An intelligent generation method of reentry trajectory of aircraft based on RBF neural network

Abstract

The application belongs to the technical field of aircraft trajectory optimization, and discloses an intelligent generation method of reentry trajectory of an aircraft based on a RBF neural network. Firstly, a reentry model of the aircraft is constructed, and a trajectory optimization problem to be solved is constructed based on the reentry model; then, an optimal sample trajectory set is generated by using a pseudospectral method according to initial discrete altitude and speed; after that, a sample trajectory is generated according to a new discrete state at each waypoint. Then, the sample set is divided according to the waypoints, and the RBF neural network is trained respectively; the input of the RBF neural network is the discrete altitude and speed state, and the output is a state-control sequence from the current state to the target point. Finally, the RBF neural network is used to generate an optimal trajectory online. The simulation verifies that the confidence of the method is high and the error is small, and the generation efficiency of the optimal trajectory can be greatly improved.

Description

Technical Field

[0001] This invention belongs to the field of aircraft trajectory optimization and relates to an intelligent generation method for aircraft reentry trajectories based on RBF neural networks. Background Technology

[0002] Hypersonic glide vehicles possess extremely high speeds and range maneuverability, enabling them to perform long-range strike missions. However, during reentry, state deviations can cause the nominal trajectory tracked during guidance to fail to meet mission requirements. Therefore, rapidly generating a nominal trajectory based on real-time conditions during reentry is a problem that needs to be solved. Existing technologies mainly suffer from the following shortcomings:

[0003] Currently, the generation of optimal reentry trajectories mainly relies on offline solutions, such as direct and indirect methods. This involves transforming the trajectory optimization problem into an optimal control problem that satisfies certain performance indicators. In practice, numerous optimal trajectory schemes are generated offline based on the aircraft's state distribution. During real-time flight, a nearby reference trajectory is selected for guidance and tracking based on the error state, but the computational efficiency of this selection process is relatively low. Currently, online optimal trajectory generation methods used in engineering applications are mainly convex optimization methods. Convex optimization methods require an objective function that is convex and a feasible region formed by constraints that is also convex. In online applications, the objective function is solved online, which suffers from sensitivity to initial values ​​and has a long computation time, resulting in poor computational efficiency. With the rise of intelligent methods, there are research methods for online trajectory generation based on supervised learning. These methods generate control variables online using neural networks and then calculate the trajectory based on these control variables, but the computational efficiency remains low. There is an urgent need to develop a method for online generation of optimal trajectories to improve efficiency. Existing related patent technologies also have certain limitations.

[0004] The patent "A Fast Method for Generating Finite-Time Trajectory of a Hypersonic Vehicle" (CN103995540A) proposes a trajectory generation method based on convex optimization. This method describes the motion model of the reentry terminal trajectory as an optimization problem, forming a nonlinear optimization problem, and then convexizes this nonlinear optimization problem, describing the optimization index and constraints as a quadratic convex problem for solution. However, this method is prone to getting trapped in local optima when solving for the optimal trajectory and depends heavily on the initial value settings, potentially resulting in low computational efficiency.

[0005] The patent "Online Trajectory Optimization Method for High-Speed ​​Gliding Vehicles Based on Deep Neural Networks" (CN118170155A) proposes an online trajectory optimization method based on deep neural networks. This method inputs state variables into a trained deep neural network to obtain the vehicle's control variables, updates the roll and angle-of-attack control commands, and the vehicle flies according to the newly generated control commands. However, this method calculates the optimal trajectory based on the control command values, which involves a large computational load and depends heavily on the computing speed of the onboard computer, making efficiency difficult to guarantee.

[0006] In summary, the core problem with existing technologies lies in the fact that current trajectory generation methods, which require online calculations to obtain the optimal trajectory during application, struggle to guarantee computational efficiency. Therefore, research is needed to develop intelligent trajectory generation algorithms to address state deviations. Intelligent trajectory generation methods can autonomously generate flight paths based on real-time state data without requiring extensive online calculations. They possess the ability to rapidly generate and adjust trajectories, ensuring that the aircraft can quickly generate a usable nominal trajectory even when state deviations occur. Summary of the Invention

[0007] To address the aforementioned problems, this invention provides an intelligent reentry trajectory generation method for aircraft based on an RBF neural network, enabling online intelligent generation of optimal trajectories. This method addresses deviations in the initial flight state caused by uncertainties by generating a large number of optimal sample trajectories using a pseudospectral method. Based on these, the RBF neural network is trained to learn the mapping relationship between the current state variables and the optimal trajectory. In online applications, the neural network rapidly generates trajectory sequences based on the current state variables, thus improving the efficiency of trajectory generation.

