Reusable vehicle cruise phase intelligent trajectory planning method

Abstract

The present application belongs to the field of reusable launch vehicle trajectory planning and intelligent control, and relates to a reusable launch vehicle cruise phase intelligent trajectory planning method. By constructing a three-degree-of-freedom mass center motion dynamics model of the cruise phase launch vehicle, an offline optimal trajectory sample library covering a wide range of working conditions is generated based on the Gauss pseudospectral method, a deep neural network is designed to learn the mapping relationship between task parameters and trajectory features, and high-quality trajectory planning initial values are output online. In combination with the adaptive collocation method, the collocation distribution is dynamically adjusted, and the nonlinear programming problem is iteratively solved with the high-quality initial values as the starting point, thereby realizing efficient and accurate optimization of the trajectory. Simulation results show that the method significantly reduces the sensitivity of online optimization to initial guesses, still has fast response capability and high robustness under complex constraints and uncertain conditions, effectively improves the autonomous trajectory planning capability of the reusable launch vehicle cruise phase, and guarantees flight reliability and control accuracy.

Description

Technical Field

[0001] This invention belongs to the field of trajectory planning and intelligent control of reusable vehicles, and particularly relates to an intelligent trajectory planning method for the cruise segment of a reusable vehicle. Background Technology

[0002] Reusable launch vehicles face challenges during the cruise phase, including complex aerodynamic environments, diverse mission constraints, and limited online computing resources. Traditional trajectory planning methods often employ model-based optimal control theory, transforming continuous trajectory optimization problems into nonlinear programming problems. However, these methods typically rely on dynamic models and initial guesses, making them ill-suited for scenarios with high uncertainties and real-time requirements.

[0003] The patent "An Online Trajectory Planning Method Based on Heuristic Search and Pre-aiming" (CN117666611A) addresses the high-speed and constant-velocity constraints and no-fly zone avoidance requirements of air-breathing combined-fuel aircraft during the cruise phase. It combines heuristic search to generate reference trajectories and then utilizes pre-aiming to achieve trajectory tracking, improving efficiency while maintaining planning accuracy. However, this method has certain limitations: the cost weight setting of the heuristic search relies on experience, making it highly subjective; the selection of pre-aiming points is limited by aircraft performance; and it is insufficiently adaptable to uncertainties such as time-varying aerodynamic parameters and external disturbances under complex operating conditions, requiring further robustness improvement.

[0004] The patent "A Rapid Trajectory Planning Method for a Combined-Powered Aircraft Considering Secondary Lift" (CN113721646A) addresses the need for changing mission objectives during the cruise phase by combining a semi-analytical estimation method to rapidly generate secondary lift trajectories. This effectively solves the problems of traditional trajectory planning, such as difficulty in adapting to changing terminal missions and slow convergence speed, thus improving the mission flexibility of the aircraft. However, while this method improves planning speed, its accuracy is lower than that of numerical optimization methods, which may affect trajectory control accuracy. Furthermore, the program angle design for the secondary lift phase is fixed, lacking the ability to adaptively adjust to different mission profiles. Under extreme conditions, this may affect flight stability and is not conducive to ensuring comprehensive mission reliability in engineering applications.

[0005] The patent "A Trajectory Design Method for Online Altitude Adjustment During the Cruise Phase of a Supersonic Vehicle" (CN118466546A) establishes an offline trajectory database for the cruise phase and performs normalization processing. Combined with linear interpolation and altitude change coefficient calculation, it quickly generates ballistic commands at the target cruise altitude, effectively solving the problem of traditional methods struggling to generate trajectory commands quickly and accurately. However, this method's trajectory database relies on offline planning at equal altitude intervals, resulting in limited coverage and poor adaptability to altitudes exceeding preset intervals or extreme altitudes. Furthermore, the fixed normalization and interpolation logic lacks adaptive adjustment capabilities for different mission profiles, potentially affecting trajectory stability under extreme conditions such as rapid altitude changes, which is detrimental to ensuring comprehensive flight reliability in engineering applications.

[0006] The paper "Boost-Cruise Trajectory Optimization for Air-breathing Hypersonic Vehicles [J]. Journal of Astronautics, 2021, 42(7): 820-829" addresses the challenges of strongly coupled and highly nonlinear trajectory optimization for air-breathing hypersonic vehicles. It employs a collocation method combined with normalization, sparse difference algorithm, and SQP algorithm to achieve a fast and high-precision solution to the trajectory optimization problem. However, this method relies on offline parameter analysis, lacks the efficiency adaptation and dynamic adjustment capabilities for online replanning, and does not consider the recycling constraints and multi-task switching scenarios required for reusability, thus limiting its applicability.

[0007] Therefore, there is an urgent need for an intelligent trajectory planning method suitable for the cruise phase of reusable vehicles, which can utilize offline data to quickly generate high-quality initial values ​​for trajectory planning online, and combine adaptive optimization strategies to achieve efficient online trajectory planning under complex constraints and uncertainties. Summary of the Invention

[0008] The purpose of this invention is to provide an intelligent trajectory planning method for the cruise segment of a reusable vehicle. This method can quickly generate high-quality initial values ​​for trajectory planning online and achieve efficient and accurate planning of the cruise segment trajectory through an adaptive point optimization strategy.

[0009] The technical solution of the present invention is as follows:

[0010] A method for intelligent trajectory planning during the cruise phase of a reusable launch vehicle includes: constructing a three-degree-of-freedom centroid motion dynamics model of the launch vehicle during the cruise phase; generating offline sample data based on the Gaussian pseudospectral method; designing an intelligent initial value predictor for trajectory planning based on a deep neural network; and optimizing the trajectory online by combining initial value prediction with an adaptive collocation method. Details are as follows:

[0011] Step 1: Construct a three-degree-of-freedom center-of-mass motion dynamic model of the launch vehicle during the cruise phase.

[0012] (1)

[0013] Among them, the superscript " " represents the first derivative; For the mass of the aircraft, For flight speed, For flight altitude, For thrust vector, , These are drag and lift, respectively. It is the acceleration due to gravity. , , These are the aircraft's trajectory inclination angle, heading angle, and roll angle, respectively. For the angle of attack.

