A method, device, medium, and product for sequential convex optimization cooperative trajectory design based on Transformer prediction.

Abstract

This application discloses a sequential convex optimization cooperative trajectory design method, device, medium, and product based on Transformer prediction, relating to the field of aerospace mid-course computational guidance technology. The method includes: inputting state information into a Transformer target trajectory predictor to obtain control action values; integrating the control action values ​​based on dynamic equations to obtain the state information at the next moment; repeating the process to obtain a time-series predicted state matrix; inputting the state information and the time-series predicted state matrix into a deep neural network model to obtain the predicted intercept point and predicted remaining flight time; constructing a trajectory optimization model based on the predicted intercept point and predicted remaining flight time; and solving the trajectory optimization model using an adaptive dynamic adjustment method based on trust region and proximity terms to obtain the trajectory optimization result. This application can achieve accurate prediction and rapid trajectory optimization under limited resources.

Description

Technical Field

[0001] This application relates to the field of aerospace mid-course computational guidance technology, and in particular to a method, device, medium and product for sequential convex optimization cooperative trajectory design based on Transformer prediction. Background Technology

[0002] Attacking high-value ground or water targets using a single near-space vehicle presents challenges such as vulnerability to interference, limited communication, and low attack accuracy. To achieve precise strikes against these targets, it is necessary to penetrate enemy defenses through resource sharing and other means, enabling coordinated operations by multiple vehicles. Multi-near-space vehicle attack scenarios are characterized by high costs and strong target interception capabilities, making the design of coordinated guidance laws crucial. One challenge in coordinated guidance law design is that ground or water targets are not stationary but moving. While near-space vehicle terminal guidance laws can dynamically correct deviations, neglecting the target's motion characteristics will significantly reduce terminal attack accuracy. Therefore, accurate and efficient target trajectory prediction is essential. A second challenge lies in inaccurate prediction of remaining flight time: inaccurate prediction will prevent multiple near-space vehicles from attacking the target at the predetermined time, reducing attack effectiveness and, in severe cases, causing the coordinated mission to fail. Existing methods for predicting remaining flight time based on proportional guidance achieve high-precision prediction, but they suffer from limitations such as non-optimal trajectories and applicability only to proportional guidance methods. Therefore, achieving high-precision prediction of remaining flight time in cooperative guidance of multiple near-space vehicles under limited onboard computing resources is of great significance. A third challenge in cooperative guidance law design lies in the fact that sequential convex optimization trajectory design methods are highly sensitive to the trust region and proximity term coefficients, resulting in slow convergence. Therefore, achieving fast and high-precision trajectory planning under the constraint of limited onboard computing resources is crucial. Summary of the Invention

[0003] The purpose of this application is to provide a method, device, medium, and product for sequential convex optimization cooperative trajectory design based on Transformer prediction, which can achieve accurate prediction and rapid trajectory optimization under limited resources.

[0004] To achieve the above objectives, this application provides the following solution:

[0005] Firstly, this application provides a sequence convex optimization cooperative trajectory design method based on Transformer prediction, including:

[0006] Construct the three-dimensional center-of-mass dynamic equations for mid-course guidance of the aircraft;

[0007] Acquire the target aircraft's status information; the status information includes: track angle, heading angle, speed, range, lateral position, and altitude;

[0008] The state information is input into the trained Transformer target trajectory predictor to obtain the type of the target aircraft and the control action values.

[0009] Integrating the control action value based on the dynamic equation yields the state information for the next moment.

[0010] The state information of the next moment is used as "state information", and the process returns to the step of "inputting the state information into the trained Transformer target trajectory predictor to obtain the type of target aircraft and control action value" until the preset number of times is reached, and the time-series prediction state matrix of the target aircraft is obtained.

[0011] The state information and the time-series prediction state matrix are input into a trained deep neural network model to obtain the predicted interception point and the predicted remaining flight time.

[0012] A trajectory optimization model is constructed based on the predicted interception point and the predicted remaining flight time.

[0013] The trajectory optimization model is solved by adjusting the sequential convex optimization method using a trust region and neighbor term-based adaptive dynamic adjustment method to obtain the trajectory optimization result.

[0014] Optionally, the trajectory optimization model includes:

[0015] Motion equation constraints: ;

[0016] in, x Status information; The derivative of the state information; g Represents the constraint vector of the dynamic equation; u The control vector is u =[ αγ ] T , α and γ These represent the angle of attack and the angle of roll, respectively. t Indicates the current time;

[0017] Performance metrics: ;

[0018] in, K α and K γ They represent α and γ Penalty coefficients for the two control variables;t 0 and t f These represent the initial time and the predicted remaining flight time in the trajectory optimization problem, respectively.

[0019] Initial and terminal state constraints: ;

[0020] in, Indicates the initial time; This represents the initial value of the track angle; This represents the initial value of the heading angle; The initial value representing the velocity; This represents the initial value of the voyage; The initial value represents the lateral position; The initial value representing the height; This represents the actual track angle at the initial moment; This represents the actual heading angle at the initial moment; This represents the actual velocity at the initial moment; This represents the actual distance traveled at the initial moment; Indicates the actual lateral position at the initial moment; This indicates the actual height at the initial moment; Indicates the remaining flight time; Represents the terminal value of the track angle; The terminal value of the heading angle; The terminal value representing speed; Indicates the final value of the journey; The terminal value representing the lateral position; The terminal value representing the height; This represents the terminal value of the desired track angle; The terminal value represents the desired heading angle; The terminal value representing the desired speed; This represents the terminal value of the expected flight distance; The terminal value represents the desired lateral position; The terminal value representing the desired height;

[0021] The angle of attack and roll angle constraints are as follows: ;

[0022] in, α min and α max These represent the minimum and maximum angles of attack, respectively. γ min and γ max These represent the minimum and maximum values ​​of the tilt angle, respectively.

