Method and device for trajectory planning of a recovery rocket power landing section based on convex optimization

Abstract

The application provides a recovery rocket powered landing section trajectory planning method and device based on convex optimization. The recovery rocket powered landing section trajectory planning method based on convex optimization comprises the following steps: a landing trajectory planning model containing engine working mode switching is established; flight time under different engine working modes is calculated based on a one-dimensional vertical motion model; the trajectory planning model is discretized and losslessly convexified by using the calculated flight time under different engine working modes, so that the trajectory planning model is converted into a convex optimization problem and solved to obtain a fuel-optimal landing reference trajectory. By establishing the landing trajectory planning model, global optimization of fuel consumption is achieved, fuel consumption is reduced, and the purpose of effectively improving the reusability efficiency and mission economy of the rocket is achieved.

Description

Technical Field

[0001] This invention belongs to the field of rocket recovery guidance technology, and in particular relates to a method and device for planning the trajectory of a recovered rocket's powered landing phase based on convex optimization. Background Technology

[0002] Developing vertical recovery technology for reusable launch vehicles is a crucial direction for reducing rocket launch costs, especially in commercial spaceflight. The powered landing phase, as the final flight stage in the vertical recovery process, is a critical link in the entire recovery flight, directly impacting the success or failure of the recovery mission. To achieve precise guidance and control during the powered landing phase, online trajectory planning technology based on numerical optimization methods has shown great application potential.

[0003] Rocket landing trajectory planning is achieved by solving a complex nonlinear optimal control problem with multiple constraints. Traditional numerical optimization methods, such as nonlinear programming, while capable of solving such problems, have significant limitations. On the one hand, their computational complexity is high and the solution time is long, making it difficult to meet the real-time solution requirements on the rocket. On the other hand, these methods are highly dependent on initial conditions, increasing the difficulty and uncertainty of the solution.

[0004] Furthermore, existing landing trajectory planning models are not well-suited to engineering realities. Previous studies often assumed a constant number of engines operating and continuous adjustment of total thrust within a throttling range. However, in actual powered landings, the number of engines needs to be dynamically adjusted, resulting in discontinuous thrust adjustment ranges. For example, in the initial landing phase, three engines need to be activated to overcome gravity, adjust attitude, and rapidly decelerate. As the rocket's altitude and speed decrease, two engines are shut down, leaving only one to achieve precise landing with high-precision thrust control (ensuring the maximum thrust acceleration of a single engine exceeds gravitational acceleration). Assuming a single engine's throttling range is [0.5, 1.0], then with three engines operating, the equivalent throttling range is [1.5, 3]. This discontinuity in the thrust adjustment range caused by variations in the number of operating engines further increases the difficulty of landing trajectory planning. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a method and apparatus for trajectory planning of the powered landing segment of a recoverable rocket based on convex optimization, in order to solve the problem of high fuel consumption during the powered landing process of existing rockets.

[0006] In a first aspect, embodiments of this disclosure provide a trajectory planning method for the powered landing phase of a recoverable rocket based on convex optimization, including: Establish a landing trajectory planning model that includes engine operating mode switching; Based on a one-dimensional vertical motion model, the flight time under different engine operating modes is calculated analytically. By using the flight time obtained under different engine operating modes, the trajectory planning model is discretized and non-destructively convexized, thereby transforming the trajectory planning model into a convex optimization problem and solving it to obtain the fuel-optimal landing reference trajectory. The engine operating modes include a first mode and a second mode; the analytical calculation of flight time under different engine operating modes based on a one-dimensional vertical motion model includes: In a one-dimensional vertical dimension, design the bang-bang fuel optimal thrust profile from the first mode thrust to the second mode thrust; Based on the optimal fuel thrust profile, and according to rocket dynamics and mass flow equations, a three-dimensional nonlinear equation set is obtained regarding the thrust magnitude of the first mode, the flight time of the first mode, and the flight time of the second mode. Solving the three-dimensional nonlinear equations yields the magnitude of the thrust in the first mode, the flight time in the first mode, and the flight time in the second mode.

