A Multi-Aircraft Cooperative Guidance and Control Method

Abstract

This application belongs to the field of aircraft guidance technology. This application provides a multi-aircraft cooperative guidance control method. The embodiments of this disclosure construct individual dynamic models of multiple aircraft swarms; employ the Chao-DBO algorithm, which integrates Tent mapping and a greedy local search strategy, to optimize the terminal handover point position, trajectory inclination angle, and azimuth angle of the aircraft from a spatial dimension, generating the terminal spatiotemporal constraints required for model prediction static planning; utilize a BP neural network trained with the RBMO algorithm to predict the remaining flight time of multiple unmanned aerial vehicles; integrate the terminal spatiotemporal constraints and the remaining flight time prediction results into the MPSP to form a mid-course cooperative guidance trajectory. This method improves the trajectory stability, time synchronization, and constraint robustness of multi-aircraft cooperative guidance, and is suitable for multi-aircraft cooperative guidance scenarios under conditions of uncontrollable time-varying speeds.

Description

Technical Field

[0001] This disclosure relates to the field of aircraft guidance technology, and in particular to a multi-aircraft cooperative guidance and control method. Background Technology

[0002] With the development of modern aircraft technology, the collaborative operation of multiple unmanned aerial vehicles (UAVs) has become a major research direction in aircraft guidance and control technology, involving the spatial deployment, geometric coordination, time synchronization, and energy management of aircraft swarms. Especially when the aircraft speed varies over time and is uncontrollable, system uncertainty increases significantly, placing higher demands on the robustness and real-time performance of spatiotemporal coordination.

[0003] Currently, commonly used aircraft guidance methods, such as sliding mode control and linear control, provide robustness and theoretical guarantees to a certain extent. However, they have limitations in handling nonlinear spatiotemporal coupling and process variable optimization in aircraft swarms, especially when facing dynamic environments and uncontrollable factors, where guidance accuracy and collaborative performance tend to decline. Meanwhile, intelligent optimization methods based on genetic algorithms and particle swarm optimization, while possessing certain global search capabilities, often exhibit slow convergence speeds in high-dimensional, multi-constraint collaborative scenarios, easily getting trapped in local optima, resulting in heavy computational burdens and difficulty in balancing real-time performance and solution quality. Furthermore, to improve trajectory planning accuracy and constraint handling capabilities, existing technologies have gradually introduced predictive control methods such as Model Predictive Control (MPC) and Model Predictive Static Programming (MPSP). Although MPC can improve accuracy through rolling optimization, its high computational complexity and significant cost of online solution make it difficult to meet the demands of rapid response applications. While MPSP has computational advantages, its over-reliance on pre-defined end constraints and the challenge of time-varying velocity and acceleration limit its applicability and robustness in practical applications.

[0004] Therefore, it is necessary to improve one or more of the problems existing in the above-mentioned related technical solutions.

[0005] It should be noted that this section is intended to provide background or context for the technical solutions of this disclosure as set forth in the claims. The description herein does not constitute an admission that it is prior art simply because it is included in this section. Summary of the Invention

[0006] The purpose of this disclosure is to provide a multi-aircraft cooperative guidance and control method, thereby overcoming, at least to some extent, one or more problems caused by the limitations and defects of related technologies.

[0007] According to embodiments of this disclosure, a multi-vehicle cooperative guidance and control method is provided, including:

[0008] Based on the flight dynamics characteristics of aircraft, an individual dynamics model of multiple aircraft groups is established, and a first objective function including a spatial cost function, a time cost function, and an energy cost function is set, as well as spatiotemporal constraints and energy constraints.

[0009] Based on the first objective function, the Chao-DBO algorithm is used to solve the terminal constraint variables of each aircraft.

[0010] A BP neural network is constructed, and the initial weights and biases of the BP neural network are optimized using the RBMO algorithm to obtain a time-of-flight prediction model.

[0011] The terminal constraint variables of each aircraft are input into the flight time prediction model for prediction, so as to obtain the flight time prediction results of each aircraft.

[0012] Construct a discretized system model and define a second objective function; the discretized system model includes discrete-form dynamic equations and output equations;

[0013] Based on the second objective function, the terminal constraint variables and flight time prediction results of each aircraft are input into the discretized system model for solution, so as to obtain the flight trajectory that satisfies the spatiotemporal constraints and energy constraints.