[0014] Step 2: Generation of offline sample data based on Gaussian pseudospectral method

[0015] For typical mission profiles during the cruise phase, including routine cruise, emergency replanning, and multi-target switching scenarios, the Gaussian Pseudospectral Method (GPM) is employed as a high-precision trajectory optimizer. Through systematic task parameter sampling and batch optimization calculations, an optimal trajectory sample library covering a wide range of operating conditions is generated, providing high-quality data support for subsequent deep neural network training. Details are as follows:

[0016] Step 2.1, Task Parameter Sampling

[0017] The cruise segment mission parameter space is defined as a multi-dimensional set of constraints, i.e. ,in: Let be the initial state vector. Initial flight speed, This is the initial flight altitude. The initial trajectory inclination angle, The initial heading angle, The initial tilt angle, This represents the initial mass. For the terminal constraint vector, and For the terminal plane position, For terminal height, For terminal speed. For process constraint boundary vectors, For maximum dynamic pressure, For maximum overload, For maximum heat flux density, To balance the gliding constraint angle. To control the constraint vector, , For the upper and lower limits of the angle of attack, , These are the upper and lower limits of thrust.

[0018] Latin Hypercube Sampling (LHS) is used to uniformly sample the task parameter space Γ, ensuring that the samples cover all critical operating conditions. The number of sampling groups... Based on the complexity of the operating conditions, each set of sampling results constitutes an independent task scenario. , .

[0019] Step 2.2: Optimization of Gaussian pseudospectral method

[0020] For each set of task scenarios The Gaussian pseudospectral method is used to transform the continuous optimal control problem into a nonlinear programming (NLP) problem, and a high-precision optimal trajectory is obtained through numerical solution. The flight time interval is mapped to the [-1,1] interval through variable transformation, and a selection is made within each stage. N A Gaussian collocation.

[0021] State variables and control variables Represented by the Lagrange interpolation polynomial:

[0022] (2)

[0023] (3)

[0024] In the formula: For Lagrange basis functions; This represents the total number of Gaussian collocation points, i.e., the number of nodes in the time-domain discretization. The more collocation points, the higher the approximate accuracy. The interpolation node index for Gaussian collocations. For the first Discrete values ​​of state variables at Gaussian collocation points For the first Discrete values ​​of control variables at Gaussian collocation points.

[0025] For continuous-time dynamic equations, the state derivatives at collocation points are... Convert to algebraic constraints:

[0026] (4)

[0027] In the formula: It is a differential matrix, consisting of Gaussian integral weights and derivatives of basis functions; Discrete index for Gaussian collocations. For the first Discretized vectors of the motion state of the aircraft's center of mass at each Gaussian collocation point. This is the end time of the cruise segment. The start time, For the first The time of a Gaussian collocation point in the original time domain.

[0028] Process constraints include dynamic pressure Overload Heat flux density Apply directly at the designated point, where , , These are the dynamic pressure, overload, and heat flux density of the launch vehicle, respectively. , , These represent the maximum permissible values ​​for the launch vehicle's dynamic pressure, overload, and heat flux density, respectively. The terminal state should satisfy the constraints of the kinetic equations.

[0029] Performance metrics transformed into NLP objective functions :

[0030] (5)

[0031] In the formula: These are the state variables at the terminal moment, including key states such as velocity, altitude, trajectory inclination, and mass. It is the first k The Gaussian integral weights of each collocation point reflect the importance of each collocation point in the time domain. It is the first k The process performance index function of each point quantifies the performance requirements at that moment, such as speed deviation, fuel consumption, etc. It is the first k Each control variable, such as angle of attack and throttle opening, can be actively adjusted. It is the first k The moment of each coordinate point is the terminal moment after discretization. It is the objective function, representing the overall performance score of trajectory optimization, used to quantify the quality of the cruise segment trajectory. It is a terminal performance index function that describes the state performance requirements at the end of the cruise segment, ensuring that key constraints are met when the transition is completed, such as the deviation between the terminal speed and the target speed, and terminal altitude constraints.

[0032] The complete nonlinear programming problem is solved using sequential quadratic programming to obtain the optimal control sequence and state trajectory. At this point, the original problem has been transformed into a discretized form, which is then optimized by resolving the discrete state variables. Control variables and terminal time Under the condition of satisfying the constraints of the dynamic equation, make the objective function Obtain the minimum value.

[0033] Step 2.3, Sample Library Construction

[0034] The parameter vector of each task It includes initial state, terminal constraints, process constraint boundaries, and control constraints, along with the corresponding optimal trajectory feature vector. Pairing to form sample pairs , build scale Offline sample library.

[0035] Step 3: Design of an intelligent predictor for initial values ​​of trajectory planning based on deep neural networks

[0036] Design a deep neural network (DNN) model to learn the complex mapping relationship from task parameters to the feature vector of the optimal trajectory, for online and rapid prediction of high-quality initial values ​​for planning.

[0037] Step 3.1, Network Structure Design

[0038] It adopts a fully connected feedforward neural network architecture with a network layer count of [number missing]. The system consists of an input layer, five hidden layers, and an output layer, with the following structure:

[0039] Input layer (layer 1): The number of neurons equals the input parameter vector. The dimension is 18 neurons, which receive standardized input parameters. ,in The mean vector is the input to the training set. The standard deviation vector is the input to the training set;

[0040] Hidden layers (layers 2-6): Layer 2 has 256 neurons, layer 3 has 128, layer 4 has 64, layer 5 has 32, and layer 6 has 16. A batch normalization (BN) layer is added after each layer to accelerate training convergence and improve generalization ability; a dropout layer is added after layer 4 to prevent overfitting.

[0041] Output layer (layer 7): The number of neurons equals the trajectory feature vector. The dimension is determined by the number of collocation points in the Gaussian pseudospectral method and the characteristic dimension of each collocation point. Initial number of collocation points Each alignment point must fully contain the key features describing the trajectory—6-dimensional state variables (flight speed, flight altitude, trajectory inclination, heading angle, bank angle, mass), 2-dimensional control variables (angle of attack, thrust), and 1-dimensional time coordinate. The total feature dimensions of a single alignment point are 9, and the total feature dimensions of the alignment points are 9. Therefore, the output layer needs to be set to 9. Each neuron has a linear activation function and directly outputs the predicted trajectory feature vector. .