[0007] Optionally, the process of obtaining a three-dimensional nonlinear equation set regarding the thrust magnitude of the first mode, the flight time of the first mode, and the flight time of the second mode based on rocket dynamics and the mass flow equation includes: Given the first and second mode thrusts, the dynamic equations are obtained by integrating the rocket's acceleration under engine thrust. These dynamic equations include velocity constraint equations. Position constraint equations and the high constraint equations for transitioning from the first mode to the second mode ; Equation ,equation sum equation A system of three-dimensional nonlinear equations is formed by combining these equations. It is a vector consisting of the thrust magnitude of the first mode, the flight time of the first mode, and the flight time of the second mode.

[0008] Optionally, the constraints for establishing the landing trajectory planning model that includes engine operating mode switching include: The constraints are as follows: dynamic equations; initial position, velocity, and mass constraints of the rocket at the start of the powered landing phase; initial attitude constraints of the rocket at the start of the powered landing phase; terminal position and velocity constraints of the rocket; vertical attitude constraints of the rocket at the terminal phase; first-mode thrust magnitude constraints; second-mode thrust magnitude constraints; motion path constraints; first-mode thrust direction constraints; second-mode thrust direction constraints; first-mode to second-mode thrust transition constraints; first-mode attitude change rate constraints; and second-mode attitude change rate constraints; the terminal phase is the end point of the powered landing phase.

[0009] Optionally, the non-destructive convexity process includes: introducing relaxation thrust. By replacing the rocket's mass and thrust vector with variables, the trajectory planning model is transformed into a convex optimization problem.

[0010] Optionally, the variable substitution for rocket mass and thrust vector includes: , , ,in For rocket mass, For thrust vector, For the logarithm of mass, For thrust acceleration vector, This is for relaxing thrust acceleration.

[0011] Optionally, the trajectory planning model can be discretized and lossless convexized to transform it into a convex optimization problem for solution, including: Introducing slack variables Furthermore, a penalty term is added to the objective function for solving convex optimization problems.

[0012] Optionally, the step of discretizing and lossless convexification of the trajectory planning model using the calculated flight times under different engine operating modes includes: By utilizing the flight time under different engine operating modes, the first mode operating segment and the second mode operating segment are discretized by equal time intervals, transforming the continuous dynamic equations into discrete linear equality constraints.

[0013] Optionally, after discretization and lossless convexization, the trajectory planning model is transformed into a convex optimization problem with second-order cone constraints. The interior point method solver is used for numerical solution, and the mass profile and after-effect acceleration profile are updated iteratively to obtain the final fuel-optimal trajectory.

[0014] Secondly, this disclosure also provides a trajectory planning device for the powered landing phase of a recoverable rocket based on convex optimization, comprising: The model building module is used to build a landing trajectory planning model that includes engine operating mode switching; The analysis module is used to analyze and calculate the flight time under different engine operating modes based on a one-dimensional vertical motion model; The non-destructive convexity processing module is used to discretize and non-destructively convexize the trajectory planning model using the flight time calculated under different engine operating modes, thereby transforming the trajectory planning model into a convex optimization problem and solving it to obtain the fuel-optimal landing reference trajectory.

[0015] The present invention provides a trajectory planning method for the powered landing segment of a recoverable rocket based on convex optimization. By establishing a landing trajectory planning model and utilizing the uniqueness of the global optimal solution of the convex optimization problem, the method ensures that the generated landing trajectory achieves global optimal fuel consumption while satisfying engineering constraints, thereby reducing fuel consumption and effectively improving the reusability efficiency and mission economy of the rocket. Attached Figure Description

[0016] The above and other objects, features and advantages of this disclosure will become more apparent from the accompanying drawings, in which like reference numerals generally denote like parts.

[0017] Figure 1 A flowchart of a trajectory planning method for the powered landing phase of a recoverable rocket based on convex optimization, provided in an embodiment of this disclosure; Figure 2 A schematic diagram of the landing system, thrust direction, and flight path angle constraints provided in the embodiments of this disclosure; Figure 3 A schematic block diagram of an electronic device provided in an embodiment of this disclosure. Detailed Implementation

[0018] The embodiments of this disclosure will now be described in detail with reference to the accompanying drawings.

