A method and device for rapid response launch into orbit of an integrated aircraft

Abstract

A method and apparatus for rapid-response launch and orbital insertion of an integrated aircraft relates to the field of aerospace technology. The method addresses the issue of rapid-response launch and orbital insertion of an aircraft. The method comprises: establishing an integrated aircraft dynamics model; setting constraints and indicator functions based on the integrated aircraft dynamics model to obtain an integrated aircraft trajectory optimization model; processing the integrated aircraft trajectory optimization model using a particle swarm algorithm to obtain a global optimal solution; and performing Gaussian pseudospectral processing on the launch storage values ​​and the global optimal solution to obtain an optimal orbital insertion trajectory. The present invention is applicable to the field of rapid spacecraft response.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and in particular to a method for rapid response launch and orbital entry of an integrated aircraft. Background Art

[0002] The Rapid Response Space System (RSS) is designed to meet the urgent space capability needs of specific users (primarily operational and tactical users). It consists of a Rapid Response Space vehicle, a Rapid Response Space launch vehicle, a Rapid Response Launch System, and a command and application system. Currently, satellite launches are expensive and time-consuming, requiring months of preparation and testing before launch, which is also extremely costly. Therefore, it is necessary to increase the development of launch vehicle technology to improve the ability to rapidly launch into orbit.

[0003] Making launch vehicles rapidly responsive and reusable is a long-term goal, currently elusive. Therefore, experts have begun researching rapid-response vehicles from multiple perspectives to meet the needs of future rapid-response space missions. These include developing specialized space rapid-response vehicles, launch vehicles adapted or designed from intercontinental missiles, air-launched launch vehicles, and reusable launch vehicles. Rapid-response vehicles can perform rapid-response launch missions, carry emergency aircraft, and deploy emergency space constellations.

[0004] The emergency constellation is deployed quickly in the event of a failure in the pre-installed constellation. This requires designing the appropriate launch point and launch window based on its orbital parameters. The spacecraft launch and orbit insertion process should be designed based on specific circumstances and launch requirements. Design results include, but are not limited to, launch timing and launch longitude.

[0005] The specific application scenario for emergency launch is as follows: Once the original satellite fails, the scenario is considered to have begun. For a period of time after the scenario begins, our satellites remain healthy, allowing for continuous emergency deployment. After a period of time, the satellites will experience a certain degree of failure, reducing the number of available satellites and increasing the location of damaged satellites. After a period of time after the scenario begins, the satellite health deteriorates further, and the number of available satellites decreases at an increasing rate. In this situation, a launch method with rapid response is required to quickly complete the network restoration task. Summary of the Invention

[0006] The present invention aims to solve the problem of rapid response launch and orbital insertion of an aircraft, and proposes an integrated method for rapid response launch and orbital insertion of an aircraft. The scheme is as follows:

[0007] A method for rapid response launch and orbital insertion of an integrated aircraft, the method comprising:

[0008] Establish an integrated aircraft dynamics model;

[0009] Setting constraints and index functions according to the integrated aircraft dynamics model to obtain an integrated aircraft trajectory optimization model;

[0010] Using a particle swarm algorithm to process the integrated aircraft trajectory optimization model to obtain a global optimal solution;

[0011] The launch storage value and the global optimal solution are processed by Gaussian pseudo-spectral method to obtain the optimal orbital trajectory.

[0012] Furthermore, a preferred embodiment is provided, wherein the constraints include differential equation constraints, initial and terminal conditions, boundary constraints, connection point constraints and path constraints.

[0013] Furthermore, a preferred embodiment is provided, wherein the integrated aircraft trajectory optimization model is processed using a particle swarm algorithm, including:

[0014] Initialize particle position and velocity;

[0015] Iteratively solving the particle parameters to obtain the particle fitness;

[0016] Update individual optimal values ​​and global optimal values ​​according to the particle fitness;

[0017] Update the position and velocity of particles according to individual optimal values ​​and global optimal values;

[0018] When the preset end conditions are met, the iteration stops and the global optimal solution is obtained.

[0019] Furthermore, a preferred embodiment is provided, wherein the preset end condition includes:

[0020] If the number of iterations exceeds the maximum number set, the update will be stopped;

[0021] If the fitness value corresponding to the global extreme value obtained by the particle swarm n times of search is less than the set threshold, the update is stopped, where n>3.

[0022] Furthermore, a preferred embodiment is provided, wherein the launch storage values ​​include a launch azimuth, two angle of attack turning parameters, three pitch angle change rates and the last stage engine operating time.

[0023] Furthermore, a preferred method is provided for performing Gaussian pseudospectral processing on the emission storage value and the global optimal solution, including:

[0024] Performing time domain transformation and energy discretization on the emission storage value and the global optimal solution;

[0025] Using a sequential quadratic programming algorithm to solve the optimal value of the discrete data;

[0026] An optimal orbital trajectory is obtained according to the optimal value.

[0027] Based on the same inventive concept, the present invention also provides an integrated aircraft rapid response launch and orbit insertion device, the device comprising:

[0028] Model building module, used to build an integrated aircraft dynamics model;

[0029] A constraint module, configured to set constraint conditions and an index function according to the integrated aircraft dynamics model to obtain an integrated aircraft trajectory optimization model;

[0030] A particle algorithm processing module, configured to process the integrated aircraft trajectory optimization model using a particle swarm algorithm to obtain a global optimal solution;

[0031] The Gaussian pseudo-spectral processing module is used to perform Gaussian pseudo-spectral processing on the launch storage value and the global optimal solution to obtain the optimal orbital trajectory.