[0008] The technical solution of the present invention:

[0009] A method for intelligent generation of aircraft reentry trajectories based on RBF neural networks, comprising the following steps:

[0010] Step 1: Re-enter the model and build it;

[0011] Step 1.1: Establishment of reentry dynamics model;

[0012] Based on the principles of reentry kinematics, a kinematic model of an aircraft can be established:

[0013] (1)

[0014] Among them, the superscript " " represents the first derivative; The geocentric distance represents the distance from the spacecraft to the Earth's center. The longitude of the point where the aircraft is projected onto the Earth's surface. The latitude of the point where the aircraft is projected onto the Earth's surface; For speed, The flight path angle, This is the heading angle. For lift, As resistance; For the mass of the aircraft, For Earth's gravitational acceleration, The tilt angle, This represents the angular velocity of rotation.

[0015] Step 1.2: Establishment of the aerodynamic model;

[0016] The aircraft dynamics model includes lift. and resistance , is represented as:

[0017] (2)

[0018] (3)

[0019] In the formula: The atmospheric density is a function of altitude, and is calculated using a fitted atmospheric model. For speed, The aerodynamic area of ​​the aircraft; These are the lift coefficient and drag coefficient, respectively, used as the angle of attack. The calculation is performed using a function of the Mach number Ma.

[0020] Step 2: Problem construction for trajectory optimization;

[0021] During the reentry mission, the thermal flux density, overload and dynamic pressure parameters during the reentry process are strictly controlled due to objective limitations such as the temperature resistance limit of the airframe material and the structural load-bearing capacity. This is to ensure the stability of thermal protection in hypersonic flight and to further improve the overall operational reliability of the airframe. All indicators must be kept within safe thresholds.

[0022] (4)

[0023] (5)

[0024] (6)

[0025] In the formula: These are dynamic pressure, heat flux density, and overload, respectively. These represent the maximum values ​​of dynamic pressure, heat flux density, and overload, respectively. Atmospheric density at sea level The first cosmic velocity, The radius of curvature of the aircraft's nose; For aircraft characteristic constants.

[0026] Upon reentry to the target's latitude and longitude, the terminal constraint has strict positional constraints, given by the following formula:

[0027] (7)

[0028] In the formula: For terminal time; For time Earth's distance at time For time Longitude at time For time latitude at time The distance from the Earth's center to the terminal point. For terminal longitude, The latitude is the terminal latitude.

[0029] The control variables for the reentry process mainly include the values ​​of the angle of attack and the roll angle. In the process of solving using the pseudospectral method, the augmented angle of attack and the roll angle are used as the state to solve, and the rates of change of the angle of attack and the roll angle are used as the control variables to solve. Therefore, the control constraints are as follows:

[0030] (8)

[0031] In the formula: For the angle of attack, For the rate of change of angle of attack, This represents the rate of change of the tilt angle; These are the minimum and maximum angles of attack. These represent the minimum and maximum values ​​of the tilt angle. For the minimum and maximum values ​​of the rate of change of angle of attack, These are the minimum and maximum values ​​of the rate of change of the tilt angle.

[0032] The minimum heating amount is selected as the performance index, i.e.:

[0033] (9)

[0034] In the formula: The initial time, This is the terminal time. The minimum value of the integral of the heat flux density from the initial time to the terminal time is selected as the performance index.

[0035] Step 3: Method for generating the optimal trajectory sample set;

[0036] Before an aircraft enters the quasi-equilibrium gliding phase, it needs to perform a high angle-of-attack downward maneuver to adjust its flight attitude and gradually transition to the energy state required for gliding. This process typically begins at a relatively high initial altitude and speed. The aircraft generates significant aerodynamic drag by increasing the angle of attack, achieving rapid deceleration and altitude reduction, thus creating conditions for subsequent equilibrium gliding. However, in actual flight, the aircraft's actual flight trajectory often deviates from the nominal trajectory. This results in a certain range of dispersion between the aircraft's actual altitude and speed states and the nominal design states when flying over certain key waypoints. This dispersion not only reflects the complexity and randomness of the flight environment but also the aircraft system's response characteristics when facing disturbances. To assess and address the impact of this dispersion on subsequent flight performance and safety, it is necessary to select representative altitude-velocity dispersion states at typical waypoints as initial conditions for subsequent trajectory optimization and analysis.