[0023] Optionally, α min =-15°; α max =15°; γ min =-90°; γ max =90°.

[0024] Optionally, the sequence convex optimization method can be adjusted using an adaptive dynamic adjustment method based on trust region and neighbor terms, specifically including:

[0025] Trust region constraints are set as follows: ;

[0026] in, K x This represents the magnitude of the trust region constraint; Q Let be a diagonal matrix, representing the trust region constraint penalty matrix; x Indicates status information; d x The state perturbation is represented by the following formula: In the formula, ref represents the reference trajectory, that is, the trajectory constructed in the previous iteration;

[0027] The neighbor term constraint is set as follows: ;

[0028] in, K u Indicates the magnitude of the neighbor term constraint; P Let be a diagonal matrix, representing the neighbor term constraint penalty matrix; d u Indicates control perturbation;

[0029] in, ; In the formula, n k This represents the number of iterations in the trajectory optimization method; K p and K Q All are greater than 0, representing the weight coefficients set by the user.

[0030] Optionally, the training method of the Transformer target trajectory predictor includes:

[0031] Acquire historical status information, corresponding historical control action values, and the type of the target aircraft;

[0032] Using the historical state information as input, and the corresponding historical control action values ​​and the type of the target aircraft as output, a Transformer model is trained to obtain a Transformer target trajectory predictor. The Transformer model adopts a multi-head attention mechanism, which obtains the attention distribution of the input historical state information in different subspaces by computing several independent attention values ​​in parallel. The Transformer model has a position encoding in the form of trigonometric functions.

[0033] Optionally, the training method for the deep neural network model includes:

[0034] Obtain historical output information corresponding to historical input information; the historical input information includes: historical state information and historical time-series prediction state matrix; the historical output information includes: historical interception points and historical remaining flight time;

[0035] Using the historical input information as input and the historical output information as output, a deep neural network is trained to obtain a deep neural network model.

[0036] Optionally, the dynamic equation is: ;

[0037] Among them, subscript i The first term in the cooperative guidance problem is... i One aircraft; θ i Indicates the first i The flight path angle of an aircraft; Indicates the first i The heading angle of the aircraft; v i Indicates the first i The speed of the aircraft; x i Indicates the first i The range of an aircraft; y i Indicates the first i The lateral position of the aircraft; z i Indicates the first i The altitude of the aircraft; γ i Indicates the first i The tilt angle of an aircraft; g Represents gravitational acceleration; and They represent the first i Aerodynamic lift and drag of an aircraft; m i Indicates the first i The mass of the aircraft.

[0038] In a second aspect, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the sequential convex optimization cooperative trajectory design method based on Transformer prediction as described above.

[0039] Thirdly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the sequential convex optimization cooperative trajectory design method based on Transformer prediction as described above.

[0040] Fourthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the sequence convex optimization cooperative trajectory design method based on Transformer prediction as described above.

[0041] According to the specific embodiments provided in this application, the following technical effects are disclosed:

[0042] This application provides a method, device, medium, and product for sequential convex optimization cooperative trajectory design based on Transformer prediction. The method includes: constructing a three-dimensional centroid dynamic equation for mid-course guidance of an aircraft; acquiring the state information of the target aircraft; the state information including: track angle, heading angle, velocity, range, lateral position, and altitude; inputting the state information into a trained Transformer target trajectory predictor to obtain the type of the target aircraft and control action values; integrating the control action values ​​based on the dynamic equation to obtain the state information at the next moment; and using the state information at the next moment as "state information". The process returns to the step of "inputting the state information into the trained Transformer target trajectory predictor to obtain the target aircraft type and control action values" until a preset number of iterations are reached, obtaining the time-series predicted state matrix of the target aircraft; the state information and the time-series predicted state matrix are input into the trained deep neural network model to obtain the predicted interception point and the predicted remaining flight time; a trajectory optimization model is constructed based on the predicted interception point and the predicted remaining flight time; the trajectory optimization model is solved using an adaptive dynamic adjustment method based on the trust region and the nearest neighbor term to obtain the trajectory optimization result. This application leverages the advantages of Transformer, such as high accuracy in predicting time-series information, low computational resource consumption, and end-to-end processing, to achieve accurate prediction of flight trajectories. Simultaneously, based on the adaptive dynamic adjustment technology of the trust region / nearest neighbor term, the optimization time is reduced while ensuring stable convergence, ensuring that the initial value-sensitive, small-convexity optimization method can converge with high accuracy and efficiency. Therefore, this application can achieve accurate prediction and rapid trajectory optimization under limited resources. Attached Figure Description

[0043] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0044] Figure 1 This is an application environment diagram of a sequence convex optimization cooperative trajectory design method based on Transformer prediction in one embodiment of this application.

[0045] Figure 2 This is a flowchart illustrating a sequential convex optimization cooperative trajectory design method based on Transformer prediction, provided as an embodiment of this application.