[0032] Furthermore, a preferred embodiment is provided, wherein the constraints include differential equation constraints, initial and terminal conditions, boundary constraints, connection point constraints and path constraints.

[0033] Based on the same inventive concept, the present invention also provides a computer-readable storage medium, which is used to store a computer program, and the computer program executes any one of the above-mentioned integrated aircraft rapid response launch into orbit methods.

[0034] Based on the same inventive concept, the present invention also provides a computer device, including a memory and a processor, wherein a computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes an integrated aircraft rapid response launch into orbit method according to any one of the above-mentioned methods.

[0035] The present invention is beneficial in that:

[0036] The present invention solves the problem of rapid response of aircraft launch into orbit.

[0037] The present invention describes a rapid-response orbital launch method for an integrated spacecraft. This method primarily utilizes a particle swarm optimization algorithm and a Gaussian pseudospectral method to simulate the trajectory optimization of a satellite-rocket combination spacecraft from the ground to a parking orbit. The method thoroughly analyzes the orbital insertion problem of the spacecraft's booster segment, presenting the performance indicator functions, state variables, differential equation constraints, optimization variables, initial and terminal conditions, and connection point constraints involved in the optimization process. Next, the Newton iteration method is employed to calculate the orbital trajectory of the booster segment of the satellite-rocket combination spacecraft using traditional iterative guidance methods. The calculated results are then used as the initial values ​​for Gaussian pseudospectral optimization calculations. Comparisons of the Newton iteration method and the Gaussian pseudospectral method reveal that the optimized booster segment achieves a shorter orbital insertion time (5 seconds), a greater orbital mass, increased orbital weight, higher orbital accuracy, and an 18.15% reduction in orbital eccentricity error, demonstrating improved orbital insertion performance after the optimization of the booster segment of the satellite-rocket combination. Finally, using a method combining particle swarm optimization and Gaussian pseudospectrum, when the launch time and launch position are not fixed, the integrated spacecraft responds quickly to the launch-into-orbit simulation, and the orbital eccentricity error and the ascent node right ascension error are small. It can be considered that the booster segment of the satellite-rocket combination spacecraft has high orbital accuracy and enters the target orbital plane, and is able to complete the rapid response launch-into-orbit mission.

[0038] The present invention is applied to the field of rapid response of spacecraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a flow chart of a method for rapid response launch and orbital insertion of an integrated aircraft according to embodiment 1;

[0040] Figure 2 This is a schematic diagram of the optimization problem described in the second embodiment;

[0041] Figure 3 This is a flowchart of iterative calculation of the boost phase of the integrated aircraft according to the fifth embodiment;

[0042] Figure 4 Schematic diagram of the particle swarm fitness curve according to the eleventh embodiment;

[0043] Figure 5 This is a schematic diagram of the optimization results of the integrated aircraft launch system at position x according to the eleventh embodiment;

[0044] Figure 6 This is a schematic diagram of the optimization results of the integrated aircraft launch system at position y according to the eleventh embodiment;

[0045] Figure 7 This is a schematic diagram of the optimization results of the integrated aircraft launch system at position z according to the eleventh embodiment;

[0046] Figure 8 The optimized result of the launch system velocity vx of the integrated aircraft described in the eleventh embodiment;

[0047] Figure 9 The optimization result of the launch system speed vy of the integrated aircraft described in the eleventh embodiment;

[0048] Figure 10 The optimization result of the launch system velocity vz of the integrated aircraft described in the eleventh embodiment;

[0049] Figure 11 is the optimization result of the integrated aircraft longitude position according to the eleventh embodiment, wherein longitude represents longitude;

[0050] Figure 12 is the optimization result of the integrated aircraft at the latitude position according to the eleventh embodiment, wherein latitude represents latitude;

[0051] Figure 13 is the optimization result of the integrated aircraft at the height position according to the eleventh embodiment, wherein height represents the height;

[0052] Figure 14 is the integrated aircraft mass optimization result described in Embodiment 11, wherein mass represents mass;

[0053] Figure 15 is the optimization result of the fixed-tether speed of the integrated aircraft according to the eleventh embodiment, wherein speed represents the speed;

[0054] Figure 16 The integrated aircraft dynamic pressure optimization result described in Implementation 11;

[0055] Figure 17 This is the axial overload optimization result of the integrated aircraft described in the eleventh embodiment;

[0056] Figure 18 The integrated aircraft angle of attack optimization result described in Implementation 11;

[0057] Figure 19 Schematic diagram of the pitch angle optimization results of the integrated aircraft described in Implementation 11. DETAILED DESCRIPTION

[0058] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in combination with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

[0059] Implementation method 1, see Figure 1 The present embodiment describes a method for rapid launch and orbital placement of an integrated aircraft, the method comprising:

[0060] Establish an integrated aircraft dynamics model;

[0061] Setting constraints and index functions according to the integrated aircraft dynamics model to obtain an integrated aircraft trajectory optimization model;

[0062] Using a particle swarm algorithm to process the integrated aircraft trajectory optimization model to obtain a global optimal solution;

[0063] The launch storage value and the global optimal solution are processed by Gaussian pseudo-spectral method to obtain the optimal orbital trajectory.