[0037] This invention selects the dispersion states of altitude and velocity at waypoints to construct a trajectory optimization problem considering the effects of uncertainty. This problem aims to explore whether, under given dispersion conditions, the aircraft can still satisfy process and terminal constraints and optimize performance indicators as much as possible. For this trajectory optimization problem, this invention employs the pseudospectral method for numerical solution. The pseudospectral method discretizes the continuous-time state and control variables on high-order orthogonal collocation points such as the Legendre-Gauss-Radau method, and approximates the state trajectory using a global Lagrange interpolation polynomial, thereby transforming the complex continuous optimal control problem into a finite-dimensional nonlinear programming problem. The dynamic equations are precisely transformed into algebraic equality constraints on the collocation points. By calling a mature nonlinear programming solver for optimization calculations, a continuous flight trajectory that satisfies the constraints under uncertainty conditions and optimizes performance indicators is finally reconstructed, achieving quantitative assessment of the impact of uncertainty and high-precision, high-efficiency trajectory optimization.

[0038] Step 4: Neural network training and application;

[0039] All flight trajectory data obtained from solving the trajectory optimization problem in step 3 are compiled into a large database. 70% of the total samples are randomly extracted from this database as the training set to train the RBF neural network. The remaining 30% of the samples are used as test samples to verify the computational accuracy of the neural network. In the training process of this invention, to avoid the loss of prediction accuracy due to large differences in the magnitude of input and output data, the input and output data are normalized separately. During RBF neural network training, the input to the RBF neural network is the initial altitude and velocity values ​​for each trajectory data point, and the output is the sequence data of altitude, velocity, latitude and longitude, flight path angle, heading angle, angle of attack, and bank angle for each trajectory. The maximum number of iterations is set to 200, and the convergence accuracy is set accordingly. When the convergence accuracy is reached, it proves that the network training is complete.

[0040] The trained RBF neural network is then transferred to an online application to assess flight status deviations at waypoints and determine whether the optimal trajectory needs updating. At waypoints, the actual flight status is compared with the determined trajectory; if any deviation in altitude or speed exceeds a set error (e.g., altitude deviation), the error is detected. speed deviation If the current actual altitude and speed are taken as input to the RBF neural network, the RBF neural network is used to regenerate the optimal tracking trajectory, which includes altitude, speed, latitude and longitude, flight path angle, heading angle, angle of attack and roll angle.

[0041] The beneficial effects of this invention are:

[0042] This invention focuses on improving the optimality and speed of aircraft reentry trajectory generation. It systematically studies and proposes an intelligent trajectory generation method that integrates the pseudospectral method and radial basis function (RBF) neural networks. Through theoretical modeling, algorithm design, extensive simulations, and comparative analyses, the effectiveness, accuracy, and engineering application potential of the proposed method are verified. This method enables the guidance system to rapidly generate a nominal trajectory based on the current actual state, enhancing the aircraft's adaptability and mission completion capabilities under state deviation conditions. Attached Figure Description

[0043] Figure 1 This is a flowchart of the overall design scheme of the present invention;

[0044] Figure 2 This is a flowchart of the sample trajectory generation process;

[0045] Figure 3 It is a set of high-resolution sample trajectories;

[0046] Figure 4 It is a set of latitude and longitude sample trajectories;

[0047] Figure 5 It is a set of velocity sample trajectories;

[0048] Figure 6 This is a comparison chart of the trajectory of the high-resolution sample and the trajectory generated by the neural network;

[0049] Figure 7 This is a comparison chart of longitude sample trajectories and neural network-generated trajectories;

[0050] Figure 8 This is a comparison chart of the latitude sample trajectory and the trajectory generated by the neural network;

[0051] Figure 9This is a comparison chart of the velocity sample trajectory and the trajectory generated by the neural network;

[0052] Figure 10 This is a comparison chart of the trajectory generated by a highly neural network, the sample trajectory, and the integral trajectory;

[0053] Figure 11 This is a comparison chart of the trajectory generated by the latitude and longitude neural network, the sample trajectory, and the integral trajectory;

[0054] Figure 12 This is a comparison chart of the trajectory generated by the velocity neural network, the sample trajectory, and the integral trajectory. Detailed Implementation

