Recoverable rocket power soft landing two-stage control method and system and medium

Abstract

The invention relates to the technical field of rocket guidance, and discloses a recoverable rocket power soft landing two-stage control method, system and medium, the method comprises the following steps: establishing a dynamical model of a first stage, introducing constraint conditions of power descent landing, controlling the rocket to reach the position of # imgabs0 # right above a landing point, and controlling the position of # imgabs0 # right above the landing point; establishing an optimization problem P0 by considering the fuel minimization of the recoverable rocket; converting a non-convex constraint in the optimization problem P0 into a convex constraint, and establishing an optimization problem P1; variable substitution is introduced into the P1, and a convex optimization problem P2 of the first stage is obtained; controlling the recoverable rocket to be vertical to a landing point according to the displacement and speed constraint of the first stage, and establishing a convex optimization problem P3 by considering the minimum fuel of the recoverable rocket; according to the method, the dynamic soft landing process of the rocket is divided into two stages, the constraint condition of the attitude of the rocket terminal is considered, it is guaranteed that the attitude of the rocket during landing is in a vertical or approximately vertical state, and therefore the reliability of vertical landing is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of rocket guidance, and particularly to a two-stage control method, system and medium for the powered soft landing of a recoverable rocket. Background Art

[0002] Powered soft landing is one of the core links of recoverable rocket technology. During the powered descent phase, by controlling the engine thrust, the rocket can decelerate and accurately locate the target landing point when returning to the earth. Compared with the traditional parachute landing method, powered soft landing has higher accuracy and flexibility, and can adapt to various complex terrain conditions, thus ensuring the safe recovery of the rocket.

[0003] Currently, most of the powered descent guidance algorithms usually simplify the rocket into a particle model, establish a dynamic equation based on this model, and construct an optimal control problem with the goal of minimizing fuel consumption. However, this particle model ignores the attitude change characteristics of the rocket, resulting in the inability to effectively consider the terminal attitude constraint. In actual operation, to ensure the safe landing of the rocket, the terminal attitude needs to be kept vertical or close to vertical. However, existing algorithms often cannot meet this requirement, and may even cause a large attitude deviation, affecting the success rate and safety of landing. Summary of the Invention

[0004] In view of the above problems, the present invention aims to provide a two-stage control method for the powered soft landing of a recoverable rocket, including the following steps: Step S1, establish a dynamic model for the first stage, introduce the constraint conditions for powered descent landing, control the rocket to a position at a height of above the landing point, and establish an optimization problem P0 considering the minimum fuel consumption of the recoverable rocket; Step S2, convert the non-convex constraints in the optimization problem P0 into convex constraints, and establish an optimization problem P1; Step S3, introduce variable substitution for P1 to obtain the convex optimization problem P2 for the first stage; Step S4, according to the displacement and velocity constraints of the first stage, control the recoverable rocket to be vertical to the landing point, and establish a convex optimization problem P3 considering the minimum fuel consumption of the recoverable rocket; Step S5, use a convex optimization algorithm to solve the convex optimization problems P2 and P3.

[0005] Based on the above solution, the displacement constraint of the rocket at the end of the first stage is , is the end displacement of the first stage.

[0006] Based on the above solution, the calculation method of the initial height of the second stage is: Based on the initial mass of the reusable rocket and taking the maximum thrust as the vertical acting force of the rocket, the maximum acceleration in the decelerating descent landing stage is obtained; According to the velocity constraint of the rocket's descent , the upper bound of the time for the rocket's vertical falling stage is obtained; Based on the calculated upper bound of the time and the maximum acceleration in the powered landing stage of the rocket, the displacement in the vertical falling stage is calculated .

[0007] Based on the above solution, the initial displacement in the second stage of step S4 , the initial velocity , is the end displacement of the first stage, is the end velocity of the first stage.

[0008] Based on the above solution, the establishment of the optimization problem P0 includes: ; where, is the thrust, is the displacement of the rocket, is the velocity of the rocket, g represents the acceleration due to gravity, ω is the angular velocity of the Earth's rotation, is the mass of the rocket, is the cross product represented by the anti-symmetric matrix of the angular velocity of the Earth's rotation , the rocket fuel burn rate , is the standard acceleration due to gravity on Earth , is the specific impulse of the rocket engine, is the amplitude range of the thrust, is the unit vector in the vertical direction, represents the maximum allowable angle between the rocket's longitudinal axis and the vertical direction, indicates that the powered landing trajectory of the rocket must be contained within a conical region with the landing point as the vertex, , , are the displacements in the x, y, and z directions respectively, represents the half vertex angle of the conical region, is the maximum velocity of the rocket, is the dry weight of the rocket, is the weight of the rocket at the end of the first stage, is the weight of the rocket at the end of the first stage, indicates that the weight at the end of the first stage cannot be less than the dry weight of the rocket, are the initial displacement, initial velocity, and initial weight of the rocket at the start of the first stage respectively, is the displacement constraint at the end of the first stage, represents the velocity constraint at the end of the first stage.

