A Method for Describing the Full Trajectory Optimization Problem of a Reusable Rocket

Abstract

The present application provides a method for describing the full - trajectory optimization problem of a reusable rocket. The method includes: dividing the full trajectory of the reusable rocket into a rising stage and a landing stage; respectively determining the motion equations and constraint conditions for the rising stage and the landing stage; determining the objective function; and optimizing the full - trajectory of the reusable rocket based on the objective function, the motion equations and constraint conditions of each stage. The method provided by the present application divides the full trajectory of the reusable rocket into a rising stage and a landing stage, and performs optimization according to the motion equations, constraint conditions and objective function of the rising stage and the landing stage, reducing the dimension of the optimization problem of the reusable rocket and solving the optimization problem of considering two motion equations at the same time after the separation of the reusable rocket.

Description

Technical Field

[0001] This application relates to the field of launch vehicle control, and particularly to a method for describing the full - trajectory optimization problem of a reusable rocket. Background Art

[0002] Compared with traditional rockets that only consider payload injection into orbit, reusable rockets need to satisfy the landing - segment constraints and soft - landing terminal constraints after the separation of boosters or the first - stage core while meeting the ascent - segment constraints and orbit - injection accuracy requirements.

[0003] Since the main engine of the rocket still needs to operate during the landing segment, which will reduce the rocket's carrying capacity, in order to minimize the loss of the carrying capacity of reusable rockets, overall consideration of the full - flight trajectory of reusable rockets has become the research focus. Summary of the Invention

[0004] To solve one of the above - mentioned technical deficiencies, this application provides a method for describing the full - trajectory optimization problem of a reusable rocket.

[0005] In the first aspect of this application, a method for describing the full - trajectory optimization problem of a reusable rocket is provided. The method includes:

[0006] Dividing the full flight of the reusable rocket into an ascent segment and a landing segment;

[0007] Respectively determining the motion equations and constraint conditions of the ascent segment and the landing segment;

[0008] Determining the objective function;

[0009] Optimizing the full - trajectory of the reusable rocket based on the objective function, the motion equations and constraint conditions of each stage.

[0010] In the second aspect of this application, an electronic device is provided, including:

[0011] A memory;

[0012] A processor; and

[0013] A computer program;

[0014] Wherein, a computer - readable storage medium stores a computer program thereon; the computer program is executed by the processor to implement the method as described in the first aspect above.

[0015] In the third aspect of this application, a computer - readable storage medium is provided, characterized in that a computer program is stored thereon; the computer program is executed by the processor to implement the method as described in the first aspect above.

[0016] The present application provides a method for describing the full - trajectory optimization problem of a reusable rocket. The method includes: dividing the full trajectory of the reusable rocket into a boost phase and a landing phase; respectively determining the motion equations and constraint conditions for the boost phase and the landing phase; determining the objective function; and optimizing the full - trajectory of the reusable rocket based on the objective function, the motion equations, and the constraint conditions of each phase. The method provided by the present application divides the full trajectory of the reusable rocket into a boost phase and a landing phase, and performs optimization according to the motion equations, constraint conditions, and objective function of the boost phase and the landing phase, reducing the dimension of the optimization problem of the reusable rocket and solving the optimization problem of considering two motion equations at the same time after the separation of the reusable rocket. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] 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 and descriptions thereof of the present application are used to explain the present application and do not constitute an improper limitation of the present application. In the drawings:

[0018] Figure 1 is a schematic flowchart of a method for describing the full - trajectory optimization problem of a reusable rocket provided by an embodiment of the present application;

[0019] Figure 2 is a schematic diagram of the full - trajectory optimization process of a reusable rocket provided by an embodiment of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0020] 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 and features in the embodiments of the present application can be combined with each other.

[0021] In the process of implementing the present application, the inventors found that since the main engine of the rocket still needs to work during the landing phase, it will reduce the carrying capacity of the rocket. Therefore, in order to minimize the loss of the carrying capacity of the reusable rocket, overall consideration of the full - flight trajectory of the reusable rocket has become the research focus.

[0022] In view of the above problems, an approach for describing the full - trajectory optimization problem of a reusable rocket is provided in the embodiments of the present application. The method includes: dividing the full trajectory of the reusable rocket into an ascent stage and a landing stage; respectively determining the motion equations and constraint conditions for the ascent stage and the landing stage; determining the objective function; and optimizing the full - trajectory of the reusable rocket based on the objective function, the motion equations, and the constraint conditions for each stage. The method provided in the present application divides the full trajectory of the reusable rocket into an ascent stage and a landing stage, and performs optimization according to the motion equations, constraint conditions, and objective function of the ascent stage and the landing stage, reducing the dimension of the optimization problem of the reusable rocket and solving the optimization problem of having to consider two motion equations at the same time after the separation of the reusable rocket.

[0023] In this embodiment, the reusable rocket is regarded as two moving bodies, namely a recovery stage and an orbital stage. That is, the reusable rocket includes a recovery - stage moving body and an orbital - stage moving body. Before separation, the recovery - stage moving body provides power, and the two have the same motion law. After separation, the two moving bodies have their own independent motion characteristics and terminal objectives. To comprehensively consider the motion processes of the three flight segments, this embodiment proposes a method for describing the full - trajectory optimization problem of a reusable rocket with two moving bodies and multiple flight segments. By analyzing the connection between the ascent stage (the ascent stage includes the pre - separation ascent stage and the orbital - stage flight segment) and the landing stage (i.e., the vertical - landing flight segment of the recovery stage) of the reusable launch vehicle, a two - moving - body, multi - stage motion model including the pre - separation ascent stage, the orbital - stage flight segment, and the landing stage of the reusable rocket is established. Combining the constraint conditions of the ascent stage and the constraint conditions of the landing stage, on the premise of being able to achieve payload injection into orbit, with the weighted sum of the least fuel consumption in the vertical - landing stage and the least fuel consumption in the orbital stage as the objective function, the full - trajectory optimization proposition of the reusable rocket is described, and then optimization is carried out according to the motion equations, constraint conditions, and objective function of the ascent stage and the landing stage.

[0024] See Figure 1 , the implementation process of a method for describing the full - trajectory optimization problem of a reusable rocket provided in this embodiment is as follows:

[0025] 101, divide the full trajectory of the reusable rocket into an ascent stage and a landing stage.

[0026] Among them, the reusable rocket includes a recovery - stage moving body and an orbital - stage moving body.

[0027] 1. Ascent stage

[0028] The ascent stage includes the pre - separation ascent stage and the orbital - stage flight segment.

[0029] During the ascending stage before separation, the motion characteristics of the recovery-stage moving body and the orbit-insertion-stage moving body are included. Among them, the recovery-stage moving body and the orbit-insertion-stage moving body are powered by the engines in the recovery-stage moving body, and the recovery-stage moving body and the orbit-insertion-stage moving body have the same motion characteristics.

[0030] During the orbit-insertion-stage flight, only the motion characteristics of the orbit-insertion-stage moving body are included.

[0031] The reference coordinate system for the ascending stage is the launch-point inertial coordinate system (i.e., the inertial coordinate system of the launch point).

[0032] In the launch-point inertial coordinate system, the coordinate origin O is the launch point, the OY axis points outwards from the surface along the line connecting the center of the earth and the launch point, the OX axis is perpendicular to the OY axis, points in the launch direction in the horizontal plane, and the angle with the meridian plane of the launch point is the launch azimuth angle, and the OZ axis satisfies the right-hand rule.

[0033] 2. Landing stage

[0034] The reference coordinate system for the landing stage is the vertical landing coordinate system.

[0035] In the vertical landing coordinate system, the coordinate origin Oe is the center of the earth, the OeYl axis points from the center of the earth to the center of mass of the reusable rocket, the OeXl axis is perpendicular to the OeYl axis in the local horizontal plane, the angle with the meridian plane where the reusable rocket is located is the launch azimuth angle, and the OeZl axis satisfies the right-hand rule.

[0036] 102. Determine the motion equations and constraint conditions for the ascending stage and the landing stage respectively.

[0037] 1. Process of determining the motion equations and constraint conditions for the ascending stage

[0038] Describe the motion equations of the rocket's ascending stage in the launch-point inertial coordinate system. Assume that the earth is a homogeneous sphere, ignore the aerodynamic lift, and only consider the effect of aerodynamic drag. The state variables include the position vectors, velocity vectors, and masses of the recovery-stage moving body and the orbit-insertion-stage moving body in the launch-point inertial coordinate system; the control variable is the thrust vector of each stage of the engine.

[0039] The ascending stage includes the ascending stage before separation and the orbit-insertion-stage flight.

[0040] During the ascending stage before separation, the motion characteristics of the recovery-stage moving body and the orbit-insertion-stage moving body are included.

[0041] Among them, the recovery-stage moving body and the orbit-insertion-stage moving body are powered by the engines in the recovery-stage moving body. Since the thrust generated by the engines in the recovery-stage moving body acts on both moving bodies (i.e., the recovery-stage moving body and the orbit-insertion-stage moving body) simultaneously, the mass of the orbit-insertion-stage moving body remains unchanged, and the recovery-stage moving body and the orbit-insertion-stage moving body have the same motion characteristics.

[0042] During the in-orbit stage of flight, it only includes the motion characteristics of the in-orbit stage moving body. Only consider the motion of the in-orbit stage moving body to send the payload into the target orbit. Since the working stage of the in-orbit stage generates thrust by the engine of the in-orbit stage moving body, only consider the flight process after the in-orbit stage separation. Since the working stage of the in-orbit stage is in a rarefied atmosphere or vacuum environment, the influence of aerodynamic drag can be ignored.

[0043] This step will determine the motion equations of the ascending stage before separation and the motion equations of the in-orbit stage of flight. Determine the constraint conditions of the ascending stage before separation and the constraint conditions of the in-orbit stage of flight.

[0044] It should be noted that in this step and subsequent steps, subscripts 1 and 2 are used to represent the state variables and control variables corresponding to the recovery stage moving body and the in-orbit stage moving body respectively.

[0045] 1) Process of determining the motion equation of the ascending stage

[0046] Specifically, the motion equations of the ascending stage before separation and the motion equations of the in-orbit stage of flight will be determined.

[0047] (1) Determine the motion equation of the ascending stage before separation

[0048] During the flight process of the ascending stage before separation, the thrust generated by the recovery stage moving body acts on both moving bodies simultaneously. The mass of the in-orbit stage moving body remains unchanged. Therefore, the motion equation of the ascending stage before separation includes the motion equation of the ascending stage before separation of the recovery stage moving body and the motion equation of the ascending stage before separation of the in-orbit stage moving body.

[0049] A. The motion equation of the ascending stage before separation of the recovery stage moving body is:

[0050]

[0051] Among them, · is the first derivative operator, P1 is the position vector of the recovery stage moving body, V1 is the velocity vector of the recovery stage moving body, T1 is the amplitude of the engine thrust of the recovery stage moving body, m1 is the mass of the recovery stage moving body, m2 is the mass of the in-orbit stage moving body, u1 is the thrust vector of the recovery stage moving body, D is the aerodynamic drag, μ is the gravitational coefficient of the earth, r1 is the distance vector between the centroid of the recovery stage moving body where the gravitational acceleration component is used and the center of the earth, and dm1 is the engine second flow rate of the recovery stage moving body.

[0052] For example, in the inertial coordinate system of the launch point, P1 = [x 1g , y 1g , z 1g T , where, [] T is the transpose operation, V1 = [V 1xg , V 1yg , V 1zg ​​T , u1 = [u 1x , u 1y , u 1z T , D = [D x , D y , D z T .