[0055] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0056] The specific implementation process of this invention is as follows: Figure 1 As shown, in the offline part, optimal trajectory data is generated using the pseudospectral method based on the flight mission. The initial state is the altitude and velocity dispersion during the gliding initial stage. A state-action sequence to the terminal point is generated. At each waypoint, a trajectory family is generated based on the new altitude and velocity dispersion, establishing a "state dispersion-trajectory sequence" sample set. An RBF neural network is trained based on this set, with its input being the current state's altitude and velocity dispersion data, and its output being the state-control sequence from the current state to the terminal point. A new neural network is trained at each waypoint, establishing a trajectory generation model. In the online part, the need to generate an optimal trajectory is determined by the state error. The optimal trajectory from the current state to the terminal point is quickly generated using the actual flight conditions. The specific implementation steps are as follows:

[0057] Step 1: Re-enter the model and build it;

[0058] Step 1.1: Establishment of reentry dynamics model;

[0059] This invention focuses on reentry vehicles and studies their reentry trajectories, thus establishing the reentry kinematics and dynamics equations of the vehicle in the position coordinate system.

[0060] (1)

[0061] In the formula: superscript " " represents the first derivative; The geocentric distance represents the distance from the spacecraft to the Earth's center. The longitude of the point where the aircraft is projected onto the Earth's surface. The latitude of the point where the aircraft is projected onto the Earth's surface; For speed, The flight path angle, This is the heading angle. For lift, As resistance; For the mass of the aircraft, For Earth's gravitational acceleration, The tilt angle, It represents the magnitude of the angular velocity of rotation.

[0062] Step 1.2: Establishment of the aerodynamic model;

[0063] The aircraft dynamics model includes lift. and resistance , which is represented as

[0064] (2)

[0065] (3)

[0066] In the formula: The atmospheric density is a function of altitude, and is calculated using a fitted atmospheric model. For the aerodynamic area of ​​the aircraft, These are the lift coefficient and drag coefficient, respectively, which are used as the angle of attack. And the calculation is performed as a function of the Mach number Ma. That is... .

[0067] Step 2: Problem construction for trajectory optimization;

[0068] Based on the dynamic model, the purpose of solving the relevant optimization problem is to find a suitable control quantity that minimizes the objective function while satisfying multiple constraints.

[0069] This invention utilizes the pseudospectral method to solve the optimization problem. The trajectory optimization problem during the reentry process of a hypersonic vehicle is to optimize a certain performance index while satisfying constraints. Based on the above modeling, minimizing the heating amount during the reentry process of the hypersonic vehicle is taken as the performance index, enabling it to reach the terminal point and meet the performance index under different initial conditions.

[0070] The trajectory optimization problem is as follows:

[0071]

[0072] In the formula: For heat flux density, The initial time, This is the terminal time. The minimum value of the integral of the heat flux density from the initial time to the terminal time is selected as the performance index. These are dynamic pressure, heat flux density, and overload, respectively. These represent the maximum values ​​of dynamic pressure, heat flux density, and overload, respectively. Atmospheric density, Atmospheric density at sea level For speed, The first cosmic velocity, It is a constant related to the radius of the aircraft's nose. The radius of curvature of the aircraft's nose; These are the aircraft characteristic constants; For lift, As resistance; For the mass of the aircraft, This refers to the acceleration due to Earth's gravity. For terminal time, The distance from the Earth's center to the terminal point. For terminal longitude, The latitude is the terminal latitude. For the angle of attack, The tilt angle, For the rate of change of angle of attack, This represents the rate of change of the tilt angle; These are the minimum and maximum angles of attack. These represent the minimum and maximum values ​​of the tilt angle. For the minimum and maximum values ​​of the rate of change of angle of attack, These represent the minimum and maximum rates of change of the roll angle. For balanced gliding conditions, the key is controlling the aircraft's maximum gliding altitude. This limitation enables the aircraft to perform corresponding maneuvers while ensuring support for the required rate of change of the flight path angle. In this invention, reentry occurs at the target's latitude and longitude, therefore the terminal constraints have strict positional constraints. The control variables during reentry mainly include the values ​​of the angle of attack and roll angle. In this invention, using the pseudospectral method, the augmented angle of attack and roll angle are solved as states, and the rates of change of the angle of attack and roll angle are solved as control variables, thus constraining the angle of attack, roll angle, and their rates of change.

[0073] Step 3: Method for generating the optimal trajectory sample set;

[0074] Before entering quasi-equilibrium gliding, the aircraft performs a high angle-of-attack downward thrust to adjust its flight attitude and gradually transition to the energy state required for gliding. However, the actual flight state of the aircraft will exhibit some dispersion when passing certain waypoints. Therefore, the dispersion states of altitude and velocity at specific waypoints are selected, and a trajectory optimization problem is constructed based on this. The pseudospectral method is used to solve the trajectory optimization problem. The solution process is as follows: Figure 2 As shown.