[0019] It should be understood that the following specific examples illustrate the implementation of this disclosure, and those skilled in the art can easily understand other advantages and effects of this disclosure from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this disclosure, and not all of them. This disclosure can also be implemented or applied through other different specific implementation methods, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this disclosure. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0020] It should be noted that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice method. Furthermore, this device and / or practice method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0021] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this disclosure. The illustrations only show the components related to this disclosure and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0022] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0023] One-dimensional vertical dimension refers to simplifying the complex three-dimensional spatial motion of the recovered rocket during the landing phase in the mathematical model by considering only the motion in the vertical (height / longitudinal) direction, while temporarily ignoring the motion in the horizontal (lateral / lateral) direction.

[0024] The Bang-Bang fuel-optimal thrust profile refers to the on-off optimal control form determined based on the maximum principle in the field of control. In order to achieve the minimum fuel consumption, the amplitude of the control variable follows a profile form that changes between the upper and lower limits over time.

[0025] This embodiment is applicable to trajectory planning for reusable rockets with multi-engine parallel configurations during the powered landing phase.

[0026] like Figure 1 As shown, this embodiment discloses a trajectory planning method for the powered landing phase of a recoverable rocket based on convex optimization, including: Establish a landing trajectory planning model that includes engine operating mode switching; Based on a one-dimensional vertical motion model, the flight time under different engine operating modes is calculated analytically. By using the flight time calculated under different engine operating modes, the trajectory planning model is discretized and non-destructively convexized, thereby transforming the trajectory planning model into a convex optimization problem and solving it to obtain the fuel-optimal landing reference trajectory.

[0027] In a specific scenario, a landing rectangular coordinate system is defined with the preset landing point as the origin. The three-degree-of-freedom center-of-mass motion of the rocket-powered landing is described under this landing coordinate system. Important engineering constraints are added, including initial and final state constraints, attitude angle constraints, attitude angle change rate constraints, thrust magnitude constraints, and flight path constraints. The magnitude of thrust in three directions is used as the control variable, and aerodynamic forces are ignored. A landing trajectory planning model including one engine operating mode switch is established. The landing trajectory planning model is used to solve the fuel-optimal trajectory optimization problem, which is a time-free fuel-optimal control problem. By selecting the coordinate system and control variables, considering the main engineering constraints in the landing process, and simplifying the model, the optimization problem is not only easier to solve, but the obtained reference trajectory can fit the expected characteristics of gradual change and rapid convergence near the terminal, which is easy to carry out trajectory tracking and guidance design.

[0028] In the one-dimensional vertical dimension, design the optimal thrust profile for bang-bang fuel, where , These represent the thrust of the three turbine sections and the thrust of the first turbine section, respectively. The optimal values ​​are the minimum permissible thrust of the three turbine sections and the maximum permissible thrust of the first turbine section. Based on the feasibility of tracking the planned trajectory, and We select values ​​close to the theoretical optimal boundary, reserving a thrust adjustment margin. Let the flight times for the three-stage and one-stage operations be respectively... , Combined with the initial position Initial velocity and initial mass Engine specific impulse A simple analytical derivation yields the analytical expression for the position and velocity at any given time. To ensure precise landing control, a sufficiently long working section for one aircraft is typically required; therefore, the altitude at which the aircraft transitions from three to one must not be lower than a threshold value. To achieve lower fuel consumption, the switching height should be set directly to the lower limit. After introducing the switching height constraint, and combining it with the terminal position and velocity constraint, we can finally obtain information about the three unknown variables. The three nonlinear equations are used to solve the two flight times. The three-engine segment is the first mode, and the one-engine segment is the second mode. In this embodiment, the three-engine and one-engine segments are illustrative of a specific example and are not limited to three-engine and one-engine segments. The first mode can also use five engines, and the second mode can use two engines. Five engines refer to five engines, and two engines refer to two engines. That is, the engine operating mode in this embodiment can be used in various application scenarios such as five engines switching to three engines, five engines switching to one engine, and three engines switching to two engines.

[0029] Based on the two flight times The landing trajectory planning model was discretized using trapezoidal methods at equal time intervals in both the three-engine and one-engine working sections. A lossless convexity optimization method was employed, introducing relaxed thrust, substituting variables for mass and thrust, and adding relaxation constraints for the initial vertical landing velocity. Ultimately, the original problem was transformed into a convex optimization problem with second-order cone constraints. An interior-point method solver was used to solve this convex optimization problem, yielding a landing reference trajectory that satisfies the constraints. Figure 1 In this context, S represents the number of iterations.

