rate at time t, and is the maximum pitch rate.

[0304] Optionally, the pitch angle inequality constraint is:

[0305]

[0306] where is the maximum deviation between the pitch angle and 90 degrees.

[0307] Optionally, the altitude inequality constraint is:

[0308] y(t) ≥ 0.

[0309] where t is any moment during the landing phase of the reusable rocket, and y(t) is the altitude at time t.

[0310] Optionally, the velocity inequality constraint is:

[0311] V y (t) ≤ 0.

[0312] where t is any moment during the landing phase of the reusable rocket, and V y (t) is the longitudinal velocity at time t.

[0313] Optionally, determine the initial state constraints for the reusable rocket landing phase, including:

[0314] Determine the position vector and longitudinal velocity equality constraints, and the mass equality constraint for the reusable rocket landing phase.

[0315] Optionally, the position vector and longitudinal velocity equality constraints are:

[0316] r0 = r(t0),

[0317] where t0 is the initial time of the reusable rocket landing phase, r0 is the position vector of the initial point of the reusable rocket landing phase, and r(t0) is the position vector at the initial time. is the longitudinal velocity at the initial point of the reusable rocket landing phase, V y (t0) is the longitudinal velocity at the initial time.

[0318] Optionally, the mass equality constraint is:

[0319] m0 = m(t0).

[0320] where t0 is the initial time of the reusable rocket landing phase, m0 is the mass of the initial point of the reusable rocket landing phase, and m(t0) is the mass at the initial time.

[0321] Optionally, determine the terminal state constraints for the reusable rocket landing phase, including:

[0322] Determine the longitudinal equality constraint and the lateral inequality constraint for the reusable rocket landing phase.

[0323] Optionally, the longitudinal equality constraint is:

[0324] y(t f ) = 0.

[0325] where t f is the terminal time of the reusable rocket landing phase, and y(t f ) is the altitude at time t f .

[0326] Optionally, the lateral inequality constraint is:

[0327]

[0328]

[0329]

[0330]

[0331] m(tf ) ≥ m nin 。

[0332] Among them, t f is the terminal moment of the landing section of the reusable rocket, and x(t f ) is the lateral position at time t f . is the maximum deviation of the lateral position, V x (t f ) is the lateral velocity at time t f . is the maximum deviation of the lateral velocity, is the angle between the thrust vector and the OX axis at time t f , is the maximum deviation between the terminal pitch angle and 90 degrees, m(t f ) is the mass at time t f , m min is the minimum mass of the reusable rocket, is the minimum landing velocity, V y (t f ) is the longitudinal velocity at time t f .

[0333] Optionally, determine the optimization objective function for the landing section of the reusable rocket, including:

[0334] Determine the optimization objective function for the landing section of the reusable rocket as:

[0335] J max = -V x (t0), J min = V x (t0)

[0336] Among them, t0 is the initial moment of the landing section of the reusable rocket, and V x (t0) is the lateral velocity at the initial moment, and J max , J min are both optimization objective functions.

[0337] Optionally, determine the optimization objective function for the landing section of the reusable rocket, including:

[0338] Determine the optimization objective function for the landing section of the reusable rocket:

[0339]

[0340] Among them, t0 is the initial moment of the landing section of the reusable rocket, t f is the terminal moment of the landing section of the reusable rocket, is the angle between the thrust vector and the OX axis at time t, and Jmax , J min are both optimization objective functions.

[0341] Optionally, calculate the feasible region of the reusable rocket landing section according to the motion equation, constraints, and optimization objective function, including:

[0342] Construct a trajectory planning problem for the landing section based on the motion equation, constraints, and optimization objective function.

[0343] In the initial state, use a numerical optimization algorithm to solve the trajectory planning problem for the landing section with J max as the optimization objective function to obtain the upper boundary of the initial lateral velocity, and, in the initial state, use a numerical optimization algorithm to solve the trajectory planning problem for the landing section with J min as the optimization objective function to obtain the lower boundary of the initial lateral velocity.

[0344] Calculate the feasible region of the landing section based on the upper boundary and the lower boundary.