[0009] Based on the above scheme, the convex optimization problem P2 is established as follows: Introduce the slack variable σ into the optimization problem P0 to transform the non-convex constraint into a convex constraint, obtaining P1; Then introduce the variable substitution: , , , and use the Taylor series to approximately expand : ; where the reference trajectory z0(t) represents the maximum fuel consumption rate, so z0(t) is the lower bound of z(t); Add the constraint: ; Obtain the final convex optimization problem P2 to be solved.

[0010] Based on the same inventive concept, the present application provides a two-stage control system for the powered soft landing of a reusable rocket, including: A first-stage control module for establishing the dynamic model of the first stage, introducing the constraint conditions for powered descent landing, and controlling the rocket to a position with a height of directly above the landing point. The first-stage control module includes: A first optimization module for establishing the optimization problem P0 considering the minimum fuel consumption of the reusable rocket; A second optimization module for transforming the non-convex constraint in the optimization problem P0 into a convex constraint and establishing the optimization problem P1; A third optimization module for introducing variable substitution for P1 to obtain the convex optimization problem P2 of the first stage; A second-stage control module for controlling the reusable rocket vertically to the landing point according to the displacement and velocity constraints of the first stage, and establishing the convex optimization problem P3 considering the minimum fuel consumption of the reusable rocket; A calculation module for solving the convex optimization problems P2 and P3 using a convex optimization algorithm.

[0011] Based on the above scheme, the control height of the first-stage control module is used as the initial displacement constraint condition for the second stage to establish the convex optimization problem of the second stage.

[0012] Based on the above scheme, it includes an initial height calculation sub-module for calculating the height at the end of the first stage according to the initial mass and maximum thrust of the rocket. The initial height calculation sub-module includes: The first calculation unit is configured to use the initial mass of the reusable rocket as a reference and the maximum thrust as the vertical force of the rocket to obtain the maximum acceleration in the decelerating descent landing phase; The second calculation unit is configured to obtain an upper bound on the time of the vertical descent phase of the rocket according to the velocity constraint of the rocket's descent ,; The third calculation unit is configured to calculate the displacement of the vertical descent phase according to the calculated upper bound on the time and the maximum acceleration of the powered landing phase of the rocket .

[0013] The present application also provides a computer-readable storage medium storing a computer program, which when executed by a processor implements the two-stage control method for powered soft landing of a reusable rocket as described above.

[0014] Compared with the prior art, the present invention has the following beneficial effects: By dividing the powered soft landing process of the rocket into two stages and establishing an optimal control problem for each stage respectively, the descent trajectory of the rocket can be controlled more precisely; First, the rocket is moved directly above the recovery point in the vertical direction, and then it descends vertically to the recovery point, taking into account the constraint conditions of the rocket's terminal attitude, ensuring that the attitude of the rocket at landing is vertical or nearly vertical, thus increasing the reliability of vertical landing. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 is a schematic diagram of the two-stage soft landing process of the present application; Figure 2 is a flowchart of the two-stage soft landing control method of the present application; Figure 3 is a comparison diagram of trajectory simulations of the present application; Figure 4 is a comparison curve of speed simulations of the present application; Figure 5 is a comparison diagram of rocket mass change simulations of the present application; Figure 6 is a comparison diagram of rocket inclination change simulations of the present application; Figure 7 is a comparison diagram of in-plane trajectory simulations of the rocket of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0016] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for the purpose of illustration and explanation of the present invention, and are not intended to limit the present invention.