[0053] Among them, x 1g is the position component of the recovery-stage moving body on the OX axis, y 1g is the position component of the recovery-stage moving body on the OY axis, z 1g is the position component of the recovery-stage moving body on the OZ axis, V 1xg is the velocity component of the recovery-stage moving body on the OX axis, V 1yg is the velocity component of the recovery-stage moving body on the OY axis, V 1zg is the velocity component of the recovery-stage moving body on the OZ axis, u 1x is the thrust component of the recovery-stage moving body on the OX axis, u 1y is the thrust component of the recovery-stage moving body on the OY axis, u 1z is the thrust component of the recovery-stage moving body on the OZ axis, D x is the component of the aerodynamic drag on the OX axis, D y is the component of the aerodynamic drag on the OY axis, D z is the component of the aerodynamic drag on the OZ axis.

[0054] The distance vector r1 between the centroid of the recovery-stage moving body and the center of the earth used to calculate the gravitational acceleration component satisfies r1 = P1 + [0, R e , 0] T , where R e is the radius of the earth.

[0055] B. The motion equation of the ascending stage before separation of the orbit-insertion stage moving body is:

[0056]

[0057] Among them, P2 is the position vector of the orbit-insertion stage moving body, V2 is the velocity vector of the orbit-insertion stage moving body, and r2 is the distance vector between the centroid of the orbit-insertion stage moving body and the center of the earth used to calculate the gravitational acceleration component.

[0058] For example, in the inertial coordinate system of the launch point, P2 = [x 2g , y 2g , z 2g T , where V2 = [V 2xg , V 2yg , V 2zg T , D = [D​​​​x , D y , D z T 。

[0059] Among them, x 2g is the position component of the in-orbit stage moving body on the OX axis, y 2g is the position component of the in-orbit stage moving body on the OY axis, z 2g is the position component of the in-orbit stage moving body on the OZ axis, V 2xg is the velocity component of the in-orbit stage moving body on the OX axis, V 2yg is the velocity component of the in-orbit stage moving body on the OY axis, V 2zg is the velocity component of the in-orbit stage moving body on the OZ axis, D x is the component of the aerodynamic drag on the OX axis, D y is the component of the aerodynamic drag on the OY axis, D z is the component of the aerodynamic drag on the OZ axis.

[0060] The distance vector r2 between the centroid of the in-orbit stage moving body and the center of the earth used to calculate the gravitational acceleration component satisfies r2 = P2 + [0, R e , 0] T , where R e is the radius of the earth.

[0061] (2) Determine the motion equation of the in-orbit stage flight segment

[0062] For the in-orbit stage flight segment, only the flight process after the separation of the in-orbit stage moving body is considered. Since the atmosphere is thin during the working stage of the in-orbit stage moving body, the influence of aerodynamic drag can be ignored. The motion equation of the in-orbit stage flight segment is:

[0063]

[0064] Among them, T2 is the engine thrust amplitude of the in-orbit stage moving body, u2 is the thrust vector of the in-orbit stage moving body, and dm2 is the engine second flow rate of the in-orbit stage moving body.

[0065] 2) The process of determining the constraint conditions of the ascending stage

[0066] Specifically, the constraint conditions of the ascending stage before separation and the constraint conditions of the in-orbit stage flight segment will be determined.

[0067] (1) Determine the constraint conditions of the ascending stage before separation

[0068] The constraint conditions of the ascending stage before separation include: launch initial state constraint conditions, thrust direction constraint conditions, vertical ascending stage constraint conditions, mass constraint conditions, and bending moment constraint conditions.

[0069] A. Launch initial state constraint conditions ​

[0070] Define the launch moment of the reusable rocket as the initial moment of the ascending stage. Then, the constraint conditions for the initial launch state are as follows:

[0071] [P1, V1, m1, P2, V2, m2](t0) = [P0, V0, m 10 , P0, V0, m 20 .

[0072] Among them, P1 is the position vector of the reusable stage moving body, V1 is the velocity vector of the reusable stage moving body, m1 is the mass of the reusable stage moving body, m2 is the mass of the orbital stage moving body, P2 is the position vector of the orbital stage moving body, V2 is the velocity vector of the orbital stage moving body, t0 is the launch moment of the reusable rocket, P0 is the position vector of the reusable rocket, V0 is the velocity vector of the reusable rocket (the projection of the velocity vector generated by the Earth's rotation at the launch point latitude in the inertial frame of the launch site), m 10 is the initial mass of the reusable stage moving body at the launch moment, m 20 is the initial mass of the orbital stage moving body at the launch moment.

[0073] The positions and velocities of the two moving bodies (i.e., the reusable stage moving body and the orbital stage moving body) are the same at the launch moment, and V0 is the projection of the velocity vector generated by the Earth's rotation at the launch point latitude in the inertial frame of the launch site.

[0074] B. Thrust direction constraint conditions

[0075] The thrust direction constraint conditions are as follows:

[0076] ‖u1‖ = 1, -1 ≤ u 1x,1y,1z ≤ 1.

[0077] Among them, u1 is the thrust vector of the reusable stage moving body, u1 = [u 1x , u 1y , u 1z T , u 1x is the thrust direction of the reusable stage moving body on the OX axis, u 1y is the thrust direction of the reusable stage moving body on the OY axis, u 1z is the thrust direction of the reusable stage moving body on the OZ axis.

[0078] C. Vertical ascending stage constraint conditions

[0079] To ensure launch safety, the reusable rocket needs to maintain a vertical ascent at the moment of just taking off, that is, the thrust direction of the reusable rocket is perpendicular to the current horizontal plane, and the flight time is the offline design value ​It is shown that to meet the terminal time constraint, the flight time of the vertical ascent stage is very short, and the influence of the Earth's rotation can be ignored. It is only necessary to ensure that the thrust direction is perpendicular to the horizontal plane at the launch moment.

[0080] Therefore, the constraint conditions for the vertical ascent stage include:

[0081] u1 = [0, 1, 0] T .

[0082] Among them, u1 is the thrust vector of the reusable stage moving body, u1 = [u 1x , u 1y , u 1z T , u 1x is the thrust direction of the reusable stage moving body on the OX axis, u 1y is the thrust direction of the reusable stage moving body on the OY axis, u 1z is the thrust direction of the reusable stage moving body on the OZ axis.

[0083] D. Mass constraint conditions

[0084] Define m f1min as the minimum remaining mass of the reusable stage moving body before separation. Then the mass of the reusable stage satisfies the following formula:

[0085] m1(t s ) ≥ m f1min .

[0086] Among them, m1 is the mass of the reusable stage moving body.

[0087] Define as the maximum flight time of the reusable stage moving body during the ascent stage. Then the separation time t s of the reusable stage satisfies the constraint:

[0088] Among them, t s is the separation moment.

[0089] E. Bending moment constraint conditions

[0090] When the reusable rocket is flying in the atmosphere, it is simultaneously affected by thrust and aerodynamic forces. To ensure structural safety, it is necessary to satisfy the bending moment constraint:

[0091] |qα| ≤ Q αmax .

[0092]

[0093] Among them, q is the dynamic pressure, V is the velocity vector of the reusable rocket, V E is the velocity generated by the Earth's rotation, and Q αmaxis the maximum allowable bending moment, α is the angle of attack (represented by the angle between the velocity vector and the thrust vector), and u is the thrust vector of the reusable rocket.

[0094] (2) Determine the constraint conditions for the in-orbit stage flight segment

[0095] The constraint conditions for the in-orbit stage flight segment include: the state constraint conditions at the separation moment, the mass constraint conditions of the in-orbit stage, and the terminal constraint conditions of the target orbit elements.

[0096] A. State constraint conditions at the separation moment

[0097] The state constraint conditions at the separation moment are:

[0098] The initial point position (P2(t s )) and the initial point velocity (V2(t s )) of the in-orbit stage flight segment are equal to the state of the reusable rocket at the separation moment.

[0099] The initial point mass of the in-orbit stage flight segment is the initial mass (m 20 ) of the in-orbit stage moving body at the launch moment.

[0100] B. Mass constraint conditions of the in-orbit stage

[0101] Define m f2min as the total mass of the launch vehicle and the payload after the fuel of the in-orbit stage moving body is exhausted. Then the mass constraint conditions of the in-orbit stage include:

[0102] m2(t f ) ≥ m f2min .

[0103] Among them, m2 is the mass of the in-orbit stage moving body, and t f is the terminal time of the in-orbit stage flight segment.

[0104] C. Terminal constraint conditions of the target orbit elements

[0105] The terminal condition of the in-orbit stage moving body is to send the payload into the target orbit. Define a f as the semi-major axis of the target orbit, e f as the eccentricity, i f as the inclination, Ω f as the longitude of the ascending node, w f as the argument of perigee, and Fun orbit () as the nonlinear relationship function between the target orbit elements and the terminal velocity position.

[0106] For example, the nonlinear relationship between the five orbit elements and the terminal velocity position is represented by the function Fun orbit() indicates that the terminal velocity and position of the launch vehicle can be constrained by restricting the orbital elements.

[0107] The terminal constraint conditions for the target orbital elements are:

[0108] [a f ,e f ,i f ,Ω f ,w f T = Fun orbit ([P2, V2](t f ))。

[0109]

[0110]

[0111]

[0112] [H x H y H z T = H = P 2f ×V 2f 。

[0113]

[0114]

[0115]

[0116] Among them, P2 is the position vector of the in-orbit stage moving body, V2 is the velocity vector of the in-orbit stage moving body, t f is the terminal time of the in-orbit stage flight segment, r2 is the distance vector between the centroid of the in-orbit stage moving body used for the gravitational acceleration component and the center of the earth, μ is the earth's gravitational coefficient, is the velocity component of the in-orbit stage moving body on the OX axis, is the velocity component of the in-orbit stage moving body on the OY axis, is the velocity component of the in-orbit stage moving body on the OZ axis, x2 is the position component of the in-orbit stage moving body on the OX axis, y2 is the position component of the in-orbit stage moving body on the OY axis, z2 is the position component of the in-orbit stage moving body on the OZ axis, R0 is the earth's radius, H is the angular momentum per unit mass, H x is the component of H on the OX axis, H y is the component of H on the OY axis, H z is the component of H on the OZ axis, P 2f is the position vector of the in-orbit stage moving body at the terminal moment, V 2f ​​is the velocity vector of the in-orbit stage moving body at the terminal moment.

[0117] 2. Process of determining the motion equation and constraint conditions during the landing stage

[0118] Considering that the flight process of the reusable rocket from the separation point to the target landing point is relatively long, in order to ensure the landing accuracy, the influence of the earth's angular velocity of rotation must be considered when planning the flight trajectory. Describing the rocket motion in the inertial coordinate system is simple, but the position of the target landing point is always changing with the rotation of the earth and is not easy to determine. Therefore, the vertical landing coordinate system is adopted for the landing stage.

[0119] Describing the motion state of the reusable rocket in the vertical landing coordinate system, the position vector of the reusable rocket is represented by the distance vector r1 between the centroid of the recovery stage moving body used for the gravitational acceleration component and the center of the earth, and the longitude and latitude (λ1, B1) of the centroid of the reusable rocket in the geocentric equatorial coordinate system. The velocity vector is represented by the velocity components (V 1x , V 1y , V 1z ) in three directions in the vertical landing coordinate system.

[0120] 1) Process of determining the motion equation during the landing stage

[0121] Specifically, the motion equation during the landing stage is:

[0122]

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131] where, · is the first derivative operator, r1 is the distance vector between the centroid of the recovery stage moving body used for the gravitational acceleration component and the center of the earth, V 1x is the velocity component of the recovery stage moving body on the O e X l axis, V 1y is the velocity component of the recovery stage moving body on the O e Yl Velocity component of the axis, V 1z For the recovery-stage moving body at O e Z l Velocity component of the axis, λ1 is the longitude of the center of mass of the reusable rocket in the geocentric equatorial coordinate system, B1 is the latitude of the center of mass of the reusable rocket in the geocentric equatorial coordinate system, A0 is the launch azimuth, m1 is the mass of the recovery-stage moving body, and T1 is the engine thrust amplitude of the recovery-stage moving body. Is the pitch angle of the recovery-stage moving body (i.e., the angle between the reusable rocket body axis and the local horizontal plane), ψ1 is the yaw angle of the recovery-stage moving body (i.e., the angle between the projection of the reusable rocket body axis on the local horizontal plane and the rocket body longitudinal axis), D x Is the air resistance at O e X l Component of the axis, D y Is the air resistance at O e Y l Component of the axis, D z Is the air resistance at O e Z l Component of the axis, ω E Is the amplitude of the earth's angular velocity of rotation, μ is the earth's gravitational coefficient, Is the pitch angular velocity of the recovery-stage moving body, ω 1ψ Is the yaw angular velocity of the recovery-stage moving body, and dm1 is the engine second flow rate of the recovery-stage moving body.