[0014] Furthermore, the individual dynamics model is as follows:

[0015]

[0016] In the formula, For the first The speed of the aircraft; This refers to the aerodynamic drag experienced by the aircraft. For the mass of the aircraft; It is the acceleration due to gravity; For the first The speed and tilt angle of the aircraft; For the first The speed deflection angle of the aircraft; For the first A flying vehicle in three-dimensional space Coordinates of direction; For the first A flying vehicle in three-dimensional space Coordinates of direction; For the first A flying vehicle in three-dimensional space Coordinates of direction; Atmospheric density; The reference area of ​​the aircraft; Zero-lift drag coefficient; This is the induced drag coefficient; For the first A single aircraft Directional acceleration command; For the first A single aircraft Directional acceleration command; It is a time constant; For the first An aircraft under a first-order inertial response model The actual acceleration in the direction; For the first An aircraft under a first-order inertial response model The actual acceleration in the direction, for The differential, for The differential, for The differential, for The differential, for The differential, for The differential, for The differential, for The differential;

[0017] The first objective function is:

[0018]

[0019] In the formula, Let the space cost function be... Let the time cost function be... Let the energy cost function be... As the first weighting factor, As the second weighting factor, It is the third weighting factor;

[0020] The spatiotemporal constraints are:

[0021]

[0022] In the formula, For the target location; The desired velocity tilt angle of the aircraft terminal; The desired velocity deflection angle of the aircraft terminal; This refers to the expected handover time between the middle and final guidance points; For the aircraft in The actual location of the spacecraft at any given time; For the aircraft in The actual velocity angle at any given moment; For the aircraft in The actual velocity deflection angle at any given moment.

[0023] Furthermore, the step of solving the terminal constraint variables of each aircraft using the Chao-DBO algorithm based on the first objective function includes:

[0024] The population is initialized using the Tent chaotic map to generate initial solutions;

[0025] The DBO algorithm employs four behavioral mechanisms to iteratively update the population of individuals in order to generate the global optimal solution. These four behavioral mechanisms include the rolling dung beetle behavior, the reproductive dung beetle behavior, the foraging dung beetle behavior, and the stealing dung beetle behavior.

[0026] A greedy local search strategy is introduced to perform a local search, and the global optimal solution obtained in the current iteration is slightly perturbed to generate a set of candidate solutions;

[0027] The fitness value of each candidate solution is calculated using the spatial cost function;

[0028] The process iterates a preset number of times to optimize the terminal constraint variables of each aircraft, ultimately ensuring that the optimization results meet the requirements of the space cost function in the first objective function.

[0029] Furthermore, the Tent mapping is initialized as follows:

[0030]

[0031] In the formula, For the first Substitute chaos value, For the first Replace the chaotic value; For control parameters, initial value It is a random number;

[0032] The perturbation update formula for the candidate solution is:

[0033]

[0034] In the formula, This is the globally optimal solution for the current iteration. For the first Candidate solutions generated by positive perturbation of candidate solutions. For the first Candidate solutions generated by negative perturbation of candidate solutions. Let be the space cost function.

[0035] Furthermore, the step of optimizing the initial weights and biases of the BP neural network using the RBMO algorithm to obtain the time-of-flight prediction model includes:

[0036] Construct a BP neural network; wherein the input layer dimension is the same as the input parameter dimension, the number of hidden layer nodes is a preset value, the activation function is the sigmoid function, and the output layer is used to output the flight time prediction results of each aircraft.

[0037] The RBMO algorithm is used to perform a global search and optimization of the initial weights and biases of the BP neural network, so as to improve the convergence speed and prediction accuracy of the network training.

[0038] The BP neural network is trained based on the optimized weights and biases to obtain the flight time prediction model.

[0039] Furthermore, the fitness function expression for the BP neural network is:

[0040]

[0041] In the formula, For the sample size, For the first The actual flight time of each sample The first prediction obtained by the BP neural network The flight time of each aircraft.

[0042] Furthermore, the discretized system model is as follows:

[0043]

[0044] In the formula, For the system at time The state variables, For the system at time The control quantity, For the system at time The output quantity, Represents a discrete time series. For discrete time steps, Let be the discrete state transition function of the system. Let be the state change function of the system. For the system in the first The observation output at each discrete time point;

[0045] State vector of the dynamic model With control vector for:

[0046]

[0047] The second objective function is:

[0048]

[0049] In the formula, For the first The control amount of the step, For the first The control amount of the step, It is a positive definite matrix. For Lagrange multipliers, For terminal deviation, It is the sensitivity matrix.

[0050] Furthermore, based on the second objective function, the steps of inputting the terminal constraint variables and flight time prediction results of each aircraft into the discretized system model for solution to obtain the flight trajectory that satisfies the spatiotemporal and energy constraints include:

[0051] Based on the discrete form of the dynamic equations and output equations, with the goal of minimizing the terminal deviation and control quantity changes in the second objective function, the control quantity is updated by iterative solution until the terminal deviation converges to a preset threshold, so as to obtain the flight trajectory of each aircraft that satisfies the spatiotemporal constraints and energy constraints.