[0046] Figure 3This is a block diagram of a Transformer target trajectory predictor provided in an embodiment of this application.

[0047] Figure 4 This is a schematic diagram of the input-output function relationship of a deep neural network provided in an embodiment of this application.

[0048] Figure 5 This is a schematic diagram illustrating the construction process of a cooperative trajectory optimization architecture for a multi-near-space spacecraft cooperative attack mission, as provided in one embodiment of this application.

[0049] Figure 6 A schematic diagram of a single aircraft trajectory curve provided in an embodiment of this application.

[0050] Figure 7 A simulation diagram of the time-angle of attack curve of a single aircraft provided in an embodiment of this application.

[0051] Figure 8 A schematic diagram of a simulation of the time-tilt angle curve of a single aircraft provided in an embodiment of this application.

[0052] Figure 9 A schematic diagram of a simulation of the time-velocity curve of a single aircraft provided in an embodiment of this application.

[0053] Figure 10 A schematic diagram of a simulation of the time-track angle curve of a single aircraft provided in an embodiment of this application.

[0054] Figure 11 A schematic diagram of a simulation of the time-heading angle curve of a single aircraft provided in an embodiment of this application.

[0055] Figure 12 This is a schematic diagram of a simulation of the trajectory curves of multiple aircraft provided in an embodiment of this application.

[0056] Figure 13 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0057] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0058] This application provides a method, device, medium, and product for sequential convex optimization cooperative trajectory design based on Transformer prediction. First, a motion model of a near-space vehicle is constructed: based on wind tunnel data, lift and drag coefficient curves related to angle of attack and Mach number are fitted to ensure the application of subsequent deep neural network prediction methods for remaining flight time and interception points, as well as sequential convex optimization methods. Then, a Transformer trajectory predictor is used to achieve high-precision and high-efficiency prediction of the target trajectory. Next, through multiple Monte Carlo simulations, high-precision prediction of remaining flight time and interception points is achieved based on a deep neural network. Furthermore, based on adaptive theory, the weight penalty matrix of the proximity term and trust region constraints is dynamically adjusted to achieve rapid and high-precision convergence of the sequential convex optimization method in complex environments. Finally, based on the aforementioned neural network interception point and remaining flight time prediction method and sequential convex optimization trajectory design method, a multi-near-space vehicle cooperative trajectory optimization architecture is constructed to achieve multi-vehicle cooperative mission objectives under highly dynamic, strongly coupled, and complex constraints, thereby improving the large-scale swarm cooperative combat capability.

[0059] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0060] The sequence convex optimization cooperative trajectory design method based on Transformer prediction provided in this application can be applied to, for example... Figure 1 In the application environment shown, terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be set up independently, integrated into server 104, or placed in the cloud or on another server.

[0061] The terminal 102 can be, but is not limited to, various desktop computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. IoT devices can include smart speakers, smart TVs, smart air conditioners, and smart in-vehicle devices. Portable wearable devices can include smartwatches, smart bracelets, and head-mounted devices. The server 104 can be implemented using a standalone server or a server cluster composed of multiple servers, or it can be a cloud server.

[0062] In one exemplary embodiment, such as Figure 2 As shown, a sequential convex optimization cooperative trajectory design method based on Transformer prediction is provided. This method is executed by a computer device, specifically by a terminal or server alone, or by both a terminal and a server. In this embodiment, the method is applied to... Figure 1 Taking server 104 as an example, the explanation includes the following steps S1 to S8. Wherein:

[0063] S1. Construct the three-dimensional centroid dynamic equations for mid-course guidance of the aircraft.

[0064] In this embodiment, by fitting and modeling the lift and drag coefficient curves, a dynamic and kinematic model for mid-course guidance of near-space vehicles is constructed, resulting in a three-dimensional center-of-mass dynamic equation.

[0065] The dynamic equation is: ;

[0066] Among them, subscript i The first term in the cooperative guidance problem is... i One aircraft; θ i Indicates the first i The flight path angle of an aircraft; Indicates the first i The heading angle of the aircraft; v i Indicates the first i The speed of the aircraft; x i Indicates the first i The range of an aircraft; y i Indicates the first i The lateral position of the aircraft; z i Indicates the first i The altitude of the aircraft; γ i Indicates the first i The tilt angle of an aircraft; g Represents gravitational acceleration; m i Indicates the first i The mass of the aircraft; and They represent the first i Aerodynamic lift and drag of an aircraft.

[0067] ;

[0068] In the formula: q i Indicates the first i The dynamic pressure of an aircraft; S i Indicates the first i Reference area of ​​each aircraft; and They represent the first i The aerodynamic lift coefficient and drag coefficient of an aircraft are obtained through aerodynamic simulation or wind tunnel data calculation and testing, and are both functions of angle of attack and Mach number.

[0069] S2. Obtain the status information of the target aircraft; the status information includes: track angle, heading angle, speed, range, lateral position and altitude.

[0070] S3. Input the state information into the trained Transformer target trajectory predictor to obtain the type of the target aircraft and the control action values.

[0071] S4. Integrate the control action value based on the dynamic equation to obtain the state information at the next moment.

[0072] S5. Take the state information of the next moment as "state information" and return to the step of "inputting the state information into the trained Transformer target trajectory predictor to obtain the type and control action value of the target aircraft" until the preset number of times is reached to obtain the time-series prediction state matrix of the target aircraft.