[0132] To ensure the controllability of the angular velocity of the rocket during flight, And ω 1ψ Two control variables are introduced.

[0133] 2) Process of determining the landing-stage constraint conditions

[0134] The process of the landing stage (i.e., the vertical landing of the recovery-stage moving body) is divided into two forms: (1) Return to the original site. The reusable rocket returns to the vicinity of the launch site for the purpose of reducing transportation costs after landing; (2) Downrange landing. The reusable rocket sets up a mobile landing platform in the flight direction for the purpose of minimizing the recoverable loss of payload capacity.

[0135] For the landing process of returning to the original site, after separation, the velocity of the reusable rocket points away from the landing site, and has a large magnitude. At this time, the RCS (Reaction Control System) nozzle needs to be used to adjust the attitude of the reusable rocket, making the rocket body face the opposite direction of the current velocity, and then start the reusable rocket engine to change the velocity direction of the reusable rocket, so that it flies towards the target landing site. Before the reusable rocket enters the dense atmosphere, the RCS nozzle is used again to adjust the attitude of the reusable rocket, making the rocket body face the opposite direction of the current velocity. When the reusable rocket re-enters the dense atmosphere, it faces serious problems of aerodynamic heat, dynamic pressure and overload. In order to ensure its own safety and the successful completion of the vertical landing mission, the reusable rocket needs to control the magnitude of the engine thrust to adjust its velocity magnitude, so that the re-entry process does not violate these hard constraints. As the flight altitude of the reusable rocket gets lower and lower and the atmospheric density gets higher and higher, due to the action of the earth's gravity, the flight velocity of the reusable rocket gradually increases, resulting in a greater aerodynamic force. Considering that the reusable rocket must fly at a small angle of attack during the flight process, the aerodynamic force is mainly manifested as aerodynamic drag. During the deceleration process of the reusable rocket by aerodynamic drag, the magnitude of the aerodynamic force will gradually decrease as the dynamic pressure decreases. When the aerodynamic force of the reusable rocket is close to the magnitude of the gravity, it reaches a state of approximate uniform motion and continues to fly towards the landing site. When the reusable rocket reaches above the target landing point and the flight altitude and velocity meet the engine ignition conditions, the reusable rocket engine ignites again to control the flight attitude, landing point velocity and position to meet the requirements of precise vertical soft landing at the same time. During the entire flight process, the attitude angle of the reusable rocket needs to be gradually adjusted, so that it changes from a state with a small angle between the separation moment and the local horizontal plane to a state that is basically perpendicular to the local horizontal plane when entering the final powered soft landing section.

[0136] For the downrange landing process, since there is no need to change the flight velocity direction after separation, the landing point position can be selected in advance by means of planning before launch according to different missions, so it saves more fuel than returning to the original site. And the engine ignition section for adjusting the landing point after separation can be cancelled. During the re-entry powered deceleration process, control the thrust direction of the engine. While reducing the velocity magnitude, adjust the landing point to the target landing site. The hard constraint conditions that need to be considered for the reusable rocket to re-enter the atmosphere and the subsequent flight process are the same as those for returning to the original site, so as to achieve vertical landing.

[0137] The constraint conditions for the landing section include, according to whether there is power in the flight section, the density of the atmosphere in the flight section, and the motion characteristics of each flight section: the initial state constraint conditions for the landing section, the mass flow rate constraint conditions, the attitude angular velocity constraint conditions, the stagnation point heat flux constraint conditions, the dynamic pressure constraint conditions, the aerodynamic overload constraint conditions, the angle constraint conditions, and the terminal state constraint conditions for the landing section.

[0138] (1) Initial state constraint conditions for the landing phase

[0139] The initial state of the landing phase (i.e., the vertical landing process of the reusable stage) is determined by the state at the moment of rocket separation. Define the moment of separation of the reusable rocket as t s as the zero point of the landing phase timer. (In this step and subsequent steps, the subscript s is used to represent the state variables at the moment of reusable rocket separation), then the initial state constraint conditions for the landing phase are:

[0140] [P1, V1, m1](t s ) = [P 1s , V 1s , m 1s

[0141] where P1 is the position vector of the reusable stage moving body, V1 is the velocity vector of the reusable stage moving body, m1 is the mass of the reusable stage moving body, t s is the separation moment, P 1s is the position vector of the reusable stage moving body at the separation moment, V 1s is the velocity vector of the reusable stage moving body at the separation moment, m 1s is the mass of the reusable stage moving body at the separation moment.

[0142] (2) Mass flow rate per second constraint conditions

[0143] The landing phase (i.e., the vertical landing process of the reusable stage) is divided into a powered flight segment and an unpowered flight segment. Since the control quantity determining the thrust amplitude is the engine mass flow rate per second, for the unpowered flight segment, the mass flow rate per second is always zero; for the powered flight segment, the mass flow rate per second can be adjusted within the range of [dm min , dm max .

[0144] The mass flow rate per second constraint conditions are:

[0145]

[0146] where dm1 is the engine mass flow rate per second of the reusable stage moving body, dm min is the minimum engine mass flow rate per second, i.e., the minimum value that the mass flow rate per second can be adjusted to, and dm max is the maximum engine mass flow rate per second, i.e., the maximum value that the mass flow rate per second can be adjusted to.

[0147] (3) Attitude angular velocity constraint conditions

[0148] ​The attitude angular velocity is used as a control variable during the landing phase (i.e., the vertical landing process of the recovery stage). The magnitude of its amplitude will affect the stability of the reusable rocket's attitude control system. Especially after the reusable rocket enters the dense atmosphere, the allowable attitude angular velocity is less than that in the rarefied atmosphere flight phase. Particularly in the final precise powered soft landing phase, the engine thrust is very large at this time, and any slight adjustment of the thrust direction will have a great moment effect on the rocket's motion around the center of mass, affecting the stability of the attitude control system. Therefore, to ensure the attitude angle of the reusable rocket at the final landing moment, the attitude angular velocity in the final stage should be restricted within a very small range. The attitude angular velocity constraint conditions are as follows:

[0149]

[0150] Among them, is the pitch angular velocity of the recovery stage moving body, ω 1ψ is the yaw angular velocity of the recovery stage moving body, ω max1 is the amplitude of the attitude angular velocity in the rarefied atmosphere section, ω max2 is the amplitude of the attitude angular velocity in the dense atmosphere section, ω max3 is the amplitude of the attitude angular velocity in the powered soft landing section.

[0151] (4) Stagnation point heat flux constraint conditions

[0152] During the vertical landing process of the reusable rocket, severe aerodynamic heat will be generated on the surface, which has a complex relationship with materials, heat transfer, etc. and is not easy to determine. To meet the limitation conditions of aerodynamic heat, it can be converted into a stagnation point heat flux constraint during the analysis. The stagnation point heat flux constraint conditions are as follows:

[0153]

[0154] Among them, Q s is the current stagnation point heat flux value of the reusable rocket, k s is the stagnation point heat flux coefficient related to the shape of the reusable rocket, ρ is the atmospheric density at the corresponding altitude, V1 is the velocity vector of the recovery stage moving body, ρ Q and V Q are the parameters for calculating the stagnation point heat flux, Q smax is the maximum value of the stagnation point heat flux, that is, the allowable maximum value of the stagnation point heat flux.

[0155] The stagnation point heat flux constraint conditions only need to be considered in the powered deceleration section before entering the dense atmosphere and the aerodynamic deceleration section after entering the atmosphere, and do not need to be considered in other flight sections.

[0156] (5) Dynamic pressure constraint conditions

[0157] The dynamic pressure constraint of a reusable rocket depends on the hinge moment generated by aerodynamic forces that increase with dynamic pressure on the one hand, and on the compressive strength of the thermal protection material on the surface of the reusable rocket on the other hand. To ensure flight safety, the dynamic pressure is required to be less than the maximum value q that the rocket body can withstand. max 。

[0158] The dynamic pressure constraint condition is as follows:

[0159] q = 0.5ρ‖V1‖ 2 ≤ q max 。

[0160] Where q is the dynamic pressure, ρ is the atmospheric density at the corresponding altitude, V1 is the velocity vector of the recovery stage moving body, and q max is the maximum value of the dynamic pressure.

[0161] The dynamic pressure constraint condition only needs to be considered in the powered deceleration stage before entering the dense atmosphere and the aerodynamic deceleration stage after entering the atmosphere. It does not need to be considered in other flight segments.

[0162] (6) Aerodynamic overload constraint condition

[0163] The overload generated by the aerodynamic force on the rocket needs to meet the requirements of the structural strength. Define the maximum value of the aerodynamic overload as n Dmax (i.e., the maximum available overload), then the aerodynamic overload constraint can be described as,

[0164]

[0165] Where n D is the aerodynamic overload, m1 is the mass of the recovery stage moving body, D x is the component of the air resistance in the O e X l axis, D y is the component of the air resistance in the O e Y l axis, D z is the component of the air resistance in the O e Z l axis, and g0 is the standard acceleration of gravity.

[0166] The aerodynamic overload constraint condition only needs to be considered in the powered deceleration stage before entering the dense atmosphere and the aerodynamic deceleration stage after entering the atmosphere. It does not need to be considered in other flight segments.

[0167] (7) Angle constraint condition

[0168] To ensure the stability of the powered soft landing stage of the reusable rocket, not only the angular velocity constraint needs to be restricted in this stage, but also the thrust direction representing the rocket attitude angle needs to be restricted within a certain range, as follows:

[0169] Powered soft landing stage

[0170] Among them, is the pitch angle of the recovery-stage moving body, is the maximum deviation between the pitch angle and the local plumb line.

[0171] During the powered soft landing stage, the angle between the velocity direction and the horizontal plane also needs to be restricted within a certain range, so as to ensure that the velocity component of the reusable rocket in the horizontal plane is very small in the final stage, as follows:

[0172] Powered soft landing stage.

[0173] Among them, V 1x is the velocity component of the recovery-stage moving body on the O e X l axis, V 1y is the velocity component of the recovery-stage moving body on the O e Y l axis, V 1z is the velocity component of the recovery-stage moving body on the O e Z l axis, Δθ V is the maximum deviation between the velocity direction and the local plumb line.

[0174] Through the angle constraint condition, it can be ensured that the angle between the thrust and the velocity direction of the reusable rocket during the powered soft landing stage is near 180 degrees, and the angle of attack is very small, so the influence of aerodynamic lift can be ignored. This constraint condition only needs to be considered in the final powered soft landing stage, and does not need to be considered in other flight stages.

[0175] (8) Terminal state constraint conditions for the landing stage

[0176] The terminal state constraint conditions for the landing stage include: landing position constraint conditions, landing velocity constraint conditions, landing attitude angle and velocity inclination constraint conditions, and landing mass constraint conditions.

[0177] A. Landing position constraint conditions

[0178] To ensure that the rocket can achieve a fixed-point soft landing, the terminal position of the rocket needs to be within the landing area, that is, the landing position constraint condition is:

[0179] h(t l ) = h l

[0180] ‖λ(t l ) - λ l ‖ ≤ Δλ l

[0181] ‖B(t l ) - B l‖≤ΔB l

[0182] where t l is the landing time at the relative separation moment, h(t l ) is the landing height at time t l , h l being the height of the desired landing point, λ(t l ) being the longitude of the reusable rocket terminal at time t l , λ l being the longitude of the reusable rocket terminal at the landing moment, Δλ l being the maximum deviation of the longitude of the reusable rocket terminal (i.e., the allowable deviation value of the longitude of the reusable rocket terminal), B(t l ) being the latitude of the reusable rocket terminal at time t l , B l being the latitude of the reusable rocket terminal at the landing moment, ΔB l being the maximum deviation of the latitude of the reusable rocket terminal (i.e., the allowable deviation value of the latitude of the reusable rocket terminal).