[0052] The technical solutions provided by the embodiments of this disclosure may include the following beneficial effects:

[0053] In the embodiments of this disclosure, the multi-UAV cooperative guidance and control method described above, on the one hand, constructs individual dynamic models of the multi-UAV swarm; employs the Chao-DBO algorithm, which integrates Tent mapping and a greedy local search strategy, to optimize the terminal handover point position, trajectory inclination angle, and azimuth angle of the UAVs in the spatial dimension, generating the terminal spatiotemporal constraints required for model prediction static planning; uses a BP neural network trained with the RBMO algorithm to predict the remaining flight time of the multiple UAVs; and integrates the terminal spatiotemporal constraints and the remaining flight time prediction results into the MPSP to form a mid-course cooperative guidance trajectory. On the other hand, this method improves the trajectory stability, time synchronization, and constraint robustness of multi-UAV cooperative guidance, and is suitable for multi-UAV cooperative guidance scenarios under conditions of uncontrollable time-varying speeds. Furthermore, it achieves precise coordination of multiple UAVs in the spatiotemporal dimension, significantly improving the accuracy, real-time performance, and robustness of the cooperative operation of the UAV swarm. Attached Figure Description

[0054] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0055] Figure 1 This diagram illustrates the steps of a multi-vehicle cooperative guidance and control method according to an exemplary embodiment of this disclosure.

[0056] Figure 2 A block diagram illustrating the principle of the Chao-DBO algorithm in an exemplary embodiment of this disclosure is shown.

[0057] Figure 3 This diagram illustrates the system framework of the multi-vehicle cooperative guidance and control method in an exemplary embodiment of this disclosure.

[0058] Figure 4 This illustrates the flight trajectories of each aircraft under time-coordinated guidance in an exemplary embodiment of this disclosure;

[0059] Figure 5 This illustration shows the curves of the yaw plane normal acceleration of each aircraft under time-coordinated guidance in an exemplary embodiment of this disclosure.

[0060] Figure 6 This illustration shows the curves of the pitch plane normal acceleration of each aircraft under time-coordinated guidance in an exemplary embodiment of this disclosure.

[0061] Figure 7 This illustration shows the curves of the distance from each aircraft to the target point over time under time-coordinated guidance in an exemplary embodiment of this disclosure.

[0062] Figure 8 This illustration shows the velocity variation curves of each aircraft over time under time-coordinated guidance in an exemplary embodiment of this disclosure;

[0063] Figure 9 The diagram shows a comparison curve of the line-of-sight angle deflection and velocity deflection of each aircraft under time-coordinated guidance in an exemplary embodiment of this disclosure.

[0064] Figure 10 The diagram shows a comparison curve of the line-of-sight tilt angle and velocity tilt angle of each aircraft under time-coordinated guidance in an exemplary embodiment of this disclosure. Detailed Implementation

[0065] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0066] Furthermore, the accompanying drawings are merely illustrative diagrams of embodiments of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities.

[0067] This example implementation provides a multi-aircraft cooperative guidance and control method. (Reference) Figure 1 As shown, the multi-vehicle cooperative guidance and control method may include:

[0068] Step S1: Based on the flight dynamics characteristics of the aircraft, establish an individual dynamics model of the multi-aircraft group, and set a first objective function including a spatial cost function, a time cost function, and an energy cost function, as well as spatiotemporal constraints and energy constraints;

[0069] Step S2: Based on the first objective function, the Chao-DBO algorithm is used to solve the terminal constraint variables of each aircraft;

[0070] Step S3: Construct a BP neural network and use the RBMO algorithm to optimize the initial weights and biases of the BP neural network to obtain the time-of-flight prediction model;

[0071] Step S4: Input the terminal constraint variables of each aircraft into the flight time prediction model for prediction, so as to obtain the flight time prediction results of each aircraft;

[0072] Step S5: Construct a discretized system model and define a second objective function; the discretized system model includes discrete-form dynamic equations and output equations;

[0073] Step S6: Based on the second objective function, input the terminal constraint variables and flight time prediction results of each aircraft into the discretized system model for solution, so as to obtain the flight trajectory that satisfies the spatiotemporal constraints and energy constraints.

