A solid rocket trajectory optimization design method based on internal trajectory parameterization modeling

Abstract

This invention belongs to the field of commercial aerospace and solid rocket optimization, and discloses a solid rocket trajectory optimization design method based on internal ballistic parameterization modeling. The method includes: determining the structural and energy characteristic parameters of the solid rocket motor; designing different types of propellant grains and constructing their geometric models; determining the internal ballistic parameterization model of the motor; constructing a dynamic model for joint optimization of the internal and external trajectories of the solid rocket; based on the dynamic model, setting the optimization objective of the joint internal and external trajectory optimization problem and representing it with a performance index function, and setting the constraints of the joint internal and external trajectory optimization problem; discretizing the dynamic model, performance index function, and constraints, converting them into a nonlinear programming problem and solving it to obtain the optimization results corresponding to each type of propellant grain; determining the performance index corresponding to each type of propellant grain based on the optimization results, and using the performance index to determine the propellant grain as the optimal design scheme.

Description

Technical Field

[0001] This invention relates to the field of commercial aerospace and solid rocket optimization, specifically to a solid rocket trajectory optimization design method based on internal trajectory parameterization modeling. Background Technology

[0002] Solid rocket technology, due to its simple structure, low cost, high reliability, and rapid response capability, has gradually become a new research hotspot in the commercial aerospace field. The performance limit of a solid rocket depends on the coupling level between two parts: the internal ballistics (the propulsion system of the solid rocket) and the external ballistics (the flight trajectory of the solid rocket). The internal ballistics subsystem generates the optimal thrust-time curve by designing the parameters of the engine and propellant grains; the external ballistics subsystem generates the optimal flight trajectory by designing the flight commands of the solid rocket.

[0003] Current solid rocket design employs a sequential "internal-to-external" approach, first designing an internal engine trajectory model based on experience or optimization, then substituting this fixed engine model into the solid rocket dynamics model for external trajectory design. This internal trajectory design focuses solely on maximizing peak thrust or total impact without coupling it to the actual energy consumption and maneuverability requirements of the solid rocket during atmospheric flight, resulting in the unrealized range potential of the rocket. Furthermore, modifications to internal trajectory parameters rely on feedback from the external trajectory, leading to low iterative efficiency. Therefore, this traditional fragmented design approach suffers from shortcomings in both performance optimization and iteration costs. Summary of the Invention

[0004] The purpose of this invention is to provide a solid rocket trajectory optimization design method based on internal trajectory parameterization modeling, in order to solve the problems that traditional serial design methods cannot fully release the range capability of solid rockets, and require a long development cycle and high testing costs.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] A solid rocket trajectory optimization design method based on internal trajectory parameterization modeling includes:

[0007] Determine the structural and energy characteristics of the solid rocket motor, design different types of propellant grains and construct their geometric models; construct the zero-dimensional internal ballistic equations of the motor, calculate the thrust and second consumption of the motor, and determine the parameterized internal ballistic model of the motor.

[0008] Based on the aforementioned internal ballistic parameterization model, a dynamic model for the joint optimization of the internal and external trajectories of a solid rocket is constructed. On the basis of the dynamic model, the optimization objective of the joint optimization problem of the internal and external trajectories is set and characterized by a performance index function, and the constraints of the joint optimization problem of the internal and external trajectories are set.

[0009] The dynamic model, performance index function, and constraints are discretized to transform the joint optimization problem of internal and external trajectories into a nonlinear programming problem. The problem is then solved using a sequential quadratic programming algorithm to obtain the optimization results for each type of propellant. Based on the optimization results, the performance index for each type of propellant is determined, and the propellant used as the optimal design scheme is determined using the performance index.

[0010] Furthermore, the structural parameters include the length and radius of the engine, the throat radius of the nozzle, and the nozzle exit area; the energy characteristic parameters include the solid propellant density, specific heat ratio, and characteristic velocity.