[0183] It should be noted that in this step and subsequent steps, the position of the target landing point is represented by the subscript l.

[0184] B. Landing speed constraint conditions

[0185] The vertical landing terminal speed needs to satisfy the constraints in the following formula:

[0186] V ylmax ≤V 1y (t l )≤0

[0187] -V xzlmax ≤V 1x (t l ),V 1z (t l )≤V xzlmax

[0188] where t l is the landing time at the relative separation moment, V 1x (t l ) is the velocity component of the recovery stage moving body at time t l on the O e X l axis, V 1y (t l ) is the velocity component of the recovery stage moving body at time t l on the O e Y l axis, V 1z (tl ) is the reusable stage vehicle t l At time O e Z l The velocity component along the Z-axis, V ylmax is the maximum touchdown velocity borne by the landing leg, V xzlmax is the maximum lateral velocity that causes tipping over.

[0189] That is, the longitudinal velocity must be downward and its magnitude must be less than the maximum touchdown velocity V that the landing leg of the reusable rocket can withstand ylmax , and the velocities in both directions in the horizontal plane must be less than the maximum lateral velocity V that may cause the rocket body to tip over xzlmax .

[0190] C. Landing attitude angle and velocity inclination angle constraint conditions

[0191] To achieve vertical landing, the terminal attitude angle and velocity inclination angle constraints of the reusable rocket are as follows:

[0192]

[0193]

[0194] where t l is the landing time relative to the separation time, is the pitch angle of the reusable stage vehicle at time t l V(t 1x (t l ) is the velocity component of the reusable stage vehicle along the O l axis at time t e X l V(t 1y (t l ) is the velocity component of the reusable stage vehicle along the O l axis at time t e Y l V(t 1z (t l ) is the velocity component of the reusable stage vehicle along the O l axis at time t e Z l axis, Δθ Vl is the maximum value of the angle between the velocity at the landing time and the rocket body.

[0195] That is, the rocket body is perpendicular to the local horizontal plane, and the angle between the velocity at the landing time and the rocket body is less than Δθ Vl .

[0196] D. Landing mass constraint conditions

[0197] The mass constraint at the rocket landing time should satisfy the following equation:

[0198] m1(t l ) ≥ m 1lmin

[0199] where t l is the landing time at the relative separation moment, m1(t l ) is the mass of the reusable rocket's recovery stage moving body at time t l , and m 1lmin is the minimum remaining mass of the reusable rocket's recovery stage moving body.

[0200] 103. Determine the objective function.

[0201] Consider the selection of performance indicators for the vertical landing trajectory planning of reusable rockets from two aspects. More remaining available fuel in the landing section of the reusable rocket can improve the ability of the reusable rocket to overcome uncertain disturbances in the landing section and improve the landing accuracy; minimizing the fuel consumed during the vertical landing process of the reusable rocket and using more fuel to increase the energy at the separation moment of the reusable rocket can reduce the pressure on the flight process of the reusable rocket's orbital stage moving body, enabling the orbital stage moving body to have more fuel to ensure the safe injection of the payload into orbit. Therefore, comprehensively consider the terminal masses of the recovery stage moving body and the orbital stage moving body in the optimization objective function, maximize the weighted sum of the two, and adjust the proportional relationship according to different mission characteristics.

[0202] Then the objective function is:

[0203] min J = -a1m1(t l ) - a2m2(t f ).

[0204] where a1 is the weight coefficient of the terminal mass of the recovery stage moving body, a2 is the weight coefficient of the terminal mass of the orbital stage moving body, t l is the landing time at the relative separation moment, m1(t l ) is the mass of the recovery stage moving body at time t l , t f is the terminal time of the orbital stage flight section, and m2(t f ) is the mass of the orbital stage moving body at time t f .

[0205] The larger the ratio of a1 to a2, the more fuel is used for recovery, and vice versa, the more fuel is used for injection.

[0206] 104. Optimize the entire trajectory of the reusable rocket based on the objective function, the motion equations of each stage, and the constraint conditions.

[0207] After obtaining the objective function, the equations of motion for each stage, and the constraints, the optimal solution of the objective function can be obtained based on the constraints through the equations of motion. The optimal solution is used to optimize the entire trajectory of the reusable rocket.

[0208] The solution process will not be elaborated here.

[0209] To minimize the loss of the reusable rocket's carrying capacity as much as possible and improve the adaptability of the reusable rocket during the ascent and landing phases, it is necessary to comprehensively consider the motion characteristics and constraints throughout the flight of the reusable rocket. The present invention proposes a method for describing the problem of optimizing the entire trajectory of a reusable rocket with two moving bodies and multiple flight segments. The reusable rocket is regarded as two moving bodies, namely the recovery-stage moving body and the orbit-insertion-stage moving body. By jointly considering the motion characteristics of the two moving bodies in different flight segments, the recovery-stage moving body provides power before separation, and they have the same motion law. After separation, the orbit-insertion-stage moving body aims to send the payload into the target orbit, while the recovery-stage moving body aims to achieve a soft landing at a fixed point, each having its own independent motion characteristics and terminal goals. On the premise of being able to achieve payload orbit insertion and the recovery-stage fixed-point landing, the motion during the ascent and landing phases is comprehensively considered to describe the problem of optimizing the entire trajectory of the reusable rocket.

[0210] Specifically, first, by analyzing the motion characteristics of the reusable rocket during the ascent and landing phases, the equations of motion for the ascent and landing phases are described respectively in the inertial coordinate system at the launch point and the vertical landing coordinate system, and after separation, the orbit-insertion-stage moving body and the recovery-stage moving body are considered as two moving bodies with different terminal goals. Then, according to the characteristics of each flight segment, only the constraints that need to be considered in this flight segment and the connection constraints between segments are described in each flight segment. Finally, to comprehensively consider the robustness and adaptability of the motion of the reusable rocket during the ascent and landing phases, an optimization objective function including the fuel consumption during the ascent and landing phases is described, thus forming a complete problem of optimizing the entire trajectory of the reusable rocket.

[0211] As Figure 2 shown, first, the description of the equations of motion for the upward flight segment, the description of the constraints for the ascent segment before separation, the description of the constraints for the orbit-insertion-stage flight segment, the description of the constraints for the recovery-stage landing segment, and the description of the objective function are carried out. Then, based on the description of the equations of motion for the upward flight segment, the description of the constraints for the ascent segment before separation, the description of the constraints for the orbit-insertion-stage flight segment, the description of the constraints for the recovery-stage landing segment, and the description of the objective function, the problem of optimizing the entire trajectory of the reusable rocket is obtained.

[0212] The method for describing the problem of optimizing the entire trajectory of the reusable rocket provided in this embodiment reduces the dimension of the optimization problem of the reusable rocket and solves the modeling problem of having to consider two equations of motion at the same time after the separation of the reusable rocket.

[0213] In addition, according to the differences in the motion characteristics of the ascent stage and the landing stage, the method for describing the full - trajectory optimization problem of the reusable rocket provided in this embodiment describes the two motions in different coordinate systems, and organically combines the variables of the two coordinate systems through coordinate transformation at the separation moment, reducing the complexity of the optimization problem.

[0214] Furthermore, by analyzing the flight process of the reusable rocket and according to the characteristics of different flight segments, the method for describing the full - trajectory optimization problem of the reusable rocket provided in this embodiment only describes the constraint conditions that need to be considered in each flight segment and ignores other constraints in each flight segment, simplifying the optimization problem.

[0215] Meanwhile, the method for describing the full - trajectory optimization problem of the reusable rocket provided in this embodiment proposes an objective function that comprehensively considers the fuel consumption in the ascent stage and the landing stage. By adjusting the weight coefficient, the reusable rocket has a certain anti - interference ability and deviation adaptation ability for both the ascent stage and the landing stage under the condition of meeting all constraints.

[0216] The method for describing the full - trajectory optimization problem of the reusable rocket provided in this embodiment can be used as the input of a numerical optimization algorithm to offline analyze the feasibility of rocket recovery in different launch missions.

[0217] This embodiment provides a method for describing the full - trajectory optimization problem of a reusable rocket, which divides the full trajectory of the reusable rocket into an ascent stage and a landing stage; respectively determines the motion equations and constraint conditions of the ascent stage and the landing stage; determines the objective function; and optimizes the full trajectory of the reusable rocket based on the objective function, the motion equations and constraint conditions of each stage. The method provided in this embodiment divides the full trajectory of the reusable rocket into an ascent stage and a landing stage, and optimizes according to the motion equations, constraint conditions and objective function of the ascent stage and the landing stage, reducing the dimension of the optimization problem of the reusable rocket and solving the optimization problem that two motion equations need to be considered at the same moment after the separation of the reusable rocket.

[0218] Based on the same inventive concept of the method for describing the full - trajectory optimization problem of the reusable rocket, this embodiment provides an electronic device, including: a memory, a processor, and a computer program.

[0219] Wherein, the computer program is stored in the memory and is configured to be executed by the processor to implement the method for describing the full - trajectory optimization problem of the reusable rocket as Figure 1 shown.

[0220] Specifically,

[0221] The full trajectory of the reusable rocket is divided into an ascent stage and a landing stage.

[0222] The motion equations and constraint conditions of the ascent stage and the landing stage are respectively determined.

[0223] Determine the objective function.

[0224] Optimize the entire trajectory of the reusable rocket based on the objective function, the equations of motion at each stage, and the constraints.

[0225] Optionally, the reusable rocket includes a recovery-stage moving body and an orbital-stage moving body.

[0226] Optionally, the reference coordinate system for the ascent stage is the inertial coordinate system of the launch point, and the reference coordinate system for the landing stage is the vertical landing coordinate system.

[0227] Optionally, in the inertial coordinate system of the launch point, the coordinate origin O is the launch point, the OY axis points outward from the surface along the line connecting the center of the Earth and the launch point, the OX axis is perpendicular to the OY axis, points in the launch direction in the horizontal plane, and the angle with the meridian plane of the launch point is the launch azimuth angle, and the OZ axis satisfies the right-hand rule.

[0228] Optionally, the ascent stage includes the pre-separation ascent stage and the orbital-stage flight segment.

[0229] In the pre-separation ascent stage, it includes the motion characteristics of the recovery-stage moving body and the orbital-stage moving body. Among them, the recovery-stage moving body and the orbital-stage moving body are powered by the engine in the recovery-stage moving body, and the recovery-stage moving body and the orbital-stage moving body have the same motion characteristics.

[0230] In the orbital-stage flight segment, it only includes the motion characteristics of the orbital-stage moving body.

[0231] Optionally, determine the equations of motion and constraints for the ascent stage, including:

[0232] Determine the equations of motion for the pre-separation ascent stage and the orbital-stage flight segment.

[0233] Determine the constraints for the pre-separation ascent stage and the orbital-stage flight segment.

[0234] Optionally, the equations of motion for the pre-separation ascent stage include the equations of motion for the pre-separation ascent stage of the recovery-stage moving body and the equations of motion for the pre-separation ascent stage of the orbital-stage moving body.

[0235] Determine the equations of motion for the pre-separation ascent stage, including:

[0236] Determine the equations of motion for the pre-separation ascent stage of the recovery-stage moving body as:

[0237]

[0238] Where, · is the first derivative operator, P1 is the position vector of the recovery-stage vehicle, V1 is the velocity vector of the recovery-stage vehicle, T1 is the magnitude of the engine thrust of the recovery-stage vehicle, m1 is the mass of the recovery-stage vehicle, m2 is the mass of the orbital-stage vehicle, u1 is the thrust vector of the recovery-stage vehicle, D is the aerodynamic drag, μ is the Earth's gravitational coefficient, r1 is the distance vector between the centroid of the recovery-stage vehicle where the gravitational acceleration component is used and the Earth's center, and dm1 is the engine mass flow rate per second of the recovery-stage vehicle.