[0064] In practice, the entire integrated spacecraft's orbital insertion process can be divided into four phases: the first-stage solid engine operating phase, the second-stage solid engine operating phase, the third-stage solid engine operating phase, and the final-stage liquid engine orbital insertion phase. The first phase includes the vertical launch phase and the angle-of-attack turn phase. The flight process is as follows: 1. Vertical launch of the rocket; 2. Angle-of-attack turn of the rocket; 3. First-stage engine operation completes, separation, and second-stage engine operation begins; 4. Second-stage separation, third-stage operation begins; 5. Third-stage operation completes, separation, and final-stage operation begins; 6. The rocket enters the parking orbit.

[0065] These four flight phases are optimized using a segmented approach. This implementation utilizes the Gaussian pseudospectral method to optimize the integrated vehicle's orbital insertion process. The optimization problem is divided into several subintervals, each of which is then processed using the Gaussian pseudospectral method. The optimization of each subinterval represents an optimal control problem for a specific trajectory. During segmented optimization, different control variables, static design variables, and path constraints can be set based on the motion characteristics of each segment.

[0066] Implementation method 2, see Figure 2 This embodiment further defines the method for rapid launch and orbital insertion of an integrated aircraft described in Embodiment 1, wherein the constraints include differential equation constraints, initial and terminal conditions, boundary constraints, connection point constraints, and path constraints.

[0067] When using the Gaussian pseudospectral method to optimize the boost phase trajectory of an integrated vehicle, the key lies in the proper design and description of each optimization factor. This implementation primarily considers eight key factors: performance indicator function, state variables, optimization design variables, differential equation constraints, initial and terminal conditions, boundary constraints, connection point constraints, and path constraints.

[0068] The performance indicator function described in this embodiment is used to measure the quality of the optimization effect, and can also be called an objective function. How to select the objective function depends on the optimization purpose of the specific optimization problem.

[0069] Due to the requirement of rapid orbital entry of the integrated spacecraft, the performance index function can be the terminal time t f Minimum, that is:

[0070] minJ=t f

[0071] In addition, this embodiment takes into account that there is no unpowered glide phase between each stage of engine operation, so there is thrust operation during the entire orbital insertion phase, fuel is continuously consumed, and the rocket mass is reduced. Therefore, the performance index of the minimum terminal time is equivalent to the orbital mass m f Maximum, that is:

[0072] minJ=-m f

[0073] This implementation aims at the rocket booster section of the integrated aircraft and establishes a differential equation of motion in the launch coordinate system. Therefore, the position, velocity, and rocket mass of the launch system can be selected as the state variables of the optimization problem, namely:

[0074] X=[x,y,z,v x ,v y ,v z ,m]

[0075] Expanded to four stages, the state variables are:

[0076] X=[x p ,y p ,z p ,v xp ,v py ,v zp ,m p ],(p=1,2,3,4)

[0077] Among them, p is the stage number.

[0078] The flight program angle is mainly considered as the optimization variable in trajectory design.

[0079] In the first stage rocket engine working phase, there are two phases, vertical launch and angle of attack turning. In the vertical launch phase, the vertical launch time t 01 It can be determined by the thrust-to-weight ratio at takeoff. After vertical takeoff, the aircraft enters an exponential angle of attack turn until the first stage engine shuts down. The angle of attack turn stage uses an exponential turn model:

[0080]

[0081] The attack angle change model in the first stage is:

[0082]

[0083] When the time is less than the vertical takeoff time, the angle of attack is zero and the pitch angle is kept at 90° to ensure vertical takeoff. Therefore, there are two optimization variables a in this stage. m and k a .

[0084] After the first stage is completed, the rocket engine separates, and then the second stage engine starts to work until t2. When the rocket is in the second stage of boost and above, the air in the environment of the rocket is relatively thin, and the impact of aerodynamic forces on the rocket body is very small and can be basically ignored. Therefore, the rocket can make large attitude angle adjustments. Usually in engineering, the pitch angle change in the second stage of boost and above is:

[0085]

[0086] Then the coefficients A, B, and C are further designed to achieve the optimal target when the engine is shut down.

[0087] In the further study of optimization theory, the optimal pitch program solved by numerical methods is very close to a linear relationship, so the pitch angle program can be further simplified to:

[0088]

[0089] Where, is the pitch angle at the end of the first stage, is the pitch angle change rate in the second stage.

[0090] The working phase of the third stage rocket engine and the final stage rocket engine is similar to the second stage, and the pitch angle change rate is:

[0091]

[0092] Where, is the pitch angle at the end of the second stage, is the pitch angle change rate in the third stage, t2 is the time when the second stage ends and the third stage begins; is the pitch angle at the end of the third stage, is the pitch angle change rate in the fourth stage, and t3 is the time when the third stage ends and the fourth stage begins.

[0093] There are five optimization variables in the flight procedure corner.

[0094] In addition to the flight program angle, the launch azimuth angle A0 is used as a design variable. The initial value of the launch azimuth angle can be calculated from the target orbit inclination i and the launch point latitude φ.

[0095]

[0096] In summary, there are six optimization variables s in the optimization problem:

[0097]

[0098] Due to the requirements of flexibility and rapidity in launching integrated spacecraft in case of emergencies, the launch time and launch longitude are also taken as optimization design variables in the integrated spacecraft trajectory optimization and orbit insertion problem, namely:

[0099]

[0100] Where t0 is the launch time, which can be a day or several hours, and is the number of seconds calculated from 0:00:00 on a particular day; λ0 is the longitude of the launch point. The number of design variables in this optimization problem increases to eight.