[0073] This embodiment uses the Transformer target trajectory predictor to predict the trajectory curve of a target aircraft.

[0074] For predicting the trajectories of high-value ground or water targets, where the trajectory information is sequential, a Transformer target trajectory predictor can be used to achieve high-precision and rapid prediction of time-series target trajectories. The Transformer target trajectory predictor block diagram is shown below. Figure 3 As shown, unlike traditional recurrent neural networks (RNNs) and long short-term memory networks (LSTMs) which receive input sequences one by one, the Transformer predictor can process all inputs at once, exhibiting parallel computing characteristics. Figure 3 As shown, the Transformer predictor used in this embodiment contains 6 encoders and 6 decoders.

[0075] The Transformer target trajectory predictor has the following characteristics: (1) self-attention mechanism; (2) no loop structure; (3) parallel computing; (4) position encoding. Its core lies in the self-attention mechanism. The Transformer predictor designed in this invention patent achieves high-precision prediction of target trajectories by using three attention layers: global attention, causal attention, and cross attention.

[0076] The global self-attention layer, part of the Transformer encoder, processes the entire input sequence, allowing each sequence element to directly access all other sequence elements. The cross-attention layer, centrally located, connects the encoder and decoder and represents the most direct way to use attention in the model. The causal attention layer performs a similar function to the global self-attention layer on the output sequence of the decoder, but with a different processing method. The Transformer target trajectory predictor used in this embodiment is an "autoregressive" model that generates text by labeling elements one by one and feeds the output back to the input. To ensure computational efficiency within the limited onboard resources of a near-space spacecraft, the output of each sequence element in the Transformer target trajectory predictor depends only on the preceding sequence elements, thus exhibiting causality.

[0077] Subsequently, under the constraint of limited computing resources for near-space vehicles, the Transformer target trajectory predictor adopts a multi-head attention mechanism, which obtains the attention distribution of the input sequence in different subspaces by computing multiple independent attention values ​​in parallel, thereby capturing potential target trajectory information in the sequence more comprehensively.

[0078] Attention-oriented mechanism Q (Query) K (key) and V The three matrices (values) are all derived from the input target historical trajectory information and are transformed into matrices through linear transformation. W 1. W 2. W 3. Calculated by dot product:

[0079] ;

[0080] Then, the result is normalized to a probability distribution using the softmax operation and multiplied by a matrix. V :

[0081] ;

[0082] In the formula, d k This represents the normalization coefficient. Divide by d k The purpose is to stabilize the gradient during backpropagation.

[0083] The Transformer-based target trajectory predictor employs a self-attention mechanism, which fails to capture the temporal sequence of the input information when processing data. To incorporate the temporal information of the input, a position encoding in the form of a trigonometric function is added to the Transformer predictor:

[0084] ;

[0085] In the formula, PE This represents the position encoding function; pos represents the encoding position; j Indicates the first j One component; d This represents the normalization coefficient under this model.

[0086] This embodiment constructs a Transformer target trajectory predictor based on the filtered flight trajectory, mainly divided into two stages: training stage and usage stage. Among them, the input data for the training stage is: (1) initial time t 0 Terminal time t f The six state information (track angle, heading angle, speed, range, lateral position and altitude) at each moment of the trajectory are obtained. The output data is (1): the control action value of the target at the current moment; (2) the type of the target (aircraft carrier / destroyer / vehicle). The input data during the usage phase is: the six state information of the trajectory at each moment is obtained by observing and filtering through sensors. The output data is: the type of the aircraft and the control action value at the current moment. Based on the dynamic equation, the six state information of the next moment is obtained by integrating the output control action value. By repeating the above process, the temporal prediction state matrix of the target is obtained. If the prediction sequence has N moments, the size of the temporal prediction state matrix is ​​N×6.

[0087] The above theory successfully constructs a trajectory prediction method that takes into account target maneuvering.

[0088] Specifically, the training method for the Transformer target trajectory predictor includes:

[0089] Acquire historical status information, corresponding historical control action values, and the type of the target aircraft;

[0090] Using the historical state information as input, and the corresponding historical control action values ​​and the type of the target aircraft as output, a Transformer model is trained to obtain a Transformer target trajectory predictor. The Transformer model adopts a multi-head attention mechanism, which obtains the attention distribution of the input historical state information in different subspaces by computing several independent attention values ​​in parallel. The Transformer model has a position encoding in the form of trigonometric functions.

[0091] S6. Input the state information and the time-series prediction state matrix into the trained deep neural network model to obtain the predicted interception point and the predicted remaining flight time.

[0092] This embodiment uses a deep neural network to achieve high-precision and rapid prediction of the remaining flight time and interception point of each aircraft in cooperative guidance.

[0093] A fast and high-precision prediction method for remaining flight time and intercept point in multi-vehicle cooperative guidance is constructed by integrating deep neural networks and adopting a sequence convex optimization approach. Unlike intrinsic neural networks, deep neural networks have multiple hidden layers, which allow complex functions to be represented with fewer parameters. In the deep neural network-based prediction method for remaining flight time and intercept point, the inputs are state information and a temporal prediction state matrix, and the outputs are the high-precision and high-efficiency predicted intercept point and remaining flight time.