[0239] The equations of motion for the ascending stage before separation of the orbital-stage vehicle are determined as follows:

[0240]

[0241] Where, P2 is the position vector of the orbital-stage vehicle, V2 is the velocity vector of the orbital-stage vehicle, and r2 is the distance vector between the centroid of the orbital-stage vehicle where the gravitational acceleration component is used and the Earth's center.

[0242] Optionally, the equations of motion for the flight stage of the orbital-stage vehicle are determined, including:

[0243] The equations of motion for the flight stage of the orbital-stage vehicle are determined as follows:

[0244]

[0245] Where, T2 is the magnitude of the engine thrust of the orbital-stage vehicle, u2 is the thrust vector of the orbital-stage vehicle, and dm2 is the engine mass flow rate per second of the orbital-stage vehicle.

[0246] Optionally, the constraint conditions for the ascending stage before separation are determined, including:

[0247] The initial launch state constraint conditions, thrust direction constraint conditions, vertical ascending stage constraint conditions, mass constraint conditions, and bending moment constraint conditions are determined.

[0248] Optionally, the initial launch state constraint conditions are as follows:

[0249] [P1, V1, m1, P2, V2, m2](t0) = [P0, V0, m 10 , P0, V0, m 20 .

[0250] Where, P1 is the position vector of the recovery-stage vehicle, V1 is the velocity vector of the recovery-stage vehicle, m1 is the mass of the recovery-stage vehicle, m2 is the mass of the orbital-stage vehicle, P2 is the position vector of the orbital-stage vehicle, V2 is the velocity vector of the orbital-stage vehicle, t0 is the launch time of the reusable rocket, P0 is the position vector of the reusable rocket, V0 is the velocity vector of the reusable rocket, and m 10 is the initial mass of the recovery-stage vehicle at the launch time, m20 is the initial mass of the in-orbit stage moving body at the launch moment.

[0251] Optionally, the thrust direction constraint conditions include:

[0252] ‖u1‖ = 1, -1 ≤ u 1x,1y,1z ≤ 1.

[0253] where u1 is the thrust vector of the recovery stage moving body, u1 = [u 1x , u 1y , u 1z T , u 1x is the thrust direction of the recovery stage moving body on the OX axis, u 1y is the thrust direction of the recovery stage moving body on the OY axis, u 1z is the thrust direction of the recovery stage moving body on the OZ axis.

[0254] Optionally, the vertical ascent stage constraint conditions include:

[0255] u1 = [0, 1, 0] T .

[0256] where u1 is the thrust vector of the recovery stage moving body, u1 = [u 1x , u 1y , u 1z T , u 1x is the thrust direction of the recovery stage moving body on the OX axis, u 1y is the thrust direction of the recovery stage moving body on the OY axis, u 1z is the thrust direction of the recovery stage moving body on the OZ axis.

[0257] Optionally, the mass constraint conditions include:

[0258] m1(t s ) ≥ m f1min .

[0259]

[0260] where m1 is the mass of the recovery stage moving body, m f1min is the minimum remaining mass of the recovery stage moving body before separation, is the maximum flight time of the recovery stage moving body during the ascent stage, t s is the separation moment.

[0261] Optionally, the bending moment constraint conditions include:

[0262] |qα| ≤ Q αmax .

[0263] ​​

[0264] Among them, q is the dynamic pressure, V is the velocity vector of the reusable rocket, and V E is the velocity generated by the Earth's rotation, and Q αmax is the maximum allowable bending moment, α is the angle of attack, and u is the thrust vector of the reusable rocket.

[0265] Optionally, determine the constraint conditions for the in-orbit stage flight segment, including:

[0266] Determine the state constraint conditions at the separation moment, the mass constraint conditions of the in-orbit stage, and the terminal constraint conditions of the target orbit elements.

[0267] Optionally, the state constraint conditions at the separation moment are:

[0268] The initial point position and the initial point velocity of the in-orbit stage flight segment are equal to the state of the reusable rocket at the separation moment.

[0269] The initial point mass of the in-orbit stage flight segment is the initial mass of the in-orbit stage moving body at the launch moment.

[0270] Optionally, the mass constraint conditions of the in-orbit stage include:

[0271] m2(t f )≥m f2min .

[0272] Among them, m2 is the mass of the in-orbit stage moving body, and m f2min is the total mass of the launch vehicle and the payload after the fuel of the in-orbit stage moving body is exhausted, and t f is the terminal time of the in-orbit stage flight segment.

[0273] Optionally, the terminal constraint conditions of the target orbit elements include:

[0274] [a f ,e f ,i f ,Ω f ,w f T =Fun orbit ([P2,V2](t f ))。

[0275]

[0276]

[0277]

[0278] [H x H y H​x T = H = P 2f × V 2f .

[0279]

[0280]

[0281]

[0282] Wherein, a f is the semi-major axis of the target orbit, e f is the eccentricity, i f is the inclination, Ω f is the longitude of the ascending node, w f is the argument of perigee, Fun orbit () is the nonlinear relationship function between the target orbit elements and the terminal velocity position, P2 is the position vector of the launch stage vehicle, V2 is the velocity vector of the launch stage vehicle, t f is the terminal time of the launch stage flight segment, r2 is the distance vector between the centroid of the launch stage vehicle where the gravitational acceleration component is used and the center of the earth, μ is the earth's gravitational coefficient, is the velocity component of the launch stage vehicle on the OX axis, is the velocity component of the launch stage vehicle on the OY axis, is the velocity component of the launch stage vehicle on the OZ axis, x2 is the position component of the launch stage vehicle on the OX axis, y2 is the position component of the launch stage vehicle on the OY axis, z2 is the position component of the launch stage vehicle on the OZ axis, H is the angular momentum per unit mass, R0 is the radius of the earth, H x is the component of H on the OX axis, H y is the component of H on the OY axis, H z is the component of H on the OZ axis, P 2f is the position vector of the launch stage vehicle at the terminal moment, V 2f is the velocity vector of the launch stage vehicle at the terminal moment.

[0283] Optionally, in the vertical landing coordinate system, the coordinate origin O e is the center of the earth, O e Y l axis points from the center of the earth to the centroid of the reusable rocket, O e Y l axis is perpendicular to O e Y l axis in the local horizontal plane, and the included angle with the meridian plane where the reusable rocket is located is the launch azimuth, O e Z l axis satisfies the right-hand rule.

[0284] ​Optionally, determine the equations of motion for the landing phase, including:

[0285] The equations of motion for the landing phase are determined as:

[0286]

[0287]

[0288]

[0289]

[0290]

[0291]

[0292]

[0293]

[0294]

[0295] where · is the first derivative operator, r1 is the distance vector between the center of mass of the reusable stage and the center of the Earth used for the gravitational acceleration component, V 1x is the velocity component of the reusable stage in the O e X l axis, V 1y is the velocity component of the reusable stage in the O e Y l axis, V 1z is the velocity component of the reusable stage in the O e Z l axis, λ1 is the longitude of the center of mass of the reusable rocket in the geocentric equatorial coordinate system, B1 is the latitude of the center of mass of the reusable rocket in the geocentric equatorial coordinate system, A0 is the launch azimuth angle, m1 is the mass of the reusable stage, T1 is the engine thrust amplitude of the reusable stage, is the pitch angle of the reusable stage, ψ1 is the yaw angle of the reusable stage, D x is the component of the air resistance in the O e X l axis, D y is the component of the air resistance in the O e Y l axis, D z is the component of the air resistance in the O e Z l axis, ω E is the amplitude of the Earth's angular velocity, μ is the Earth's gravitational coefficient, For the pitch angular velocity, ω, of the recovery-stage vehicle 1ψ For the yaw angular velocity of the recovery-stage vehicle, and dm1 is the engine mass flow rate per second of the recovery-stage vehicle.

[0296] Optionally, determine the constraint conditions for the landing phase, including:

[0297] Determine the initial state constraint conditions, mass flow rate per second constraint conditions, attitude angular velocity constraint conditions, stagnation point heat flux constraint conditions, dynamic pressure constraint conditions, aerodynamic overload constraint conditions, angle constraint conditions, and terminal state constraint conditions for the landing phase.

[0298] Optionally, the initial state constraint conditions for the landing phase include:

[0299] [P1, V1, m1](t s ) = [P 1s , V 1s , m 1s

[0300] where P1 is the position vector of the recovery-stage vehicle, V1 is the velocity vector of the recovery-stage vehicle, m1 is the mass of the recovery-stage vehicle, t s is the separation moment, P 1s is the position vector of the recovery-stage vehicle at the separation moment, V 1s is the velocity vector of the recovery-stage vehicle at the separation moment, m 1s is the mass of the recovery-stage vehicle at the separation moment.

[0301] Optionally, the mass flow rate per second constraint conditions include:

[0302]

[0303] where dm1 is the engine mass flow rate per second of the recovery-stage vehicle, dm min is the minimum engine mass flow rate per second, dm max is the maximum engine mass flow rate per second.

[0304] Optionally, the attitude angular velocity constraint conditions include:

[0305]

[0306] where is the pitch angular velocity of the recovery-stage vehicle, ω 1ψ is the yaw angular velocity of the recovery-stage vehicle, ω max1 is the attitude angular velocity amplitude in the rarefied atmosphere section, ω max2 is the attitude angular velocity amplitude in the dense atmosphere section, ω max3 is the attitude angular velocity amplitude in the powered soft landing section.

[0307] ​Optionally, the stagnation heat flux constraint conditions include:

[0308]

[0309] Among them, Q s is the current stagnation heat flux value of the reusable rocket, k s is the stagnation heat flux coefficient related to the shape of the reusable rocket, ρ is the atmospheric density at the corresponding altitude, V1 is the velocity vector of the recovery stage moving body, ρ Q and V Q are the parameters for calculating the stagnation heat flux, Q smax is the maximum value of the stagnation heat flux.

[0310] Optionally, the dynamic pressure constraint conditions include:

[0311] q = 0.5ρ‖V1‖ 2 ≤q max .

[0312] Among them, q is the dynamic pressure, ρ is the atmospheric density at the corresponding altitude, V1 is the velocity vector of the recovery stage moving body, q max is the maximum value of the dynamic pressure.

[0313] Optionally, the aerodynamic overload constraint conditions include:

[0314]

[0315] Among them, n D is the aerodynamic overload, m1 is the mass of the recovery stage moving body, D x is the component of the air resistance in the O e X l axis, D y is the component of the air resistance in the O e Y l axis, D z is the component of the air resistance in the O e Z l axis, n Dmax is the maximum value of the aerodynamic overload, g0 is the standard acceleration of gravity.

[0316] Optionally, the angle constraint conditions include:

[0317] Powered soft landing section.

[0318] Powered soft landing section.

[0319] Among them, is the pitch angle of the recovery stage moving body, is the maximum deviation of the pitch angle from the local plumb line, V 1xFor the velocity component of the recovery - level moving body in the O e X l axis, V 1y For the velocity component of the recovery - level moving body in the O e Y l axis, V 1z For the velocity component of the recovery - level moving body in the O e Z l axis, Δθ V is the maximum deviation between the velocity direction and the local plumb line.

[0320] Optionally, the terminal - state constraint conditions for the landing phase include: landing - position constraint conditions, landing - velocity constraint conditions, landing - attitude - angle and velocity - inclination - angle constraint conditions, and landing - mass constraint conditions.