[0345] Optionally, the initial state includes the initial command value range, the initial height value range, the initial lateral position value range, and the initial longitudinal velocity value range.

[0346] Optionally, in the initial state, use a numerical optimization algorithm to solve the trajectory planning problem for the landing section with J max as the optimization objective function to obtain the upper boundary of the initial lateral velocity, and, in the initial state, use a numerical optimization algorithm to solve the trajectory planning problem for the landing section with J min as the optimization objective function to obtain the lower boundary of the initial lateral velocity, including:

[0347] Select the first number of samples within the initial mass value range.

[0348] Select the second number of samples within the initial height value range.

[0349] Select the third number of samples within the initial lateral position value range.

[0350] Select the fourth number of samples within the initial longitudinal velocity value range.

[0351] Traverse the initial state, and based on the selected samples, use a numerical optimization algorithm to solve the trajectory planning problem for the landing section with J max as the optimization objective function to obtain the upper boundary of the initial lateral velocity, and, traverse the initial state, and based on the selected samples, use a numerical optimization algorithm to solve the trajectory planning problem for the landing section with J min as the optimization objective function to obtain the lower boundary of the initial lateral velocity.

[0352] Optionally, calculate the feasible region of the landing section based on the upper boundary and the lower boundary, including:

[0353] Based on the first quantity, the second quantity, the third quantity, the fourth quantity, the upper boundary, and the lower boundary, the following feasible landing section region is formed:

[0354]

[0355] N = I × J × K × L.

[0356] Wherein, I is the first quantity, J is the second quantity, K is the third quantity, L is the fourth quantity, x 0max is the maximum value in the value range of the initial lateral position, x 0min is the minimum value in the value range of the initial lateral position, is the upper boundary, is the lower boundary, x is the lateral position, y is the longitudinal position, V x is the lateral velocity.

[0357] The computer-readable storage medium provided in this embodiment, on which the computer program is executed by a processor to determine the motion equation of the reusable rocket landing section; determine the constraints of the reusable rocket landing section; determine the optimization objective function of the reusable rocket landing section; and calculate the feasible region of the reusable rocket landing section according to the motion equation, constraints, and optimization objective function. The computer-readable storage medium provided in this embodiment calculates the feasible region of the reusable rocket landing section through the motion equation, constraints, and optimization objective function of the reusable rocket landing section, so that the calculation of the feasible region of the reusable rocket landing section fully considers the motion and constraint characteristics of the landing section process, thereby improving the convergence of the calculation of the feasible region of the reusable rocket landing section.

[0358] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present application can be implemented in various computer languages. For example, object-oriented programming languages such as Java and interpreted scripting languages such as JavaScript.

[0359] This application is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices produce a means for realizing the functions specified in one or more of the flows Figure 1 one or more of the flows and / or blocks Figure 1 or a means for realizing the functions specified in one or more of the blocks.

[0360] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory produce a manufactured article including an instruction means that realizes the functions specified in one or more of the flows Figure 1 one or more of the flows and / or blocks Figure 1 or a means for realizing the functions specified in one or more of the blocks.

[0361] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for realizing the functions specified in one or more of the flows Figure 1 one or more of the flows and / or blocks Figure 1 or a means for realizing the functions specified in one or more of the blocks.

[0362] Although the preferred embodiments of the present application have been described, those skilled in the art can make additional changes and modifications once they know the basic creative concepts. Therefore, the appended claims are intended to be construed to include the preferred embodiments as well as all changes and modifications falling within the scope of the present application.

[0363] Obviously, those skilled in the art can make various changes and variations to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalent technologies, the present application is also intended to include these modifications and variations.