[0075] The trajectory optimization problem of this invention mainly focuses on reaching the target point with the minimum heating amount at different states. Trajectory datasets are generated at the first waypoint with different initial states. The initial state at the next waypoint is based on the state deviation from the previous trajectory data, and so on, generating trajectory datasets for each waypoint. A neural network is then trained based on these datasets. The initial and final states of the aircraft are shown in Table 1, and the process constraints are shown in Table 2.

[0076] Table 1 Initial Terminal Parameters of the Aircraft

[0077]

[0078] Table 2. Aircraft Process Constraint Parameters

[0079]

[0080] The initial scatter samples generated using the pseudospectral method totaled 2500. Due to the uneven distribution of the optimized dataset, all optimized data were interpolated to obtain state-control variable data at 1-second intervals. The state variables in the trajectory dataset include altitude, longitude, latitude, velocity, flight path angle, and heading angle; as well as drag acceleration and dynamic pressure profiles required for subsequent tracking and guidance. This dataset contains approximately 2.5 million data points. The altitude and latitude / longitude trajectory data are shown below. Figures 3-5 As shown.

[0081] Step 4: Neural Network Training and Application;

[0082] The input layer of the RBF neural network is set to highly velocity distributed data, i.e. ,in Altitude dispersion values ​​at each waypoint The velocity distribution at each waypoint; for example, at the first waypoint. Points were taken at 500m intervals for distances between 65 and 70km. Points are taken at 50 m / s intervals from 5500 to 6000 m / s; the output layer of the neural network is set as a sequence of state control variables from the current state to the terminal point. ,in It is a height sequence. It is a longitude sequence. It is a latitude sequence. It is a velocity sequence. This is a sequence of flight path angles. For heading angle sequence, Angle of attack sequence, If the tilt angle sequence is used, a trajectory generation model based on an RBF neural network can be constructed. After the RBF neural network is trained, it can be used for rapid online trajectory generation.

[0083] The key to training an RBF neural network lies in the selection of its function center point and the calculation of parameter weights. This paper uses the orthogonal least squares method to train the network, and its parameters are updated based on the output data matrix, that is, the existence of the hidden layer output to the target output. Satisfy its

[0084]

[0085] Then the weight update is complete. Output as the target. For hidden layer output, The minimum error that is satisfied.

[0086] The initial 2500 trajectory data points were divided into a training set (70%) and a test set (30%). The simulation results of the neural network were compared, and a randomly selected sample was used for analysis. Figures 6-9 It can be seen that the altitude error is within 100m, the latitude and longitude error is within 0.02°, and the speed error is within 4m / s.

[0087] The optimal trajectory generation method described above is then transferred to an online application. At each waypoint, the deviation of the flight state is assessed to determine whether the optimal trajectory needs to be updated. If the error is large, the altitude and velocity of the current waypoint are used as inputs to the neural network.

[0088] To verify the confidence level of the neural network-generated data, the angle of attack and roll angles generated by the neural network were interpolated using a fourth-order Runge-Kutta integral. The integrated trajectory was then compared with the trajectory generated by the neural network and the trajectory data optimized by GPOPS. Figures 10-12The comparison between trajectory generation by the neural network and that generated by the pseudospectral method is shown. The deviations of both state and control variables are below 1e-5, thus ensuring the optimality of the neural network. Comparing the trajectory generation rate, the time required for the trained neural network to generate the optimal trajectory is reduced by two orders of magnitude compared to the pseudospectral method, ensuring its rapid online trajectory generation. Linear interpolation of the control variables (angle of attack, roll angle) generated by the network, followed by integration using the dynamic equations, yields the integrated trajectory. The deviation from the optimal trajectory is also very small, ensuring its feasibility as a guidance command. The generalization ability of the neural network is verified using the Monte Carlo algorithm. Different initial states are randomly selected and input into the neural network to obtain the required sequence of states and control variables. The mean square error is calculated and compared with the optimal dataset, as shown in Table 3. This demonstrates that the proposed method has high confidence and generalization ability.