[0094] The input-output function relationship is as follows: Figure 4 As shown, the formula is expressed as:

[0095] ;

[0096] In the formula: t f Indicates the predicted remaining flight time; "Describes the predicted intercept point"; "deep_neural_network" indicates a time-of-flight and intercept point predictor using a deep neural network; "Time_series_prediction_status" represents the time-series prediction status matrix. x target This indicates the target status information.

[0097] The method for predicting flight time and interception point based on deep neural networks is constructed through the following six steps:

[0098] (1) Initialize the parameters of the deep neural network: Considering that the deep neural network contains multiple hidden layers, a large number of parameter calculations are required to achieve the fitting of the mapping relationship. Therefore, the parameter initialization process is very important and will significantly affect the convergence process of the neural network.

[0099] (2) Forward propagation: Based on a nonlinear trajectory planning solver, a neural network training dataset is constructed through large-scale Monte Carlo simulation tests. It should be noted that the nonlinear trajectory planning solver requires a large amount of computing resources and is not suitable for the limited computing resources of near-space vehicles. Then, the output is predicted through a deep neural network based on a large amount of training data.

[0100] (3) Calculate the training loss: Compare the predicted output with the true value in the training set and calculate the loss function for the remaining flight time.

[0101] (4) Backpropagation and parameter update: Based on the loss function of the remaining flight time, the gradient of each parameter is calculated, thereby realizing the task of dynamically adjusting the parameters to be trained.

[0102] (5) Multiple iterations: Because the prediction of the remaining flight time and the interception point in the cooperative guidance of near-space vehicles is a highly nonlinear and rapidly time-varying complex problem, it is necessary to ensure model convergence through multiple iterations to achieve high-precision and high-efficiency prediction of the terminal flight time and the interception point.

[0103] (6) Evaluation Model and Application: Evaluate and test the performance of the Remaining Flight Time and Interception Point Predictor based on Deep Neural Network.

[0104] The aforementioned deep neural network-based predictor of remaining flight time and interception point achieves high-precision and high-efficiency prediction of waiting time and interception point, improving upon the problems of inaccurate time prediction or excessive computational resource consumption in existing methods.

[0105] Specifically, the training method for the deep neural network model includes:

[0106] Obtain historical output information corresponding to historical input information; the historical input information includes: historical state information and historical time-series prediction state matrix; the historical output information includes: historical interception points and historical remaining flight time;

[0107] Using the historical input information as input and the historical output information as output, a deep neural network is trained to obtain a deep neural network model.

[0108] S7. Construct a trajectory optimization model based on the predicted interception point and the predicted remaining flight time.

[0109] The sequential convex optimization trajectory design method serves as the underlying approach, enabling rapid and high-precision calculation of the flight trajectory that satisfies the optimal performance indicators for initial and terminal state constraints. The trajectory optimization problem is modeled as follows:

[0110] Motion equation constraints: ;

[0111] in, x The state information is a vector. x =[ θψ v vxyz ] T ; θ Indicates the track angle; ψ v Indicates the heading angle; v Indicates speed; x Indicates the distance traveled; y Indicates lateral position; z Indicates altitude; The derivative of the state information; g Represents the constraint vector of the dynamic equation; uThe control vector is u =[ αγ ] T , α and γ These represent the angle of attack and the angle of roll, respectively. t Indicates the current time.

[0112] To ensure that the inner-loop attitude tracking control system can effectively track the outer-loop guidance commands, the smoothness of the control curve must be guaranteed. Therefore, the performance index design for the optimization problem is as follows: ;

[0113] in, K α and K γ They represent α and γ Penalty coefficients for the two control variables; t 0 and t f These represent the initial time and the predicted remaining flight time in the trajectory optimization problem, respectively; the predicted remaining flight time is directly output by the deep neural network initial value generator.

[0114] Initial and terminal state constraints: ;

[0115] Among them, subscript i The first term in the cooperative guidance problem is... i One aircraft; θ i Indicates the first i The flight path angle of an aircraft; Indicates the first i The heading angle of the aircraft; v i Indicates the first i The speed of the aircraft; x i Indicates the first i The range of an aircraft; y i Indicates the first i The lateral position of the aircraft; z i Indicates the first i The altitude of the aircraft; γ i Indicates the first i The tilt angle of an aircraft; g Represents gravitational acceleration; and They represent the first i Aerodynamic lift and drag of an aircraft; m iIndicates the first i The mass of the aircraft.

[0116] The angle of attack and heel angle (guidance command) constraints are as follows: ;

[0117] in, α min and α max These represent the minimum and maximum angles of attack, respectively. γ min and γ max These represent the minimum and maximum values ​​of the tilt angle, respectively. α min =-15°; α max =15°; γ min =-90°; γ max =90°.

[0118] S8. Using the adaptive dynamic adjustment method based on trust region and neighbor term, the sequence convex optimization method is adjusted and then the trajectory optimization model is solved to obtain the trajectory optimization result.

[0119] This embodiment dynamically adjusts the penalty matrix coefficients based on the adaptive approach to achieve fast and efficient convergence of the sequential convex optimization trajectory design method.

[0120] The trajectory optimization problem described above needs to be solved using subsequent sequential convex optimization methods. For complex, high-dimensional, strongly nonlinear trajectory solving problems, existing sequential convex optimization methods suffer from problems such as small convergence radius, low terminal state control accuracy, slow convergence, and even non-convergence. To improve these issues, adaptive theory is used to dynamically adjust the penalty coefficients of the trust region and neighbor term constraints.