[0074] The aforementioned multi-UAV cooperative guidance and control method constructs individual dynamic models for the multi-UAV swarm. It employs the Chao-DBO algorithm, which integrates Tent mapping and a greedy local search strategy, to optimize the terminal handover point position, trajectory inclination angle, and azimuth angle from a spatial perspective, generating the terminal spatiotemporal constraints required for model prediction static planning. A BP neural network trained with the RBMO algorithm is used to predict the remaining flight time of multiple UAVs. The terminal spatiotemporal constraints and remaining flight time prediction results are integrated into the MPSP (Multi-Planetary Pilot-Side) to form the mid-course cooperative guidance trajectory. Furthermore, this method improves the trajectory stability, time synchronization, and constraint robustness of multi-UAV cooperative guidance, making it suitable for multi-UAV cooperative guidance scenarios under uncontrollable, time-varying speed conditions. It also achieves precise coordination of multiple UAVs in the spatiotemporal dimension, significantly improving the accuracy, real-time performance, and robustness of the cooperative operation of the swarm.

[0075] Below, we will refer to Figures 1 to 10 The steps of the multi-vehicle cooperative guidance and control method described in this example embodiment will be explained in more detail.

[0076] In step S1, based on the flight dynamics characteristics of the aircraft, an individual dynamics model of the multi-aircraft group is established, and a first objective function including a spatial cost function, a time cost function, and an energy cost function is set, as well as spatiotemporal constraints and energy constraints.

[0077] Specifically, based on the requirements of multi-UAV collaborative missions, a kinematic and dynamic model of the multi-UAV swarm is established, clarifying the system's end-point position constraints, time synchronization constraints, and energy-related constraints. On this basis, an overall optimization objective function (i.e., the first objective function) is constructed, which includes position coordination error terms, time synchronization error terms, and energy consumption weight terms to achieve comprehensive optimization.

[0078] In step S1, firstly, based on the flight mechanics characteristics of the aircraft, an individual dynamics model of the multi-unmanned aerial vehicle swarm is established as the basis for swarm cooperative optimization. This model can accurately describe the velocity, attitude, position, and overload response characteristics of the aircraft, and its specific form is as follows:

[0079] (1)

[0080] in, For the first The speed of the aircraft; This refers to the aerodynamic drag experienced by the aircraft. For the mass of the aircraft; It is the acceleration due to gravity; For the first The speed and tilt angle of the aircraft; For the first The speed deflection angle of the aircraft; For the first The position of an aircraft in three-dimensional space; Atmospheric density; The reference area of ​​the aircraft; Zero-lift drag coefficient; This is the induced drag coefficient; and They are the first A single aircraft and Directional acceleration command; It is a time constant; and They are the first The actual acceleration of an aircraft under a first-order inertial response model.

[0081] Furthermore, when setting the overall optimization objective function, the spatial performance, time synchronization, and energy consumption of the collaborative mission of the aircraft swarm are comprehensively considered. The final optimization objective is formed by decomposing the spatial cost function, time cost function, and energy cost function, and then weighting and fusing them. The specific steps are as follows:

[0082] The space cost function is:

[0083] (2)

[0084] As a weighting factor; These represent the terms for maximizing spatial coverage, uniform spatial distribution of multiple aircraft, minimizing the handover distance difference among multiple aircraft, handover distance penalty, and handover field of view penalty, respectively. The specific expressions for each term are as follows:

[0085] (3)

[0086] (4)

[0087] (5)

[0088] (6)

[0089] (7)

[0090] in, Indicates the total number of aircraft, index ; As a weighting factor; This indicates the angle formed between adjacent aircraft and the target from the target's perspective; For aircraft The line-of-sight angle between the object and the target It is the average value of the angle; For aircraft Distance to the target; This is the average distance between all aircraft and the target; This is the maximum detection radius of the aircraft; For the field of view; It is an aircraft The end-view inclination angle and the end-view deflection angle, It is an aircraft The terminal velocity tilt angle and terminal velocity deflection angle; This is the maximum field of view of the aircraft; This is the tolerance value for error.

[0091] The time cost function is:

[0092] (8)

[0093] in Indicates the total number of aircraft, index .

[0094] The energy cost function is:

[0095] (9)

[0096] These represent minimizing the mid-course guidance acceleration term, maximizing the mid-to-late shift handover velocity term, and minimizing the variance term of the multi-aircraft shift handover velocity term, respectively. The specific expressions for each term are as follows:

[0097] (10)

[0098] (11)

[0099] (12)

[0100] Among them, control input Indicates aircraft Control commands during flight; This represents the total discrete-time step size. For discrete time intervals; It is any small positive number; For aircraft terminal velocity; This represents the average speed of all aircraft.

[0101] Furthermore, we synthesize and establish the optimized objective function:

[0102] (13)

[0103] in, This is the weighting factor.

[0104] The optimization objective function integrates factors such as spatial performance, time synchronization, and energy consumption in multi-vehicle cooperative flight. By weighted summation of each cost term and optimization under system spatiotemporal constraints, it can achieve the global optimal solution while meeting mission requirements.