[0011] When designing different types of propellant grains, the basic shape of the propellant grain is cylindrical, the outer diameter of the propellant grain is the same as the engine radius, and the length of the propellant grain is no greater than the length of the engine. Different types of propellant grains have openings with different structures set at the center of the basic shape.

[0012] Furthermore, a zero-dimensional internal ballistic equation for the engine is constructed, the engine's thrust and second consumption are calculated, and the parameterized internal ballistic model of the engine is determined, including:

[0013] Based on the internal ballistic pressure calculation formula, combined with the nozzle throat area, burning rate coefficient, burning rate index and the energy characteristic parameters, the combustion chamber pressure is calculated.

[0014] Based on the combustion model of the propellant grain, the second consumption is calculated by using the burning rate coefficient, burning rate exponent, and the energy characteristic parameters and combustion chamber pressure.

[0015] The thrust coefficient is calculated using energy characteristic parameters, combined with nozzle exit pressure, sea level pressure, combustion pressure, and the aforementioned structural parameters.

[0016] The thrust is calculated by combining the thrust coefficient, the structural parameters, and the energy characteristic parameters.

[0017] Using the combustion rate index and combustion rate coefficient as the design parameters, and considering the thrust and second consumption as functions related to the design parameters, the internal ballistic parameterized model of the engine is obtained.

[0018] Furthermore, with the range of solid rockets ,high directional velocity High-altitude velocity ,quality Angle of attack For state variables, the rate of change of angle of attack To control the amount Combined with the engine's internal ballistic parameterization model and The dynamic model for the joint optimization of the internal and external trajectories of the solid rocket is obtained:

[0019] ;

[0020] Among them, add “” above the parameter " indicates the derivative of the parameter; For speed, For the trajectory inclination angle, It is the acceleration due to gravity. As resistance, For lift, This is the reference area for solid rockets; for different burn rate indices and burn rate coefficient The calculated thrust and time per second They are also different; and Considered as and The relevant functions are represented as follows: and .

[0021] Furthermore, the optimization objective of the joint internal and external ballistic optimization problem is set and characterized by a performance index function, expressed as:

[0022] ;

[0023] in, For performance indicators, For terminal height, For time, At the initial moment, For the terminal time, The coefficient of the regularization term must satisfy the following condition: ; It represents the derivative with respect to time.

[0024] Furthermore, constraints are set for the joint optimization problem of internal and external ballistics, including:

[0025] Process constraints:

[0026] ;

[0027] in, and Each is a range The lower and upper bounds of the constraints and They are respectively height The lower and upper bounds of the constraints and respectively directional velocity The lower and upper bounds of the constraints and They are the high-altitude velocities. The lower and upper bounds of the constraints and Angle of attack The lower and upper bounds of the constraint;

[0028] Terminal constraints: ; express The high-speed velocity at any given moment;

[0029] Control constraints: ; and Control Quantity The lower and upper bounds of the constraint;

[0030] Parameter constraints:

[0031] ;

[0032] in, , These are the lower and upper bounds of the burn rate index, respectively. , These are the lower and upper bounds of the burn rate coefficient, respectively.

[0033] Furthermore, the dynamic model, performance index function, and constraints are discretized to transform the joint optimization problem of internal and external trajectories into a nonlinear programming problem, including:

[0034] First, the continuous time domain is divided into multiple sub-intervals, and the state and control variables are parameterized at the Legendre-Gauss-Lobatto integration points in each sub-interval. The dynamic model is transformed into algebraic constraints through differential matrices. The performance index function is discretized into an integral objective function. The constraints are explicitly embedded into discrete nodes, thereby transforming the joint optimization problem of internal and external trajectories into a nonlinear programming problem.

[0035] Furthermore, the process of solving the problem using the sequential quadratic programming algorithm includes:

[0036] An initial point is set for the generated nonlinear programming problem, and the Hessian matrix is ​​updated using the BFGS quasi-Newton method to accelerate convergence. In each iteration, the solution of the QP subproblem is used to update the control variable, and the filter method is introduced to handle constraint violation problems to ensure global convergence.