[0030] Establishing a landing coordinate system, such as Figure 2 As shown, the origin of the coordinate system is located at the landing point and rotates with the Earth. The OY axis is perpendicular to the local horizontal plane, pointing upwards as positive. The OX and OZ axes are within the local horizontal plane, with the OX axis pointing to the same azimuth as the launch azimuth. The landing trajectory planning model established under the landing system is shown below.

[0031] Problem 0: Objective function: , Constraints: (1) Constraints of the dynamic equations: , (2) Initial position, velocity, and mass constraints: , (3) Initial attitude constraints: , (4) Terminal position and speed constraints: , (5) Terminal vertical attitude constraint: , (6) Thrusting magnitude constraints of the three turbine sections: , (7) Thrust magnitude constraint of the first section: , (8) Motion path constraints: , (9) Thrusting direction constraint of the three-stage engine section: , (10) Thrust orientation constraint of the first section: , (11) Thrusting connection constraints when switching from three engines to one engine: , (12) Attitude change rate constraint of the three sections: , (13) Attitude change rate constraint of section 1: , In the formula, For the rocket at all times acceleration, For the rocket at all times The rate of change in mass, The initial position, The initial velocity, This represents the initial mass of the rocket at the start of the landing phase. and These are the initial pitch and yaw attitude angles, For terminal location, For terminal speed, This is the theoretical specific impulse of a single engine. The acceleration due to gravity is constant, as the altitude does not change significantly during the landing phase. , This is the initial gravitational acceleration. and These represent the upper and lower limits of the permissible operating conditions for the three machine sections, respectively. and These represent the upper and lower limits of the permissible operating conditions for the first section of the machine. This refers to the nominal thrust of a single engine under 100% operating conditions. The maximum permissible flight path angle, and These are the maximum permissible thrust pointing angles for the third and first turbine sections, respectively. The after-effect acceleration of the two surrounding machines after shutdown is modeled as follows: , in and These are the set constants, The vertical height at the moment when the three machines switch to one machine. For location, For speed; , and At time respectively Rockets , and Position coordinates along the axis, For a moment The right limit at the next instant, For a moment The left limit at the next instant For time parameters, and These are the pitch and yaw attitude angles, respectively.

[0032] The two flight times based on one-dimensional vertical motion are calculated as follows: Considering the real-time change in rocket mass with fuel consumption, the following one-dimensional vertical dynamic model is established.

[0033] The expression for the acceleration of a rocket under engine thrust is: , in, They represent The magnitude of the thrust under machine operation. For the real-time quality of the rocket.

[0034] The mass flow rate of the rocket is calculated as follows: , in, This represents the total thrust of the current engine. This refers to the specific impulse of the engine.

[0035] Real-time quality Represented as initial mass Subtract the mass of fuel consumed. For the three-stage unit, its acceleration can be rewritten as: , For the first section, the initial mass in the denominator of its acceleration should be the remaining mass after the completion of the third section's work, i.e. Then the acceleration of section one is: , in, This represents the initial mass of the rocket at the start of the landing phase.

[0036] Given the thrust of three engines and one engine thrust In this case, by integrating the above acceleration, Obtain the target position when the rocket lands. Target speed at landing And the height of three machines turning into one machine The dynamic equations are: Velocity constraint equations : , Position constraint equations : , Three-machine-to-one-machine height constraint equation : , in, The target location for landing. For the target speed at landing, The initial velocity at the current moment, The initial velocity at the current moment, Let gravitational acceleration be the acceleration due to gravity. As mentioned earlier, considering the feasibility of tracking the planned trajectory, a thrust adjustment margin is reserved, and we take... ,in This represents the maximum permissible thrust of a single engine section. Therefore, the above equations, when combined, form a system containing three unknowns. , and The nonlinear equation system: , in This three-dimensional nonlinear equation system can be solved quickly and stably using the robust Levenberg-Marquardt (LM) method.

[0037] The convexity transformation and solution of the trajectory optimization problem are as follows: By applying a lossless convexity method, relaxation thrust is introduced. And perform variable substitution. , , Simultaneously, combining the calculated flight time, an equal-time discretization strategy is adopted, taking time intervals in the three-aircraft working segment and the one-aircraft working segment respectively. , discrete points, and Let be a constant, and the quantities at each discrete point be distinguished by the subscripts 3 and 1. Let the time interval between each discrete point be denoted as . , Furthermore, by incorporating initial vertical velocity relaxation, Problem 0 can be transformed into a convex optimization problem as shown below, defined as Problem 1: Objective function: , As a penalty item, This is the penalty coefficient.