[0321] Optionally, the landing - position constraint conditions include:

[0322] h(t l ) = h l

[0323] ‖λ(t l ) - λ l ‖ ≤ Δλ l

[0324] ‖B(t l ) - B l ‖ ≤ ΔB l

[0325] where t l is the landing time relative to the separation moment, h(t l ) is the landing altitude at time t l , h l is the altitude of the desired landing point, λ(t l ) is the longitude of the reusable - rocket terminal at time t l , λ l is the longitude of the reusable - rocket terminal at the landing moment, Δλ l is the maximum deviation of the longitude of the reusable - rocket terminal, B(t l ) is the latitude of the reusable - rocket terminal at time t l , B l is the latitude of the reusable - rocket terminal at the landing moment, ΔB l is the maximum deviation of the latitude of the reusable - rocket terminal.

[0326] Optionally, the landing - velocity constraint conditions include:

[0327] V ylmax ≤ V 1y (t l ) ≤ 0

[0328] -V xzlmax ≤V 1x (t l ),V 1z (t l )≤V xzlmax

[0329] Among them, t l is the landing time at the relative separation moment, V 1x (t l ) is the velocity component of the recovery-stage moving body at time t l on the O e X l axis, V 1y (t l ) is the velocity component of the recovery-stage moving body at time t l on the O e Y l axis, V 1z (t l ) is the velocity component of the recovery-stage moving body at time t l on the O e Z l axis, V ylmax is the maximum touchdown velocity borne by the landing leg, V xzlmax is the maximum lateral velocity that causes tipping.

[0330] Optionally, the landing attitude angle and velocity inclination constraints include:

[0331]

[0332]

[0333] Among them, t l is the landing time at the relative separation moment, is the pitch angle of the recovery-stage moving body at time t l , V 1x (t l ) is the velocity component of the recovery-stage moving body at time t l on the O e X l axis, V 1y (t l ) is the velocity component of the recovery-stage moving body at time t l on the O e Y l axis, V 1z (t l ) is the velocity component of the recovery-stage moving body at time t l on the O e Z l axis, Δθ Vlis the maximum value of the angle between the velocity at the landing moment and the rocket body.

[0334] Optionally, the landing mass constraint conditions include:

[0335] m1(t l ) ≥ m 1lmin

[0336] where t l is the landing time at the relative separation moment, m1(t l ) is the mass of the reusable stage moving body at time t l , and m 1lmin is the minimum remaining mass of the reusable stage moving body.

[0337] Optionally, determining the objective function includes:

[0338] Determine the following objective function:

[0339] min J = -a1m1(t l ) - a2m2(t f ).

[0340] where a1 is the weight coefficient of the terminal mass of the reusable stage moving body, a2 is the weight coefficient of the terminal mass of the injection stage moving body, t l is the landing time at the relative separation moment, m1(t l ) is the mass of the reusable stage moving body at time t l , t f is the terminal time of the injection stage flight segment, and m2(t f ) is the mass of the injection stage moving body at time t f .

[0341] This embodiment provides an electronic device that divides the entire process of a reusable rocket into a rising stage and a landing stage; determines the motion equations and constraint conditions of the rising stage and the landing stage respectively; determines the objective function; and optimizes the entire trajectory of the reusable rocket based on the objective function, the motion equations and constraint conditions of each stage. The electronic device provided in this embodiment divides the entire process of the reusable rocket into a rising stage and a landing stage, and optimizes according to the motion equations, constraint conditions and objective function of the rising stage and the landing stage, reducing the dimension of the optimization problem of the reusable rocket and solving the optimization problem of considering two motion equations at the same moment after the separation of the reusable rocket.

[0342] Based on the same inventive concept of the method for describing the optimization problem of the entire trajectory of a reusable rocket, this embodiment provides a computer-readable storage medium, on which a computer program is stored. The computer program is executed by a processor to implement the method for describing the optimization problem of the entire trajectory of a reusable rocket as Figure 1 shown.

[0343] Specifically,

[0344] The reusable rocket's entire journey is divided into an ascent stage and a landing stage.

[0345] The equations of motion and constraint conditions for the ascent stage and the landing stage are determined respectively.

[0346] The objective function is determined.

[0347] Based on the objective function, the equations of motion and constraint conditions for each stage, the entire trajectory of the reusable rocket is optimized.

[0348] Optionally, the reusable rocket includes a recovery-stage moving body and an orbit-insertion-stage moving body.

[0349] Optionally, the reference coordinate system for the ascent stage is the inertial coordinate system of the launch point, and the reference coordinate system for the landing stage is the vertical landing coordinate system.

[0350] Optionally, in the inertial coordinate system of the launch point, the coordinate origin O is the launch point, the OY axis points outward from the surface along the line connecting the center of the earth and the launch point, the OX axis is perpendicular to the OY axis, points in the launch direction in the horizontal plane, and the angle with the meridian plane of the launch point is the launch azimuth angle, and the OZ axis satisfies the right-hand rule.

[0351] Optionally, the ascent stage includes the pre-separation ascent stage and the orbit-insertion-stage flight segment.

[0352] In the pre-separation ascent stage, the motion characteristics of the recovery-stage moving body and the orbit-insertion-stage moving body are included. Among them, the recovery-stage moving body and the orbit-insertion-stage moving body are powered by the engine in the recovery-stage moving body, and the recovery-stage moving body and the orbit-insertion-stage moving body have the same motion characteristics.

[0353] In the orbit-insertion-stage flight segment, only the motion characteristics of the orbit-insertion-stage moving body are included.

[0354] Optionally, determining the equations of motion and constraint conditions for the ascent stage includes:

[0355] Determining the equations of motion for the pre-separation ascent stage and the orbit-insertion-stage flight segment.

[0356] Determining the constraint conditions for the pre-separation ascent stage and the orbit-insertion-stage flight segment.

[0357] Optionally, the equation of motion for the pre-separation ascent stage includes the equation of motion for the pre-separation ascent stage of the recovery-stage moving body and the equation of motion for the pre-separation ascent stage of the orbit-insertion-stage moving body.

[0358] Determining the equation of motion for the pre-separation ascent stage includes:

[0359] Determining the equation of motion for the pre-separation ascent stage of the recovery-stage moving body as:

[0360]

[0361] Wherein, · is the first derivative operator, P1 is the position vector of the recovery-stage moving body, V1 is the velocity vector of the recovery-stage moving body, T1 is the engine thrust amplitude of the recovery-stage moving body, m1 is the mass of the recovery-stage moving body, m2 is the mass of the orbit-insertion-stage moving body, u1 is the thrust vector of the recovery-stage moving body, D is the aerodynamic drag, μ is the earth's gravitational coefficient, r1 is the distance vector between the centroid of the recovery-stage moving body where the gravitational acceleration component is used and the earth's center, and dm1 is the engine mass flow rate per second of the recovery-stage moving body.

[0362] The motion equation of the ascending stage before separation of the orbit-insertion-stage moving body is determined as:

[0363]

[0364] Wherein, P2 is the position vector of the orbit-insertion-stage moving body, V2 is the velocity vector of the orbit-insertion-stage moving body, and r2 is the distance vector between the centroid of the orbit-insertion-stage moving body where the gravitational acceleration component is used and the earth's center.

[0365] Optionally, determining the motion equation of the flight stage of the orbit-insertion-stage moving body includes:

[0366] The motion equation of the flight stage of the orbit-insertion-stage moving body is determined as:

[0367]

[0368] Wherein, T2 is the engine thrust amplitude of the orbit-insertion-stage moving body, u2 is the thrust vector of the orbit-insertion-stage moving body, and dm2 is the engine mass flow rate per second of the orbit-insertion-stage moving body.

[0369] Optionally, determining the constraint conditions of the ascending stage before separation includes:

[0370] Determining the launch initial state constraint conditions, thrust direction constraint conditions, vertical ascending stage constraint conditions, mass constraint conditions, and bending moment constraint conditions.

[0371] Optionally, the launch initial state constraint conditions are:

[0372] [P1, V1, m1, P2, V2, m2](t0) = [P0, V0, m 10 , P0, V0, m 20 .

[0373] Among them, P1 is the position vector of the reusable booster, V1 is the velocity vector of the reusable booster, m1 is the mass of the reusable booster, m2 is the mass of the orbital stage, P2 is the position vector of the orbital stage, V2 is the velocity vector of the orbital stage, t0 is the launch time of the reusable rocket, P0 is the position vector of the reusable rocket, V0 is the velocity vector of the reusable rocket, m 10 is the initial mass of the reusable booster at the launch time, m 20 is the initial mass of the orbital stage at the launch time.

[0374] Optionally, the thrust direction constraint conditions include:

[0375] ‖u1‖ = 1, -1 ≤ u 1x,1y,1z ≤ 1.

[0376] Among them, u1 is the thrust vector of the reusable booster, u1 = [u 1x , u 1y , u 1z T , u 1x is the thrust direction of the reusable booster on the OX axis, u 1y is the thrust direction of the reusable booster on the OY axis, u 1z is the thrust direction of the reusable booster on the OZ axis.

[0377] Optionally, the vertical ascent section constraint conditions include:

[0378] u1 = [0, 1, 0] T .

[0379] Among them, u1 is the thrust vector of the reusable booster, u1 = [u 1x , u 1y , u 1z T , u 1x is the thrust direction of the reusable booster on the OX axis, u 1y is the thrust direction of the reusable booster on the OY axis, u 1z is the thrust direction of the reusable booster on the OZ axis.

[0380] Optionally, the mass constraint conditions include:

[0381] m1(t s ) ≥ m f1min .

[0382]

[0383] Among them, m1 is the mass of the reusable booster, m f1min is the minimum remaining mass of the reusable booster before separation,​​ For the maximum flight time of the ascending stage of the recoverable vehicle, t s is the separation moment.

[0384] Optionally, the bending moment constraint conditions include:

[0385] |qα| ≤ Q αmax .

[0386]

[0387] where q is the dynamic pressure, V is the velocity vector of the reusable rocket, V E is the velocity generated by the Earth's rotation, Q αmax is the maximum allowable bending moment, α is the angle of attack, and u is the thrust vector of the reusable rocket.

[0388] Optionally, the constraint conditions for the flight segment of the orbital stage include:

[0389] Determine the state constraint conditions at the separation moment, the mass constraint conditions of the orbital stage, and the terminal constraint conditions of the target orbit elements.

[0390] Optionally, the state constraint conditions at the separation moment are:

[0391] The initial point position and the initial point velocity of the flight segment of the orbital stage are equal to the state of the reusable rocket at the separation moment.

[0392] The initial point mass of the flight segment of the orbital stage is the initial mass of the orbital vehicle at the launch moment.

[0393] Optionally, the mass constraint conditions of the orbital stage include:

[0394] m2(t f ) ≥ m f2min .

[0395] where m2 is the mass of the orbital vehicle, and m f2min is the total mass of the launch vehicle and the payload after the fuel of the orbital vehicle is exhausted, and t f is the terminal time of the flight segment of the orbital stage.

[0396] Optionally, the terminal constraint conditions of the target orbit elements include:

[0397] [a f , e f , i f , Ω f , w f T = Fun orbit ([P2, V2](t f ))。 ​

[0398]

[0399]

[0400]

[0401] [H x H y H z T =H=P 2f ×V 2f .

[0402]

[0403]

[0404]

[0405] Among them, a f is the semi-major axis of the target orbit, e f is the eccentricity, i f is the inclination angle, Ω f is the longitude of the ascending node, w f is the argument of perigee, Fun orbit () is the non-linear relationship function between the target orbit elements and the terminal velocity position, P2 is the position vector of the launch vehicle stage moving body, V2 is the velocity vector of the launch vehicle stage moving body, t f is the terminal time of the launch vehicle stage flight segment, r2 is the distance vector between the center of mass of the launch vehicle stage moving body where the gravitational acceleration component is used and the center of the earth, μ is the earth's gravitational coefficient, is the velocity component of the launch vehicle stage moving body on the OX axis, is the velocity component of the launch vehicle stage moving body on the OY axis, is the velocity component of the launch vehicle stage moving body on the OZ axis, x2 is the position component of the launch vehicle stage moving body on the OX axis, y2 is the position component of the launch vehicle stage moving body on the OY axis, z2 is the position component of the launch vehicle stage moving body on the OZ axis, R0 is the radius of the earth, H is the angular momentum per unit mass, H x is the component of H on the OX axis, H y is the component of H on the OY axis, H z is the component of H on the OZ axis, P 2f is the position vector of the launch vehicle stage moving body at the terminal moment, V 2f is the velocity vector of the launch vehicle stage moving body at the terminal moment.