[0037] Furthermore, after solving the sequential quadratic programming problem, the optimization results for each type of propellant are obtained, including the optimal burning rate index, the optimal burning rate coefficient, and the corresponding control variables. The optimization results for each type of propellant are substituted into the dynamic model to calculate the corresponding flight trajectory, and the terminal altitude is determined from the flight trajectory. The terminal altitude and the corresponding control variables are substituted into the performance index function to calculate the performance index. The performance indexes for each type of propellant are compared, and the propellant with the smallest performance index is selected as the optimal design scheme.

[0038] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, it implements the solid rocket trajectory optimization design method based on internal trajectory parameterization modeling.

[0039] A computer-readable storage medium storing a computer program; when executed by a processor, the computer program implements the solid rocket trajectory optimization design method based on internal trajectory parameterization modeling.

[0040] Compared with the prior art, the present invention has the following technical features:

[0041] This invention combines a parameterized internal ballistic model with an external ballistic model to construct a joint optimization problem for internal and external trajectories. The Gaussian pseudospectral method is used to solve the optimal problem, achieving joint parameter optimization of internal and external trajectories. This invention abandons the traditional "internal-to-external" sequential design mode in solid rocket design, enabling rapid determination of propellant type, burn rate index, burn rate coefficient, and optimal control variables, significantly improving solid rocket performance. Furthermore, the internal ballistic model construction ensures that the optimization results satisfy the physical laws of the engine, guaranteeing the feasibility of the optimization results. This invention has been applied to the joint optimization design of internal and external trajectories for long-range rockets with excellent design results, providing strong support for the design and technological development of solid rockets in commercial aerospace. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the process of the present invention;

[0043] Figure 2 The diagram shows the geometric models of three types of propellant grains for solid rocket motors; (a) and (b) are the right and front views of a circular hole propellant grain; (c) and (d) are the right and front views of a star hole propellant grain; (e) and (f) are the right and front views of a wing-shaped propellant grain.

[0044] Figure 3 A simulation comparison of the time-height curves of the embodiments of the present invention with those of traditional design methods;

[0045] Figure 4 A simulation comparison of the time-velocity curves of the embodiments of the present invention and the traditional design method;

[0046] Figure 5 This is a simulation comparison of the time-thrust curves of the embodiments of the present invention and the traditional design method. Detailed Implementation

[0047] To address the problems existing in the current technology, there is an urgent need for a joint design method that incorporates the internal and external trajectories into a unified optimization framework. This would enable a high degree of matching between the engine energy release pattern and the atmospheric flight environment and terminal indicators in the early stages of development, thereby improving the carrying capacity of solid rockets and significantly shortening the development cycle.

[0048] This invention provides a solid rocket trajectory optimization design method based on internal trajectory parameterization modeling, see [link to relevant documentation]. Figure 1 This includes the following steps:

[0049] Step 1: Determine the structural and energy characteristics of the solid rocket motor, design different types of propellant grains and construct their geometric models; construct the zero-dimensional internal ballistic equations of the motor, calculate the thrust and second consumption of the motor, and determine the parameterized internal ballistic model of the motor.

[0050] Step 1.1: Determine the structural parameters based on the external dimensions of the solid rocket and nozzle, including the length and radius of the engine and the throat radius of the nozzle. and nozzle exit area Determine energy characteristic parameters, including solid propellant density, based on the engine's propellant formulation. (Typical value 1500~2000 kg / m³), specific heat ratio (Typical value 1.1~1.3) and characteristic velocity (Typical values: 1,500~2,000 m / s).

[0051] Step 1.2: Using the length and radius of the engine as constraints, design different types of propellant grains and construct their geometric models; the basic shape of the propellant grain is cylindrical, the outer diameter of the propellant grain is consistent with the radius of the engine, and the length of the propellant grain is not greater than the length of the engine.