[0038] Constraints: (1) Dynamic equation: , , (2) Initial position, velocity, and mass constraints: , , , , (3) Initial attitude constraints: , (4) Terminal position and velocity constraints: , (5) Terminal vertical attitude constraint: , (6) Thrusting magnitude constraints of the three turbine sections: , (7) Thrust magnitude constraint of the first section: , (8) Motion path constraints: , , (9) Thrusting direction constraint of the three-stage engine section: , (10) Thrust orientation constraint of the first section: , (11) Constraints on the connection between three machines and one machine: , , (12) Attitude change rate constraint of the three sections: , (13) Attitude change rate constraint of section 1: , (14) Relaxation term constraint: , In the formula It is a relatively large fixed penalty coefficient. , For the third section and the first section Value profile (mass profile). This represents the rocket's position at the corresponding moment in the three engine stages. This represents the rocket velocity at the corresponding moment in each of the three engine stages. This is the logarithm of the mass of the three machine sections at the corresponding moment. The rocket's position at the corresponding moment in section one. This represents the rocket velocity at the corresponding moment in the first stage. Let be the logarithm of the mass of a machine section at a corresponding moment. This refers to the relaxation thrust acceleration at the corresponding moment in the three turbine sections. This represents the relaxation thrust acceleration at the corresponding moment in the turbine section. This represents the thrust acceleration at the corresponding moment in the three turbine sections. This represents the thrust acceleration at the corresponding moment in the first section. For location, 3 and 1 represent the third depot and the first depot, respectively. Let x represent the rocket velocity, and z represent the coordinate axes. For the combinations of parameters in this embodiment, the meaning of the combined values ​​can be clearly understood based on the functions of each parameter. For natural numbers, This is the initial velocity relaxation term.

[0039] , Each time a solution is obtained, the value is updated based on the result of the previous solution, and initialized as follows: , , This is the after-effect acceleration profile of the first section. Similarly, it is updated based on the previous solution result in each solution iteration, initialized to... By solving Problem 1 several times (usually 2-3 times) and updating the mass profile and aftereffect acceleration profile in the next solution based on the results of each solution, the flight trajectory with optimal fuel consumption can be obtained in the end.

[0040] The method disclosed in this embodiment has the following effects: Achieving optimal landing trajectory planning for fuel consumption: The landing trajectory planning model is solved using convex optimization methods. By leveraging the uniqueness of the global optimal solution of the convex optimization problem, the generated landing trajectory is ensured to achieve global optimal fuel consumption while satisfying all engineering constraints such as engine number switching, attitude constraints, and landing speed constraints. This effectively improves the reusability efficiency of the rocket and the economy of the mission.

[0041] High computational efficiency and robustness: The original problem is transformed into a convex optimization model with polynomial time complexity and low computational cost, which can meet the needs of online engineering applications; combined with the mature interior point method, the algorithm is guaranteed to converge quickly and be stable and reliable, with excellent robustness.

[0042] High adaptability: The method in this embodiment can dynamically plan the trajectory based on real-time status parameters such as rocket speed, position, and mass, overcoming the shortcomings of traditional offline solutions that cannot cope with flight uncertainties, significantly improving adaptability to shift handover status deviations, and enhancing the deviation correction capability of the rocket's powered soft landing phase.

[0043] Wide applicability: The method in this embodiment has universal scalability and can be extended to other rocket models with multi-engine configurations. Without reconstructing the core algorithm, only the model parameters need to be adjusted to achieve rapid trajectory planning under various engine number switching combinations such as five engines to three engines and three engines to two engines.

[0044] This embodiment also discloses a trajectory planning device for the powered landing phase of a recoverable rocket based on convex optimization, including: The model building module is used to build a landing trajectory planning model that includes engine operating mode switching; The analysis module is used to analyze and calculate the flight time under different engine operating modes based on a one-dimensional vertical motion model; The non-destructive convexity processing module is used to discretize and non-destructively convexize the trajectory planning model using the flight time calculated under different engine operating modes, thereby transforming the trajectory planning model into a convex optimization problem and solving it to obtain the fuel-optimal landing reference trajectory.