[0042] Step 3.2, Network Training and Optimization

[0043] We use weighted mean squared error (WMSE) as the loss function, taking into account the differences in importance of different components in the trajectory feature vector, and assign weights to the state variables, control variables, and time series respectively:

[0044] (6)

[0045] in, For loss function, The number of samples in the training set; , , The first Predicted state sequence, control sequence, and time series for each sample; , , These are the corresponding actual values; , and These are weighting coefficients, highlighting the importance of the accuracy of state variable prediction.

[0046] Using the Adam optimizer, set the learning rate. Momentum parameters and Weight decay coefficient Batch size and epoch size are set. An early stopping strategy is adopted, stopping training when the validation set loss does not decrease for a consecutive epochs to avoid overfitting. A cosine annealing learning rate scheduler is used, which decays the learning rate to 0.1 times the current value every b epochs to improve the accuracy of later training. a and b can be set according to the actual situation.

[0047] The inputs to the training set, validation set, and test set during data preprocessing. With output Standardization is performed separately, with input standardization using... Output standardization adopts ,in Output the mean vector for the training set. The network outputs a standard deviation vector for the training set during training. Through reverse standardization The final prediction result is obtained. The weights of each layer are initialized using the He initialization method. and bias Initialize to Vector. During iterative training, for each epoch, the training set is divided according to the batch size, and forward propagation is performed to calculate the loss. The gradients of each parameter are calculated using the backpropagation algorithm. The parameters are updated using the Adam optimizer. After each epoch, the loss on the validation set is calculated. ,when Reaching the preset accuracy threshold When training is complete, stop training. After training, evaluate the model performance using the test set and calculate the test set loss. with average relative error ,Require .

[0048] Step 3.3, Initial Value Generation

[0049] When using online applications, for real-time task parameters (Based on the initial state collected by the sensors, mission terminal requirements, constraint boundaries, and control constraints), generate initial values ​​for trajectory optimization according to the following steps:

[0050] Step 3.3.1: Using data obtained from offline training and ,right Standardization is performed to obtain standardized real-time task parameters. ;

[0051] Step 3.3.2, will Input the trained DNN model, output the model after forward propagation. The trajectory feature vector is obtained after inverse standardization. ,in , , These are the predicted state sequence, control sequence, and time series, respectively.

[0052] Step 3.3.3: The initial state and control values ​​are reconstructed using cubic spline interpolation, based on... , , Reconstructing continuous initial state curves With control initial value curve :

[0053] (7)

[0054] (8)

[0055] in, and For cubic spline interpolation functions, ensure and Its first derivative is continuous.

[0056] Step 3.3.4: Based on the Pontryagin minimum principle of optimal control, costate variables... With state variables satisfy , Using the Hamiltonian function, the initial values ​​of the costate variables are roughly estimated using the numerical difference method based on the state and control initial values ​​predicted by the DNN. :

[0057] (9)

[0058] in, These are preliminary guesses of the costate variables. This is the collocational discrete index for the Gaussian pseudospectral method.

[0059] The final set of initial values ​​generated is ,in The predicted terminal time serves as the starting point for online trajectory optimization.

[0060] Step 4: Online trajectory optimization combining initial value prediction and adaptive point collocation method

[0061] Using the initial values ​​predicted by DNN as the initial points of the adaptive point allocation method, and through dynamic adjustment of the point allocation distribution and NLP iterative solution, online fast and accurate trajectory optimization is achieved, meeting the real-time and accuracy requirements of the cruise segment of reusable launch vehicles.

[0062] The adaptive collocation method, based on the Gaussian pseudospectral method, dynamically adjusts the number and distribution of collocation points through error estimation. It increases collocation points in regions with high trajectory curvature and large dynamic residuals, and merges collocation points in regions with gentle trajectories and small residuals, achieving the preset accuracy requirements with minimal computational cost. Indicators include:

[0063] (10)

[0064] (11)

[0065] in, For dynamic residuals, For matching points The predicted value of the state derivative at a given point is obtained by calculating the differential matrix. For the first Predicted state derivative values ​​at each Gaussian collocation point The collocation density reflects the relative magnitude of the error at each collocation point. , For Gaussian collocations The normalized dynamic residuals.

[0066] The initial value set generated in step 3 is imported into the adaptive Gaussian pseudospectral optimizer as the initial point, using the same Gaussian collocation as the offline sample generation. Based on the initial collocation and the imported initial values, an online NLP problem is constructed, with performance metrics and constraints consistent with the offline optimization. The lightweight SQP solver IPOPT is used for fast solving, with an upper limit on the number of iterations set, to obtain the first optimized solution. and the corresponding dynamic residuals Calculate the maximum dynamic residual. ,like And the rate of change of the collocation points is 0. If the residual accuracy threshold is met, constraint verification and online output are performed; otherwise, collocation point adjustment is performed. The new number of collocation points is then obtained. With the distribution of collocation points Update the allocation time series .

[0067] Based on the new collocation distribution, a cubic spline interpolation method is used to transform the previous optimization solution. Interpolate to the new collocation point to obtain the new initial value. With new allocation points New initial value Using this as input, we re-solve the NLP problem to obtain a new optimized solution. and dynamic residuals Calculate the maximum dynamic residual. With the rate of change of the collocation point , For the point density threshold, if and If convergence occurs, perform constraint verification and online output; otherwise, let... , Then, the point allocation is readjusted adaptively until the maximum number of iterations is reached, at which point the process stops.

[0068] Constraint verification and online output: This involves checking whether the optimized trajectory satisfies all path constraints and boundary constraints. ,satisfy and If the constraints are satisfied, proceed to the next step; otherwise, adjust the constraint weights and solve again. The continuous optimization trajectory will be... , time step Discretization yields a discrete trajectory sequence. , and the corresponding time series ; Convert discrete trajectory sequences into guidance commands executable by the launch vehicle, including altitude commands. Speed ​​command Angle of attack command and throttle command The data is transmitted in real time to the launch vehicle control system via the data bus for flight control during the cruise phase.