[0052] In this embodiment of the invention, in order to control the combustion surface of the propellant, openings of different shapes are designed at the center of the basic shape to form different types of propellant grains as an internal ballistic scheme; the propellant grains include circular hole propellant grains, star hole propellant grains, and wing-shaped propellant grains, such as... Figure 2 As shown in (a) to (f); a round-hole propellant is a propellant with a round hole in the internal axial direction; a star-shaped propellant is a propellant with a star-shaped hole in the internal axial direction, which is formed by multiple rectangular star holes along the circumference; a wing-shaped propellant is a propellant formed by multiple diverging wing columns at the rear end of the round hole, based on a round-hole propellant.

[0053] Based on the geometric model of the propellant grain and the formulas for calculating the area and volume of a cylinder, the burning surface area of ​​different types of propellant grains at any cross-section can be calculated. .

[0054] Step 1.3: Construct the engine's zero-dimensional internal ballistic equations and calculate the engine's thrust. and time per second .

[0055] ① Calculate the combustion chamber pressure based on the internal ballistic pressure calculation formula. ,have:

[0056] (1);

[0057] in, This represents the throat area of ​​the nozzle. This is the combustion rate coefficient. This refers to the burn rate index.

[0058] ② A combustion model based on the propellant charge is used to calculate the consumption per second. ,have:

[0059] (2);

[0060] ③ Calculate the thrust coefficient ,have:

[0061] (3);

[0062] in, This refers to the nozzle outlet pressure. This refers to sea level pressure.

[0063] ④ Calculate thrust ,have:

[0064] (4);

[0065] Step 1.4, for different types of propellant charges, in equations (2) and (4), except for the burning rate index and burn rate coefficient All other parameters are known; therefore, the burn rate index is used. and burn rate coefficient As a parameter to be designed and The corresponding range of change is and ,in , These are the lower and upper bounds of the burn rate index, respectively. , These are the lower and upper bounds of the burn rate coefficient, respectively; and the subsequent optimization process is to start from... and The optimal combustion rate index and the optimal combustion rate coefficient are obtained through optimization.

[0066] For different and The calculated thrust and time per second They are also different, therefore they can be and Considered as and The relevant functions are represented as follows: and That is, the internal ballistic parameterization model of the engine.

[0067] Step 2: Combine the internal ballistic parameterization model to construct a dynamic model for the joint optimization of the internal and external trajectories of a solid rocket; based on the dynamic model, set the optimization objective of the joint optimization problem of internal and external trajectories and characterize it with a performance index function, and set the constraints of the joint optimization problem of internal and external trajectories.

[0068] Step 2.1, based on the range of the solid rocket... ,high directional velocity High-altitude velocity ,quality Angle of attack For state variables, the rate of change of angle of attack To control the amount An external ballistic dynamics model is constructed, which is then combined with the engine's internal ballistic parameterization model. and The dynamic model for the joint optimization of the internal and external trajectories of the solid rocket is obtained:

[0069] (5);

[0070] Among them, add “” above the parameter " indicates the derivative of the parameter; For speed, For the trajectory inclination angle, It is the acceleration due to gravity. As resistance, The formulas for calculating lift, drag, and lift are as follows: and , and These are the drag coefficient and lift coefficient of a solid rocket, respectively. Atmospheric density, This is the reference area for solid rockets.

[0071] Step 2.2: Based on the aforementioned dynamic model, the optimization objective of the joint internal and external trajectory optimization problem is set as maximizing the flight altitude of the solid rocket. Simultaneously, to smooth the trajectory, a regularization term for the control variable is introduced into the optimization objective, which is then expressed as a performance index function:

[0072] (6);

[0073] in, For performance indicators, For terminal height, For time, At the initial moment, For the terminal time, The regularization coefficients set manually must satisfy the following conditions: , It represents the derivative with respect to time.