[0045] This embodiment uses the Levenberg-Marquardt algorithm as the basic solution algorithm for three-dimensional nonlinear equations. To further enhance the convergence efficiency and robustness of the solution process, it can be extended and integrated with other high-performance nonlinear equations solution algorithms, including various trust region improvement algorithms and quasi-Newton improvement algorithms.

[0046] This embodiment designs a relaxation scheme for the initial vertical velocity constraint. This relaxation scheme can be further extended to other equality constraints in the landing trajectory planning model to improve the feasible region coverage and solution stability of the optimization problem.

[0047] The method of this embodiment can be operated on an electronic device, which includes a memory and a processor. The memory is used to store non-transitory computer-readable instructions. Specifically, the memory may include one or more computer program products, which may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may, for example, include random access memory (RAM) and / or cache memory. The non-volatile memory may, for example, include read-only memory (ROM), a hard disk, flash memory, etc.

[0048] The processor may be a central processing unit (CPU) or other processing unit with data processing and / or instruction execution capabilities, and may control other components in the electronic device to perform desired functions. In one embodiment of this disclosure, the processor is used to run the computer-readable instructions stored in the memory, causing the electronic device to perform all or part of the steps of the convex optimization-based trajectory planning method for the powered landing segment of a recoverable rocket according to the foregoing embodiments of this disclosure.

[0049] Those skilled in the art will understand that, in order to solve the technical problem of how to achieve a good user experience, this embodiment may also include well-known structures such as communication buses and interfaces, and these well-known structures should also be included within the protection scope of this disclosure.

[0050] like Figure 3 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present disclosure. It illustrates a structural schematic diagram suitable for implementing the electronic device in the embodiment of the present disclosure. Figure 3 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of the embodiments disclosed herein.

[0051] like Figure 3 As shown, an electronic device may include a processing unit (such as a central processing unit, graphics processing unit, etc.) that can perform various appropriate actions and processes based on a program stored in read-only memory (ROM) or a program loaded from a storage device into random access memory (RAM). The RAM also stores various programs and data required for the operation of the electronic device. The processing unit, ROM, and RAM are interconnected via a bus. Input / output (I / O) interfaces are also connected to the bus.

[0052] Typically, the following devices can be connected to the I / O interface: input devices, such as sensors or visual information acquisition devices; output devices, such as displays; storage devices, such as magnetic tapes or hard drives; and communication devices. Communication devices allow electronic devices to exchange data wirelessly or via wired communication with other devices, such as edge computing devices. Although Figure 3 Electronic devices with various devices are shown, but it should be understood that it is not required to implement or have all of the devices shown. More or fewer devices may be implemented or have instead.

[0053] In particular, according to embodiments of this disclosure, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of this disclosure include a computer program product comprising a computer program carried on a non-transitory computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device, or installed from a storage device, or installed from a ROM. When the computer program is executed by a processing device, all or part of the steps of the convex optimization-based trajectory planning method for the powered landing phase of a recoverable rocket according to embodiments of this disclosure are performed.

[0054] For a detailed description of this embodiment, please refer to the corresponding descriptions in the foregoing embodiments, which will not be repeated here.

[0055] A computer-readable storage medium according to embodiments of the present disclosure stores non-transitory computer-readable instructions. When these non-transitory computer-readable instructions are executed by a processor, all or part of the steps of the convex optimization-based trajectory planning method for the powered landing segment of a recoverable rocket according to the foregoing embodiments of the present disclosure are performed.

[0056] The aforementioned computer-readable storage media include, but are not limited to: optical storage media (e.g., CD-ROM and DVD), magneto-optical storage media (e.g., MO), magnetic storage media (e.g., magnetic tape or portable hard drive), media with built-in rewritable non-volatile memory (e.g., memory card), and media with built-in ROM (e.g., ROM cartridge).

[0057] For a detailed description of this embodiment, please refer to the corresponding descriptions in the foregoing embodiments, which will not be repeated here.

[0058] The basic principles of this disclosure have been described above with reference to specific embodiments. However, it should be noted that the advantages, benefits, and effects mentioned in this disclosure are merely examples and not limitations, and should not be considered as essential features of each embodiment of this disclosure. Furthermore, the specific details disclosed above are for illustrative and facilitative purposes only, and are not limitations. These details do not limit the scope of this disclosure to the necessity of employing the aforementioned specific details for implementation.