[0101] This embodiment also establishes a motion differential equation in the launch system. The differential equation constraints include seven quantities, including the three position components x, y / , and z in the launch system, three velocity components, and the mass of the rocket. The dynamic differential equation constraints are:

[0102]

[0103]

[0104] Where, T is the engine thrust, I sp is the engine specific impulse.

[0105] At the same time, the flight process is simplified by assuming an instantaneous equilibrium assumption during flight, ignoring angular velocity and angular acceleration, and assuming that the rocket's roll angle is zero and the yaw angle is very small, which approximates that the rocket only moves in the pitch plane.

[0106] The initial conditions of the state variables are the initial state values ​​of the launch system and the takeoff mass of the rocket:

[0107] X0=[x0,y0,z0,v x0 ,v y0 ,v z0 ,m0]

[0108] The terminal condition is the orbital element of the target parking orbit, which can be converted from the position and velocity of the terminal state. The terminal condition is:

[0109] [a f ,e f,i f ,Ω f ,ω f ,f f ]

[0110] The above six terminal variables are the six numbers of the target orbit.

[0111] The boundary constraints described in this embodiment are specifically:

[0112] In the optimization process, the value range of the state variables and the value range of the design variables are given at each stage:

[0113]

[0114] Where p is the number of stages, X pmin and X pmax are the minimum and maximum values ​​of the seven state variables in the four stages, s min and s max are the minimum and maximum values ​​of the six design variables.

[0115] The connection point constraints described in this embodiment are specifically:

[0116] In this embodiment, the state variable is X=[x, y, z, v x ,v y ,v z ,m], Since the four ballistic trajectories are continuous and there is separation of the rocket engine, except for the rocket mass, time and other state variables should change continuously.

[0117]

[0118] Among them, mDryFirst is the mass of the first-stage rocket engine excluding fuel, mDrySecond is the mass of the second-stage rocket engine excluding fuel, and mDryThird is the mass of the third-stage rocket engine excluding fuel.

[0119] The path constraints described in this embodiment are specifically:

[0120] The path constraint is an inequality constraint that must be satisfied during the flight of the integrated aircraft. In this implementation, dynamic pressure and axial overload are considered:

[0121]

[0122] Among them, q max is the maximum dynamic pressure of the integrated aircraft. In this embodiment, q max Take 0.06MPa, n xmax The maximum axial overload of the integrated aircraft is 16g.

[0123] Implementation Method 3: This implementation method further limits the method for rapid response launch and orbital insertion of an integrated aircraft described in Implementation Method 1. The integrated aircraft trajectory optimization model is processed using a particle swarm algorithm, including:

[0124] Initialize particle position and velocity;

[0125] Iteratively solving the particle parameters to obtain the particle fitness;

[0126] Update individual optimal values ​​and global optimal values ​​according to the particle fitness;

[0127] Update the position and velocity of particles according to individual optimal values ​​and global optimal values;

[0128] When the preset end conditions are met, the iteration stops and the global optimal solution is obtained.

[0129] The particle swarm algorithm described in this embodiment processes the integrated aircraft trajectory optimization model as follows:

[0130] (1) Initialization:

[0131] Randomly generate the position of the initial particle in the search space (In this embodiment, the launch time and launch point longitude of the integrated aircraft) and its speed Initial individual particle extreme position P i Located The fitness value of this particle is calculated based on the fitness function (the difference between the right ascension of the ascending node of the entry orbit and the right ascension of the ascending node of the target orbit in this launch case). This value can be used as the initial individual extreme value, and the position of the best particle among all individual extreme values ​​is taken as the global extreme value point, and its fitness value is the global optimal value.

[0132] (2) Evaluate each particle:

[0133] The difference between the right ascensions of the two ascending nodes obtained by each iteration is the fitness value of the particle. The smaller the difference between the right ascensions of the two ascending nodes, the closer the entry orbit is to the target orbit. If the objective function value is better than the individual extreme value of the particle, the best position of the particle becomes P i , and update the individual extreme value accordingly. If the objective function value is better than the global extreme value, then update P g To the current particle, record the emission time and emission point longitude corresponding to the particle, and update the global extreme value.

[0134] (3) Particle update:

[0135] Update the position and velocity of each particle according to the following formula:

[0136]

[0137]

[0138]

[0139] Where w is the inertia weight. For basic PSO, the w value can be regarded as 1. Generally, when the value of w is between [0.8, 1.2], the algorithm converges faster. is the velocity of particle i in the dth dimension at the kth iteration; C1 and C2 are learning factors that adjust the upper limit of the step size moving towards the two extreme points. Usually, C1 = C2 = 2; r1 and r2 are two independent random numbers uniformly distributed in [0,1]; is the position of particle i in the dth dimension in the kth iteration; p i d is the individual extreme position of particle i in the dth dimension in the kth iteration; p gd is the global extreme position of the entire particle swarm in the dth dimension. is the particle velocity v of each dimension d Assume that the value range of the particle's d-dimensional position is in the interval In, usually desirable

[0140] (4) Check whether the end conditions are met:

[0141] If the number of iterations exceeds the maximum number set, the calculation will stop. In addition, if the fitness value corresponding to the global extreme value obtained by the particle swarm after multiple consecutive searches changes less than a certain threshold, the iteration will also stop and the optimal solution will be obtained. If neither of these conditions is met, the calculation will return to the second step and continue.