[0074] Step 2.3 sets the constraints for the joint optimization problem of internal and external ballistics, including process constraints, terminal constraints, control quantity constraints, and parameter constraints, as follows:

[0075] Process constraints are the conditions that a solid rocket's state must satisfy during flight:

[0076] (7);

[0077] in, and Each is a range The lower and upper bounds of the constraints and They are respectively height The lower and upper bounds of the constraints and respectively directional velocity The lower and upper bounds of the constraints and They are the high-altitude velocities. The lower and upper bounds of the constraints and Angle of attack The lower and upper bounds of the constraint.

[0078] Terminal constraints are constraints that limit the terminal state of a solid rocket:

[0079] (8);

[0080] in, express High velocity at any given moment.

[0081] Control constraints are for control variables Constraints on value selection:

[0082] (9);

[0083] in, and Control Quantity The lower and upper bounds of the constraint.

[0084] Parameter constraints are applied to the combustion rate index in the internal ballistic parameterization model of the engine. and burn rate coefficient The constraints are in the following form:

[0085] (10);

[0086] Step 3: Discretize the dynamic model, performance index function, and constraints to transform the joint optimization problem of internal and external trajectories into a nonlinear programming problem, and solve it using a sequential quadratic programming algorithm to obtain the optimization results for each type of propellant. Based on the optimization results, determine the performance index for each type of propellant, and use the performance index to determine the propellant as the optimal design scheme.

[0087] Step 3.1: The Gaussian pseudospectral method is used to discretize the dynamic model equation (5), performance index function equation (6), and constraint condition equations (7) to (10), transforming the joint optimization problem of internal and external trajectories into a nonlinear programming (NLP) problem. This invention selects the Gaussian pseudospectral method as the core discretization tool because it has spectral accuracy convergence characteristics and strong constraint processing capabilities when dealing with high-dimensional dynamic systems, and is particularly suitable for the nonlinear and multi-constraint characteristics in the joint optimization of internal and external trajectories of solid rockets.

[0088] In the specific implementation, the continuous time domain is first... Divided into N The process involves dividing the problem into sub-intervals and parameterizing the state and control variables at the Legendre-Gauss-Lobatto (LGL) integration points in each sub-interval. The dynamic model equation (5) is transformed into algebraic constraints using a differential matrix. The performance index function equation (6) is discretized into an integral objective function. Constraint equations (7) to (10) are explicitly embedded into discrete nodes (points obtained by discretizing the sub-intervals). This process transforms the original infinite-dimensional optimization problem into a finite-dimensional nonlinear programming (NLP) problem, ensuring computational feasibility while maintaining high accuracy. The discretization strategy of this invention specifically optimizes the node distribution for the strong nonlinear characteristics of solid rockets, avoiding the accuracy loss of traditional trapezoidal or Euler methods during the combustion mutation stage, thus laying a reliable foundation for subsequent solutions. The Gaussian pseudospectral method is an existing technology, and its relevant formulas are omitted here.

[0089] Step 3.2: For the generated nonlinear programming problem, the Sequential Quadratic Programming (SQP) algorithm is used to solve it. Specifically, an initial point is set, and the Hessian matrix is ​​updated using the BFGS quasi-Newton method to accelerate convergence. In each iteration, the solution to the QP subproblem is used to update the control variable. Meanwhile, a filter method is introduced to handle constraint violation problems and ensure global convergence. The SQP algorithm is an existing technology, and its relevant formulas are omitted here.

[0090] Step 3.3: After solving the sequential quadratic programming problem, the optimization results for each type of propellant can be obtained, including the optimal burning rate index, the optimal burning rate coefficient, and the corresponding control variables. Substitute the optimization results for each type of propellant into equation (5) to calculate the corresponding flight trajectory, and determine the terminal altitude from the flight trajectory. ;Will Substitute the corresponding control variables into equation (6) to calculate the performance index. Compare the performance indicators corresponding to each type of propellant column. The propellant grain with the lowest performance index is selected as the optimal design scheme to complete the ballistic optimization design of solid rocket.