[0121] Trust region constraints are set as follows: ;

[0122] in, K x This represents the magnitude of the trust region constraint; Q Let be a diagonal matrix, representing the trust region constraint penalty matrix, which is obtained through user setting; x Indicates status information; d x The perturbation representing state information is calculated using the following formula: In the formula, ref represents the reference trajectory, that is, the trajectory constructed in the previous iteration;

[0123] The neighbor term constraint is set as follows: ;

[0124] in,K u Indicates the magnitude of the neighbor term constraint; P The matrix is ​​a diagonal matrix, obtained through user settings, representing the neighbor term constraint penalty matrix; d u This indicates control perturbation.

[0125] The above formulas together constitute the control state constraint terms. It is important to note that, regardless of whether it is a trust region constraint or a neighboring term constraint, given... K x and K u Below, add a diagonal matrix. Q or P The size of the elements in the middle will lead to a reduction in state or control perturbations, thereby ensuring that the sequential convex optimization method can be solved within the feasible region, and will not exhibit the phenomenon of slow or non-convergent trajectory convergence due to excessively large iteration step size.

[0126] Whether the sequential convex optimization method can converge quickly depends on two points: (1) the quality of the initial value (initial control history conjecture) setting; and (2) the quality of the trust region and neighbor term penalty coefficient setting. This embodiment does not discuss the effect of the initial value, but focuses on the quality of the trust region and neighbor term penalty coefficient setting. This embodiment is based on the adaptive exponential adjustment theory, dynamically adjusting the coefficients in the trust region and neighbor term:

[0127] in, ; In the formula, n k This represents the number of iterations in the trajectory optimization method; K p and K Q All are greater than 0, representing the weight coefficients set by the user.

[0128] The principle behind setting the dynamic adaptive method is: at the start of iteration, the number of iterations... n k The matrix is ​​very small, therefore P and Q The medium coefficient is relatively small, resulting in state perturbation d x With control perturbation d u The larger number of iterations ensures rapid convergence of the trajectory during the initial iterations; in contrast, the number of iterations decreases in the final iterations. n k Increase, matrix P and Q The coefficient increases, causing d x With d u The smaller step size further ensures high-precision trajectory convergence with small step size in the last few iterations.

[0129] Based on the aforementioned dynamic adjustment method of trust region and neighbor term constraints, the solution process of the sequential convex optimization method is divided into an initial setting process and an iterative loop process.

[0130] The initial setup process includes four steps: (1) determining initial and terminal state constraints; (2) designing performance indicators; (3) determining the remaining flight time; and (4) establishing initial control and state conjectures (initial values) based on existing variable coefficient proportional guidance methods to reduce the sensitivity of trajectory optimization methods to initial values.

[0131] The iterative loop process consists of two steps: (1) solving the convex problem using a convex optimization solver, taking into account the initial and final state constraints and performance indicators; and (2) adaptively adjusting the neighboring terms and trust region constraints using the above method to ensure that the iterative process has both high accuracy and high efficiency. The cutoff condition for the above iterative loop is that the number of iterations reaches the maximum value or meets the minimum error tolerance requirement.

[0132] Finally, a collaborative trajectory optimization architecture for mid-course guidance of multiple near-space vehicles is constructed.

[0133] The cooperative trajectory optimization method employs a Transformer-based method for rapid target trajectory prediction at the upper level, aiming to achieve fast target trajectory prediction. The middle level method uses a neural network-based method for predicting remaining flight time and interception points, enabling rapid and high-precision prediction of flight time and interception points for each aircraft. The lower level method is an adaptive sequential convex optimization method, achieving trajectory construction with optimal performance indicators including initial and terminal state constraints. The upper level method dynamically predicts the target trajectory through online computation, the middle level method predicts interception points and provides high-precision estimates of remaining flight time, constructing the cooperative flight time through averaging, and the lower level method implements online solution to the trajectory optimization problem.

[0134] The specific implementation method is as follows: For cooperative attack missions involving multiple near-space vehicles, the cooperative trajectory optimization architecture construction process is as follows:

[0135] (1) Implement a fast and high-precision target trajectory prediction task based on Transformer under the condition of limited computing resources for near-space spacecraft. The input is the target motion state obtained by the observer filtering; the output is the time-series flight trajectory of the target.

[0136] (2) To meet the requirements of time-coordinated strike missions involving multiple near-space vehicles, a high-precision mapping relationship between input, flight time, and interception point is constructed based on a deep neural network, enabling efficient and accurate prediction of the remaining flight time and interception point for each vehicle. The input consists of the current state of the vehicle and the target trajectory; the output is the predicted remaining flight time and interception point.

[0137] (3) By dynamically adjusting the penalty matrix coefficients of the neighbor term and trust region constraints through adaptive thinking, the sequential convex optimization method can achieve fast, reliable and high-precision convergence through robust stabilization technology. The inputs are the initial and expected terminal state constraints, performance indicators, remaining flight time, penalty matrices of neighbor term and trust region constraints, and control input constraints; the output is the time-series flight trajectory that satisfies all constraints and performance indicators optimally.