Claims

1. A calculation method for the feasible region of the landing section of a reusable rocket based on numerical optimization, characterized in that The method includes: Determine the motion equation of the reusable rocket during the landing phase; Determine the constraints of the reusable rocket during the landing phase; Determine the optimization objective function of the reusable rocket during the landing phase; Calculate the feasible region of the reusable rocket during the landing phase according to the motion equation, constraints, and optimization objective function; The determination of the motion equation of the reusable rocket during the landing phase includes: In the target coordinate system, determine the motion equation of the reusable rocket during the landing phase as: D = 0.5ρS ref C D ‖V‖V; Wherein, the origin O of the target coordinate system is at the landing point, the OY axis is perpendicular to the local horizontal plane of the target point and points to the sky, and the OX axis is in the local horizontal plane of the target point and points to the launch point; is the first-order derivative operator, is the 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 gravitational acceleration in the target coordinate system, T is the engine thrust amplitude, I sp is the specific impulse of the engine, g0 is the gravitational acceleration at sea level, is the pitch angular velocity, ρ is the atmospheric density, S ref is the reference area, C D is the aerodynamic drag coefficient; The determination of the constraints of the reusable rocket during the landing phase includes: Determine the process constraints of the reusable rocket during the landing phase; Determine the initial state constraints of the reusable rocket during the landing phase; Determine the terminal state constraints of the reusable rocket during the landing phase; The calculation of the feasible region of the reusable rocket during the landing phase according to the motion equation, constraints, and optimization objective function includes: Construct a trajectory planning problem for the landing phase based on the motion equation, constraints, and optimization objective function; In the initial state, use a numerical optimization algorithm to solve the land segment trajectory planning problem with J max as the optimization objective function, and obtain the upper boundary of the lateral initial velocity. Also, in the initial state, use a numerical optimization algorithm to solve the land segment trajectory planning problem with J min as the optimization objective function, and obtain the lower boundary of the lateral initial velocity; Calculate the feasible region of the landing phase based on the upper and lower boundaries.

2. The method according to claim 1, wherein In the feasible region, the reusable rocket moves in the longitudinal plane.

3. The method according to claim 1, wherein In the target coordinate system, the reusable rocket during the landing phase of the reusable rocket is a particle, and the reusable rocket responds to the program angle command in real time, and the engine thrust is along the axis of the reusable rocket.

4. The method according to claim 1, wherein The determination of the process constraints of the reusable rocket during the landing phase includes: Determine the thrust amplitude inequality constraint, pitch angle inequality constraint, pitch angular velocity inequality constraint, height inequality constraint, and velocity inequality constraint of the reusable rocket during the landing phase.

5. The method according to claim 4, characterized in that, The thrust amplitude inequality constraint is: T min T(t) is less than or equal to T and greater than or equal to T max ; Among them, t is any moment in the landing section of the reusable rocket, T(t) is the engine thrust amplitude at time t, T min is the minimum value of the engine thrust, and T max is the maximum value of the engine thrust.

6. The method according to claim 4, wherein The pitch angular velocity inequality constraint is: where \(t\) is any moment during the landing phase of the reusable rocket, is the pitch angular velocity at time \(t\), is the maximum value of the pitch angular velocity.

7. The method according to claim 4, wherein The pitch angle inequality constraint is: Among them, is the maximum deviation between the pitch angle and 90 degrees.

8. The method according to claim 4, wherein The height inequality constraint is: y(t)≥0; Wherein, t is any moment during the landing phase of the reusable rocket, and y(t) is the height at moment t.

9. The method according to claim 4, characterized in that The velocity inequality constraint is: V y (t) ≤ 0; Among them, t is any moment in the landing section of the reusable rocket, and V y (t) is the longitudinal velocity at moment t.

10. The method according to claim 1, characterized in that, The determination of the initial state constraints of the reusable rocket during the landing phase includes: Determine the position vector and longitudinal velocity equality constraint, and mass equality constraint of the reusable rocket during the landing phase.

11. The method according to claim 10, wherein The position vector and longitudinal velocity equality constraint is: Among them, \(t_0\) is the initial moment of the landing section of the reusable rocket, \(\vec{r}_0\) is the position vector of the initial point of the landing section of the reusable rocket, and \(\vec{r}(t_0)\) is the position vector at the initial moment. is the longitudinal velocity of the initial point of the landing section of the reusable rocket, \(V\) y (t_0) is the longitudinal velocity at the initial moment.