[0017] The present invention provides a two-stage control method for the powered soft landing of a recyclable rocket, which can solve the problem of vertical deviation of the terminal attitude. The powered soft landing section of the recyclable rocket is divided into two stages, as Figure 1 shown. In the first stage, the rocket is controlled to a certain height directly above the landing point, from point A to point C; in the second stage, the rocket is then vertically controlled to the landing point, from point C to point D. Then, according to the different constraint conditions of the two stages, the optimal control problem of minimum fuel consumption is established for each stage. As Figure 2 shown, the specific steps are as follows: Step S1: Establish the dynamic model of the first stage, consider the problem P0 of minimum fuel consumption powered descent guidance (PDG) of the three-degree-of-freedom recyclable rocket, introduce the constraint conditions of powered descent landing, and control the rocket to a position with a height of directly above the landing point. The particle dynamics of the rocket corresponds to a double integrator with variable mass moving in a constant gravitational field with the earth coordinate system as the reference, which is expressed as follows; ; where, is the thrust, is the displacement of the rocket, is the velocity of the rocket, g represents the gravitational acceleration, ω is the angular velocity of the earth's rotation, , , g and ω ∈ , is the mass of the rocket, is the cross product represented by the anti-symmetric matrix of the angular velocity of the earth's rotation , the rocket burning rate , is the standard gravitational acceleration of the earth , is the specific impulse of the rocket engine, is the amplitude range of the thrust, means that the angle between the longitudinal axis of the rocket and the vertical direction cannot be greater than , is the unit vector in the vertical direction, means the maximum allowable angle between the longitudinal axis of the rocket and the vertical direction, means that the powered landing trajectory of the rocket must be contained within the conical region with the landing point as the vertex, , , are the displacements in the x, y, and z directions respectively, means the half apex angle of the conical region, is the maximum velocity of the rocket, means that the magnitude of the rocket's velocity does not exceed , It indicates that the weight at the end of the first stage should not be less than the dry weight of the rocket. It represents the initial state of the rocket at the start of the first stage. It represents the displacement constraint of the rocket at the end of the first stage. It represents the velocity constraint of the rocket at the end of the first stage.

[0018] Step S2. To handle the non-convex constraint of the rocket thrust , slack variables are introduced to transform the non-convex constraint into a convex constraint. The transformed optimization problem P1 can be expressed as: .

[0019] Step S3. For P1, variable substitution is introduced , , , and at the same time, using the Taylor series to approximately expand , we can get: ; where the reference trajectory represents the maximum fuel consumption rate, so is the lower bound of.

[0020] To ensure that the physical constraints on are not violated, additional constraints need to be added: ; In summary, through the above variable substitution, the convex optimization problem P2 that finally needs to be solved in the first stage can be obtained: .

[0021] Step S4. After the end of the first stage, the terminal state of the rocket is the initial state of the second stage. The optimization objectives of the two stages are the same, but the terminal displacement constraint and velocity constraint have changed, and other constraint conditions remain unchanged. The three-degree-of-freedom fuel-saving PDG problem P3 of the recoverable rocket in the second stage can be expressed as: ; where is the end displacement of the first stage and also the initial height of the second stage, is the end velocity of the first stage, satisfying .

[0022] This application discovers through a large number of numerical simulations that: although the mass continuously decreases during the rocket recovery process, due to the short time of the powered landing stage, the mass change of the rocket is not significant, and the impact on the acceleration during the deceleration process is not large either. Therefore, The calculation method is as follows: Based on the initial mass of the reusable rocket and taking the maximum thrust as the vertical force of the rocket, the maximum acceleration in the decelerating descending landing stage is obtained. Note that the gravitational acceleration value needs to be subtracted during the calculation process; According to the velocity constraint of the rocket's descent , so if the rocket can land safely when descending at the maximum velocity , other velocities are also acceptable, thus obtaining the upper bound of the time for the rocket's vertical descent stage; Based on the calculated upper bound of the time and the maximum acceleration in the powered landing stage of the rocket, the displacement in the vertical descent stage is calculated ; According to the above method, the calculated can ensure that the reusable rocket can land safely at the reusable landing point at any velocity less than or equal to the maximum velocity at the altitude.

[0023] According to the present invention, the initial altitude calculation method can be adapted to different rocket models and mission requirements, and the calculated values can be adjusted according to the rocket model and mission needs to ensure that the terminal attitude of the rocket is vertically upward, meeting the actual application scenarios of reusable rockets.

[0024] Step S5, according to the above steps, the fuel-saving problem can be transformed into a convex optimization problem. Therefore, existing and relatively mature convex optimization algorithms can be used to solve the convex optimization problems P2 and P3, which will not be elaborated here.

[0025] To verify the feasibility of the method in this application, a rocket powered descent simulation mission is selected for verification. The parameters of the reusable rocket are selected as follows: , , , , , , , , , and the initial state of the rocket is set as: , .

[0026] Based on the above parameters, the end displacement of the first stage, i.e., the initial altitude of the second stage is: .

[0027] According to the transformed convex optimization problem and parameters, a convex optimization toolbox is used for solution, the reusable rocket is controlled, and a comparison is made with the existing single-stage convex optimization algorithm, as Figures 3 to 7As shown, both of the two lossless convex optimization algorithms can adjust the centroid position of the rocket to the recovery point, and the terminal velocity of the rocket is zero, that is, soft landing can be achieved.