[0069] The beneficial effects of this invention are:

[0070] This invention addresses the challenges of complex aerodynamic environments and limited online computing resources during the cruise phase of reusable launch vehicles by proposing an intelligent trajectory planning method. This method effectively solves the problems of traditional trajectory planning methods, such as heavy reliance on initial guesses, low online computation efficiency, and insufficient adaptability to complex operating conditions, thus significantly improving the reliability of cruise phase flight missions and overall system performance. This invention provides high-quality data support for online planning by offline construction of an optimal trajectory sample library covering a wide range of operating conditions. A deep neural network-based intelligent initial value predictor for trajectory planning achieves rapid and accurate mapping from mission parameters to optimal trajectory features. This initial value prediction not only significantly reduces the number of iterations in online optimization but also lowers the demand for online computing resources, adapting to the real-time requirements of the cruise phase of reusable launch vehicles. An adaptive point optimization strategy is introduced to achieve a dynamic balance between accuracy and efficiency. Compared to traditional numerical optimization methods with fixed points, this invention uses real-time evaluation of dynamic residuals and point density to dynamically increase points in areas with high trajectory curvature and significant errors, and merge points in areas with smooth trajectories. This satisfies the preset accuracy requirements with minimal computational cost, effectively resolving the contradiction between high accuracy and real-time performance under complex constraints. Meanwhile, this invention possesses strong robustness and adaptability to various operating conditions. The offline sample library covers a wide range of variations in initial states, terminal requirements, and constraint boundaries. The neural network model enhances its generalization ability through techniques such as batch normalization and dropout. The adaptive collocation method can dynamically cope with uncertainties such as time-varying aerodynamic parameters and external disturbances, enabling the trajectory planning scheme to converge stably even under extreme conditions such as rapid altitude changes and sudden changes in mission objectives. This solves the problems of traditional heuristic search weights relying on experience and the uneven error distribution of the fixed collocation method, significantly improving flight stability in complex environments. Attached Figure Description

[0071] Figure 1 This is a general block diagram of the intelligent trajectory planning method for the cruise segment of a reusable launch vehicle;

[0072] Figure 2 It is a cruise phase altitude-time curve of a reusable launch vehicle;

[0073] Figure 3 It is a cruise phase speed-time curve of a reusable launch vehicle;

[0074] Figure 4 It is a trajectory angle-time curve of the cruise segment of a reusable launch vehicle;

[0075] Figure 5 It is a cruise segment range-time graph for reusable launch vehicles;

[0076] Figure 6 It is a time-of-attack curve of the cruise phase of a reusable launch vehicle;

[0077] Figure 7 It is a cruise phase mass-time curve of a reusable launch vehicle;

[0078] Figure 8 It is a three-dimensional geographic location map of the cruise segment of a reusable launch vehicle. Detailed Implementation

[0079] The embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0080] like Figure 1 As shown, the present invention provides an intelligent trajectory planning method for the cruise segment of a reusable launch vehicle, comprising:

[0081] Step 1: Construct a three-degree-of-freedom dynamic model of the center of mass motion of the launch vehicle during the cruise phase;

[0082] Step 2: Generation of offline sample data based on Gaussian pseudospectral method;

[0083] Step 3: Design of an intelligent predictor for initial values ​​of trajectory planning based on deep neural networks;

[0084] Step 4: Online trajectory optimization combining initial value prediction and adaptive point matching method.

[0085] Specifically, the specific steps of the present invention are as follows:

[0086] Step 1: Construct a three-degree-of-freedom center-of-mass motion dynamic model of the launch vehicle during the cruise phase.

[0087] (12)

[0088] Among them, the superscript " " represents the first derivative; For the mass of the launch vehicle, For flight speed, For flight altitude, For thrust vector, , These are drag and lift, respectively. It is the acceleration due to gravity. , , These are the launch vehicle's trajectory inclination angle, heading angle, and roll angle, respectively. For the angle of attack.

[0089] Step 2: Generation of offline sample data based on Gaussian pseudospectral method

[0090] For typical mission profiles during the cruise phase, including routine cruise, emergency replanning, and multi-target switching scenarios, the Gaussian Pseudospectral Method (GPM) is adopted as a high-precision trajectory optimizer. Through systematic task parameter sampling and batch optimization calculations, an optimal trajectory sample library covering a wide range of operating conditions is generated, providing high-quality data support for subsequent deep neural network training. The specific implementation is as follows:

[0091] Step 2.1, Task Parameter Sampling

[0092] The cruise segment mission parameter space is defined as a multi-dimensional set of constraints, i.e. ,in: Let be the initial state vector. The initial flight speed, with a value range of... ; The initial flight altitude, with a range of values. ; The initial trajectory inclination angle, with a value range of... ; The initial heading angle, with a range of values. ; The initial tilt angle, with a range of values. ; The initial mass has a range of values. . For the terminal constraint vector, , The terminal plane position, with a range of values. ; The terminal height has a range of values. ; For terminal speed, the range of values ​​is... . For process constraint boundary vectors, The maximum dynamic pressure is within a certain range. ; The maximum overload value range is [value range]. ; The maximum heat flux density, with a range of values. ; To balance the gliding constraint angle, the range of values ​​is... . To control the constraint vector, , These are the upper and lower limits of the angle of attack, and their values ​​range. ; , The upper and lower limits of thrust, and the range of values. .

[0093] Latin Hypercube Sampling (LHS) is used to uniformly sample the task parameter space Γ, ensuring that the samples cover all critical operating conditions. The number of sampling groups... The number of groups is set to 2000 based on the complexity of the operating conditions. Each group of sampling results constitutes an independent task scenario. ( ).

[0094] Step 2.2: Optimization of Gaussian pseudospectral method

[0095] For each set of task scenarios The Gaussian pseudospectral method is used to transform the continuous optimal control problem into a nonlinear programming (NLP) problem, and a high-precision optimal trajectory is obtained through numerical solution. The flight time interval is mapped to the [-1,1] interval through variable transformation, and a selection is made within each stage. N A Gaussian collocation.

[0096] State variables and control variables Represented by the Lagrange interpolation polynomial:

[0097] (13)

[0098] (14)

[0099] In the formula: For Lagrange basis functions; This represents the total number of Gaussian collocation points, i.e., the number of nodes in the time-domain discretization. The more collocation points, the higher the approximate accuracy. The interpolation node index for Gaussian collocations. For the first Discrete values ​​of state variables at Gaussian collocation points For the first Discrete values ​​of control variables at Gaussian collocation points.

[0100] For continuous-time dynamic equations, the state derivatives at collocation points are... Convert to algebraic constraints:

[0101] (15)

[0102] In the formula: It is a differential matrix, consisting of Gaussian integral weights and derivatives of basis functions; Discrete index for Gaussian collocations. For the first Discretized vectors representing the motion state of the vehicle's center of mass at each Gaussian collocation point. This refers to the end time of the cruise phase. The start time, For the first The time of a Gaussian collocation point in the original time domain.