[0138] (4) In the collaborative trajectory optimization method, the upper-layer method is a Transformer-based fast target trajectory prediction method, aiming to achieve rapid prediction of the target trajectory; the middle-layer method is a neural network-based method for predicting remaining flight time and interception point, achieving fast and high-precision prediction of the flight time and interception point of each aircraft; the lower-layer method is an adaptive sequential convex optimization method, achieving trajectory construction with optimal performance indicators including initial and terminal state constraints. The upper-layer method dynamically predicts the target trajectory through online calculation, the middle-layer method predicts the interception point and provides a high-precision estimate of the remaining flight time and constructs the collaborative flight time through averaging, and the lower-layer method solves the trajectory optimization problem. The overall collaborative trajectory optimization architecture of the method is as follows: Figure 5 As shown.

[0139] This embodiment provides a sequential convex optimization cooperative trajectory design method based on Transformer prediction. Based on training data, this embodiment rapidly predicts the target's maneuver trajectory using Transformer. This embodiment utilizes deep neural networks to achieve high-precision and efficient prediction of interception points and remaining flight time, which is beneficial for subsequent cooperative flight of multiple near-space vehicles. This embodiment dynamically adjusts the penalty matrix of the trust region and proximity constraints through an adaptive mechanism, achieving rapid convergence of the sequential convex optimization trajectory design method under limited onboard computing resources. Addressing future operational needs, the three-layer cooperative trajectory optimization architecture proposed in this embodiment achieves the mission objective of efficient and rapid cooperative trajectory optimization for multiple near-space vehicles, which is beneficial for future highly dynamic and rapidly changing complex battlefield situations.

[0140] To verify the effectiveness and feasibility of the sequential convex optimization cooperative trajectory planning method based on Transformer prediction, this embodiment conducts simulation verification and analysis on mid-course cooperative guidance for multiple near-space vehicles. The initial state and desired terminal state constraints of vehicle 1 are shown in Table 1:

[0141] Table 1 Initial and Desired Terminal States of Near-Space Vehicle 1

[0142]

[0143] The flight trajectory of near-space vehicle 1 is as follows Figure 6 As shown; the guidance command curves for angle of attack and heel angle are as follows: Figures 7-8As shown; the velocity curve is as follows Figure 9 As shown; the curves of track angle and heading angle are as follows Figures 10-11 As shown. Compared with the expected six terminal states, the terminal state control errors are as follows: track angle error is 0.0009 degrees; heading angle error is 0.0012 degrees; speed error is 0.0004 m / s; range error is -0.9931 m; lateral position error is 0.9278 m; and altitude error is -0.1591 m.

[0144] Figure 6 This indicates that the three-dimensional flight trajectory was relatively smooth, without significant jitter. Meanwhile, Figure 6 The numerical simulation results above show that the errors in each terminal state are relatively small. The terminal position error is 1.5 meters, which meets the error requirements at the end of mid-course guidance. Although slight jitter appeared in both the angle of attack and tilt angle curves, Figures 7-8 This indicates that the curve is relatively smooth overall, which is beneficial for the subsequent attitude tracking control system. Figures 9-11 This indicates that the speed, track angle, and heading angle curves have achieved high-precision convergence, and the curves are smooth overall without significant jitter or large amplitude.

[0145] For the cooperative trajectory optimization task of multiple near-space vehicles, the initial states and desired terminal states of vehicles 2 and 3 are constrained as shown in Tables 2 and 3:

[0146] Table 2 Initial and Desired Terminal States of Near-Space Vehicle 2

[0147]

[0148] Table 3 Initial and Desired Terminal States of Near-Space Vehicle 3

[0149]

[0150] The terminal state control errors of aircraft 2 are as follows: track angle error of 0.0036 degrees; heading angle error of -0.0001 degrees; speed error of -0.0069 m / s; range error of 2.2761 m; lateral position error of 8.2315 m; and altitude error of 4.2157 m. The terminal state control errors of aircraft 3 are as follows: track angle error of 0.6052 degrees; heading angle error of 0.4203 degrees; speed error of -0.03088 m / s; range error of -8.5708 m; lateral position error of 4.6756 m; and altitude error of 2.9099 m. Figure 12 This represents the coordinated trajectory curves of three near-space vehicles.

[0151] from Figure 12As can be seen from the above simulation results, by optimizing the trajectory, the three aircraft can be transformed from their initial configuration into a cooperative configuration with the same range, the same lateral position, and a flight altitude difference of 200 meters. This achieves the mission objective of cooperative trajectory planning and is conducive to large-scale cooperative cluster operations.

[0152] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 13 As shown, this computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operating system and computer programs stored in the non-volatile storage media. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communicating with external terminals via a network connection. When the computer program is executed by the processor, it implements a sequence convex optimization cooperative trajectory design method based on Transformer prediction.