[0105] To ensure that the fleet of aircraft accurately reaches the designated spatial point and meets attitude requirements at the terminal stage, the aforementioned spatiotemporal constraints further clarify the terminal state constraints:

[0106] (14)

[0107] in, For the target location; The desired terminal velocity tilt angle and velocity deflection angle of the aircraft; This refers to the expected handover time between the middle and final guides.

[0108] In step S2, based on the first objective function, the Chao-DBO algorithm is used to solve the terminal constraint variables of each aircraft.

[0109] Specifically, a chaotic sequence based on Tent mapping is used for population initialization, and a greedy strategy is introduced to improve local search capabilities, forming an improved dung beetle optimization algorithm (i.e., Chao-DBO algorithm). This algorithm is used to solve the terminal constraint variables of multiple unmanned aerial vehicles and the corresponding optimization solutions.

[0110] The process of step S2 is as follows: Figure 2 As shown, based on the cost function set in step S1, the Chao-DBO is used to solve the terminal states of each spacecraft. To address the uneven initial population distribution caused by random initialization, Tent chaotic mapping is used to generate initial solutions. Tent chaotic mapping effectively avoids the problems of initial population clustering or excessive dispersion by ensuring that the population covers key regions of the solution space. The specific formula is as follows:

[0111] (15)

[0112] in, For the first Replace the chaotic value; For control parameters, initial value It is a random number.

[0113] The improved dung beetle optimization algorithm retains the four major behavioral mechanisms of DBO: dung beetle rolling behavior, dung beetle breeding behavior, dung beetle foraging behavior, and dung beetle stealing behavior. Each behavioral mechanism plays a different role in the solution space, and the update rules for each behavioral mechanism are as shown in equations (16)-(19):

[0114] (16)

[0115] (17)

[0116] (18)

[0117] (19)

[0118] in, These represent the rolling, breeding, foraging, and stealing dung beetles, respectively. individual Location at any given moment These are all preset constants of the algorithm. Used to simulate changes in light intensity For deflection angle, They are mutually independent random vectors. and These are the upper and lower boundaries of the safe zone for dung beetle reproduction. and These represent the upper and lower boundaries of the optimal foraging area for dung beetles. This indicates the current local optimum. This represents the globally optimal position during the algorithm's iteration process.

[0119] To further improve the quality of the solution, a greedy local search strategy is adopted. A small perturbation is applied to the global optimal solution obtained in the current iteration to generate a set of candidate solutions. The fitness value of each candidate solution is then calculated using the space cost function defined in step S1. The perturbation update formula for the candidate solutions is as follows:

[0120] (20)

[0121] in, This represents the globally optimal solution in the current iteration. They represent the first Candidate solutions generated by positive and negative perturbations of each candidate solution. Let be the space cost function.

[0122] Through the above-mentioned Tent chaotic mapping initialization, iterative updates of the four behavioral mechanisms, and greedy local search optimization, Chao-DBO continuously optimizes the terminal state of each spacecraft after a preset number of iterations, and finally makes the optimization result meet the spatial cost function requirements set in step S1.

[0123] In steps S3 and S4, a BP neural network is constructed, and the initial weights and biases of the BP neural network are optimized using the RBMO algorithm to obtain the flight time prediction model. The terminal constraint variables of each aircraft are input into the flight time prediction model for prediction to obtain the flight time prediction results of each aircraft.

[0124] Specifically, the Red-billed Blue Magpie Optimizer (RBMO) algorithm is used to perform a global search and optimization of the initial weights and thresholds of the BP neural network, establish a flight time prediction model, and output the flight time prediction results for each aircraft.

[0125] The terminal states of each aircraft obtained in step S2 are combined with the initial conditions in step S1 to form an input vector, which is then substituted into the BP neural network flight time prediction model based on RBMO optimization. Through the model's nonlinear mapping and iterative optimization capabilities, accurate prediction of the flight time of each aircraft is achieved. The specific implementation process is as follows:

[0126] First, a BP neural network structure is constructed. The dimension of the input layer is consistent with the dimension of the input parameters mentioned above. The number of hidden layer nodes is determined through experiments. The Sigmoid function is selected as the activation function to achieve non-linear transformation of the input parameters. The output layer is used to output the predicted flight time values ​​of each aircraft.

[0127] Secondly, the initial weights and biases of the BP neural network are optimized using the RBMO algorithm to improve the convergence speed and prediction accuracy of the network training. The optimized weights and biases are then input into the BP network for training, thereby performing time-of-flight prediction.

[0128] During the training of the BP neural network, the following fitness function is used to optimize the model:

[0129] (twenty one)

[0130] in, For the sample size, For the first The actual flight time of each sample The first number predicted by the BP neural network is... The flight time of each aircraft.