[0103] Process constraints include dynamic pressure Overload Heat flux density Apply directly at the designated point, where , , These are the dynamic pressure, overload, and heat flux density of the launch vehicle, respectively. , , These represent the maximum permissible values ​​for the launch vehicle's dynamic pressure, overload, and heat flux density, respectively. The terminal state should satisfy the constraints of the kinetic equations.

[0104] Performance metrics transformed into NLP objective functions :

[0105] (16)

[0106] In the formula: These are the state variables at the terminal moment, including key states such as velocity, altitude, trajectory inclination, and mass. It is the first k The Gaussian integral weights of each collocation point reflect the importance of each collocation point in the time domain. It is the first k The process performance index function of each point quantifies the performance requirements at that moment, such as speed deviation, fuel consumption, etc. It is the first k Each control variable, such as angle of attack and throttle opening, can be actively adjusted. It is the first k The moment of each coordinate point is the terminal moment after discretization. It is the objective function, representing the overall performance score of trajectory optimization, used to quantify the quality of the cruise segment trajectory. It is a terminal performance index function that describes the state performance requirements at the end of the cruise segment, ensuring that key constraints are met when the transition is completed, such as the deviation between the terminal speed and the target speed, and terminal altitude constraints.

[0107] The complete nonlinear programming problem described above is solved using sequential quadratic programming to obtain the optimal control sequence and state trajectory. At this point, the original problem has been transformed into a discretized form, which can be solved by optimizing the discrete state variables. Control variables and terminal time Under the condition of satisfying the constraints of the dynamic equation, make the objective function Obtain the minimum value.

[0108] Step 2.3, Sample Library Construction

[0109] The parameter vector for each task It includes the initial state, terminal constraints, process constraint boundaries, and control constraints, along with the corresponding optimal trajectory feature vectors. Pairing to form sample pairs , build scale Offline sample library.

[0110] Step 3: Design of an intelligent predictor for initial values ​​of trajectory planning based on deep neural networks

[0111] Design a deep neural network (DNN) model to learn the complex mapping relationship from task parameters to the feature vector of the optimal trajectory, for online and rapid prediction of high-quality initial values ​​for planning.

[0112] Step 3.1, Network Structure Design

[0113] It adopts a fully connected feedforward neural network architecture with a network layer count of [number missing]. The structure of the layers (input layer + 5 hidden layers + output layer) is as follows:

[0114] Input layer (layer 1): The number of neurons equals the input parameter vector. The dimension is 18 neurons, which receive standardized input parameters. ,in Input the mean vector into the training set. Input the standard deviation vector into the training set;

[0115] Hidden layers (layers 2-6): Layer 2 has 256 neurons, layer 3 has 128, layer 4 has 64, layer 5 has 32, and layer 6 has 16. A batch normalization (BN) layer is added after each layer to accelerate training convergence and improve generalization ability; a dropout layer with a dropout rate of 0.2 is added after layer 4 to prevent overfitting.

[0116] Output layer (layer 7): The number of neurons equals the trajectory feature vector. The dimension is determined by the number of collocation points in the Gaussian pseudospectral method and the characteristic dimension of each collocation point. Initial number of collocation points =30, each coordinate point must fully contain the key features describing the trajectory—6-dimensional state variables (flight speed, flight altitude, trajectory inclination, heading angle, bank angle, mass), 2-dimensional control variables (angle of attack, thrust), and 1-dimensional time coordinate. The total feature dimension of a single coordinate point is 9 dimensions, and the total feature dimension of 30 coordinate points is 30 × 9 = 270 dimensions. Therefore, the output layer needs to set 270 neurons, and the activation function is a linear activation function, directly outputting the predicted trajectory feature vector. .

[0117] Step 3.2, Network Training and Optimization

[0118] We use weighted mean squared error (WMSE) as the loss function, taking into account the differences in importance of different components in the trajectory feature vector, and assign weights to the state variables, control variables, and time series respectively:

[0119] (17)

[0120] in, For loss function, The number of samples in the training set; , , The first Predicted state sequence, control sequence, and time series for each sample; , , These are the corresponding actual values; , , These are weighting coefficients, highlighting the importance of the accuracy of state variable prediction.

[0121] Using the Adam optimizer, the learning rate Momentum parameters , Weight decay coefficient Epoch=200, employing an early stopping strategy: training stops when the validation set loss shows no decrease for 20 consecutive epochs to avoid overfitting. Batch Size=32, balancing training speed and memory usage. A cosine annealing learning rate scheduler is used, decaying the learning rate to 0.1 times its current value every 50 epochs to improve training accuracy in later stages.

[0122] The inputs to the training set, validation set, and test set during data preprocessing. With output Standardization is performed separately, with input standardization using... Output standardization adopts ,in Output the mean vector for the training set. The network outputs a standard deviation vector for the training set during training. Through reverse standardization The final prediction result is obtained. The weights of each layer are initialized using the He initialization method. bias Initialize to Vector. During iterative training, for each epoch, the training set is divided according to the batch size, and forward propagation is performed to calculate the loss. The gradients of each parameter are calculated using the backpropagation algorithm. The parameters are updated using the Adam optimizer. After each epoch, the loss on the validation set is calculated. ,when Reaching the preset accuracy threshold When training is complete, stop training. After training, evaluate the model performance using the test set and calculate the test set loss. with average relative error ,Require .

[0123] Step 3.3, Initial Value Generation

[0124] When using online applications, for real-time task parameters (Based on the initial state collected by the sensors, mission terminal requirements, constraint boundaries, and control constraints), generate initial values ​​for trajectory optimization according to the following steps:

[0125] Step 3.3.1: Using data obtained from offline training and ,right Standardization process is performed to obtain ;

[0126] Step 3.3.2, will Input the trained DNN model, output the model after forward propagation. The trajectory feature vector is obtained after inverse standardization. ,in , , These are the predicted state sequence, control sequence, and time series, respectively.

[0127] Step 3.3.3: The initial state and control values ​​are reconstructed using cubic spline interpolation, based on... , , Reconstructing continuous initial state curves With control initial value curve :

[0128] (18)

[0129] (19)

[0130] in, , For cubic spline interpolation functions, ensure , Its first derivative is continuous.