[0406] Optionally, in the vertical landing coordinate system, the coordinate origin O e is the center of the earth, O e Y l ​The axis points from the earth's center to the centroid of the reusable rocket, O e X l The axis is perpendicular to O in the local horizontal plane e Y l The axis, and the angle between the meridian plane where the reusable rocket is located and the axis is the launch azimuth angle, O e Z l The axis satisfies the right-hand rule.

[0407] Optionally, determine the equations of motion for the landing phase, including:

[0408] Determine the equations of motion for the landing phase as:

[0409]

[0410]

[0411]

[0412]

[0413]

[0414]

[0415]

[0416]

[0417]

[0418] where, · is the first derivative operator, r1 is the distance vector between the centroid of the recovery stage moving body and the earth's center used for the gravitational acceleration component, V 1x is the velocity component of the recovery stage moving body in the O e X l axis, V 1y is the velocity component of the recovery stage moving body in the O e Y l axis, V 1z is the velocity component of the recovery stage moving body in the O e Z l axis, λ1 is the longitude of the centroid of the reusable rocket in the geocentric equatorial coordinate system, B1 is the latitude of the centroid of the reusable rocket in the geocentric equatorial coordinate system, A0 is the launch azimuth angle, m1 is the mass of the recovery stage moving body, T1 is the engine thrust amplitude of the recovery stage moving body, is the pitch angle of the recovery stage moving body, ψ1 is the yaw angle of the recovery stage moving body, D x is the air resistance in the O e X lComponent of the axis, D y is the air resistance at O e Y l Component of the axis, D z is the air resistance at O e Z l Component of the axis, ω E is the amplitude of the angular velocity of the Earth's rotation, μ is the coefficient of the Earth's gravitational force, is the pitch angular velocity of the recovery-stage moving body, ω 1ψ is the yaw angular velocity of the recovery-stage moving body, dm1 is the engine's mass flow rate per second of the recovery-stage moving body.

[0419] Optionally, determine the constraint conditions for the landing stage, including:

[0420] Determine the initial state constraint conditions, mass flow rate constraint conditions, attitude angular velocity constraint conditions, stagnation point heat flux constraint conditions, dynamic pressure constraint conditions, aerodynamic overload constraint conditions, angle constraint conditions, and terminal state constraint conditions for the landing stage.

[0421] Optionally, the initial state constraint conditions for the landing stage include:

[0422] [P1, V1, m1](t s ) = [P 1s , V 1s , m 1s

[0423] where P1 is the position vector of the recovery-stage moving body, V1 is the velocity vector of the recovery-stage moving body, m1 is the mass of the recovery-stage moving body, t s is the separation moment, P 1s is the position vector of the recovery-stage moving body at the separation moment, V 1s is the velocity vector of the recovery-stage moving body at the separation moment, m 1s is the mass of the recovery-stage moving body at the separation moment.

[0424] Optionally, the mass flow rate constraint conditions include:

[0425]

[0426] where dm1 is the engine's mass flow rate per second of the recovery-stage moving body, dm min is the minimum mass flow rate of the engine, dm max is the maximum mass flow rate of the engine.

[0427] Optionally, the attitude angular velocity constraint conditions include:

[0428]

[0429] where, ​For the pitch angular velocity of the recovery - stage vehicle, ω 1ψ For the yaw angular velocity of the recovery - stage vehicle, ω max1 For the attitude angular velocity amplitude in the rarefied - atmosphere section, ω max2 For the attitude angular velocity amplitude in the dense - atmosphere section, ω max3 For the attitude angular velocity amplitude in the powered - soft - landing section.

[0430] Optionally, the stagnation - heat - flux constraint conditions include:

[0431]

[0432] Among them, Q s is the current stagnation - heat - flux value of the reusable rocket, k s is the stagnation - heat - flux coefficient related to the shape of the reusable rocket, ρ is the atmospheric density at the corresponding altitude, V1 is the velocity vector of the recovery - stage vehicle, ρ Q and V Q are the parameters for calculating the stagnation heat flux, Q smax is the maximum value of the stagnation heat flux.

[0433] Optionally, the dynamic - pressure constraint conditions include:

[0434] q = 0.5ρ‖V1‖ 2 ≤q max .

[0435] Among them, q is the dynamic pressure, ρ is the atmospheric density at the corresponding altitude, V1 is the velocity vector of the recovery - stage vehicle, q max is the maximum value of the dynamic pressure.

[0436] Optionally, the aerodynamic - overload constraint conditions include:

[0437]

[0438] Among them, n D is the aerodynamic overload, m1 is the mass of the recovery - stage vehicle, D x is the component of the air resistance along the O e X l axis, D y is the component of the air resistance along the O e Y l axis, D z is the component of the air resistance along the O e Z l axis, n Dmax is the maximum value of the aerodynamic overload, g0 is the standard acceleration of gravity.

[0439] Optionally, the angle constraint conditions include:

[0440] Powered soft landing stage.

[0441] Powered soft landing stage.

[0442] Among them, is the pitch angle of the reusable rocket stage, is the maximum deviation between the pitch angle and the local plumb line, V 1x is the velocity component of the reusable rocket stage along the O e X l axis, V 1y is the velocity component of the reusable rocket stage along the O e Y l axis, V 1z is the velocity component of the reusable rocket stage along the O e Z l axis, Δθ V is the maximum deviation between the velocity direction and the local plumb line.

[0443] Optionally, the terminal state constraint conditions for the landing stage include: landing position constraint conditions, landing velocity constraint conditions, landing attitude angle and velocity inclination constraint conditions, and landing mass constraint conditions.

[0444] Optionally, the landing position constraint conditions include:

[0445] h(t l ) = h l

[0446] ‖λ(t l ) - λ l ‖ ≤ Δλ l

[0447] ‖B(t l ) - B l ‖ ≤ ΔB l

[0448] Among them, t l is the landing time relative to the separation moment, h(t l ) is the landing altitude at time t l , h l is the altitude of the desired landing point, λ(t l ) is the longitude of the reusable rocket terminal at time t l , λ l is the longitude of the reusable rocket terminal at the landing moment, Δλ l is the maximum deviation of the longitude of the reusable rocket terminal, B(t l ) is the latitude of the reusable rocket terminal at time t l , B l is the latitude of the reusable rocket terminal at the landing moment, ΔBl The maximum deviation of the terminal latitude of the reusable rocket.

[0449] Optionally, the landing speed constraint conditions include:

[0450] V ylmax ≤V 1y (t l )≤0

[0451] -V xzlmax ≤V 1x (t l ),V 1z (t l )≤V xzlmax

[0452] Where t l is the landing time relative to the separation moment, V 1x (t l ) is the velocity component of the recovery stage moving body at time t l on the O e X l axis, V 1y (t l ) is the velocity component of the recovery stage moving body at time t l on the O e Y l axis, V 1z (t l ) is the velocity component of the recovery stage moving body at time t l on the O e Z l axis, V ylmax is the maximum touchdown speed borne by the landing leg, V xzlmax is the maximum lateral speed causing tipping.

[0453] Optionally, the landing attitude angle and velocity inclination constraint conditions include:

[0454]

[0455]

[0456] Where t l is the landing time relative to the separation moment, is the pitch angle of the recovery stage moving body at time t l V 1x (t l ) is the velocity component of the recovery stage moving body at time t l on the O e X l axis, V 1y (t l ) is the velocity component of the recovery stage moving body at time tl Velocity component in the O e Y l axis, V 1z (t l ) is the motion body of the recovery stage at time t l Velocity component in the O e Z l axis, Δθ Vl is the maximum value of the angle between the velocity at the landing moment and the rocket body.

[0457] Optionally, the landing mass constraint conditions include:

[0458] m1(t l ) ≥ m 1lmin

[0459] where t l is the landing time relative to the separation moment, m1(t l ) is the mass of the motion body of the recovery stage at time t l , and m 1lmin is the minimum remaining mass of the motion body of the recovery stage.

[0460] Optionally, determining the objective function includes:

[0461] Determine the following objective function:

[0462] minJ = -a1m1(t l ) - a2m2(t f ).

[0463] where a1 is the weight coefficient of the terminal mass of the motion body of the recovery stage, a2 is the weight coefficient of the terminal mass of the motion body of the orbit injection stage, t l is the landing time relative to the separation moment, m1(t l ) is the mass of the motion body of the recovery stage at time t l , t f is the terminal time of the orbit injection stage flight segment, and m2(t f ) is the mass of the motion body of the orbit injection stage at time t f .

[0464] This embodiment provides a computer-readable storage medium that divides the entire process of a reusable rocket into an ascent stage and a landing stage; determines the motion equations and constraint conditions for the ascent stage and the landing stage respectively; determines the objective function; and optimizes the entire trajectory of the reusable rocket based on the objective function, the motion equations, and the constraint conditions of each stage. The computer-readable storage medium provided in this embodiment divides the entire process of the reusable rocket into an ascent stage and a landing stage, and performs optimization according to the motion equations, constraint conditions, and objective function of the ascent stage and the landing stage, reducing the dimensionality of the optimization problem of the reusable rocket and solving the optimization problem of considering two motion equations at the same time after the separation of the reusable rocket.

[0465] 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.) that contain 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.

[0466] The present application is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram can be implemented by computer program instructions, and the combination of the processes and / or blocks in the flowchart and / or block diagram can also 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, so that the instructions executed by the processor of the computer or other programmable data processing devices generate means for realizing the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1 the function specified in one block or multiple blocks.

[0467] 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, so that the instructions stored in the computer-readable memory generate a manufactured article including an instruction device, and the instruction device realizes the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1 the function specified in one block or multiple blocks.

[0468] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus, so that a series of operation steps are executed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions for implementing the process Figure 1 in one process or a plurality of processes and / or boxes Figure 1 steps for the functions specified in one box or a plurality of boxes.

[0469] Although the preferred embodiments of the present application have been described, additional changes and modifications can be made by those skilled in the art once they learn of the basic creative concept. Therefore, the appended claims are intended to be construed to cover the preferred embodiments as well as all changes and modifications falling within the scope of the present application.

[0470] Obviously, those skilled in the art can make various changes and modifications 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 method for describing the full - trajectory optimization problem of a reusable rocket, characterized in that, The method includes: Dividing the reusable rocket throughout its flight into an ascending stage and a landing stage; Respectively determining the equations of motion and constraint conditions for the ascending stage and the landing stage; Determining the objective function; Optimizing the entire trajectory of the reusable rocket based on the objective function, the equations of motion, and the constraint conditions for each stage; The ascending stage includes the pre-separation ascending stage and the in-orbit stage flight; Determining the equations of motion and constraint conditions for the ascending stage, including: Determining the equations of motion for the pre-separation ascending stage and the in-orbit stage flight; Determining the constraint conditions for the pre-separation ascending stage and the in-orbit stage flight; The equation of motion for the pre-separation ascending stage includes the equation of motion for the pre-separation ascending stage of the recovery stage vehicle and the equation of motion for the pre-separation ascending stage of the in-orbit stage vehicle; Determining the equation of motion for the pre-separation ascending stage, including: Determining the equation of motion for the pre-separation ascending stage of the recovery stage vehicle as: Among them, is the first derivative operator, P1 is the position vector of the recovery-stage moving body, V1 is the velocity vector of the recovery-stage moving body, T1 is the engine thrust amplitude of the recovery-stage moving body, m1 is the mass of the recovery-stage moving body, m2 is the mass of the in-orbit-stage moving body, u1 is the thrust vector of the recovery-stage moving body, D is the aerodynamic drag, μ is the Earth's gravitational coefficient, r1 is the distance vector between the centroid of the recovery-stage moving body used for the gravitational acceleration component and the Earth's center, and dm1 is the engine second flow rate of the recovery-stage moving body; Determining the equation of motion for the pre-separation ascending stage of the in-orbit stage vehicle as: Wherein, P2 is the position vector of the in-orbit stage vehicle, V2 is the velocity vector of the in-orbit stage vehicle, and r2 is the distance vector between the centroid of the in-orbit stage vehicle used for the gravitational acceleration component and the center of the earth.