[0131] Finally, after the BP neural network is trained, the initial conditions and terminal states of each aircraft are input into the trained model, and the corresponding flight time prediction results are output, providing data support for the subsequent synchronization of flight time of multiple unmanned aerial vehicles.

[0132] In steps S5 and S6, a discretized system model is constructed, and a second objective function is set. The discretized system model includes discrete dynamic equations and output equations. Based on the second objective function, the terminal constraint variables and flight time prediction results of each aircraft are input into the discretized system model for solution, so as to obtain the flight trajectory that satisfies the spatiotemporal constraints and energy constraints.

[0133] Specifically, to achieve precision and stability in the coordinated flight of aircraft swarms, a discretized system model is constructed, including discrete-form dynamic equations and output equations:

[0134] (twenty two)

[0135] in They represent the system at time t. State variables, control variables, and output variables; It represents a discrete time series.

[0136] Referring to the dynamic model in step S1, the state vector and control vector are selected as follows:

[0137] (twenty three)

[0138] Combining formulas (1) and (23), The specific component form is as follows:

[0139] (twenty four)

[0140] The goal is to achieve the target at the specified terminal time. To guide the aircraft toward the target while meeting specific terminal angle requirements, the terminal output vector is defined as follows:

[0141] (25)

[0142] in The end angle; The deflection angle at the end; This refers to the spatial location at the end point.

[0143] Let the desired terminal state be The actual state of the terminal calculated by the system dynamic model is Then the terminal deviation can be defined as:

[0144] (26)

[0145] Taylor expansion of the above equation:

[0146] (27)

[0147] Linearizing equation (22), we get:

[0148] (28)

[0149] Furthermore, it can be deduced that:

[0150] (29)

[0151] (30)

[0152] By iteratively updating the state variables in formula (28), we can obtain:

[0153] (31)

[0154] In the formula:

[0155] (32)

[0156] Since the initial state is a given value, then .available:

[0157] (33)

[0158] In the formula: .

[0159] To ensure the smoothness of the aircraft's trajectory control and satisfy the terminal constraints, the optimization objective function (i.e., the second objective function) of MPSP is:

[0160] (34)

[0161] in, For the first The control amount of the step, For the first The control amount of the step, It is a positive definite matrix. For Lagrange multipliers, For terminal deviation, It is the sensitivity matrix.

[0162] To minimize this Lagrange function, for and Take the derivatives separately, and set the derivatives to zero:

[0163] (35)

[0164] By solving the above equations simultaneously, the optimal control quantity can be obtained. With Lagrange factor This updates the control input.

[0165] (36)

[0166] Repeat the above process iteratively, continuously updating the control variables until the terminal deviation converges to the preset threshold, and finally generate the aircraft flight trajectory that meets the requirements.

[0167] In one specific embodiment

[0168] The BP neural network includes a DBO optimization module, an MPSP algorithm module, and a time prediction module.

[0169] The population is initialized using the Tent chaotic map to generate initial solutions;

[0170] The DBO algorithm uses four behavioral mechanisms to update the initial solution in order to generate the global optimal solution. These four behavioral mechanisms include the rolling dung beetle behavior, the reproductive dung beetle behavior, the foraging dung beetle behavior, and the stealing dung beetle behavior.

[0171] A greedy local search strategy is introduced to perform a local search, and the global optimal solution obtained in the current iteration is slightly perturbed to generate a set of candidate solutions;

[0172] The fitness value of each candidate solution is calculated using the spatial cost function;

[0173] The process iterates a preset number of times to optimize the terminal constraint variables of each aircraft, ultimately ensuring that the optimization results meet the requirements of the space cost function in the first objective function.

[0174] In one embodiment, this application provides a spatiotemporal cooperative guidance method for multiple unmanned aerial vehicles (UAVs) based on the coupling of improved dung beetle optimization and model predictive static programming (i.e., a multi-UAV cooperative guidance and control method), and the corresponding system framework diagram is shown below. Figure 3As shown, the system includes an improved dung beetle optimization module (i.e., DBO optimization module), an RBMO-BP neural network time prediction module, and an MPSP module (i.e., MPSP algorithm module). The system's processing steps include: first, establishing a dynamic model of the multi-UAV swarm and clarifying spatiotemporal constraints, energy constraints, and overall optimization objectives; then, solving for the candidate terminal states of each UAV through the improved dung beetle optimization module; next, in the RBMO-BP neural network time prediction module, using an RBMO-optimized BP neural network to predict the feasible arrival time windows of each UAV and selecting the coordination time accordingly; finally, inputting the selected time and the terminal constraint solution into the MPSP module for solving to generate a mid-course coordinated guidance trajectory that meets convergence and real-time requirements. Through this process, this application improves the time synchronization and overall cooperative robustness of the UAV swarm while ensuring trajectory stability and constraint adaptability.