[0142] (5) Calculation of right ascension of ascending node:

[0143] After determining the particle position with the minimum right ascension of the ascending node, we plug it back into the trajectory solution to obtain the post-entry orbit. This orbit has the smallest difference between the right ascension of the ascending node and the right ascension of the target orbit, indicating that the entry and target orbits are most consistent under this launch condition.

[0144] This implementation randomly initializes the position and velocity of particles, allowing the search process to cover the entire solution space. This increases the diversity of the algorithm and allows for the discovery of better solutions in the global space. The algorithm calculates the fitness of each particle based on its current position, assessing the quality of the solution corresponding to that position and guiding the search process towards a more optimal solution. The algorithm evaluates the quality of each particle's solution and seeks a better position for each particle. The algorithm updates the individual and global optimal values ​​based on the particle's fitness. The algorithm compares the current particle's fitness with the individual and global optimal values, updating each particle's individual and global optimal values. This allows tracking the historical optimal solution of each particle and the optimal solution of the entire population. The algorithm uses the individual and global optimal values ​​to adjust the particle's position and velocity, directing the search toward more promising solutions. This accelerates convergence and increases the chances of finding a better solution. The algorithm stops iteration and obtains the global optimal solution by determining a preset termination condition, such as when the number of iterations reaches an upper limit or convergence conditions are met. This avoids infinite iterations and conserves computing resources.

[0145] Implementation 4: This implementation further defines the integrated aircraft rapid response launch and orbital insertion method described in Implementation 3. The preset termination conditions include:

[0146] If the number of iterations exceeds the maximum number set, the update will be stopped;

[0147] If the fitness value corresponding to the global extreme value obtained by the particle swarm n times of search is less than the set threshold, the update is stopped, where n>3.

[0148] Implementation method five, see Figure 3 This embodiment further defines the method for rapid launch and orbital insertion of an integrated aircraft described in Embodiment 1, wherein the launch stored values ​​include the launch azimuth, two angle of attack turn parameters, three pitch angle change rates, and the operating time of the final stage engine.

[0149] The launch parameters discussed in this embodiment are a set of parameters calculated based on the characteristics of the integrated vehicle, taking the launch point and target orbit parameters as primary considerations. These parameters are then used to achieve the final orbital insertion accuracy of the integrated vehicle. The launch parameters discussed in this embodiment include the launch azimuth, two angle of attack turn parameters, and three pitch angle change rates, representing six optimized design variables. Together with the operating time of the final stage engine, this results in a total of seven launch parameters for the integrated vehicle.

[0150] During the optimization simulation process, it was found that the range of the optimized design variables and the range of the state variables would affect the optimization results and the speed of iterative convergence. Even for less reasonable parameter ranges, the optimization iteration calculation would not converge. Therefore, before optimization, a set of launch parameters can be calculated first, and then a standard trajectory can be iteratively calculated. This trajectory data can be used as the initial value of the optimization calculation to ensure the convergence of the optimization.

[0151] The calculation steps for the emission elements are as follows:

[0152] (1) Calculate the emission table of each element: within the value range of each emission element, take a certain iteration step size, and cyclically calculate each set of emission elements and their corresponding terminal point orbit data.

[0153] (2) Select a set of launch elements in the firing table of step (1) whose terminal orbit data is close to the target orbital element number. This embodiment mainly considers the semi-major axis, eccentricity and orbital inclination.

[0154] (3) Using the emission parameters selected in step (2) as initial values, use the Newton iteration method to calculate more accurate final values ​​of these quantities.

[0155] The traditional trajectory design process generally involves using the Newton iteration method to iteratively calculate the launch azimuth, flight program parameters, and the shutdown time of the final stage engine to meet the terminal condition F(x) = 0. This embodiment uses Newton iteration to address situations where the terminal constraint ratio is smaller than the control variable.

[0156] The update form of Newton iteration method is:

[0157] x i+1 =x i -[F'(x i )] -1 F(x i )

[0158] Where F'(x) is the value of the Jacobian matrix of F(x) at x. If the dimension of x is large, the following formula can be used to update the iteration:

[0159] x i+1 =x i -G T (GG T ) -1 F(x i )

[0160] Where G=F'(x i ).

[0161] The specific calculation process of the Newton iteration method for iterative calculation of emission parameters is as follows:

[0162] (1) Given the launch azimuth angle A0, the angle of attack turning parameter a m 、k a , pitch angle change rate The final stage engine working time t4 is assigned an initial value

[0163] (2) Calculate the trajectory parameters by calculating the semi-major axis difference Δa0, eccentricity difference Δe0, and orbit inclination Δi0 between the practical endpoint orbit parameters and the target orbit parameters. If the accuracy requirements are met, terminate; otherwise, continue.

[0164] (3) Let the launch azimuth Angle of attack parameters Pitch angle change rate Last stage engine operating time by Calculate the trajectory parameters and calculate the semi-major axis difference Δa1, eccentricity difference Δe1, and orbit inclination Δi1 between the practical endpoint orbit parameters and the target orbit parameters. If the accuracy requirements are met, terminate; otherwise, continue.

[0165] (4) According to the calculation method of the launch azimuth, the semi-major axis difference Δa is calculated after each launch element is increased by a small amount δ. i , eccentricity difference Δe i , orbital inclination difference Δi i , where i = 1, 2, ..., 7, corresponding to the number of emitted elements.