[0091] Example.

[0092] In one embodiment of the present invention, when constructing the internal ballistic parameterization model, the parameters of the solid rocket are set as follows: the engine length is 3600mm and the radius is 215mm; the nozzle throat diameter... The nozzle exit area is 40mm. Set the solid propellant density to 0.1 m². It has a specific heat ratio of 1800 kg / m³. The characteristic velocity is 1.2. It is 1700 m / s; and The corresponding range of change is and .

[0093] In the process of constructing the joint optimization problem of internal and external trajectories of solid rockets and They are 0m and 300000m respectively; and They are 0m and 50000m respectively; and They are 0 m / s and 3000 m / s respectively; and The speeds are 0 m / s and 1000 m / s respectively. and These are -10° and 10° respectively; and The values ​​are -6° / s and 6° / s, respectively.

[0094] The optimization results of this embodiment are compared with the simulation results of the traditional design method (serial design method). The simulation results are as follows: Figures 3 to 5 As shown; the maximum height obtained using the traditional design method is 35.124 km, and the maximum speed is 3154.34 m / s; the maximum height obtained using the optimized result of this embodiment is 41.696 km, and the maximum speed is 3273.26 m / s, both of which are better than the results of the traditional design method; Figure 5 It is evident that this is because traditional design methods employ a sequential design approach, considering only the highest energy utilization rate when designing the internal trajectory. This results in a thrust curve with low thrust and long flight time. However, the use of low thrust leads to prolonged flight in dense atmosphere, resulting in significant aerodynamic deceleration. This invention employs joint optimization of internal and external trajectories, taking into account the influence of air resistance during the design process. It utilizes high thrust to enable the rocket to quickly traverse dense atmosphere, reducing energy loss caused by aerodynamic drag. Therefore, the maximum flight altitude and maximum speed are improved compared to traditional design methods. Simulations have verified the superiority of this invention in terms of solid rocket performance.

[0095] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A solid rocket trajectory optimization design method based on internal trajectory parameterization modeling, characterized in that, include: Determine the structural and energy characteristics of the solid rocket motor, design different types of propellant grains and construct their geometric models; Construct the zero-dimensional internal ballistic equations of the engine, calculate the engine's thrust and second consumption, and determine the parameterized internal ballistic model of the engine, including: Based on the internal ballistic pressure calculation formula, combined with the nozzle throat area, burning rate coefficient, burning rate index and the energy characteristic parameters, the combustion chamber pressure is calculated. Based on the combustion model of the propellant grain, the second consumption is calculated by using the burning rate coefficient, burning rate exponent, and the energy characteristic parameters and combustion chamber pressure. The thrust coefficient is calculated using energy characteristic parameters, combined with nozzle exit pressure, sea level pressure, combustion pressure, and the aforementioned structural parameters. The thrust is calculated by combining the thrust coefficient, the structural parameters, and the energy characteristic parameters. Using the burning rate index and burning rate coefficient as the parameters to be designed, and considering the thrust and second consumption as functions related to the parameters to be designed, the internal ballistic parameterization model of the engine is obtained. Based on the aforementioned internal ballistic parameterization model, a dynamic model for the joint optimization of the internal and external trajectories of a solid rocket is constructed. On the basis of the dynamic model, the optimization objective of the joint optimization problem of the internal and external trajectories is set and characterized by a performance index function, and the constraints of the joint optimization problem of the internal and external trajectories are set. Among them, the range of solid rockets ,high directional velocity High-altitude velocity ,quality Angle of attack For state variables, the rate of change of angle of attack To control the amount Combined with the engine's internal ballistic parameterization model and The dynamic model for the joint optimization of the internal and external trajectories of the solid rocket is obtained: ； Among them, add "" above the parameter " indicates the derivative of the parameter; For speed, For the trajectory inclination angle, It is the acceleration due to gravity. As resistance, For lift, for different burn rate indices and burn rate coefficient The calculated thrust and time per second They are also different; and Considered as and The relevant functions are represented as follows: and ; The dynamic model, performance index function, and constraints are discretized to transform the joint optimization problem of internal and external trajectories into a nonlinear programming problem. The problem is then solved using a sequential quadratic programming algorithm to obtain the optimization results for each type of propellant. Based on the optimization results, the performance index for each type of propellant is determined, and the propellant used as the optimal design scheme is determined using the performance index.