[0175] In a specific embodiment, to verify the effectiveness and superiority of the proposed cooperative control law for uncontrollable speed aircraft based on improved DBO and MPSP joint optimization, simulation tests were conducted on the aforementioned time-series cooperative trajectory planning method. The simulation results are as follows: Figures 4 to 10 As shown. The simulation scenario uses the coordinated operation of four aircraft as an example. It is assumed that the predicted target coordinates are... The initial tilt angle component is selected as The initial deflection angles are respectively The initial velocities are respectively The initial position coordinates are respectively . Figure 4 The three-dimensional flight trajectories of the four aircraft are shown, indicating that the trajectories of each aircraft are smooth and the guidance process is stable and convergent. Figure 5 and Figure 6 The curves showing the changes in lateral and normal command accelerations are presented. The overall changes are stable, indicating that the guidance law effectively ensures flight stability. Figure 7 The data showed the distance changes between the aircraft and the mid-to-terminal handover point. Some aircraft experienced slight fluctuations in distance during flight, but all were able to reach the handover point on time, verifying the effectiveness of the timing control. Figure 8 The curve showing the aircraft's speed changing over time demonstrates smooth speed regulation, which contributes to terminal accuracy and guidance stability. Figure 9 The comparison curves of line-of-sight angle deflection and velocity deflection of each aircraft under time-coordinated guidance are shown. Figure 10The comparison curves of the line-of-sight (LAS) tilt angle and velocity tilt angle of each aircraft under time-series cooperative guidance are shown. It can be seen that the LAS and velocity tilt angles, as well as the LAS and velocity tilt angles of each aircraft, eventually tend to be consistent, indicating that the guidance law has a good correction effect in the yaw and pitch directions. In summary, the method of this application can effectively generate cooperative control schemes, thereby ensuring detection coverage while ensuring that aircraft are evenly distributed in front of the target, and balancing flight stability and terminal accuracy.

[0176] The aforementioned multi-UAV cooperative guidance and control method achieves two main objectives. First, it constructs individual dynamic models of the multi-UAV swarm. The Chao-DBO algorithm, integrating Tent mapping and a greedy local search strategy, optimizes the terminal handover point position, trajectory inclination angle, and azimuth angle from a spatial perspective, generating the terminal spatiotemporal constraints required for model prediction static planning. A BP neural network trained with the RBMO algorithm is used to predict the remaining flight time of the multiple UAVs. The terminal spatiotemporal constraints and remaining flight time prediction results are integrated into the MPSP (Multi-Planetary Pilot Path) to form the mid-course cooperative guidance trajectory. Second, this method improves the trajectory stability, time synchronization, and constraint robustness of multi-UAV cooperative guidance, making it suitable for multi-UAV cooperative guidance scenarios under uncontrollable, time-varying speed conditions. Furthermore, it achieves precise coordination of multiple UAVs in the spatiotemporal dimension, significantly improving the accuracy, real-time performance, and robustness of the cooperative operation of the swarm.

[0177] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of this disclosure, "a plurality of" means two or more, unless otherwise explicitly specified.

[0178] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0179] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the appended claims.

Claims

1. A multi-vehicle cooperative guidance and control method, characterized in that, include: Based on the flight dynamics characteristics of aircraft, an individual dynamics model of multiple aircraft groups is established, and a first objective function including a spatial cost function, a time cost function, and an energy cost function is set, as well as spatiotemporal constraints and energy constraints. Based on the first objective function, the Chao-DBO algorithm is used to solve the terminal constraint variables of each aircraft. A BP neural network is constructed, and the initial weights and biases of the BP neural network are optimized using the RBMO algorithm to obtain a time-of-flight prediction model. The terminal constraint variables of each aircraft are input into the flight time prediction model for prediction, so as to obtain the flight time prediction results of each aircraft. Construct a discretized system model and define a second objective function; the discretized system model includes discrete-form dynamic equations and output equations; Based on the second objective function, the terminal constraint variables and flight time prediction results of each aircraft are input into the discretized system model for solution, so as to obtain the flight trajectory that satisfies the spatiotemporal constraints and energy constraints; among which, The steps for solving the terminal constraint variables of each aircraft using the Chao-DBO algorithm based on the first objective function include: The population is initialized using the Tent chaotic map to generate initial solutions; The DBO algorithm employs four behavioral mechanisms to iteratively update the population of individuals in order to generate the global optimal solution. These four behavioral mechanisms include the rolling dung beetle behavior, the reproductive dung beetle behavior, the foraging dung beetle behavior, and the stealing dung beetle behavior. A greedy local search strategy is introduced to perform a local search, and the global optimal solution obtained in the current iteration is slightly perturbed to generate a set of candidate solutions; The fitness value of each candidate solution is calculated using the spatial cost function; The process is iterated a preset number of times to optimize the terminal constraint variables of each aircraft, ultimately ensuring that the optimization results meet the requirements of the space cost function in the first objective function. The discretized system model is as follows: In the formula, For the system at time The state variables, For the system at time The control quantity, For the system at time The output quantity, Represents a discrete time series. For discrete time steps, Let be the discrete state transition function of the system. Let be the state change function of the system. For the system in the first The observation output at each discrete time point; State vector of the dynamic model With control vector for: The second objective function is: In the formula, For the first The control amount of the step, For the first The control amount of the step, It is a positive definite matrix. For Lagrange multipliers, For terminal deviation, It is the sensitivity matrix.