[0166] (5) Calculate the Jacobi matrix:

[0167]

[0168] (6) Correct the emission parameters and return to step (2) for calculation.

[0169] To summarize, first determine the various launch parameters and initial values, then use the fourth-order Runge-Kutta method to perform the first iterative calculation of the integrated spacecraft trajectory. If the terminal spacecraft orbital insertion conditions are met, the calculation is terminated; if not, calculate the Jacobi matrix in the Newton iteration method, and update the values ​​of the various launch parameters. Then, use the updated values ​​to iteratively calculate the integrated spacecraft boost phase trajectory again until the orbital insertion conditions are met.

[0170] Implementation 6: This implementation further limits the integrated aircraft rapid response launch and orbital insertion method described in Implementation 1, and performs Gaussian pseudospectral processing on the launch storage value and the global optimal solution, including:

[0171] Performing time domain transformation and energy discretization on the emission storage value and the global optimal solution;

[0172] Using a sequential quadratic programming algorithm to solve the optimal value of the discrete data;

[0173] An optimal orbital trajectory is obtained according to the optimal value.

[0174] The Gaussian pseudospectral method processing flow described in this embodiment is as follows:

[0175] (1) Time domain transformation

[0176] The time interval of GPM is [-1,1], but the optimal control problem is [t0,t f ], so we need to change the time from t0, t f Transform to the interval [-1,1] and define a new variable τ∈[-1,1] to complete the time domain transformation, that is,

[0177]

[0178] (2) Discreteness of state variables and control variables

[0179] The Gaussian quadrature formula and Lagrange interpolation method can discretize the optimal control problem at the LG (Legendre-Gauss) point, which is an N-order Legendre polynomial:

[0180]

[0181] Interpolate the state variable x at N+1 LG nodes:

[0182]

[0183]

[0184] In the formula

[0185]

[0186] Similarly, the control quantity can also be approximated by using a similar method, using discrete control structure Lagrange interpolation polynomials

[49] :

[0187]

[0188] Among them, u(τ) is the control quantity of the original problem, and U(τ) is the control quantity expression obtained by approximating the Legendre value polynomial. is the Legendre interpolation basis function, i=1,2,…,N.

[0189]

[0190] (3) Discrete dynamic equations

[0191] In the Gaussian pseudospectral method, only after obtaining the discrete results of the control and state variables can we further process the dynamic equations:

[0192]

[0193] Let τ = τ k , The above formula can be transformed into:

[0194]

[0195] Where:

[0196]

[0197] Where i = 0, 1, ..., N; k = 0, 1, ..., N. D is the N × (N + 1)-dimensional state differential matrix. The dynamic equation can be expressed as follows:

[0198]

[0199] (4) Discrete terminals, path constraints, and performance indicators

[0200] After completing the discretization of the LG collocation points, the terminal state in the Gaussian pseudospectral method needs to be expressed in the form of Gaussian integral, that is:

[0201]

[0202] Where:

[0203]

[0204] Discrete path constraints on LG collocation points, namely:

[0205] C(X k ,U k ,τ k ;t0,t f )≤0,k=1,2,...,N

[0206] Similarly, the performance index approximated by the Gaussian integral formula is:

[0207]

[0208] (5) After the above mathematical transformation, the Gaussian pseudospectral method calculation process for solving the optimal control problem is: solve the state quantity X at the discrete node i (i=0,1,…,N), control quantity U i (i=0,1,…,N), and the initial and final time t0, t f, ultimately making the performance index reach the minimum value, while also meeting the terminal constraints, dynamic constraints, boundary conditions, etc., and then using the SQP method to solve. The SQP method described in this embodiment is a very effective solution method with better convergence and higher efficiency.

[0209] The idea behind sequential quadratic programming (SQP) is to first model the integrated aircraft trajectory optimization process as an optimal control problem. This is then discretized using the Gaussian pseudospectral method, transforming it into a nonlinear programming problem, which is then solved using the SQP method. Among the many methods for solving nonlinear programming problems, the SQP method is a very effective approach. It exhibits better convergence and efficiency than other algorithms.

[0210] Using Taylor expansion, in X k The objective function is simplified to become a quadratic function, and the constraint function can also be made linear. The mathematical description of SQP is as follows:

[0211]

[0212]

[0213] make:

[0214] S=XX k

[0215] The above problem becomes a question about the variable S, namely:

[0216]

[0217]

[0218] make:

[0219]

[0220]

[0221]

[0222] The general form of the quadratic programming problem can be obtained from the above formula, which is:

[0223]

[0224]

[0225] The solution steps are: get the optimal solution S * After that, take it as the next search direction, denoted as S k , and then use one-dimensional search to get the approximate solution X k+1. Then continue to iterate until the optimal solution is obtained.

[0226] Embodiment 7: This embodiment provides an integrated aircraft rapid response launch and orbit insertion device, the device comprising:

[0227] Model building module, used to build an integrated aircraft dynamics model;

[0228] A constraint module, configured to set constraint conditions and an index function according to the integrated aircraft dynamics model to obtain an integrated aircraft trajectory optimization model;

[0229] A particle algorithm processing module, configured to process the integrated aircraft trajectory optimization model using a particle swarm algorithm to obtain a global optimal solution;

[0230] The Gaussian pseudo-spectral processing module is used to perform Gaussian pseudo-spectral processing on the launch storage value and the global optimal solution to obtain the optimal orbital trajectory.