2. The method according to claim 1, wherein The reusable rocket includes a recovery stage vehicle and an in-orbit stage vehicle.

3. The method according to claim 2, characterized in that, The reference coordinate system for the ascending stage is the launch point inertial coordinate system, and the reference coordinate system for the landing stage is the vertical landing coordinate system.

4. The method according to claim 3, wherein In the launch point inertial coordinate system, the coordinate origin O is the launch point, the OY axis points outward from the surface along the line connecting the center of the earth and the launch point, the OX axis is perpendicular to the OY axis, points in the launch direction in the horizontal plane, and the angle with the meridian plane of the launch point is the launch azimuth angle, and the OZ axis satisfies the right-hand rule.

5. The method according to claim 4, wherein In the pre-separation ascending stage, it includes the motion characteristics of the recovery stage vehicle and the in-orbit stage vehicle. Among them, the recovery stage vehicle and the in-orbit stage vehicle are powered by the engine in the recovery stage vehicle, and the recovery stage vehicle and the in-orbit stage vehicle have the same motion characteristics; In the in-orbit stage flight, it only includes the motion characteristics of the in-orbit stage vehicle.

6. The method according to claim 5, wherein Determining the constraint conditions for the pre-separation ascending stage, including: Determining the launch initial state constraint conditions, thrust direction constraint conditions, vertical ascending stage constraint conditions, mass constraint conditions, and bending moment constraint conditions.

7. The method according to claim 6, characterized in that, The launch initial state constraint conditions are: [P1, V1, m1, P2, V2, m2](t0) = [P0, V0, m 10 , P0, V0, m 20 ; Wherein, P1 is the position vector of the recovery-stage vehicle, V1 is the velocity vector of the recovery-stage vehicle, m1 is the mass of the recovery-stage vehicle, m2 is the mass of the injection-stage vehicle, P2 is the position vector of the injection-stage vehicle, V2 is the velocity vector of the injection-stage vehicle, t0 is the launch time of the reusable rocket, P0 is the position vector of the reusable rocket, V0 is the velocity vector of the reusable rocket, m 10 is the initial mass of the recovery-stage vehicle at the launch time, m 20 is the initial mass of the injection-stage vehicle at the launch time.

8. The method according to claim 6, wherein The thrust direction constraint conditions include: ‖u1‖ = 1, -1 ≤ u 1x,1y,1z ≤ 1; Among them, u1 is the thrust vector of the recovery-stage moving body, u1 = [u 1x , u 1y , u 1z T , u 1x is the thrust direction of the recovery-stage moving body on the OX axis, u 1y is the thrust direction of the recovery-stage moving body on the OY axis, u 1z is the thrust direction of the recovery-stage moving body on the OZ axis.​ 9. The method according to claim 6, characterized in that, The vertical ascending stage constraint conditions include: u1＝[0,1,0] T ； Among them, u1 is the thrust vector of the recovery-stage moving body, u1 = [u 1x , u 1y , u 1z T , u 1x is the thrust direction of the recovery-stage moving body on the OX axis, u 1y is the thrust direction of the recovery-stage moving body on the OY axis, u 1z is the thrust direction of the recovery-stage moving body on the OZ axis.​ 10. The method according to claim 6, characterized in that The mass constraint conditions include: m1(t s )≥m f1min ; t s ≤t ref ; Among them, m1 is the mass of the recovery-stage moving body, and m f1min is the minimum remaining mass of the recovery-stage moving body before separation, and t ref is the maximum flight time of the recovery-stage moving body during the ascending stage, and t s is the separation moment.

11. The method according to claim 6, wherein The bending moment constraint conditions include: |qα| ≤ Q αmax ; Among them, q is the dynamic pressure, V is the velocity vector of the reusable rocket, and V E is the velocity generated by the Earth's rotation, and Q αmax is the maximum allowable bending moment, α is the angle of attack, and u is the thrust vector of the reusable rocket.

12. The method according to claim 5, wherein Determining the constraint conditions for the in-orbit stage flight, including: Determining the separation moment state constraint conditions, in-orbit stage vehicle mass constraint conditions, and target orbit element terminal constraint conditions.

13. The method according to claim 12, wherein The separation moment state constraint conditions are: The initial point position of the in-orbit stage flight and the initial point velocity of the in-orbit stage flight are equal to the state of the reusable rocket at the separation moment; The initial point mass of the in-orbit stage flight is the initial mass of the in-orbit stage vehicle at the launch moment.

14. The method according to claim 12, wherein The in-orbit stage vehicle mass constraint conditions include: m2(t f )≥m f2min ; where, m2 is the mass of the in-orbit stage moving body, m f2min is the total mass of the launch vehicle and the payload after the fuel of the in-orbit stage moving body is exhausted, t f is the terminal time of the in-orbit stage flight segment.

15. The method according to claim 3, characterized in that, In the vertical landing coordinate system, the coordinate origin O e is the center of the earth, and O e Y l axis points from the center of the earth to the centroid of the reusable rocket. O e X l axis is perpendicular to the O e Y l axis in the local horizontal plane, and the included angle with the meridian plane where the reusable rocket is located is the launch azimuth angle. O e Z l axis satisfies the right-hand rule.

16. The method according to claim 15, wherein Determining the constraint conditions for the landing stage, including: Determine the initial state constraint conditions of the landing section, the mass flow rate constraint conditions, the attitude angular velocity constraint conditions, the stagnation point heat flux constraint conditions, the dynamic pressure constraint conditions, the aerodynamic overload constraint conditions, the angle constraint conditions, and the terminal state constraint conditions of the landing section.

17. The method according to claim 16, wherein The initial state constraint conditions of the landing section include: [P1,V1,m1](t s )=[P 1s ,V 1s ,m 1s ​ Wherein, P1 is the position vector of the recovery-stage moving body, V1 is the velocity vector of the recovery-stage moving body, m1 is the mass of the recovery-stage moving body, and t s is the separation moment, P 1s is the position vector of the recovery-stage moving body at the separation moment, V 1s is the velocity vector of the recovery-stage moving body at the separation moment, and m 1s is the mass of the recovery-stage moving body at the separation moment.

18. The method according to claim 16, characterized in that, The mass flow rate constraint conditions include: wherein, dm1 is the engine second flow rate of the recovery-stage moving body, dm min is the minimum second flow rate of the engine, and dm max is the maximum second flow rate of the engine.

19. The method according to claim 16, wherein The attitude angular velocity constraint conditions include: Among them, is the pitch angular velocity of the recovery-stage vehicle, ω 1ψ is the yaw angular velocity of the recovery-stage vehicle, ω max1 is the attitude angular velocity amplitude in the rarefied atmosphere section, ω max2 is the attitude angular velocity amplitude in the dense atmosphere section, ω max3 is the attitude angular velocity amplitude in the powered soft landing section.

20. The method according to claim 16, characterized in that The stagnation point heat flux constraint conditions include: Among them, Q s is the current stagnation heat flux value of the reusable rocket, k s is the stagnation heat flux coefficient related to the shape of the reusable rocket, ρ is the atmospheric density at the corresponding altitude, V1 is the velocity vector of the recovery stage moving body, ρ Q and V Q are parameters for calculating the stagnation heat flux, Q smax is the maximum value of the stagnation heat flux.

21. The method according to claim 16, wherein The dynamic pressure constraint conditions include: q = 0.5ρ‖V1‖ 2 ≤ q max ; where q is the dynamic pressure, ρ is the atmospheric density at the corresponding altitude, V1 is the velocity vector of the recovery-stage moving body, and q max is the maximum value of the dynamic pressure.

22. The method according to claim 16, wherein The aerodynamic overload constraint conditions include: Among them, n D is the pneumatic overload, m1 is the mass of the moving body of the recovery stage, D x is the component of the air resistance along the O e X l axis, D y is the component of the air resistance along the O e Y l axis, D z is the component of the air resistance along the O e Z l axis, n Dmax is the maximum value of the pneumatic overload, and g0 is the standard gravitational acceleration.

23. The method according to claim 16, wherein The angle constraint conditions include: Powered soft landing phase; Powered soft landing phase; Among them, is the pitch angle of the recovery-stage moving body, is the maximum deviation between the pitch angle and the local plumb line, V 1x is the velocity component of the recovery-stage moving body along the O e X l axis, V 1y is the velocity component of the recovery-stage moving body along the O e Y l axis, V 1z is the velocity component of the recovery-stage moving body along the O e Z l axis, Δθ V is the maximum deviation between the velocity direction and the local plumb line.

24. The method according to claim 16, wherein The terminal state constraint conditions of the landing section include: landing position constraint conditions, landing speed constraint conditions, landing attitude angle and speed inclination constraint conditions, and landing mass constraint conditions.

25. The method according to claim 24, wherein The landing position constraint conditions include: h(t l ) = h l ‖λ(t l ) - λ l ‖ ≤ Δλ l ‖B(t l ) - B l ‖ ≤ ΔB l Among them, t l is the landing time at the relative separation moment, h(t l ) is the landing altitude at time t l , h l is the altitude of the desired landing point, λ(t l ) is the longitude of the reusable rocket terminal at time t l , λ l is the longitude of the reusable rocket terminal at the landing moment, Δλ l is the maximum deviation of the longitude of the reusable rocket terminal, B(t l ) is the latitude of the reusable rocket terminal at time t l , B l is the latitude of the reusable rocket terminal at the landing moment, ΔB l is the maximum deviation of the latitude of the reusable rocket terminal.

26. The method according to claim 24, wherein The landing speed constraint conditions include: V ylmax ≤V 1y (t l )≤0 -V xzlmax ≤V 1x (t l ),V 1z (t l )≤V xzlmax Among them, t l is the landing time at the relative separation moment, V 1x (t l ) is the velocity component of the recovery-stage moving body at time t l on the O e X l axis, V 1y (t l ) is the velocity component of the recovery-stage moving body at time t l on the O e Y l axis, V 1z (t l ) is the velocity component of the recovery-stage moving body at time t l on the O e Z l axis, V ylmax is the maximum touchdown velocity borne by the landing leg, V xzlmax is the maximum lateral velocity that causes tipping.

27. The method according to claim 24, wherein The landing attitude angle and speed inclination constraint conditions include: Among them, t l is the landing time at the relative separation moment, is the pitch angle of the recovery stage moving body at time t l , V 1x (t l ) is the velocity component of the recovery stage moving body at time t l on the O e X l axis, V 1y (t l ) is the velocity component of the recovery stage moving body at time t l on the O e Y l axis, V 1z (t l ) is the velocity component of the recovery stage moving body at time t l on the O e Z l axis, Δθ Vl is the maximum value of the angle between the velocity at the landing moment and the rocket body.

28. The method according to claim 24, wherein The landing mass constraint conditions include: m1(t1)≥m 1lmin where t l is the landing time at the relative separation moment, m1(t l ) is the mass of the recovery-stage moving body at time t l , and m 1lmin is the minimum remaining mass of the recovery-stage moving body.

29. The method according to claim 3, wherein The determination of the objective function includes: Determine the following objective function: minJ = -a1m1(t l ) - a2m2(t f ); Among them, a1 is the weight coefficient of the terminal mass of the recovery-stage moving body, a2 is the weight coefficient of the terminal mass of the orbital-stage moving body, t l is the landing time relative to the separation moment, m1(t l ) is the mass of the recovery-stage moving body at t l moment, t f is the terminal time of the orbital-stage flight segment, m2(t f ) is the mass of the orbital-stage moving body at t f moment.

30. An electronic device, characterized in that, Include: 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 1-29.

31. 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 1-29.

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