[0028] Through comparison, it can be seen that the terminal attitude of the rocket obtained by the existing lossless convex optimization is inclined, and the inclination angle of the rocket is about 30°. However, the two-stage lossless convex optimization algorithm proposed by the present invention can adjust the terminal attitude of the rocket to the vertical state, and the inclination angle of the rocket is 0°. First, the rocket is moved to directly above the recovery point vertically, and then it descends vertically to the recovery point, ensuring that the terminal attitude of the rocket is vertically upward.

[0029] By adjusting the terminal attitude in this application, the vertical attitude can reduce the impact load during landing, protect the structural integrity of the rocket, and improve the recovery success rate; at the same time, the fuel is optimally controlled to achieve economy under the premise of ensuring attitude constraints.

[0030] Based on the same inventive concept, this application provides a two-stage control system for the powered soft landing of a recoverable rocket, including: A first-stage control module, used to establish the dynamic model of the first stage, introduce the constraint conditions for powered descent landing, and control the rocket to a position with a height of directly above the landing point. The first-stage control module includes: A first optimization module, used to establish the optimization problem P0 considering the fuel saving of the recoverable rocket; A second optimization module, used to convert the non-convex constraints in the optimization problem P0 into convex constraints and establish the optimization problem P1; A third optimization module, used to introduce variable substitution for P1 to obtain the convex optimization problem P2 of the first stage; A second-stage control module, used to control the recoverable rocket to land vertically to the landing point according to the displacement and velocity constraints of the first stage, and establish the convex optimization problem P3 considering the fuel saving of the recoverable rocket; A calculation module, used to solve the convex optimization problems P2 and P3 using the convex optimization algorithm.

[0031] The control height of the first-stage control module is used as the initial displacement constraint condition of the second stage to establish the convex optimization problem of the second stage.

[0032] The system further includes an initial height calculation sub-module, used to calculate the height at the end of the first stage according to the initial mass and maximum thrust of the rocket. The initial height calculation sub-module includes: A first calculation unit, used to take the initial mass of the recoverable rocket as a reference and the maximum thrust as the vertical acting force of the rocket to obtain the maximum acceleration of the decelerated descent landing section; A second calculation unit, used to calculate according to the velocity constraint , obtain the upper bound of the time of the vertical falling section of the rocket; A third calculation unit, configured to calculate the displacement of the vertical falling section according to the calculated upper bound of the time and the maximum acceleration of the powered landing section of the rocket .

[0033] According to the present invention, a computer-readable recording medium storing computer-executable instructions can be provided. When the computer-executable instructions are executed by a processor, the processor can be prompted to execute the large language model training method as described above.

[0034] It should be noted that the flowcharts and block diagrams in the accompanying drawings illustrate the possible architectures, functions, and operations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagram may represent a module, a program segment, or a part of code, and the module, the program segment, or the part of code contains at least one executable instruction for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than marked in the accompanying drawings. For example, two consecutive blocks shown may actually be executed substantially in parallel, and they may sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, and the combination of blocks in the block diagram and / or flowchart, can be implemented by a dedicated hardware-based system for performing the specified functions or operations, or can be implemented by a combination of dedicated hardware and computer instructions.

[0035] The above are only the preferred embodiments of the present application and are not used to limit the present application. For those skilled in the art, various changes and modifications can be made to the present application. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

[0036] Although the specific implementation manners of the present invention are described above, they are not limitations on the protection scope of the present invention. Those skilled in the art should understand that, based on the technical solutions of the present invention, various modifications or deformations that can be made without creative efforts by those skilled in the art are still within the protection scope of the present invention.

Claims

1. A two-stage control method for recyclable rocket-powered soft landing, characterized in that, It includes the following steps: Step S1, establish the dynamic model of the first stage, introduce the constraint conditions for powered descent landing, control the rocket to the position with a height of directly above the landing point, and establish the optimization problem P0 considering the minimum fuel consumption of the reusable rocket; Step S2: Convert the non-convex constraints in the optimization problem P0 into convex constraints to establish the optimization problem P1; Step S3: Introduce variable substitution in P1 to obtain the convex optimization problem P2 in the first stage; Step S4: According to the displacement and velocity constraints of the reusable rocket in the first stage, control the reusable rocket in the second stage to vertically reach the landing point, and establish the convex optimization problem P3 considering the minimum fuel consumption of the reusable rocket; Step S5: Use the convex optimization algorithm to solve the convex optimization problems P2 and P3.

2. The two-stage control method for recoverable rocket-powered soft landing according to claim 1, characterized in that The displacement constraint of the rocket at the end of the first stage is , which is the end displacement of the first stage and also the initial displacement of the second stage.