2. The multi-vehicle cooperative guidance and control method according to claim 1, characterized in that, The individual dynamics model is as follows: In the formula, For the first The speed of the aircraft; This refers to the aerodynamic drag experienced by the aircraft. For the mass of the aircraft; It is the acceleration due to gravity; For the first The speed and tilt angle of the aircraft; For the first The speed deflection angle of the aircraft; For the first A flying vehicle in three-dimensional space Coordinates of direction; For the first A flying vehicle in three-dimensional space Coordinates of direction; For the first A flying vehicle in three-dimensional space Coordinates of direction; Atmospheric density; The reference area of ​​the aircraft; Zero-lift drag coefficient; This is the induced drag coefficient; For the first A single aircraft Directional acceleration command; For the first A single aircraft Directional acceleration command; It is a time constant; For the first An aircraft under a first-order inertial response model The actual acceleration in the direction; For the first An aircraft under a first-order inertial response model The actual acceleration in the direction, for The differential, for The differential, for The differential, for The differential, for The differential, for The differential, for The differential, for The differential; The first objective function is: In the formula, Let the space cost function be... Let the time cost function be... Let the energy cost function be... As the first weighting factor, As the second weighting factor, It is the third weighting factor; The spatiotemporal constraints are: In the formula, For the target location; The desired velocity tilt angle of the aircraft terminal; The desired velocity deflection angle of the aircraft terminal; This refers to the expected handover time between the middle and final guidance points; For the aircraft in The actual location of the spacecraft at any given time; For the aircraft in The actual velocity angle at any given moment; For the aircraft in The actual velocity deflection angle at any given moment.

3. The multi-vehicle cooperative guidance and control method according to claim 2, characterized in that, The initialization of the Tent mapping is as follows: In the formula, For the first Substitute chaos value, For the first Replace the chaotic value; For control parameters, initial value It is a random number; The perturbation update formula for the candidate solution is: In the formula, This is the globally optimal solution for the current iteration. For the first Candidate solutions generated by positive perturbation of candidate solutions. For the first Candidate solutions generated by negative perturbation of candidate solutions. Let be the space cost function.

4. The multi-vehicle cooperative guidance and control method according to claim 3, characterized in that, The steps of optimizing the initial weights and biases of a BP neural network using the RBMO algorithm to obtain the time-of-flight prediction model include: Construct a BP neural network; wherein the input layer dimension is the same as the input parameter dimension, the number of hidden layer nodes is a preset value, the activation function is the sigmoid function, and the output layer is used to output the flight time prediction results of each aircraft. The RBMO algorithm is used to perform a global search and optimization of the initial weights and biases of the BP neural network, so as to improve the convergence speed and prediction accuracy of the network training. The BP neural network is trained based on the optimized weights and biases to obtain the flight time prediction model.

5. The multi-vehicle cooperative guidance and control method according to claim 4, characterized in that, The fitness function expression for a BP neural network is: In the formula, For the sample size, For the first The actual flight time of each sample The first prediction obtained by the BP neural network The flight time of each aircraft.

6. The multi-vehicle cooperative guidance and control method according to claim 5, characterized in that, Based on the second objective function, the steps of inputting the terminal constraint variables and flight time prediction results of each aircraft into the discretized system model for solution to obtain the flight trajectory that satisfies the spatiotemporal and energy constraints include: Based on the discrete form of the dynamic equations and output equations, with the goal of minimizing the terminal deviation and control quantity changes in the second objective function, the control quantity is updated by iterative solution until the terminal deviation converges to a preset threshold, so as to obtain the flight trajectory of each aircraft that satisfies the spatiotemporal constraints and energy constraints.

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