[0231] Implementation method eight: This implementation method describes an integrated aircraft rapid response launch and orbital insertion device, wherein the constraints include differential equation constraints, initial and terminal conditions, boundary constraints, connection point constraints, and path constraints.

[0232] Implementation method nine: A computer-readable storage medium described in this implementation method is used to store a computer program, and the computer program executes an integrated aircraft rapid response launch into orbit method described in any one of implementation methods one to six.

[0233] Embodiment 10. A computer device described in this embodiment includes a memory and a processor, wherein a computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes an integrated aircraft rapid response launch into orbit method according to any one of Embodiments 1 to 6.

[0234] Implementation method 11, see Figures 4 to 18 This embodiment provides a specific implementation of the integrated aircraft rapid response launch and orbital insertion method provided in embodiment 1, and verifies its results. Specifically:

[0235] Scenario description: To meet the needs of emergencies, on January 1, 2024, a three-stage solid rocket will launch an integrated spacecraft into a circular orbit with a target orbital altitude of 500km, an orbital inclination of 98°, and an ascending node right ascension of 200°. The estimated orbital insertion position is at an argument of perigee of 0° and a true anomaly of 314.4°. The three-stage solid rocket booster and the last-stage liquid engine will first transport the spacecraft to a lower parking orbit, and then the last-stage engine will transport the integrated spacecraft to the target mission orbit. The parking orbit is a near-circular orbit with an altitude of about 200km, an orbital inclination of 98°, and an ascending node right ascension of 200°. This embodiment describes the process of the integrated spacecraft entering orbit from launch to parking orbit.

[0236] The launch parameters calculated by Newton iteration are used as the initial values ​​of the launch. The launch parameters are shown in Table 1.

[0237] Table 1 Initial launch parameters

[0238]

[0239] Calculate a launch using the parameters in Table 1 as the initial launch parameters to determine the various launch parameters and initial values. The fourth-order Runge-Kutta method can be used to perform the first iteration to calculate the integrated vehicle trajectory.

[0240] The particle swarm optimization algorithm is used to optimize the launch time and launch location. The particle dimension is 2, representing the launch time and the longitude of the launch point. The population size N is 100, and the number of iterations T is 100.

[0241] The global optimal particle of the simulation results is:

[0242] gBest = [43843, 103.445]

[0243] The simulation results show that the launch time is 43843s and the launch point longitude is 103.445°. The particle swarm fitness curve is shown in Figure 4 shown.

[0244] The optimal result is obtained after the number of iterations reaches 52. At this time, the fitness value is:

[0245] gBestValue = 1.227 × 10 -5

[0246] The above formula indicates that the minimum difference between the right ascension of the ascending node of the entry orbit and the right ascension of the ascending node of the target orbit under different launch conditions is 1.227*10 -5 The right ascension values ​​of the two ascending nodes are: 200.00001227 and 200 respectively.

[0247] The parameters calculated by the algorithm by substituting the global optimal launch time and launch point longitude are shown in Table 2. As can be seen from this table, the orbital elements obtained by the calculation are consistent with the orbital elements of the target orbit, indicating that the launch time and launch point longitude obtained by the algorithm are correct.

[0248] Table 2 Number of orbital elements at the entry point

[0249]

[0250] The Gaussian pseudospectral method is used to obtain the iterative results of various flight parameters, see Table 3.

[0251] Table 3 Flight parameter optimization results

[0252]

[0253]

[0254] The results of the position optimization of the integrated aircraft in the launch system are shown in Figure 5 、 Figure 6 and Figure 7 The results of the position optimization of the integrated aircraft in the launch system are shown in Figure 8 、 Figure 9 and Figure 10 The optimization results of the integrated aircraft's latitude and longitude position are shown in Figure 11 、 Figure 12 and Figure 13 .

[0255] Simulation results show that the parking orbit has a semi-major axis of 6571.266 km, an eccentricity of 0.0006624, an inclination of 98°, and an ascending node right ascension of 200.00077°. The right ascension error is 0.00077°. The launch time is 12:10:33 hours on January 1, 2024. The launch point longitude is 103.445°.

[0256] The total flight time of the integrated vehicle was 358 seconds, with the first stage flying for 67 seconds, the second stage for 62 seconds, the third stage for 55 seconds, and the last stage operating for 174 seconds. After the first stage flight, the first stage engine separated, reducing its mass by 1,300 kg. The vehicle then entered the second stage flight phase, where its mass decreased by 558 kg after the second stage engine separation. The third stage rocket engine ignited, reducing its mass by 220 kg after separation. The simulation results were consistent with the initial rocket parameters. At the time of third stage separation and last stage operation, the Earth-fixed velocity reached 7,395 m / s. At this point, the position and velocity converted into orbital elements yielded a semi-major axis of 5,842 km and an eccentricity of 0.1266. After separation, the booster will naturally descend into the atmosphere, eliminating the need for additional propellant braking to deorbit. After 358 seconds, the integrated vehicle entered a parking orbit with an entry mass of 600.15 kg and an entry velocity of 7,871.9 m / s.