[0089] Table 3. Monte Carlo verification mean square error results

Claims

1. A method for intelligent generation of aircraft reentry trajectories based on RBF neural networks, characterized in that, The steps are as follows: Step 1: Re-enter the model and build it; Step 2: Problem construction for trajectory optimization; Control the heat flux density, overload and dynamic pressure parameters during the reentry process to ensure that all indicators do not exceed the safety threshold; (4) (5) (6) In the formula: These are dynamic pressure, heat flux density, and overload, respectively. These are the maximum values ​​of dynamic pressure, heat flux density, and overload, respectively. Atmospheric density at sea level The first cosmic velocity, The radius of curvature of the aircraft's nose; These are the aircraft characteristic constants; Upon reentry to the target's latitude and longitude, the terminal constraint has strict positional constraints, given by the following formula: (7) In the formula: For terminal time; For time Earth's distance at time For time Longitude at time For time latitude at time The distance from the Earth's center to the terminal point. For terminal longitude, The terminal latitude; The control variables for the reentry process include the values ​​of the angle of attack and the roll angle. In the pseudospectral method, the augmented angle of attack and the roll angle are used as the state variables for solution, while the rates of change of the angle of attack and the roll angle are used as the control variables. Therefore, the control constraints are as follows: (8) In the formula: For the angle of attack, For the rate of change of angle of attack, This represents the rate of change of the tilt angle; These are the minimum and maximum angles of attack. These represent the minimum and maximum values ​​of the tilt angle. For the minimum and maximum values ​​of the rate of change of angle of attack, These represent the minimum and maximum rates of change of the tilt angle; The minimum heating amount is selected as the performance index, i.e.: (9) In the formula: The initial time, For terminal time; The minimum value of the integral of the heat flux density from the initial time to the terminal time is selected as the performance index. Step 3: Method for generating the optimal trajectory sample set; At waypoints, the dispersion of altitude and velocity is selected to construct a trajectory optimization problem that considers the effects of uncertainty, and the pseudospectral method is used for numerical solution. Step 4: Neural network training and application; All flight trajectory data obtained from solving the trajectory optimization problem in step 3 are compiled into a database. 70% of the total number of samples are randomly extracted from the database as the training set to train the RBF neural network; the remaining 30% of the samples are used as test samples to verify the computational accuracy of the neural network. During training, the input and output data are normalized respectively. The input of the RBF neural network is the initial altitude and velocity values ​​of each trajectory data, and the output is the sequence data of altitude, velocity, latitude and longitude, flight path angle, heading angle, angle of attack and roll angle of each trajectory. The trained RBF neural network is migrated to an online application. At waypoints, deviations in its flight status are assessed to determine whether the optimal trajectory needs to be updated. At waypoints, the actual flight status is compared with the determined trajectory. If any deviation in altitude or speed exceeds the set error, the current actual altitude and speed are used as inputs to the RBF neural network. The RBF neural network is then used to regenerate the optimal tracking trajectory, which includes altitude, speed, latitude and longitude, flight path angle, heading angle, angle of attack, and roll angle.

2. The intelligent generation method for aircraft reentry trajectory based on RBF neural network according to claim 1, characterized in that, Step 1 is as follows: Step 1.1: Establishment of reentry dynamics model; A kinematic model of the aircraft is established based on the principles of reentry kinematics. (1) Among them, the superscript " " represents the first derivative; The geocentric distance represents the distance from the spacecraft to the Earth's center. The longitude of the point where the aircraft is projected onto the Earth's surface. The latitude of the point where the aircraft is projected onto the Earth's surface; For speed, The flight path angle, For heading angle; For lift, As resistance; For the mass of the aircraft, For Earth's gravitational acceleration, The tilt angle, Indicates the angular velocity of rotation; Step 1.2: Establishment of the aerodynamic model; The aircraft dynamics model includes lift. and resistance , is represented as: (2) (3) In the formula: The atmospheric density is a function of altitude, and is calculated using a fitted atmospheric model. For speed, The aerodynamic area of ​​the aircraft; These are the lift coefficient and drag coefficient, respectively, used as the angle of attack. The calculation is performed using a function of the Mach number Ma.

3. The intelligent generation method for aircraft reentry trajectory based on RBF neural network according to claim 1, characterized in that, The solution process in step 3 is as follows: The pseudospectral method discretizes the continuous-time state and control variables on high-order orthogonal collocation points such as Legendre-Gauss-Radau, and approximates the state trajectory using a global Lagrange interpolation polynomial, thereby transforming the complex continuous optimal control problem into a finite-dimensional nonlinear programming problem, in which the dynamic equations are transformed into algebraic equality constraints on collocation points; by calling the nonlinear programming solver for optimization calculation, a continuous flight trajectory that satisfies the constraints under uncertainty conditions and optimizes the performance index is finally reconstructed, thus achieving trajectory optimization.

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