2. The solid rocket trajectory optimization design method based on internal trajectory parameterization modeling according to claim 1, characterized in that, The structural parameters include the engine's length and radius, the nozzle's throat radius, and the nozzle's exit area; the energy characteristic parameters include the solid propellant density, specific heat ratio, and characteristic velocity. When designing different types of propellant grains, the basic shape of the propellant grain is cylindrical, the outer diameter of the propellant grain is the same as the engine radius, and the length of the propellant grain is no greater than the length of the engine. Different types of propellant grains have openings with different structures set at the center of the basic shape.

3. The solid rocket trajectory optimization design method based on internal trajectory parameterization modeling according to claim 1, characterized in that, The optimization objective of the joint internal and external ballistic optimization problem is set and characterized by a performance index function, expressed as: ； in, For performance indicators, For terminal height, For time, At the initial moment, For the terminal time, The coefficient of the regularization term must satisfy the following condition: ; It represents the derivative with respect to time.

4. The solid rocket trajectory optimization design method based on internal trajectory parameterization modeling according to claim 1, characterized in that, Set constraints for the joint optimization problem of internal and external ballistics, including: Process constraints: ； in, and Each is a range The lower and upper bounds of the constraints and They are respectively height The lower and upper bounds of the constraints and respectively directional velocity The lower and upper bounds of the constraints and They are the high-altitude velocities. The lower and upper bounds of the constraints and Angle of attack The lower and upper bounds of the constraint; Terminal constraints: ; express The high-speed velocity at any given moment; Control constraints: ; and Control Quantity The lower and upper bounds of the constraint; Parameter constraints: ； in, , These are the fuel rate indexes. The lower and upper bounds, , These are the combustion rate coefficients. The lower and upper bounds.

5. The solid rocket trajectory optimization design method based on internal trajectory parameterization modeling according to claim 1, characterized in that, The dynamic model, performance index function, and constraints are discretized to transform the joint optimization problem of internal and external trajectories into a nonlinear programming problem, including: First, the continuous time domain is divided into multiple sub-intervals, and the state and control variables are parameterized at the Legendre-Gauss-Lobatto integration points in each sub-interval. The dynamic model is transformed into algebraic constraints through differential matrices. The performance index function is discretized into an integral objective function. The constraints are explicitly embedded into discrete nodes, thereby transforming the joint optimization problem of internal and external trajectories into a nonlinear programming problem.

6. The solid rocket trajectory optimization design method based on internal trajectory parameterization modeling according to claim 1, characterized in that, After solving the sequential quadratic programming problem, the optimization results for each type of propellant are obtained, including the optimal burn rate index, the optimal burn rate coefficient, and the corresponding control variables. The optimization results for each type of propellant are substituted into the dynamic model to calculate the corresponding flight trajectory, and the terminal altitude is determined from the flight trajectory. The terminal altitude and the corresponding control variables are substituted into the performance index function to calculate the performance index. The performance indexes for each type of propellant are compared, and the propellant with the smallest performance index is selected as the optimal design scheme.

7. A terminal device, comprising a processor, a memory, and a computer program stored in the memory; characterized in that, When the processor executes the computer program, it implements the solid rocket trajectory optimization design method based on internal trajectory parameterization modeling as described in any one of claims 1-6.

8. A computer-readable storage medium storing a computer program; characterized in that, When the computer program is executed by the processor, it implements the solid rocket trajectory optimization design method based on internal trajectory parameterization modeling as described in any one of claims 1-6.

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