3. The two-stage control method for recyclable rocket-powered soft landing according to claim 2, characterized in that, The initial height of the second stage The calculation method is as follows: Based on the initial mass of the reusable rocket and taking the maximum thrust as the vertical force of the rocket, obtain the maximum acceleration in the decelerated descent landing section; According to the velocity constraint of the rocket's descent , the upper bound of the time for the vertical descent section of the rocket is obtained; Based on the calculated upper bound of time and maximum acceleration during the powered landing phase of the rocket, the displacement during the vertical descent phase is calculated. .

4. A two-stage control method for recoverable rocket-powered soft landing according to claim 3, characterized in that The initial displacement in the second stage in step S4 , the initial velocity , is the end displacement of the first stage, is the end velocity of the first stage.

5. A two-stage control method for recyclable rocket-powered soft landing according to claim 1, characterized in that, The establishment of the optimization problem P0 includes: ； Among them, is the thrust, is the displacement of the rocket, is the velocity of the rocket, g represents the acceleration due to gravity, ω is the angular velocity of the Earth's rotation, is the mass of the rocket, is the cross product represented by the antisymmetric matrix of the angular velocity of the Earth's rotation , the rocket burning rate , is the standard acceleration due to gravity on Earth , is the specific impulse of the rocket engine, is the amplitude range of the thrust, is the unit vector in the vertical direction, represents the maximum allowable angle between the longitudinal axis of the rocket and the vertical direction, represents that the powered landing trajectory of the rocket must be contained within a conical region with the landing point as the vertex, , , are the displacements in the x, y, and z directions respectively, represents the half apex angle of the conical region, is the maximum velocity of the rocket, is the dry weight of the rocket, is the weight of the rocket at the end of the first stage, represents that the weight at the end of the first stage cannot be less than the dry weight of the rocket, are the initial displacement, initial velocity, and initial weight of the rocket at the start of the first stage respectively, is the displacement constraint at the end of the first stage, represents the velocity constraint at the end of the first stage.

6. The two-stage control method for recoverable rocket-powered soft landing according to claim 5, characterized in that, The establishment of the convex optimization problem P2 is: Introduce the slack variable σ into the optimization problem P0 to convert the non-convex constraints into convex constraints to obtain P1; Reintroduce the variable substitution: , , , and use the Taylor series to approximately expand : ； Among them, the reference trajectory z0(t) represents the maximum fuel consumption rate, so z0(t) is the lower bound of z(t); Add the constraints: ； Obtain the final convex optimization problem P2 to be solved.

7. A two-stage control system for the powered soft landing of a recyclable rocket, characterized in that, It includes: The first-stage control module is used to establish the dynamic model of the first stage, introduce the constraint conditions for powered descent landing, and control the rocket to a position with a height of above the landing point. The first-stage control module includes: The first optimization module is used to establish the optimization problem P0 considering the minimum fuel consumption of the reusable rocket; The second optimization module converts the non-convex constraints in the optimization problem P0 into convex constraints to establish the optimization problem P1; The third optimization module introduces variable substitution in P1 to obtain the convex optimization problem P2 in the first stage; The second-stage control module is used to control the reusable rocket in the second stage to vertically reach the landing point according to the displacement and velocity constraints in the first stage, and establish the convex optimization problem P3 considering the minimum fuel consumption of the reusable rocket; The calculation module is used to solve the convex optimization problems P2 and P3 using the convex optimization algorithm.

8. A two-stage control system for recoverable rocket-powered soft landing according to claim 7, characterized in that The control height of the first-stage control module As the initial displacement constraint condition of the second stage, a convex optimization problem of the second stage is established.

9. A two-stage control system for recyclable rocket-powered soft landing according to claim 8, characterized in that, It includes an initial height calculation sub-module, which is used to calculate the height at the end of the first stage according to the initial mass and maximum thrust of the rocket. The initial height calculation sub-module includes: The first calculation unit is used to obtain the maximum acceleration in the decelerated descent landing section based on the initial mass of the reusable rocket and taking the maximum thrust as the vertical force of the rocket; A second computing unit, configured to obtain an upper bound on the time of the vertical falling section of the rocket according to the velocity constraint of the rocket's descent , and obtain an upper bound on the time of the vertical falling section of the rocket A third calculation unit, configured to calculate the displacement of the vertical falling section based on the calculated upper bound of time and the maximum acceleration of the powered landing section of the rocket .

10. A computer-readable storage medium, characterized in that, It stores a computer program, and when the computer program is executed by a processor, it implements the two-stage control method for the powered soft landing of a reusable rocket as described in any one of claims 1 to 6.

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