[0059] In this disclosure, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. The block diagrams of devices, apparatuses, devices, and systems involved in this disclosure are merely illustrative examples and are not intended to require or imply that they must be connected, arranged, or configured in the manner shown in the block diagrams. As those skilled in the art will recognize, these devices, apparatuses, devices, and systems can be connected, arranged, and configured in any manner. Words such as "comprising," "including," "having," etc., are open-ended terms meaning "including but not limited to," and are used interchangeably with them. The terms "or" and "and" as used herein refer to the terms "and / or," and are used interchangeably with them unless the context clearly indicates otherwise. The term "such as" as used herein refers to the phrase "such as but not limited to," and is used interchangeably with it.

[0060] Additionally, as used herein, the "or" used in a list of items beginning with "at least one" indicates a separate list, such that a list of, for example, "at least one of A, B, or C" means A or B or C, or AB or AC or BC, or ABC (i.e., A and B and C). Furthermore, the word "exemplary" does not imply that the described example is preferred or better than other examples.

[0061] It should also be noted that in the systems and methods of this disclosure, the components or steps can be decomposed and / or recombined. These decompositions and / or recombinations should be considered as equivalent solutions to this disclosure.

[0062] Various changes, substitutions, and modifications can be made to the techniques described herein without departing from the teachings defined in this embodiment. Furthermore, the scope of this embodiment is not limited to the specific aspects of the processes, machines, manufacturing processes, events, means, methods, and actions described above. Currently existing or later-developed processes, machines, manufacturing processes, events, means, methods, or actions that perform substantially the same functions or achieve substantially the same results as the corresponding aspects described herein can be utilized. Therefore, this embodiment includes such processes, machines, manufacturing processes, events, means, methods, or actions within its scope.

[0063] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use this disclosure. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein can be applied to other aspects without departing from the scope of this disclosure. Therefore, this disclosure is not intended to be limited to the aspects shown herein, but rather to be carried out within the widest scope consistent with the principles and novel features disclosed herein.

[0064] The above description has been given for purposes of illustration and description. Furthermore, this description is not intended to limit the embodiments of this disclosure to the forms disclosed herein. Although numerous exemplary aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, alterations, additions, and sub-combinations therein.

Claims

1. A trajectory planning method for the powered landing phase of a recoverable rocket based on convex optimization, characterized in that, include: Establish a landing trajectory planning model that includes engine operating mode switching; Based on a one-dimensional vertical motion model, the flight time under different engine operating modes is calculated analytically. By using the flight time calculated under different engine operating modes, the trajectory planning model is discretized and non-destructively convexized, thereby transforming the trajectory planning model into a convex optimization problem and solving it to obtain the fuel-optimal landing reference trajectory. The engine operating modes include a first mode and a second mode; the analytical calculation of flight time under different engine operating modes based on a one-dimensional vertical motion model includes: In a one-dimensional vertical dimension, design the bang-bang fuel-optimal thrust profile from the first mode thrust to the second mode thrust; Based on the optimal fuel thrust profile, and according to rocket dynamics and mass flow equations, a set of three-dimensional nonlinear equations is obtained regarding the thrust magnitude of the first mode, the flight time of the first mode, and the flight time of the second mode. Solving the three-dimensional nonlinear equations yields the magnitude of the thrust in the first mode, the flight time in the first mode, and the flight time in the second mode.

2. The trajectory planning method for the powered landing phase of a recoverable rocket based on convex optimization according to claim 1, characterized in that, Based on rocket dynamics and the mass flow equation, a set of three-dimensional nonlinear equations is obtained regarding the thrust magnitude of the first mode, the flight time of the first mode, and the flight time of the second mode, including: Given the first and second mode thrusts, the dynamic equations are obtained by integrating the rocket's acceleration under engine thrust. These dynamic equations include velocity constraint equations. Position constraint equations and the high constraint equations for transitioning from the first mode to the second mode ; Equation ,equation sum equation A system of three-dimensional nonlinear equations is formed by combining the equations. It is a vector consisting of the thrust magnitude of the first mode, the flight time of the first mode, and the flight time of the second mode.