[0153] Those skilled in the art will understand that Figure 13 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0154] In one exemplary embodiment, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0155] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0156] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0157] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0158] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0159] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0160] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0161] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A sequence convex optimization collaborative trajectory design method based on Transformer prediction, characterized in that, The method comprises the following steps: constructing a three-dimensional mass center dynamics equation of a midcourse guidance of a target aircraft; obtaining state information of the target aircraft; the state information comprises a track angle, a heading angle, a speed, a range, a lateral position and an altitude; inputting the state information into a trained Transformer target trajectory predictor to obtain a type of the target aircraft and a control action value; integrating the control action value based on the dynamics equation to obtain state information at a next time; taking the state information at the next time as the state information and returning to the step of inputting the state information into the trained Transformer target trajectory predictor to obtain the type of the target aircraft and the control action value until a preset number of times is reached, to obtain a time series prediction state matrix of the target aircraft; inputting the state information and the time series prediction state matrix into a trained deep neural network model to obtain a predicted intercept point and a predicted remaining flight time; constructing a trajectory optimization model according to the predicted intercept point and the predicted remaining flight time; solving the trajectory optimization model by adjusting a sequence convex optimization method based on a trust region and a neighbor item adaptive dynamic adjustment method to obtain a trajectory optimization result; the deep neural network model training method comprises the following steps: The trust region constraint is set as: ; wherein, K x denotes the amplitude of the trust region constraint; Q is a diagonal matrix, denoting the trust region constraint penalty matrix; x denotes the state information, d x denotes the perturbation of the state information, and the calculation formula is: ; in the formula, ref represents a reference trajectory, that is, a trajectory constructed in the last iteration; The proximity term constraint is set as: ; wherein, K u denotes the magnitude of the proximity constraint; P is a diagonal matrix, denoting the proximity constraint penalty matrix; d u denotes the control perturbation; wherein, ; ; in which, n k represents the number of iterations in the trajectory optimization method; K p and K Q are greater than 0, respectively representing the weight coefficients set by the user; obtaining historical input information corresponding to historical output information; the historical input information comprises historical state information and a historical time series prediction state matrix; the historical output information comprises a historical intercept point and a historical remaining flight time; training a deep neural network by taking the historical input information as input and the historical output information as output to obtain a deep neural network model. the trajectory optimization model comprises 2. The sequence convex optimization co-trajectory design method based on Transformer prediction according to claim 1, characterized in that, αγ Equation of motion constraints: ; in, x Status information; The derivative of the state information; g Represents the constraint vector of the dynamic equation; u The control vector is u =[ γ ] T , α and γ These represent the angle of attack and the angle of roll, respectively. t Indicates the current time; Performance indicators: ; wherein, K α with K γ respectively denote α and γ penalty coefficients for the two control quantities; t 0 with t f respectively denote the initial time and the predicted remaining flight time in the trajectory optimization problem; Initial and terminal state constraints: ; wherein represents the initial time; represents the initial value of the track angle; represents the initial value of the heading angle; represents the initial value of the speed; represents the initial value of the distance; represents the initial value of the lateral position; represents the initial value of the altitude; represents the actual track angle at the initial time; represents the actual heading angle at the initial time; represents the actual speed at the initial time; represents the actual distance at the initial time; represents the actual lateral position at the initial time; represents the actual altitude at the initial time; represents the remaining flight time; represents the terminal value of the track angle; represents the terminal value of the heading angle; represents the terminal value of the speed; represents the terminal value of the distance; represents the terminal value of the lateral position; represents the terminal value of the altitude; represents the terminal value of the desired track angle; represents the terminal value of the desired heading angle; represents the terminal value of the desired speed; represents the terminal value of the desired distance; represents the terminal value of the desired lateral position; represents the terminal value of the desired altitude; The angle of attack and the angle of sideslip are constrained by: ; wherein α min and α max respectively represent the minimum and maximum values of the angle of attack; γ min and γ max respectively represent the minimum and maximum values of the angle of roll.

3. The sequence convex optimization co-trajectory design method based on Transformer prediction according to claim 2, characterized in that, α min =-15°； α max =15°； γ min =-90°； the training method of the Transformer target trajectory predictor comprises max =90°。 4. The Transform er-based prediction sequence convex optimization co-trajectory design method of claim 1, wherein, obtaining historical state information and corresponding historical control action values and a type of a target aircraft; training a Transformer model by taking the historical state information as input and the corresponding historical control action values and the type of the target aircraft as output to obtain a Transformer target trajectory predictor; the Transformer model adopts a multi-head attention mechanism to obtain attention distribution of the historical state information in different subspaces by parallel computing a plurality of independent attention values; the Transformer model has a position encoding in a trigonometric function form. θ 5. The Transform er-based prediction-based sequence convex optimization co- trajectory design method of claim 1, wherein, The kinetic equation is: ; wherein, γ i denotes the track angle of the i th aircraft; denotes the heading angle of the i th aircraft; v i denotes the speed of the i th aircraft; x i denotes the range of the i th aircraft; y i denotes the lateral position of the i th aircraft; z i denotes the altitude of the i th aircraft; A memory, a processor and a computer program stored on the memory and capable of running on the processor, characterized in that the processor executes the computer program to implement the sequence convex optimization collaborative trajectory design method based on Transformer prediction of any one of claims 1-5. i denotes the bank angle of the i th aircraft; g denotes the gravitational acceleration; and denote the aerodynamic lift and drag of the i th aircraft, respectively; m i denotes the mass of the i th aircraft.

6. A computer device comprising: The computer program is executed by the processor to implement the sequence convex optimization collaborative trajectory design method based on Transformer prediction of any one of claims 1-5.

7. A computer-readable storage medium having stored thereon a computer program, characterized in that, ​ 8. A computer program product comprising a computer program, characterized in that, The computer program, when executed by the processor, implements the method of claim 1-5 for sequence convex optimization collaborative trajectory design based on Transformer prediction.

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