[0131] Step 3.3.4: Based on the Pontryagin minimum principle of optimal control, costate variables... With state variables satisfy , Using the Hamiltonian function, the initial values ​​of the costate variables are roughly estimated using the numerical difference method based on the state and control initial values ​​predicted by the DNN. :

[0132] (20)

[0133] in, These are preliminary guesses of the costate variables. This is the collocational discrete index for the Gaussian pseudospectral method.

[0134] The final set of initial values ​​generated is ,in The predicted terminal time serves as the starting point for online trajectory optimization.

[0135] Step 4: Online trajectory optimization combining initial value prediction and adaptive point collocation method

[0136] Using high-quality initial values ​​predicted by DNN as the initial iteration points of the adaptive point allocation method, and dynamically adjusting the point allocation distribution and NLP iterative solution, online fast and accurate trajectory optimization is achieved, meeting the real-time and accuracy requirements of the cruise segment of reusable launch vehicles.

[0137] The adaptive collocation method, based on the Gaussian pseudospectral method, dynamically adjusts the number and distribution of collocation points through error estimation. It increases collocation points in regions with high trajectory curvature and large dynamic residuals, and merges collocation points in regions with gentle trajectories and small residuals, achieving the preset accuracy requirements with minimal computational cost. Key indicators include:

[0138] (twenty one)

[0139] (twenty two)

[0140] in, For dynamic residuals, For matching points The predicted value of the state derivative at a given point is obtained by calculating the differential matrix. For the first Predicted state derivative values ​​at each Gaussian collocation point The collocation density reflects the relative magnitude of the error at each collocation point. , For Gaussian collocations The normalized dynamic residuals.

[0141] The initial value set generated in step 3 is imported into the adaptive Gaussian pseudospectral optimizer as the initial iteration points. Gaussian collocations consistent with those used in offline sample generation are employed, with an initial number of collocations... =30. Based on the initial collocation and imported initial values, an online NLP problem is constructed. Its performance indicators and constraints are consistent with those of the offline optimization. The lightweight SQP solver IPOPT is used for fast solving, and the maximum number of iterations is set to 200 to obtain the first optimized solution. and the corresponding dynamic residuals Calculate the maximum dynamic residual. , For the residual accuracy threshold, if If the rate of change of the collocation points is 0, then constraint verification and online output are performed; otherwise, collocation point adjustment is performed. For conditions satisfying... , that is, the distribution point with large residual error Insert a new Gaussian collocation between its adjacent collocations. Satisfying the Legendre polynomial ; for satisfying , that is, continuous distribution points with small residuals , merged into Given a set of points, take the midpoint of the interval as the merged set of points. The new number of points is obtained. With the distribution of collocation points Update the allocation time series .

[0142] Based on the new collocation distribution, a cubic spline interpolation method is used to transform the previous optimization solution. Interpolate to the new collocation point to obtain the new initial value. With new allocation points New initial value Using this as input, we re-solve the NLP problem to obtain a new optimized solution. and dynamic residuals Calculate the maximum dynamic residual. With the rate of change of the collocation point , For the point density threshold, if and If the result is positive, then convergence occurs, and constraint verification and online output are performed; otherwise, let... , The point allocation is readjusted adaptively, with an upper limit of the number of iterations. Second-rate.

[0143] Constraint verification and online output: This involves checking whether the optimized trajectory satisfies all path constraints and boundary constraints. ,satisfy and If the constraints are satisfied, proceed to the next step; otherwise, adjust the constraint weights and solve again. The continuous optimization trajectory will be... , time step Discretization yields a discrete trajectory sequence. , and the corresponding time series ; Convert discrete trajectory sequences into guidance commands executable by the launch vehicle, including altitude commands. Speed ​​command Angle of attack command Throttle command The data is transmitted in real time to the launch vehicle control system via the data bus for flight control during the cruise phase.

[0144] To verify the feasibility of the proposed intelligent trajectory planning method for the cruise segment of a reusable launch vehicle, simulation verification was conducted. With minimizing fuel consumption as the optimization objective, the core process of "offline sample training - online initial value prediction - adaptive point optimization" was fully executed. Newton's iteration method was used to iteratively calculate the angle of attack command and thrust at each moment. This segment's mission was a cruise capability with a range of 500 km. Simulation results are as follows: Figures 2 to 8 As shown. Figures 2 to 3 Altitude-time curves and velocity-time curves of the reusable launch vehicle under the objective of minimizing fuel consumption during the cruise phase are presented respectively. During the 0-400s flight time, the altitude climbs from the initial value to about 28.2km, always meeting the process constraints and altitude stability requirements. The speed remains constant at 1185.27m / s with a speed change rate of 0. The fuel consumption rate and thrust output are precisely matched, which meets the optimization objective of minimum fuel consumption. Figure 4 The trajectory angle-time curve is given under the target of minimum fuel consumption during the cruise segment, with the trajectory angle gradually increasing from 0 to 1.7°. Figure 5 A range-time curve for the reusable launch vehicle is presented, showing that the launch vehicle's range gradually increases from 200km to approximately 700km, with the range accumulating linearly over time, thus achieving a cruise capability with a range of 500km. Figure 6The curve of the angle of attack of the reusable launch vehicle as a function of time is presented. The angle of attack gradually increases from 5.17° to 10.11° to adapt to the aerodynamic requirements during flight and ensure flight stability. Figure 7 A mass-time curve of the reusable launch vehicle during the cruise phase is presented. The launch vehicle mass gradually decreases from 147.5t to 133.7t, at which point fuel consumption is lowest. Figure 8 The three-dimensional geographic location map clearly shows the launch vehicle's flight trajectory in the longitude-latitude-altitude coordinate system. The trajectory is smooth and continuous without inflection points, closely following the preset flight path, and there are no deviations from the constraint boundaries. In summary, using the intelligent trajectory planning method for the cruise segment proposed in this invention, the launch vehicle can smoothly complete the acceleration task during the cruise segment, and all flight parameters meet the process constraints and terminal requirements, verifying the effectiveness and engineering applicability of the method.