3. The trajectory planning method for the powered landing phase of a recoverable rocket based on convex optimization according to claim 1, characterized in that, The constraints for establishing the landing trajectory planning model that includes engine operating mode switching include: The constraints are as follows: dynamic equations; initial position, velocity, and mass constraints of the rocket at the start of the powered landing phase; initial attitude constraints of the rocket at the start of the powered landing phase; terminal position and velocity constraints of the rocket; vertical attitude constraints of the rocket at the terminal phase; first-mode thrust magnitude constraints; second-mode thrust magnitude constraints; motion path constraints; first-mode thrust direction constraints; second-mode thrust direction constraints; first-mode to second-mode thrust transition constraints; first-mode attitude change rate constraints; and second-mode attitude change rate constraints; the terminal phase is the end point of the powered landing phase.

4. The trajectory planning method for the powered landing phase of a recoverable rocket based on convex optimization according to claim 1, characterized in that, The non-destructive convexity process includes: introducing relaxation thrust. By replacing the rocket's mass and thrust vector with variables, the trajectory planning model is transformed into a convex optimization problem.

5. The trajectory planning method for the powered landing phase of a recoverable rocket based on convex optimization according to claim 4, characterized in that, The variable substitution for rocket mass and thrust vector includes: , , ,in For rocket mass, For thrust vector, For the logarithm of mass, For thrust acceleration vector, This is for relaxation thrust acceleration.

6. The trajectory planning method for the powered landing phase of a recoverable rocket based on convex optimization according to claim 4, characterized in that, The trajectory planning model is discretized and lossless convexized to transform it into a convex optimization problem for solution, including: Introducing slack variables Furthermore, a penalty term is added to the objective function for solving convex optimization problems.

7. The trajectory planning method for the powered landing phase of a recoverable rocket based on convex optimization according to claim 4, characterized in that, The process of discretizing and lossless convexification of the trajectory planning model using the calculated flight times under different engine operating modes includes: By utilizing the flight time under different engine operating modes, the first and second mode operating segments are discretized at equal time intervals, transforming the continuous dynamic equations into discrete linear equality constraints.

8. The trajectory planning method for the powered landing phase of a recoverable rocket based on convex optimization according to claim 7, characterized in that, After discretization and lossless convexization, the trajectory planning model is transformed into a convex optimization problem with second-order cone constraints. The interior point method solver is used for numerical solution, and the mass profile and after-effect acceleration profile are updated iteratively to obtain the final fuel-optimal trajectory.

9. A trajectory planning device for the powered landing phase of a recoverable rocket based on convex optimization, characterized in that, include: The model building module is used to build a landing trajectory planning model that includes engine operating mode switching; The analysis module is used to analyze and calculate the flight time under different engine operating modes based on a one-dimensional vertical motion model; The non-destructive convexity processing module is used to discretize and non-destructively convexize the trajectory planning model using the flight time calculated under different engine operating modes, thereby transforming the trajectory planning model into a convex optimization problem and solving it to obtain the fuel-optimal landing reference trajectory. The engine operating modes include a first mode and a second mode; the analytical calculation of flight time under different engine operating modes based on a one-dimensional vertical motion model includes: In a one-dimensional vertical dimension, design the bang-bang fuel-optimal thrust profile from the first mode thrust to the second mode thrust; Based on the optimal fuel thrust profile, and according to rocket dynamics and mass flow equations, a set of three-dimensional nonlinear equations is obtained regarding the thrust magnitude of the first mode, the flight time of the first mode, and the flight time of the second mode. Solving the three-dimensional nonlinear equations yields the magnitude of the thrust in the first mode, the flight time in the first mode, and the flight time in the second mode.

10. The trajectory planning device for the powered landing phase of a recoverable rocket based on convex optimization according to claim 9, characterized in that, Based on rocket dynamics and the mass flow equation, a set of three-dimensional nonlinear equations is obtained regarding the thrust magnitude of the first mode, the flight time of the first mode, and the flight time of the second mode, including: Given the first and second mode thrusts, the dynamic equations are obtained by integrating the rocket's acceleration under engine thrust. These dynamic equations include velocity constraint equations. Position constraint equations and the high constraint equations for transitioning from the first mode to the second mode ; Equation ,equation sum equation A system of three-dimensional nonlinear equations is formed by combining the equations. It is a vector consisting of the thrust magnitude of the first mode, the flight time of the first mode, and the flight time of the second mode.

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