[0257] The changes in the optimization results of the integrated aircraft mass and ground-fixed speed are shown in Figure 14 and 15 , the dynamic pressure and axial overload changes of the integrated aircraft are shown in Figure 16 and 17 , the dynamic pressure of the integrated aircraft first increases and then decreases, mainly concentrated in the position below 80km, with the maximum dynamic pressure of 0.0557MPa. The maximum axial overload is 15.44g at the end of the third level. Both the dynamic pressure and the axial overload meet the constraints. In the first-level angle of attack turning stage, the maximum negative angle of attack is 6.10146°, which is consistent with the parameter optimization results. In the second level and above, the pitch angle gradually decreases according to the rate of change. The maximum negative angle of attack during the entire flight occurs at the end of the third level, and the maximum negative angle of attack is -26.28°. Changes in angle of attack and pitch angle are shown in Figure 18 and 19 .

[0258] The above further describes the technical solution provided by the present invention in detail in conjunction with the accompanying drawings in order to highlight the advantages and benefits, and is not intended to limit the present invention. Any modification, combination of implementation methods, improvement and equivalent replacement of the present invention based on the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for rapid response launch of an integrated aircraft into orbit, characterized in that: The method comprises: Establish an integrated aircraft dynamics model; Setting constraints and index functions according to the integrated aircraft dynamics model to obtain an integrated aircraft trajectory optimization model; Using a particle swarm algorithm to process the integrated aircraft trajectory optimization model to obtain a global optimal solution; Performing Gaussian pseudospectral processing on the launch storage value and the global optimal solution to obtain an optimal orbital trajectory; The constraints include differential equation constraints, initial and terminal conditions, boundary constraints, connection point constraints and path constraints; The boundary constraints are as follows: In the optimization process, the value range of the state variables and the value range of the design variables are given at each stage: Where, is the number of stages, and are the minimum and maximum values ​​of the seven state variables in the four stages, and are the minimum and maximum values ​​of the six design variables; The connection point constraints are as follows: in, is the mass of the first stage rocket engine excluding fuel, is the mass of the second stage rocket engine excluding fuel, is the mass of the third-stage rocket engine excluding fuel; The path constraints are as follows: in, is the maximum dynamic pressure of the integrated aircraft; It is the maximum axial overload of the integrated aircraft; The launch storage values ​​include launch azimuth, two angle of attack turning parameters, three pitch angle change rates and the last stage engine working time; Performing Gaussian pseudospectral processing on the emission storage value and the global optimal solution, including: Performing time domain transformation and energy discretization on the emission storage value and the global optimal solution; The sequential quadratic programming algorithm is used to solve the optimal value of discrete data; An optimal orbital trajectory is obtained according to the optimal value.

2. The method for rapid launch of an integrated aircraft into orbit according to claim 1, characterized in that: The process of processing the integrated aircraft trajectory optimization model using a particle swarm algorithm includes: Initialize particle position and velocity; Iteratively solving the particle parameters to obtain the particle fitness; Update individual optimal values ​​and global optimal values ​​according to the particle fitness; Update the position and velocity of particles according to individual optimal values ​​and global optimal values; When the preset end conditions are met, the iteration stops and the global optimal solution is obtained.

3. The method for rapid launch and orbital entry of an integrated aircraft according to claim 2, characterized in that: The preset end conditions include: If the number of iterations exceeds the maximum number set, the update will be stopped; If the fitness value corresponding to the global extreme value obtained by the particle swarm n times of search is less than the set threshold, the update is stopped, where n>3.

4. An integrated aircraft rapid response launch and orbital insertion device, characterized in that: The device comprises: Model building module, used to build an integrated aircraft dynamics model; A constraint module, configured to set constraint conditions and an index function according to the integrated aircraft dynamics model to obtain an integrated aircraft trajectory optimization model; A particle algorithm processing module, configured to process the integrated aircraft trajectory optimization model using a particle swarm algorithm to obtain a global optimal solution; a Gaussian pseudo-spectral processing module, configured to perform Gaussian pseudo-spectral processing on the launch storage value and the global optimal solution to obtain an optimal orbital insertion trajectory; The constraints include differential equation constraints, initial and terminal conditions, boundary constraints, connection point constraints and path constraints; The boundary constraints are as follows: In the optimization process, the value range of the state variables and the value range of the design variables are given at each stage: Where, is the number of stages, and are the minimum and maximum values ​​of the seven state variables in the four stages, and are the minimum and maximum values ​​of the six design variables; The connection point constraints are as follows: in, is the mass of the first stage rocket engine excluding fuel, is the mass of the second stage rocket engine excluding fuel, is the mass of the third-stage rocket engine excluding fuel; The path constraints are as follows: in, is the maximum dynamic pressure of the integrated aircraft; It is the maximum axial overload of the integrated aircraft; The launch storage values ​​include launch azimuth, two attack angle turning parameters, three pitch angle change rates and the last stage engine working time; The launch storage values ​​include launch azimuth, two angle of attack turning parameters, three pitch angle change rates and the last stage engine working time; Performing Gaussian pseudospectral processing on the emission storage value and the global optimal solution, including: Performing time domain transformation and energy discretization on the emission storage value and the global optimal solution; The sequential quadratic programming algorithm is used to solve the optimal value of discrete data; An optimal orbital trajectory is obtained according to the optimal value.

5. A computer-readable storage medium, characterized in that The computer-readable storage medium is used to store a computer program, and the computer program executes the integrated aircraft rapid response launch into orbit method according to any one of claims 1-3.

6. A computer device, characterized in that: It includes a memory and a processor, wherein a computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes an integrated aircraft rapid response launch into orbit method according to any one of claims 1 to 3.

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