12. The method according to claim 10, wherein The mass equality constraint is: m0 = m(t0); Wherein, t0 is the initial moment during the landing phase of the reusable rocket, m0 is the mass at the initial point of the reusable rocket during the landing phase, and m(t0) is the mass at the initial moment.

13. The method according to claim 1, wherein The determination of the terminal state constraints of the reusable rocket during the landing phase includes: Determine the longitudinal equality constraint and lateral inequality constraint of the reusable rocket during the landing phase.

14. The method according to claim 13, wherein The longitudinal equality constraint is: y(t f ) = 0; where t f is the terminal time of the reusable rocket's landing phase, and y(t f ) is the altitude at time t f .

15. The method according to claim 13, characterized in that The lateral inequality constraint is: m(t f )≥m min ; where t f is the terminal time of the landing phase of the reusable rocket, x(t f ) is the lateral position at time t f , is the maximum deviation of the lateral position, V x (t f ) is the lateral velocity at time t f , is the maximum deviation of the lateral velocity, is the angle between the thrust vector and the OX axis at time t f , is the maximum deviation between the terminal pitch angle and 90 degrees, m(t f ) is the mass at time t f , m min is the minimum mass of the reusable rocket, is the minimum landing velocity, V y (t f ) is the longitudinal velocity at time t f .

16. The method according to claim 1, wherein The determination of the optimization objective function of the reusable rocket during the landing phase includes: Determine the optimization objective function of the reusable rocket during the landing phase as: J max = -V x (t0), J min = V x (t0) Among them, t0 is the initial moment of the landing section of the reusable rocket, and V x (t0) is the lateral velocity at the initial moment, and J max , J min are all optimization objective functions.

17. The method according to claim 1, characterized in that The determination of the optimization objective function of the reusable rocket during the landing phase includes: Determine the optimization objective function of the reusable rocket during the landing phase: Among them, t0 is the initial moment of the landing section of the reusable rocket, and t f is the terminal moment of the landing section of the reusable rocket, is the angle between the thrust vector and the OX axis at time t, and J max and J min are both optimization objective functions.

18. The method according to claim 1, characterized in that, The initial state includes an initial instruction value range, an initial height value range, an initial lateral position value range, and an initial longitudinal velocity value range.

19. The method according to claim 18, wherein In the initial state, a numerical optimization algorithm is used to solve the land segment trajectory planning problem with J max as the optimization objective function to obtain the upper boundary of the initial lateral velocity. Also, in the initial state, a numerical optimization algorithm is used to solve the land segment trajectory planning problem with J min as the optimization objective function to obtain the lower boundary of the initial lateral velocity, including: Select a first number of samples within the initial mass value range; Select a second number of samples within the initial height value range; Select a third number of samples within the initial lateral position value range; Select a fourth number of samples within the initial longitudinal velocity value range; Traverse the initial state, and based on the selected samples, use a numerical optimization algorithm to solve the land segment trajectory planning problem with J max as the optimization objective function to obtain the upper boundary of the lateral initial velocity, and traverse the initial state, and based on the selected samples, use a numerical optimization algorithm to solve the land segment trajectory planning problem with J min as the optimization objective function to obtain the lower boundary of the lateral initial velocity.

20. The method according to claim 19, wherein Calculating the feasible region of the landing section 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, form the following feasible region of the landing section: N = I × J × K × L; Wherein, I is the first quantity, J is the second quantity, K is the third quantity, L is the fourth quantity, x 0max is the maximum value in the value range of the initial horizontal position, x 0min is the minimum value in the value range of the initial horizontal position, is the upper boundary, is the lower boundary, x is the horizontal position, y is the vertical position, V x is the horizontal velocity.

21. An electronic device, characterized in that, Including: A memory; A processor; And A computer program; Wherein, the computer program is stored in the memory and is configured to be executed by the processor to implement the method according to any one of claims 1-20.

22. A computer-readable storage medium, characterized in that, A computer program is stored thereon; the computer program is executed by a processor to implement the method according to any one of claims 1-20.

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