Claims

1. A method for intelligent trajectory planning during the cruise segment of a reusable launch vehicle, characterized in that, Includes the following steps: Step 1: Construct a three-degree-of-freedom dynamic model of the center of mass motion of the launch vehicle during the cruise phase; Step 2: Generation of offline sample data based on Gaussian pseudospectral method; For the cruise mission profile, including cruise, emergency replanning, and multi-target switching scenarios, the Gaussian pseudospectral method (GPM) is used as the trajectory optimizer. Through systematic task parameter sampling and batch optimization calculation, an optimal trajectory sample library covering a wide range of working conditions is generated. Step 3: Design of an intelligent predictor for initial values ​​of trajectory planning based on deep neural networks; Design a deep neural network (DNN) model to learn the complex mapping relationship from task parameters to the feature vector of the optimal trajectory, for online rapid prediction of initial planning values; Step 4: Online trajectory optimization combining initial value prediction and adaptive point matching method; The initial value predicted by DNN is used as the initial point of the adaptive point matching method. By dynamically adjusting the point matching distribution and solving iteratively by NLP, online fast and accurate trajectory optimization is achieved, which meets the real-time and accuracy requirements of the cruise segment of reusable launch vehicles. Step 3 is as follows: Step 3.1, Network Structure Design It adopts a fully connected feedforward neural network architecture with a network layer count of [number missing]. The system consists of three layers: an input layer, five hidden layers, and an output layer. Step 3.2, Network Training and Optimization We use weighted mean squared error as the loss function, taking into account the differences in importance of different components in the trajectory feature vector, and assign weights to the state variables, control variables, and time series respectively: (6) in, For loss function, The number of samples in the training set; , , The first Predicted state sequence, control sequence, and time series for each sample; , , These are the corresponding actual values; , and These are the weighting coefficients; Using the Adam optimizer, set the learning rate. Momentum parameters and Weight decay coefficient Batch size and step size (Epoch); adopt an early stopping strategy, stop training when the validation set loss does not decrease for a consecutive Epochs to avoid overfitting; use a cosine annealing learning rate scheduler, decay the learning rate to 0.1 times the current value every b Epochs to improve the accuracy of later training; set a and b according to the actual situation. Step 3.3, Initial Value Generation When using online applications, for real-time task parameters The initial values ​​for trajectory optimization are generated by following these steps: (Including the initial state collected by sensors, mission terminal requirements, constraint boundaries, and control constraints.) Step 3.3.1: Using data obtained from offline training and , The mean vector is the input to the training set. The standard deviation vector is the input to the training set; for Standardization is performed to obtain standardized real-time task parameters. ; Step 3.3.2, will Input the trained DNN model, output the model after forward propagation. The trajectory feature vector is obtained after inverse standardization. ,in , , These are the predicted state sequence, control sequence, and time series, respectively. Step 3.3.3: The initial state and control values ​​are reconstructed using cubic spline interpolation, based on... , , Reconstructing continuous initial state curves With control initial value curve : (7) (8) in, and For cubic spline interpolation functions, ensure and Its first derivative is continuous; Step 3.3.4: Based on the Pontryagin minimum principle of optimal control, costate variables... With state variables satisfy , Using the Hamiltonian function, the initial values ​​of the costate variables are roughly estimated using the numerical difference method based on the state and control initial values ​​predicted by the DNN. : (9) in, These are preliminary guesses of the costate variables. For the collocation and discrete index of the Gaussian pseudospectral method; The final set of initial values ​​generated is ,in The predicted terminal time serves as the starting point for online trajectory optimization.

2. The intelligent trajectory planning method for the cruise segment of a reusable launch vehicle according to claim 1, characterized in that, Step 1 is as follows: (1) Among them, the superscript " " represents the first derivative; For the mass of the aircraft, For flight speed, For flight altitude, For thrust vector, , These are drag and lift, respectively. It is the acceleration due to gravity. , , These are the aircraft's trajectory inclination angle, heading angle, and roll angle, respectively. For the angle of attack.

3. The intelligent trajectory planning method for the cruise segment of a reusable launch vehicle according to claim 1, characterized in that, Step 2 is as follows: Step 2.1, Task Parameter Sampling The cruise segment mission parameter space is defined as a multi-dimensional set of constraints, i.e. ,in: Let be the initial state vector. Initial flight speed, This is the initial flight altitude. The initial trajectory inclination angle, The initial heading angle, The initial tilt angle, The initial mass; For the terminal constraint vector, and For the terminal plane position, For terminal height, For terminal speed; For process constraint boundary vectors, For maximum dynamic pressure, For maximum overload, For maximum heat flux density, To balance the gliding constraint angle; To control the constraint vector, , For the upper and lower limits of the angle of attack, , These are the upper and lower limits of thrust; The Latin hypercube sampling (LHS) method is used to uniformly sample the task parameter space Γ, ensuring that the samples cover all critical operating conditions, and the number of sampling groups is [not specified]. Based on the complexity of the operating conditions, each set of sampling results constitutes an independent task scenario. , ; Step 2.2: Optimization of Gaussian pseudospectral method For each set of task scenarios The Gaussian pseudospectral method is used to transform the continuous optimal control problem into a nonlinear programming (NLP) problem, and a high-precision optimal trajectory is obtained through numerical solution. The flight time interval is mapped to the [-1,1] interval through variable transformation, and selection is made within each stage. N A Gaussian collocation; State variables and control variables Represented by the Lagrange interpolation polynomial, For the mass of the aircraft, For flight speed, For flight altitude, For thrust vector, , , These are the aircraft's trajectory inclination angle, heading angle, and roll angle, respectively. For the angle of attack: (2) (3) In the formula: For Lagrange basis functions; This represents the total number of Gaussian collocation points, i.e., the number of nodes in the time-domain discretization. The more collocation points, the higher the approximate accuracy. The interpolation node index for Gaussian collocations. For the first Discrete values ​​of state variables at Gaussian collocation points For the first Discrete values ​​of control variables at Gaussian collocation points; For continuous-time dynamic equations, the state derivatives at collocation points are... Convert to algebraic constraints: (4) In the formula: It is a differential matrix, consisting of Gaussian integral weights and derivatives of basis functions; Discrete index for Gaussian collocations. For the first Discretized vectors of the motion state of the aircraft's center of mass at each Gaussian collocation point. This is the end time of the cruise segment. The start time, For the first The time of a Gaussian collocation point in the original time domain; Process constraints include dynamic pressure Overload Heat flux density Apply directly at the designated point, where , , These are the dynamic pressure, overload, and heat flux density of the launch vehicle, respectively. , , These are the maximum permissible values ​​for the dynamic pressure, overload, and heat flux density of the launch vehicle, respectively; the terminal state should satisfy the constraints of the dynamic equations. Performance metrics transformed into NLP objective functions : (5) In the formula: These are the state variables at the terminal moment, including velocity, altitude, trajectory angle, and mass; It is the first k The Gaussian integral weights of each collocation point reflect the importance of each collocation point in the time domain. It is the first k The process performance index function of each coordinate point quantifies the performance requirement at that moment. It is the first k Control variables for each allocation point; It is the first k The moment of each coordinate point, i.e. the terminal moment after discretization; It is the objective function, representing the overall performance score of trajectory optimization, used to quantify the quality of the cruise segment trajectory; It is a terminal performance index function that describes the state performance requirements at the end of the cruise segment, ensuring that key constraints are met when the transition is completed. The complete nonlinear programming problem is solved using sequential quadratic programming to obtain the optimal control sequence and state trajectory; the discrete state variables are optimized. Control variables and terminal time Under the condition of satisfying the constraints of the dynamic equation, make the objective function To obtain the minimum value; Step 2.3, Sample Library Construction The parameter vector for each task It includes initial state, terminal constraints, process constraint boundaries, and control constraints, along with the corresponding optimal trajectory feature vector. Pairing to form sample pairs , build scale Offline sample library.

4. The intelligent trajectory planning method for the cruise segment of a reusable launch vehicle according to claim 1, characterized in that, The network structure for step 3.1 is as follows: The input layer is layer 1: the number of neurons equals the input parameter vector. The dimension is 18 neurons, which receive standardized input parameters. ,in The mean vector is the input to the training set. The standard deviation vector is the input to the training set; The hidden layers are layers 2-6: layer 2 has 256 neurons, layer 3 has 128, layer 4 has 64, layer 5 has 32, and layer 6 has 16; a batch normalization (BN) layer is added after each layer to accelerate training convergence and improve generalization ability; a dropout layer is added after layer 4 to prevent overfitting. The output layer is the 7th layer: the number of neurons equals the trajectory feature vector. The dimension is determined by the number of collocation points in the Gaussian pseudospectral method and the characteristic dimension of each collocation point; the initial number of collocation points Each coordinate point includes flight speed, flight altitude, trajectory inclination, heading angle, bank angle, mass, angle of attack, thrust, and a 1-dimensional time coordinate. The total feature dimensions of a single coordinate point are 9, and the total feature dimensions of the coordinate points are 9. Therefore, the output layer needs to be set to 9. Each neuron has a linear activation function and directly outputs the predicted trajectory feature vector. .

5. The intelligent trajectory planning method for the cruise segment of a reusable launch vehicle according to claim 1, characterized in that, In step 3.2, the inputs to the training set, validation set, and test set are processed during data preprocessing. With output Standardization is performed separately, with input standardization using... , The mean vector is the input to the training set. Given the standard deviation vector as input to the training set, the output standardization is achieved using... ,in Output the mean vector for the training set. The network outputs a standard deviation vector for the training set during training. Through reverse standardization The final prediction result is obtained; the weights of each layer are initialized using the He initialization method. and bias Initialize to Vector; During iterative training, for each epoch, the training set is divided according to the batch size, and forward propagation is performed to calculate the loss. The gradients of each parameter are calculated using the backpropagation algorithm. The parameters are updated using the Adam optimizer; after each epoch, the loss on the validation set is calculated. ,when Reaching the preset accuracy threshold When the time comes, stop training; After training, the model performance is evaluated using the test set, and the test set loss is calculated. with average relative error ,Require .

6. The intelligent trajectory planning method for the cruise segment of a reusable launch vehicle according to claim 1, characterized in that, Step 4 is as follows: The adaptive collocation method, based on the Gaussian pseudospectral method, dynamically adjusts the number and distribution of collocation points through error estimation. It increases collocation points in regions with high trajectory curvature and large dynamic residuals, and merges collocation points in regions with gentle trajectories and small residuals, achieving the preset accuracy requirements with minimal computational cost. Indicators include: (10) (11) in, For dynamic residuals, For matching points The predicted value of the state derivative at a given point is obtained by calculating the differential matrix. For the first Predicted state derivative values ​​at each Gaussian collocation point The collocation density reflects the relative magnitude of the error at each collocation point. , For Gaussian collocations The normalized dynamic residuals, Indicates the first A Gaussian collocation The initial state variables at that location, Indicates the first A Gaussian collocation Initial control variables at the location; The initial value set generated in step 3 is imported into the adaptive Gaussian pseudospectral optimizer as the initial point, using the same Gaussian collocation as the offline sample generation. Based on the initial collocation and the imported initial values, an online NLP problem is constructed, with performance indicators and constraints consistent with the offline optimization. The lightweight SQP solver IPOPT is used for fast solving, with an upper limit on the number of iterations set, to obtain the first optimized solution. and the corresponding dynamic residuals ; Calculate the maximum dynamic residual ,like And the rate of change of the collocation points is 0. If the residual accuracy threshold is met, constraint verification and online output are performed; otherwise, collocation point adjustment is performed to obtain the new number of collocation points. With the distribution of collocation points Update the allocation time series , Indicates the initial predicted end time of the cruise segment. Indicates the start time of the cruise segment. This represents the normalized time coordinates of the new Gaussian collocation points after collocation adjustment; Based on the new collocation distribution, a cubic spline interpolation method is used to transform the previous optimization solution. Interpolate to the new collocation point to obtain the new initial value. With new allocation points New initial value Using this as input, we re-solve the NLP problem to obtain a new optimized solution. and dynamic residuals ; Calculate the maximum dynamic residual With the rate of change of the collocation point , For the point density threshold, if and If convergence occurs, perform constraint verification and online output; otherwise, let... , The point allocation is readjusted adaptively, and the iteration stops when the maximum number of iterations is reached. Constraint verification and online output: This involves checking whether the optimized trajectory satisfies all path constraints and boundary constraints. ,satisfy and If the constraints are satisfied, proceed to the next step; otherwise, adjust the constraint weights and solve again; continuously optimize the trajectory. , time step Discretization yields a discrete trajectory sequence. , and the corresponding time series ; Convert discrete trajectory sequences into guidance commands executable by the launch vehicle, including altitude commands. Speed ​​command Angle of attack command and throttle command The data is transmitted in real time to the launch vehicle control system via the data bus for flight control during the cruise phase.

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